(SAT Prep) Find the value of x in each of the following exercises:

Answer:

[tex]\large\boxed{(1+2x^3)^2=4x^6+4x^3+1}[/tex]

Step-by-step explanation:

[tex](1+2x^3)^2\\\\\bold{METHOD\ 1:}\\\\(1+2x^3)^2=(1+2x^3)(1+2x^3)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(1)(1)+(1)(2x^3)+(2x^3)(1)+(2x^3)(2x^3)\\\\=1+2x^3+2x^3+4x^6\qquad\text{combine like terms}\\\\=1+4x^3+4x^6[/tex]

[tex]\bold{METHOD\ 2:}\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(1+2x^3)^2=1^2+2(1)(2x^3)+(2x^3)^2\\\\=1+4x^3+2^2(x^3)^2\\\\=1+4x^3+4x^6[/tex]

Answer:

39mm

Step-by-step explanation:

Final answer:

Using the scale factor of 3:1, the length of side WZ from trapezoid WXYZ can be calculated by dividing the known length of side SV from trapezoid STUV by the scale factor. The length of WZ is found to be 51 mm.

Explanation:

If trapezoid STUV is a scaled version of trapezoid WXYZ with a scale factor of 3:1, we can use this scale factor to determine the length of side WZ given the lengths of ST and SV. To find the length of WZ, we divide the length of SV by the scale factor. Since SV = 153 mm and the scale factor is 3, we perform the division 153 mm / 3 to get 51 mm as the length of WZ.

A proportion is a mathematical statement that two ratios or fractions are equal. It is used to express the equality of two fractions that compare two numbers or quantities to each other. For example, if we have two fractions a/b and c/d, a proportion states that these two fractions are equivalent: a/b = c/d. Proportions are fundamental in various branches of mathematics and applications, including solving problems involving scales, maps, and ratios in real-life scenarios.

Answer:

4m

Step-by-step explanation:

since it is not multiplication, there would be no power.

think of it as 2m + 1m + 1m

The answer is 4m

I hope this helped! If so, please mark brainliest!

Answer:

0.033

Step-by-step explanation:

Use binomial probability:

P = nCr pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

Here, p = 0.5, q = 0.5, and n = 11.

We need to find P when r is 0, 1, and 2, then add up the results to get the total probability.

r = 0:

P = ₁₁C₀ (0.5)⁰ (0.5)¹¹⁻⁰

P ≈ 0.0005

r = 1:

P = ₁₁C₁ (0.5)¹ (0.5)¹¹⁻¹

P ≈ 0.0054

r = 2:

P = ₁₁C₂ (0.5)² (0.5)¹¹⁻²

P ≈ 0.0269

Therefore, the total probability is:

P = 0.0005 + 0.0054 + 0.0269

P = 0.0328

Round to the thousandths place, the probability is 0.033.

Answer:

There is no answer.

0 is rational since it can be written as a fraction (0/5, 0/69)

1 is obviously rational. 7/8 is .875 and 5 1/4 is 5.25

Answer:

[tex]9\ pounds[/tex]

Step-by-step explanation:

Let

x ----> the number of pounds of a DVD player

we know that

The number of pounds of a DVD player multiplied by the cost per pound ($0.55) plus the charge of $6.99 must be equal to $11.94

so

The linear equation that represent this situation is

[tex]0.55x+6.99=11.94[/tex]

solve for x

subtract 6.99 both sides

[tex]0.55x=11.94-6.99[/tex]

[tex]0.55x=4.95[/tex]

divide by 0.55 both sides

[tex]x=9\ pounds[/tex]

Answer:

m/d = V

Step-by-step explanation:

Answer:

m/d=V

Step-by-step explanation:

I did the quiz

Answer:

B. x² + 16x + 15

Step-by-step explanation:

Area of parallelogram = base x height

A = (x + 15) (x + 1) = x² + 16x + 15

Answer:

The fractions [tex]\frac{3}{9},\frac{3}{10},\frac{3}{11},\frac{3}{12}[/tex] are not in order from least to greatest.

Step-by-step explanation:

Given order of fractions from least to greatest:

[tex]\frac{3}{9},\frac{3}{10},\frac{3}{11},\frac{3}{12}[/tex]

To check if the fractions are in correct order.

Solution:

The fractions given have same numerators but different denominators.

For fractions the higher the denominator the lower is the value of that fraction.

Thus, in the given list the least value fraction will be the fraction with the greatest denominator which is [tex]\frac{3}{12}[/tex] and the greatest value fraction will be the fraction with the least denominator which is [tex]\frac{3}{9}[/tex]

So, the order of the fractions from least to greatest is not correct. Instead the order is from greatest to least.

The correct order from least to greatest should be:

[tex]\frac{3}{12},\frac{3}{11},\frac{3}{10},\frac{3}{9}[/tex].

Answer:

Paul. He has made 60 pizzas after 9 days.

Step-by-step explanation:

Paul makes 12 pizzas the first day and 6 pizzas each day after that.

So, after 9 days Paul will make total [12 + (9 - 1)6] = 60 pizzas.

Now, Cindy makes 16 pizzas the first day and 4 pizzas each day after that.

So, after 9 days Cindy will make total [16 + (9 - 1)4] = 48 pizzas.

Therefore, after 9 days Paul will make more pizzas and the number is 60 pizzas. (Answer)

Answer:

B

Step-by-step explanation:

To find the value after 20 years, use the future value of a series formula with the given parameters, resulting in an approximate amount of $9,321.

To find the value of $300 saved annually at 4.5% interest compounded annually after 20 years, we use the future value of a series formula:

FV = [tex]P * ((1 + r)^n - 1) / r[/tex]

Where:

Substituting the given values:

FV = $300 * ((1 + 0.045)^20 - 1) / 0.045

= $300 * ((1.045)^20 - 1) / 0.045

= $300 * (2.398 - 1) / 0.045

= $300 * 1.398 / 0.045

= $300 * 31.07

= $9,321

Therefore, after 20 years, the value will be approximately $9,321.

Answer:

The scale factor is 2

x=11 units

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The ratio of its corresponding sides is called the scale factor

In this problem

Triangles RST and MNO are similar

so

[tex]\frac{NO}{ST}=\frac{MN}{RS}[/tex]

substitute the given values

[tex]\frac{x}{5.5}=\frac{6}{3}[/tex]

solve for x

[tex]\frac{x}{5.5}=2[/tex]

[tex]x=2(5.5)\\x=11\ units[/tex]

The scale factor of triangle RST to triangle MNO (enlargement) is equal to 2

Answer:

The sum would be a₅ = 506.25!

Step-by-step explanation:

Given that,

first term a₁ = 1600

common ratio (r) =

We need to find the fifth term of the geometric progression

We know that the nth term formula

aₙ = a₁rⁿ-¹

where a₁ is first term and r is the common ratio

n is the number of terms

So, n = 5

a₅ = 1600

a₅ = 1600*

a₅ = 1600*81/256

a₅ =

a₅ = 506.25                  

Answer:

116.64

Step-by-step explanation:

116.64 is the correct answer

when a1 = 1500 the a6 = 116,64

Answer:

[tex]\large\boxed{\theta=k\pi,\ k\in\mathbb{Z}}[/tex]

Step-by-step explanation:

[tex]\sec\thets\cdot\sin\theta=0\iff \sec\theta=0\ \vee\ \sin\theta=0\\\\\sec\theta\neq0\ \text{for any value of}\ \theta\\\\\sin\theta=0\Rightarrow\theta=k\pi\ \text{where}\ k\in\mathbb{Z}[/tex]

Answer:

The volume of the prism will be given by 204.7 cubic cm.

Step-by-step explanation:

The area of a triangle whose three side lengths are given is equal to

Δ = [tex]\sqrt{s(s - a)(s - b)(s - c))}[/tex] .......... (1)

Where, a, b, and c are the three side lengths and s is the half perimeter i.e.

[tex]s = \frac{a + b + c}{2}[/tex] ......... (2)

Now, in our case, [tex]s = \frac{6 + 7 + 6}{2} = 9.5[/tex] {From equation (2)}

So, Δ = [tex]\sqrt{9.5(9.5 - 6)(9.5 - 7)(9.5 - 6)} = 17.05[/tex] sq. cm.

{From equation (1)}

Hence, the volume of the prism will be given by (17.05 × 12) = 204.7 cubic cm. (Answer)

Answer:

No, Mary is incorrect. If you turn the fractions into decimals, 1/4 would be 0.25 and 1/8 would be 0.12½. Since 0.25 is greater than 0.12½, Mary is incorrect.

Mary's reasoning is incorrect because in fractions, the larger the denominator, the smaller the fraction's value, making 1/4 greater than 1/8.

Mary's reasoning that 1/8 is greater than 1/4 because 8 is greater than 4 is not correct. In the context of fractions, the larger the denominator (the bottom number), the smaller each part of the whole it represents. Thus, 1/4 is actually greater than 1/8 because dividing something into 4 parts results in larger parts than dividing it into 8 parts. This can be further understood by transforming both fractions into equivalent fractions with a common denominator or by converting them into decimal form (0.25 for 1/4 and 0.125 for 1/8) to directly compare their sizes.

Answer:

1/8(A)+(3/4)(168-A)=76 is an equation to find the mass of A, the mass of A is 80 grams.

Step-by-step explanation:

What do we know?

Both sacks together are 168 grams. Therefore;

A+B=168

One eighth of sack A and three quarters of sack B is equal to 76 grams. Therefore;

1/8(A)+(3/4)B=76

Let's solve using the substitution method to find A. First, we need to isolate and then substitute B for an expression containing A.

A+B=168

B=168-A

Now that we have isolated B, we can substitute '160-A' for B in the other equation.

1/8(A)+(3/4)(168-A)=76

1/8(A)-3/4(A)+126=76

1/8(A)-3/4(A)+126=-50

-5/8(A)=-50

A=80

Answer: $4

Step-by-step explanation:

2d + 14 = 22

subtract 14

2d = 8

divide by 2

d = $4

each bag of Doritos costs $4

Elizabeth spent a total of $8 on 2 large bags of Doritos after spending $14 on soda, which means each bag costs $4.

To determine the price of each bag of Doritos, we need to subtract the amount spent on soda from the total amount spent. Elizabeth spent $14 on soda and had a total of $22 in expenses. So, the money spent on Doritos is the difference between the total amount and the soda amount.

Amount spent on Doritos = Total amount - Amount spent on soda

Amount spent on Doritos = $22 - $14

Amount spent on Doritos = $8

Since Elizabeth bought 2 large bags of Doritos, we can find the price per bag by dividing the total amount spent on Doritos by 2.

Price per bag of Doritos = Total spent on Doritos / Number of bags

Price per bag of Doritos = $8 / 2

Price per bag of Doritos = $4 per bag

Therefore, each large bag of Doritos costs $4.

Answer:

AC = 146

Step-by-step explanation:

Given that B  is the midpoint of AC, then

AB = BC, that is

9x + 1 = 6x + 25 ( subtract 6x from both sides )

3x + 1 = 25 ( subtract 1 from both sides )

3x = 24 ( divide both sides by 3 )

x = 8

Hence

AC = AB + BC = 9x + 1 + 6x + 25 = 15x + 26, thus

AC = (15 × 8) + 26 = 120 + 26 = 146

Answer:

146

Step-by-step explanation:

AB = BC (Definition of midpoint) so:

9x+1=6x+25.

Solve it as you would any other algebraic equation  >>>  9x+1=6x+25  >>>  9x+1-1=6x+25-1  >>>  9x=6x+24  >>>  -6x+9x=6x-6x+24  >>>  3x=24  >>>  3x/3=24/3  >>>  x=8

AB=9x+1  >>>  AB=9*8+1  >>>  AB=73

BC=6x+25  >>>  BC=6*8+25  >>>  BC=73

AC=AB+BC  >>>  AC=73+73  >>>  AC=146

Answer:

[tex] 3 {x}^{3} - 25 {x}^{2} + 35x - 23 = 0[/tex]

Step-by-step explanation:

We want to create an equation that will have the solution

[tex]x = \frac{1}{3},x = 4 + \sqrt{7}i,x = 4 - \sqrt{7}i[/tex]

This implies that:

[tex]3x -1= 0,x -( 4 + \sqrt{7}i) = 0,x - ( 4 - \sqrt{7}i) = 0[/tex]

We put the roots in factored form by reversing the zero product principle to get:

[tex](3x -1)(x -( 4 + \sqrt{7}i))(x - ( 4 - \sqrt{7}i)) = 0[/tex]

We expand the last two parenthesis to get:

[tex](3x - 1)( {x}^{2} - 4x + \sqrt{7}ix - 4x - \sqrt{7}ix + 16 - 7 {i}^{2}) = 0 [/tex]

We simplify to get:

[tex](3x - 1)( {x}^{2} - 8x + 23) = 0[/tex]

We expand further to obtain:

[tex]3 {x}^{3} - 25 {x}^{2} +35x - 23 = 0[/tex]

Answer:

The "I" figure is 13 years old. Her brother is 16. Her Sister is 11. Her mother is 47.

Step-by-step explanation:

13+16=29

29+11=40

40+47=87

Answer:

C) Y = -45

Step-by-step explanation:

Y/9 + 5 = 0

Y/9 = -5

y = -5 * 9

Y= -45

Answer:

AB = 40 cm

Distance = [tex]10\sqrt{3}[/tex] cm

Step-by-step explanation:

Draw two heights DE and CF. These heights together with bases of trapezoid form rectangle DEFC. In this rectangle, DC=EF=20 cm.

Consider right triangle ADE. In this triangle, angle ADE has the measure of 30° (the sum of the measures of all interior angles is always 180°, so m∠ADE=180°-60°-90°=30°)

Leg opposite to 30° angle is equal to half of the hypotenuse, so

[tex]AE=\dfrac{1}{2}AD=\dfrac{1}{2}\cdot 20=10\ cm[/tex]

Similarly, in triangle CBF, BF=10 cm.

Hence,

[tex]AB=AE+EF+FB=10+20+10=40\ cm[/tex]

The height of the trapezoid (the second leg of triangle ADE) is the distance between DC and AB. By the Pythagorean theorem,

[tex]AD^2=AE^2+DE^2\\ \\DE^2=20^2-10^2=400-100=300\\ \\DE=\sqrt{300}=10\sqrt{3}\ cm[/tex]

The cost of each bush is $ 18.49

Let "f" be the cost of each flower

Let "b" be the cost of each bush

Given that Mrs. Kelly buys 15 flowers and 3 bushes for a total cost of $160.32

15 flowers x cost of each flower + 3 bushes x cost of each bush = 160.32

[tex]15 \times f + 3 \times b = 160.32[/tex]

15f + 3b = 160.32  ----- eqn 1

Each bush costs $11.50 more than each flower

Cost of each bush = 11.50 + cost of each flower

b = 11.50 + f  ------ eqn 2

Let us solve eqn 1 and eqn 2 to find values of "b" and "f"

Substitute eqn 2 in eqn 1

15f + 3(11.50 + f) = 160.32

15f + 34.5 + 3f = 160.32

18f = 160.32 - 34.5

18f = 125.82

Substitute f = 6.99 in eqn 2

b = 11.50 + 6.99 = 18.49

Thus the cost of each bush is $ 18.49

By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3

Step-by-step explanation:

The supplementary angles are:

∵ ∠1 and ∠2 are supplementary

∴ m∠1 + m∠2 = 180° ⇒ (1)

∵ ∠3 and ∠4 are supplementary

∴ m∠3 + m∠4 = 180° ⇒ (2)

We can equate the left hand sides of (1) and (2) because the right hand sides are equal

∴ m∠1 + m∠2 = m∠3 + m∠4 ⇒ (3)

∵ ∠1 ≅ ∠4

∴ m∠1 = m∠4

- Substitute m∠4 by m∠1 in (3)

∴ m∠1 + m∠2 = m∠3 + m∠1

- Subtract m∠1 from both sides

∴ m∠2 = m∠3

∴ ∠2 ≅ ∠3

By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3

Learn more:

You can learn more about supplementary angles in brainly.com/question/10483199

#LearnwithBrainly

The y intercept is (0, 12)

Solution:

Given function is:

[tex]f(x) = 8x^5 - 3x^3 + 12[/tex]

To find: y intercept

y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.

To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y

Substitute x = 0 in given function

[tex]f(0) = 8(0) -3(0) + 12[/tex]

y = 0 - 0 + 12

y = 12

Thus y - intercept is (0, 12)

Answer:

Step-by-step explanation:

Write a numerical expression that represents the number of increments it will take to reach -60 feet

Answer:

(-60) ÷ (-10)

Step-by-step explanation:

Answer:

[tex]\frac{14}{6}[/tex]

Step-by-step explanation:

A mixed fraction of the form [tex]a\frac{b}{c}[/tex] can be converted into an improper fraction by writing it in the form [tex]\frac{(ac)+b}{c}[/tex] . By applying this formula , we can see that [tex]2\frac{2}{6} = \frac{12 +2}{6} =\frac{14}{6}[/tex] . As numerator is greater than the denominator , we can see that the answer is greater than one and thus it is an improper fraction.

Answer:

The median refer to the middle

value or number when arranged ascendingly or descendingly therefore the MEDIAN IS 36.8

Step-by-step explanation:

By arranging the numbers ascendingly we have

5.9, 11.2, 13.9, 16.6, 22.9, 36.8, 43.1, 43.7, 44.2, 45.1, 49

Therefore the median which is the number at the centre is 36.8