Answers
For problem 22, the x intercept is the point (-4,0) as this is where the S shaped curve crosses through the horizontal x axis. See the attached diagram for a visual of what I'm talking about. Note the highlighted point in red.
Related Questions
I need help please :( !!!
Answers
Number of cans donated the second week = 146
Number of cans donated the third week = c, where c is some positive number
Add up the three values (132, 146, and c) to get 132+146+c. I'm choosing not to simplify because each answer choice hasn't simplified either.
The expression of 132+146+c represents the total amount of cans donated for weeks 1 through 3. We want "at least 325 cans", so that means the expression is 325 or larger. That translates to this inequality
[tex]132+146+c \ge 325[/tex]
The "greater than or equal to" sign indicates we want that sum to be 325 or larger.
Now we solve for c
[tex]132+146+c \ge 325[/tex]
[tex]278+c \ge 325[/tex]
[tex]278+c-278 \ge 325-278[/tex]
[tex]c \ge 47[/tex]
So the amount of cans donated for week three needs to be 47 or larger. If you collect exactly 47 cans for week three, then you meet the goal of 325 total cans. If you collect more than 47 cans for week three, then you exceed the goal of 325 total cans.
------------------------------------
In summary we have the inequality
[tex]132+146+c \ge 325[/tex]
which solves to
[tex]c \ge 47[/tex]
Meaning that the answer is choice D
Vivian measured 2/5 cup of onions, 1/3 cup of celery, and 1/2 cup of carrots. How many cups of vegetables did Vivian measure out for her vegetable soup?
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Solve the quadratic equation by completing the square.
x^+12x+30=0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Form:
( x + _ )^2 = _
or
( x - _ )^2 = _
Solution:
x = _
^ Please use the template above to answer ^
Answers
( x + 6 )^2 = 6 or ( x + 6 )^2 = 6
Solution:
x = -6 + √6, x = -6 - √6
Explanation:To solve the quadratic equation \(x^2 + 12x + 30 = 0\) by completing the square, first, rewrite the equation in the form \(x^2 + 2ax + a^2 = (x + a)^2\). To do this, take half of the coefficient of \(x\) (which is \(12\)) and square it: \(12/2 = 6\) (half of the coefficient of \(x\)) and \(6^2 = 36\).
Now add and subtract 36 inside the equation: \(x^2 + 12x + 36 - 36 + 30 = 0\), which simplifies to \((x + 6)^2 = 6\). This is the completed square form.
To solve for \(x\), take the square root of both sides:[tex]\(x + 6 = \pm \sqrt{6}\). Then solve for \(x\): \(x = -6 + \sqrt{6}\) and \(x = -6 - \sqrt{6}\). These are the two solutions for \(x\).[/tex]
Completing the square is a method used to solve quadratic equations by converting the equation into a perfect square form, making it easier to solve for the unknown variable \(x\).
Russells previous test scores are 70,74,87,85 what score does he need to get an average of 80
Answers
For the 5th test score, an 80 average needs 400 as the total score. So 400-316 = 84 on the next test.
Answer:
84 is the score that you Russell needs on the next test to achieve an average of at least 80.
Step-by-step explanation:
Russell's test scores are: 70,74,87 and 85
Average of the test scores = A = 80
Let thescore needed to achieve an average of 80 be x
Average = [tex]\frac{\text{Sum of terms}}{\text{Number of terms}}[/tex]
[tex]A=\frac{70+74+87+85+x}{5}[/tex]
[tex]80=\frac{70+74+87+85+x}{5}[/tex]
[tex]70+74+87+85+x=400[/tex]
[tex]x=400-(70+74+87+85)=84[/tex]
84 is the score that you Russell needs on the next test to achieve an average of at least 80.
What is 2/3x = 4/15?
Answers
2/3x = 4/15 =
x = 4/15 / 2/3 = 4/15 x 3/2 = 12/30 = 2/5
x = 2/5
all i know is x=25 its hard for me to explain.
what is the radius of a circle given by the equation x^2+(y-3)^2=21
Answers
Find the critical value zα/2 that corresponds to a 98% confidence level.
Answers
A critical value is the point on the scale of the test statistic (z test in this case) outside which we reject the null hypothesis, and is taken from the level of significance of the test. The critical values can be obtained from the standard distribution tables for z and for this case, it is equivalent to:
critical value zα/2 at 98% confidence level = 2.326
Answer: 2.326
Answer:
2.33
Step-by-step explanation:
Use the graph below to answer the following question:
What is the average rate of change from x = –4 to x = 1?
–3
–1
0
1
Answers
average rate of change = (-1 - 4) / 1 - (-4) = -5 / 5 = -1
The average rate of change from x = –4 to x = 1 is 3.
Explanation:To find the average rate of change from x = –4 to x = 1, we need to calculate the change in y-values and divide it by the change in x-values. Given that the slope of the line is 3, we can use the formula for average rate of change: (change in y) / (change in x). In this case, the change in x is 1 - (-4) = 5, and the change in y is 3 * 5 = 15. Therefore, the average rate of change is 15 / 5 = 3.
Vera and her roommates ate 1 1/3 pints of ice cream on Friday night and 1 1/6 pints of ice cream on Saturday night. How many pints did they eat in all
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1 1/3 + 1 1/6
add the 1 +1 = 2
add 1/3 + 1/6 ( find common denominator, which in this case is 6)
so 1/3 becomes 2/6
2/6 + 1/6 = 3/6 which reduces to 1/2
they ate 2 1/2 pints total
Evaluate the function rule for the given value. Y=6*4 for x=-3
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y=24
Which statement is true about the discontinuation of the function F(x)? F(x)=x+1/6x^2-7x-3
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there are holes at x= 3/2 and x=-1/3
1.Find the area of each triangle with the given heights and bases
a. h = 6 inches; b = 10 inches
b. h = 9 centimeters; b = 4 centimeters
c. h = 13 yards; b = 20 yards
Answers
Answer: 1.)
A. 30in^2
B. 18cm^2
C. 130yd^2
2.) The formula for the area of a triangle is half the base times the height. So 1/2 x 40 x 32 = 640cm^2
3.) 17 yards. The fence that enclose Sondra's backyard is a right triangle whose sides measuring 8 yards, 15 yards and 17 yards respectively.
4.) From the Pythagorean Theorem we know:
hypotenuse^2 = side^2 + side^2
hypotenuse^2 = 36 + 36
hypotenuse = square root (72)
hypotenuse = 8.48528... feet
5.) a. 5
b. √128
c. √221
Area of triangle are [tex]30inches^{2}[/tex] in part(a),
[tex]18[/tex] [tex]centimerters^{2}[/tex] in part(b) and [tex]130[/tex] [tex]yards^{2}[/tex] in part(c)
What is Triangle?
In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
What is area?
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
According to questions, we have the following
In part (a.), h = [tex]6[/tex] inches; b = [tex]10[/tex] inches
In part (b.), h =[tex]9[/tex] centimeters; b =[tex]4[/tex] centimeters
In part (c.) h = [tex]13[/tex] yards; b = [tex]20[/tex] yards
We have to find the area of each triangle with the given heights and bases.
Now, Area of triangle in part a
[tex]=\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]
[tex]=\frac{1}{2}[/tex]×[tex]6[/tex]×[tex]10[/tex]
[tex]=30inches^{2}[/tex]
Area of triangle in part b
[tex]=\frac{1}{2}[/tex]×[tex]9[/tex]×[tex]4[/tex]
[tex]=18[/tex] [tex]centimerters^{2}[/tex]
Area of triangle in part c
[tex]=\frac{1}{2}[/tex]×[tex]13[/tex]×[tex]20[/tex]
[tex]=130[/tex] [tex]yards^{2}[/tex]
Hence, we can conclude that area of triangle are [tex]30inches^{2}[/tex] in part(a),
[tex]18[/tex] [tex]centimerters^{2}[/tex] in part(b) and [tex]130[/tex] [tex]yards^{2}[/tex] in part(c)
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how do u graph this
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[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\[/tex]
[tex]\bf \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]
so hmmm [tex]\bf \begin{array}{llcll} f(x)=&0.5sin(x)&+2\\ &\uparrow &\uparrow \\ &A&D \end{array}[/tex]
instead of going up/down by 1unit, it goes up/down by half
and then it's shifted upwards by 2, so the midline will end up at y = 2
but basically the same sin(x) graph, just a bit shorter due to the smaller amplitude.
Find the factorization of the polynomial below.
2x²+7x+6
A. (2x+2)(x+4)
B. (2x+2)(x+3)
C. (2x+3)(x+1)
D. (2x+3)(2x+2)
Answers
2x^2+7x+6
x^2+7x+12
(x+3)(x+4)
(2x+3)(x+2)
The best answer is none of the above.
When foiling the answer choices,
A: 2x^2+10x+8
B: 2x^2+8x+6
C: 2x^2+5x+3
D: 4x^2+10x+6
Answer:
(2x+3)(x+2)
Step-by-step explanation:
i hope this helps
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 8−x−1 intersect are the solutions of the equation 4−x = 8−x−1. (4 points) Part B: Make tables to find the solution to 4−x = 8−x−1. Take the integer values of x between −3 and 3. (4 points) Part C: How can you solve the equation 4−x = 8−x−1 graphically? (2 points) Part A:
Answers
A. We have two lines: y = 4-x and y = 8-x^-1
Given two simultaneous equations that are both to be true, then the solution is the points where the lines cross. The intersection is where the two equations are equal. Therefore the solution that works for both equations is when
4-x = 8-x^-1
This is where the two lines will cross and that is the common point that satisfies both equations.
B. 4-x = 8-x^-1
x 4-x 8-x^-1
______________
-3 7 8.33
-2 6 8.5
-1 5 9
0 4 -
1 3 7
2 2 7.5
3 1 7.67
The table shows that none of the x values from -3 to 3 is the solution because in no case does
4-x = 8-x^-1
To find the solution we need to rearrange the equation to find for x:
4-x = 8-x^-1
Multiply both sides with x:
4x-x^2 = 8x-1
x^2+4x-1=0
x= -4.236, 0.236
Therefore there are two points that satisfies the equation.
Find y:
x=-4.236
y = 4-x = 4 – (-4.236) = 8.236
y = 8-x^-1 = 8-(-4.236)^-1 = 8.236
x=0.236
y = 4-x = 4 – (0.236) = 3.764
y = 8-x^-1 = 8-(0.236)^-1 = 3.764
Thus the two lines cross at 2 points:
(-4.236, 8.236) & (0.236, 3.764)
C. To solve graphically the equation 4-x = 8-x^-1
We would graph both lines: y = 4-x and y = 8-x^-1
The point on the graph where the lines cross is the solution to the system of equations.
Just graph the points on part B on a cartesian coordinate system and extend the two lines. The solution is, as stated, the point where the two lines cross on the graph.
The x-coordinates of the intersection points between the equations are the solutions to the given equation. Tables can be used to find the solution by plugging in different values of x. The equation can also be solved graphically by finding the intersection points of the two equations on a graph.
Explanation:Part A:
The x-coordinates of the points where the graphs of the equations y = 4−x and y = 8−x−1 intersect are the solutions of the equation 4−x = 8−x−1. To find the intersection points, we set the two equations equal to each other and solve for x.
Part B:
To find the solution to 4−x = 8−x−1, we can create a table by plugging in different integer values of x between -3 and 3. Substitute each value of x into the equation and solve for y. The values of x and y that make the equation true are the solutions.
Part C:
The equation 4−x = 8−x−1 can be solved graphically by plotting the two equations on a graph and finding the points of intersection. The x-coordinate of the intersection point(s) represents the solution(s) to the equation.
Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Two rectangular tiles, rectangle PQRS with vertices at P 5, 7. Q is at 9, 7. R is at 9, 12. S is at 5, 12 . Rectangle JKLM with vertices J 4, 5. K is at 6, 5. L is at 6, 10. M is at 4, 10. Which statement is correct?
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The tile PQRS is bigger than tile JKLM. A rectangle is a two-dimensional shape that has two sets of equal parallel planes. Thus, its area is equal to the length multiplied by its width.
tile PQRS = (9-5)*(12-7) = 20 units²
tile JKLM = (6-4)*(10-5) = 10 units²
Tile PQRS is larger by 10 units².
For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?
Answers
m^2 - 4*18*2 = 0
m^2 = 144
m = +/-12
so its m = 12 or -12
Answer:
12
Step-by-step explanation:
A triangle has a perimeter of 48" and the dimensions of each side are given as X + 3, 4x-1, 2X -3 solve for the value of X and determine the length of each side
Answers
SO we can add all three sides to find perimeter of triangle.
SO perimeter is = x+3 + 4x - 1 + 2x - 3
= 7x -1
As perimeter is 48.
So we can write 7x - 1 = 48
7x - 1 = 48
On adding 1 on both sides.
7x- 1+ 1 = 48 +1
7x = 49
On dividing 7 on both sides.
[tex] \frac{7x}{7} = \frac{49}{7} [/tex]
[tex]x= 7[/tex]
So length of first side is = x+3 = 7+3 = 10
Length of second side = 4x - 1 = 4*7 - 1 = 27
Length of third side = 2x - 3 = 2*7 - 3 = 11
So side of triangle = 10 . 27 , 11
The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r. The equation solved for P is P = . What is the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years? $60 $80 $90 $100
Answers
we know that
The simple interest formula is equal to
[tex]I=Prt[/tex]
where
I represents simple interest
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=5\ years\\ P=?\\ I=\$40\\r=0.10[/tex]
[tex]I=Prt[/tex]
Solve for P
[tex]P=I/(rt)[/tex]
substitute the values
[tex]P=40/(0.10*5)=\$80[/tex]
therefore
the answer is
[tex]\$80[/tex]
This net folds into the cube shown beside it. On the cube, which letter will be on the side opposite D?
Answers
Without more information or a diagram, it's hard to give a specific answer. However, on a cube net, the face opposite 'D' is likely the one not directly connected to 'D' on the plane of the net.
Explanation:Unfortunately, without a diagram or more context, it's difficult to provide a definitive answer to the question. However, typically on a cube net, sides that are opposite each other when the net is folded into a cube are adjacent (next to each other) on the net. For example, if 'D' were on a flat square in the center of the net, the squares directly connected to it (on the top, bottom, left, and right) on the plane of the net would end up being the sides adjacent to 'D' when the cube is formed. The square not connected directly to 'D' on the plane would be opposite 'D' once the cube is formed.
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The tides around Cherokee Bay range between a low of 1 foot to a high of 5 feet. The tide is at its lowest point when time, t, is 0 and completes a full cycle over a 24 hour period. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
Answers
Low tide height = 1 ft
High tide height = 5 ft
Tide period, T = 24 houts
Let the height of the tide be modeled by the expression
h(t) = K + A cos(bt)
Because the period is 24, therefore
b = (2π)/24 = π/12
That is,
h(t) = K + Acos[(πt)/12]
When r=0, h = 1, therefore
K + A cos(0) = 1, ot
K + A = 1 (1)
When t = 12 (half cycle), h = 5, therefore
K + A cos(π) = 5, or
K - A = 5 (2)
Add (1) and (2):
2K = 6
K = 3
From(1), obtain
A = 1 - 3 = - 2
Answer:
The required function is h(t) = 3 - 2 cos[(πt)/12]
The amplitude is 2 feet
The period is 24 hours
The midline of the function is h = 3 feet
A graph of the function is shown below.
Answer:
C) Amplitude = 2 feet; period = 24 hours; midline: y = 3
Step-by-step explanation:
above
Which graph correctly represents
x + 2y ≤ 4?
Answers
2y < = -x + 4
y < = -1/2x + 2
u will have a solid line (because there is an = sign in the problem)....the slope will be -1/2...so ur line is going down....u have a y int (where ur line crosses the y axis at (0,2).....u have an x int (where ur line crosses the x axis at (0,4)..ur line will be shaded below the line.
Step-by-step explanation:
[tex]x + 2y \leq 4[/tex]
To graph this inequality we replace <= symbol with = sign
[tex]x + 2y =4[/tex]
subtract x on both sides
[tex]2y =-x+4[/tex]
divide both sides by 2
[tex]y= \frac{-1}{2} x +2[/tex]
Graph the equation using a table
LEts assume some number for x and find out y
x [tex]y= \frac{-1}{2} x +2[/tex]
-2 3
0 2
2 1
Now graph the equation using points (-2,3) (0,2)(2,1)
use solid line for graphing
Now use test point (0,0) for shading
[tex]x + 2y \leq 4[/tex]
[tex]0 + 2(0) \leq 4[/tex]
[tex]0 \leq 4[/tex] true
So we shade the region that contains (0,0)
the graph is attached below
Which of the following equations represents a quadratic function?
y(y + 4)(y - 6) = 0
z2 + 2 = 3z(z2 - 1)
(2x - 3)(4x + 5) = 10x
(3b)(5b – 7)(b + 8) = 0
Answers
A quadratic equation is one in which the highest exponent of a variable is 2. We can solve this problem by expanding each choices then find which has highest exponent equal to 2.
y(y + 4)(y - 6) = 0 ---> By expansion we get y^3, therefore highest exponent is 3.
z2 + 2 = 3z(z2 - 1) ---> By expansion we get z^3, therefore highest exponent is 3.
(2x - 3)(4x + 5) = 10x ---> By expansion we get x^2, therefore highest exponent is 2.
(3b)(5b – 7)(b + 8) = 0 ---> By expansion we get b^3, therefore highest exponent is 3.
The answer to this problem is therefore:
(2x - 3)(4x + 5) = 10x
The total area of your neighbor's backyard is 900 ft2. she wants to use 240 ft2 more area for landscaping than for a pool. how much area will she use for the pool? the landscaping?
Answers
P = pool
L + P = 900
L = P + 240
P + 240 + P = 900
2P = 660
Pool = 330 sq ft
Landscaping = 570 sq ft
The area used for the pool is 330 ft² and the area used for landscaping is 570 ft².
1. The sum of the areas for the pool and landscaping equals the total area of the backyard:
[tex]\[ P + L = 900 \][/tex]
2. The area for landscaping is 240 ft² more than the area for the pool:
[tex]\[ L = P + 240 \][/tex]
Now we can substitute the expression for L from the second equation into the first equation:
[tex]\[ P + (P + 240) = 900 \][/tex]
Combining like terms gives us:
[tex]\[ 2P + 240 = 900 \][/tex]
Subtract 240 from both sides to isolate the term with P:
[tex]\[ 2P = 900 - 240 \] \[ 2P = 660 \][/tex]
Divide both sides by 2 to solve for P:
[tex]\[ P = \frac{660}{2} \] \[ P = 330 \][/tex]
Now that we have the area for the pool, we can find the area for landscaping by substituting P back into the second equation:
[tex]\[ L = 330 + 240 \] \[ L = 570 \][/tex]
Therefore, the area used for the pool is 330 ft² and the area used for landscaping is 570 ft².
Rita is saving money to buy a game. So far she has saved $15, which is three-fifths of the total of the game. How much does the game cost?
Answers
15 /3 = 5. so each 1/5 is $5
5*5 = 25
so the game costs $25
Last year the profit for a company was $560,000. This year's profit decreased by 7.1%. Find this year's profit.
Answers
Profit this year is
560,000−560,000×0.071
=520,240
The original value of the car is $18,000 it depreciates by 15% every year what is the value of the car after three years
Answers
A=p (1-r)^t
A the value of the car after 3 years ?
P current value 18000
R rate of depreciation 0.15
T time 3 years
A=18,000×(1−0.15)^(3)
A=11,054.25
how can exponential and logarithmic functions be created to use in real world situations?
Answers
Use of Logarithmic function
We can find use of logarithmic function in measuring earthquake (Richter Scale) , the brightness of stars , and chemistry(pH balance , measure of acidity and alkalinity)
For example:
In Richter Scale , a logarithmic function that is used to measure the magnitude of earthquake.
If A = measure of amplitude of earthquake wave.
[tex]A_o[/tex] = Amplitude of smallest detectable wave.
From this we can find R the Richter scale measure of magnitude of earthquake.
[tex]R = log \frac{A}{A_o} [/tex]
Use of Exponential Function:
Exponential function may use in finding compound interest , population growth , radioactivity decay , etc.
For example :
As we know the formula for compound interest is
[tex]A = P(1+ \frac{r}{n})^{nt} [/tex]
Where P is principal amount , r = rate of interest(decimal) , n is the number of compounding period , t is time.
For
Factor 4x^2 - 25 show your work Help Plz!
Answers
= (2x)^2 - 5^2 .................using a^2 - b^2 = (a+b)(a-b)
= (2x + 5)(2x - 5)
C =5/9(F-32). Covert 12 degrees Celsius to Fahrenheit. Round to nearest degree
Answers
F - 32 = 12 / 5/9 = 12 * 9/5 = 21.6
F = 32 + 21.6 = 53.6 = 54 to nearest degree