Which of the following is the name of this figure?
trapezoid
parallelogram
rectangle
rhombus

Answer:

y=-2.5[tex]x^{2}[/tex]+4.5x+1.5

Step-by-step explanation:

standard form of equation of parabola is,

y=a[tex]x^{2}[/tex]+bx+c

For x=0

1.5=0a+0b+c

1.5=c

For x=-2,

2.5=4a-2b+c

substituting the value of c

2.5=4a-2b+1.5

on solving,

4a-2b=1____________(1)

For x=4,

-60.5=16a+4b+c

substituting the value of c,

-60.5=16a+4b+1.5

on solving,

16a+4b=-62_______(2)

Multiplying equation 1 by 2,

8a-4b=2_______(3)

adding equation 2 and 3

16a+4b+8a-4b=-62+2

24a=-60

on solving,

a=-2.5

substituting the value of a in equation 1,

10-2b=1

2b=9

b=4.5

hence, equation of parabola in standard form is,

y=-2.5[tex]x^{2}[/tex]+4.5x+1.5

Answer:

Part 1

The given information represented as a function, f(x) is;

f(x) = 150 - 10·x

Part 2

Please find attached the given information represented as a graph is created with Microsoft Excel

Part 3

Mrs. Dyal will run out of pencils after giving away pencils for 15 weeks

Step-by-step explanation:

The word problem relates to linear functions of the form f(x) = y = m·x + c

The given parameters are;

The number of pencils Mrs. Dyal has at the start of the year = 150 pencils

The number of pencils Mrs. Dyal gives away per week = 10 pencils

Part 1

Let "x" represent the number of weeks at which Mrs. Dyal is giving away the pencils

Given that she gives away 10 pencils each week, we have the function that represent the number of pencils remaining after "x" weeks is given as follows;

f(x) = 150 - 10×x.

The number of weeks, "x", that passes before Mrs. Dyal runs out of pencil (f(x) = 0) is given as follows;

f(x) = 0 = 150 - 10 × x

∴ 150 Pencils = 10 Pencils/Week × x

x = 150 Pencils/(10 Pencils/Week) = 15 Weeks

x = 15 Weeks

Therefore Mrs. Dyal will run out of Pencil at when x = 15 Weeks

Part 2

The function can be represented as a graph using the table of values as follows ;

Pencil remaining  [tex]{}[/tex]              Number of weeks

150                      [tex]{}[/tex]                    0

140                       [tex]{}[/tex]                    1

130                      [tex]{}[/tex]                     2

120                      [tex]{}[/tex]                     3

110                      [tex]{}[/tex]                      4

100                      [tex]{}[/tex]                     5

90                      [tex]{}[/tex]                      6

80                      [tex]{}[/tex]                      7

70                      [tex]{}[/tex]                      8

60                      [tex]{}[/tex]                      9

50                      [tex]{}[/tex]                      10

40                      [tex]{}[/tex]                      11

30                      [tex]{}[/tex]                      12

20                      [tex]{}[/tex]                      13

10                      [tex]{}[/tex]                       14

0                      [tex]{}[/tex]                        15

The domain = 0 ≤ x ≤ 15 {x ∈ N including 0}

The range = 0 ≤ f(x) ≤ 150

From the graph of the function created with Microsoft Excel, Mrs Dyal has no more Pencils left when x = 15 weeks

Given the data from the question, the correct statement is: the ratio 1:5 is less than 3:10

To otain the comparison of both ratios, we shall determine the value of each ratio. This is illustrated below:

1 : 5 = 1 / 5

1 : 5 = 0.2

3 : 10 = 3 / 10

3 : 10 = 0.3

SUMMARY

Thus, we can conclude that 1:5 is less than 3:10

Learn more about ratios:

https://brainly.com/question/2462048

#SPJ1

Answer:

Kindly check attached picture for circle illustration.

Step-by-step explanation:

The whole circle = 1

Half the circle = semicircle = 1/2

Half the semicircle = 1/4

Half of 1/4 = 1/8

Hence, Geraldo would obtain 1/8

Normal calculation:

1/2 ÷ 2

1/2 * 2/1 = 1/4

Quotient = 1/4

Quotient / 2

1/4 ÷ 2

1/4 * 1/2

= 1/ 8

Answer:

Slope is -3/4

Y intercept is 7

y= -3/4x+7

Answer:

3(x+y)+15xy

Step-by-step explanation:

Write an algebraic expression for the verbal expression: three times the sum of X and Y increase by five times the product of x and 3y.

Sum of x and y = x+y

three times the sum of X and Y = 3(x+y)

product of x and 3y  = x(3y) = 3xy

five times the product of x and 3y = 5(3xy) = 15xy

Three times the sum of X and Y increase by five times the product of x and 3y will be expressed as;

3(x+y) + 15xy

Hence the required algebraic expression is 3(x+y)+15xy

Answer:

12

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] \frac{6}{x - 1} = \frac{4}{x + 2} [/tex]

[tex]6x + 12 = 4x - 4[/tex]

[tex]6x - 4x = - 12 - 4[/tex]

[tex]2x = - 16[/tex]

[tex]x = - 8[/tex]

Answer:

-2x+8

Step-by-step explanation:

Answer: Line C

Step-by-step explanation:

Because when you use the slope formula on it you get a negative slope. Also the line in going down unlike the other lines which are goign up.

Answer:

I think is 2/3

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

COP is slope which is rise over run.

Answer:

(B).

Step-by-step explanation:

√x(x + 3)(x - 6) = √x(x² - 3x - 18) = [tex]\sqrt{x^{5} }[/tex] - 3[tex]\sqrt{x^{3} }[/tex] - 18√x

Answer:

-18x-36y

Step-by-step explanation:

Distributive Property:

-9*2x=-18x

-9*4y=-36y

-18x-36y

Answer:

-27

Step-by-step explanation:

x+23−23=−4−23

x=−27

Answer:

y=2(-2)+3

y=-1

y=2(-1)+3

y=1

y=2(0)+3

y=3

y=5

y=7

Answer:

(From left to right)

1st y (output):   -1

2nd y (output):   1

3rd y (output):   3

4th y (output):   5

5th y (output):   7

Step-by-step explanation:

Substitute each x (input) into the given equation and solve. For example, to get the first y (output), substitute "-2" into the "x" in the equation, giving you "y = 2(-2) +3", then solve it.

Multiply 2(-2) to get -4, then add 3 to get -1.

Answer: 52

Step-by-step explanation:

42-(-10) first since your multiplying the two negative signs with each other it turns into a positive and looks like 42+10 and 42+10=52

Answer:

8.28 is the difference in times in which the students completed the lap.

Step-by-step explanation:

Subtract 74.20 and 65.92 and that gives you your answer.

Answer: the answer is 23

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

10+8+5=23

Answer:

Your potential zeros are ± 1/2, ± 3/2, ± 1, and ± 2.

Répondre:

8/15

Explication étape par étape:

Prendre:

Longueur = x

Largeur = y

Zone du rectangle = Longueur * largeur

Un cinquième de longueur = x / 5

Un tiers de largeur = x / 3

Zone d'origine = xy

Nouvelle dimension:

Longueur = x + x / 5 = (5x + x) / 5 = 6x / 5

Largeur = x + x / 3 = (3y + y) / 3 = 4y / 3

Nouvelle zone = 6x / 5 * 4y / 3

Nouvelle zone = (24/15) xy

Fraction de la nouvelle zone par rapport à la zone d'origine:

(24/15) xy: xy

24/15: 1

24/15

= 8/5

Answer:

I think the scale factor would be 1/6

Answer:

1/6

Step-by-step explanation:

3 feet = 3*12 = 36

Scale factor = 6/36 = 1/6

Answer:

C) 5

Step-by-step explanation:

The measure of angle TSU is 75°. (180° - 105° because it is a flat angle)

The sum of all the angles of a triangle is 180° as well.

You can write an equation to solve for x.

12x + 9x + 75 = 180

Isolate x.

12x + 9x = 180 - 75

12x + 9x = 105

Add the 12 and the 9.

21x = 105

Find what x is.

x = 105 ÷ 21

x = 5

Sara brought a total of 5 cartons of blackberries. Since it said that Sara brought 6 cartons and you know that the cost of the blackberries are $2, you multiply 6 with 2 but its 12. But if Sara  brought 2 cartons of raspberries it will be $3. Now you subtract 6 with 2 since you used 2 cartons on raspberries and now multiply $2 with 4 and get 8. 8+3=11, which is exactly how much she needs. This means that Sara brought 4 cartons of blackberries.

Answer:

y-intercept of the function [tex]y=\frac{2}{3}x-3[/tex] is -3.

Step-by-step explanation:

We need to find the function that had the same y-intercept as the function [tex]y=\frac{2}{3}x-3[/tex]

(Note: Since the options are not given, so I will find the y-intercept of the given equation and you can match it with the functions and find the y-intercept of the required function)

The equation given [tex]y=\frac{2}{3}x-3[/tex] is written in slope-intercept form i.e [tex]y=mx+b[/tex] where m is slope and b is y-intercept.

Comparing equation [tex]y=\frac{2}{3}x-3[/tex] with [tex]y=mx+b[/tex] we get the value of b = -3

So, y-intercept of the function [tex]y=\frac{2}{3}x-3[/tex] is -3.

Now, for the options (not included) in the question, you can find y-intercept and function that have y-intercept = -3 will be the answer.

Answer:

x= −3/5y +3 y= -5/3 + 5

Step-by-step explanation:

Answer:

If we are solving for y we move all terms that don't contain y to the right side and solve.

So y = 5 - 5x/3