What is the function rule for the line

Answer:

83

Step-by-step explanation:

You're given two vertical angles, and vertical angles are congruent. This means that (6x - 7) = (4x + 23); x = 15. Plug it into ABC (which is (6x - 7)) to get 6(15) - 7 = 90 - 7 = 83

Answer:

[tex]y = \frac{5x}{2} - 5[/tex]

Step-by-step explanation:

Given the equation 5x - 2y = 10, to write the equation in slope-intercept form, we need to write it in the standard format y = mx+c where m is the slope/gradient and c is the intercept.

From the equation given  5x - 2y = 10, we will make y the subject of the formula as shown;

[tex]5x - 2y = 10\\\\subtract \ 5x \ from \ both \ sides\\\\5x - 2y - 5x = 10 - 5x\\\\-2y = 10-5x\\\\Dividing \ both \ sides\ by \ -2;\\\\\frac{-2y}{-2} = \frac{10-5x}{-2}\\ \\[/tex]

[tex]y = \frac{10}{-2} - \frac{5x}{-2} \\\\y = -5 + \frac{5x}{2}\\\\y = \frac{5x}{2} - 5[/tex]

Hence the equation that represents the first equation written in slope-intercept form is [tex]y = \frac{5x}{2} - 5[/tex]

Answer:

[tex]x=7[/tex]

Step-by-step explanation:

[tex]-5(x-2)=-25[/tex]

Expand the brackets on the left side of the equation.

[tex]-5(x)-5(-2)=-25[/tex]

[tex]-5x+10=-25[/tex]

Add -10 on both sides.

[tex]-5x+10-10=-25-10[/tex]

[tex]-5x=-35[/tex]

Divide both sides by -5.

[tex]\displaystyle \frac{-5x}{-5} =\frac{-35}{-5}[/tex]

[tex]x=7[/tex]

Answer:

[tex] \boxed{\sf x= 7} [/tex]

Step-by-step explanation:

[tex] \sf Solve \: for \: x: \\ \sf \implies - 5(x - 2) = - 25 \\ \sf Divide \: both \: sides \: of \: - 5 (x - 2) = - 25 \: by \: - 5: \\ \sf \implies \frac{ - 5(x - 2)}{ - 5} = \frac{ - 25}{ - 5} \\ \\ \sf \frac{ \cancel{ - 5}}{ \cancel{ - 5}} = 1 : \\ \sf \implies x - 2 = \frac{ - 25}{ - 5} \\ \\ \sf \frac{ - 25}{ - 5} = \frac{5 \times \cancel{ - 5}}{ \cancel{ - 5}} = 5 : \\ \sf \implies x - 2 = \boxed{ \sf 5} \\ \\ \sf Add \: 2 \: to \: both \: sides: \\ \sf \implies x + ( \boxed{ \sf 2} - 2) =5 + \boxed{ \sf 2} \\ \\ \sf 2 - 2 = 0 : \\ \sf \implies x = 5 + 2 \\ \\ \sf 5 + 2 = 7 : \\ \sf \implies x= 7[/tex]

Answer:

151200 possible combinations

Step-by-step explanation:

There are 10 digits 0 - 9  ( 0,1,2,3,4,5,6,7,8,9)

There are 10 choices for the first digit

10

There are 9 choices for the second digit

9

There are 8 choices for the third digit

8

and so on  since we can only use each digit once

10 *9*8 *7 *6*5

151200 possible combinations

Answer:

Step-by-step explanation:

Let L be the length of this rectangle

The length of a rectangle is 2 feet less than four times the width

● L+2 = 4w

The area of this rectangle is 38.2 ft^2

● L*w = 38.2

The system of equations is

L+2 = 4w => L-4w =2

L*w = 38.2 => L= 38.2/w

Replace L by 38.2/w in L-4w =2

● L-4w = 2

● (38.2/w)-4w = 2

●(38,2-4w^2)/w = 2

● 38.2-4w^2 = 2w

● 38.2-4w^2-2w = 0

● -4w^2-2w+38.2 =0

Multiply by -1 to reduce the - signs

● 4w^2+2w-38.2 =0

This is a quadratic equation so we will use the discriminant

□□□□□□□□□□□□□□□□□

The discriminant is b^2-4ac

● b= 2 (2w)

● a= 4 (4w^2)

● c= -38.2 (the constant term)

b^2-4ac =2^2-4*4*(-38.2) = 615.2 > 0

The discriminant is positive so we have two solutions w and w' :

●●●●●●●●●●●●●●●●●●●●●●●●

w= (-2-24.8)/8 = -3.35

24.8 is the root square of 615.2(the discriminant)

●w is negative

● a distance is always positive so this value isn't a solution

w'= (-2+24.8)/8 =2.85 > 0

So this value is a solution for our equation

■■■■■■■■■■■■■■■■■■■■■■■■■■

w= 2.85 feet

Answer:

w=3.35

Step-by-step explanation:

The length of a rectangle is two feet less than four times the width:

length=4W-2

A=L*W

A=(4W-2)(W)

38.2=4W^2-2W

4W^2-2W-38.2=0  complete the square to find the solution add term(b/2)²

4W²-2W+1/4=38.2+1/4

4(W²-W/2+1/16)=38.45

4(w-1/4)^2=38.45

(w-1/4)²=38.45/4=9.6125

w-1/4=+ or -√9.6125 ( since it is width it has to be positive

w=√9.6125+1/4 = 3.35

Answer:

D.  [tex]\boxed{x = 5}[/tex]

Step-by-step explanation:

Let the number be x

Condition:

[tex]\frac{1}{10} x + 2 = \frac{1}{2} x[/tex]

[tex]\frac{x}{10} -\frac{x}{2} = -2\\LCM = 10\\Multiplying \ both \ sides \ by \ 10\\x - 5(x) = -2(10)\\x -5x = -20\\-4x = -20[/tex]

Dividing both sides by -4

x = 5

Answer:

[tex]\boxed{5.0}[/tex]

Step-by-step explanation:

Let the number be [tex]x[/tex].

1/10 of x is added to 2, the result is half of x.

[tex]2+\frac{1}{10} x=\frac{1}{2} x[/tex]

[tex]2=\frac{1}{2} x-\frac{1}{10} x[/tex]

[tex]2=\frac{2x}{5}[/tex]

[tex]10=2x[/tex]

[tex]\frac{10}{2} =x[/tex]

[tex]5=x[/tex]

The number is 5.0

Answer:

The correct option is;

A table with 6 columns and 2 rows. The first row, x, has entries, negative 3, negative 1, 2, 5, 10. The second row, y, has entries, negative 7.5, negative 2.5, 5.0, 12.5, 25

Please find attached the graphs of the table data

Step-by-step explanation:

Each of the given table data of in the tables are analysed to find direct variation;

Table 1

x,               -3,                 -1,                 2,                5,                10

y,              -4.5,              -3.0,             -1.5,             0.0,              1.5              

-4.5/-3  = 1.5 ≠ -3.0/-1 = 3

No direct variation

Table 2      

x,             -5.5,               -4.5,            -3.5,            -2.5,             -1.5

y,              10,                   8,                 6,              4,                  2

10/(-5.5) = -20/11  ≠ 8/(-4.5) = -16/9

However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2

Adjusted direct variation

Table 3              

x,              -5.5,               -5.5,             -5.5,           -5.5,            -5.5

y,              -3,                    -1,                 2,                5 ,              10                  

-3/(-5.5) ≠ -1/-5.5

No direct variation

Table 4

x,              -3,                    -1,                2,                  5,             10

y,              -7.5,                 -2.5,            5.0 ,              12.5,         25  

 -7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10

Direct variation exists        

Answer:

so D

Step-by-step explanation:

Answer:

Volume of the smaller cone = 8.34 cm³

Step-by-step explanation:

"If two figures are similar, their dimensions will be proportional.

Following this rule,

Ratio of the dimensions of two cones = [tex]\frac{\text{Radius of the large cone}}{\text{Radius of the small cone}}[/tex]

                                                               = [tex]\frac{r_2}{r_1}[/tex]

                                                               = [tex]\frac{5}{2}[/tex]

                                                               = 2.5

Similarly, "ratio of the volumes of two similar figures is cube of the dimensional ratio".

Ratio of the volumes = (ratio of the dimensions)³

[tex]\frac{V_1}{V_2}=(2.5)^3[/tex]

[tex]\frac{131}{V_2}=15.625[/tex]

[tex]V_2=\frac{131}{15.625}[/tex]

    = 8.384 cm³  

    ≈ 8.4 cm³

Therefore, volume of the smaller cone is 8.4 cm³.                          

Answer:

(x*(1+a))*0.8 = 400; x = 500/1+a

Step-by-step explanation:

First, increase the number (which we will call x) by a%

x*(1+a) -> You do 1 + a because if you wanted to increase let's say 5 by 20% you would do 5 + 5*0.2 and if you factor that out it becomes 5(1+0.2)

Next, decrease it by 80%.

(x*(1+a))*0.8

Finally, make it into an equation.

(x*(1+a))*0.8 = 400

If you solve it, you get:

x(1+a) = 500

x = 500/1+a

Answer:

2

Step-by-step explanation:

Five and above, round up. Four and below, round down.

Answer:

2

Step-by-step explanation:

anything less then five is rounded down anything above 5 is rounded to the higher number

Answer:

a) A₁ = 18 unit²

b) A₂ = 20 unit²

c) A₃ = 12 unit²

d) A₄ = 12 unit²

Step-by-step explanation:

a) Given that the side length of square is 6 units, we have;

The height of the square = The height of the triangle = 6 units

The base of the triangle = The side length of the square = 6 units

The area of a triangle A₁ = 1/2×base×height = 1/2×6×6 = 18 unit²

b) The side of the square A₂ forms an hypotenuse side to the side length 2 and 4 on sides of the circumscribing square

The length of the side = √(4^2 + 2^2) = 2·√5

A₂ = The area of a square =Side² = (2·√5)² = 20 unit²

c) The base length of the triangle, A₃ + 2 = The side length of the circumscribing square = 6 units

∴ The base length of the triangle, ₃₂ = 6 - 2 = 4 units

The height of the triangle, A₃ = The  side length of the circumscribing square = 6 units

The area of a triangle A₃ = 1/2×base×height = 1/2×4×6 = 12 unit²

d) Figure, A₄, is a parallelogram;

The area of a parallelogram = Base × Height

The base of the parallelogram, A₄ + 4 = 6 units

Therefore, the base of the parallelogram, A₄ = 6 - 4 = 2 units

The height of the parallelogram = The  side length of the circumscribing square = 6 units

The area of a parallelogram A₄ = 2× 6 = 12 unit².

Answer:

The measure of angle x is 122.5 degrees.

The measure of angle y is 57.5 degrees

Step-by-step explanation:

180=y+x

y=x-65

180= (x-65)+x

180=2x-65

245=2x

x=122.5

y=122.5-65= 57.5

Answer:

The correct answer is A.) The measure of angle x is 122.5 degrees. The measure of angle y is 57.5 degrees.

Step-by-step explanation:

I just did the test on edge 2021 and got it right!

Answer:

Step-by-step explanation:

Draw the solid line y = 3x.  Now shade the region below this line.

I will simply invent a point:  (2, -1).  Here y = -1 and x = 2.  Either this point is in the shaded region or it is not.  Substituting 2 for x in y  ≤ 3x, we get

y ≤ 3(2), or y ≤ 6.  Is -1 less than 6?  YES.  So the (arbitrarily chosen) point (2, -1) is a solution of the given inequality.

Answer:

D. the hours of daylight in a city throughout the year

Step-by-step explanation:

The hours of daylight in a city throughout the year represent the negative linear correlation coefficient. Then the correct option is D.

Independent quantities with an inverse relationship tend to move in different directions.

In essence, any figure between 0 and -1 denotes an opposing movement of the equity stocks.

When the correlation coefficient becomes less than 0, there is a negative (opposite) correlation. This suggests that both parameters are moving in the obverse direction.

The hours of daylight in a city throughout the year represent the negative linear correlation coefficient

Then the correct option is D.

More about the negative linear correlation coefficient link is given below.

https://brainly.com/question/12400903

#SPJ2

Answer:

11.3, or 12 if you need a whole number

Step-by-step explanation:

1 L = 1,000 mL. After adding all of your mL, you get 11,300. Divide that by 1,000 to get 11.3. To fully refill all of her fish tanks, she would need to refill it 12 times, but if you're looking for an exact number, 11.3.

Answer:

1607

Step-by-step explanation:

The mean (or average) of a data set is the sum of all of the data divided by the number of data in the set. In this case, that would be:

(1606 + 1607 + 1606 + 1607 + 1607 + 1609) / 6

= 9642 / 6

= 1607

Answer: 1,607

Step-by-step explanation: The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set.

Work is attached below.

Answer:

James has 8 cousins

Step-by-step explanation:

Bryan =5

Jane =Bryan + 11=5+11=16 ( Bryan has 11 cousins less than Jane)

James: 1/2 Jane=16/2=8 cousins ( Jane has twice as James)

Answer:

y = - 4

Step-by-step explanation:

Locate x = - 1 then follow the line down until it meets the curve and read the corresponding value on the y- axis at this point.

For x = - 1, y = - 4

Answer:

First box is 120.7016, second box is 63.585, third box is 28.26, and the fourth box is 12.56.

Step-by-step explanation:

You get these answers by using the area formula for a circle which is piR^2. If it says diameter divide it by 2 to get the radius.

Answer:

B.

Step-by-step explanation:

Again, to find the equation of the line, we need to find the slope and y-intercept. First, let's find the slope. Let (-1,5) be x₁ and y₁ respectively and (1,3) be x₂ and y₂, respectively. So:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-5}{1--1}=\frac{-2}{2}=-1[/tex]

So the slope is -1.

Now, to find the y-intercept, we can use the point-slope form. I'm going to keep using (-1,5) as the coordinate. Thus:

[tex]y-y_1=m(x-x_1)\\y-5=-1(x-(-1))\\y-5=-(x+1)\\y-5=-x-1\\y=-x+4[/tex]

This is slope-intercept form. We want the answer to be in standard form, where:

[tex]Ax+By=C[/tex]

A, B, and C are integers (and, conventionally, A is positive).

Thus, we need to rearrange the terms:

[tex]y=-x+4\\y+x=4\\x+y=4[/tex]

The answer is B.

Note how the triangles here have the angles between the marked sides. The tickmarks indicate which pair of sides are the same length. The SAS sequence has "A" in the middle of the two "S" letters to mean that the angles are between the sides.

------------

Extra info:

The first pair of triangles can be proven congruent by SAS.

SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the two triangles are said to be congruent.

Here, we have,

In the first pair of triangles the included angle of a triangle are equal to two sides and the included angle of another triangle, therefore by SAS postulate the two triangles are said to be congruent.

In the second figure, the pair of triangles are congruent by ASA postulate not SAS.

In the third figure, the pair of triangles are not congruent by any postulate or theorem [Because there is no SSA rule].

In the fourth figure, the pair of triangles are congruent by SSS postulate not SAS.

Hence, The first pair of triangles can be proven congruent by SAS.

learn more on congruent click:

https://brainly.com/question/12413243

#SPJ7

Answer:

[tex]Depth = 100m[/tex]

Step-by-step explanation:

Given

Initial Level = 340 m

Number of stages = 4

Difference in each stage = 60 m

Required

Determine the depth of the submarine after 4 stages

First, we have to calculate the total distance moved towards the surface of the sea;

This is calculated as

[tex]Total\ Distance = Number\ of\ Stages * Difference\ in\ each\ stage[/tex]

[tex]Total\ Distance = 4 * 60m[/tex]

[tex]Total\ Distance = 240m[/tex]

This implies that the submarine moved a total distance of 240 metres;

It;'s new depth is calculated as follows;

[tex]Depth = Initial\ Depth - Total\ Distance[/tex]

[tex]Depth = 340m - 240m[/tex]

[tex]Depth = 100m[/tex]

Hence, its new depth after 4 stages of rising is 100m

===============================================

First we need the equation of line AB. Compute the slope through (-3,-1) and (4,4)

m = (y2-y1)/(x2-x1)

m = (4-(-1))/(4-(-3))

m = (4+1)/(4+3)

m = 5/7

This is the slope through points A and B, ie the slope of line AB.

To get the slope of line BC, we flip the fraction and change the sign.

Doing so has us go from 5/7 to -7/5. Note how 5/7 and -7/5 multiply to -1.

The slope of line BC is -7/5. Let m = -7/5.

--------

Use (x,y) = (4,4) along with m =-7/5 to find the equation of line BC

y = mx+b

4 = (-7/5)(4) + b

4 = -28/5 + b

20 = -28 + 5b ... multiply every term by 5 to clear out the fraction

20+28 = 5b

48 = 5b

5b = 48

b = 48/5

With m = -7/5 and b = 48/5, we go from y = mx+b to y = (-7/5)x+48/5

The slope intercept form for line BC is y = (-7/5)x+48/5

--------

Let's get this into standard form Ax+By = C

y = (-7/5)x+48/5

5y = -7x + 48 .... multiply everything by 5

7x+5y = 48 .... is one way to represent the equation in standard form

-7x - 5y = -48 ... your teacher has decided (for some reason) to multiply both sides by -1

Answer:

-5y-7y=-48

Step-by-step explanation:

distance between BC (4,4) C(x,y)

BC is perpendicular on AB (perpendicular line has opposite reciprocal slope)

slope of AB=y2-y1/x2-x1=4-(-1)/4-(-3)=5/7

slope of BC=-7/5

now input the value of B (4.4) and C(x,y)

y=mx+b

4=-7/5(4)+b

b=4+28/5

b=48/5

y=-7/5x+48/5

5y=-7x+48

5y+7x=48 multipy by -1

-5y-7y=-48

Answer:

590mph

Step-by-step explanation:

Speed with wind = 5525÷ 8.5

= 650mph

speed against wind = 4505÷8.5

= 530mph

speed without wind = (650mph+530mph)÷2

= 590mph

Answer:

Step-by-step explanation:

[tex]8a - 5b - (6a - 9b)[/tex]

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression.

[tex]8a - 5b - 6a + 9b[/tex]

Collect like terms

[tex]2a + 4b[/tex]

Factor out 2 from the expression

[tex]2(a + 2b)[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

2(a + 2b)

Step-by-step explanation:

Answer:

[tex]x = 10[/tex]

Step-by-step explanation:

If we have our proportion set up like this:

[tex]\frac{5}{n} = \frac{16}{32}[/tex]

Then using the cross products property, we can find the value of n.

The property states that the two numbers that are diagonal to each other DIVIDED by the number diagonal to the variable will equal the variable.

So:

[tex]32\cdot5 = 160\\160\div16 = 10[/tex]

Hope this helped!

Answer:

22

Step-by-step explanation:

Let the first number be x.

Let the second number be y.

(x+y)/2 = 11

x-y=4

Solve for x in the second equation.

x = 4 + y

Put x as 4 + y in the first equation and solve for y.

(4+y+y)/2 = 11

4 + 2y = 22

2y = 18

y = 9

Put y as 9 in the second equation and solve for x.

x = 4 + 9

x = 13

Find the sum of the numbers x and y.

x + y

13 + 9

= 22

Answer:

[tex]22[/tex]

Step-by-step explanation:

let the numbers be x and y

[tex] \frac{x + y}{2} = 11 \\ x - y = 4[/tex]

so,

[tex] \frac{x + y}{2} = 11 \\ x +y = 11 \times 2 \\ x + y = 22[/tex]

So they asked to find the sum of the two numbers

And the answer is 22

Answer:

  80°

Step-by-step explanation:

The sum of the measures of the acute angles in a right triangle is 90°. The sum of ratio measures in the ratio 8 : 1 is (8+1) = 9. Thus, each of those measures stands for 90°/9 = 10°. Then the angle ratio is ...

  80° : 10° = 8 : 1

The measure of the largest acute angle in the triangle is ...

  10° × 8 = 80°

Answer:

[tex]\frac{77\pi }{3}[/tex] cm³

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex]πr³ ( r is the radius )

Here diameter = 4 cm , hence r = 4 ÷ 2 = 2 cm

V = [tex]\frac{4}{3}[/tex]π × 2³ = [tex]\frac{4}{3}[/tex]π × 8 = [tex]\frac{32\pi }{3}[/tex] cm³

Thus

combined volume = [tex]\frac{32\pi }{3}[/tex] + 15π = [tex]\frac{32\pi }{3}[/tex] + [tex]\frac{45\pi }{3}[/tex] = [tex]\frac{77\pi }{3}[/tex] cm³

Answer:

3/4

Step-by-step explanation:

Explanation:

List out the total number of outcomes = {1,2,3,4,5,6,7,8,9,10,11,12}

We have 12 items in this list.

From this list, highlight the outcomes that are less than 9. So we will have this smaller list of {1,2,3,4,5,6,7,8} which has 8 items in it.

There are 8 ways to get what we want (a number less than 9) out of 12 outcomes total

The probability is therefore 8/12 = 2/3