**Answer:** The equation is (y=x+6)

**Step-by-step explanation:**

Lets assume the equation to be y=mx+c,

where,

m=slope of the line

c=constant

Since we know that,

slope=m=tanx

where x is the angle between x-axis and line

tanx=

[tex]tanx= \frac{perpendicular}{base}[/tex]

so here it will be,

[tex]tanx=\frac{10-6}{4-0} \\= > tanx=1\\= > m=1[/tex]

Also, c=6 as we can clearly see from the graph

Therefore the equation of line is => **y= x +6**

Two splice plates are cut from a piece of sheet steel that has an overall length of 18 3/4 in. The plates are 10 1/2 in. and 6 15/16 in. long. How much material remains from the original piece if each saw cut removes 1/16 in.?

Total material remains from **original** piece if overall **length **of sheet is

[tex]18\frac{3}{4}[/tex] in and two plates are cut of length [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in ,two saw of length 1/16 in is **35 / 16 in.**

As given,

Overall **length** of steel sheet=[tex]18\frac{3}{4}[/tex] in

=(75 /4) in

=(300 /16)in

Length of two plates is [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in

Total length of two plates=[tex]10 \frac{1}{2} + 6\frac{15}{16}[/tex]

=(21 /2) +(95/16)

=(168 +95)/16

=263 /16

Total length of saw cut=(1/16) +(1/16)

=2/16

Material remains from **original** piece=(300/16) - (263/16 +2/16)

= 35 /16

Therefore, total material remains from original piece if overall **length **of sheet is [tex]18\frac{3}{4}[/tex] in and two plates are cut of length [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in ,two saw of length 1/16 in is 35 / 16 in.

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7x+12=x-6

I need help!!!!

**Answer:**

x = -3

**Step-by-step explanation:**

You have to isolate x:

7x + 12 = x - 6

7x = x - 6 - 12 = x - 18

6x = -18

x = -3

Mandy and 6 of her teammates each sold an equal number of

shirts to raise money for their tennis team. If a total of 56 shirts

were sold, how many shirts did each person sell?

Each person will sell 8 **shirts **if 56** shirts** were sold

Mandy and 6 of her teammates each sold an equal number of **shirt**

Mandy is one person, let add 1 plus six to get the total number

1 + 6

= 7

The total number of shirts sold is 56 **shirts**

Since there are 7 people, the number of** shirt **that each person will sell can be calculated by dividing 56 by 7

= 56/7

= 8

Hence 8 **shirts** will be sold by each person

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Question 1 (1 point)Given the graph below, is this relation a function?MathMLXBlarSubmit

To be a function, a relation can't have more than 1 value of 'y' for the same value of 'x'

For example, if you have points (3,7) and (3,-6) does not represent a function but points (3,7) and (-3,7) does.

In this problem, none of the graphed pairs have 2 or more values of 'y' for a single value of 'x'. They are all different, so **yes, this relation is a function**

:) Please help!!!!!!

**Answer:**

1/2, 1/5, 1/7, 1/9, 1/28

7/14, 7/21, 7/42, 7/49

10/18, 10/20, 10/50, 10/100

On a piece of paper, graph y + 2 > -3x - 3. Then determine which answer

choice matches the graph you drew.

A

D

(0,-5)

• A. Graph A

• B. Graph B

C. Graph C

D. Graph D

**Answer:**

D

**Step-by-step explanation:**

The line needs to be dotted since the boundary is not included.

Eliminate A and C.The line should be shaded above because of the > sign.

Eliminate B.m^2+7m-51/4=0 by completimg square

By **completing squares**, we will see that the two solutions of the **quadratic equaiton** are:

m = -7 + √(145)/2

m = -7 - √(145)/2

How to solve by completing squares?Here we have the **quadratic equation:**

m^2 + 7m - 51/4 = 0

If we multiply both sides by 4, we will get

4m^2 + 28m - 51 = 0

Now, remember the **relation**:

(a + b)^2 = a^2 + 2ab + b^2

Then to complete the squares we can write:

(2m)^2 + 2*14*m + (14)^2 - (14)^2 - 51 = 0

(2m + 14)^2 - 14^2 - 51 = 0

(2m + 14)^2 = 145

We already **completed squares**, now the solutions are:

2m = -14 ± √145

m = (-14 ± √145)/2

m = -7 + √(145)/2

m = -7 - √(145)/2

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About how many times heavier is the largest dog when compared with the smallest dog?

The number of times heavier that the **largest** dog is when compared with the smallest **dog**** **is B. 41**.**

It should be noted that from the information given, the biggest dig is the St **Bernard** and it has 145 pounds.

Also, it should be noted that the smallest dog is **Yorkie** and it had 3.5 pounds. Therefore, it should be noted that the number of times heavier will be:

= Weight of biggest fog / Weight of smallest **dog**

= 145 / 3.5

= 41.

It is 41 times **heavier**.

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Hi can someone please help me out?

Happy Halloween!

**Answer:**

A=14

B=pi 7^2

**Step-by-step explanation:**

All you need to do is put pi symbol on calculator and x by 7 squared to get answer

Now answer the question:

Juan and his children went into a grocery store and he bought $4 worth of apples and

bananas. Each apple costs $1 and each banana costs $0.50. He bought a total of 6

apples and bananas altogether. Determine the number of apples, x, and the number

of bananas, y, that Juan bought.

Juan bought apples and

bananas.

Juan bought 2 Apples and 4 Bananas.

X=2 and Y=4

X=2 and Y=4

**Answer:**

2 apples and 4 bananas

**Step-by-step explanation:**

**Given info:**

**Question given:**

*Determine the number of apples, x, and the number of bananas, y, that Juan bought. *

**Solution:**

*Since, we know that;*

*apples = x*

*bananas = y*

*Cost of each apple = $1 & Cost of each banana = $ 0.50*

*Total = 6*

* *

*The equation that represents the following information:*

*x + y = 6*

*x + 0.5y = 4*

*We can multiply the top equation by -1 so it becomes -x -y = 6*

*-x - y = 6*

*x + 0.5y = 4 *

*Now, we can use elimination to cancel out the x.*

*-0.5y = -2*

*y = 4*

*Because y=4, x must be 2 since x+y=6. So, *

*x = 2 and y = 4*

*Which means;*

*Juan bought 2 apples and 4 bananas.*

**~kavinsky**

Betsy's Bakery packages muffins in boxes of one dozen. If Besty bakes 1,152 muffins on Saturdays, how many boxes are ready to sell?

**Answer:**

96 boxes of muffins

**Step-by-step explanation:**

so how you would get to this answer would be 1152÷12

12 is equal to a dozen and so that is why you divide it by 12

the answer would be 96

Think About the Process The length of cell A is 4 x 10^-5 length to cell B's length? Use pencil and paper. Is it easier to find notation or in standard form? Explain your reasoning. m. The length of cell B is 0.000002 the ratio when the numbers m. What is the are expressed ratio of cell A's in scientific

**Ratio **of **length** of cell A to the **length **of cell B will be 20 : 1.

**What is mean by Ratio?**

A **ratio **indicates how many times one **number contain **in another number. The **ratio **of two number is **written **as x : y, which is equivalent to x/y.

Where, x and y are **individual amount **of two quantities.

And, Total **quantity **gives after combine as x + y.

Given that;

**Length **of cell A = 4 x 10⁻⁵

**Length **of cell B = 0.000002 = 2 x 10⁻⁶.

Now,

**Length **of cell B into **scientific notation** = 2 x 10⁻⁶

Hence, The **ratio **of the length of cell A to cell B = 4 x 10⁻⁵ / 2 x 10⁻⁶

= 2 x 10⁻⁵⁺⁶

= 2 x 10¹

= 20

Thus, **Ratio **of **length** of cell A to the length of cell B is 20 : 1.

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hi can you please help me

The area of the kitchen will be:

[tex]\begin{gathered} A=w\cdot l \\ \text{where:} \\ w=\text{width}=36-24=12ft \\ l=\text{length}=8ft \\ A=12\cdot8 \\ A=96ft^2 \end{gathered}[/tex]

The first three terms of an arithmetic sequence are x, 2x + 4, 5x. Find the value of x.

The value of x for the given **arithmetic sequence **is ** x = 4.**

A series of numbers called an** arithmetic progression **or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a **common difference** of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.

Given,

First three terms of an **arithmetic sequence** are** x, 2x + 4, 5x**

The difference of 1 and 2 term equals the difference of 3 and 2 term.

⇒ 2x + 4 - x = 5x - 2x - 4

⇒ x + 4 = 3x - 4

⇒ 2x = 8

**⇒ x = 4**

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find the x intercepts of f(x)=x^4+x^3-4x^2-4x

The x **intercepts **are 0, 1, -2, 2.

What is **intercepts**?

The term "**intercept**" refers to the x- and y-**intercepts** of of a given equation. The x-**intercept **is the point at which a line crosses the x-axis and the y-**intercept** is the point at which a line crosses the y-axis.

In the linear equation, we have the general form as y=mx+b

where m and b are constants.

We have to find the x **intercept **of the given function.

Given equation is [tex]x^{4} +x^{3} -4x^{2} -4x[/tex]

put this equation equals to 0

x^{4} +x^{3} -4x^{2} -4x = 0

[tex]x(x^{3} +x^{2} -4x-4)=0[/tex]

from this x = 0

x =1 is also the root of the equation

we get [tex]x^{2} -4=0[/tex]

from this

x = -2, 2

The **intercept are **0,1,2,-2.

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Data were collected on the distance a baseball will travel when hit by a baseball bat at a certain speed. The speed, s, is measured in miles per hour, and distance, y, is

measured in yards. The line of fit is given by ý = 3.98 +53.59s.

If the ball travels for a duration of 5 seconds, what is the predicted distance of the ball?

O 267.95 feet

O271.93 feet

O 283.87 feet

O287.85 feet

The predicted **distance** of the ball is 271.93 feet.

The **speed** of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time. Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Given Data

The speed, s, is measured in miles per **hour**, and **distance**, y, is

measured in yards.

The line of fit is given by ý = 3.98 +53.59s.

When s = 5 sec

y = 3.98 + 53.59(5)

y = 3.98 + 267.95

y = 271.93

The predicted **distance** of the ball is 271.93 feet.

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find the ratio of 15k to 65k

**Answer:**

**Step-by-step explanation:**

If its 15000:65000

Then we divide both sides by 1000 first :

15 : 65

Then we divide both sides by 5 :

3 : 13

This is simplified

If K is a unit then it will be 3k : 13k by doing the above steps but skipping the first.

Hope this helped and have a good day

HELP I WILL GIVE YOU POINTS!

Describe in words the one transformation that maps

ΔABC to ΔA'B'C'

∆ABC to ∆A′B′C′

. Make sure that you include specific details (Reflection – over which axis, Rotation – direction, degrees, and center of rotation, Translation – direction(s) and number of units). 15 points

Answer:

ΔABC

∆ABC

is transformed by a:

Type of Transformation:

Details of transformation:

The **description** of the one **transformation** that **maps** ∆ABC to ∆A'B'C' is a rotation counterclockwise, 90 degrees, with the center at the origin

A **rotation transformation** can be described as the angular motion of a rigid, **geometric** figure around a point

The **vertices** on the **triangle ∆ABC** are;

The vertices on the triangle ∆A'B'C' are;

A'(2, -5), B'(4, -7), C'(5, -5)The **rotation** of a point A(x, y), 90° **counterclockwise** about the **origin** gives the point A'(-y, x)

The reflection of a point (x, y) across the y–axis gives the point A'(-x, y)

Therefore;

The coordinates of the vertices of∆ABC following a 90° counterclockwise rotation gives;

A(-5, -2) → A'(2, -5)

B(-7, -4) → B'(4, -7)

C(-5, -5) → C'(5, -5)

Therefore;

The transformation that maps ∆ABC to ∆A'B'C' is therefore a rotation of 90° counterclockwise about the origin

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Find the perimeter of the triangle

**Answer:30 in.**

**Step-by-step explanation:13+5+12**

Consider the following function.

f(x) = (x − 3)2, x ≥ 3

Find the inverse function

f −1.

The **inverse equation **of the function is f'1(x) = 3 + √x

**Inverse functions **are the opposite of an original equation. This means that for a function f(x), the **inverse **of the function f(x) is f-(x)

The **function **f(x) is given as

f(x) = (x - 3)^2, x ≥ 3

As a general rule, we start by writing f(x) as a variable (say f(x) = y).

So, the **equation** of the **function **becomes

y = (x - 3)^2

The next step is to switch/swap the positions of x and y in the **equation**

The **equation **becomes

x = (y - 3)^2

Make y the **subject **of the **formula **in the equation

The **equation **becomes

y = 3 + √x

Express as an **inverse function**

f'1(x) = 3 + √x

Hence, the equation of the **inverse function **is f'1(x) = 3 + √x

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You have $50 in your bank account. Each week you plan to deposit $8 from your allowance and $20 from your paycheck. The equation b=50+(20+8)w gives the amount b in your account after w weeks. How many weeks from now will you have $210 in your bank account?

If you have $50 in your bank account and each week you plan to deposit $8 from your allowance and $20 from your paycheck. The number of **weeks **from now that you will have $210 in your bank **account **is: 5.71w.

The given **equation **is:

b=50+(20+8)w

Where:

b is the amount in your account after w weeks.

w = Number of **week**

Hence,

b = 50+(20+8)w

b = 50+28w

b-50 = 28w

(b-$50)/28 = w

(210-$50)/28 = w

160/28 = w

5.71 = w

Therefore we can conclude that you will have the **amount **of $210 in your account in 5.71 weeks.

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For

f(x) = 4x

and

g(x) = x10,

find the following.

(a)

(f + g)(x)

(b)

(f − g)(x)

(c)

(f · g)(x)

(d)

(f/g)(x)

,

x ≠ 0

The **addition**, **subtraction**, **multiplication** and **division** of the two **functions** are 4 · x + x¹⁰, 4 · x - x¹⁰, 4 · x¹¹ and 4 / x⁹, respectively.

How to determine the expression resulting from operations between functions

In functions there are two **fundamental operations** (**addition**, **multiplication**) and two **derivate operations** (**subtraction**, **division**). In this problem we must look for the following definitions:

**Addition**

(f + g)(x) = f(x) + g(x)

**Subtraction**

(f - g)(x) = f(x) - g(x)

**Multiplication**

(f · g)(x) = f(x) · g(x)

**Division**

(f / g)(x) = f(x) / g(x), for x ≠ 0.

If we know that f(x) = 4 · x and g(x) = x¹⁰, then the expression behind the operations are, respectively:

**Addition**

(f + g)(x) = 4 · x + x¹⁰

**Subtraction**

(f - g)(x) = 4 · x - x¹⁰

**Multiplication**

(f · g)(x) = (4 · x) · x¹⁰ = 4 · x¹¹

**Division**

(f / g)(x) = (4 · x) / x¹⁰ = 4 / x⁹

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is the relation in this graph a function ?

**Answer:**

No it's not a function

**Step-by-step explanation:**

You can use the vertical line test to determine whether it's a function or not. If the vertical line touches the graph at more than one point, the graph is not a function therefore the answer is no.

In a game of cornhole, Sasha tossed a bean bag and it landed at the edge of the hole. The hole can be represented by the equation x2 + y2 = 5, and the path of the bean bag can be represented by y = 0.5x2 – 1.5x – 4. To which points could she have tossed her bean bag?

A. (–1, –2) or (–2, 1)

B. (1, –2) or (2, 1)

C. (–1, 2) or (–2, –1)

D. (1, 2) or (2, –1)

The **points **are (1, -2) or (2, 1).

An **equation **is a mathematical **statement **that is made up of **two expressions connected **by an **equal **sign.

For **example**, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

The equation for the hole

x² + y² = 5.............(1)

and, **equation** for bean bag can be **represented **by

y = 0.5x² – 1.5x – 4............................(2)

By solving above **two equation **we get

0.25 [tex]x^4[/tex] + 1.5 x³ -0.75 x² -12 x +11 =0

we het x1=1 and x2 = 2

then y1= -2 and y2 = 1

hence, the **points **are (1, -2) or (2, 1).

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factor of the following expression:

81x^4-16y^2

**Answer:**

See below

**Step-by-step explanation:**

(9x^2 - 4 y ) * (9x^2 + 4 y )

he figure on the left represents a scale drawing of the figure on the right.

pls help its due in 10 min

The **scale** of the drawing is expressed as, 1 inch : 2.5 yards.

A **scale factor** describes to what size an original image has been **reduced** or **enlarged**. If the **scale factor** of an **enlargement** is 2, it means every side lengths of the original image is increased times two to get the new image after **enlargement**.

On the other hand, if the **reduction** was done using a **scale factor** of 0.5 or 1/2, it means the size of the original image was reduced by half to get the new side lengths of the new image.

The **scale factor** of a **scale drawing** = dimension of new image/corresponding dimension of original image.

The figure by the right is the original figure, while the one on the left is the **scale drawing** which is the new figure.

**Scale **of the drawing = 1 inches to 5/2 yards

**Scale** = 1 inch : 2.5 yards.

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q=p(r+s)

Solve for p

P = q/(r + s) …. By dividing both sides by r + s

(-2,-5) (-3,5) fin the slope from the pair of points

**The slope of the line from the pair of given points would be **[tex]m = 5[/tex].

Hope this helps!

Bill and ross are twins, their brother mark was born on the same day as twins but is three year older. if mark was born in 1990, in what year did the three boys get total age 21

**Step-by-step explanation:**

x = age of one of the twin boys

when they had together 21 years of age,

Bill was x years old

Ross was x years old

Mark was x+3 years old

so, we have

x + x + (x + 3) = 21

3x + 3 = 21

3x = 18

x = 6

Bill and Ross were 6 years old.

Mark was 6+3 = 9 years old.

Mark was born in 1990.

1990 + 9 = 1999

so, it was 1999 when they had together 21 years of age.

Suppose an online store has an item on sale for 10% off the original price. By what perceny does the store have to increase the price of the item in order to sell it for the original amount

The most appropriate choice of **percentage** will be given by-

The store have to increase the price of the item by [tex]11\frac{1}{9}[/tex] % in order to sell it for the original amount.

**What is Percentage?**

**Percentage **is a ratio expressed as a percentage of 100.

Let the original price be x

Percentage decrease in price due to sale = 10%

Decrease in price due to sale = [tex]\frac{10}{100} \times x[/tex]

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

New price = ([tex]x - \frac{x}{10}[/tex])

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

= [tex]\frac{9x}{10}[/tex]

Now,

Increase in price from [tex]\frac{9x}{10}[/tex] to [tex]x[/tex] = [tex]\frac{x}{10}[/tex]

Percentage by which the store have to increase the price of the item in order to sell it for the original amount =

[tex]\frac{\frac{x}{10} }{\frac{9x}{10} } \times 100[/tex]

=[tex]\frac{x}{10} \times \frac{10}{9x} \times 100[/tex]

= [tex]\frac{100}{9}[/tex]

= [tex]11\frac{1}{9}[/tex] %

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