Answers
(a) To make use of the forms of the equation for a line this problem requires, we must first calculate the slope (m) of the line between the two given points. That is computed by ...
... m = (change in y)/(change in x)
... m = (8 -3)/(2 -0) = 5/2
The second given point tells us the y-intercept (b) is 3, so the equation for the line is ...
... y = mx + b
... y = 5/2x + 3
(b) As in part (a), we must calculate the slope of the line. That is ...
... m = (change in y)/(change in x)
... m = (4 -3)/(1 -3) = 1/(-2) = -1/2
Using the first point (h, k) in the point-slope form of the equation of a line, we have ...
... y -k = m(x -h)
... y -4 = -1/2(x -1) . . . . . point-slope equation
Simplifying this, we get
... y = -1/2x +1/2 +4
... y = -1/2x +9/2 . . . . . slope-intercept equation
(c) The slopes of the two equations are different, so they must intersect at exactly one point. The equations are consistent.
(d) We can substitute the "y" from one equation into the other to give ...
... 5/2x +3 = -1/2x +9/2
... 3x = 3/2 . . . . . . . add 1/2x -6/2
... x = 1/2 . . . . . . . . divide by 3
Using the first equation to find y:
... y = (5/2)·(1/2) +3 = 5/4 +12/4
... y = 17/4
The point of intersection is (x, y) = (1/2, 17/4).
Related Questions
will mark braniest 2 left also add me i help
Answers
Answer:
-9
Step-by-step explanation:
(x-2) is 3 more than (x-5), because -2 is 3 more than -5.
3 more than -12 is -9.
_____
If you like, you can solve for x.
... x -5 = -12
... x = -7 . . . . . add 5
Now find the value of x-2
... x -2 = -7 -2 = -9
Choose the correct simplification of the expression 3 times b all over a to the power of negative 2.
3a2b
a to the 2nd power over 3 times b
3 times a to the 2nd power all over b
Already simplified
pleaseee help
Answers
Answer:
Step-by-step explanation:
The question will look like (3b)/(a^-2)
To simplify, note the (a^-2). It is a negative, so flip the placement of the monomial. Note that the term is located in the decimal, so when it is flipped, it goes to the numerator (vice versa if it is opposite)
(3b)/(a^-2) = (3b)(a²)
3a²b, or (A) is your answer choice
~
Answer:
Option A) 3a2b
Step-by-step explanation:
The work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below:
Step 1: 4(2x − 4) = 8 + 2x + 8
Step 2: 6x − 8 = 16 + 2x
Step 3: 6x − 2x = 16 + 8
Step 4: 4x = 24
Step 5: x = 6
In which step did the student first make an error and what is the correct step?
Step 2; 8x − 4 = 2(6 + x + 6)
Step 2; 8x − 16 = 16 + 2x
Step 3; 6x − 2x = 16 − 8
Step 3; 6x + 2x = 16 + 8
Answers
Answer:
The answer is B. Step 2; 8x − 16 = 16 + 2x
Hope This Helps!
Triangles △ABC and △DEF are similar. Find the lengths of the sides of △DEF, if AB=2 cm, BC=3 cm, CA=4 cm, DE=1.5 cm.
Answers
DE = 1.5 cm, EF = 2.25 cm, FD = 3 cm
Step-by-step explanation:Side DE corresponds to side AB and is (1.5 cm)/(2 cm) = 3/4 the length of it.
Because the triangles are similar, all pairs of corresponding sides have the same ratio. That is, the side lengths in ΔDEF are 3/4 of those in ΔABC.
... EF = (3/4)×BC = (3/4)×(3 cm)
... EF = 2.25 cm
... FD = (3/4)×CA = (3/4)×(4 cm)
... FD = 3 cm
The lengths of the sides of triangle △DEF, given that AB=2 cm, BC=3 cm, CA=4 cm, and DE=1.5 cm, would be EF = 2.25 cm and DF = 3 cm.
Explanation:If triangles △ABC and △DEF are similar, then the ratio of the corresponding sides is the same. We know AB = 2 cm which corresponds to DE = 1.5 cm in the triangle △DEF. The ratio of AB to DE is 2cm:1.5cm or 4:3. Let's compute the sides of the triangle △DEF using this ratio:
EF corresponds to BC in triangle △ABC. Using the ratio 4:3, EF = BC * (3/4) = 3cm * 3/4 = 2.25 cm DF corresponds to CA in triangle △ABC. Using the ratio 4:3, DF = CA * (3/4) = 4cm * 3/4 = 3 cmLearn more about Similar Triangles here:https://brainly.com/question/32489731
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find each missing measure, measure of angle 1,2,3,4
Answers
Answer:
75°56°124°41°Step-by-step explanation:
∠1 is complementary to 15°, so is 90° -15° = 75°
∠2 completes the triangle with angles 49° and 75°, so is 180° -49° -75° = 56°
∠3 is supplementary to ∠2, so is 180° -56° = 124°
∠4 is complementary to 49°, so is 90° -49° = 41°
Two similar pyramids A and B have surface areas of 135cm^2 and 60cm^2 respectively . The volume of pyramid A is 405 cm^3 work out the volume of pyramid B
Answers
Answer:
120 cm^3
Step-by-step explanation:
The surface areas are in the ratio 60 to 135 so the single dimensions are in the ratio √60 to √135.
Therefore the volumes are in the ratio (√60)^3 to (√135)^3 or 60^3/2 to 135^3/2.
So Volume of Pyramid B / Volume of Pyramid A
= 60^3/2 / 135^3/2.
Therefore we have the equation 60^3/2 / 135^3/2 = V / 405 where V is the volume of pyramid B.
V = (60^3/2 * 405) / 135^3/2
= 120 cm^3
Answer:
120cm³
Step-by-step explanation:
√135/√60=3/2
3/2=1.5
1.5³=3.375
405/3.375=120
120cm³
Please help 200*50/-9+564*-4= ? I
Answers
Answer:
-3367 1/9
Step-by-step explanation:
This is what calculators are for.
Perform the multiplication and division before the addition.
... = 10000/-9 -2256
... = -1111 1/9 -2256
... = -3367 1/9
_____
If you don't have a calculator, the Google and Bing search boxes can be relied upon to use the correct order of operations.
On a hot summers day 262 people used the public swimming pool. The daily prices are 1.50 for children and 2.00 for adults. The receipts for admission totalled 470.00. How many children and how many adults swam st the pool that day?
Answers
Let x represent the number of adults who swam at the pool. Then (262-x) is the number of children. Multiplying these numbers by the corresponding admission charge will give the associated receipts. We are given the total of receipts, so we can write the equation ...
... 2.00x +1.50(262-x) = 470.00
... 0.50x +393.00 = 470.00 . . . . . simplify
... 0.50x = 77.00 . . . . . . . . . . . . . . .subtract 393
... 77.00/0.50 = x = 154 . . . . . . . . . divide by the coefficient of x
... (262-x) = 108 . . . . . . . . . . . . . . . .find the number of children admitted
CORRECT ANSWER = BRAINLIEST
A right rectangular prism has these dimensions: Length − Fraction 1 and 1 over 2 units Width − Fraction 1 over 2 unit Height − Fraction 3 over 4 unit How many cubes of side length Fraction 1 over 4 unit are required to completely pack the prism without any gap or overlap?
Answers
Answer:
36
Step-by-step explanation:
The length of 1 1/2 units is equivalent to 3/2 = 6/4 = 6×(1/4) = 6 cubes.
The width of 1/2 units is equivalent to 2/4 = 2×(1/4) = 2 cubes.
The height of 3/4 units is equivalent to 3×(1/4) = 3 cubes.
Then, in terms of cubes, the dimensions are 6 × 2 × 3. The volume is the product of these dimensions, so is ...
... 6 × 2 × 3 = 36 . . . . cubes
Answer:
36Step-by-step explanation:
Which number(s) below would NOT in scientific notation and why? 4.5 x 10^4 6 x 10^7 12.5 x 10^3 4.2 x 10^-8 2.355 x 10^6 0.45 x 10^3
Answers
Scientific notation has exactly one non-zero digit to the left of the decimal point in the mantissa. The numbers listed above do not.
_____
Comment on these numbers
There may be good reasons for writing the numbers in this form. For example, in engineering, it is often useful to have the exponent be a multiple of 3. In other instances, writing the number in these forms may facilitate arithmetic. However good the reasons may be, these numbers are not in in the form defined as "scientific notation."
What is the result of isolating x^2 in the equation below? y^2-3x^2=6
A. x^2 = y^2/3 -2
B. x^2 = -y^2/3 -2
C. x^2 = y^2/3 + 2
D. x^2 = -y^2/3 + 2
Answers
Answer:
A. x^2 = y^2/3 -2
Step-by-step explanation:
Add 3x^2 to both sides of the equation. We do this so that the coefficient of x^2 is positive. It can be less confusing that way.
... y^2 = 3x^2 +6
Divide by 3.
... y^2/3 = x^2 +2
Subtract 2.
... y^2/3 -2 = x^2 . . . . . matches selection A.
Answer:
A. x^2 = y^2/3 -2
Step-by-step explanation:
According to the diagram which of the following statement is true?
Cos x =4/5
Sin x = 5/3
Tan x = 5/4
Cos x = 3/5
Answers
We know that :
✿ [tex]\mathsf{Cos\theta = \frac{Adjacent\;Side}{Hypotenuse}}[/tex]
✿ [tex]\mathsf{Sin\theta = \frac{Opposite\;Side}{Hypotenuse}}[/tex]
✿ [tex]\mathsf{Tan\theta = \frac{Opposite\;Side}{Adjacent\;Side}}[/tex]
From the Figure :
✿ [tex]\mathsf{Cosx = \frac{4}{5}}[/tex]
✿ [tex]\mathsf{Sinx = \frac{3}{5}}[/tex]
✿ [tex]\mathsf{Tanx = \frac{3}{4}}[/tex]
Only 1st Statement is True
1st Option is the Answer
Find approximations for the input where the functions share a solution.
Answers
Answer:
x ≈ 0, x ≈ 2.5
Step-by-step explanation:
The left point of intersection is very near the y-axis, where x=0.
The right point of intersection is somewhat below the midpoint between x=2 and x=4. It seems to be just about at the midpoint between that midpoint (x=3) and the line at x=2. We estimate the value at about x=2.5.
_____
If we knew the actual function definitions, we could solve for the points of intersection.
HELP ASAP PLEASE you make $20 an hour and work fro 40 hours a week, you are paid biweekly and have $185 total deducted from your paycheck, what is your gross annual earnings?
Answers
Answer:
615
Step-by-step explanation:u make $20 a week and u worked 40 hours u jus do 40*20=$800
800-185=615 im pretty sure hope this helps
Answer:
Weekly net pay is $36790
Weekly gross pay is $41600
Step-by-step explanation:
Net pay is the gross pay minus taxes
Net pay = gross pay - taxes
Gross pay = hours worked * hourly rate
Net pay = hours worked * hourly rate - taxes
We know the
hours worked = 40
Hourly rate = 20
tax rate = 185 bi weekly = 185/2 = 92.5 weekly
Net pay = 40 * 20 - 92.5
Net pay = 800-92.5
Net pay = 707.5
This is the weekly net pay
Assuming we work 52 weeks a year
Weekly net pay is 52* 707.5 = 36790
Weekly gross pay is 40*20 * 52 = 41600
Sarah bikes 4/5 km in 2 min. What is the unit rate and what does it mean?
Answers
Answer:
The unit rate is [tex]\frac{2}{5}[/tex] km per minute. It means sarah bikes [tex]\frac{2}{5}[/tex] km in 1 minute or the speed of sarah is [tex]\frac{2}{5}[/tex] km per minute.
Step-by-step explanation:
It is given that Sarah bikes [tex]\frac{4}{5}[/tex] km in 2 min. It means Sarah covers [tex]\frac{4}{5}[/tex] km in 2 min.
The units rate is defined as
[tex]\text{Unit rate}=\frac{\text{Distance covered}}{\text{Time Taken}}[/tex]
[tex]\text{Unit rate}=\frac{(\frac{4}{5})}{2}[/tex]
[tex]\text{Unit rate}=\frac{4}{5}\times \frac{1}{2}[/tex]
[tex]\text{Unit rate}=\frac{2}{5}[/tex]
Therefore the unit rate is [tex]\frac{2}{5}[/tex] km per minute. It means sarah bikes [tex]\frac{2}{5}[/tex] km in 1 minute or the speed of sarah is [tex]\frac{2}{5}[/tex] km per minute.
polynomial are given:P
[tex] p |x | = {x}^{3} - 3 {x}^{2} + 2x - 1[/tex]
show if
[tex]x = 1[/tex]
is the root of the polynomial.
Erpress the polynomial
[tex]p |x| [/tex]
in the tratment
[tex]p |x| = (x - 1)( {x}^{2} + ax + b) + c[/tex]
Answers
Answer:
x = 1 is not a rootp(x) = (x -1)(x^2 -2x +0) -1Step-by-step explanation:
a) p(1) = 1³ -3·1² +2·1 -1 = 1 -3 +2 -1 = -1 . . . . not zero
b) Dividing p(x) by x-1 gives x² -2x +0 with a remainder of -1 (as found in part (a)). So the function can be written as ...
... p(x) = (x -1)(x² -2x +0) -1
_____
Polynomial division can be done using synthetic division or long division. The latter can be done by hand or by using any of several on-line calculators. Attached is output from one of them.
PLEASE HELP ASAP!
How do I solve and simplify these problems using distributive property?
2x + 10
2(3x + 5)
Answers
2x + 10 can be simplified using the distributive property by factoring a 2 out of each term.
2(x + 5)
2(3x + 5) can be solved by applying the distributive property, by multiplying each term inside the parentheses by 2.
6x + 10
what is 31 and 5/250 as a decimal
Answers
Answer:
31.020
Step-by-step explanation:
Multiply the fraction by 4/4 to get the denominator to 1000. Simplify to a denominator of 100 if you like. Then use place value to write your number.
... 31 + 5/250 = 31 + 20/1000 . . . . thirty-one and twenty thousandths
... = 31 + 0.020 = 31.020 . . . or . . . 31.02
A triangle is 3 inches wide and 1 inch tall. If its enlarged to a height of 4 inched, how wide will it be?
Answers
12 in
Step-by-step explanation:If the dilation is uniform, both height and width will be multiplied by 4.
New height = (1 in) × 4 = 4 in
New width = (3 in) × 4 = 12 in
What is the decimal value of sin S?
(Round your answer to the nearest thousandth if necessary.)
Answers
Answer:
0.471
Step-by-step explanation:
The mnemoic SOH CAH TOA reminds you that ...
... Sin = Opposite/Hypotenuse
... sin(S) = 32/68 ≈ 0.471
bao and Calvin use 6 lemon to make every 4 quarts of lemonade, they want to make 12 quarts of lemonade. how many lemons do they need?
Answers
The sum of two numbers is 65 . One number is 4 times as large as the other. What are the numbers?
Answers
Answer:
13
Step-by-step explanation:
65=5x(because number A is four times number B therefore, it is really B five times)
Then divide both sides by 5.
13=x
To find two numbers when their sum is 65 and one number is 4 times the other, the smaller number is 13, and the larger number is 52.
number, and 4x be the larger number.
Write an equation: x + 4x = 65.
Solve the equation: 5x = 65, x = 13.
The smaller number is 13, and the larger number is 4 times 13, which is 52.
why write a quadratic function whose graph has the given characteristics vertex :(2,3) point on graph (0,-1)
Answers
f(x) = -(x -2)² +3
Step-by-step explanation:We can fill in the vertex (h, k) values immediately in the vertex form ...
... f(x) = a(x -h)² +k
To find the value of a, we solve the equation for a at some point other than the vertex. The given point is (0, -1), so we can use that:
... -1 = a(0 -2)² +3
... -4 = 4a . . . . . . . . . subtract 3, simplify
... -1 = a . . . . . . . . . . . divide by 4
Now, we know the function is ...
... f(x) = -(x -2)² +3
Solve for u: u/p + u/q =m, if , p≠−q
Answers
Answer:
The solution for u is:
[tex]u = \frac{mpq}{q+p}[/tex]
Step-by-step explanation:
The first step to solve this problem is finding the least common multiplicator between p and q, that is pq, so:
[tex]\frac{u}{p} + \frac{u}{q} = m[/tex]
[tex]\frac{uq + up}{pq} = m[/tex]
[tex]uq + up = mpq[/tex]
[tex]u(q + p) = mpq[/tex]
[tex]u = \frac{mpq}{q+p}[/tex]
The required solution of the given equation for u is equal to
(m(p × q)) / (q + p).
Given that:
Equation: u/p + u/q = m, if p ≠ -q
To solve for u in the equation u/p + u/q = m, use the method of finding a common denominator and simplifying the expression.
First, need to find a common denominator for the fractions u/p and u/q. The common denominator in this case would be (p × q).
Multiplying the equation by (p × q) to get,
u(q) + u(p) = m(p × q)
Next, combine the terms with u as:
u × q + u × p = m(p × q)
Now, factor out u as:
u(q + p) = m(p × q)
To solve for u, divide both sides of the equation by (q + p):
u = (m(p × q)) / (q + p)
Therefore, the solution for u is u = (m(p × q)) / (q + p).
Learn more about Divide here:
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Please help me with this question I took a picture of it
Answers
Answer:
40
Step-by-step explanation:
36 = 90% × (number of questions)
36/0.90 = (number of questions) = 40 . . . . . divide by the coefficient of the variable
There were 40 questions on the test.
Solve log x2 + 1 = 5. Round to the nearest thousandth if necessary.
Answers
Answer:
x = 100
Step-by-step explanation:
Answer:
the solutions are x = -100,100
Step-by-step explanation:
The given logarithmic equation is [tex]\log x^2 +1=5[/tex]
Subtract 1 to both sides
[tex]\log x^2=4[/tex]
Remove logarithm, we get
[tex]x^2=10^4[/tex]
Take square root both sides
[tex]\sqrt{x^2}=\pm\sqrt{10^4}\\\\x=\pm10^2\\\\x=\pm100[/tex]
Therefore, the solutions are x = -100,100
PLEASE HELP ASAP!!!!
Answers
System
p + m = 100.8m = 0.4·10Solution
p = m = 5 — 5 lb peanuts and 5 lb mixtureStep-by-step explanation:(a) Generally, the equations of interest are one that models the total amount of mixture, and one that models the amount of one of the constituents (or the ratio of constituents). Here, there are two constituents and we are given the desired ratio, so three different equations are possible describing the constituents of the mix.
For the total amount of mix:
... p + m = 10
For the quantity of peanuts in the mix:
... p + 0.2m = 0.6·10
For the quantity of almonds in the mix:
... 0.8m = 0.4·10
For the ratio of peanuts to almonds:
... (p +0.2m)/(0.8m) = 0.60/0.40
Any two (2) of these four (4) equations will serve as a system of equations that can be used to solve for the desired quantities. I like the third one because it is a "one-step" equation.
So, your system of equations could be ...
p + m = 100.8m = 0.4·10___
(b) Dividing the second equation by 0.8 gives
... m = 5
Using the first equation to find p, we have ...
... p + 5 = 10
... p = 5
5 lb of peanuts and 5 lb of mixture are required.
All of the triangles are 45-45-90 triangles. Find x
Please show how you did it.
Answers
Answer:
3/√2
Step-by-step explanation:
find the details in the attachment (this is not the shortest way).
The shortest way is: to prove ED=AB, then to calculate x=AB/√2=3/√2.
surveying crew located three points on a map that formed the vertices of a triangular area. A coordinate grid in which on unit equals 20 miles is place over the map so that the vertices are located at (0, -1), (-3, -9), and (3, -2). Find the area of the triangle using determinants?
Answers
Answer:
5400 mi²
Step-by-step explanation:
The area is half the absolute value of the sum of the determinants of the points taken pairwise in some consistent order around the polygon. For a triangle, this sum of determinants can also be written as the determinant of a 3×3 matrix of the coordinates with the third column being 1.
... Area = (1/2)|D|
where D = ...
[tex]\left|\begin{array}{ccc}0&-1&1\\-3&-9&1\\3&-2&1\end{array}\right|=\left|\begin{array}{cc}0&-1\\-3&-9\end{array}\right|+\left|\begin{array}{cc}-3&-9\\3&-2\end{array}\right|+\left|\begin{array}{cc}3&-2\\0&-1\end{array}\right|\\\\=-3+33-3=27[/tex]
Then the area is (in grid squares) ...
... Area = (1/2)|27| = 13.5 . . . . grid squares
Each grid square is (20 mi)² = 400 mi², so 13.5 grid squares is ...
... 13.5 × 400 mi² = 5400 mi²
From 1994 to 1995 the sales of a book decreased by 80%. If the sales in 1996 were the same as in 1994, by what percent did they increase from 1995 to 1996?
Answers
400%
Step-by-step explanation:Suppose sales in 1994 were 100 of some unit. Then in 1995, they were ...
... 100 - 80% × 100 = 100 × (1 - 0.80) = 100 × 0.20 = 20 . . . . units
Then the percent increase to sales of 100 units in 1996 can be found from ...
... percent change = ((new value) - (old value))/(old value) × 100%
... = (100 -20)/20 × 100%
... = 80/20 × 100%
... = 400%
The increase from 1995 to 1996 was 400%.