Given the expression: 12x2 + 18x − 12 Part A: What is the greatest common factor? Explain how to find it. (3 points) Part B: Factor the expression completely. Show all necessary steps. (5 points) Part C: Check your factoring from Part B by multiplying. Show all necessary steps. (2 points)

There are 6 whole weeks will it take her to save $160.

We have to given that;

Amy is going on a road trip with her friends and needs to save $160.

And, she starts saving 18% of her weekly earnings at the pool,

Now, Let number of weeks it take her to save $160 is, x

Hence, We get;

160 = 160 x 0.18 x t

t = 1/0.18

t = 5.55 weeks

Thus, There are 6 whole weeks will it take her to save $160.

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Based on the calculations, Helen needs to buy 60 feet of fence panels for her rectangular garden in the backyard

From the question, we have the following parameters that can be used in our computation:

This means that

Perimeter = 20 yards

By metrric unit of conversion, we have

1 yard = 3 feet

So, we have

Perimeter = 20 * 3 feet

Evaluate

Perimeter = 60 feet

Hence, she needs to buy 60 feet of fence panels

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The partitions coordinate are (7, -2).

We have the coordinates (8, -5) and (4, 7)

Ratio = 1 :3

Using Section Formula

x = ( 4 + 24)/ 4

x = 28/4

x= 7

and, y= (7 - 15)/4

y = -8/4

y= -2

Thus, the partitions coordinate are (7, -2).

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Answer:

cos(45°) = √2/2

B is correct.

Answer:

Step-by-step explanation: Here if we put [tex]x=0[/tex] then we will get initial temperature. That is [tex]T_0=70+20=90[/tex].

The temperature will cools down [tex]70(0.8)^{10}+20=27.52(approx)[/tex].

So the final temperature after 10 minutes will be :[tex]90-27.52=62.48(approx)[/tex].

Final Answer: The temperature is 62.48 degree Celsius.

The matrix after the row operation is:

[tex]\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right][/tex]

We have,

We use the operation R1 → R1/9.

This will give us,

Row 1 values will change to 9/9, 4/9, -9/9

So,

1, 4/9, -1

Now,

[tex]\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right][/tex]

Thus,

The matrix after the row operation is:

[tex]\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right][/tex]

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Answer:

The answer for x is 2

Step-by-step explanation:

write the equation

log6(36)= x

rewrite the equation as, x = log6(36) [ formula used; logb x=y; x=y^b]

so, x^6=36

     x^6=2^6[ 36=2^6=2*2*2*2*2*2]

thus, x=2

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One possible representation of such a vector is u = (3, 2), which has a magnitude of approximately 3.605 and makes an angle of about 33.69 degrees with the positive x-axis in the standard Cartesian coordinate system.

Firstly, it is important to understand the meaning of the double vertical bars (|| ||), which denote the magnitude or length of a vector. For instance, if we have a vector

=> v = (2, 3),

then its magnitude can be computed as

=>  ||v|| = √(2² + 3²) = √13.

Similarly, if we have a vector u = (u₁, u₂), then its magnitude can be expressed as

=>  ||u|| = √(u₁² + u₂²).

The given condition

=> ||-4u|| ≈ 14.42

can be rewritten as

=>  4||u|| ≈ 14.42

=>  ||u|| ≈ 3.605.

This means that the magnitude of vector u is approximately equal to 3.605.

Therefore, to obtain a possible representation of vector u with a magnitude of approximately 3.605, we can solve the following system of equations:

||u|| = √(u₁² + u₂²) ≈ 3.605

θ = tan⁻¹(u₂/u₁)

Note that there are infinitely many solutions to this system, since the direction of u is not uniquely determined.

However, one possible solution is u = (3, 2), which has a magnitude of

=> ||u|| = √(3² + 2²) = √13 ≈ 3.605

and makes an angle of

=> θ = tan⁻¹(2/3) ≈ 33.69 degrees

with the positive x-axis.

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Probability of landing on space with polka dots = 3/8.

Probability of landing on space with stripes = 1/2.

Probability of landing on space with stripes and even numbers = 1/4.

Probability of landing on space with stripes or even numbers = 5/8.

Hence the code is 'AFCH'.

From the definition of Probability we know that,

Probability of event = (Number of Favorable outcomes)/(Total number of outcomes)

Here total number of spaces = 8.

Number of space with polka dots = 3 [space numbered 1, 4, 6]

Number of space with stripes = 4 [space numbered 0, 2, 3, 5, 7]

Number of space with stripes and even numbers = 2 [the space numbered 0 and 2]

Probability of landing on space with polka dots = 3/8 (A)

Probability of landing on space with stripes = 4/8 = 1/2 (F)

Probability of landing on space with stripes and even numbers = 2/8 = 1/4 (C)

So, Probability of landing on space with stripes or even numbers

= Probability of landing on space with polka dots + Probability of landing on space with stripes - Probability of landing on space with stripes and even numbers

= 3/8 + 1/2 - 1/4

= (3 + 4 - 2)/8

= 5/8 (H).

Hence the code will be 'AFCH'.

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Answer: 2.1468 times 10^15

Step-by-step explanation: you times them together

The expression that is equivalent to 2.76 is two and nineteen twenty fifths

The number in the question is given as 2.76

This means that we have

Number = 2.76

We can rewrite this as a mixed number.

2 + a/b

Such that:

a/b = 0.76

From the list of options, we have

two and nineteen twenty fifths = 2 + 19/25 = 2.76

This means that the correct expression is two and nineteen twenty fifths

Hence, the expression that is equivalent to 2.76 is two and nineteen twenty fifths

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Complete question

Which of the following is equivalent to 2.76?

2.76%

27.6%

two and nineteen twenty fifths

twenty five over nineteen

The value of the variable x is 51.340 degrees

Note that their are six different trigonometric identities in mathematics.

These identities are;

Also, these identities have their different ratios, they are;

sin θ= opposite/hypotenuse

tan θ = opposite/adjacent

cos θ = adjacent/hypotenuse

From the information given, we have that;

Opposite = 10cm

Adjacent = 8cm

Substitute the values

tan x = 10/8

Divide the value, we have;

tan x = 1.25

Find the tangent inverse, we get;

x = 51. 340 degrees

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Step-by-step explanation:

If this is a regular pentagon , it has FIVE sides of equal length

 64 ÷ 5 = 12.8 units = AB

Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

[tex]\sf P =\dfrac{F}{1+r\div n}^{(nt)[/tex]

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

[tex]\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}[/tex]

[tex]\sf P = \dfrac{1000}{(1.0375)^{10}}[/tex]

[tex]\sf P = \dfrac{1000}{1.4450}[/tex]

[tex]\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)[/tex]

Therefore, the price of the zero coupon bond is $692.04.

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The length of the given rectangular cuboid is: 9 cm

In geometry, a rectangular prism is defined as a polyhedron with two congruent as well as parallel bases. It is also referred to as a cuboid. A rectangular prism is one that possesses six faces, and then all the faces are located in a rectangle shape and possess twelve edges. Whenever its cross-section along the length, it is referred to as a prism.

The formula for the volume of a prism is given by the formula:

V = L * W * H

Where:

L is length

W is width

H is height

We have that Volume = 432 cm³

Thus:

6 * L * 8 = 432

48L = 432

L = 432/48

L = 9 cm

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using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Answer:

25% probability

Step-by-step explanation:

2x2=4

1x1=1

1 out 4 is shaded red

1 out of 4 is 1/4 which is 25%

The lateral surface area of the pyramid is 112 sq. in.

The correct answer is an option (B)

From the attached figure of the net of a square pyramid, we can observe that the side length of the square base is 8 in and height of the lateral triangular face is 7 in.

The lateral surface area of the pyramid is equal to the area of the four triangular faces of the pyramid.

Using the formula of the area of triangle, the lateral surface area would be,

A = 4 × (1/2 × base × height)

A = 4 × (1/2 × 8 × 7)

A = 4 × (4 × 7)

A = 4 × 28

A = 112 sq. in.

This is the required lateral surface area.

The correct answer is an option (B) 112 in²

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Find the complete question below.

The net below shows a square pyramid. What is the lateral surface area? A. 176 in^2

B. 112 in^2

C. 64 in^2

D. 210 in^2

Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

Answer:

80 points

Step-by-step explanation:

If score in English is x points and score in math is 5% higher then score in math

y = x + 0.05x

where 0.05 = 5% expressed as decimal

0.05x refers to the 5% increase in score

y = math score

y = x(1 + 0.05)

y = 1.05x

Given score in math = 84 this becomes

84 = 1.05x

x = 84/1.05

x = 80

So Emily's score in English was 80 points

The team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.

We can derive an inequality from the problem statement which is:

8X + 12Y ≥ 1000

This inequality represents the amount of money the basketball team needs to raise by selling donuts.

X is the number of half dozen boxes sold

Y is the number of full dozen boxes sold.

To find a solution in terms of the given context, we can plug in different values for X and Y that satisfy the inequality. For example:

If the team sells 50 half dozen boxes and 50 full dozen boxes, they will make:

8(50) + 12(50) = $400 + $600 = $1000

So this is a valid solution that meets the fundraising goal.

If the team sells 100 half dozen boxes and 0 full dozen boxes, they will make:

8(100) + 12(0) = $800

This is not enough to meet the fundraising goal, so it is not a valid solution.

If the team sells 0 half dozen boxes and 100 full dozen boxes, they will make:

8(0) + 12(100) = $1200

This is more than the fundraising goal, so it is a valid solution, but the team may not want to sell so many full dozen boxes.

Therefore, one solution in terms of the given context is that the team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.

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The maximum number of toothbrushes the dentist can purchase is 50.

Let's denote the number of toothbrushes the dentist orders by "x".

If the dentist orders less than 50 toothbrushes, then the cost of the toothbrushes will be 2.58x.

If the dentist orders 50 or more toothbrushes, then the cost of the toothbrushes will be 1.24x.

There is a base cost of [tex]$48[/tex] for printing the dentist's name and address on the toothbrushes.

The total cost of the order can be expressed as:

Total cost = 48 + (2.58x) for x < 50

Total cost = 48 + (1.24x) for x ≥ 50

The maximum number of toothbrushes the dentist can purchase, given that the budget is [tex]$110[/tex].

So we can set up an equation:

Total cost = 110

For x < 50:

48 + 2.58x = 110

2.58x = 62

x ≈ 24.03

For x ≥ 50:

48 + 1.24x = 110

1.24x = 62

x ≈ 50

The maximize number of toothbrushes, we choose the larger value of x, which is x ≈ 50.

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The regular admission price for one adult is $17.50.

We have,

Let's first determine the total cost of admission after the coupons have been applied.

Since each person has a coupon for $5 off, the total discount for the group is $5 x 6 = $30.

The total cost of admission after the discount.

$105 - $30

= $75.

Let A be the regular admission price.

Since each person paid the same price after the discount, we can set up the following equation:

6(A - $5) = $75

We subtract $5 from the regular price A because that is the amount of the coupon discount.

We can simplify the equation as follows:

6A - $30 = $75

6A = $105

A = $17.50

Therefore,

The regular admission price for one adult is $17.50.

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The value of x in the quadrilateral is 70 degrees

To find the value of the fourth interior angle, we can use the fact that the sum of all four interior angles is equal to 360 degrees. We can set up an equation:

85 + 150 + 55 + x = 360

where x is the fourth interior angle we want to find. To solve for x, we can first simplify the left side of the equation by adding the known angles:

290 + x = 360

Then, we can isolate x by subtracting 290 from both sides:

x = 360 - 290

x = 70

Therefore, the value of x when the interior angles of the quadrilateral are 85, 150, and 55 degrees is 70 degrees. This means that the four interior angles of the quadrilateral are 85, 150, 55, and 70 degrees, and their sum is indeed equal to 360 degrees.

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Answer: elephant

Step-by-step explanation:

3/5 x 345 = 207

345 > 207

(A) The preimage is ABC.

(B) The image is A'B'C'.

(C) The coordinates of the output are:

A(0,9) reflects over the line of reflection to A'(0,-9).

B(-4,4) reflects over the line of reflection to B'(4,-4).

C(0,4) reflects over the line of reflection to C'(0,-4).

In geometry, a reflection is a type of transformation where a figure is flipped over a line, called the line of reflection. In this problem, ABC-A'B'C' is a reflection, which means that it is a transformation of a figure where each point of the original figure has a corresponding point in the reflected figure such that the line of reflection is the perpendicular bisector of the line segment joining each point to its corresponding point.

A) The preimage is the original figure, which is ABC.

B) The image is the reflected figure, which is A'B'C'.

C) The coordinates of the output are:

A(0,9) reflects over the line of reflection to A'(0,-9).

B(-4,4) reflects over the line of reflection to B'(4,-4).

C(0,4) reflects over the line of reflection to C'(0,-4).

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