Solve the two step equation
5x-11=34
Show your work

Answer:

I'm pretty sure it's 91

Step-by-step explanation:

8th square number is 64 and the 3rd cube number is 27 so add them together and you get 91

Answer:

\(y+1=\frac{1}{2}(x-6)\)

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so the slope of the line to be found is 1/2.

Substituting into point-slope form, the equation is

\(y+1=\frac{1}{2}(x-6)\)

Answer:

the width of the rectangle is 24 centimeters and the length is 31 centimeters.

Step-by-step explanation:

We first have to write an equation for this, but let's just recall that the area of a rectangle is equal to the length times the width. A=L×W.

A is the area

L is the length

W is the width.

So, for our equation we can start out by putting that 744= ? times ?.

So, we are given that the length is 7 more than the width. We are going to have to translate that to represent the length.

We need a variable. Let's use the letter "W," the width of the rectangle.

W=W.

The length is 7 more than the width, so it is L=W+7.

Length represents the W+7

Width represents W.

Now, we can complete our equation.

744=W(W+7).

Simplify the expression.

744=\(W^{2}\)+7W.

Alright, you may be thinking on how we are going to solve this problem. This equation correlates with quadratic functions.

Let's complete the square.

In a quadratic function, the standard from is y=\(ax^{2} +bx+c\).

We need to find the c value.

We can do this by applying a formula. The formula states that c= b/2 and the whole thing squared. In other words, \((\frac{b}{2} )^{2}\).

In this case, the b value is 7.

square 7, which is 49 and square 2 which is 4.

Now, the c value is 49/4.

We have now just created a perfect square trinomial.

Not only do we add 49/4 to W squared plus 7W, we also add 49/4 to 744.

744 plus 49/4 is 756/25.

Now, we have \(W^{2}+7w+\frac{49}{4} = 756.25\)

Change W squared plus 7w plus 49/4 to a binomial squared.

Just take the square root of the a value, W, and 49/4 for c. the square root of W squared is W. the square root of 49/4 is 7/2.

Those values are to the power of 2.

In other words, \((W+\frac{7}{2})^{2} =756.25\)

To isolate for W, take the square root of both sides.The square root of W plus 7/2 squared is just W+7/2. The square root of 756.25 is 27.5

There are two solutions for W because square roots be positive or negative, but we are dealing with positive since negative doesn't make sense with the context of the problem.

We have \(W+3.5 or \frac{7}{2}=27.5\)

Isolate for W by subtracting both sides by 3.5 You get to W=24.

Therefore, the width of the rectangle is 24 centimeters.

Alright, we found the width. We now need to find the length. The problem stated that the rectangle was 7 more than the width. So, 24+7=31. Therefore, the length of the rectangle is 31 centimeters.

L=31cm

W=24cm.

I hope this was helpful! I wish you have an amazing day!

Answer:

C i think

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

use the side splitter theorem

6/12 = x/18 (replacing AQ with x)

12x = 108 (cross multiply)

x = 9

Answer:$102

Step-by-step explanation:

15% of $120 is $18 so 120-18 is $102

Answer:

$102

Step-by-step explanation:

15 of 120 is 18. We can find this by using the equation (120 x 15)/100

When we subtract 18 from 120 we get 102.

hope this helps!

Answer:

((1+2)x3) + (4x5) = 29

Step-by-step explanation:

Since 4x5 = 20 and 3x3 = 9, and 9 + 20 = 29, we put parenthesis around 1+2,

we get,

((1+2)x3) + (4x5) = 29

This is true because,

(3x3) + (4x5) = 29

(9) + (20) = 29

29 = 29

Answer:

i think it's b4

Step-by-step explanation:

Answer:

p=4

q=2

s=1

t=1/2

Step-by-step explanation:

8,p,q,s,t,1/4

number of terms=6

first term a=8

last term a_{n}=1/4

\(a_{n}=ar^{n-1}\\\frac{1}{4}=8(r)^{6-1}\\\frac{1}{32}=r^5\\(\frac{1}{2})^5=r^5\\r=\frac{1}{2}\\p=8\times r=8 \times (\frac{1}{2})=4\\q=pr=4 \times(\frac{1}{2})=2\\s=qr\\s=2 \times (\frac{1}{2})=1\\t=sr\\=1 \times (\frac{1}{2})=\frac{1}{2}\)

Answer:

240

Step-by-step explanation:

Answer:

B should be worth more points.

Step-by-step explanation:

Given -  Consider a randomly shuffled deck of ten cards labeled

              {1, 1, 2, 2, 3, 3, 4, 4, 5, 5}, of which game play requires three

               to be drawn.

To find - Which one should be worth more points:

              A getting a pair of matching cards within the three,

              or B getting a set of three cards that can be arranged such

              that the sum of two of them is the value of the third.

Proof -

Given that, three cards has to be drawn.

So, total number of ways the card be drawn = ¹⁰C₃

                                                                      = \(\frac{10!}{3! (10-3)!}\)

                                                                      = \(\frac{10!}{3! 7!}\)

                                                                      = \(\frac{10.9.8.7!}{3! 7!}\)

                                                                      = \(\frac{10.9.8}{3.2.1}\)

                                                                      = 120

⇒¹⁰C₃ = 120

Now,

Given that, A getting a pair of matching cards within the three

Sample space = { (1,1,2), (1,1,3).(1,1,4),(1,1,5);

                            (2,2,1),(2,2,3),(2,2,4),(2,2,5);

                             (3,3,1),(3,3,2),(3,3,4),(3,3,5);

                              (4,4,1),(4,4,2),(4,4,3),(4,4,5);

                              (5,5,1),(5,5,2),(5,5,3),(5,5,4) }

⇒n(A) = 20

Also,

B getting a set of three cards that can be arranged such that the sum of two of them is the value of the third

Sample space = { (1,1,2),(1,2,3),(1,3,4),(1,4,5),(2,2,4),(2,3,5) }

⇒n(B) = 6

Now,

P(A) = \(\frac{20}{120} = \frac{1}{6}\) = 0.167

P(B) = \(\frac{6}{120} = \frac{1}{20}\) = 0.05

We can see that, P(B) < P(A)

⇒B should be worth more points.

We have the next equation

the y- intercept is where x=0

so we need to substitute the value of x=0 and find the value of y

the y-intercept is (0,1)

the x-intercept is where y=0

so wee need to substitute the value of y=0 and find the value of x

the x-intercept is (-5,0)

The exponential function that models a 15% decay is: y = (0.85)^t^(1/2)

To find the base that could be written in the blank to make the exponential function model a 15% decay, we can start by understanding the nature of exponential decay.

The general formula for exponential decay is given by:

y = A(1 - r)^t

Where:

y represents the final amount or value after time t.

A is the initial amount or value.

r is the decay rate (expressed as a decimal).

t is the time.

In this case, we want to find the decay rate (r) that corresponds to a 15% decay. A 15% decay means that the final amount is 85% of the initial amount. So, we can write the equation as:

y = A(1 - 0.15)^t

Simplifying further:

y = A(0.85)^t

Comparing this equation to the given form y = (_)t^(1/2), we see that the base in the blank must be 0.85.

Therefore, the exponential function that models a 15% decay is:

y = (0.85)^t^(1/2)

This equation represents a scenario where the initial value or amount (A) is being reduced by 15% over time (t), with the exponent of 1/2 indicating that the decay occurs at a square root rate.

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Answer:

31.01

Step-by-step explanation:

A= πr^2= π · 3.142 ≈31.01432

Answer:

Alessa's car would be able to drive 337.5 miles with 15 gallons of gas.

C. a translation and a dilation

Step-by-step explanation:

the other person isn't wrong they just put it in the wrong order

Answer:c

Step-by-step explanation:took the test

Answer:

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.

give thanks for more! your welcome!

Step-by-step explanation:

The numerical value of x in the similar pair of triangle is 10.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

From the diagram,

Side A of the small triangle = 10

Side B of the small triangle = x + 2

Side A of the Big triangle = 10 + x

Side B of the big triangle = x + 14

Hence;

Ratio of Side A to Side B of the small triangle = 10 / x + 2

Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14

Since the triangle area similar, equate the two ratio and solve for x.

10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )

Cross multiply

10( x + 14 ) = ( 10 + x )( x + 2 )

Expand using FOIL method

10x + 140 = 10x + 20 + x² + 2x

10x + 140 = x² + 12x + 20

x² + 12x + 20 = 10x + 140

x² + 12x + 20 - 10x - 140 = 0

x² + 2x - 120 = 0

Factor the left side of the equation

( x - 10 )( x + 12 ) = 0

Hence;

x - 10 = 0 and x + 12 = 0

x = 10 and x = -12

Since the dimension of the triangle cannot be negative,

x = 10

Therefore, the value of x is 10.

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The equation to determine t, the number of years when the new price increases to $0.10 is 0.05 x 1.0205^t = 0.10.

An equation is a mathematical statement of the equality of mathematical expressions.

Equations use the equation symbol (=) to establish equality.

The price of electricity per kilowatt-hour in 1979 = $0.05

The annual rate of increase = 2.05% or 0.0205

Let the number of years after 1979 = t

The expected new price of electricity per kilowatt-hour after 1979 = $0.10

The equation to determine t, the number of years = 0.05 x 1.0205^t

The equation to determine t, the number of years when the new price is $0.10 can be formed by equating 0.05 x 1.0205^t to 0.10.

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Answer:

Let x be the number of additional outfits.

5 + x < 11

There are 5/9 groups in 1

6 divided by 9/5 is 3 1/3.

An improper fraction is a non integer where the numerator is greater than the denominator. An example is 9/5.

In order to determine the the number of groups of 9/5 that are in 1, divide 1 by 9/5

1 ÷ 9/5

1 × 5/9

9/9 × 5/9 = 5/9

6 ÷ 9/5

6 × 5/9 = 10 / 3 = 3 1/3

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16-4>10

Difference means subtracting

The given expression is

We have to solve the power of 2.

Then, we use the property for negative exponents.

This means we have to move the power to the denominator.

Answer:

1/7140

Step-by-step explanation:

42x5=210

210x34=7140

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By using the given scale, we will see that the real distance is 240km

We know that the scale of the map is 1 cm to 12km, so we just need to take the distance in centimeters on the map, and multiply that number by 12 km.

We know that on the map, the distance between Cardiff and London is 20cm, then the real distance is 12km times that, so we will get:

real distance = 20*12km = 240km

The real distance between Cardiff and London is  240 kilometers.

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Answer:

942 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where S is the surface area, r is the radius, and h is the height.

Substituting the given values, we get:

S = 2 x 3.14 x 10^2 + 2 x 3.14 x 10 x 5

S = 628 + 314

S = 942

Therefore, the surface area of the cylinder is 942 square millimeters.

Transformations are used to move a function from one position to another. The new function g(x) is \(g(x) = \frac{1}{x-1} - 6\)

Given that

\(f(x) = \frac 1x\)

When shifted 6 units down. the rule of transformation is:

\((x,f(x)) \to (x,f(x) - 6)\)

So, we have:

\(f'(x) = f(x) - 6\)

\(f'(x) = \frac 1x - 6\)

When shifted 1 unit left. the rule of transformation is:

\((x,g(x)) \to (x -1,f'(x))\)

So, we have:

\(g(x) = f'(x - 1)\)

\(g(x) = \frac{1}{x-1} - 6\)

Hence, the new function g(x) is \(g(x) = \frac{1}{x-1} - 6\)

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The value of distance AB is 187.5 units

Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other.

sine rule can be expressed as;

a/sinA = b/sinB = c/sinC

The opposite side to angle A is BC

the opposite side to angle C is AB

therefore;

A = 180-( 117 +24)

A = 180- 141

A = 39°

290/sin 39 = x/ sin24

xsin39 = 290 × sin24

0.629x = 117.95

x = 117.95/0.629

x = 187.5

therefore the distance AB is 187.5

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The line or points has a slope value of -1

From the question, we have the following statement that can be used in our computation:

The slope of -3 up to positive 3

For a start, we represent the above parameters using an ordered pair

The ordered pair is represented as

(x, y) = (-3, 3)

The slope of the point is then calculated using the following slope formula

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (-3, 3) and (0, 0)

The coordinate (0, 0) represents the origin

Substitute the known values in the above equation

So, we have the following equation

Slope = (3 - 0)/(-3 - 0)

Evaluate the difference

So, we have the following equation

Slope = (3)/(-3)

Evaluate the quotient

So, we have the following equation

Slope = -1

Hence, the slope is -1

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