The length of a rectangle is 9cm more than four times the width. If the perimeter of the rectangle is 78 cm, what are its dimensions

Answer:

x=2.51

Step-by-step explanation:

-2.49=-5+x

-5+x=-2.49

-5+x+5=-2.49+5

x=2.51

Answer:

1. The percentage change is 74% and it is a percentage decrease

2. The percentage change is 15% and it is a percentage decrease

3. The percentage change is 20% and it is a percentage decrease

4. The percentage change is 43% and it is a percentage increase

5. The percentage change is 40% and it is a percentage decrease

6. The percentage change is 39% and it is a percentage decrease

Step-by-step explanation:

Given

[tex]1.\ Original = 5; New = 1.3[/tex]

[tex]2.\ Original = 160; New = 136[/tex]

[tex]3.\ Original = 15; New = 12[/tex]

[tex]4.\ Original = 7; New = 10[/tex]

[tex]5.\ Original = $30; New = $18[/tex]

[tex]6.\ Original = 9.6; New = 5.9[/tex]

Required

Determine the percentage change and state whether it's an increase or decrease

Percentage change is calculated as:

[tex]\%Change = \frac{New - Original}{Original} * 100\%[/tex]

[tex]1.\ Original = 5; New = 1.3[/tex]

[tex]\%Change = \frac{1.3 - 5}{1.3} * 100\%[/tex]

[tex]\%Change = \frac{-3.7}5} * 100\%[/tex]

[tex]\%Change = \frac{-3.7 * 100\%}{5}[/tex]

[tex]\%Change = \frac{-370\%}{5}[/tex]

[tex]\%Change = -74\%[/tex]

The percentage change is 74% and it is a percentage decrease

[tex]2.\ Original = 160; New = 136[/tex]

[tex]\%Change = \frac{136 - 160}{160} * 100\%[/tex]

[tex]\%Change = \frac{-24}{160} * 100\%[/tex]

[tex]\%Change = \frac{-24 * 100\%}{160}[/tex]

[tex]\%Change = \frac{-2400\%}{160}[/tex]

[tex]\%Change = -15\%[/tex]

The percentage change is 15% and it is a percentage decrease

[tex]3.\ Original = 15; New = 12[/tex]

[tex]\%Change = \frac{12- 15}{15} * 100\%[/tex]

[tex]\%Change = \frac{-3}{15} * 100\%[/tex]

[tex]\%Change = \frac{-3* 100\%}{15}[/tex]

[tex]\%Change = \frac{-300\%}{15}[/tex]

[tex]\%Change = -20\%[/tex]

The percentage change is 20% and it is a percentage decrease

[tex]4.\ Original = 7; New = 10[/tex]

[tex]\%Change = \frac{10- 7}{7} * 100\%[/tex]

[tex]\%Change = \frac{3}{7} * 100\%[/tex]

[tex]\%Change = \frac{3* 100\%}{7}[/tex]

[tex]\%Change = \frac{300\%}{7}[/tex]

[tex]\%Change = 43\%[/tex] -- (approximated)

The percentage change is 43% and it is a percentage increase

[tex]5.\ Original = $30; New = $18[/tex]

[tex]\%Change = \frac{18- 30}{30} * 100\%[/tex]

[tex]\%Change = \frac{-12}{30} * 100\%[/tex]

[tex]\%Change = \frac{-12* 100\%}{30}[/tex]

[tex]\%Change = \frac{-1200\%}{30}[/tex]

[tex]\%Change = -40\%}[/tex]

The percentage change is 40% and it is a percentage decrease

[tex]6.\ Original = 9.6; New = 5.9[/tex]

[tex]\%Change = \frac{5.9- 9.6}{9.6} * 100\%[/tex]

[tex]\%Change = \frac{-3.7}{9.6} * 100\%[/tex]

[tex]\%Change = \frac{-3.7* 100\%}{9.6}[/tex]

[tex]\%Change = \frac{-370\%}{9.6}[/tex]

[tex]\%Change = -39\%[/tex] -- (approximated)

The percentage change is 39% and it is a percentage decrease

Answer:

x=8

Step-by-step explanation:

1. Subtract the 3 from both side so the new equation states 4x=32

2. Divide both sides by 4 for the final answer of x=8

Answer:

Step-by-step explanation:

Answer:

The answer is 6.75 calories or [tex]6 \frac{3}{4}[/tex]

Step-by-step explanation:

First, we need to find out how many calories per 1/3 minute.

4 1/2 divided by 2 = 2 1/4 or 2.25

2 1/4 or 2.25 x 3 = [tex]6 \frac{3}{4}[/tex] or 6.75 calories

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Answer:

-4 < x < -8

Step-by-step explanation:

Given solve -x > 8 or -x < 4.

Solve each inequality first

-x > 8

Divide both sides by -1

-x/-1 > 8/-1

x < -8

Also if -x < 4

Divide both sides by -1

-x/-1 < 4/-1

x > -4

Combine both inequality x < -8 and x > -4

-4 < x < -8

Hence the solution set is -4 < x < -8

Answer:

3, 4, and 5

Step-by-step explanation:

Given: We're looking for x, x+1, and x+2

Requirements: (x+1)+(x+2)=3(x)

Solve equation:

x+1+x+2=3x

2x+3=3x

3=x

This means the three consecutive integers are 3, 3+1, and 3+2 which is the same as 3, 4, and 5

Answer:

Find the asymptotes.

Vertical Asymptotes:

x

=

−

2

Horizontal Asymptotes:

y

=

0

No Oblique Asymptotes

Answer:

Read Under

Step-by-step explanation:

Just did the quiz. First one is "a + b"

Second spot put "a+b/2"

Third put "c/2"

Finally put "CE" and then "BE"

A parallelogram is a quadrilateral , In which opposite sided are equal and parallel to each other.

The coordinate of point C are (a + b , c)

The coordinates of the midpoint of diagonal BD are [tex](\frac{a+b}{2},\frac{c}{2} )[/tex]

AC and BD intersect at point E with coordinates [tex](\frac{a+b}{2},\frac{c}{2} )[/tex]

By the definition of midpoint, AE ≅ CE  and BE ≅ DE.

Therefore, diagonals AC and BD bisect each other.

Properties of Parallelogram shown below,

Since, Diagonals of a parallelogram bisect each other. Therefore, point E is the mid point of both diagonal AC and BD.

Let us consider , coordinate of point C are (x, y)

By using mid point formula,

                Coordinate of point E =  [tex](\frac{x}{2},\frac{y}{2} )[/tex]

                        [tex](\frac{a+b}{2},\frac{c}{2} )=(\frac{x}{2},\frac{y}{2} )[/tex]

  So,     [tex]C(x,y)=(a+b,c)[/tex]

E is the point at which both diagonal bisect to each other. Therefore, E is the mid point of both diagonal AC and BD.

So, coordinate of point E are [tex](\frac{a+b}{2},\frac{c}{2} )[/tex]

Thus, By the definition of midpoint, AE ≅ CE  and BE ≅ DE.

Therefore, diagonals AC and BD bisect each other.

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Answer and Step-by-step explanation:

Question #10.

We are told to fill in the blank that corresponds to a property of congruence for like KM and line KM.

A property that states that something is equal to itself if the Reflexive Property of Congruence.

The Reflexive Property of Congruence is the answer. This is because it comes from a latin word called reflexus (also known as reflect), which is when something is the same of itself. In this case, the line KM is reflexive, or congruent to itself because when reflected, it reflects onto itself.

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Answer:

yes constant; 65

Step-by-step explanation:

Answer:

Step-by-step explanation:

1,83 x 10^2

Answer:

4 is D = 23

Step-by-step explanation:

the coefficient is the number before the letter

Answer:

(4,-2.5)

Step-by-step explanation:

because you move to the right it is a positive x-axis point and since you are moving down it is a negative y- axis point

Answer:

-3,-4.5

Step-by-step explanation:

Answer: 1/2x + 1/3

Step-by-step explanation:

Given:

1/4(x) + 3/4(x) - 1/2(x) + 1 - 2/3

Step 1: Combine like terms

1/4(x) and 3/4(x) have a common denominator of 4.  This means that you can add them together.

1/4(x) + 3/4(x) = 4/4(x) = x

Step 2: Find the common denominator of x in step 1 and combine like terms  

x - 1/2(x) = 2/2(x) - 1/2(x)

Now that we have the common denominator of x, we can combine like terms.  Its the same as adding or subtracting fractions without a variable.  In this case, you must subtract 1/2(x) from 2/2(x).

2/2(x) - 1/2(x) = 1/2(x)

Step 3: Find the common denominator of the constants and combine like terms

1 - 2/3 = 3/3 - 2/3

Now combine like terms.  Simply subtract 2/3 from 3/3.

3/3 - 2/3 = 1/3

Step 4: Write the simplified equation

1/2(x) + 1/3

This is the answer

Answer:

Answer A

Step-by-step explanation:

In the equation [tex]\dfrac{10}{x^2-1}=\dfrac{15}{3x-3}[/tex], 1 makes the denominator zero and 1 is the solution of the equation derived from cross multiplication.

Given :

Option A)

Given :

[tex]\dfrac{10}{x^2-1}=\dfrac{15}{3x-3}[/tex]

The above expression is not defined for x equal to 1 so, 1 is an extraneous solution.

Simplify the above equation by doing the cross multiplication.

[tex]10(3x-3)=15(x^2-1)[/tex]

[tex]30(x-1)=15(x-1)(x+1)[/tex]

2 = x + 1

x = 1

In the given equation 1 makes the denominator zero and 1 is the solution of the equation derived from cross multiplication.

Therefore, the correct option is A) and therefore, no need to check the other options.

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Answer:

[tex]w=-9/8[/tex]

Step-by-step explanation:

We are given the equation [tex]-2 \frac{1}{4} = 2w[/tex]. To solve this equation, we can divide both sides by 2 to get that [tex]w = -2\frac{1}{4} \div 2 = -\frac{9}{8}[/tex].

Answer:

w = - [tex]\frac{9}{8}[/tex]

Step-by-step explanation:

Given

- 2 [tex]\frac{1}{4}[/tex] = 2w ( change the mixed number to an improper fraction )

- [tex]\frac{9}{4}[/tex] = 2w ( multiply both sides by 4 to clear the fraction )

- 9 = 8w ( divide both sides by 8 )

- [tex]\frac{9}{8}[/tex] = w

Answer:  The density of the second substance = [tex]1.7\text{ g cm}^{-3}[/tex]

Step-by-step explanation:

[tex]\text{Relative density }=\dfrac{\text{Density of substance}}{\text{Density of reference}}[/tex]

Given: Density of a substance is [tex]3.4 \text{ g cm}^{-3}[/tex] .

Its relative density relation to another substance = 2.0

Substitute all values in the formula , we get

[tex]2=\dfrac{3.4}{\text{Density of reference}}\\\\\Rightarrow\ {\text{Density of reference}=\dfrac{3.4}{2}\\\\\Rightarrow\ {\text{Density of reference}=1.7 \text{ g cm}^{-3}[/tex]

Hence, the density of the second substance = [tex]1.7\text{ g cm}^{-3}[/tex]

Answer:

$6.615

Step-by-step explanation:

Okay, does the value 3.5 represent the quantity of rice bought?

Let us assume this answer is yes, then we can go ahead and estimate the cost of the rice as

Total Cost =1.89*3.5

Total Cost =$6.615

87 i think Step-by-step explanation:

Answer: 36

Step-by-step explanation:

Sry I got 12 but I changed it since 36 is correct

Answer:

36

Step-by-step explanation:

( 3 * 2 ) ^(2)

Remember the order of operations;

1. Parenthesis

2. Exponents

3. Multiplication or Division

4. Addition or subtraction

( 3 * 2 ) ^ (2)

Simplify what is in parenthesis first.

(6)^(2)

Now simplify the exponent. Remember, the power or the degree to which the base is at is telling one the number of times one needs to multiply the base by itself;

36

Answer:

The answer is 60

Step-by-step explanation

54

55

56

59

60 The middle number

62

65

66

68

Answer:

60

Step-by-step explanation:

"Median in the middle"

put the set of numbers in order from least to greatest. If you end up having an even amount of numbers in the set, you add the two numbers in the middle then divide by 2 to find the median.

54, 55, 56, 59, 60, 62, 65, 66, 68

55, 56, 59, 60, 62, 65, 66

56, 59, 60, 62, 65

59, 60, 62

60

Answer:

In real the wall will be: 96 ft

Step-by-step explanation:

Given that the scale is

It means 1 inch will represent 4 ft.

so

1 inch = 4ft

Given that the measurement of the “ridge” of your new house on blueprints is 24 inches.

Thus,

24 inches = 24 × 4ft           ∵ 1 inch = 4ft

                = 96 ft              

Therefore, in real the wall will be: 96 ft

Answer: The height of the flagpole is 12 feet.

Step-by-step explanation:

Let the height of the flagpole be 'H'.

So, from the figure, we can conclude that, the height and shadow of the flagpole is in proportion to the height and shadow of the stick.

Given:

Height of stick is,

Shadow of the stick is,

Shadow of the flagpole is,

Now, as these are in proportion, we have

Plug in the given values and solve for 'H'. This gives,

Hence, the height of the flagpole is 12 feet.

Answer:

a>12.5.

Step-by-step explanation:

you need to look at the discriminant in the quadratic formula:

[tex]b^{2} -4ac[/tex]

coming from the quadratic polynomial

[tex]ax^{2} +bx+c=0[/tex]

In our case, b=10 and c=2, hence, the discriminant is

[tex]10^2-4*a*2 \\100-8a[/tex]

We will obtain non-real values if the discriminant is less than zero.

Therefore, this condition is written as

[tex]100-8a<0[/tex]

and we must solve for a. It yields

[tex]100<8a\\a>\frac{100}{8} \\a>12.5[/tex]

Hence, the answer is a>12.5.

The values of a that will result in this equation having non-real solutions must e greater than 12.5

Given the quadratic equation  ax^2 + 10x + 2 = 0

For the equation to have non-real solutions, then b^2 - 4ac < 0

From the given equation;

a = a

b = 10

c = 2

Substitute the given parameters into the formula;

10^2 - 4a(2) < 0

100 - 8a < 0

-8a < -100

8a > 100

a > 12.5

Hence the values of a that will result in this equation having non-real solutions must e greater than 12.5

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Answer:

132

Step-by-step explanation:

you have to reduce the expression by solving 0.09 divided by 1.21 bc of the PEMDAS rule you do 1st parentheses first which is 0.1089 then do the second set of () which is 0.000825 then divide the 2 answers for 132

Answer:

y=17x-55

Step-by-step explanation:

y-(-4)=17(x-3)

y+4=17x-51

y=17x-55

Answer: 100 rides are needed to break even.

Step-by-step explanation:

C(x)=15x+2000 - x is the number of rides.

R(x)=35 x , where x is the number of rides

35x=15x+2000

35-15x=2000~subtract 15x from both sides~

20x=2000 ~simplify~

x=2000/20 ~dividing both sides by 20~

x=100

Step-by-step explanation:

Magnesium chloride (MgCl2).

Answer:a

A

Step-by-step explanation:

Edge 2021

Answer:

349

Step-by-step explanation:

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