Use the diagram below to answer questions 4-5.
what is the value of x?

The fromula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

a) (-1, -8), (-7, -4)

substitute

[tex]m=\dfrac{-4-(-8)}{-7-(-1)}=\dfrac{-4+8}{-7+1}=\dfrac{4}{-6}=-\dfrac{2}{3}[/tex]

b) (2.1, 3.8), (3.1, 7.6)

substitute

[tex]m=\dfrac{7.6-3.8}{3.1-2.1}=\dfrac{3.8}{1}=3.8[/tex]

Answer:

The standard form like [tex](a+bi)[/tex] will be:  [tex]15+8i[/tex]

Step-by-step explanation:

Given expression is:   [tex]2\sqrt{-16}+\sqrt{225}[/tex]

First factoring out -16 as (-1×16) , we will get....

[tex]2\sqrt{-1}*\sqrt{16}+\sqrt{225}[/tex]

Now, replacing [tex]\sqrt{-1}[/tex] as  [tex]i[/tex] .......

[tex]2i\sqrt{16}+\sqrt{225}[/tex]

Finally, simplifying the radicals in the above expression, we will get......

[tex]2i*4+15\\ \\ =15+8i[/tex]

Thus, the standard form like [tex](a+bi)[/tex] will be:  [tex]15+8i[/tex]

Answer:

tttgtgt

Step-by-step explanation:

gtgtggtt

Answer:

On 4/5 gallon of gasoline, hybrid car will travel 36 miles of distance.

Step-by-step explanation:

Suppose, non hybrid car travel "x" distance in 1 gallon of gasoline

then, hybrid will travel " 1 4/11* x" distance in 1 gallon of gasoline

Given that, non hybrid car travel, x = 33 miles per gallon

Then, hybrid car travel, 1 4/11*x = 1 4/11* 33 = 45 miles per gallon

On 1 gallon of gasoline hybrid car travel= 45 miles

On 4/5 gallon of gasoline hybrid car will travel= 4/5*45= 36 miles

On 4/5 gallon of gasoline, hybrid car will travel 36 miles of distance.

There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

1. SSS   (side, side, side)

SSS Triangle

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal.

For example:

triangle is congruent to:   triangle

(See Solving SSS Triangles to find out more)

If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

2. SAS   (side, angle, side)

SAS Triangle

SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.

For example:

triangle is congruent to: triangle

(See Solving SAS Triangles to find out more)

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

3. ASA   (angle, side, angle)

ASA Triangle

ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.

For example:

triangle is congruent to: triangle

(See Solving ASA Triangles to find out more)

If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

4. AAS   (angle, angle, side)

AAS Triangle

AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal.

For example:

triangle is congruent to: triangle

(See Solving AAS Triangles to find out more)

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

5. HL   (hypotenuse, leg)

This one applies only to right angled-triangles!

triangle HL   or   triangle HL

HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs")

It means we have two right-angled triangles with

the same length of hypotenuse and

the same length for one of the other two legs.

It doesn't matter which leg since the triangles could be rotated.

For example:

triangle is congruent to: triangle

(See Pythagoras' Theorem to find out more)

If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

Caution! Don't Use "AAA"

AAA means we are given all three angles of a triangle, but no sides.

AAA Triangle

This is not enough information to decide if two triangles are congruent!

Because the triangles can have the same angles but be different sizes:

triangle is not congruent to: triangle

Without knowing at least one side, we can't be sure if two triangles are congruent.

The five postulates and theorems that can prove triangles are congruent are Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Angle-Side (AAS), Angle-Side-Angle (ASA), and Hypotenuse-Leg (HL). These are based on comparing angles and sides of the triangles.

In geometry, congruent triangles are triangles that have the same size and shape, meaning they have equal side lengths and angles. There are several postulates and theorems that can be used to prove that triangles are congruent. They include:

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Answer:A)The conditional relative frequency among widowed employees of those widowed working at grade 2 or below= 28/42 = 66.67%

Step-by-step explanation:

In a  two way frequency table, conditional relative frequency is it’s a fraction that tells us how many elements of of a group have a certain characteristic.

Here In a study about the relationship between marital status and job level, 8,235 males at a large manufacturing firm reported their job grade (from 1 to 4, with 4 being the highest) and their marital status.

from the given two way frequency table,

Number of widowed employees at grade 1 =8

Number of widowed employees at grade 2=20

∴ Number of widowed employees at grade 2 or below=8+20=28

And the total widowed employees working =42

Now the conditional relative frequency among widowed employees of those widowed working at grade 2 or below=[tex]\frac{\text{Number of widowed employees at grade 2 or below}}{\text{Total widowed employees}}=\frac{28}{42}=0.6667=66.67%[/tex]

Therefore, the conditional relative frequency among widowed employees of those widowed working at grade 2 or below= 28/42 = 66.67%

To calculate the conditional relative frequency among widowed employees for those at grade 2 or below, the number of widowed employees at these grades (28) is divided by the total number of widowed employees (42), yielding a frequency of approximately 66.67%. The answer is option A.

The question asks us to find the conditional relative frequency among widowed employees of those working at grade 2 or below at a large manufacturing firm. To find this, we look at the two-way table provided and sum the number of widowed employees in job grades 1 and 2, which gives us

8 + 20 = 28 widowed employees. We then divide this number by the total number of widowed employees to get the conditional relative frequency:

28/42*100 =  66.67%.

Therefore, among widowed employees, approximately 66.67% work at job grade 2 or below. The answer is option A.

2 : 2.5 = 3 : w

w = 2.5 * 3 : 2

w = 3.75

Answer:

the answer is p=5.75t

Step-by-step explanation:

The answer is B: 4.5 cm, 7.5 cm

Here's why: 7.5 is 3 cm more than 4.5, and when added together, 7.5 + 7.5 + 4.5 + 4.5 = 24.

The formula of a perimeter of a rectangle: P = 2(w + l)

w - width, l - length

We have:

P = 24cm and l = (w + 3)cm

Substitute:

24 = 2(w + w + 3)

24 = 2(2w + 3)     |use distributive property

24 = (2)(2w) + (2)(3)

24 = 4w + 6      |subtract 6 from both sides

18 = 4w     |divide both sides by 4

w = 18/4

w = 9/2

w = 4.5 cm

l = 4.5 + 3 = 7.5cm

slope (m) = rate.    $40 per hour is the rate, so m = 45

y-intercept (b) = one time fee.   $45 is the flat rate which is the one time fee, so b = 45

y = mx + b

y = 40x + 45

Answer: A

Any rational number added to 0.6 will produce a rational number.

Adding any rational number to 0.6 will produce a rational number. Rational numbers include whole numbers, fractions, and terminating or repeating decimals.

The question asks which number, when added to 0.6, produces a rational number. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Since 0.6 is already a rational number (it can be expressed as 6/10 or 3/5), adding any other rational number to it will also produce a rational number. Examples of rational numbers include whole numbers, fractions, and terminating or repeating decimals.

Therefore, any number that is rational (such as 0, 1/2, 3, 4.5, etc.) will produce a rational number when added to 0.6.

Seth:

Equation 7.50x + 15y = 750, where x is the number of hours Seth works and y is the number of lawns he mows.

Karen:

Equation 6x + 4y = 700, where x is the number of hours Karen works and y is the number of dogs she walks.

Part A: Converting it in function for by solving for y first.

Solving 7.50x + 15y = 750, equation we get

7.50x + 15y = 750

15y = -7.50x + 750

Solving 6x + 4y = 700 for y, we get

6x + 4y = 700

4y = -6x + 700

On comaring with slope-intercept form y=mx+b, we got slope for Seth equation is -1/2 and slope for Karen is -3/2.

If we take absolute of those -1/2 and -3/2 we get 1/2 and 3/2.

Therefore, Karen has the higher slope. We can see the graph that blue line has greater slope as it's increasing/decreasing with greater rate.

In function form we could write equation as

Part B : y-intercept of Karen equation is 175 and y-intercept of Seth equation is 50.

Part C: If both students work 80 hours for the month.

Let us plug x =80 in each of the equations.

Seth would earn $10 from mowing lawn.

Therefore, the number of lawns Seth has to mow = 10/15 = 0.67 that is approximately 1 lawn.

Karen would earn $50 from walking dog.

So, the number of dogs Karne has to walk = 55/4 = 13.75 that ia approximately 14 dogs.

Part D: If Karen begins charging $8 per hour for babysitting and Seth begins earning $8 per hour.

The equations would become : 8x + 15y = 750, 8x + 4y = 700.

Answer:

Seth:

Equation 7.50x + 15y = 750, where x is the number of hours Seth works and y is the number of lawns he mows.

Karen:

Equation 6x + 4y = 700, where x is the number of hours Karen works and y is the number of dogs she walks.

Part A: Converting it in function for by solving for y first.

Solving 7.50x + 15y = 750, equation we get

7.50x + 15y = 750

15y = -7.50x + 750

y = -1/2x + 50

Solving 6x + 4y = 700 for y, we get

6x + 4y = 700

4y = -6x + 700

y= -3/2x + 175.

On comaring with slope-intercept form y=mx+b, we got slope for Seth equation is -1/2 and slope for Karen is -3/2.

If we take absolute of those -1/2 and -3/2 we get 1/2 and 3/2.

Therefore, Karen has the higher slope. We can see the graph that blue line has greater slope as it's increasing/decreasing with greater rate.

In function form we could write equation as

f(x) = -1/2x + 50 and

f(x) = -3/2x + 175.

Part B : y-intercept of Karen equation is 175 and y-intercept of Seth equation is 50.

Therefore, Karen has greater y-intercept.

This means Karen earns $175 by just walking dogs.

Part C: If both students work 80 hours for the month.

Let us plug x =80 in each of the equations.

y = -1/2x + 50  => y = -1/2(80) + 50 = -40 +50 = $10.

Seth would earn $10 from mowing lawn.

Therefore, the number of lawns Seth has to mow = 10/15 = 0.67 that is approximately 1 lawn.

y = -3/2x + 175  => y = -3/2(80) + 175 = -120 +175 = $55.

Karen would earn $50 from walking dog.

So, the number of dogs Karne has to walk = 55/4 = 13.75 that ia approximately 14 dogs.

Therefore, the number of lawns Seth has to mow is less than the number of dogs Karen has to walk.

Part D: If Karen begins charging $8 per hour for babysitting and Seth begins earning $8 per hour.

The equations would become : 8x + 15y = 750, 8x + 4y = 700.

It would not effect the graph much. Even the y-intercepts would remain same.

There would be a slightly change in slopes.

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Step-by-step explanation:

You want to use the distributive property, i.e. the possibility to distribute a multiplication to both terms of an sum/subtraction.

In this case, if you think of 395 as of 400-5, you have

[tex] 5 \times 395 = 5 \times (400-5) [/tex]

And you can use the distributive property to write

[tex] 5 \times (400-5) = 5\times 400 - 5\times 5[/tex]

Both of these multiplications are easy to perform in your mind:

[tex] 5\times 400 - 5\times 5 = 2000 - 25 = 1975[/tex]

The solution to 5×395=5×(_ - _) is found by calculating the multiplication, 5 x 395 = 1975. Then we find two numbers that result in 1975 when multiplied by 5 and subtracted; one example could be 396 and 1. Thus, the equation can be 5×395=5×(396 - 1).

In order to solve the problem 5×395=5×(_ - _) using mental math, we first compute the multiplication of 5 and 395, which is 1975. Now, we need to find two numbers that, when multiplied by 5 and subtracted, give us 1975. As there can be multiple possible pairs, one potential solution could be 5×(395+1) = 5×396 = 1980. So, the two numbers are 396 and 1, and the complete equation would be 5×395=5×(396 - 1).

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Answer:

The answer is B sweetheart.

Step-by-step explanation:

A unit rate is a rate with one in the denominator, an example being 55 mph where the 'per hour' is based on one hour. Proportions are the equality of two ratios, while unit scales represent ratios used in scaled models or drawings and do not require a value of 1. Option C) is the correct answer.

A unit rate is a type of rate that expresses the comparison of two different quantities, where one of the quantities is fixed at a value of 1. When looking at the options provided, a unit rate is best described as: A. a rate with one in the numerator.

This definition is not accurate because the unit rate refers to having 1 in the denominator. So, the correct answer to what a unit rate is: C. a rate with one in the denominator. An example of a unit rate would be traveling 55 miles in one hour, which can be written as (55/1) miles per hour or simply 55 mph.

A proportion on the other hand is an equivalence between two ratios. For instance, if we say 1/2 = 3/6, we're explaining that these two fractions, or ratios, are proportionate because they represent the same value when simplified. In contrast, a unit scale, like those often found on maps, does not necessarily have a value of 1 in its ratio.

The completed statement with regards to the area of the rectangle WXYZ can be presented as follows;

AD/WZ = 1/2, AB/WX = 1/2 Because the ratio of the corresponding side lengths is 1/2, the ratio of the areas is equal to ( 1 / 2 ) to the second power. To find the area, solve the proportion 30/x = 1 / 4 to get x = 120

The steps by which the area of the rectangle WXYZ is found can be presented as follows;

The area of the rectangle ABCD = 30 square inches

AD/WZ = 1/2, and AB/WX = 1/2

The ratio of the corresponding sides in the rectangles ABCD and WXYZ is 1/2

Therefore, scale factor of the lengths of the sides of rectangle ABCD to the lengths of the sides of the rectangle WXYZ is 1/2

The scale factor of the lengths = 1/2

The scale factor of area = (Scale factor for length)²

The scale factor for the area of the rectangles is therefore; (1/2)² = 1/4

Area of rectangle ABCD/(Area of rectangle WXYZ) = 1/4

30/x = 1/4

x is; 30/(1/4) = 120

Area of the rectangle ABCD is about 120 square inches

The complete question found from a similar question on the website can be presented as follows;

Rectangle ABCD is similar to rectangle WXYZ. The area of ABCD is 30 square inches. Explain how to find the area x of WXYZ. AD/WZ = 1/2

AB/WX = 1/2. Because the ratio of corresponding side lengths is 1/2, the ratio of the area is equal to (___/___) to the second power. To find the area, solve the proportion 30/x = __/___ to get x = ___

Answer:

Option C: x=7

Step-by-step explanation:

We are given an equation in x and asked to solve for x

The given equation is

[tex]\frac{x+3}{5} =2[/tex]

To solve for x, we have to have only x on the left side.

So multiply the equation both sides by 5 first

We get x+3 =2(5) =10

Subtract 3 to get

x =10-3 =7

Hence 7 is the answer.

We can verify the answer by substituting for x in the given equation.

Substitute x=7 we get (7+3)/5 = 2

Thus answer is right.

In a generic rectangle, split 54 into 50 and 4, and 32 into 30 and 2. Set up these numbers around a rectangle divided into four boxes. Each box is the product of the row and column which intersect at the box. Adding up the values in the boxes gives you the product of 54 and 32.

To use a generic rectangle in multiplying 54 by 32, you first need to break both numbers down. This is part of a strategy known as partial products.

For example, think of 54 as (50 + 4) and 32 as (30 + 2). Then, set up these numbers around a rectangle, splitting it into four sections or boxes. On one side of the rectangle, put 50 and 4, and on the other side put 30 and 2. Each box represents the product of the row and column that intersect at that box.

Now, calculate the content of each box. For instance, the top left box would have 50 x 30 = 1500. The top right box would have 50 x 2 = 100. The bottom left box would have 4 x 30 = 120, and the bottom right box would have 4 x 2 = 8. The sum of the values inside the boxes (1500 + 100 + 120 + 8) results in 1728, which is the product of 54 and 32.

Using the generic rectangle to multiply numbers is a visual strategy that helps with breaking down more complex multiplication, especially when it involves larger numbers.

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Each 1/8 is 0.125, so 7*0.125 in relation to 7/8 as a decimal is 0.875.  Answer C.

Answer:

Step-by-step explanation:

As per the problem, we are given that

Toy store owner gave 47 balloons to his customers.

And there are 7 balloons left.

So we can find the total number of balloons the Toy store owner start with by adding the given numbers.

Hence total number of balloons the Toy store owner start with[tex]=47+7=54[/tex]

Final answer:

The toy store owner had 54 balloons originally. This is found by adding the 7 balloons left to the 47 given away.

Explanation:

The question is asking to find the total number of balloons the toy store owner originally had. To solve this, we use simple addition. If the owner gave away 47 balloons and has 7 left, you would add the two numbers together to find the original amount.

Step-by-Step Explanation:

Therefore, the toy store owner originally had 54 balloons.

Answer in the attachment.

Used:

[tex]\sec x=\dfrac{1}{\cos x}\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x[/tex]

The first transformation that is applied first is vertical shift.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

To apply the transformation on the function the order should be follow is

e than one transformation. Apply the transformations in this order:

1. Start with parentheses (look for possible horizontal shift)

(This could be a vertical shift if the power of x is not 1.)

2. Deal with multiplication (stretch or compression)

3. Deal with negation (reflection)

Hence, the transformation applied is vertical shift.

Learn more about transformation here:

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3° and 177°

supplementary angles sum to 180°

let x be an angle then the other angle is 59x

x + 59x = 180

60x = 180 ( divide both sides by 60 )

x = [tex]\frac{180}{60}[/tex] = 3

the angles are 3° and (59 × 3 )= 177°

To find the measures of two supplementary angles where one is fifty-nine times larger than the other, set up an equation x + 59x = 180, and solve for x. The smaller angle is 3 degrees, and the larger angle is 177 degrees.

The measure of an angle is fifty-nine times the measure of a supplementary angle. To solve this, we can set up an equation where x is the measure of the smaller angle, and therefore, 59x is the measure of the larger angle. Since angles are supplementary, their sum is 180 degrees. So, our equation is x + 59x = 180. Solving for x, we find that x = 3 degrees and 59x = 177 degrees.

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Hello,

Please, see the attached file.

Thanks.

Answer : option A

[tex]P(t)= -16t^2 -88t +720[/tex]

Top of a tall boulder = 57 foot

To find the time taken for the pebble to hit the boulder

We set p(t) = 57  and solve for t

[tex]57= -16t^2 -88t +720[/tex]

Subtract 57 on both sides

[tex]0= -16t^2 -88t +720-57[/tex]

[tex]0= -16t^2 -88t +663[/tex]

[tex]0= -(16t^2 +88t -663)[/tex]

apply quadratic formula to solve for t

[tex]t= \frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

plug in the values a = 16, b= 88 and c= -663

[tex]t = \frac{-88+-\sqrt{88^2-4(16)(-663)}}{2*16}[/tex]

[tex]t= \frac{-39}{4}[/tex] and  [tex]t= \frac{17}{4}[/tex]

t= -9.75  and t = 4.25

Time cannot be negative. So we ignore negative answer

the time taken for the pebble to hit the boulder is 4.25 seconds

Answer:Total number of side pieces [tex] = 14[/tex]

Step-by-step explanation:

To find the number of side pieces we use formula = [tex] \frac{Area of wooden plank}{Area of 1 side piece} [/tex]

Area of wooden plank [tex]= length \times width[/tex]

Length of wooden plank [tex] =\frac{77}{8}feet =\frac{77}{8} \times 12 [/tex] inches

Length [tex] = \frac{231}{2} [/tex] inches

Width of plank [tex] = \frac{9}{16} foot = \frac{9}{16} \times 12 =\frac{27}{4}[/tex] inches

Area of plank[tex]= \frac{231}{2} \times \frac{27}{4} [/tex] sq inches

Area of 1 side piece [tex]= \frac{33}{4} \times \frac{27}{4}[/tex] sq inches

Now using formula

Number of pieces [tex]= \frac{Area wooden plank}{Area of 1 side piece} [/tex]

[tex] =(\frac{231}{2} \times \frac{27}{4} )\div (\frac{33}{4} \times \frac{27}{4}) [/tex]

Converting division into multiplication we get,

[tex] =(\frac{231}{2} \times \frac{27}{4} )\times (\frac{4}{27} \times \frac{4}{33} )[/tex]

On solving we get

[tex]= 14[/tex]

Total number of side pieces [tex] = 14[/tex]

[tex]-2-\dfrac{3}{4}x=10\ \ \ \ |+2\\\\-\dfrac{3}{4}x=12\ \ \ \ |\cdot(-4)\\\\3x=-48\ \ \ \ |:3\\\\\boxed{x=-16}\\\\Answer:\ a.)\ -16[/tex]

Final answer:

To solve the equation -2 - 3/4x = 10, you first add 2 to both sides of the equation, then multiply both sides by -4/3 to get x alone. The solution to the equation is x = -16, which is option (a).

Explanation:

To solve the equation −2 − 3/4x = 10, we need to isolate x. First, we can add 2 to both sides of the equation:

−3/4x = 10 + 2

−3/4x = 12

Next, we multiply both sides by the reciprocal of −3/4, which is −4/3 to get x alone:

(−4/3)*(−3/4)x = 12(−4/3)

x = −16

Therefore, the solution is −16, which corresponds to option (a) −16.

y = f(x) + n  moves it n units up

y = f(x) - n  moves it n units down

y = f(x + n) moves it n units left

y = f(x - n) moves it n units right

y = nf(x) stretches it in the y-direction

y = 1/n f(x) compresses it

y = f(nx) compresses it in the x-direction

y = f(1/n x) stretches it

y = −f(x) Reflects it about x-axis

y = f(−x) Reflects it about y-ax

Look at the picture.

Answer: y = 3cos(x - 0.5π) + 2

D the 2 represents the two sets of length and width pairs

2(l + w) = 2l + 2w , that is 2 times length + 2 times width

Factor each one to see what they have in common:

15x² = 3 * 5 * x * x

42x³ = 2 * 3 * 7 * x * x * x

They both have: 3, x, x

When multiplied together, 3 * x * x = 3x²

Answer: 3x²