Factor the expression using the GCF.

The expression $32z-48$ factored using the GCF is

For the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.

As given in the question,

Geometric mean GM = 30

Let us assume the first number is x

and second number i.e. 9 times of the first number is 9x

By the formula GM = [tex]\sqrt{x.y}[/tex]

Now putting the value

30 = [tex]\sqrt{x.9x}[/tex]

30 = [tex]\sqrt{9x^{2} }[/tex]

30 = 3x (∴ square root of 9 is 3 and sq root of x² is x)

10 = x  (by dividing both the side by 3)

Therefore, for the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.

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1. The length of RS is 5.

2. The length of JK is 6.

3. The length of RT is 4.

4. The perimeter of triangle JKL is 24.

What do you mean by right angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

According to data in the diagram of the given question:

We have :

The ΔJKL, ΔRKS and ΔRTS are right-angle triangle.

The length of RK=3 and KS=4

We are using pythagoras theorem for determine the length of RS,

(RK)²+(KS)²=(RS)²

(3)²+(4)²=(RS)²

9+16=(RS)²

25=(RS)²

(5)²=(RS)²

RS=5

∴ The the length of RS is 5.

Now, we need to find the length of JK,

JK=2(RK)=2(3)=6

JK=6       [Because RK is midpoint of the side JK]

We have given value of KS=4 and the side KS is the opposite side of RT,

So, that's why the value of RT=4.

Now, we will find the perimeter of ΔJKL,

JK=6, KL=8 and we need to find the side JL,

(JK)²+(RL)²=(JL)²

(6)²+(8)²= (JL)²

36+64=(JL)²

100=(JL)²

(10)²=(JL)²

JL=10

The perimeter of the triangle ΔJKL,

Perimeter=6+8+10=24

Therefore, the perimeter of the triangle is 24.

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The asked percentages are given as

1. 90 is 100% of 90.

2. 9 is 10% of 90.

3. 27 is 30% of 90.

A percentage is a particular number or fraction in every hundred. The denominator of the fraction is 100, and it is represented by the symbol "%."

The purpose of percentage calculations is to determine the percentage of a whole in terms of 100. A percentage can be determined using one of two methods:

It should be noted that when the denominator is not a power of 100, the second technique of percentage computation is not used.

Given, a comb has 90 teeth.

1. Find out what percentage of 90 is 90 now.

Let the percentage be x,

(x/100) × 90 = 90

x = (90 × 100)/90

x = 100 %

2. Now, find what percent of 90 is 9.

Let the percentage be x,

(x/100) × 90 = 9

x= (9 × 100)/ 90

x = 10%

3. Now, find what percent of 90 is 27.

Let the percentage be x,

(x/100) × 90 = 27

x= (27 × 100)/ 90

x = 30%

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The winner received 53 of the 75 votes in the student gov. election according to provided ratio.

What is ratio?

In arithmetic, a magnitude relation shows range times one number contains another.

Main body:

Because the ratio of students who voted for the winner compared to all students who voted is 0.70

we can rewrite this as:

0.70 = 70/100

And, because we know the total number of students who voted is 75 and if we call the number of students who voted for the winner s , we can then write this relationship and solve for s :

[tex]\frac{70}{100} = \frac{s}{75}[/tex]

Multiplying both sides by 75.

75*[tex]\frac{70}{100} = \frac{s}{75}[/tex]*75

s= 75*70/100

s = 5250/100

s = 52.5

s ≈ 53.

Hence ,The winner received 53 of the 75 votes.

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A) 1,100 hours is equal to approximately 104days in Saturn.

B) You need to know how hours make 1day in Saturn. i.e 10 hours 34minutes or 10.567hours.

From the question note that the number of hours in one day is different for each planet.

Hence for Saturn;

1 day =  10hours.34minutes

X day   =1,100 hours

Note; 34 minutes in hours will be:

60 minutes  =1hour

34/60      =0.567hour

Thus;

10hours.34minutes   =   10hours +0.567hour

                                   =10.567hours

To find the number of days in 1,100 hours, we cross multiply;

X day  * 10.567hours =1,100 hours * 1 day

       X day  =     1,100 hours * 1 day

                               10.567hours

       X day    =104.1  ≈ 104 days

Therefore, you need to know the number of hours that makes a day in Saturn.i.e 10 hours 34minutes or 10.567hours.

.  Again, 1,100 hours is equal to approximately 104days in Saturn.

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Answer:

Step-by-step explanation:

a) 1/2 of 18 = ?

→ 1/2 of 18

→ (1/2) × 18

→ 18/2 = 9

So, answer is 9.

b) 2/3 of 27 = ?

→ 2/3 of 27

→ (2/3) × 27

→ 54/3 = 18

So, answer is 18.

Answer:

slope = - [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 8) and (x₂, y₂ ) = (10, 2) ← 2 ordered pairs from the table

m = [tex]\frac{2-8}{10-1}[/tex] = [tex]\frac{-6}{9}[/tex] = - [tex]\frac{2}{3}[/tex]

Answer:

area of rhombus=1/2*36*22.5

=405cm^2

Step-by-step explanation:

The coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

 T'(-8, -4) , U'(-8, -6) , V'(-3, -9) , W'(-3, -7)

When a point P(x, y) is rotated 270° counterclockwise around the origin, we flip x and y and reverse the sign of x.

Thus,

The rule to rotate a point P(x, y)  after a rotation 270° counterclockwise around the origin is:

P(x, y) → P'(y, -x)

From the Graph,

In our case, we have the points

T = (4, -8)

U = (6, -8)

V = (9, -3)

W = (7, -3)

Thus, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

P(x, y)          →        P'(y, -x)

T (4, -8)       →       T'(-8, -4)

U  (6, -8)      →       U'(-8, -6)

V  (9, -3)      →        V'(-3, -9)

W  (7, -3)     →        W'(-3, -7)

Therefore, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

 T'(-8, -4) , U'(-8, -6) , V'(-3, -9) , W'(-3, -7)

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The value of angle 5 is 115°

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).

angle 2 is 65°

angle 6 = angle 2 = 65°( corresponding angles)

angle 6 + angle 5 = 180( angles on a straight line)

65 + angle 5 = 180

angle 5 = `180 - 65

angle 5 = 115°

In conclusion, angle 5 is 115°

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Answer:

its A.

Step-by-step explanation:

Answer: 64.95

Step-by-step explanation: The formula is (3√3 s2)/2 so using that we can find the answer which is, 64.95

Reflection at point y = -6 will have coordinates as

preimage      image

Q(0, -9)          Q' (0, -6)

R(4, -9)           R' (4, -6)

S(6, -8)           S' (6, -5)

T(2, -8)           T' (2, -5)

The transformation involve is reflection and this is a type of transformation that produces the mirror image of the preimage

The transformation rule to get the mirror image is (x, y) → (x, y + 3)

The coordinates are applied as follows

Q(0, -9) → (0, -9 + 3) → Q' (0, -6)

R(4, -9) → (4, -9 + 3) → R' (4, 6)

S(6, -8) → (6, -8 + 3) → S' (6, -5)

T(2, -8) → (2, -8 + 3) → T' (2, -5)

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Answer:

Step-by-step explanation:

there is probably a way to do this w/o calculus,  but I cheated and used that.

A = Length * Width

A = x * ( 650 -2x)

A = 650x -2[tex]x^{2}[/tex]

d/dx ( A = 650x -2[tex]x^{2}[/tex])

0=650 -4x

4x = 650

x = 135 m

A= 650*135 -2*[tex]135^{2}[/tex]

A = 51,300  [tex]m^{2}[/tex]

The percent discount given to Suav in the local grocery store is

information given in the problem

The item Suav wants to buy in the grocery store is priced at $21

After the discount, and before tax, the price is $19.53

The discount is found by subtraction as follows

discount = price at the store - price before tax

discount = $21 - $19.53

discount = 1.47

Discount in percent

the problem is discount of the price at the store

percentage deals with a fraction hundred and used as follows

= 1.47/21 * 100

= 7/100 * 100

= 7%

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The standard form of  (3 x 10^199) + (2 × 10^201). is 2.03 x 10^201

The expression given is (3x10^199)+(2*10^201) we need to write it in the standard form

Take 10^199 from the equation

=10^199((3x1)+(2x10^2))

=10^199(3+(2x100))

=10^199(3+200)

=10^199(203)

=203x10^199

2.03 x 10^201

1. there are 201 zeros after 2 and 199 zeros after 3

2. difference  between  201 and 199 is 2

3. on adding both of them the 3 will come 2 spaces to the right of 2

The value of (3 x 10^199) + (2 × 10^201). is 2.03 x 10^201

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The number written on the board is 2 2/5

A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0. where, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. where, x and y are variables, A and B are coefficients and C is a constant.

represent the number on the board by x, the result of the second student by y , therefore the result of the first student is 2y

solving for the first student, 12+x= 2y

for the second student , 3x= y

substituting 3x for y in first equation

12+ x= 2(3x)

12+x= 6x

collecting like terms

5x= 12

divide both side by5

x= 12/5= 2 2/5.

Therefore the number on the board is 2 2/5

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Answer:

c

Step-by-step explanation:

To find a perpendicular line, you must compare the slopes. With the equation y=2x-5, we're looking for the inverse/opposite slope of -1/2.

Option A still has a slope of 2. Option B, when everything is in the format of mx+b = y format is -x-4=-2y. which gives us 1/2 but not -1/2. C when everything is on the right side gives us -2y=x-6. Divide both sides by -2 to get the y by itself and you're left with y = -1/2x+3. Now we found the equation that gives us the -1/2 slope we were looking for.

Answer/Step-by-step explanation:

[tex]-\frac{8}{27} a^{15} = (-\frac{2}{3})^{3} * (a^3)^5 = (-\frac{2}{3} a^{5})^3[/tex]

I hope this helps!

Answer:

solve for x 7 (5x+9)=- (x-9) 7(5x + 9) = −(x − 9) 7 ( 5 x + 9) = - ( x - 9) Simplify 7(5x+9) 7 ( 5 x + 9). Tap for more steps... 35x+63 = −(x−9) 35 x + 63 = - ( x - 9) Simplify −(x−9) - ( x - 9).

Step-by-step explanation:

Rewrite 0+0+7(5x+9)= -(x----9)

Apply the distributive property. 7 (5x) + 7.9= - (x-9)

Answer:

                                 x1  y1    x2  y2

1. 0 - explanation - (4, -2)   (9, -2)     -2 - -2

                                                              4 - 9 (put a fraction bar when you put the y2 and y1 together and put the x2 and y2 in the denominator spot) basically -2 subtract -2 equals 0

2. it would be defined or 0

Answer: 3150

Step-by-step explanation:

We know that 50×2%s is 100%, so 50×63 should result in the total amount of throws she attempts, which is 3150.

Answer: zero slope

Step-by-step explanation:

When the slope of a line is zero it creates a horizontal line.

The value of 9 pounds of blueberries is $24.75.

The value of 5 pounds of blueberries is $13.75.

The fact that the Blueberry Farm sells 6 pounds of blueberries for $16.50 implies that the cost per pound will be:

= $16.50 / 6

= $2.75

Therefore, 9 pounds of blueberries cost:

= Cost per pound × 9

= $2.75 × 9

= $24.75

5 pounds of blueberries will cost:

= 5 × $2.75

= $13.75

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The standard deviation of the length of this plant be 25.

m = 60(mean)

Let the standard deviation be s,

As, the probability for 50<x<70 be 0.75

Z = (x−m)/s

for x=50,

Z=0

for x=70,

Z=(70−50)/s=20/s

Now, the probability for 50<x<70 be,

P(50<x<70) = 0.75

In the standard form 0<z<(20/s)

using Z-table, the area from 0 to 20/s,

= 0.75

s = 25

Hence, the standard deviation of the length of this plant be 25.

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Answer:

SA = 148 cm²

Step-by-step explanation:

the opposite faces of the cuboid are congruent , then

SA = 2(6 × 5) + 2(4 × 5) + 2(6 × 4)

     = 2(30) + 2(20) + 2(24)

     = 60 + 40 + 48

     = 148 cm²

Answer:

These lines are neither parallel nor perpendicular.  

Step-by-step explanation:

Parallel lines are lines that never intersect and perpendicular intersect at a ninety degree angle.

Using desmos, you can find your solution.

I hope this helps

-No one

50 would be the reliability of that measure  by standard error.

What is the standard deviation?

A measure that has no random error and no true score (i.e., is only random error) has zero reliability. A measure that has random error.

50 would be the reliability of that measure .

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If 1/5 of Joanna's monthly savings is $55 the equation of her savings is

The solution to the equation is $275

information from the question include

Joanna saves $55 each month from her part-time job

She saves 1/5 of her earnings

let x represent the Joanna's earnings

The equation of Joanna savings is represented in the form

1/5 of x = 55

This equation deals with multiplication and the term 'of' as used in math represents multiplication

Hence 1/5 of x = 1 / 5 * x = x/5

x/5 = 55

multiplying both sides by 5

x = 275

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