Given the function g(x) = 3x² - 5, find the values of t such that g(x) = -7/2t.​

Answer:

a.  (-3, 6)

b. 268.3 m

Step-by-step explanation:

a. Determine the coordinates of the tennis court.

Let (x,y) be the coordinates of the tennis court. Since we have equal distances from the tennis court to each residence, we have using the equation for distance between two points (x₁,y₁) and (x₂,y₂), d = √[(y₂ - y₁)² + (x₂ - x₁)²]. Using the first two residences, (-6, 12) and (0,0) as (x₂,y₂) and (x, y) = (x₁,y₁), So,

d = √[(12 - y)² + (-6 - x)²]

d = √[(12 - y)² + (6 + x)²]

d = √[(144 - 24y + y² + 36 + 12x + x²]

d = √x² + y² + 12x - 24y + 180

d² = x² + y² + 12x - 24y + 180  (1)

Also, with (x₂, y₂) = (0,0) we have

d = √[(0 - y)² + (0 - x)²]

d = √[( - y)² + (- x)²]

d = √[y² + x²]

d = √[x² + y²]

d² = x² + y²  (2)

Also, with (x₂, y₂) = (3,9) we have

d = √[(9 - y)² + (3 - x)²]  

d = √[(81 - 18y + y² + 9 - 6x + x²]

d = √(x² + y² - 6x - 18y + 90)

d² = x² + y² - 6x - 18y + 90 (3)

Substituting (2) into (1), we have

d² = x² + y² + 12x - 24y + 180   (1)

d² = d² + 12x - 24y + 180  (1)

d² - d² = 12x - 24y + 180

12x - 24y + 180 = 0

12x - 24y = -180

dividing through by 12, we have

x - 2y = -15  (4)

Substituting (2) into (3), we have

d² = x² + y² - 6x - 18y + 90 (3)

d² = d² - 6x - 18y + 90 (3)

d² - d² = - 6x - 18y + 90

- 6x - 18y + 90 = 0

- 6x - 18y = -90

dividing through by -6, we have

x + 3y = 15 (5)

Subtracting (5) from (4), we have

x - 2y = -15  (4)

-

x + 3y = 15 (5)

-5y = -30

y = -30/-5

y = 6

substituting y = 6 into (4), we have

x - 2y = -15

x - 2(6) = -15

x - 12 = -15

x = 12 - 15

x = -3

So, the coordinates of the tennis court is (-3, 6)

b. What is the distance from a residence to the court to the nearest 10th of a metre? (1unit=40m).

Using equation (2),

d² = x² + y²  (2) where x and y are the coordinates of the tennis court, and x = -3 and y = 6

So,

d² = x² + y²  

d² = (-3)² + (6)²  

d² = 9 + 36  

d² = 45

d = √45 units

Since 1 unit = 40 m,

d = √45 × 40 m

d = 6.708 × 40 m

d = 268.33 m

d ≅ 268.3 m to the nearest tenth of a metre

Answer:

Tina worked [tex]3 \frac{5}{6}[/tex] hours on Friday.

Step-by-step explanation:

To solve for how many hours Tina worked on Friday you have to add up all the hours worked then subtract that from 15 hours to get the remainder.

Step 1 : Add up all the hours worked so far.

[tex]3\frac{1}{2}[/tex] + 4 + [tex]2\frac{1}{6}[/tex]  + [tex]1\frac{1}{2}[/tex] = ?

We need to turn these mixed numbers into improper fractions first so we can add. Let's turn them all into sixths.

[tex]3 \frac{3}{6}[/tex] + 4 + [tex]2\frac{1}{6}[/tex] + [tex]1 \frac{3}{6}[/tex] = [tex]11\frac{1}{6}[/tex]

Allright, so now we know that Tina already worked 11 and 1/6 hours already, so we subtract that from 15 to find how many hours she worked on Friday.

Step 2 : Subtract [tex]11\frac{1}{6}[/tex] from 15.

15 - [tex]11\frac{1}{6}[/tex] = [tex]3 \frac{5}{6}[/tex]

Therefore Tina worked [tex]3 \frac{5}{6}[/tex] hours on Friday.

Hope this helps, please mark brainliest if possible. Have a great day.

Answer:

4 1/3 inches   Smaller piece

16 2/3 inches   Larger piece

Step-by-step explanation:

x + (2x + 8) = 21

3x + 8 = 21

3x = 13

x = 13/3

x = 4 1/3 inches   Smaller piece

2x + 8 = 8 2/3 + 8

2x + 8 = 16 2/3 inches   Larger piece

Answer:

B. 6 x 1/3 = 2

Step-by-step explanation:

2 is 1/3 of 6

So multiplying 6/1 (6) bu 1/3 :

6/1 * 1/3 = 6 / 3 = 2

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

ur mom kid

Step-by-step explanation:fotnite

Answer:

D would be the answer

Step-by-step explanation:

Took the test got it correct <33 good luck

[tex]\longrightarrow{\green{C.\: {x}^{7}}}[/tex] 

Step-by-step explanation:

[tex]( {x}^{5} )( {x}^{2} ) \\\\ = {x}^{5 + 2} \\\\ = {x}^{7} \\\\ (∵ {a}^{m} \times {a}^{n} = {a}^{m + n} )[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]

Answer:

Gradient = -5

Step-by-step explanation:

The gradient of a line is the slope of the line.

The standard form of the line equation is y = mx  + b

where m is the slope ( or gradient) b is the y - intercept.

Given :

2y = -10x + 1

[tex]y = -\frac{10}{2} x + \frac{1}{2}\\\\y = -5x + \frac{1}{2}\\\\Therefore , \ gradient \ is \ -5[/tex]

The gradient of the line whose equation is 2y=-10x+1 is -5.

Gradient could be a measure of how steep a slope or a line is.

The equation of the road is 2y=-10x+1

y=-5x+1/2

Therefore the gradient of the line is that the coefficient of x which is -5.

Hence the gradient of the line is -5.

Learn more about gradient at https://brainly.com/question/23016580

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Answer:250

Step-by-step explanation:

j+m=5

50(j+m)=50x5=250

Answer:

If you mean 5(j + m) and j + m = 5 then you answer is 6j + 6m = 5.

If you mean 50j + m and j + m = 5 then there is no solution.

Step-by-step explanation:

j + m = 5

5(j + m)

5(j + m) + j + m = 5

5j + 5m + j + m

6j + 6m = 5

Answer:

$4.35

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

Temperature after 1 minute = 140 - 5(1)

Temperature after 2 minutes = 140 - 5(2)

Temperature after 3 minutes = 140 - 5(3),

- and so on.

So the function is

y = 140 - 5x.

The temperature of the steak after a certain number of minutes can be described as the function

y = 140 - 5x

A linear equation with one variable has the standard form Cx + D = 0. In this case, the variable is x and C are coefficient, while D is a constant.

Let the certain number of minute is x.

Since the temperature decreases at 5° F per minute, then after x minutes, it will decrease 5x.

Initial temperature = 140° F

Then the present temperature, y = 140 - 5x.

Therefore, the temperature of the steak after a certain number of minutes can be described as the function

y = 140 - 5x

Learn more about temperature here -

https://brainly.com/question/22777948

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Answer:

Let the measure of the complementary angle be x so that the measure of the other angle is 14x. The total measure of the angles is 180 degrees.

Answer:

Can I have your points because you stole it

my precious points

your answer is helpless

Answer:

he got 8 different colors to choose from for the first stripe. he has to choose from 7 for the second (one choose less bc he alrdy took one color)

that alone makes 56 different ways for just two stripes.

he will use 5 stripes in total, so the calculation is:

8*7*6*5*4 = 6720

(8!-3! would also work with the calculator 8! uses all the naturalnumbersfrom 1 to 8 and multiplies them)

Answer:

0.89 m is the answer

Step-by-step explanation:

the wall, the ground and portion of pipe form a right angle triangle with pipe portion being the hypotenuse.

for a right triangle

[tex]{hypotenuse}^{2} = {base}^{2} + {height}^{2} [/tex]

here we have base = 3m and height = 2m.

thus

[tex] {h}^{2} = {3}^{2} + {2 }^{2} \\ = 9 + 4 \\ = 13 \\ h = \sqrt{13} [/tex]

portion of pipe overhanging = 4.5 - sqrt (13)

= 4.5 - 3.61

= 0.89 m

Answer:

[tex]\displaystyle d = 4[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

Point (-3, 5)

Point (1, 5)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

Step-by-step explanation:

1/4

Answer:

answer is A. you can see each intervals slowly to know this

Answer:

yards of wire left on the roll = 500 - r(3)

Step-by-step explanation:

9 feet = 3 yards we need to find how much wire is left on the roll after she builds a certain amount of robots. she uses 9 feet or 3 yards per robot so we have to multiply the amount of robots (r) by 3 yards and subtract that from 500 yards or the total amount of wire she has and that gives us the total amount of wire she has left. Hope this helps.

Given:

Steven charges $31.25 for 5 hours and $43.75 for 7 hours.

To find:

The equation that represents the relationship.

Solution:

Let x represent the number of hours Steven babysits and y represent the amount he charges.

Then the two points on the function are (5,31.25) and (7,43.75). So, the equation of the line that passes through these two points is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-31.25=\dfrac{43.75-31.25}{7-5}(x-5)[/tex]

[tex]y-31.25=\dfrac{12.5}{2}(x-5)[/tex]

[tex]y-31.25=6.25(x-5)[/tex]

On further simplification, we get

[tex]y-31.25=6.25(x)-6.25(5)[/tex]

[tex]y-31.25=6.25x-31.25[/tex]

[tex]y=6.25x-31.25+31.25[/tex]

[tex]y=6.25x[/tex]

Therefore, the required equation for the given situation is [tex]y=6.25x[/tex].

Answer:

B and D

Step-by-step explanation:

Multiplying exponents just adds them.

Answer:

B + D

Step-by-step explanation:

Answer:

M1=44 M2=136 M3=44 M4=136

Step-by-step explanation:

M3= 44 so M1=44 due to opposite angles being equal

then if two of the angles add to 88

360-88= 272

divide 272 by 2 as M2 and M4 are equal

272/2=136

Answer:

m∠1 = 44°

m∠2 = 136°

m∠4 = 136°

Step-by-step explanation:

m∠1 explanation:

I got it from m∠3 since they're both congruent

m∠2 explanation:

Since we already have the measure of 3 and 1, we can easily add both of the measures (44 + 44 = 88°) then subtract it from 360° (total) = 272°

Then since both measures (2 and 4) are congruent (measuring the exact same length and angle) we can divide 272° ÷ 2 = 136°

m∠4 explanation:

I got it from m∠2 since they're both congruent

Step-by-step explanation:

6/20

3/10 (simplified)

do you want the percentage?

Answer:

[tex]\frac{3}{10}[/tex]

Step-by-step explanation:

The multiplies of 3 from 1-20 are:

3, 6, 9, 12, 15, 18

Since there are [tex]20-1+1=20[/tex] numbers from 1-20 inclusive, the probability that a ball is a multiple of 3 is [tex]\frac{6}{20}=\boxed{\frac{3}{10}}[/tex]

Answer:

yes

Step-by-step explanation:

when I add 65+72 and the answer gave me and I find the square root of that number

(the answer is) = 6466602

Answer:

First you convert the mixed numbers into improper fraction

[tex]8\frac{3}{8} = \frac{67}{8} \\\\6 \frac{3}{4} = \frac{27}{4}[/tex]

Solution

[tex]A=\frac{\frac{27}{4} + \frac{67}{8} }{2}[/tex]

[tex]A=\frac{\frac{54 + 67}{8} }{2}[/tex]

[tex]A\frac{\frac{121}{8} }{2}[/tex]

[tex]A=\frac{121}{8}[/tex] * [tex]\frac{1}{2}[/tex]

[tex]A= \frac{121}{16}[/tex]

[tex]A= 7 \frac{9}{16}[/tex]

Step-by-step explanation:

Answer:

∠ B = 45°, ∠ F = 22°

Step-by-step explanation:

Since the triangles are similar then corresponding angles are congruent, so

∠ B = ∠ E = 45°

∠ F = ∠ C = 22°