Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms? A. (3 × 13^2) + (2 × 15^2) B. (2 × 13^3) + (2 × 15^2) C. (3 × 15^2) + (2 × 13^2) D. (3 × 13^2) × (2 × 15^2)

[tex]\bf \stackrel{\textit{perimeter of a rectangle}}{P=2(L+w)}~~ \begin{cases} L=length\\ w=width\\ \cline{1-1} P=66 \end{cases}\implies 66=2(L+w) \\\\\\ 33=L+w\implies \boxed{33-w=L} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of a rectangle}}{A=Lw}\qquad \implies 216=Lw\implies 216=(33-w)w \\\\\\ 216=33w-w^2\implies w^2-33w+216=0 \\\\\\ (w-24)(w-9)=0\implies w= \begin{cases} 24\\ 9 \end{cases}[/tex]

now, both values are valid, so if "w" is either one, "L" is the other.

Answer:

The correct answer is option C

a = 10√3, b = 5√3, c = 15 and d = 5

Step-by-step explanation:

Points to remember

The angles of a right angled triangle, 30°, 60° and 90° then sides are in the ratio, 1: √3 : 2

To find the value of variables

From the figure we can see 2 right angled triangle with angle 30, 60 and 90

we get, d= 5 then b = 5√3

b = 5√3  the c = 5√3 * √3 = 15

and a = 2 * 5√3 = 10√3

Therefore the correct answer is option C

a = 10√3, b = 5√3, c = 15 and d = 5

Answer:

d.[tex]a=10\sqrt3,b=5\sqrt3,c=15,d=5[/tex]

Step-by-step explanation:

We have to find the value of each variable.

[tex]\frac{P}{H}=sin\theta[/tex]

[tex]\frac{b}{10}=sin 60^{\circ}[/tex]

[tex]\frac{b}{10}=\frac}\sqrt3}{2}[/tex]

[tex]b=10\times \frac{\sqrt3}{2}=5\sqrt3[/tex]

[tex]\frac{d}{10}=cos 60^{\circ}[/tex]    ([tex]cos\theta=\frac{base}{hypotenuse}[/tex])

[tex]d=\frac{1}{2}\times 10=5[/tex]

[tex]\frac{b}{a}=sin30^{\circ}[/tex]

[tex]\frac{5\sqrt3}{a}=\frac{1}{2}[/tex]

[tex]a=10\sqrt3[/tex]

[tex]\frac{b}{c}}=tan 30^{\circ}[/tex]   ([tex]tan\theta=\frac{p}{b}[/tex])

[tex]\frac{5\sqrt3}{c}=\frac{1}{\sqrt3}[/tex]

[tex]c=5\sqrt3\times \sqrt3=15[/tex]

[tex]a=10\sqrt3,b=5\sqrt3,c=15,d=5[/tex]

Hence, option d is true.

Answer:

The answer is D.

Step-by-step explanation:

This is because the first part of the expression is the conjugate and youre given -5. The second part of the expression is the imaginary part and youre given 4i.

Answer:

C

Step-by-step explanation:

Given a complex number in the form

a + bi then the conjugate is a - bi

Note the real part remains unchanged while the sign of the imaginary part is negated.

Given

- 5 + 4i then the conjugate is - 5 - 4i → C

Answer:

1.) ∠GAC and ∠CAF are complementary and acute angles

2.) 27°

3.) m∠CAG+m∠GAD=180°

Step-by-step explanation:

2.) because you solve for x:

63°+x°=90°

x= 27°

Answer:

C. 17 - 12 = d + 12 - 12

Step-by-step explanation:

You need to get d by itself and in order to do that you need to subtract 12

Answer:

[tex]\boxed{x \leq 4.50}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rrcl}\textbf{Words:} & \text{x} & \text{less than or equal to} & \text{4.50}\\\textbf{Symbols:} & x & \leq & 4.50\\\end{array}[/tex]

Answer:

Step-by-step explanation:

Substitute all values for x and y into their placement

y<1-6x

(1)<1-6(-1)

1<7

The coordinate pair is (-1,1)

1.So, what you do is remove the () from -8q.

2. Time -8q by one and it equals -8q.

3. Combined -4q and -8q, that equals -12q

4q + 10 is the equivalent expression of −4q−(−8q)+10

An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. For instance, the algebraic formula 3x² + 2xy + c

Given

-4q - (-8q ) + 10

using BODMAS

-4q + 8q +10

4q + 10

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Answer:

the answer is where the 2 points intersect... A. (2,3)

Step-by-step explanation:

Answer:

The correct option is A.

Step-by-step explanation:

The given system of equations is

[tex]y=-\frac{1}{2}x+4[/tex]

[tex]y=2x-1[/tex]

All the points on a line is are the solutions of the equation of line.

From the graph it is clear that the lines intersect each other at point (2,3). It means both the lines passes through the point (2,3) and point (2,3) is the solution of given system of equations.

Since (2,3) is the solution of given system of equations, therefore the correct option is A.

Answer:

A)16

Step-by-step explanation:

Given

f(x)=5x^2+9x-2

Remainder theorem states that when f(x) is divided by x-a then the remainder can be calculated by calculating f(a).

Now Using the remainder theorem to divide 5x^2+9x-2 by x+3 to find the remainder:

f(x)=5x^2+9x-2

f(-3) = 5(-3)^2 +9(-3) -2

       =5(9) - 27 -2

       = 45-29

       = 16 !

Exact Form: √3/3

Decimal Form: 0.57735026

sorry if i got it wrong, i tried my best on this :)

The value of the expression tan π/6 is √3/3 or approximately 0.5774.

The value of the expression tan π/6 is √3/3 or approximately 0.5774.

To find this value, we can remember that tan θ = sin θ / cos θ. So, tan(π/6) = sin(π/6) / cos(π/6).

Thus, tan(π/6) = (√3/2) / (1/2) = √3/3.

Answer:90+33 = 123

123-180=77

So 77

Step-by-step explanation:

Answer:

The answer is 77

Answer:

r = 17 units

Step-by-step explanation:

The radius is the distance from the centre (- 7, - 1) to the point on the circle

(8, 7)

Use the distance formula to calculate the radius (r)

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 7, - 1) and (x₂, y₂ ) = (8, 7)

r = [tex]\sqrt{(8+7)^2+(7+1)^2}[/tex]

  = [tex]\sqrt{15^2+8^2}[/tex]

  = [tex]\sqrt{225+64}[/tex]

  = [tex]\sqrt{289}[/tex] = 17 units

Answer:

Yes

Explaination:

They are similar and the ratio is still the same. The artwork's shape didn't change we just resized it by multiplyting its length and width by 2.

Answer:

8 projects

Step-by-step explanation:

28 : 3,5 = 8

Final answer:

Mia can complete 8 full projects with 28 yards of ribbon by dividing the total yards by the yards needed per project, after converting 3 1/2 yards to an improper fraction (7/2).

Explanation:

The subject of this question is Mathematics, and the question would typically fall under a middle school grade level. To solve the problem about the number of projects Mia can complete, we need to use division. Mia has a total of 28 yards of ribbon and needs 3 1/2 yards of ribbon for each project. By converting the mixed number to an improper fraction, we get 7/2 yards per project; then we can divide the total yards by the yards needed per project.

To calculate how many full projects Mia can complete:

Mia can complete 8 full projects with the ribbon she has.

Answer:

1/4

Step-by-step explanation:

To find the slope of a line from two points we use

m = (y2-y1)/(x2-x1)

m = (3-2)/ (3--1)

   = (3-2)/(3+1)

  =1/4

Step-by-step explanation:

A(-1,2) and B(3,3) then AB=(4,1).

Normal vector

n=(-1,4)

Our line contains point A(-1,2) and has normal vector n=(-1,4) is

[tex](d) : - 1(x + 1) + 4(y - 2) = 0[/tex]

[tex](d ): - x - 1 + 4y - 8 = 0[/tex]

[tex](d) : - x + 4y - 9 = 0[/tex]

No 5/8 is bigger because half of 8 is 4 and 5 is greater than 4

In comparing 1/2 gallon and 5/8 gallon, using equivalent fractions shows that 5/8 gallon is larger than 1/2 gallon.

In the comparison of 1/2 gallon and 5/8 gallon, it's important to remember that fractions provide a way of representing parts of a whole. With fractions, the numerator represents the part while the denominator represents the total parts. So here, the fraction 5/8 represents 5 parts of a total 8 parts, where 1 gallon is considered the 'whole' or 'total' amount.

To determine if 1/2 is greater or less than 5/8, we want to make the denominators the same for comparison. Multiply the numerator and the denominator of the first fraction (1/2) by four to get it to the same denominator as the second one. This results in 4/8 for the first fraction.

Now, comparing 4/8 and 5/8, we find that 5/8 is greater than 4/8. Therefore, 5/8 gallon is indeed more than 1/2 gallon.

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ANSWER

[tex] ( {x}^{2} + 9)({x} - 1)(x + 1)[/tex]

EXPLANATION

The given function is

[tex] {x}^{4} + 8 {x}^{2} - 9[/tex]

Split the middle term

[tex] {x}^{4} + 9 {x}^{2} - {x}^{2} - 9[/tex]

Factor by grouping;

[tex]{x}^{2} ( {x}^{2} + 9) -1 ({x}^{2} + 9)[/tex]

Factor further to get:

[tex] ( {x}^{2} + 9)({x}^{2} - 1)[/tex]

Apply difference of two squares to get:

[tex] ( {x}^{2} + 9)({x} - 1)(x + 1)[/tex]

Answer:

[tex](x^2+9)(x-1)(x+1)[/tex]

Step-by-step explanation:

We would need to let u = x^2 and use middle term factorization first. let's do this:

if u = x^2, then x^4 + 8x^2 – 9 would be

u^2+8u-9

Middle term factorization of this is:

(u+9)(u-1)

now replacing back u = x^2:

(x^2+9)(x^2-1)

Using the formula a^2 - b^2 = (a+b)(a-b), we can write (x^2 - 1) as (x+1)(x-1).

So, the final factored form is:  (x^2+9)(x-1)(x+1)

Answer:

1. 0.09

2. 0.21

3. 0.49

Step-by-step explanation:

If the probability that Yuri will make a free throw is 0.3, then the probability that Yuri will not make a free throw is 1-0.3=0.7.

1. The probability that Yuri will make two consecutive free throws is

[tex]0.3\cdot 0.3=0.09[/tex]

2. The probability that he will make the first and not the second in two free throws is

[tex]0.3\cdot 0.7=0.21[/tex]

3. The probability that he will make neither of the two free throws is

[tex]0.7\cdot 0.7=0.49[/tex]

Answer:

0.78

Step-by-step explanation:

Divide: 5/18

Answer:

function defined on different intervals by different domain rules

hope it helps

The terms absolute value, continuous function, step function, and piecewise-defined function are matched with their respective definitions: the absolute value measures distance from zero, a continuous function has a graph without breaks, a step function has a graph with horizontal steps, and a piecewise-defined function has different rules for different intervals.

Matching Vocabulary to Definitions

Let's match each mathematical term to its correct definition:

Absolute value - This is the function whose output equals the input for non-negative numbers, and whose output is the opposite of a negative input. It can be thought of as the distance from zero on the number line, regardless of direction.

Continuous function - A function whose graph has no breaks is known as continuous. It means you can draw the function without lifting your pen off the paper, indicating it has no jumps or holes.

Step function - Such a function has a graph that consists of horizontal line segments. The value of the function changes in 'steps' rather than smoothly.

Piecewise-defined function - When a function is defined on different intervals by different domain rules, it is known as a piecewise-defined function. It's like having multiple functions strung together each applicable to different parts of the domain.

median: 3

lower quartile: approximately 2.25

higher quartile: approximately 4.75

minimum: 0

maximum: 6

hope that helps

The simplified expression is 3.5r - 7.

To simplify the expression 6.4r - 7 - 2.9r, first, combine like terms by subtracting the coefficients of 'r'.

This yields (6.4 - 2.9)r. Simplifying the coefficients gives 3.5r. Then, subtract 7. Therefore, the simplified expression is 3.5r - 7.

This means that when you distribute the 'r', you multiply it by 3.5, then subtract 7 from the result.

The simplified expression is 3.5r - 7.

Complete question :- Simplify 6.4r - 7 - 2.9r.

Answer:$4.23

Step-by-step explanation:

Answer:

4.23 is the answer if its wrong let me know what mistakes i made

This may be what you're looking for:

Answer:

36 in.³

Step-by-step explanation:

volume = length × width × height

volume = 6 in. × 3 in. × 2 in.

volume = 36 in.³

Answer:

A)

Step-by-step explanation:

The expression (a + b)(x + y) is not equivalent to (a + x)(b + y). When the terms are distributed, (a + x)(b + y) yields a different result compared to the original expression.

The expression (a + b)(x + y) is equivalent to a(x + y) + b(x + y) and (b + a)( y + x) because the order of addition in each element doesn't change the overall result. However, the expression (a + x)(b + y) is not equivalent to the original expression.

To understand why, let's distribute the terms in each equivalent expression:

(a + b)(x + y) = ax + ay + bx + by

(b + a)( y + x) = ay + ax + by + bx = ax + ay + bx + by

a(x + y) + b(x + y) = ax + ay + bx + by

As you can see, all these three expressions give the same result when distributed. But, if we now distribute the terms in (a + x)(b + y):

(a + x)(b + y) = ab + ay + bx + xy

It's clear that it does not yield the same result. Thus, option A) (a + x)(b + y) is not equivalent to the original expression (a + b)(x + y).

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Answer:

[tex]y=-x+4[/tex]

Step-by-step explanation:

We want to find the equation of the line passing through (2,2) and perpendicular to the line with equation y=x.

The given line y=x has slope n=1.

The line that is perpendicular to this line has slope m=-1

The equation is given by the formula;

[tex]y-y_1=m(x-x_1)[/tex]

we plug in the slope and the point to get;

[tex]y-2=-1(x-2)[/tex]

[tex]y-2=-x+2[/tex]

[tex]y=-x+2+2[/tex]

The required equation is

[tex]y=-x+4[/tex]

Answer:

X= 0, X=-3, X=1

Step-by-step explanation:

Answer:

A=1/2 h(b1+b2)

Step-by-step explanation:

h being the height and b1 being base one and b2 being base two

Answer:

(-4, -2)

Step-by-step explanation:

The x-coordinate would stay the same, but the y-coordinate would be halved.  Thus, the corresponding point would be (-4, -2).

Answer:

-6x ≥ 24

x = ≤ 4

Step-by-step explanation:

Number = x

The product of the number and -6.

-6x

The product is at least 24.

-6x ≥ 24

Solve the problem

-6x ≥ 24

Divide by -6 and we change the sign

x = ≤ 4

Answer:

Step-by-step explanation: