Terrence and Lee were selling magazines for a charity. In the first week, Terrance sold 30% more than Lee. In the second week, Terrance sold 12 magazines, but Lee did not sell any. If Terrance sold 50% more than Lee by the end of the second week, how many magazines did Lee sell? Choose any model to solve the problem. Show your work to justify your answer.

Answer:

5.65685424949 or 5.66

Step-by-step explanation:

In a right-angled triangle, the longest side/leg is called the hypotenuse.

The formula to solve for the hypotenuse is:

hyp^2= side^2+side^2

If the hypotenuse of the triangle is already given then we have to solve for a side.

The formula to solve for the side is:

side^2= hyp^2-side^2

This formula to solve for the side is the opposite of solving for the hypotenuse which is the longest side/leg of the right-angled triangle.

In this question we have to solve for the side.

There are two sides in this triangle. Let's name those sides side a and side b. Side a is already given.

hyp= 9

side a = 7

side^2 = hyp^2-side^2

side b = 9^2 - 7^2

side b = 81 - 49

side b = 32

side b = √32

side b= 5.65685424949. to 2 decimal places -> 5.66

Answer:

12 = x

Step-by-step explanation:

The | | mean absolute value.  Pretty much making every number within the sign a positive.

|-7| + 5 = x

7 + 5 = x

12 = x

Hope this helps.

Whenever you see this " | | "  character, it means that whatever negative number in between those characters are always positive.

It converts -7 to just 7.  This makes the question 7+5.

Giving you the answer 12.

Answer:

p < 0

Step-by-step explanation:

Given

- 3(p - 7) > 21

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.

p - 7 < - 7 ( add 7 to both sides )

p < 0

Answer:

Option B, y = 4.6x + 5.2

Step-by-step explanation:

Slope-intercept form:  y = mx + b

Step 1:  Use those two points to get slope

m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

m = [tex]\frac{42 - 19}{8 -3}[/tex]

m = [tex]\frac{23}{5}[/tex]

m = 4.6

Step 2:  Find the y - intercept

Use point slope formula:  (y - y1) = m(x - x1)

(y - 19) = 4.6(x - 3)

y - 19 + 19 = 4.6x - 13.8 + 19

y  = 4.6x + 5.2

Answer:  Option B, y = 4.6x + 5.2

Answer:

x = 5

Step-by-step explanation:

Given

2x - 2 + 5 = 13, that is

2x + 3 = 13 ( subtract 3 from both sides )

2x = 10 ( divide both sides by 2 )

x = 5

Answer :after four years the price of car depreciate

Final answer:

It will take approximately 4 years for the car to depreciate to $4520 using the declining-balance method of depreciation with a depreciation rate of 30%.

Explanation:

To calculate the number of years it would take for the car to depreciate to $4520, we can use the declining-balance method of depreciation. The declining-balance method is based on a fixed percentage of the remaining value of the asset. In this case, the rate of depreciation is 30%, so the car's value will decrease by 30% each year.

Let's start by finding the value of the car after one year. We can use the formula:

Value after one year = Initial value - (Rate of depreciation * Initial value)

Plugging in the values, we get:

Value after one year = $18820 - (0.3 * $18820) = $18820 - $5646 = $13174

Now, let's find the value after the second year:

Value after two years = $13174 - (0.3 * $13174) = $13174 - $3952.2 = $9221.8

We continue this process until we reach a value of $4520. By the time the car's value reaches $4520, it will have taken approximately 4 years.

Answer:

The length of an edge of the cube = x = [tex]\sqrt[3]{1000}[/tex] = 10 feet

Step-by-step explanation:

i.) A cube has a volume of 1000 cubic feet.

ii) A cube has edges which are all the same length, let us say that the length of an edge of the cube = x feet.

iii) therefore the volume of the cube is = [tex]x^{3}[/tex] = 1000 cubic feet

iv) therefore the length of an edge of the cube = x = [tex]\sqrt[3]{1000}[/tex] = 10 feet

Final answer:

The length of an edge of a cube with a volume of 1000 cubic feet is 10 feet. If each smaller cube has linear dimensions one tenth those of the larger cube, then the volume of each smaller cube is 1 cubic foot.

Explanation:

The volume of a cube is calculated by raising the length of one of its edges to the power of three (cubing it). Since we know the volume of the cube is 1000 cubic feet, we can determine the length of an edge by finding the cube root of the volume. The cube root of 1000 cubic feet is 10 feet, so the length of an edge of the cube is 10 feet.

To find the volume of the smaller cubes mentioned, we note that if their dimensions are one tenth of the larger cube, then each side of a smaller cube will be 10 feet divided by 10, which is 1 foot. The volume of each small cube is then 1 foot cubed, which is 1 cubic foot.

For a visual reference, imagine a larger cube divided evenly into smaller cubes, where the length of each side of the big cube is ten times that of the smaller ones. The result is that each smaller cube's volume is the original volume divided by the cube of 10 (since there are 10 layers of small cubes along each dimension of the big cube).

The correct inequality among the given options is -a > -c. Thus, option A is correct.

To determine the correct inequality among the given options, we need to compare the values of the variables a, b, and c in the number line.

Given: a = -4, b = 1, and c = 7

Let's evaluate each option:

A. -a > -c:

Substituting the values, we have -(-4) > -(7), which simplifies to 4 > -7.

This is true.

B. -a < -b:

Substituting the values, we have -(-4) < -(1), which simplifies to 4 < -1.

This is false.

C. a > 0:

Substituting the value, we have -4 > 0. This is false since -4 is not greater than 0.

Based on the comparisons, the correct inequality is A. -a > -c.

Therefore, the correct answer is A. -a > -c.

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When you subtract the y values you find that each increase in x decreases y by 4.

X is going from 4 to 82 which is 78 units.

78 x 4 = 312

Subtract 312 from the last y value:

209 - 312 = -103

The answer is -103

Answer:

When x = 82, y = -103

Step-by-step explanation:

So an arithmetic sequence is a sequence whose terms differ by a constant value. To find the value of the [tex]n^{th}[/tex] term we need to form an equation for the sequence.

First we need to find the difference between the values of the sequence. In this case the difference is -4:

217 - 221 = -4,  209 - 213 = -4

So the equation is:

[tex]n^{th}[/tex] term = -4n + c

Now we need to find the c, so we substitute the [tex]n^{th}[/tex] term and the term number and solve the equation:

221 = (-4 x 1) + c

221 = -4 + c

c = 225

So the final equation is:

[tex]n^{th}[/tex] term = -4n +225

Now all we need to do is substitute into the equation and find the answer:

[tex]n^{th}[/tex] term = (-4 x 82) + 225

[tex]n^{th}[/tex] term = -328 +225

[tex]n^{th}[/tex] term = -103

The ball reaches the ground after 7.76 s

Step-by-step explanation:

The motion of the ball along the vertical direction is a free fall motion, which is affected by the force of gravity only; therefore it is a uniformly accelerated motion (=constant acceleration), so we can use the following suvat equation:

[tex]s=ut-\frac{1}{2}gt^2[/tex]

where

s is the displacement

u is the initial vertical velocity

[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity

t is the time

In this problem,

u = 38 m/s

Also, we want to find the time t at which the ball hits the ground again: so, when the displacement becomes zero again,

s = 0

Therefore the equation becomes:

[tex]0=38t-\frac{1}{2}9.8t^2\\0=38t-4.9t^2[/tex]

And solving for t,

[tex]t(38-4.9t)=0[/tex]

we have two solutions:

t = 0 (instant at which the ball is kicked)

[tex]38-4.9t=0\\t=\frac{38}{4.9}=7.76 s[/tex]

which is the solution to the problem.

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Numbers are 4 and 8

Step-by-step explanation:

Step 1:

Let the numbers be x and y. Given that their sum is 12 and difference is 4. Form equations for this data.

⇒ x + y = 12 ------ (1)

⇒ x - y = 4 -------- (2)

Subtract eq (2) from (1)

⇒ 2x = 8

⇒ x = 4

Step 2:

Find y.

⇒ y = 12 - x = 12 - 4 = 8

[tex]$-\frac{1}{2}\cdot2=-1[/tex]

Slope of the line h is 2.

The equation for line h is y = 2x + 4.

Solution:

General equation of a line is y = mx + c,

where m is the slope of the line and c is the y-intercept.

In the given image, line g and line h are intersecting lines and perpendicular to each other.

Equation of line g is [tex]y=-\frac{1}{2} x+2[/tex].

Slope of the line g ([tex]m_1[/tex]) = [tex]-\frac{1}{2}[/tex]

If two lines are perpendicular, then the product of the slopes is –1.

⇒ [tex]m_1 \cdot m_2=-1[/tex]

To find the slope of the line h:

[tex]$\Rightarrow-\frac{1}{2} \cdot m_2=-1[/tex]

[tex]$\Rightarrow m_2=-1 \times(-2)[/tex]

[tex]$\Rightarrow m_2=2[/tex]

Slope of the line h is 2.

To find the equation of a line h:

Line h passing through the point (0, 4) and slope 2.

Point-slope formula:

[tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex]

[tex]\left(y-4)=2\left(x-0\right)[/tex]

[tex]y-4=2x[/tex]

[tex]y=2x+4[/tex]

The equation for line h is y = 2x + 4.

The system of equations representing the amounts of Drink A and B made by the company is 1) a = b + 30 and 2) 0.20a + 0.15b = 100.5, where a is the amount in liters of Drink A and b is the amount in liters of Drink B.

Let's denote the number of liters of Drink A by the variable a and the number of liters of Drink B by the variable b. Based on the information given, we can establish a system of two equations in two variables that express the relationships between a and b. The first equation is a = b + 30, expressing the fact that the company makes 30 more liters of Drink A than Drink B.

The second equation is 0.20a + 0.15b = 100.5, which expresses the fact that the sum of 20% of a (the amount of real fruit juice in Drink A) and 15% of b (the amount of real fruit juice in Drink B) equals the total amount of real fruit juice used by the company, which is 100.5 liters.

So the system of equations is:

1) a = b + 30

2) 0.20a + 0.15b = 100.5

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To determine the number of liters of Drink A and Drink B made, we can set up a system of equations using the given information.

To write a system of equations, we need to define the variables that represent the number of liters of Drink A and Drink B. Let's use:

A = number of liters of Drink A made

B = number of liters of Drink B made

From the given information, we can create the following equations:

A = B + 30 (since there are 30 more liters of Drink A than Drink B)

0.20A + 0.15B = 100.5 (since the company used 100.5 liters of real fruit juice)

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(a) 10^5/10^2 = 1000
(b) x^2/x^6 = 1/(x^4)
(c) x^4y/xy^8 = x^3/y^7

a) To rewrite the expression 10^5/10^2 as the product of two fractions, we can write it as (10^5)/(10^2) = (10 * 10 * 10 * 10 * 10) / (10 * 10).

Next, we can simplify this expression by canceling out the common factors in the numerator and denominator. Since both the numerator and denominator have 10 as a common factor, we can simplify further to get (10 * 10 * 10 * 10 * 10) / (10 * 10) = 10 * 10 * 10 = 1000.

Therefore, the equivalent and simpler expression for 10^5/10^2 is 1000.

(b) For the expression x^2/x^6, we can rewrite it as (x * x) / (x * x * x * x * x * x).

Next, we can simplify this expression by canceling out the common factors in the numerator and denominator. Since both the numerator and denominator have x as a common factor, we can simplify further to get (x * x) / (x * x * x * x * x * x) = 1 / (x * x * x * x).

Therefore, the equivalent and simpler expression for x^2/x^6 is 1/(x^4).

(c) To rewrite the expression x^4y/xy^8 as the product of two fractions, we can write it as (x * x * x * x * y) / (x * y * y * y * y * y * y * y).

Next, we can simplify this expression by canceling out the common factors in the numerator and denominator. Since both the numerator and denominator have x and y as common factors, we can simplify further to get (x * x * x * x * y) / (x * y * y * y * y * y * y * y) = (x^3) / (y^7).

Therefore, the equivalent and simpler expression for x^4y/xy^8 is x^3/y^7.

Complete question :-

Rewrite each expression as the product of two fractions, one of which is equal to . Then, write it as an equivalent, but simpler, expression.. (a) 10^5/10^2 (b) x^2/x^6 (c) x^4y/xy^8

The probability of selecting either a multiple of 4 or a multiple of 5 is [tex]\frac{11}{25}[/tex] or 0.44

Solution:

Given that, A number is chosen at random from 1 to 50

selecting either a multiple of 4 or a multiple of 5

Sample space is given as:

{ 1, 2, 3, ................, 50 }

Muliples of 4 = 4, 8, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52

Favorable outcomes = 12

Muliples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Favorable outcomes = 10

The probability is given as:

[tex]Probability = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}[/tex]

[tex]probability = \frac{12}{50} + \frac{10}{50}\\\\probability = \frac{12+10}{50}\\\\probability = \frac{22}{50}\\\\probability = \frac{11}{25} \text{ or } 0.44[/tex]

Thus probability of selecting either a multiple of 4 or a multiple of 5 is [tex]\frac{11}{25}[/tex] or 0.44

The probability of selecting either a multiple of 4 or a multiple of 5 is 11/25.

A multiple of a number is the product of an integer and that number.

The first step is to determine the numbers that are a multiple of 4. They are  4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48.  There are 12 numbers.

The second step is to determine the numbers that are a multiple of 5. They are : 5, 10 15, 20, 25, 30, 35, 40, 45, 50. There are 10 numbers.

Probability of picking a multiple of 4 or 5 = 12/50 + 10/50 = 22/50 = 11/25

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Answer:

  B.  T<-4, -2>, r(90°, O)

Step-by-step explanation:

Point A' is 4 units left and 2 units down from point A, so the translation is T<-4, -2>.

Segment C"D" is on the -x axis, 90° counterclockwise from segment C'D' on the +y axis. Since rotation angles are measured the same way other angles are measured (positive is CCW), the rotation is +90° about the origin.

The congruence transformation that maps the quadrilateral ABCD to A''B''C''D'' is [tex]T_{ < -4, \, -2 > } \circ T_{90^{\circ}}, origin > (ABCD)[/tex] which corresponds with the option B.

B. [tex]T_{ < -4, \, -2 > } \circ T_{90^{\circ}}, origin > (ABCD)[/tex]

A congruent transformation, which is also a rigid transformation is one in which the size and shape of the original figure is preserved.

The coordinates of the vertices of the quadrilaterals ABCD and A'B'C'D' indicates that the transformation from the quadrilateral ABCD to the quadrilateral A'B'C'D' is a translation of 4 units to the left and 2 units downwards, which can be expressed as T<-4, -2>

The side D'C' in the quadrilateral A'B'C'D' is vertical while the side D''C'' in the quadrilateral A''B''C''D'' is horizontal and due to the order of the letters D'' and C'' in D''C'' arranged from left to right suggesting a 90° counterclockwise rotation about the origin, which is a T90°, origin

The congruence transformation that maps ABCD to A''B''C''D'' therefore is the option B, [tex]T_{ < -4, \, -2 > }\circ T_{90^{\circ}}, origin > (ABCDE)[/tex]

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Answer:

i think it is 68

Step-by-step explanation:

12 x 3 = 36

8 x 4 = 32

36 + 32 = 68

Answer:

5/12

Step-by-step explanation:

Answer:

no graphs r shown...

Step-by-step explanation:

up 1 on y axis then up one for every 3 xs

Answer:

1 3/5

Step-by-step explanation:

Answer:

y = -3x + 3

Step-by-step explanation:

Parallel lines have the same slope.

The given line has a slope of -3, its parallel line will also have a slope of -3... m = -3

y = -3x + c

When x = 1, y = 0

0 = -3(1) + c

c = 3

y = -3x + 3

Answer: [tex]62.92 \frac{mi}{h}[/tex]

Step-by-step explanation:

If we are asked about how fast a car is going, this means we are asked about its velocity [tex]v[/tex], which is defined by the relation between the traveled distance [tex]d[/tex] and time [tex]t[/tex]:

[tex]v=\frac{d}{t}[/tex]

Where:

[tex]d=(330+\frac{1}{3}) mi=330.33 mi[/tex] is the traveled distance

[tex]t=(5+\frac{1}{4}) h=5.25 h[/tex] is the time

Solving the equation with the given information:

[tex]v=\frac{330.33 mi}{5.25 h}[/tex]

Finally:

[tex]V=62.92 \frac{mi}{h}[/tex] This is the car's velocity

Answer:

The speed of the car is 77.72 miles per hour

Step-by-step explanation:

To find out how fast is a car travelling when it traveled 330 and 1/3 miles in 4 and 1/4 hours following formula will be used

     Speed=  [tex]\frac{Distance}{Time}[/tex]

Total distance = 330 and 1/3

                        = 330+ 0.33

                        =  330.33 miles

Total time = 4 and 1/4

                 =  4 + 0.25

                 =  4.25 hrs

putting the values in equation we get speed of car

Speed= [tex]\frac{330.33}{4.25}[/tex]

Speed   = 77.72 miles per hour

So the speed of the car is 77.72 miles per hour

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Answer:

Step-by-step explanation:

4 A + 7K= $83

5 A + 7 K= +7= $90

It means one adult ticket costs 7 more than a kid ticket. If I replace A with K+7 in equation one,  it'll look like

4(K+7) + 7 K= $83

=> 4 K +28+ 7 K= $83

=> 11 K= 83-28= 55

K=5

A= 12

Answer:

  all non-negative real numbers, [0, ∞)

Step-by-step explanation:

Replacing x in the parent function √x with (x+5) shifts the graph horizontally, but has no effect on the vertical extent of the graph. It still ranges from 0 to +∞.

The range of √(x+5) is [0, ∞).

Answer:

[tex]9x^{5}y^{5}[/tex] yards.

Step-by-step explanation:

Given that the area of a rectangle (A) is [tex]45x^{8}y^{9}[/tex] square yards.

If the length of the rectangle (L) is given to be [tex]5x^{3}y^{4}[/tex] yards, then we have to find the width (W) of the rectangle in yards.

Now, A = L × W

⇒ [tex]W = \frac{A}{L} = \frac{45x^{8}y^{9}}{5x^{3}y^{4}} = (\frac{45}{5})\times (\frac{x^{8}}{x^{3}}) \times (\frac{y^{9}}{y^{4}}) = 9x^{8 - 3}y^{9 - 4} = 9x^{5}y^{5}[/tex] yards. (Answer)

Answer

pi*R^2

Step-by-step explanation:

Answer:

Pi feet squared

Step-by-step explanation:

area of circle formula is pi radius squared substitute radius as 1²

Answer:

1161/100

Step-by-step explanation:

Step-by-step explanation:

[tex]cos \: x = sin \: (2x + 57) \\ \\ \therefore \: sin(90 \degree - \: x) = sin \: (2x + 57) \\ \\ \therefore \:90 - \: x = 2x + 57 \\ \\ 90 + 57 \: = 2x + 3 \\ \\ \therefore \:3x = 147 \\ \\ \therefore \: x = \frac{147}{3} \\ \\ \huge \orange{ \boxed{\therefore \: x = 49 \degree}}[/tex]

Answer:

-1, -3/4, -5/8, -1/20, 0

Step-by-step explanation:

-1/20 = -2/40

-5/8 = -25/40

-3/4 = -30/40

0 = 0/40

-1 = -40/40

x - 2y = -4 is the standard form of equation

Solution:

Given equation is:

[tex]y = \frac{1}{2}x + 2[/tex]

We have to write the equation in standard form

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers

From given,

[tex]y = \frac{1}{2}x + 2[/tex]

Simplify the above equation

[tex]y = \frac{x+4}{2}\\\\2y = x + 4[/tex]

Shift the variable terms to the left side of the equation and everything else to the right side

[tex]x - 2y = -4[/tex]

Thus the standard form of equation is found