Answer:
Q(x) = [tex](x+3)^{2}+5[/tex] is the final equation.
Step-by-step explanation:
By translation of the graph 3 units upward direction, it means that the y-value of the function is increased by 3 unit at each value of x.
Given , P(x) = [tex](x+3)^{2}+2[/tex]
We can actually translate the graph in any direction, and for that we have to make the necessary changes. If we translate the graph in the positive x direction, then we have to substitute (x - 3) instead of x in the equation.
Since we are translating the graph upwards ,
Q(x) = [tex](x+3)^{2}+2[/tex] + 3
Q(x) = [tex](x+3)^{2}+5[/tex]
This is the final equation of the graph after translation.
if the sum of the interior angles of a regular n-gon is 900 degrees, then n=what?
Answer:
n=7
Step-by-step explanation:
let n be number of sides.
(n-2)180=900
n-2=900/180=5
n=5+2=7
A baby was born and then began to gain weight at a rate of 1.5 pounds per month. After 4 months, the baby's weight was 16 pounds. Write an equation for the function W ( t ) , W(t), representing weight, in pounds, of the newborn baby t t months after birth.
Answer:
w=1.5t+12
Step-by-step explanation:
that's the right answer
The equation for the function W(t) representing the weight of the newborn baby t months after birth is W(t) = 16 + 1.5t
To solve this problem
We can make use of the given data.
The infant gained weight at a pace of 1.5 pounds each month, reaching 16 pounds at the end of 4 months. With this knowledge, the equation can be written as follows:
W(t) = Initial weight + (Rate of weight gain per month) * (Number of months)
W(t) = 16 + (1.5 * t)
So, the equation for the function W(t) representing the weight of the newborn baby t months after birth is W(t) = 16 + 1.5t
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Thomas brings over 1/2 of his marble collection. He divides these marbles equally among 3 friends. What fraction of Thomas's entire marble collection did each friend get?
Answer:
Each of the three friends will get one-sixth of the Thomas's enitre marble collection.
Step-by-step explanation:
Fraction of the total marble collection brought by Thomas = [tex]\frac{1}{2}[/tex]
Now, Thomas divides these marbles equally among his three friends. So, each of the three friends will get one-third of the total marble collection brought by Thomas.
Fraction of total marble collection got by each friend = [tex]\frac{1}{3} \;of\;fraction\;of\;total\;marble\;collection\;brought\;by\;Thomas[/tex]
= [tex]\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}[/tex]
∴ Each of the three friends of Thomas will get one-sixth of his entire collection of marbles.
John wants to pay off a $2,100 bill in the next 13 months. What is the approximate amount that he will have to set aside each month to reach his goal?
$154
$167
$162
$187
Answer:the approximate amount that he will have to set aside each month to reach his goal is $162
Step-by-step explanation:
Total amount of bill that John wants to pay off js $2,100. $2,100 bill in the next 13 months. To determine the amount that he will have to set aside each month to reach his goal, we would divide the total bill by the number of months. It becomes
2100/13 = 161.538
The approximate amount is $162
Answer:
$162
Step-by-step explanation:
$2,100/13
A recent article in the Cincinnati Enquirer reported that the mean labor cost to repair a heat pump is $90 with a standard deviation of $22. Monte’s Plumbing and Heating Service completed repairs on two heat pumps this morning. The labor cost for the first was $75 and it was $100 for the second. Assume the distribution of labor costs follows the normal probability distribution. Compute z values for each.
Answer:
Z value for the first pump = -0.68
Z value for the second pump = 0.45
Step-by-step explanation:
Data provided in the question:
Mean labor cost to repair a heat pump = $90
Standard deviation = $22
Labor cost for the first, X₁ = $75
Labor cost for the Second, X₂ = $100
Now,
Z value for the first pump = [X₁ - Mean] ÷ Standard deviation
thus,
Z value for the first pump = [ $75 - $90] ÷ $22
= - 0.68
Z value for the second pump = [X₁ - Mean] ÷ Standard deviation
thus,
Z value for the second pump = [ $100 - $90] ÷ $22
= 0.45
Answer:
z1= -0.6818
z2= 0.45
Step-by-step explanation:
Mean labor cost to repair the heat pump is μ= $90
standard deviation σ= $22
Labor cost for the first heat pump X_1= $75
labor cost for the second heat pump is X_2= $100
z value for the first heat pump
[tex]z_1= \frac{X_1-\mu}{\sigma}[/tex]
⇒ [tex]z_1= \frac{75-90}{22}[/tex]
= -0.6818
z value for the second heat pump
[tex]z_2= \frac{X_2-\mu}{\sigma}[/tex]
⇒[tex]z_2= \frac{100-90}{22}[/tex]
= 0.45
An investor invested a total of $2,300 in two mutual funds. One fund earned a 8% profit while the other earned a 2% profit. If the investors total profit was $82, how much was invested in each mutual fund
Answer: the amount invested on the first mutual fund is $600 and the the amount invested on the second mutual fund is $1700
Step-by-step explanation:
Let x represent the amount of money that the investor invested in one mutual fund.
Let y represent the amount of money that the investor invested in the second mutual fund.
An investor invested a total of $2,300 in two mutual funds. This means that
x + y = 2300
Considering the first mutual fund, it earned a 8% profit. This means that amount earned is
8/100 × x = 0.08x
Considering the second mutual fund, it earned a 2% profit. This means that amount earned is
2/100 × y = 0.02y
If the investors total profit was $82, it means that
0.08x + 0.02y = 82 - - - - - - - - 1
Substituting x = 2300 - y into equation 1, it becomes
0.08(2300 - y) + 0.02y = 82
184 - 0.08y + 0.02y = 82
- 0.08y + 0.02y = 82 - 184
- 0.06y = - 102
y = - 102/- 0.06 = 1700
x = 2300 - y = 2300 - 1700
x = 600
PLEASE HELP WITH QUESTION!!!!!
Find the sum of the series:
The sum of the given series [tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] is 130.
Step-by-step explanation:
The sum of series need to be found is [tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] .
Apply sum rule,
[tex]\sum x_n+y_n=\sum x_n+\sum y_n[/tex]
[tex]\sum _{a=1}^{10}\:\left(2a+2\right).[/tex] =[tex]\sum 2a+\sum 2[/tex].
Apply the constant multiplication rule,
[tex]\sum c\cdot a_n=c\cdot \sum a_n[/tex] .
[tex]\sum 2\cdot a=2\cdot \sum a[/tex].
[tex]\sum _{a=1}^{10}n[/tex] = 1+2+3+4+5+6+7+8+9+10.
[tex]\sum _{a=1}^{10}n[/tex] = 55.
[tex]\sum 2\cdot a[/tex]=2×55.
[tex]\sum 2\cdot a [/tex]=110.
To find [tex]\sum _{a=1}^{10}2[/tex],
Apply sum rule, [tex]\sum _{k=1}^n\:a\:=\:a\cdot n[/tex] ,
[tex]\sum _{a=1}^{10}2[/tex] =2×10.
[tex]\sum _{a=1}^{10}2[/tex] = 20.
[tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] = 110+20.
[tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] =130.
Identify the monomial function described as odd or even, and indicate whether a is positive or negative.
Answer:
Case 1: As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.
It is an 'odd' function with 'positive' a.
Case 2: As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.
It is an 'even' function with 'negative' a.
Case 3: As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
It is an 'even' function with 'positive' a.
Case 4: As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.
It is an 'odd' function with 'negative' a.
Step-by-step explanation:
Let us consider a monomial function:
f(x) = axⁿ
Case 1:
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.
This happens only if a is 'positive' and n is 'odd'. So, it is an 'odd' function with 'positive' a.
Case 2:
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.
This happens only if a is 'negative' and n is 'even'. So, it is an 'even' function with 'negative' a.
Case 3:
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
This happens only if a is 'positive' and n is 'even'. So, it is an 'even' function with 'positive' a.
Case 4:
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.
This happens only if a is 'negative' and n is 'odd'. So, it is an 'odd' function with 'negative' a.
Keywords: monomial function, odd function, even function
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Identify the monomial function described as odd or even, and indicate whether a is positive or negative.
How do you do this question?
Answer:
7
Step-by-step explanation:
To find the maximum possible value of f(2), assume f(x) is a line with the greatest possible slope. In this case, 5.
f(x) = 5x − 3
f(2) = 5(2) − 3
f(2) = 7
Triangles Q R S and X Y Z are shown. Angles Q S R and X Z Y are right angles. Angles Q R S and X Y Z are congruent. The length of Y Z is 9, the length of X Z is 12, and the length of hypotenuse X Y is 15. Given △QRS ~ △XYZ, what is the value of tan(Q)? Three-fifths Three-fourths Four-fifths Four-thirds
Answer:
Three-fourths
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
∠QSR≅∠XZY ---> given problem
∠QRS≅∠XYZ ---> given problem
so
△QRS ~ △XYZ ----> by AA Similarity theorem
Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
That means
[tex]\frac{QS}{XZ}=\frac{QR}{XY}=\frac{RS}{YZ}[/tex]
∠Q≅∠X
∠R≅∠Y
∠S≅∠Z
In the right triangle XYZ
Find the tangent of angle X
[tex]tan(X)=\frac{YZ}{XZ}[/tex] ---> opposite side angle X divided by adjacent side angle X
substitute the given values
[tex]tan(X)=\frac{9}{12}[/tex]
Simplify
[tex]tan(X)=\frac{3}{4}[/tex]
Remember that
∠Q≅∠X
so
[tex]tan(Q)=tan(X)[/tex]
therefore
[tex]tan(Q)=\frac{3}{4}[/tex] ---->Three-fourths
A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
A. 22B. 33C. 55D. 77E. 88
Answer:
B. 33
Step-by-step explanation:
Let the number of Fuji trees be F, the number of gala be G and the total number of trees be x.
10% cross pollinated, this means 1/10 cross pollinated or 0.1x
Number of Fuji plus cross pollinated is 187.
And cross pollinated is 3/4 of total or let’s say 0.75 of total which is 0.75x
Now, adding 0.1x + 0.75x would equal 187
0.85x = 187
x = 187/0.85 = 220 trees
The total number of trees is 220.
The number of gala trees is thus 220 - 187 = 33 trees
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the _____.
a. variance
b. standard error
c. residual
d. predicted interval
Answer:
Option C. Residual
Step-by-step explanation:
Residuals are defined as:
Residual is the error that are not explained by the regression line.It is defined as the difference between observed value of dependent variable and the predicted variable.Residual = Observed value - Predicted value[tex]e = y_{\text{observed}}- \hat{y}[/tex], where e is the residual.Residuals are the unexplained differences.Thus,
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the residuals.
Option C. Residual
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the residual.
The following information should be considered:
Residual should be the error i.e. not described by the regression line. It shows the difference between the observed value and the predicted value.Therefore we can conclude that option c is correct.
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a rectangular picture 16 inches by 20 inches has a frame of uniform width. Find the width of the frame if the total area of the picture and the frame is 672 square inches
Answer: 22
Step-by-step explanation:
The area of the picture =l×b = 20×16=320
The length of the frame is 16
If the width is x ( and it's uniform)
672- 320= 352
Area of the frame = 16× x=352
x=352/16
x = 22
Total width is 42 inch.
Given that,
Length of picture is 16 inch and width is 20 inch.Total area with frame is 672 sq in.We need to find the width of frame.According to the scenario, computation of the given data are as follows,
Total area of picture = 16 [tex]\times[/tex] 20 = 320 sq in.
So Frame area = 672 - 320 = 352
Now, length of frame = 16
Let, width of frame = w
So, 16 [tex]\times[/tex] w = 352
W = 352 [tex]\div[/tex] 16
W = 22 inch
So total width is 22 + 20 = 42 inch.
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Bricklayers use the formula N= 7LH to estimate the number of bricks N needed to build a wall H give. In terms of the length and the number of bricks. b. What is the height of a wall that is 30 feet long and requires 2135 bricks to build?
Answer:
The height of the wall is approximately 10.17 feet.
Step-by-step explanation:
Given,
Length of wall = 30 feet
Total number of bricks = 2135
We have to find out the height of the wall.
To find out the height of wall, we have given the formula;
[tex]N=7LH[/tex]
Where N stands for number of bricks, L stands for length of wall and H stands for height of wall.
So we substitute the given values, we get;
[tex]2135=7\times30\times H\\\\2135=210H\\\\H=\frac{2135}{210}=10.166\approx10.17\ ft\\[/tex]
Hence the height of the wall is approximately 10.17 feet.
A regular hexagon is inscribed in a circle, the diameter of the circle is d; what is the circumference of the hexagon ?
Answer:
3d
Step-by-step explanation:
A regular hexagon has six equivalent triangles, each triangle having one side of that of the hexagon. if the diameter of the circle in which the hexagon is inscribed is d , then its radius will be
[tex]r=\frac{d}{2}[/tex]
this radius also happens to be one of the side of the equivalent triangle whose one side is also the side of hexagon. since length of one side of hexagon is
[tex]\frac{d}{2}[/tex]
the circumference of the hexagon will be [tex]6 (\frac{d}{2} )\\\\thus \\circumference \\of \\hexagon = 3d[/tex]
find the radius of the oblique cylinder (PLEASE HELP EXTRA POINTS)
Answer:
The radius of the oblique cylinder is 4 cm.
Step-by-step explanation:
Given:
The volume of the oblique cylinder = [tex]192 \pi cm^3[/tex]
Height of the cylinder = 12 cm
To Find:
Radius of the oblique cylinder = ?
Solution:
we know that the volume of the oblique cylinder
=>[tex]\text{base area of the cylinder} \times \text{height of the cylinder}[/tex]------------------------------(1)
where base area of the cylinder is the area of the circle
so area of the circle = base area
[tex]\pi r^2[/tex] = base area---------------(2)
Substituting (2) in (1)
[tex]192 \pi = \pi r^2 \times height[/tex]
[tex]192 \pi = \pi \times r^2 \times height[/tex]
[tex]192 \pi = \pi \times r^2 \times 12[/tex]
[tex]\frac{192 \pi}{ \pi \times 12}= r^2[/tex]
[tex]\frac{192}{12}= r^2[/tex]
[tex]16= r^2[/tex]
[tex] r^2 =16[/tex]
[tex] r =\sqrt{16}[/tex]
r=4
Let $f(x) = x^2$ and $g(x) = \sqrt{x}$. Find the area bounded by $f(x)$ and $g(x).$
Answer:
[tex]\large\boxed{1\dfrac{1}{3}\ u^2}[/tex]
Step-by-step explanation:
Let's sketch graphs of functions f(x) and g(x) on one coordinate system (attachment).
Let's calculate the common points:
[tex]x^2=\sqrt{x}\qquad\text{square of both sides}\\\\(x^2)^2=\left(\sqrt{x}\right)^2\\\\x^4=x\qquad\text{subtract}\ x\ \text{from both sides}\\\\x^4-x=0\qquad\text{distribute}\\\\x(x^3-1)=0\iff x=0\ \vee\ x^3-1=0\\\\x^3-1=0\qquad\text{add 1 to both sides}\\\\x^3=1\to x=\sqrt[3]1\to x=1[/tex]
The area to be calculated is the area in the interval [0, 1] bounded by the graph g(x) and the axis x minus the area bounded by the graph f(x) and the axis x.
We have integrals:
[tex]\int\limits_{0}^1(\sqrt{x})dx-\int\limits_{0}^1(x^2)dx=(*)\\\\\int(\sqrt{x})dx=\int\left(x^\frac{1}{2}\right)dx=\dfrac{2}{3}x^\frac{3}{2}=\dfrac{2x\sqrt{x}}{3}\\\\\int(x^2)dx=\dfrac{1}{3}x^3\\\\(*)=\left(\dfrac{2x\sqrt{x}}{2}\right]^1_0-\left(\dfrac{1}{3}x^3\right]^1_0=\dfrac{2(1)\sqrt{1}}{2}-\dfrac{2(0)\sqrt{0}}{2}-\left(\dfrac{1}{3}(1)^3-\dfrac{1}{3}(0)^3\right)\\\\=\dfrac{2(1)(1)}{2}-\dfrac{2(0)(0)}{2}-\dfrac{1}{3}(1)}+\dfrac{1}{3}(0)=2-0-\dfrac{1}{3}+0=1\dfrac{1}{3}[/tex]
The area bounded by the functions f(x) and g(x) in graph below.
The given function are f(x)=x² and g(x)=√x.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
To find the area between two curves defined by functions, integrate the difference of the functions. If the graphs of the functions cross, or if the region is complex, use the absolute value of the difference of the functions.
Area bounded = |x²-√x|
Find the domain by finding where the expression is defined.
Interval Notation:
[0,∞)
Set-Builder Notation:{x|x≥0}
Therefore, the area bounded by the functions f(x) and g(x) in graph below.
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Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?
A. $506.00
B. $726.24
C. $900.00
D. $920.24
E. $926.24
Answer:
E. $926.24
Step-by-step explanation:
The total amount of interest paid is shown below:
1. For 6 months, the interest would be
= Invested amount × interest rate
= $10,000 × 2%
= $200
2. For 12 months, the interest would be
= (Invested amount + interest paid for 6 months) × interest rate
= ($10,000 + $200) × 3%
= $10,200 × 3%
= $306
3. For 18 months, the interest would be
= (Invested amount + interest paid for 6 months + interest paid for 12 months ) × interest rate
= ($10,000 + $200 + $306) × 4%
= $420
Now the total interest would be
= $200 + $306 + $420.24
= $926.24
The common stock of Manchester & Moore is expected to earn 13 percent in a recession, 6 percent in a normal economy, and lose 4 percent in a booming economy. The probability of a boom is 5 percent while the probability of a recession is 45 percent. What is the expected rate of return on this stock?
Answer:
8.65%
Step-by-step explanation:
Given information:
Recession Return = 13%
Normal Return = 6%
Boom Return = -4%
Probability of a recession = 45 %
Probability of a boom = 5 %
Probability of a normal = 100 - 45 - 5 = 50%
We need to find the expected rate of return on this stock.
Expected rate of return is the sum of products of probability and returns of each state of economy.
Expected rate of return [tex]=13\%\times 45\%+6\%\times 50\%+(-4\%)\times 5\%[/tex]
[tex]=5.85\%+3\%-0.2\%[/tex]
[tex]=8.65\%[/tex]
Therefore, the expected rate of return on this stock is 8.65%.
PLEASE HELP
Which system of inequalities is represented by the graph?
A. y less than or equal to-2x+4 and y greater than or equal to x-6
B. y less than or equal to2x+4 and y greater than or equal to -x -6
C. y less than or equal to 2x-4 and y greater than or equal to -x-6
D. y less than or equal to 2x+4 and y greater than or equal to -x+6
Answer:
The answer to your question is letter B
Step-by-step explanation:
Process
1.- Find two points of each line
Line A (-2, 0) (-1, 2)
Line B (-1. - 5) (-6, 0)
2.- Find the slope and equation of each line
Line A
[tex]m = \frac{2 - 0}{-1 + 2}[/tex]
[tex]m = \frac{2}{1}[/tex]
m = 2
y - 0 = 2(x + 2)
y = 2x + 4
Line B
[tex]m = \frac{0 + 5}{-6 + 1}[/tex]
[tex]m = \frac{5}{-5}[/tex]
m = -1
y - 0 = -1(x + 6)
y = -x - 6
3.- Find the inequalities
Line A, we are interesteed in the lower area of the line, so the inequality is
y ≤ 2x + 4
Line B, we are also interested in the lower area of the line so the inequality is
y ≥ - x - 6
Answer:B
Step-by-step explanation:
Use matrices to determine the vertices of the reflected figure. Then graph the image and the pre-image on the same coordinate grid.
Triangle XYZ with vertices X(2, -9), Y(-6, 0) and Z(-5, -5), reflected over the y-axis.
A.
B.
C.
D.
(pictures below)
Answer:
see below for the matrix multiplicationgraph CStep-by-step explanation:
Reflection across the y-axis is a left-right reflection that changes only the sign of the x-coordinate. The transformation matrix (as for any rotation and/or reflection) can be 2-dimensional, and can left-multiply the coordinate matrix that has coordinate pairs as column vectors. The transformed coordinates show up as column vectors in the result matrix.
The only graphs showing left-right reflections are those of choices C and D. Only choice C has the points properly plotted on the graph.
The correct answer is graph C, or the third option.
Just got it right on edge 2020, hope this helps!! :)
Make a Venn Diagram from the following information to answer below question?25 students played soccer 4 boys played soccer and baseball 3 girls played soccer and baseball 10 boys played baseball 4 girls played baseball 9 students played tennis 3 boys played soccer and tennis 3 girls played soccer and tennis 3 boys played baseball and tennis 1 girl played baseball and tennis 1 boy played all three sports 1 girl played all three sports How many students played soccer, but not baseball or tennis?
To find the number of students who played soccer but not baseball or tennis, we need to analyze the given information and use the formula A = (A ∩ B) + (A ∩ C) + (A - A ∩ B ∩ C). Substituting the given values, we find that 32 students played soccer but not baseball or tennis.
Explanation:To determine how many students played soccer but not baseball or tennis, we need to analyze the information given in the Venn diagram provided. Let's label the regions of the Venn diagram:
A represents the set of students who played soccer.
B represents the set of students who played baseball.
C represents the set of students who played tennis.
From the given information, we know that:
A = 25A ∩ B = 4A ∩ C = 3B = 10B ∩ C = 4C = 9A ∩ B ∩ C = 1To find the number of students who played soccer but not baseball or tennis, we need to calculate the value of A without the intersection of the other sets. Using the formula:
A = (A ∩ B) + (A ∩ C) + (A - A ∩ B ∩ C),
we can substitute the given values:
A = 4 + 3 + (25 - 1)
A = 32
Therefore, 32 students played soccer but not baseball or tennis.
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average rate of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
A. 0.5< t < 0.75
B. 1.75< t < 2.0
C. 2.0 < t < 2.5
D. 2.5 < t < 3.0
E. 3 < t < 3.5
Answer:
C. 2.0 < t < 2.5
Step-by-step explanation:
Diameter of track (D) = 2 miles, Average rate (A) = 3 miles per hour
A = distance/ time
time (t) = distance/A
distance around the track (circumference) = πD = 3.142 × 2 miles = 6.284 miles
t = 6.284miles/3miles/hour = 2.1 hour
Therefore, 2.0 < t < 2.5
In the XY-Plane above, the circle has center (h,k) and radius 10. What is the value of k?
Answer:
k = +/- 6
Step-by-step explanation:
In the XY-Plane above, the circle has center (h,k) and radius 10. What is the value of k?
The concluding part of this question will be
Two coordinates are given, (4,0) and (20,0)
equation of a circle
([tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
We can then have two equations of the circle and solve simultaneously
([tex](4-h)^{2} +(-k)^{2} =10^{2}[/tex] .............................1
([tex](20-h)^{2} +(-k)^{2} =10^{2}[/tex] ......................................2
combining the two equation to solve
(20-h)^2 - (4-h)^2 = 0
20^2 - 40h +h^2 -4^2 + 8h -h^2 = 0
20^2 - 42 = 32h
h = 12
(4-12)^2 + (-k)^2 = 100
k^2 = 36
k = +/- 6
Among all pairs of numbers with a sum of 232, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.
Answer:
Step-by-step explanation:
232/2=116
so 116,116 has maximum product
The legs of a right triangle are in the ratio of 3 to 1. If the length of the hypotenuse of the triangle is 40√40, then the perimeter of the triangle is betweenA. 14 and 15B. 13 and 14C. 12 and 13D. 11 and 12E. 10 and 11
Answer:
A. Between 14 and 15.
Step-by-step explanation:
Let x be the one leg of the right triangle.
We have been given that the legs of a right triangle are in the ratio of 3 to 1. So, the other leg of the right triangle would be 3x.
We are also told that the length of the hypotenuse of the triangle is √40.
Using Pythagoras theorem, we can set am equation as:
[tex]x^2+(3x)^2=(\sqrt{40})^2[/tex]
Let us solve for x.
[tex]x^2+9x^2=40[/tex]
[tex]10x^2=40[/tex]
[tex]\frac{10x^2}{10}=\frac{40}{10}[/tex]
[tex]x^2=4[/tex]
Take square root of both sides:
[tex]x=\sqrt{4}[/tex]
[tex]x=2[/tex]
The other leg would be [tex]3x\Rightarrow 3\cdot 2=6[/tex].
The perimeter of the triangle would be:
[tex]\text{Perimeter of triangle}=2+6+\sqrt{40}[/tex]
[tex]\text{Perimeter of triangle}=2+6+6.324555[/tex]
[tex]\text{Perimeter of triangle}=14.324555[/tex]
Therefore, the perimeter of the triangle is between 14 and 15 and option A is the correct choice.
At the used bookstore, Keisha bought 24 novels. If 3/8 of the book the books are mystery novels and the rest are science fiction novels, how many science fiction novels did Keisha buy?
Keisha bought 15 science fiction novels.
Step-by-step explanation:
Given,
Number of novels bought by Keisha = 24
Mystery novels = 3/8 of total novels
Mystery novels = [tex]\frac{3}{8}*24=\frac{72}{8}[/tex]
Mystery novels = 9
Let,
x represent the number of science fiction novels.
Mystery novels + Science fiction novels = Total novels
[tex]9+x=24\\x=24-9\\x=15[/tex]
Keisha bought 15 science fiction novels.
Keywords: fraction, addition
Learn more about fractions at:
brainly.com/question/1466393brainly.com/question/1479138#LearnwithBrainly
Xander collected four times as many stamps as his cousin.If xander collected 60 stamps,then how many did his cousin collect What is the variable and the Equation
Answer:the number of stamps that his cousin collected is 20. The variable is x which represents number of stamps. The equation is
4x = 60
Step-by-step explanation:
Let x represent the number of stamps that his cousin collected.
Xander collected four times as many stamps as his cousin. This means that the number of stamps that Xander collected is 4x
If xander collected 60 stamps, then it means that
4x = 60
x = 60/4 = 20 stamps
Final answer:
The number of stamps Xander's cousin collected is determined by dividing the number of stamps Xander collected, which is 60, by 4. Therefore, his cousin collected 15 stamps.
Explanation:
If Xander collected four times as many stamps as his cousin, and Xander collected 60 stamps, we can determine how many stamps his cousin collected by setting up an equation. Let's define c as the number of stamps Xander's cousin collected. According to the information provided, Xander collected four times this amount, so we have the equation 4c = 60. To find the value of c, we divide both sides of the equation by 4:
c = 60 / 4
c = 15
Therefore, Xander's cousin collected 15 stamps.
What error did the student make in their work?
A) There is a calculation error (added, subtracted, multiplied or divided incorrectly).
B) BD is the midsegment and should be multiplied by 2, not AE.
C) BD is the midsegment and should be multiplied by 1/2, not AE.
D) AE is the midsegment and should be multiplied by 1/3.
Answer:
B
Step-by-step explanation:
just swap around which one you multiply by 2 as they have multiplied the larger one by 2 instead of the smaller one.
Answer:
B.
Step-by-step explanation:
The error is on the first line:
4x + 20 = 2(3x + 5) is correct
- because AE = 2BD.
Allison works for a computer software company. She earns \$225$225dollar sign, 225 per week plus \$25$25dollar sign, 25 for each software package that she sells that week. If she wants to earn at least \$400$400dollar sign, 400 this week, what is the minimum number of software packages that she must sell this week?
Answer:
7 software packages
Step-by-step explanation:
Given,
Signing amount = $ 225,
Additional amount for each software package = $ 25
Thus, the total amount for x software packages = signing amount + additional amount for x packages
= 225 + 25x
If total amount ≥ $ 400
225 + 25x ≥ 400
25x ≥ 400 - 225
25x ≥ 175
[tex]\implies x \geq \frac{175}{25}=7[/tex]
Hence, the minimum number of software packages that she must sell would be 7.
Final answer:
Alison needs to sell at least 7 software packages this week on top of her base salary to earn at least $400.
Explanation:
Alison wants to earn at least $400 this week by selling software packages. She earns a base $225 per week plus $25 for each software package sold. To determine the minimum number of software packages Alison must sell, we subtract her base salary from her desired earnings for the week:
Required earnings (>=$400) - Base salary ($225) = Sales required from software packages
$400 - $225 = $175
Now divide the sales required from software packages by the amount earned per package:
$175 / $25 = 7
Therefore, Alison needs to sell at least 7 software packages to meet her goal of $400