Translate this sentence into an equation.
21 more than Diane's savings is 74.
Use the variable d to represent Diane's savings

Answer:

200 km/hr

Step-by-step explanation:

We can find the speed by dividing the distance by the time taken for the trip.

[tex]\sf \boxed{Speed = \dfrac{distance }{time}}[/tex]

 [tex]\sf r = \dfrac{300}{t}[/tex]

In the above equation, substitute t = 1.5 hours and find the train's rate.

[tex]\sf r = \dfrac{300}{1.5}\\\\= \dfrac{300*10}{1.5*10}\\\\= \dfrac{3000}{15}\\\\r = 200 \ kilometers \ per \ hour[/tex]

Greetings from Brasil...

Let Ca be the function for Plan A and Cb the function for Plan B.

According to the problem statement, we can conclude that:

where C is the cost and n is the number of videos

Cost that the user will pay for having watched n videos

Ca = cost of Plan A

Cb = cost of Plan B

Is there any point (n) that Ca will be equal to Cb??? Let's equate the functions to check if there is a common point and if there is, what would it be.

Ca = Cb

3n + 8 = 5n

2n = 8

n = 4

In n = 4 we have a condition for the cost that does not matter Ca or Cb.

I will present 2 ways to solve:

1 - building the graph of the functions and observing the points where the Y axis (cost axis) its smaller

2 - assigning 2 points - below n = 4 and above n = 4 - to observe the cost behavior

1 - see attachment

2 - let's choose the points n = 1 and n = 10 (as already said, n=4 does not matter Ca or Cb - meeting point / intersection point)

n = 1

Ca(1) = 3.1 + 8 = 11

Cb(1) = 5.1 = 5

Ca > Cb, then Cb better to the user

n = 10

Ca(10) = 3.10 + 8 = 38

Cb(10) = 5.10 = 50

Ca < Cb, then Ca better to the user

We can come to the following conclusion:

0 < n < 4 → better use Plan B (in this interval the cost to the user will be lower with Plan B)

n = 4 → It doesn't matter to use Plan A or Plan B.

n > 4 → better use Plan A (for n above 4 the cost to the user will be lower with Plan A)

3 1/2 subtracted from 4 7/8 is equal to 3/8.

A fraction is a quantity that is not a non-integer. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/2.

A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a fraction is which the numerator is less than the denominator. An example of a mixed number is 3 1/2.

Subtraction is the mathematical operation that is used to determine the difference of two or more numbers. The sign used to represent subtraction is -.

[tex]3\frac{1}{2} - 4\frac{7}{8}[/tex]

[tex]-1\frac{4 - 7}{8}[/tex]

[tex]-1\frac{-3}{8}[/tex] = 3/8.

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The mistake done by Maya consists in operating the power expression (- 3)³ in a wrong manner.

A procedure of solution is shown and we must check if Maya did all the right steps to get a correct result. We proceed to present our procedure to be compared with that of Maya to find the mistake, that is, the step in which all divergences start.

(a³ - b³) / 5, a = 2, b = - 3    Given      

[2³ - (- 3)³] / 5                      Substitution

[8 - (- 27)] / 5                       Definition of power / Power with negative base

(8 + 27) / 5                          Additive inverse of an additive inverse

35 / 5                                  Definition of addition

7                                          Definition of division / Result

The mistake done by Maya consists in operating the power expression (- 3)³ in a wrong manner.

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Answer:

31°

Step-by-step explanation:

A bisector splits an angle into two congruent parts.

In the home run derby competition the percent of hits that were home run is: 25.8%

Information about the problem:

To solve this exercise we have to apply the percentage formula:

hits were home (%) = (home runs/ hits) * 100

hits were home (%) = (32/ 124) * 100

hits were home (%) = 0.2580 * 100

hits were home (%) = 25.8%

Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.

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My possible absolute value is -3 ≤ lx - 2l ≤ 3

What is Absolute Value?

The absolute value (or modulus) l x l of a real number x is the non - negative value of x without regard to its sign. For example, the absolute value of 5 is 5 , and the absolute value of -5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.

Now, the question is:

what is a possible absolute value inequality to represent -1≤x≤5

The representation of inequality -1≤x≤5 of  absolute value will be :

-3 ≤ lx - 2l ≤ 3

Now, add 2 to each segment of the system of inequalities to solve for x while keeping the equation  balanced:

-3 + 2 ≤ x -2 + 2 ≤ 3+2

-1 ≤ x ≤ 5

Hence, my possible absolute value is -3 ≤ lx - 2l ≤ 3

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Answer:

8 + 3x < 2 + x the answer would be x<-3

2x + 23 ≤ 11 the answer would be [tex]x\leq -6[/tex]

1)  8 + 3x < 2

To solve this, you first want to subtract 8 from both sides to isolate 3x on one side.

This gives you 3x < 2 - 8, which can be simplified to 3x < -6.

After you have this, you want to get x on its own. To do this, divide both sides of the inequality by 3 to get x < -6

2)  2x + 23 [tex]\leq[/tex] 11

For this one, we use the same steps. First, subtract 23 from both sides to isolate 2x, giving us 2x [tex]\leq[/tex] 11 - 23, which we simplify down to 2x [tex]\leq[/tex] -12.

From here, we divide both sides of the inequality by 2 to get x on its own. This gives us x [tex]\leq[/tex] -6

All numbers to the equation 2(x-8) + 4x = 6(x-2)-4 are solutions.

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

Given:

2(x-8) + 4x = 6(x-2)-4

On further solving

2x- 16 + 4x = 6x - 12 -4

2x + 4x -6x = -12 -4 +16

6x -6x = 0

6x = 6x

As, both sides are equivalent, all numbers are solutions.

Hence, All numbers are solutions.

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Based on the segment addition postulate, we have:

19. AB = 11

20. BD = 43

21. CY = 33

22. CD = 32

23. XC = 11

24. CZ = 44

25. ST = 24

26. AC = 20

Given the following:

AB = BC = CX = YZ

AD = 54

XY = 22

XZ = 33

Applying the segment addition postulate, we would have the following:

19. AB = YZ

YZ = XZ - XY

Substitute

YZ = 33 - 22

YZ = 11

AB = YZ = 11

AB = 11

20. BD = AD - AB

Substitute

BD = 54 - 11

BD = 43

21. CY = XY + CX

CX = AB = 11

Substitute

CY = 22 + 11

CY = 33

22. CD = AD - 2(AB)

CD = 54 - 2(11)

CD = 32

23. XC = AB = 11

XC = 11

24. CZ = CX + XY + YZ

CZ = 11 + 22 + 11

CZ = 44

25. 4x + 12x = 32 [segment addition postulate]

16x = 32

x = 2

ST = 12x = 12(2)

ST = 24

26. 14 + 3x - 4 = 4x + 4 [segment addition postulate]

10 + 3x = 4x + 4

10 - 4 = 4x - 3x

6 = x

x = 6

AC = 4x + 4 = 4(6) - 4

AC = 20

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The exact trigonometric ratios for the angle x is second quadrant.

Given Radian equals to θ = 27π / 4, we need to find all the Trigonometric ratios for the same -

Lets calculate the value of θ first.

We know π equals 180 degree angle and 2π equals 360 degree, hence with each 2π the radian moves back to zero degree. Which means

θ = 27π / 4 can be reduced to θ = 3π / 4

Hence θ = 135 degree which can be represented as below -

As This lies in second quadrant, hence  on x-axis (Value of base , needs to be taken as -1)

sin θ = 1/√2                            cosec θ = √2

cos θ = -1/√2                          sec θ = - √2

tan θ = -1                               cot θ = - 1

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

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Answer:

-3n+12

Step-by-step explanation:

Term to term rule:

9-6=3

6-3=3

3-0=3

term to term rule is -3

-3 x n + 9 - (-3)

-3n + 12

The cost percentage is 3.61 %.

A cost is the worth of money that has been expended in the production or delivery of a good or service and is therefore no longer accessible for use in accounting, retail, research, or accounting.

A percentage is calculated by dividing a value or a number by its sum, then multiplying the result by 100. The percentage calculation formula is ( value / total value) × 100%.

The cost of all ingredients mixed in the stew is $2.76.

The total sales is $435.98.

57 gallons of stew are sold per week.

Therefore, the total sales per week is

= $2.76 × 57 = $157.32

Hence, the cost percentage of food is:

= ( 2.76 × 57 ) / 435.98

= 157.32 / 435.98

= 0.361

= 3.61 %

The cost percentage of the food is 3.61 %.

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We write 5.14*10^5 to convert from 5.14*10^5.

What is scientific notation?

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The approximate radius of the cylinder  is 4.5m

The formula for calculating the surface area of cylinder is expressed as:

SA = 2πr(r+h)

where

r is the radius

h is the height

Given the following parameters

SA = 221.1 square meters

height = 7.8m

Substitute

221.1= 2(3.14)r(r+7.8)

221.1 = 6.28r^2 + 15.6r

Factorize to have

6.28r^2 + 15.6r - 221.6 = 0

On factoring, the value of the radius is 4.5 meters

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Answer:

the answer is A

Step-by-step explanation:

I hope it helps you

Answer: [tex]-1 \frac{19}{24}[/tex]

Step-by-step explanation:

5/6 + (−2 5/8)=

5/6 + (−2 - 5/8)=

5/6 −2 - 5/8=

(5/6 −2 - 5/8)*24/24=      ==> 24 is the LCM of 6 and 8

[tex]\frac{(5*24/6 -2*24-5*24/8)}{24}[/tex]=

[tex]\frac{(120/6 -48-120/8)}{24}[/tex]=

[tex]\frac{(20-48-15)}{24}[/tex]=

(-28-15)/24=

-43/24 =

(-24-19)/24=

-24/24 -19/24=

-(24/24 +19/24)=[tex]-1 \frac{19}{24}[/tex]

Answer:

answer of the first one

x+1>3 equal to x>2 by subtracting 1 from each side

so x>2 equal ]2,infinity[

answer of the second

-4<x<2 so the quantity of x is all the numbers from -4 to 2 but when it be greater than or smaller than without saying or equal we put the brackets opened so the result is ]-4,2[

but i can,t understand 3 and 4

The height of this cone is 3( 1 +  [tex]\frac{l}{r}[/tex] ). Which have the same volume and surface area.

Given that

The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeters) of the cone.

The formula for the surface area S of a right cone is S=πr2+πrl, where r is the radius of the base and l is the slant height.

To find

The height of the cone.?

So, according to the question

We have,

The surface area of the cone = The volume of the cone.

We know that

The surface area of the cone,

  S = πr²+πrl

And,

The volume of the cone,

 V = [tex]\frac{1}{3} \pi r^2h[/tex]

So, from question

The surface area of the cone = The volume of the cone

  S = V              

Now, put the all values,

 πr²+πrl =  [tex]\frac{1}{3} \pi r^2h[/tex]

πr(r+ l)  =  [tex]\frac{1}{3} \pi r^2h[/tex]

 (r+l) =  [tex]\frac{1}{3}[/tex] × [tex]\frac{\pi r^2h}{\pi r}[/tex]

 (r+l) =  [tex]\frac{1}{3}[/tex] × rh

 [tex]\frac{3(r+l)}{r}[/tex] = h

  h = 3( [tex]\frac{r}{r} + \frac{l}{r}[/tex] )

   h = 3( 1 +  [tex]\frac{l}{r}[/tex] )

So the height of this cone is 3( 1 +  [tex]\frac{l}{r}[/tex] ).

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Answer:

[tex](f + g)( \times ) = { \times }^{4} [/tex]

Answer:

A; x= 8

B; x= -5

C; x= -12

Step-by-step explanation:

a =>  (7x-1)+(15x+5) = 180

22x +4 = 180

22x = 176

x= 8

b=> (x+135)= 130

x= -5

c=> x+60=48

x= -12

1-  if the main coefficient isn't always 1, divide each facets by way of the coefficient so that the resulting equation has a leading coefficient of 1.

2- write the equation within the form ax²+ bx = c

3- write the left aspect of the equation because the rectangular of a binomial and simplify the proper side if possible.

4- add the rectangular of half of the coefficient of the linear time period to both aspects of the equation.

5- practice the rectangular root property for equation and solve as usual.

What do you mean by quadratic?

Quadratics can be defined as a polynomial equation of a second degree, which means that it incorporates a minimum of one time period that is squared. it's also referred to as quadratic equations. the general shape of the quadratic equation is: ax² + bx + c = 0.

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The square root of - 10 is not a real number but a complex number, an irrational number.

Numbers can be classified in real numbers and complex numbers. Real numbers are classified in natural numbers (i.e. 1, 4, 5), whole numbers (i.e. 0, 1, 4, 5), integers (i.e. - 4, -1, 0, 5, 6) and rational numbers (i.e. 5 / 7, 0, - 13 / 3) and part of the irrational numbers (i.e. √3, π) and the rest of irrational numbers are complex numbers (i.e. i 4, - 4 + i 5).

In consequence, the square root of - 10 is not a real number but a complex number, an irrational number.

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Answer:

9

Step-by-step explanation:

a quotient is the result of dividing one number by the other, so we know 8 is being divided by 2

8÷2 is 4

five more just means adding 5

so we are left with 4+5 which =9

Answer:

3/4 or 0.75

Step-by-step explanation:

8-4x=2x

-4x-2x=-8

-6x=-8

x=-6/-8

=3/4 or 0.75

To solve for x, the equation -fx -g = h is correctly rewritten as x = -h/f - g/f.

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given the equation in the question;

-fx - g = h

Solve for x.

To solve for x simply means to make x the subject of the formula or equation.

-fx - g = h

Add g to both side

-fx - g + g = h + g

Negative g and positive g cancels out.

-fx = h + g

Now, divide each term in the equation by the coefficient of x

-fx/-f = h/-f + g/-f

x = -h/f + (-g/f)

x = -h/f - g/f

Therefore, to solve for x, the equation -fx -g = h is correctly rewritten as x = -h/f - g/f.

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The value of the expression when x = 7 is 70

Algebraic expressions are expressions made up of variables, terms, coefficients, factors and constants.

They are also made up of mathematical operations such as addition, multiplication, division, subtraction, etc.

Given the expression;

2x^2- 5x - 3

To determine the the value, we substitute the value of x a 7 into the expression, we have;

2(7)² - 5(7) - 3

expand the bracket

2(49) - 25 - 3

98 - 25 - 3

Find the difference

70

Thus, the value of the expression when x = 7 is 70

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The relation of Kathy that is not a function is: A. {(1, 10), (2, 20), (3, 30)}.

A relation is not a function if there are more than one y-value (range element) that is assigned to one x-value (domain element).

In the first relation, the x-value 1, has three different y-values, 10, 20 , and 30.

However, In the second, third, and fourth relations, each of the x-values has exactly one y-value that corresponds to it. These are all relations that represent functions except the relation in A.

Therefore, the relation of Kathy that is not a function is: A. {(1, 10), (2, 20), (3, 30)}.

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Using the common factors, the expression can be rewritten as follows:

The expression can be represented as follow using common factor.

1 / 4 x³y + 3 / 4 xy²

Using the common factors,

The common factors of 1 / 4 x³y  and  3 / 4 xy² is 1 / 4 xy.

Therefore,

1 / 4 x³y + 3 / 4 xy² = 1 / 4 xy (x² + 3y)

Therefore, rewriting 1 / 4 x³y + 3 / 4 xy² using the common factors is 1 / 4 xy (x² + 3y).

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