The question​ of the week! (Please show your work!)

Sarah's craft project uses pieces of yarn that are 1/8 yard long. She has a piece of yarn that is 3 yards long. How many 1/8 yard pieces can she cut and still have 1 1/4 yards left?

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

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 formula of a slope:

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

We have (4, -5) and (0, -13).

Substitute:

[tex]m=\dfrac{-13-(-5)}{0-4}=\dfrac{-13+5}{-4}=\dfrac{-8}{-4}=2[/tex]

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 phrase 'five more than twice the square root of four' is a mathematical expression which evaluates to 9. The operation uses addition, multiplication, and square root.

The student is asking for the result of a mathematical expression combining addition, multiplication, and square root operations. It can be written like "5 + 2(sqrt(4))". The square root of four (sqrt(4)) is two. So, the expression becomes "5 + 2*2", which equals 5 plus 4, resulting in 9. Therefore, five more than twice the square root of four equals nine.

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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:

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.

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

The slope of the linear equation C(x) = 8x + 50 is 8, indicating an $8 charge per mile, and the y-intercept is 50, the flat towing fee. Similar service-based costs from other examples also follow this linear model, with their unique slopes and y-intercepts corresponding to the per-hour or per-mile charges and flat fees.

The function C(x) = 8x + 50 represents the cost of towing a vehicle, where C is the cost in dollars, and x is the number of miles the vehicle is towed. The slope of this line is 8, which indicates that the cost increases by $8 for every mile the vehicle is towed. The y-intercept is 50, representing the flat fee charged regardless of the distance towed, which is the cost when x (the number of miles) is 0.

Relating to the other examples provided, we can see a pattern in how these equations are structured for service-based costs. For instance, in Aaron's Word Processing Service, the total cost equation is y = 32x + 31.50, where the slope is 32 representing the hourly charge, and the y-intercept is 31.50, the fixed cost. Similarly, for Ethan's household appliance repairs, the equation is y = 20x + 25, with a slope of 20 and a y-intercept of 25. All these models illustrate how fixed fees and variable rates per service hour or mile can be represented in a linear equation format.

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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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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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Answer is (3,1)

x + y = 4

2x + 3y = 9

We multiply the first equation by -2  to eliminate x

-2x - 2y = -8

2x + 3y = 9

-------------------(add both equations)

0 + y = 1

So y =1

Now plug in 1 for y in first equation

x + y = 4

x + 1 = 4

Subtract 1 on both sides

x = 3

Answer is (3,1)

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

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

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.

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 = ___

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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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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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.

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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Answer: ∠Z = 117.2°

Step-by-step explanation:

∠X and ∠Y are isosceles so they are congruent (equal to each other)

5x + 33 = 33x + 42

-5x           -5x          

         33 = 28x + 42

        -42            -42

        -9   =  28x

        [tex]\frac{-9}{28} = \frac{28x}{28}[/tex]

        [tex]-\frac{9}{28} = x[/tex]

************************************************************

∠X + ∠Y + ∠Z = 180°                Triangle angle sum theorem

5x + 33 + 33x + 42 + ∠Z = 180°

38x + 75 + ∠Z = 180°

        -75              -75

38x          + ∠Z = 105°

38[tex](-\frac{9}{28})[/tex]      + ∠Z = 105°

-12.2         + ∠Z = 105°

+12.2                     +12.2

                     ∠Z = 117.2°

Answer:

Dodecahedron

Step-by-step explanation:

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

The first one is correct it is a Quadratic Polynomial.

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

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]