Movies are on sale for 1/4 the original price. If the original price is $20, which expression gives the sale price?

x = 32, y = 11.31, z = 33.94

Step-by-step explanation:

Step 1: Let the triangle be ΔABC with B as the right angle. Let the hypotenuse be intersected by the altitude drawn from B at D. So there are 3 triangles, ΔABC, ΔADB and ΔBDC.

Step 2: To find x, y and z, use Pythagoras theorem where square of hypotenuse is equal to sum of squares of the other two sides of the right triangle.

Step 3: Make equations based on the theorem for all 3 triangles.

In ΔABC, (4+x)² = 12² + z²

⇒ 16 + 8x + x² = 144 + z²

⇒ x² + 8x - z² = 128 --------- (1)

In ΔADB, 12² = 4² + y²

⇒ 144 = 16 + y²

⇒ y² = 128 ------- (2)

In ΔBDC, z² = x² + y²

⇒ z² = 128 + x² ------ (3)

Substituting (3) in (1) ⇒ x² + 8x - (128 + x²) = 128

⇒ x² + 8x - 128 - x² = 128

⇒ 8x = 256

⇒ x = 32

From (3), z² = 128 + 32² = 128 + 1024 = 1152

⇒ z = 33.94

From (2), y² = 128

⇒ y = 11.31

Louise’s answer is not correct

Step-by-step explanation:

Let us revise how to solve (ax + b)²

The answer of square a binomial contains three terms: (1st)² + 2(1st)(2nd) + (2nd)²

∵ The bracket is (5x³ + 3)²

- Square the first term

∴ The first term of the answer = (5x³)² = (5)²(x³)² = [tex]25x^{6}[/tex]

- Multiply the 1st , the 2nd term and 2

∴ The second term of the answer = 2(5x³)(3) = 2(5)(3)x³ = 30x³

- Square the 2nd term

∴ The third term of the answer = (3)² = 9

∴ (5x³ + 3)² =  [tex]25x^{6}[/tex] + 30x³ + 9

∵ Louise’s answer is (5x³)² + (3)² =  [tex]25x^{6}[/tex] + 9

- By comparing the his answer with the answer above, he did

   not find the middle term

∴ Louise’s answer is not correct

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Answer:

Sample Response: Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.

Step-by-step explanation:

Sample Response ^^^

Answer:

value of x is greater than -8.

Step-by-step explanation:

5-(x+5)>-2(x+4)

we need to find value of x.

consider

5-(x+5)>-2(x+4)

using distributive property, we get

5-x-5>-2x-2×4

5-x-5>-2x-8

nowsimplify both side

-x+2x>-8

transfer -2x form RHS To LHS

-x+2x-8

x>-8

therefor, value of x is greater than-8.

Amount of tax on the book (s) is $0.72

Step-by-step explanation:

⇒ 6 × 12 = 100 × s

⇒ 72 = 100s

⇒ s = 72/100 = 0.72

Answer:

[tex]\large \boxed{\text{21.86 ft}^{2}}[/tex]

Step-by-step explanation:

Area of shaded region = area of square - area of semicircle

1. Area of square

A = s² = (6 ft)² = 36 ft²

2. Area of semicircle

Area of circle = πr²

Area of semicircle = ½πr²

r = 3 ft, so

A = ½π(3 ft)² = ⁹/₂π ft³

3. Area of shaded region

A = area of square - area of semicircle

[tex]\begin{array}{rcl}A & = & \mathbf{\left(36 - \dfrac{9}{2} \pi \right )} \textbf{ ft}^{\mathbf{2}}\\\\ &\approx & \left (36 - 14.1372\right)\text{ ft}^{2}\\ & \approx & \mathbf{21.86}\textbf{ ft}^{\mathbf{2}} \\\end{array}\\\text{The area of the shaded figure is approximately $\large \boxed{\textbf{21.86 ft}^{\mathbf{2}}}$}[/tex]

Answer:

Set #9 are congruent triangles.

Step-by-step explanation:

They are the same shape and size. If I were to flip them over, they would mach up.

Answer:

cap its only 10

Step-by-step explanation:

Value of x is 25°

Step-by-step explanation:

⇒ (2x + 45°) + (4x - 15°) = 180°

⇒ 6x + 30° = 180°

⇒ 6x = 150°

⇒ x = 25°

Step-by-step explanation:

Adjacent angles of a parallelogram are Supplementary.

[tex] \therefore \: (2x + 45 \degree) + (4x - 15 \degree) = 180 \degree \\ \\ \therefore \: 6x + 30 \degree = 180 \degree \\ \\ \therefore \: 6x = 180 \degree - 30 \degree \\ \\ \therefore \: 6x = 150 \degree \\ \\ \therefore \: x = \frac{150 \degree }{6} \\ \\ \huge \red{ \boxed{\therefore \: x = 25 \degree }}[/tex]

Answer:

Mikhail's age is 25 years old

Step-by-step explanation:

Let's make an equation: Say Mikhail is x, so Gabby would be 2*x=2x

If the sum of their ages equals 75, then x+2x=75, and x=2x=3x, so 3x=75.

75/3=25

Final answer:

Gabby's age is twice Mikhail's age, and the sum of their ages is 75. By setting up and solving a system of equations, we can determine that Mikhail's age is 25.

Explanation:

To solve this problem, we can set up a system of equations using the information given. Let's say Gabby's age is represented by 'G' and Mikhail's age is represented by 'M'. We know that G = 2M and the sum of their ages is 75, so we can write the equation G + M = 75. Now we have a system of equations:

G = 2M and G + M = 75.

To solve this system, we can substitute the value of G from the first equation into the second equation: 2M + M = 75. Combine like terms: 3M = 75. Divide both sides by 3: M = 25. So Mikhail's age is 25 years old.

Answer:3

Step-by-step explanation:

Divide 18 by 6

Answer:

3 miles

Step-by-step explanation:

If each lap is one mile, 18 times = 1/6 + 1/6 + ... + 1/6. This is equal to 18*1/6 by definition of multiplication, and 18*1/6 = 18 divided by 6 because fractions are just big division symbols. This gives 3 or 3 miles.

Answer:

3x+2

Step-by-step explanation:

We want to find an expression that is equivalent to:

[tex]x+1-x+2x+x+1[/tex]

We regroup similar terms to get:

[tex]x-x+2x+x+1+1[/tex]

We now combine the similar terms to obtain:

[tex]3x+2[/tex]

Therefore the expression that is equivalent to:  x + 1 − x + 2x + x + 1 is [tex]3x+2[/tex]

Answer:

3x + 2

Step-by-step explanation:

3x + 2

Solve by simplifying the given expression OR substitute 1 for x in each expression.

x + 1 − x + 2x + x + 1 → x − x + 2x + x + 2 → 3x + 2

OR

x + 1 − x + 2x + x + 1 → 1 + 1 − 1 + 2(1) + 1 + 1 = 5

3x + 2 → 3(1) + 2 = 5

The expression [tex]8x^2 + 10x[/tex] factors to [tex]2x(4x + 5)[/tex] and has solutions x = 0 and x = -5/4.

We first need to understand what it represents. In this expression, [tex]x[/tex] is the variable, and the terms [tex]8x^2[/tex] and [tex]10x[/tex] are polynomial terms where:

[tex]8x^2[/tex] indicates that the variable [tex]x[/tex] is raised to the power of 2, meaning it is multiplied by itself ([tex]x \times x[/tex]) and then scaled by a factor of 8.

[tex]10x[/tex] means that the variable [tex]x[/tex] is multiplied by 10.

The first term is [tex]8x^2[/tex].

The second term is [tex]10x[/tex].

In this case, the terms are not like terms because one is [tex]x^2[/tex] and the other is [tex]x[/tex]. Therefore, they cannot be combined further. The expression is simplest as it stands, which is:  [tex]8x^2 + 10x[/tex]

Factoring out [tex]2x[/tex] gives us:

[tex]2x(4x + 5)[/tex]

Thus, [tex]8x^2 + 10x[/tex] can also be expressed as [tex]2x(4x + 5)[/tex]. This is useful if you are trying to find the roots of the equation (setting it equal to zero) since it can help identify the values of [tex]x[/tex] that satisfy the equation [tex]8x^2 + 10x = 0[/tex].

This gives two possible solutions for x:

2 * x = 0 which leads to x = 0

4 * x + 5 = 0 which leads to x = -5/4

Answer:

6-8x

Step-by-step explanation:

-2+3x+8+(-11x)

-2+3x+8-11x

-2+8+3x-11x

6+3x-11x

6-8x

Answer:

Step-by-step explanation:

x=-5

Answer:

It would be A) -5

Step-by-step explanation:

So it could be any number if it’s the x value. So it can’t be C or D

if it passes through (-5,4), then the x would have to be -5

therefore it is A

Answer:if u I simplified then 17x

Step-by-step explanation:

Like terms are 10+7=17+x=17x

Answer:

1/14

Step-by-step explanation:

2/7 to 4 means 2/7 to 4/1

This gives

2/7

4/1

rearranging, we have;

2/7 * 1/4

2 * 1

7 * 4

= 2/28

to reduce to the simplest form, we'll divide the numerator and denominator by 2 ( the HCF of both)

1/14

To write the ratio 2/7 to 4 as a fraction in simplest form, multiply both the numerator and denominator of 2/7 by 4. Simplify the resulting fraction by dividing both the numerator and denominator by their common factor, which is 4. The simplest form of the ratio is 2/7.

To write the ratio 2/7 to 4 as a fraction in simplest form, we need to multiply both the numerator and denominator of 2/7 by 4. This gives us (2 * 4) / (7 * 4) = 8/28. Since both 8 and 28 have a common factor of 4, we can simplify the fraction further.

Dividing both the numerator and denominator by 4, we get 8/28 = 2/7.

Therefore, the ratio 2/7 to 4 as a fraction in simplest form is 2/7.

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Answer:

Mary reached the airport in 40 minutes

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Time it takes John to go from home to the train station = 30 minutes

Time it takes John to go from the train station to the airport = 55 minutes

Mary left 25 minutes later and reached the airport 20 minutes earlier than John

2. How long did it take Mary to get to the airport?

Total time it takes John to reach the airport = Time it takes John to go from home to the train station + Time it takes John to go from the train station to the airport

Total time it takes John to reach the airport = 30 + 55

Total time it takes John to reach the airport = 85 minutes

Now, let's calculate the time it takes Mary to reach the airport, this way:

Total time it takes John to reach the airport - minutes Mary left later - minutes Mary got to the airport earlier than John

85 - 25 - 20 = 85 - 45 = 40

Mary reached the airport in 40 minutes

Answer: Mary got to the airport in 40 Minutes.

Answer:

2.2r

Step-by-step explanation:

3.7r - 1.5r =

= r(3.7 - 1.5)

= r×2.2

= 2.2r

Yo sup??

given expression: 3.7r-1.5r

3.7r-1.5r

=3.7r+(-1.5r)

=2.2r

Hope this helps.

Answer:

5,12,13

Step-by-step explanation:

i think thats what the other person meant to say, either way, these numbers are correct

Answer: 5, 12, 13

Step-by-step explanation:

Answer:

One piece of candy costs $0.52.

Step-by-step explanation:

5.2/10=0.52

Answer:4.21,4.22,4.23, 4.24

Step-by-step explanation:

4 1/5 is 4.2 as a decimal and the numbers between 4.2 and 4.5 as numbers with 2 places past the decimal place are the ones above.

The number with two decimal places that are bigger than 4(1/5) and smaller than 4.25 is 4.22.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

4(1/5)

= 21/5

= 4.2

Now,

Two decimal numbers between 4.2 and 4.25.

4.21, 4.22, 4.23, and 4,24.

Thus,

The number is 4.22.

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Answer:

A. {x / x ≠ -2, 3}

Step-by-step explanation:

In the graph, we can find the vertical asymptotes of the given graph is at x = -2 and x = 3.

You can see the vertical line red dotted line in the graph. That is called vertical asymptotes.

The vertical asymptotes cannot be the domain of the functions.

All other integers are domain except x = -2 and x = 3.

Therefore, answer is A. {x / x ≠ -2, 3}

Answer:

-360

Step-by-step explanation:

1. Add 9 + 21 and subtract 9 - 21

2. That would be (30)(-12)

3. Then multiply 30 x -12

4. You get -360

Final answer:

The number 13,809 in expanded form is expressed as 10,000 + 3,000 + 800 + 9, which corresponds to option 'D'.

Explanation:

To write the number 13,809 in expanded form, we break the number down into its place values and then write it as a sum of each digit multiplied by its place value. For the number 13,809 this would be:

(1 × 10,000) for the ten-thousands place,

(3 × 1,000) for the thousands place,

(8 × 100) for the hundreds place,

(0 × 10) for the tens place (which is actually 0 and usually omitted in expanded form), and

(9 × 1) for the ones place.

The expression that represents 13,809 in expanded form is therefore 10,000 + 3,000 + 800 + 9, which corresponds to option 'D'.

Answer:

No

Step-by-step explanation:

in order for a slope to be perpendicularit needs to me the opposite recipricol

so to be perpendicular to 3/2 it would be -2/3

Answer:

2 and 1/4

Step-by-step explanation:

Dysgraphia learning disability . Dysgraphia is a neurological disease in which a person struggles to express their ideas in writing form appropriate to their age and mental capacity .

Children who have dysgraphia typically have confusing, uneven handwriting that varies in slant, form, upper- and lower-case letters, as well as cursive and print styles. They also have a tendency to copy or write things slowly.

Dysgraphia is a neurological disease in which a person struggles to express their ideas in writing form appropriate to their age and mental capacity even after receiving proper instruction and schooling. Various signs of dysgraphia might appear at various ages. It is regarded as a learning disability.

The disorder's origin is uncertain, however in adulthood, parietal lobe injury is frequently a contributing factor. Treatment for motor abnormalities to help control writing movements may be part of dysgraphia treatment, which varies. Other therapies could deal with memory loss or other neurological issues.

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Answer:

[tex]x < 4[/tex]

Step-by-step explanation:

When the circle is open that means it is not equal to and the line is going to the left so it is less than

Answer: x<4

Step-by-step explanation: