Jaclyn has $120 saved and earns $40 each month in allowance. Pedro has $180 saved and earns $20 a month in allowance.
If they both save their entire allowances, how long will it take before Jaclyn and Pedro have saved the same amount of money?
Enter your answer in the box

Answer:y=-x+3

Step-by-step explanation:

The coordinate of the midpoint AB is (1/2, 1/2)

From the question, the coordinates of the points are given as

A = (-2, 2)

B = (3, -1)

The midpoint of a line or points is then calculated using the following midpoint formula

Midpoint = 1/2 * (x₂ + x₁, y₂ + y₁)

Where x and y are the coordinates of A and B

Substitute the known values in the above equation

So, we have the following equation

AB = 1/2 * (-2 + 3, 2 - 1)

Evaluate the sum

AB = 1/2 * (1, 1)

Evaluate the products

AB = (1/2, 1/2)

Hence, the midpoint is (1/2, 1/2)

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Answer:

D

Step-by-step explanation:

(14x + 18) and 116 are corresponding angles and are congruent, then

14x + 18 = 116 ( subtract 18 from both sides )

14x = 98 ( divide both sides by 14 )

x = 7

There were 13 salmon fillets that the restaurant served.

The solution to this math problem involves fractions, especially percentage. A percentage is a fraction of a hundred. The literal meaning of percentage is "per 100". Percentage is often referred to as percent. The symbol or sign for percentage is %. The number beside the symbol/sign is the numerator, so for example, 10% can also be written as 10/100.

We're given that 25% of the dinner specials served by the restaurant were salmon fillets. In order to find out how many salmon fillets were served, we only need to multiply 52 by 25%.

52 × 25% =

52 × 25/100 =

(52 × 25)/100 =

1,300/100 = 13

There were indeed thirteen salmon fillets served by the restaurant.

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The measure of the angle PRS is given as follows:

m<PRS = 45º.

As stated in this problem, these following angles are given:

MRQ and and QRN form a ray, hence they are supplementary angles.

For supplementary angles, the sum of the measures is of 180º, hence the measure x of angle QRN is calculated as follows:

142 + x = 180

x = 180 - 142

x = 38º.

The entire diagram forms an angle of 360º, hence:

142 + 38 + 90 + m<MRS = 360º.

270 + m<MRS = 360º

m<MRS = 90º.

The segment PR bisects the angle MRS, dividing into two angles of 90º/2 = 45º, as a bisection of an angle basically splits the angle in half hence these following measures are identified:

The diagram is given by the image at the end of the answer.

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Answer:

x = 1, y = 1

Step-by-step explanation:

This Question involves the concept of Solving Simulteanous Equations.

Simulteanous Equations are 2 sets of equation with 2 unknownes to solve. Methods used are Substitution and Elimination methods, use either to solve unless question specify a method.

Example:

2x + 4y = 67

3x + 9y = 90

We are given the 2 equations:

y = 2x - 1 (Equation 1)

2x + y = 3 (Equation 2)

We are asked to use the Substitution Method.

We first substitute Equation 1 to Equation 2 to find the value of x.

2x + (2x - 1) = 3

2x + 2x - 1 = 3

4x - 1 = 3

4x = 3 + 1

4x = 4

x = 4 ÷ 4 = 1

Now we can substitute x into Equation 1 to find the value of y.

y = 2(1) - 1

y = 2 - 1 = 1

The remainder when  2 to the 100th power is divided by 5 is 8.

The remainder when 2 to the 100th power is divided by 5 is 8. We can achieve the accurate result by using the exponential formula where:

a^mn = a^m(n)

So, applying this here, we will have

2^10 (10)/5

Recall that multiplying 10 by 10 will give us 100. What was done in this case is simply splitting the figures up to make the division simpler. The exponential law was applied here.

Now, 2^10/5

204.8

The remainder as we can see from this result is 8. Thus we arrive at the answer 8.

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Answer: B

Step-by-step explanation:

The root at [tex]x=-5[/tex] cuts through the x-axis, and has a multiplicity of one. So, it corresponds to a factor of [tex](x+5)[/tex].

The root at [tex]x=-2[/tex] bounces off the x-axis, and has a multiplicity of two. So, it corresponds to a factor of [tex](x+2)^2[/tex].

The root at [tex]x=3[/tex] cuts through the x-axis, and has a multiplicity of one. So, it corresponds to a factor of [tex](x-3)[/tex].

The root at [tex]x=7[/tex] bounces off the x-axis, and has a multiplicity of two. So, it corresponds to a factor of [tex](x-7)^2[/tex].

Answer:

23

Step-by-step explanation:

4h = 92

Divide both sides by 4 to get h by itself

h = 23

The values of g(x) at x = 1, 2 and 3 are 2, 8 and 14 respectively.

Which table contains the values of g(x)?

Since f(x) = 3x - 4 and g(x) = f(2x)

so, in f(x) = 3x - 4, we can replace x with 2x:  

g(x) = f(2x) = 3(2x) - 4 = 6x - 4

when x = 1:

g(x) = 6(1) - 4

      = 6 - 4 = 2

when x = 2:

g(x) = 6(2) - 4

      = 12 -  4 = 8

when x = 3:

g(x) = 6(3) - 4

      = 18 -  4 = 14

Therefore, when x = 1, 2 and 3, their corresponding values of g(x) are 2, 8 and 14.  So 4th table contains the values of g(x).

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Answer: D

Step-by-step explanation: I Chose D and got it right for my quiz.

two lines are parallel if their slope is equal

equation of line is

y=mx+c

where m=slope

for y=2x-5

m=2

for -x+2y=-5

2y=-5+x

y=-5/2+x/2

m=1/2

lines are nor parallel becuase m (slope) is not equal

now we will test for perpendicularity

perpendicular lines have slopes that are reciprocal of each other

first line , m=2

second line, m=1/2

2 and 1/2 are reciprocals

therefore, the lines are perpendicular

The value of x is 11.

What is an equation?

Equations are mathematical statements which contains two algebraic expressions on both sides of an equal to '=' sign. it represents the relationship of equality among the expressions.

We are given an equation (7x+4)+(10x-11)=180

We open brackets and simplify the equation by adding similar values we get

17x-7=180

17x=187

on dividing both sides by 17 we get

x=11

Hence the value of x is 11

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Answer:

a) Difference of squares:

[tex]10000 - {x}^{2} [/tex]

b) The area of the parking lot decreases because x^2 is subtracted from 10,000.

[tex]10000 - {1}^{2} = 10000 - 1 = 9999[/tex]

[tex]10000 - {2}^{2} = 10000 - 4 = 9996[/tex]

Answer:

using the quadratic formula

Step-by-step explanation:

x= 3/2

Answer:

wow your so goood

Step-by-step explanation:

Answer:

x =(8-√204)/2=4-√ 51 = -3.141

x =(8+√204)/2=4+√ 51 = 11.141

Step-by-step explanation:

Factoring  x2-8x-35

The first term is,  x2  its coefficient is  1 .

The middle term is,  -8x  its coefficient is  -8 .

The last term, "the constant", is  -35

Step-1 : Multiply the coefficient of the first term by the constant   1 • -35 = -35

Step-2 : Find two factors of  -35  whose sum equals the coefficient of the middle term, which is   -8 .

     -35    +    1    =    -34

     -7    +    5    =    -2

     -5    +    7    =    2

     -1    +    35    =    34

Age of Judy = 12 yrs old

Age of x = 8 yrs old

Age of Mukta= 16 yrs old

Ratio between the 3 ages = 12 : 8 : 16

Since all the three numbers are divisible by 4

Therefore the ratio comes out to be 3 : 2 : 4 or 3 ratio 2 ratio 4

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Answer:

= 12 : 8 : 16

all the three numbers are divisible by 4

the ratio is 3 : 2 : 4

The value of x in the given equation is 24.

Given equation:

(2/3)x + 4 = (5/6)x

We have to find the value of x by eliminating the fraction.

Fraction

Fraction is  termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 2/4 is a fraction where the upper part denotes the numerator and the lower part is the denominator.

LCM (3,6) = 6

Multiplying the whole equation by 6, we get:-

(2/3)x*6 + 4*6 = (5/6)x*6

4x + 24 = 5x

5x - 4x = 24

x = 24

Hence, the value of x is 24.

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Wherever you see the letter [tex]x[/tex] in the equation, you write [tex]4[/tex], [tex]0[/tex] or [tex]-4[/tex] and perform arithmetic operations. Good luck!

Answer: m = 24

Step-by-step explanation:

The right side of the table is the x value, and the left side is the y value.

Pick two points, I will pick (1,35) and (3,83).

Once you pick the points, input them in the rise over run formula:

y2-y1/x2-x1

83-35/3-1 = 48/2 = 24

The sequence that shows the numbers in order from least to greatest is A. |-8.23| < 8 1/5 < 8.3

It's important to note that arranging numbers from the least to the greatest simply means ascending order.

In this case, it's vital to note that the negative value is the smallest. Then 8 1/5 is 8.2. This conea after. The greatest number is 8.3 since it's the biggest.

In conclusion, the correct option is A.

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Answer:

Increase

Step-by-step explanation:

You start at 15 yards then proceed to MOVE UP(Increase) 3 more yards getting you to 18.

Answer:

increase

Step-by-step explanation:

because your going 3 more yards on a number line you would travel right

I WILL FIND THE GRADIENT FIRST

[tex]m = \frac{y2 - y1}{x2 - x1} \\ = \frac{5 - ( - 8)}{8 - 4} \\ m = \frac{5 + 8}{4} \\ m = \frac{13}{4} [/tex]

THE GENERAL EQUATION OF A STRAIGHT LINE IS y=mx+c

I will use the point (8,5)

to find the value of c

[tex]5 = \frac{13}{4} (8) + c \\ 5 = \frac{104}{4} + c \\ c = 5 - \frac{104}{4} \\ c = - \frac{84}{4} \\ c = -21[/tex]

THE EQUATION IS

[tex]y = \frac{13}{4} x - 21[/tex]

1) Gathering the data

1/5 inch

7/20 inches long

2) Let's them divide, 7/20 by 1/5 inches

When divide fractions, we multiply the reciprocal of the second fraction

and if possible we can simplify

The probability that Gary will get exactly 3 text messages in a 2-hour portion of his work day using the Poisson distribution, what is the time interval of interest: 2 hours

Gary will get calls according to Poisson distribution with an average # of calls per hour = 15.

Let x be the Poisson random Variable Such that X ~Poisson (15).

We need to find P(x≤3) in 2 hours.

Thus, the time interval of interest is 2 hours.

Probability is the likelihood  of an event occurring. It can range from an impossible event  to a probability to an absolute certainty. In mathematics, probability is on a scale of 0-1. Zero means the event is impossible, like rolling  seven dice with only the numbers 1-6. One is an event that will happen, that's for sure. An example of a specific event is tomorrow is Friday if today is Thursday. It will definitely  happen. The median is 0.5 or half and these events are equally likely. A good example of half probability  is tossing a coin. It gets straight heads or tails.

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A. The slope of the function = 1.5.

a = 15; b = 3; c = 3; d = 1.5

B. y-intercept (b) = 7.5

C. The equation of the function is: y = 1.5x + 7.5.

The height in 10 years is approximately 17.5 feet.

The equation of a function can be expressed as y = mx + b, if we know the value of the slope, m, and the value of the y-intercept, b.

Part A:

Using the two points on the graph, we can find the slope of the function as shown below:

The two points are (3, 12) and (5, 15):

Slope of the function = (15 - 12)/(5 - 3)

= 3/2

Slope (m) = 1.5.

Thus, the values that represents each letters would be:

a = 15; b = 3; c = 3; d = 1.5

Part B: The y-intercept of the function

The y-intercept of the function can be defined as the initial tree height which is the point where the line intercepts the y-axis of the graph.

Substitute m = 1.5 and (x, y) = (3, 12) into y = mx + b to find the y-intercept (b) of the function:

12 = 1.5(3) + b

12 = 4.5 + b

12 - 4.5 = b

7.5 = b

b = 7.5

y-intercept (b) = 7.5

Part C: To write the equation of the function, substitute m = 1.5 and b = 7.5 into y = mx + b:

y = 1.5x + 7.5.

Therefore, the initiate tree height is 7.5 feet, and it increases at a rate of 1.5 feet per year.

To find the height in 10 years, substitute x = 10 into the equation of the function, y = 1.5x + 7.5:

y = 1.5(10) + 7.5

y = 10 + 7.5

y = 17.5 feet

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The sigma notation for the sequence 22, 28, 34, 40, 46 is as follows:

[tex]\sum_{n = 0}^{n = 4} 22 + 6n[/tex]

A sequence is represented in sigma notation according to the following rule:

[tex]\sum_{n = 0}^{n = N-1} a + bn[/tex]

In which the parameters are described as follows:

In the context of this problem, the sequence is:

22, 28, 34, 40, 46.

Hence the values of these parameters are given as follows:

Hence the sigma notation of the sequence is given by:

[tex]\sum_{n = 0}^{n = 4} 22 + 6n[/tex]

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Hello! First, let's remember:

We can write a point as a cartesian coordinate (x, y).

The exercise has given two points, A(4,3) and B(8,1).

To calculate the slope of a line, we can use the formula below:

Let's consider A equal to the first point (4, 3) = (x1, y1), and B will be the second point (8, 1) = (x2, y2). Replacing these values in the formula:

To find this length, we have to use another formula. Now we will calculate the distance between two points:

Still considering A (4, 3) = (x1, y1), and B (8, 1) = (x2, y2), let's replace the values in the formula:

This value will be the medium point. To calculate it, we'll use another formula:

Still considering the same values for (x1, y1) and (x2, y2), let's replace them:

The midpoint of segment AB will be at point X (6, 2).

You can see this line represented in a cartesian plan below: