Which expressions are equivalent to 7 (negative three-fourths x minus 3)? Select two options.

Final answer:

To solve the equation 5(x+2)=24-2x, distribute, combine like terms, solve for x, and check the solution. The solution x = 2 satisfies the equation, so it is valid.

Explanation:

To solve the equation 5(x+2)=24-2x, we can justify each step as follows:

Distribute the 5 to the terms inside the parentheses: 5x + 10 = 24 - 2x

Combine like terms on both sides of the equation: 5x + 2x = 24 - 10

Combine the x terms: 7x = 14

Divide both sides of the equation by 7 to solve for x: x = 2

Check the solution by substituting it back into the original equation: 5(2+2) = 24 - 2(2)

Simplify the left side: 5(4) = 24 - 4

Multiply: 20 = 20

The solution x = 2 satisfies the equation, so it is valid.

Answer:

y=4x+40

Step-by-step explanation:

The equation  best shows the relationship between x and y is y = 4x + 40.

Given that,

John's total earnings, y, from selling x bars of ice cream

So based on this, the following equation should be considered

y = 4x + 40

Therefore, the last option is correct.

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Answer:

810 cubes

Step-by-step explanation:

step 1

Find the volume of the rectangular prism

The volume of the rectangular prism is

[tex]V=LWH[/tex]

we have

[tex]L=2\frac{1}{2}\ in=2+\frac{1}{2}=\frac{5}{2}\ in[/tex]

[tex]W=2\ in\\H=6\ in[/tex]

substitute

[tex]V=(\frac{5}{2})(2)(6)[/tex]

[tex]V=30\ in^3[/tex]

step 2

Find the volume of the cube

The volume of the cube is

[tex]V=b^3[/tex]

where

b is the length side of the cube

we have

[tex]b=\frac{1}{3}\ in[/tex]

substitute

[tex]V=(\frac{1}{3})^3[/tex]

[tex]V=\frac{1}{27}\ in^3[/tex]

step 3

Find out how many unit cubes with edge lengths of 1/3 inch can fit inside the prism

Divide the volume of the prism by the volume of the cube

[tex]30:\frac{1}{27}=30(27)=810\ cubes[/tex]

Missing value is Decreased by 20%

Step-by-step explanation:

We need to find the missing term.

As we can see from the figure we go from Decreased 10% and then decreased 10% to reach the final goal.

If we directly go from starting point to end point the total will be decreased by 20% as (10%+10%= 20%)

So, Missing value is Decreased by 20%

(–4, 3) (4, –3) (–3, –4) (3, 4)

this is a rather simple yet complex concept the easiest way to solve these is to do the exact opposite.

so in this instance it is refrcted across the y-axiss so we swap ONLY the x value NOT the Y ie (-4,3) would switch to (4,3)

same thing would apply if it reflected across x-axis ex (-4,-3)

If it reflect across orgin you change both signs. ex (4,-3)

ie.

(–4, 3) (4, –3) (–3, –4) (3, 4)

changes to

(4, 3) (-4, –3) (3, –4) (-3, 4)

hope it helps

The coordinates of the image of vertex R after a reflection across the y-axis is (3, 4).

A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state.

Given is a point R = (-3, 4) we need to find the coordinates of the point R after it being reflected over y-axis,

So, we know that,

When dealing with reflection of a line or shape or a figure in the coordinate plane, especially if it is reflected across the y-axis, you just have to give the opposite of the given (original) x- coordinate in order to give a symmetric figure.

The rule of reflection over y-axis is =

(x, y) = (-x, y)

So,

R = (-3, 4), after it being reflected over y-axis =

R' = (3, 4)

Hence the coordinates of the image of vertex R after a reflection across the y-axis is (3, 4).

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Answer:

[tex]Apple\ muffin\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Bran\ muffin\\10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4\\15\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6\\20\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8\\35\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 14[/tex]

Step-by-step explanation:

[tex]For\ 5\ apple\ muffins, bran\ muffin=2\\\\Ratio\ of\ bran\ muffin\ to\ apple\ muffin=\frac{number\ of\ bran\ muffin}{number\ of\ apple\ muffin}\\\\Ratio\ of\ bran\ muffin\ to\ apple\ muffin=\frac{2}{5}\\\\Bran\ muffin=\frac{2}{5}\times apple\ muffin\\\\When\ apple\ muffin=10\\\\Bran\ muffin=\frac{2}{5}\times 10=4\\\\When\ apple\ muffin=15\\\\Bran\ muffin=\frac{2}{5}\times 15=6\\\\When\ apple\ muffin=20\\\\Bran\ muffin=\frac{2}{5}\times 20=8[/tex]

[tex]When\ apple\ muffin=35\\\\Bran\ muffin=\frac{2}{5}\times 35=14[/tex]

Answer:

426.9 Km²

Step-by-step explanation:

The shaded area is the area of the triangle subtract the area of the circle.

Area of triangle = 0.5 bh ( b is the base and h the perpendicular height )

Here b = 40 and h = 27, thus

Area = 0.5 × 40 × 27 = 20 × 27 = 540 Km²

Area of circle = πr² ← r is the radius

Here the diameter is 12, thus radius = 12 ÷ 2 = 6

Area = π × 6² = 36π ≈ 113.1 Km²

Shaded area = 540 - 113.1 = 426.9 Km²

Answer:

c) 8.6

Step-by-step explanation:

Take the coordinates of the two points.

(0,8) and (7,3)

Formula:

√(x₁ - x₂)² + (y₁ - y₂)²

Substitute:

√(0 - 7)² + (8 - 3)²

√(-7)² + (5)²

√(49) + (25)

√(74) ≈ 8.6

The question appears to be incomplete as it doesn't provide the necessary coordinates for calculating the length of a line segment. The distance formula or Pythagorean theorem would generally be used to calculate this in Mathematics.

Given the format of the question, it seems that it's incomplete or missing the relevant coordinates we need to calculate the length of a line segment. Normally in mathematics, we would use the distance formula, or Pythagorean theorem, to compute the length of a line segment between two points in a plane. The formula is √[(x₂-x₁)² + (y₂-y₁)²], where (x₁,y₁) and (x₂, y₂) are the coordinates of the two points. In this scenario, without information about the coordinates, we can't compute the length of a line segment. However, if you provided me with the coordinates, I can guide you in computing the length of the line segment.

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Answer:

x=14

Step-by-step explanation:

not sure what your asking for???

x-5=9

x=14

Answer:

x = 3.6

Step-by-step explanation:

The 2 chords intersect inside the circle, thus

The product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord, that is

5x = 6 × 3 = 18 ( divide both sides by 5 )

x = 3.6

Answer:

y=-4/3x+2

Step-by-step explanation:

Answer:

THE ANSWER IS 1.2068965517

Step-by-step explanation:

Answer:

34+22=56+16=72 100-72=28 feet

Step-by-step explanation:

Answer:

x=-12

Step-by-step explanation:

2-3/4x=11

3/4x=2-11

3/4x=-9

x=-9/(3/4)

x=(-9/1)(4/3)

x=-36/3

x=-12

Answer:

x-2

Step-by-step explanation:

x-4+2 = x-2

Answer:

x^2 - 2x - 8

Step-by-step explanation:

Answer:

Angles: 42°, 114°, 24°, 30°, 150°.

Step-by-step explanation:

Pie Charts

They represent the comparative values of a given variable subject to study. The whole pie is cut in angular sections where all the angles must sum 360°. If the sum of all the values is S and one particular value is x, then the angle of its circular section is given by

[tex]\displaystyle angle=\frac{x}{S}\ 360^o[/tex]

We have the staff of an office is S=60. When asked about their favorite type of takeaway we get:

Pizza: 7. Its corresponding angle is

[tex]\displaystyle angle=\frac{7}{60}\ 360^o=42^o[/tex]

Curry 19.

[tex]\displaystyle angle=\frac{19}{60}\ 360^o=114^o[/tex]

Fish & chips 4

[tex]\displaystyle angle=\frac{4}{60}\ 360^o=24^o[/tex]

Kebab 5

[tex]\displaystyle angle=\frac{5}{60}\ 360^o=30^o[/tex]

Other 25

[tex]\displaystyle angle=\frac{25}{60}\ 360^o=150^o[/tex]

We can see the sum of all angles is 360°

The angles for the pie chart are as follows:

- Pizza: 42 degrees

- Curry: 114 degrees

- Fish & chips: 24 degrees

- Kebab: 30 degrees

- Other: 150 degrees

These angles can be used to create a pie chart that accurately represents the favorite take-away choices of the office staff.

To calculate the size of each angle for the pie chart representing the favorite take-away choices of the 60 office staff, we need to determine the percentage each category represents in the total.

First, add up the frequencies:

Pizza + Curry + Fish & chips + Kebab + Other = 7 + 19 + 4 + 5 + 25 = 60

Now, calculate the percentage for each category:

- Pizza: (7/60) * 100% = 11.67%

- Curry: (19/60) * 100% = 31.67%

- Fish & chips: (4/60) * 100% = 6.67%

- Kebab: (5/60) * 100% = 8.33%

- Other: (25/60) * 100% = 41.67%

Now that we have the percentages, we can calculate the corresponding angles for the pie chart.

Each percentage corresponds to a fraction of the total 360 degrees in a circle.

So, for example, Pizza would be (11.67/100) * 360 = 42 degrees, Curry would be (31.67/100) * 360 = 114 degrees, and so on.

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Answer: 251,203

Step-by-step explanation:

Martin pays 965 every month for seven years. Therefore,

965×12×7= 81,060

Then, he has a balloon payment of 170,143 to make. Therefore, totaal financed price he paid for his home is 81,060+170,143= 251,203.

Answer: 251,203

Step-by-step explanation:

Martin pays 965 every month for seven years. Therefore,

965×12×7= 81,060

Then, he has a balloon payment of 170,143 to make. Therefore, totaal financed price he paid for his home is 81,060+170,143= 251,203.

Answer:

4

Step-by-step explanation:

The first digit after the decimal point is the tenths place. in this case, it would be 4

Answer:

4 Is in the tenths place

Step-by-step explanation:

7 in the hundreds

2 in the tens

9 in the ones

4 in the tenths

6 in the hundredths

Answer: 2

Step-by-step explanation:

2 times 4 = 8

8 plus 6 = 14

14 divided by 2 = 7

7 squared = 49

49 minus 9 = 40

40 divided by 2 = 20

In this problem we convert the operations into an equation and solve it step by step until we get two possible answers. We pick the one that fits the conditions of the problem, which gives us 9 as the positive number the student had originally thought of.

Let's denote the number you are thinking of as x. Following your sequence of operations we can translate this into an equation:

(((4x + 6) / 2)² - 9) / x = 20

Solving this equation can be done step by step:

Since you mentioned that the number you thought of was positive, we disregard 0.25 (since the squared result after the first operations would be too small to subtract 9 and still divide by the original number to get 20). Therefore, the number you thought of was 9.

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Answer:

1.067

Step-by-step explanation:

Answer:

25Ncm^2

Step-by-step explanation:

Pressure = force/area

Force = 2000N

Area = 80cm^2

Therefore,

Pressure = 2000/80

= 25Ncm^2

Answer:

Length is w-5

Area  = length x width

84 = (w-5)w

84 = w^2 - 5w

0 = w^2 - 5w - 84

0 = (  w     -    12 )( w   +     7    )

w + 7 = 0 leads to negative measures.

w-12=0 ---> w = 12

width is 12, length is 5 less, or 7

The dimensions of the rectangle are 12 feet by 7 feet, determined by solving the quadratic equation derived from the relationship between the length and width and the given area of the rectangle.

To find the dimensions of a rectangle where the length is five feet less than its width and the area is 84 square feet, we can set up an equation. Let's define the width of the rectangle as w feet. Then, the length would be w - 5 feet. Since the area of a rectangle is defined as the product of its length and width, we get the following equation:

w times (w - 5) = 84

Expanding the left side gives us:

w^2 - 5w = 84

To solve this quadratic equation, move all terms to one side to set the equation to zero:

w^2 - 5w - 84 = 0

Factoring the quadratic equation, we look for two numbers that multiply to give -84 and add to give -5. These numbers are -12 and +7. So the equation factors as follows:

(w - 12)(w + 7) = 0

The solutions to the equation are w = 12 and w = -7. However, width cannot be negative in this context, so we discard w = -7. Thus, the width is 12 feet and the length is 12 - 5 = 7 feet.

Therefore, the dimensions of the rectangle are 12 feet by 7 feet.

Answer:

The height of the pyramid is 13.3 inches

Step-by-step explanation:

Let

h ----> the height of the pyramid

b ---> the base of the square pyramid

we know that

Applying the Pythagorean Theorem

[tex]15^2=h^2+(\frac{b}{2})^2[/tex]

see the attached figure to better understand the problem

we have

[tex]b=14\ in[/tex]

substitute

[tex]15^2=h^2+(\frac{14}{2})^2[/tex]

Solve for h

[tex]225=h^2+49\\h^2=225-49\\h^2=176\\h=\sqrt{176}\ in\\h=13.3\ in[/tex]

Answer:

Let the quadratic equation be  [tex]2x^2 +12x+ 6[/tex]

Step 1: Take the coefficients of the [tex]x^2[/tex] term and divide the entire equation

Here the coefficient of [tex]x^2[/tex] is 2

So  dividing the entire equation by 2, we get

[tex]x^2 +6x+ 3[/tex]

Step 2:  Move the constant term to the right side of the equation

[tex]x^2 +6x = - 3[/tex]

Step 3: Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation

[tex](\frac{b}{2})^2[/tex] =  [tex](\frac{6}{2})^2[/tex] = [tex](3)^2[/tex]  =  9

[tex]x^2 +6x + 9 = - 3 +9[/tex]

[tex](x+3)^2 = 6[/tex]

Step 4: Take the square root on both sides of the equation

[tex](x+3) = \sqrt{6}[/tex]

[tex]x+3 = \pm 2.45[/tex]

Step 5 Subtract 3 from both sides:

[tex]x+3 - 3 = \pm 2.45 -3[/tex]

[tex]x = \pm 2.45 -3[/tex]

x =  2.45 - 3   or x = -2.45 - 3

x = - 0.55  or  x = -5.45

Answer:

The term to add is

[tex]-\frac{1}{3} x[/tex]

Step-by-step explanation:

Let

b ----> the term to add

we have

[tex]\frac{5}{6}x-4+b=\frac{1}{2} x-4[/tex]

Solve for b

Adds 4 both sides

[tex]\frac{5}{6}x+b=\frac{1}{2} x[/tex]

subtract 5/6x both sides

[tex]b=\frac{1}{2} x-\frac{5}{6}x[/tex]

Remember that

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

substitute

[tex]b=\frac{3}{6} x-\frac{5}{6}x[/tex]

[tex]b=-\frac{2}{6} x[/tex]

Simplify

[tex]b=-\frac{1}{3} x[/tex]

therefore

The term to add is

[tex]-\frac{1}{3} x[/tex]

Answer:

A

Step-by-step explanation:

Answer:

Length of the ladder used by worker = 17 feet

Step-by-step explanation:

Given:

Height of the window from the ground = 13 ft

Distance of fence from the building = 3 ft

Distance of ladder from the building = (3+8) = 11 ft

We have to find the length of the ladder.

Let the length of the ladder be 'x'

From the diagram we can also say that 'x' is the hypotenuse of the right angled triangle.

Using Pythagoras formula:

⇒ [tex]hypotenuse\ 'x' =\sqrt{(perpendicular)^2+(base)^2}[/tex]

Here base length = 11 ft

Perpendicular = 13 ft

Plugging the values:

⇒ [tex]x=\sqrt{(13)^2+(11)^2}[/tex]

⇒  [tex]x=\sqrt{(169+121)}[/tex]

⇒ [tex]x= \sqrt{290}[/tex]

⇒ [tex]x=17.02[/tex] feet

The length of the ladder = 17 feet to its nearest tenth.

The worker will need a ladder that is approximately 8.5 feet long. This calculation is based on the Pythagorean theorem, considering the ladder's placement 8 feet from the fence and the need to reach a window 13 feet above the ground.

To find the length of the ladder the worker needs, we can use the Pythagorean theorem, as the ladder, the distance from the building, and the distance from the fence form a right triangle.

Let:

L be the length of the ladder.

D be the distance from the building to where the ladder rests (8 ft).

F be the distance from the fence to where the ladder rests (3 ft).

According to the Pythagorean theorem, we have:

[tex]L^2 = D^2 + F^2[/tex]

Substitute the known values:

[tex]L^2 = 8^2 + 3^2[/tex]

[tex]L^2 = 64 + 9[/tex]

[tex]L^2 = 73[/tex]

Now, take the square root of both sides:

L ≈ √73 ≈ 8.54 ft (rounded to the nearest tenth)

So, the worker will need a ladder that is approximately 8.5 feet long to safely reach the window 13 feet above the ground when placed 8 feet from the fence for stability.

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Answer:

Tony make 4 half-court shots and misses 16 half-court shots.

Step-by-step explanation:

Given:

Points earned for every successful, half-court shots = [tex]20[/tex]

Points deducted for missing the shots = [tex]5[/tex] or [tex]-5[/tex]

Total number of shots in the game = [tex]20[/tex]

Final points earned by Tony = [tex]0[/tex]

According to the question:

Let the number of successful half-court shot be [tex]x[/tex]

And the number of shots missed be [tex]20-x[/tex]

So,

In terms of points we can re-write it as:

⇒ [tex]20(x)-5(20-x) =0[/tex]

⇒ [tex]20x-100+5x=0[/tex]

⇒ [tex]25x-100=0[/tex]

⇒ [tex]25x-100+100=100[/tex]

⇒ [tex]25x=100[/tex]

⇒ [tex]\frac{25x}{25} =\frac{100}{25}[/tex]

⇒ [tex]x=\frac{100}{25}[/tex]

⇒ [tex]x=4[/tex]

Tony make 'x' shots that is 4 and the number of shot he missed is (20-x) =(20-4)=16

Answer:

C)Rhomus

Step-by-step explanation:

a rhombus is parallel

The correct answer is option C. The shape Amily's riddle best describes is Rhombus.

Let's analyze the riddle step by step to determine which shape Amily is describing.

1. Quadrilateral: The shape has four sides.

2. All sides are parallel: This indicates that opposite sides are parallel to each other, which means the shape is a type of parallelogram.

3. 4 angles, but they are not all equal: This means that although the shape has four angles, they are not all the same measure.

Given these clues, let's evaluate each option:

A) Pentagon: This is a five-sided shape, not a quadrilateral. So, this option is incorrect.

B) Rectangle: A rectangle has four sides and opposite sides are parallel. However, all the angles in a rectangle are equal (each angle is 90 degrees). So, this option is also incorrect.

C) Rhombus: A rhombus has four sides and opposite sides are parallel. Additionally, all sides are of equal length. However, a rhombus can have angles that are not all equal (typically, it has two pairs of equal angles). Given the description, this could be a potential answer, but let’s also consider the last option.

D) Trapezoid: A trapezoid has one pair of parallel sides. However, the riddle specifies that all sides are parallel, which does not match the definition of a trapezoid.

Given that the shape described has all sides parallel and the angles are not all equal, the best match is C) Rhombus.

Answer:

The answer is [6 18}

Step-by-step explanation:

I just took the test :)

The product of the matrices [4 2] and [-2 5 7 -1] is a 1x4 matrix. The resulting matrix is [-8 -4 20 10].

In order to find the product of two matrices, we need to ensure that the number of columns in the first matrix matches the number of rows in the second matrix. The first matrix, [4 2], has 1 row and 2 columns (1x2), while the second matrix, [-2 5 7 -1], has 2 rows and 4 columns (2x4). Since the number of columns in the first matrix matches the number of rows in the second matrix, we can proceed with matrix multiplication.

To compute the product, we perform the following steps:

Step 1: Take the first row of the first matrix and multiply each element by the corresponding element in the first column of the second matrix.  

- First element: 4 * (-2) = -8  

- Second element: 2 * (-2) = -4

Step 2: Take the first row of the first matrix and multiply each element by the corresponding element in the second column of the second matrix.  

- Third element: 4 * 5 = 20  

- Fourth element: 2 * 5 = 10

Step 3: Now, we have the elements for the first row of the resulting matrix: [-8 -4 20 10].

Step 4: Repeat the above steps for the second row of the first matrix.

Step 5: Combine the results to form the final product matrix: [-8 -4 20 10].

So, the product of the matrices [4 2] and [-2 5 7 -1] is the 1x4 matrix

[-8 -4 20 10].

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