Yossi used to have a square garage with ft of floor space. recently built an addition to it. The garage is still a​ square, but now it has​ 50% more floor space. What was the length of one side of the garage​ originally? What is the length of one side of the garage​ now? What was the percent increase in the length of one​ side?

The correct answer regarding the factoring of the expression 25x² - 15x + 2 is:

B. The expression is the sum of two terms. He needs to factor out the common factor. The correct factored form is (5x - 1)(5x - 2).

An expression is factored placing the common terms in evidence, and then simplifying the entire expression according to these terms.

For this problem, the expression is:

25x² - 15x + 2.

After the first step, he found the following factorization:

5x(5x - 1) - 2(5x - 1).

However, this procedure is incomplete, as (5x - 1) is common to both terms of the subtraction. Thus the completely simplified expression is:

(5x - 1)(5x - 2).

As:

The correct option is:

B. The expression is the sum of two terms. He needs to factor out the common factor. The correct factored form is (5x - 1)(5x - 2).

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{5}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is 5 and that it passes through (-1 , 2)

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ 5}(x-\stackrel{x_1}{(-1)}) \implies y -2= 5 (x +1) \\\\\\ y-2=5x+5\implies {\LARGE \begin{array}{llll} y=5x+7 \end{array}}[/tex]

The final endpoint values are: (12,-6)

The midway point of a line or segment is referred to as the midpoint. It creates an evenly spaced division in the line. In essence, it divides the lines into two.

According to the question, the coordinates of a line LN is given as:  N (-8,2) and Midpoint M M(2,-4).

To calculate the midpoint, use the standard midpoint formula which is represented as below:

Midpoint =[tex]\frac{x1 + x2 }{2}[/tex] and [tex]\frac{y1 + y2 }{2}[/tex]

From the given data, the values are:

X1 = -8; Y1 = 2; X = 2; Y = -4

Therefore, the calculated midpoint is:

2 = -8 + [tex]\frac{x2}{2}[/tex] = 12

4 = 2 + [tex]\frac{y2}{2}[/tex] = -6

Hence, the final endpoint values are (12,-6)

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Answer:

26 < d < 30

Step-by-step explanation:

D is greater than 26 but less than 30.

Someone older than 26​, but less than 30 years of age will be written as 26 < x < 30.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

A certain population demographic may be defined as someone older than 26​, but less than 30 years of age.

Let 'x' be the age of someone.

If the age of someone is greater than 26, then the inequality is written as,

26 < x            ...1

If the age of someone is smaller than 30, then the inequality is written as,

x < 30           ...2

Combine both inequalities, then we have

26 < x < 30

Someone older than 26​, but less than 30 years of age will be written as 26 < x < 30.

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[tex]\large \bf \implies{53.1 \degree}[/tex]

[tex] \bf \longrightarrow \: sin \: α = \frac{8}{10} = 0.8 \\ \\\bf \longrightarrow \: α = arc \: sin (0.8)= 53.1°[/tex]

Answer:

there is a 5 by 5 square

Step-by-step explanation:

Answer:

In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equalStep-by-step explanation:

The original number is represented by x So, the result is the multiplier of 2.

Quotients are the number that is obtained by dividing one number by another number.

Dividend ÷ Divisor = Quotients

It is given that Multiply the number 4. Add 6 to the product. Divide this sum by 2. Subtract 3 from the quotient.

Let x = original number

(4x + 6)/2 - 2

= (4x /2 + 6/2) - 2

= 2x + 3 -2

= 2x+1

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The complete question is;

Write a conjecture that relates the result of the process to the original number selected. Represent the original number as x. What is the result?

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=7\\ \theta =280 \end{cases}\implies s=\cfrac{(280)\pi (7)}{180}\implies s=\cfrac{98\pi }{9}\implies s\approx 34.21[/tex]

Answer:

1. 26, cuz 17+9=26

2. 50, cuz 60-10=50

3. 19, cuz 33-14=19

Hope these will help you as you can't just ask for answers.

Simplification - The process of making something less complicated and therefore easier to do or understand, or the thing that results from this process .

What is the simplification rule?

The general rule to simplify expressions is PEMDAS - stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Replace Question mark .

1.) 1/2 = 1× x / 2 ×10

     1/2 = x / 20

     x = 20 / 2

      x = 10.

2.) 3/4 = 3 x 5 / 4× x

     3/4 = 15 / 4x

     12x = 60

x = 60 / 12

x = 5

3.) 7/8 = 7× 3 / x × 3

     7/8 = 21 / 3x

      21x = 21 × 8

        x = 8

4.) 2/3 = x×4 / 3  × 4

2/3 = 4x / 12

12x = 24

x =2 .

5.) 6/12 = (6/6) / (12/x)

1/2 = 1 / (12/x)

1/2 = x/12

2x = 12

x = 6.

6.) 3 / 15 = (3 /x) /(15 / 3)

3/15 = (3/x) / 5

3/15 = 3/5x

15x = 15× 3

x =3.

7.) 175/250 = (x/25) / (250/25)

taking LHS

175/250 = 7/ 10

Solve RHS

(x/25) / (250/25)

(x/25) / (10) = x/250

x/250 = 7/10

x = 175.

8.) 28 /56 = (28/28) / (x/28)

28/56 = 1/ (x/28)

28 / 56 = 28 /x

x =56 .

9.) 14/16 =(14/x) / (x/2)

14/16 = 14/x × 2/x

14 /16 = 28  /x²

1 /16 = 2/ x²

x² =32 .

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Answer:

2(s+20)

Step-by-step explanation:

hope this helps

Answer: son is 10 years old and father is 40 years old

Step-by-step explanation:

Let the present age of son is x years

Then the present age of father is 4x years

4x+20=2(x+20)

4x+20=2x+40

4x+20-20=2x+40-20

4x=2x+20

4x-2x=2x+20-2x

2x=20

Divide both parts of the equation by 2:

x=10 years

4x=4(10)

4x=40 years

Answer:

27(-⁴)

³

= 3³(-⁴/³)

= 3(-⁴)

= 1

81

Answer:

It would be A

Step-by-step explanation:

The correct way to find the sum p+q, where p is positive and q is negative, is to start from the point representing p on the number line and move to the left by the magnitude of q.

Let's place the positive number p on the number line, starting from the origin (0) and moving to the right by p units. Now, let's place the negative number q on the number line by moving q units to the left from the origin.

To find the sum p+q, we need to consider the relative positions of p and q. Since p is positive, we have moved to the right on the number line. However, since q is negative, it is also positioned to the left of the origin. To add p and q, we need to consider their magnitudes and the direction they point in.

The correct way to find the sum p+q is to start from the point representing p and then move to the left by the magnitude of q. This corresponds to moving p units to the right and then q units to the left. The endpoint of this combined movement represents the sum p+q on the number line.

Hence the correct option is (a).

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110% percent of female students visited the math lab.

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

Comparing two amounts while rebasing the second amount to 100 is the simplest way to use percentages.

During the final exam, the number of students that visited the math lab is 172 in total.

Of the total number of students, 4 out of 11 were male.

Therefore, the total number of females that visited the math lab is:

no. of females = 11 - 4 = 7.

Therefore, the percentage of female students who visited the math lab is :

[tex]F=\frac{7}{11} \times 172\\\\F=109.4\\F=110[/tex]

Therefore, the percentage of female students who visited the math lab is 110%.

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The function written in vertex form is

[tex]g(x) =4x^2+88x =4(x+ 11)^2 - 484[/tex]

This is further explained below.

Generally, the equation for the function is  mathematically given as

g(x) = 4x2 + 88x

Therefore,

g(x) = a(x +11)2 + k

[tex](x +11)x^{2} as\ x^2 + 22x +121[/tex]

[tex]g(x) = a(x^2 +22x +121) + k\\\\g(x) = ax^2+ 22ax +121a + k[/tex]

Equate eq(a) with eq(b) We obtain,

[tex]4x^2 + 88x = ax^2 + 22ax +121a + k[/tex]

Examine the x coefficients on both sides of the equation.

a=4 and 22a= 88 ; 121a + k = 0

121(4) = -k

k = -484

[tex]g(x) =4x^2+88x =4(x+ 11)^2 - 484[/tex]

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CQ

Write g(x) = 4x2 + 88x in vertex form. The function written in vertex form is g(x) = ___ (x +11)² +____.

Cost of 20 yards of ribbon is $13.32.

Given,

The cost of 6 ½ yards of ribbon = $9.75

We have to find the cost of 20 yards of ribbon.

First of all we have to find the cost of 1 yard of ribbon:

Cost of 1 yard of ribbon = ( 6 ½ yards of ribbon) / (cost of 6 ½ yards of ribbon)

Cost of 1 yard of ribbon = 6 ½ / 9.75 = 6.5 / 9.75 = 0.66666

That is cost of 1 yard of ribbon is $0.666 approximately.

Now, we have to find the cost of 20 yards of ribbon:

Cost of 20 yards of ribbon = (cost of 1 yard of ribbon) x 20

Cost of 20 yards of ribbon = 0.666 x 20 = 13.32

That is cost of 20 yards of ribbon is $13.32.

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After the evaluation of the given expression n² + 4, the correct option is (3) 85, 68, and 40.

So, n² + 4:

Therefore, after the evaluation of the given expression, the correct option is (3) 85, 68, and 40.

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Alex has received a rate of return of 0.25, or 25%, on his investment.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To calculate the rate of return that Alex has received, we can use the formula:

rate of return = (final value - initial value) / initial value

where the final value is the value of the investment after the period of time in question, and the initial value is the value of the investment at the beginning of that period.

In this case, the final value is $1,250 and the initial value is $1,000, so we have:

rate of return = (1250 - 1000) / 1000 = 0.25

Therefore, Alex has received a rate of return of 0.25, or 25%, on his investment.

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Answer:

14 girls divided by their percentage 0.4 the result will be

35 students

The area of park in terms of scale drawing is 79200 square yards with scale drawing of a rectangular park is 8 inches wide and 11 inches long.

Area of rectangle=Length * width.

Given:

scale length of rectangular park = 11 inch =

scale width of rectangular park = 8 inch

scale length / actual length of park = scale width/ actual width of park

11/330= 8/ actual width of park

1/30 =  8/ actual width of park

actual width of park = 240

So,

Area = length* width

=330*240

= 79200 square yards

Hence, the area of the actual parking is 79200 square yards.

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Mid point of the points  A(-5, 3) and B(5, -1) is point C(0,1)

Mid point is a point that lies at the center of any measured distanced.

The points are written in the coordinate forms having first term as 'x' coordinate value called as abscissa and second term as 'y' coordinate value called as ordinate.

A = (x₁ , y₁) = (-5 , 3)

B = (x₂ , y₂) = (5 , -1)

Mid point formula  [tex]( \frac{x1 +x2}{2} , \frac{y1+y2}{2} )[/tex],  is used to find the midpoint of a line.

Mid point of the points  A(-5, 3) and B(5, -1) ,

x₁ = -5

x₂ = 5

y₁ = 3

y₂ = -1

So, mid point C =  [tex]( \frac{(-5)+5}{2} , \frac{3+(-1)}{2} )[/tex]

C =  [tex]( \frac{0}{2} , \frac{2}{2} )[/tex]

C = (0 , 1) = (x , y)

The mid point of the points A(-5, 3) and B(5, -1) is point C(0 , -1)

The plotting of line segment is shown in the picture.

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Answer:

150x8=1,200 so that much more

Step-by-step explanation:

Darryl will need to save an additional $187.50 per month for the next 8 months in order to accomplish his original goal of saving $150 per month for 18 months.

In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a quantity.

Expressions can be simple or complex, and they can be used to perform mathematical operations, make comparisons, or evaluate functions.

An expression can contain any combination of numbers, variables, and operators, such as addition, subtraction, multiplication, division, and exponentiation.

For example, 3 + 5, 2x - 7, and (4a + 2b) / (3c - d) are all examples of expressions.

We have,

Darryl intended to save $150 a month for 18 months, which would have given him a total savings of:

$150/month x 18 months

= $2,700

However, after 10 months, he has only managed to save $1,200.

This means he fell short of his goal by:

$2,700 - $1,200

= $1,500

To accomplish his original goal, he will need to save an additional $1,500. Since he has 8 months left to save, he will need to save:

$1,500 / 8 months

= $187.50 per month

Therefore,

Darryl will need to save an additional $187.50 per month for the next 8 months in order to accomplish his original goal of saving $150 per month for 18 months.

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Solve for [tex]t[/tex] when [tex]h=0[/tex], given [tex]v_0=0[/tex] and [tex]h_0 = 4[/tex].

[tex]0 = -16t^2 + 4 \implies 16t^2 = 4 \implies t^2 = \dfrac14 \implies t = \dfrac12[/tex]

so it will take half a second for the ball to hit the ground.

Answer:

14.

Step-by-step explanation:

1) if mr. Oliveros spent 10$ for his ticket, then the rest sum of his money is 45-10=35$;

2) according to the condition mr. Oliveros spends 35$ for unknown number tickets for students, where 2.5$ for each student. Using this conditiion it is possible to calculate the number of student tickets:

35/2.5=14.

Answer:

3 miles

Step-by-step explanation:

The correct answer will be option b

let x= 5.764764               (1)

multiply both the sides by 1000

1000x = 5764.764              (2)

now substract equation one from equation (2)

999x =  5764

x = 5764/999  

In mathematics, a rational number is a number that can be expressed as the quotient or fraction

p

/

q

of two integers, a numerator p and a non-zero denominator q.[1] For example,

−3

/

7

is a rational number, as is every integer (e.g. 5 =

5

/

1

). The set of all rational numbers, also referred to as "the rationals",[2]

A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example:

3

/

4

= 0.75), or eventually begins to repeat the same finite sequence of digits over and over (example:

9

/

44

= 0.20454545...).[6] This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones

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Step-by-step explanation:

a || b means that a is parallel with b.

a ≅ b means a is congruent with b. that mags that if you orient a and b alike and then put them on top of each other, there is nothing that stands out. they perfectly cover each other.

for angles alone this simply means they have the same size.

A true.

when a line (like in this case r) intersects parallel lines (like in this case p and q), then the angles at the intersections must be the same for p and q.

after all, parallel means that both lines emulate each other's behavior exactly - except for the physical location itself.

B in general is not true. it would only be true, if also r || s.

C true. for the same reasons as A.

D true. for the same reasons as A.