Given:
A linear function starting at point C at (3, –2) and ending at point D at (–2, 3).
To find:
The rate of change and the initial value.
Solution:
If a linear function passes through two points [tex](x_1,y_1)\text{ and }(x_2,y_2)[/tex], then the equation of linear function is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The given linear function passes through (3,-2) and (-2,3). So, the equation is
[tex]y-(-2)=\dfrac{3-(-2)}{-2-3}(x-3)[/tex]
[tex]y+2=\dfrac{3+2}{-5}(x-3)[/tex]
[tex]y+2=\dfrac{5}{-5}(x-3)[/tex]
[tex]y+2=-(x-3)[/tex]
Subtracting 2 on both sides, we get
[tex]y=-x+3-2[/tex]
[tex]y=-x+1[/tex]
On comparing this equation with slope intercept form [tex]y=mx+b[/tex], where, m is slope and b is y-intercept, we get
[tex]m=-1[/tex] and [tex]b=1[/tex]
Therefore, the rate of change is -1 and the initial value is 1.
Which speed is the fastest? Group of answer choices LaTeX: 4\:miles\:in\:\frac{1}{3}\:hours4 m i l e s i n 1 3 h o u r s LaTeX: \frac{1}{3}\:mile\:in\:4\:hours1 3 m i l e i n 4 h o u r s LaTeX: \frac{1}{2}\:mile\:in\:3\:hours
Answer:
4 miles in 1/3 houra
Step-by-step explanation:
Which speed is the fastest? Group of answer choices LaTeX:
The formula for speed =
Distance (miles) / Time (hours)
A) 4 miles in 1/3 hours
= 4 / 1/3
= 4 ÷ 1/3
= 4 × 3
= 12 miles per hour
B)1/3 miles in 4 hours
=1/3 miles/4 hours
= 1/3 ÷ 4 miles per hour
= 1/3 × 1/4 miles per hour
= 1/12 miles per hour
C) 1/2 miles in 3 hours
= 1/2 miles / 3 hours
= 1/2 ÷ 3
= 1/2 × 1/3
= 1/6 miles per hour
The fastest speed is A, 4 miles in 1/3 houra
please help i don’t understand
Answer:
well i dont either
Step-by-step explanation: i'm
weird
Use the distributive property to evaluate the expression
4(9 + 1)
PLZ I NEED HELP I FORGOT HOW TO DO THIS
Please I need some answers
Answer:
1 = 2x 2= -3 4 =3
Step-by-step explanation:
Answer:
1. 5x-3=-15
2. -15/5=-3
3. -15/-3=5
Step-by-step explanation:
Hope this helps :)
HELP ME PLZZZ
I really need the help with it
Cell phone plan a cost 70 per month but gives you a free 500 dollar phone plan b coat 50 dollors but has no phone. How long would it take them to reach the same proce
Answer:
Number of month = 25 month
Step-by-step explanation:
Given:
Plan A $70 per month and $500 phone cost
Plan B $50 per month No phone
Assume;
Number of month = x
So,
50x + 500 = 70x
20x = 500
x = 25
Number of month = 25 month
Fred's art project involves a series of parallel stripes. If he starts by drawing the line 8x+2y=7, select all the equations that could represent lines that could also be drawn for his art project.
Options:
A. [tex]y-1 = 4(x + 8)[/tex]
B. [tex]y = -4x + 15[/tex]
C. [tex]16x + 4y = 9[/tex]
D. [tex]y=-4x[/tex]
E. [tex]4x + 2y = 3[/tex]
Answer:
B. [tex]y = -4x + 15[/tex]
C. [tex]16x + 4y = 9[/tex]
D. [tex]y=-4x[/tex]
Step-by-step explanation:
Given
[tex]8x + 2y = 7[/tex]
Required
Select all equations that could be used.
Equation that could be used in place of [tex]8x + 2y = 7[/tex] must have the same slope.
Calculating the slope of [tex]8x + 2y = 7[/tex]
Make y the subject
[tex]2y = 7 - 8x[/tex]
[tex]y = \frac{7}{2} - \frac{8x}{2}[/tex]
[tex]y = \frac{7}{2} - 4x[/tex]
[tex]y = - 4x + \frac{7}{2}[/tex]
Using y = mx + b
Where
[tex]m = slope[/tex]
The slope is -4
Option A.
[tex]y-1 = 4(x + 8)[/tex]
Open bracket
[tex]y - 1=4x + 32[/tex]
Collect Like Terms
[tex]y - 4x = 32 + 1[/tex]
[tex]y - 4x = 33[/tex]
Make y the subject
[tex]y = 4x + 33[/tex]
The slope of this line is 4;
Hence, it can not be used.
Option B.
[tex]y = -4x + 15[/tex]
The slope of this line is -4;
Hence, it can be used.
Option C.
[tex]16x + 4y = 9[/tex]
Solve for4y
[tex]4y=9 - 16x[/tex]
Solve for y
[tex]\frac{4y}{4} =\frac{9}{4} - \frac{16x}{4}[/tex]
[tex]y =\frac{9}{4} - 4x[/tex]
[tex]y = - 4x + \frac{9}{4}[/tex]
The slope of this line is -4;
Hence, it can be used.
D. [tex]y=-4x[/tex]
The slope of this line is -4;
Hence, it can be used.
E. [tex]4x + 2y = 3[/tex]
Solve for 2y
[tex]2y = 3 - 4x[/tex]
Solve for y
[tex]\frac{2y}{2} = \frac{3}{2} - \frac{4x}{2}[/tex]
[tex]y = \frac{3}{2} - 2x[/tex]
The slope of this line is -2;
Hence, it can not be used.
From the calculations above, equations B, C and D are equivalent
If x < 3, the arrow points to the left.
True or false
Answer:
true
Step-by-step explanation:
You will get brainliest and 5 stars.
Greg went to see a play at a theater downtown. The play started at 7:20 P.M. The first act was 1 hour and 20 minutes long. Intermission lasted for 55 minutes, and the second act was 55 minutes long. What time was it when the play finished?
Please Help, the correct answer will get brainliest.
Answer:
Yes I will help
Step-by-step explanation:
Solve the inequality
M + 9 > 6
Answer:
m>-3
Step-by-step explanation:
6-9 = -3
m>-3
. -1/11 plus -9/11
Step-by-step explanation:
the answer is equals to
-10/11
Answer:
-10/11
Step-by-step explanation:
Mr. Gonzalez drove 30 miles in March. He drove 5 times as many miles in March as he did in January. He drove 2 times as many miles in February as he did in January. How many miles did Mr. Gonzalez drive in February?
Step-by-step explanation:
Given information :
Mr. Gonzalez drove 30 miles in March. In January, she drove 1/5 as much as in March.
30 ÷ 5 = 6 miles in January
in JanuaryShe drove 2 times as many miles in February as she did in January. In January, she drove 30 miles.
6 x 2 = 12 miles in February
When 11 is subtracted from twice a number, the square root of the result is 4. Find the number.
Answer: I think 27/2
Explanation:
Let number = x:
√(2x - 11) = 4
Now to get x, we undo the square root by squaring both sides:
[√(2x - 11)]² = 4²
(2x - 11) = 16
2x = 27
x = 27 / 2
Hope this helps!
Look at the right triangle shown below. Which of the folllowing could not be the triangle’s dimensions?
Answer:
5,12,13
Step-by-step explanation:
The sides are almost close for the distance and so 5 doenst go with 12 and 13, its too small. For dimensions while the other numbers are close to being related. Do you know what I mean?
Hope this helped a little tho!
Which two fractions are equal to 2?
yea 2/1 and 4/2..........
Which compound inequality could be represented by the graph?
Pls help
Answer:
I think 3 is right . uihhhujh
Laquan will give each guest at his party ¹⁄₂ of a cake. How many cakes should he order if 17 people are attending his party?
Answer:
9 cakes
Step-by-step explanation:
If each of the 17 people will eat 1/2 of a cake, you would 17*1/2 cakes. This is 17/2, or 8.5. You cannot usually order 8.5 cakes, so you would round up. 9 cakes.
Find rhe x- and y- intercerpts of the following relationships.(There may be more then one)
[tex]3x^{2} + 2y^2 = 24[/tex]
Answer:
see explanation
Step-by-step explanation:
Given
3x² + 2y² = 24
To find the x- intercepts , let y = 0 in the equation and solve for x
3x² + 2(0)² = 24, that is
3x² = 24 ( divide both sides by 3 )
x² = 8 ( take the square root of both sides )
x = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ← x- intercepts
To find the y- intercepts. let x = 0 in the equation and solve for y
3(0)² + 2y² = 24 , that is
2y² = 24 ( divide both sides by 2 )
y² = 12 ( take the square root of both sides )
y = ± [tex]\sqrt{12}[/tex] = ± 2[tex]\sqrt{3}[/tex] ← y- intercepts
Translate the following sentence into an inequality: Twice a number plus
two is less than the difference of x and six.
Answer:
hey your really cute thats all
Step-by-step explanation:
;) love you bubs see you someday, now
Write the equation of a line perpendicular to y =
3
x-3 and whose y-intercept is (0,12).
Answer:
y=-1/3x+12
Step-by-step explanation:
The slope of a line that is perpendicular to another is the negative reciprocal of the first. The slope of the line is 3 so the negative reciprocal will be -1/3.
Using the point-slope formula we can solve for the equation of a line with a slope of -1/3 and a point of (0,12).
The point slope formula is
y-y1=m(x-x1).
y-12=-1/3(x-0) -------------->Distribute: y-12=-1/3x ---------------> Isolate the y by moving the 12 to the other side. y=-1/3x+12
Uma pipa é presa a um fio esticada que forma um ângulo de 45c com o solo. O comprimento do dia é 80m. Determine a altura da pipa em relação ao solo. Dado raiz de 2 = 1,41
WHAT IS X???
1.2/0.96 = 3.0/x
Answer:
x= 2.4
Step-by-step explanation:
Answer:
2.4 or 12/5
Step-by-step explanation:
1.2/0.96=3/x
convert the decimal into a fraction---- 6/5 /0.96= 3/x
Simplify the complex fraction-----5/4 = 3/x
simplify the equation using cross-mulitpication----- 5 x = 12
divide both sides of the equation by 5--- x= 12/5
Check if the solution is in the defined range
Alternitive form:
x=2 2/5, x =2.4
16. An experiment is carried out to determine how different pH values of soil will affect the growth of tomato plants. In this
experiment, the independent variable could be the
1. Type of the tomato plant
2. Amount of soil provided
3. Colour the of tomato
4. Light intensity
Step-by-step explanation:
2. Amount of soil provided.
In order to give different pH values of the soil, the amount of soil can directly affect this independent variable.
Write an express for the perimeter of the figure shown by combing like terms.
Answer:
30c + 6 i believe
Step-by-step explanation:
A box of pancake mix states that 1 1/2 cups of pancake mix and 1 cup of water are needed to make 8 pancakes. How many cups of pancake mix and water are needed to make 12 pancakes?
A. 2 cups of pancake mix and 1 1/2 cups of water
B. 2 1/2 cups of pancake mix and 1 3/4 cups of water
C. 2 1/4 cups of pancake mix and 1 1/2 cups of water
D. 2 3/4 cups of pancake mix and 1 1/4 cups of water
Answer:
I think your answer is B
Step-by-step explanation:
Answer:
boot
Step-by-step explanation:
What statement is true about the extreme value of the givin quadratic equation y=-3x^2+12x-30
A) the equation has a maximum value with a y-coordinate of -21
B) the equation has a minimum value with a y-coordinate of -27
C) the equation has a minimum value with a y-coordinate of -21
D) the equation has a maximum value with a y-coordinate of -27
Answer:
I,dont know but use M A T H W A Y it will explain with all the stepp by step and answere hope it help
Step-by-step explanation:
I'll mark you brainliest if you give me the correct answer?
Answer and Step-by-step explanation:
We are asked to turn this fraction ([tex]\frac{9}{10}[/tex]) into an equivalent fraction, but with a denominator of 100.
[tex]\frac{9 <- Numerator}{10<-Denominator}[/tex]
All we have to do is multiply the numerator and denominator by 10, since 10 times 10 equals 100.
[tex]\frac{9}{10} * \frac{10}{10} = \frac{90}{100}[/tex]
The answer is:
[tex]\frac{90}{100}[/tex]
#teamtrees #WAP (Water And Plant)
Answer:
90/100
Step-by-step explanation:
9/10, when multiplied by 10/10, is 90/100.
Hope this helps!
xoxo,
cafeology
What is x?
3/6=5.5/x
Answer:
x = 11
Step-by-step explanation:
3/6=5.5/x
Cross multiply.
3 * x = 6 * 5.5
x = 2 * 5.5
x = 11