Find the x of the triangle

The rate of change of the graph of what the health club charges is; 43

The rate of change is simply the slope of the graph which is the change in y-values per change in corresponding x-values. Thus;

Rate of change here is;

Slope = (y₂ - y₁)/(x₂ - x₁)

We have two coordinates as; (3, 169) and (8, 384) which represents the graph of what the health club charges.

Thus;

Rate of change = (384 - 169)/(8 - 3)

Rate of change = 43

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Answer: x = [tex]\frac{ \sqrt{7}-5}{2}[/tex]

              x = [tex]\frac{ -\sqrt{7}-5}{2}[/tex]

Step-by-step explanation:

[tex](2x + 5)^{2} - 7 = 0[/tex]

Add 7 to both sides of the equation.

[tex](2x + 5)^{2} - 7 + 7= 0 + 7[/tex]

Subtracting 7 from itself leaves 0.

[tex](2x + 5)x^{2} =7[/tex]

Take the square root of both sides of the equation.

[tex]2x + 5 = \sqrt{7} \\2x + 5 = -\sqrt{7}[/tex]

Subtract 5 from both sides of the equation.

[tex]2x + 5 - 5 = \sqrt{7} - 5 \\2x + 5 - 5 = - \sqrt{7} - 5[/tex]

Subtracting 5 from itself leaves 0.

[tex]2x = \sqrt{7} - 5 \\2x = - \sqrt{7} - 5[/tex]

Subtract 5 from [tex]\sqrt{7}[/tex].

[tex]2x = \sqrt{7} - 5[/tex]

Subtract 5 from [tex]-\sqrt{7}[/tex].

[tex]2x = -\sqrt{7} - 5[/tex]

Divide both sides by 2.

[tex]\frac{2x}{2} =\frac{ \sqrt{7}-5}{2} \\\frac{2x}{2} =\frac{- \sqrt{7}-5}{2}[/tex]

Dividing by 2 undoes the multiplication by 2.

[tex]x=\frac{ \sqrt{7}-5}{2}\\x=\frac{ -\sqrt{7}-5}{2}[/tex]

The measure of the base of the triangle is 14 ft.

A triangle is a polygon with three sides.  The sum of angles in a triangle is 180 degrees.

Therefore, the area of a triangle can be calculated as follows:

area of a triangle  = 1 / 2 bh

where

Therefore,

area of the triangle = 28 ft²

height of the triangle = 4 ft

base of the triangle = ?

Hence,

area of the triangle  = 1 / 2 × b × 4

28 = 1 / 2 × b × 4

28 = 4b / 2

28 = 2b

divide both sides by 2

b = 28 / 2

b = 14

Therefore,

base of the triangle = 14 ft

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The measure of the base of the triangle would be; 14 ft.

A triangle is a polygon with three sides.  The sum of angles in a triangle is 180 degrees.

Therefore, the area of a triangle can be calculated by the formula;

The area of a triangle  = 1 / 2 b h

where

b = base

h = height

Thus,

The area of the triangle is 28 ft²

The height of the triangle = 4 ft

The base of the triangle =?

Hence,

Area = 1 / 2 × b × 4

28 = 1 / 2 × b × 4

28 = 4b / 2

28 = 2b

Then divide both sides by 2

b = 28 / 2

b = 14

Therefore, the base of the triangle is 14 ft

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Mac drives 2921 miles per week as compared to Tia

Comparing numbers is a technique for determining if one number is equal to, smaller than, or larger than the other numbers. To compare two numbers, we write them using several symbols. In our daily lives, we make comparisons of figures, such as the daily temperature, the cost of things used on a regular basis, our height and weight, etc. The number with more digits is greater than the number with fewer digits when they are natural numbers.

Miles drove by Tia = 127 miles a week

Miles driven by Mac = Miles driven by Tia*23

= 127*23

2921

So, Mac drove 2921 miles

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Answer:

The correct graph would be D.

Step-by-step explanation:

Since the sign is greater than, we know that it will be a open circle. So, our answer is c. or d.

To solve this problem, distribute, and you get:

3x+9>x+33

Subtract 3x on both sides.

9>-2x+33

Subtract 33 on both sides

9-33=

-24

-24>-2x

Divide by -2 on both sides.

Since we divided by a negative, switch the signs.

12<x

Now, find a graph that is equal to 12<x.

The correct graph would be D.

Hope this helps! ~~

The restaurant can make 992 pancakes in 2 hours

Given

The restaurant uses 124 cups every hour

Each cup can be used to make 4 pan cakes.

Since 1/4 cups of mix can make one pancake.

All the pancakes are in equal size

Since 4 pancakes can be made from one cup of mix

The restaurant uses 124 cups of mix which means

For an hour the restaurant produces 4 x 124 pancakes Which is equal to 496 pancakes

In two hours The restaurant can make double that of one hour

Hence 496 x 2

992

The restaurant can make 992 pancakes in two hours

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[tex]=\sqrt{10*8} \\=\sqrt{80} \\=\sqrt{16*5} \\=\sqrt{16} *\sqrt{5} \\=4\sqrt{5}[/tex]

⇒The SECOND option is The BEST answer .

Δ...BUT also the THIRD OPTION CAN be the answer but it is not simplified completely. IT IS SAFE TO CHOOSE THE SECOND OPTION because it is completely simplified.

Answer:

8

Step-by-step explanation:

D=wp+4

D-4=wp

D-4/w=p

p=100-4/12

p=96/12

p=8

Answer:

Dp/(wp+4)=p

Step-by-step explanation:

Number 1 D=wp+4

p×D=wp×p+4×p

=Dp=wp²+4p

=Dp=p(wp+4)

=from here you will divide both sides (wp+4) to get your answer

Number 2. 100p/(12p+4)=p

so from here 4 will divide 100 25 times leaving the answer 25p/12p=p

Some of the math sums in which the result is under 13 are (5+2), (6+3), (7+5), etc.

According to the question,

We have the following information:

Math sums under 13

Now, we have to find mathematical expressions involving addition but the condition is that the result should be under 13.

Now, we know that we can have 2 or more than 2 numbers in sums but to make it easy we will have only two numbers.

Now, we will take some first numbers in some math sums to be 5, 6 and 7.

Now, the second digit can be found easily by subtracting the numbers from 13.

So, the digits should be less than the result we get.

13-5 = 8

So, it can be less than 8.

13-6 = 7

So, it can be less than 7.

In this way, we can take any digit less than these numbers.

Hence, some of the math sums in which the result is under 13 are (5+2), (6+3), (7+5), etc.

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The ratio of pens Meredith has to ratio of pens Brody has is 2 : 1

The of pencils Meredith has to ratio of pencils Brody has is 1 : 2

Ratio refers to the number representing a comparison between two named quantities.

Comparison of their ratios of pens to pencils:

Ratio of pens Meredith has to ratio of pens Brody has = 8 pens : 4 pens

= 8 / 4

= 2 / 1

= 2 : 1

Ratio of pencils Meredith has to ratio of pencils Brody has = 9 pencils : 9 pencils

= 1 / 1

= 1 : 1

So therefore, their ratio of pens is 2 : 1 and their ratio of pencils is 1 : 1

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Answer: by gamelover

commission of each accessory = $2

commission of each phone = $9

Given:

Commission on 18 phones and 21 accessories = $204 commission on 6 phones and 14 accessories = $82.

To find:

the price of each phone and the price of each accessory.

Solution:

let the commission of each phone be P and the accessory be A.

according to the question,

18P + 21A = 204

6P + 7 A = 68 -----i

6P + 14 A = 82 ------ii

by substitution of i in equation ii,

68 - 7A + 14A = 82

7A = 14

A = 2

commission of each accessory = $2

to find the commission on each phone:

6P + 7 x 2 = 68

6P = 54

P= 9

commission of each phone = $9

Hence, the required answers are 2 and 9.

The two figures are not the same size because 6/3 twice less than 8/4.

A scale factor is defined as the factor that shows how much a figure is greater or smaller than the original size that it's been compared to.

From the square diagram that is given the smaller square is double the larger square.

This can be calculated by dividing the bigger sides by the smaller sides.

That is ;

6/3 =2

8/4 = 2

It can therefore be concluded that the two square shapes are not of the same size as the smaller square is two time smaller that the bigger square.

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The Z-score for the 40-week gestation period baby weights 2450 grams is -0.86 is smaller.

The provided deals with Z-scores. A Z-score shows how many standard deviations away from the mean an element is. A numerical evaluation of a value's relationship to the mean within a group of values is called a Z-score. Z-scores can also be favorable or unfavorable.

The score is above the mean, as indicated by the positive value.

The score is below average as indicated by the negative value.

Given the information,

The mean weight and standard deviation of newborns born after a gestation of 32 to 35 weeks are 2700 grams and 800 grams, respectively.

Consequently, the 33-week gestation baby's Z-score is 2250 grams.

Z = σx − μ​ = (2250−2700) / 800 ​= -450 / 800 ​= −0.5625

The goal is to calculate the Z-score for babies born at 33 weeks gestation.

There is sufficient data to infer, based on the Z-score, that the 33-week gestation period falls 0.56 standard deviations below the mean.

According to the data, babies that are born after a gestation of 40 weeks have a mean weight of 2900 grams and an average range of 445 grams.

Consequently, the baby's Z-score at 40 weeks of pregnancy, weighing 2450 grams, is

Z = σx − μ ​= 385 / 2450 − 2900 ​= 385 / -450 ​= -0.86

The goal is to calculate the Z-score for baby weights at 40 weeks of gestation.

There is sufficient data to infer, based on the Z-score, that the 40-week gestation time falls 0.86 standard deviations below the mean.

The infant weighs 2250 grams at 33 weeks gestation, and the Z-score is -0.56.

The baby weighs 2450 grams at 40 weeks of pregnancy, and the Z-score is -0.86.

Since the infant weighs 2450 grams during 40 weeks of gestation, the Z-score for that period is lesser at -0.86.

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Answer:

A is actually correct :)

Step-by-step explanation:

1/5^6

:]

Total change to Dracula account balance will be the account balance is $40.

What is mean by subtraction?

The operation of taking the difference of two number is called Subtraction.

Given that;

Dracula made a deposit of $220 into his checking account.

Dracula made two withdrawals of $80 each.

Now, Total change to his account after transaction will be calculated as;

Total amount in Dracula account = $220

And, Total withdrawals amount = 2 x $80

                                                = $160

Thus, Money in account after transaction = $220 - $160

                                                               = $40

Therefore, Total change to Dracula account balance will be the account balance is $40.

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To find the set of a quadratic inequation, we first need to find the roots of the quatradic equation. The roots can be found by using the same inequality but changing the inequality sign the euqal sign:

Let's use the Bharkara Equation to find the roots:

So we get the roots x = 3 and x = -5. This are the point at which the graph changes its sign.

The quadratic term (the one multiplying x²) is 1, which is positive. Because of that, the parabola of the quadratic expression has a minimum vertex:

For the drawing, it can be seen that when x is between -5 and 3, the equation has a negative sign, while when x is lower than -5 or greater than 3 the expression has positive sign. We want the expression:

So, when it is greater than 0, meaning positive. Then, the set that solves the quadratic inequation is:

For the given question, the line AC and DF are found to be parallel lines.

Parallel lines are two or more lines which lie within the same plane but never intersect.

The basic properties listed below make it simple to identify parallel lines.

For the given parts:

Part 19: Line AC || Line DF

57° + ∠B = 180° (linear pair)

∠B = 123°

∠B = 123° (corresponding angles are equal)

Thus, Line AC || Line DF

Part 20: Line AC || Line DF

∠B = 143°  (vertically opposite angles)

Then, ∠B + 37°  = 143° + 37°  = 180° (linear pair)

Thus, Line AC || Line DF

Part 21: Line AC || Line DF

62° + ∠B = 180° (linear pair)

∠B = 118°

And, ∠E = 62° (alternate interior angles)

So, ∠B + ∠E = 118° + 62° = 180° (linear pair)

Thus, Line AC || Line DF

Part 22: Line AC || Line DF

∠B = 180° - 115° = 65°

∠B = 65° (alternate interior angles)

Thus, Line AC || Line DF

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Explanation:

Think of a set of dominoes. If domino A pushes over B, which pushes over C, then ultimately A caused C to fall over. So that's how we combine both A=B and B=C to end up with A = C.

You could also think of it using this kind of arrow notation

[tex]\text{If }A \to B \text{ and } B \to C, \ \text{then }A \to C[/tex]

Or you can think of it like going from city A to city B, then to city C. Ultimately you have gone from city A to city C.

The perimeter of a square having area of 36[tex]cm^{2}[/tex] is equal to 24cm

Square of area A= 36[tex]cm^{2}[/tex]

We know that a square is a quadrilateral( a closed figure with four sides) with all 4 sides equal in length. Let the measure of one side of a square be x. from the formula to find out the area of a square we know that

Area of a square A = [tex]x^{2}[/tex]

∴From the data given in the problem

[tex]x^{2}[/tex] = 36

⇒x = √36

⇒x = 6

∴The measure of one side of a square = x cm = 6 cm

We know that the perimeter of a square = x+x+x+x = 4x

∴The perimeter of the given square = 4x = 4 × 6 = 24cm

Hence we get by solving as done above that for a square of area 36cm^2

the perimeter of the square is 24cm

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The percentage decline in profits (to the nearest tenth) is 7.4%.

The smallest percentage fall in profits as a percentage of sales occurred in the food business between 1966 and 1970.  

A percentage is any quantity or ratio that may be expressed as a portion of 100. If we want to calculate a percentage of a number, we should first divide it by 100 before multiplying it by the remainder. The proportion, therefore, denotes a component per 100. The word percent denotes a percentage of 100.

Percentage = (Difference / Total) * 100

According to the question,

Decline percentage = ((2.7-2.5)/2.7)*100

                                 = 7.4%

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Answer:

-7.2s - 11.4

Step-by-step explanation:

Answer:

-7.2s -11.4

Step-by-step explanation:

Distribute the 3 to each value in the parentheses by multiplying

you get -7.2s -11.4

According to the formula of cylindrical volume, we can find out that the rate at which the height of the water level is changing is [tex]\frac{3}{200\pi } inch/min[/tex].

Water is increasing at a rate of ( 3/200π ) inch/min in a cylindrical tank.

It is given to us that, for a right cylindrical tank,

Radius of the base, r = 20 inch ----- (1)

The rate of water poured into the cylindrical tank,

[tex]\frac{dV}{dt}[/tex] = 6 cubic inch per min ------- (2)

We have to find out the rate of change of height when the water level is 12 inches high.

This implies, we need to calculate [tex]\frac{dh}{dt}[/tex].

To find out [tex]\frac{dh}{dt}[/tex] , we have to use the equation for the volume of a right cylinder.

Let us say, the volume of cylinder is represented as V

We know, the formula of volume of a cylinder is

[tex]V = \pi r^{2} h[/tex] ------(3)

Substituting the value of r from equation 1 in equation 3, we will get

[tex]V = \pi r^{2} h\\= > V = \pi 20^{2} h\\= > V = \pi 400 h[/tex] ----- (4)

Differentiate equation (4) with respect to time,

[tex]\frac{d}{dt} V = \frac{d}{dt}[ \pi 400 h]\\= > \frac{dV}{dt}= \pi 400\frac{dh}{dt}[/tex] ----- (5)

Substituting the value of [tex]\frac{dV}{dt}[/tex] from equation (2) in equation (5), we have

[tex]6 = \pi 400\frac{dh}{dt}\\= > \frac{dh}{dt} = \frac{6}{400\pi }\\= > \frac{dh}{dt} = \frac{3}{200\pi } inch/min[/tex]

Thus, [tex]\frac{3}{200\pi } inch/min[/tex]  is the rate at which the height of the water level is changing.

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Answer:

77.2

Step-by-step explanation:

A rise or a decline may be represented by an exponential function in either direction.

This is further explained below.

A)

The exponential function is represented as follows for fuel A:

f(x)=2.96(1.04)^x

A representation of an exponential function looks like this:

y=a b^x

Where b is the rate being calculated.

b=1.04

Since b (which is equivalent to 1.04) is bigger than 1, it follows that the price of gasoline A is going up.

B)

A representation of an exponential function may be seen in the table.

To get the cost of gasoline type B, just divide the current price by the price that was in effect just a moment ago.

Therefore, we have:

[tex]\begin{aligned}&b=\frac{3.41}{3.22} \\&b=1.06\end{aligned}[/tex]

1.06 is a higher number than 1.04, by way of comparison (the rate of fuel A).

Consequently, gasoline B had a bigger percentage shift in price than fuel A did.

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According to the solution of the fractions. Hiroko cuts her string into 6 equal-size pieces.

A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces.​The numerator and denominator of positive common fractions are both natural integers. The denominator shows how many of the numerator's equal parts make up a unit or whole, while the numerator reflects the number of equal parts.

When a fraction is divided, it reciprocated i.e, denominator and numerator change their places. So, in given fraction-

4÷4/6=4×6/4

     =6

Therefore, Hiroko cuts her string into 6 equal pieces.

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Ana is traveling North America, she can exchange for 150 Canadian dollars, 2500 pesos.

Canada's official currency is the Canadian dollar. There is no standard disambiguating form, nevertheless, prominent style guides frequently recommend abbreviation Can$ to distinguish it from other dollar-denominated currencies. It is abbreviated with dollar sign $. There are 100 cents (¢) in it.

Due to the common loon depicted on its reverse, the dollar coin and occasionally the money itself are referred to as "loonies" by English-speaking Canadians, currency dealers, and analysts.

The Canadian dollar ranks behind the U.S. dollar, the euro, the yen, and sterling as the fifth most widely held reserve currency in the world, making up around 2% of all reserves. Because of Canada's relatively stable economy, strong sovereign position, and stability of its judicial and political systems, the Canadian dollar is favored by central banks.

5 pesos = 0.3 Canadian dollars

5\0.3 pesos = 1 Canadian dollars

[tex]150 Canadian dollars= \frac{5}{0.3} * 150 pesos = 2500 pesos[/tex]

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To find out if the system has a single solution, we have to check wheter its equations are not equivalent to one another and no equation contraticds the others.

If these are some cases, we will find out while we answer, because you will either find an equation that the variable can have any number or we will get to an equation that is wrong for any value of the variable.

To find the solution, we will have to reduce the system to two variable and then to one variable.

To do this, we can pick a variable to get rid of and pair equations so we can achieve this.

Let's get rid of variable y by elimination.

Firstly, we can see that the first equations can by simplifies by dividing it by 3:

Now, since we want to eliminate y, we need to match its coefficient with another equation, but with opposite sign.

The second equation has a coefficient of -2 on y, so if we multiply the first simplified equation by -2, we will get:

Now, we can add this equation with the second:

Now, we will do similarly but with the last equation. The coefficient of y on it is -4, so we multiply the first simplified equation by (-4):

And add the third equation to it:

Notice that we can change the sign of all terms on this equation:

Now, we have two equations and two variable:

However, notice that the left side of the equations are equivalent, because if we multiply the first equation by two, we will get the pair:

So, the left side is equivalent, but the right sides are different, this means that one equation contradicts the other, That is, there is no possible pair of x and z so that these equations are both true.

This means that there is no solution to this system of equations.

Answer:

20

Step-by-step explanation:

I took the test and passed I hope this helps.

Answer:

nicholas' score is -120 points

Step-by-step explanation:

-85-35=-120

Step-by-step explanation:

I assume you need the equation in slope-intercept form :

y = ax + b

"a" is the slope, "b" is the y-intercept (the y-value when x = 0).

the slope is defined as ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

let's use the 2 points, where the line intersects the x- and the y- coordinate axis : (0, 9) and (9, 0)

that gives us "b" already : the y-value when x = 0 is 9.

about the slope "a" :

x changes by +9 (from 0 to 9).

y changes by -9 (from 9 to 0).

the slope is then -9/+9 = -1/1 = -1

and the equation is

y = -x + 9