Read the problem and answer the question below:

Jason and his 3 brothers want to buy a gift for their mother. They have $314 saved. Each of them will save $17 a week until they have at least $515 for her gift. How much money will they save after 3 weeks? Will they have enough money to buy the gift?

1. What are the hidden questions?

2. Write an equation that can be used to answer each hidden question.

3. Write and solve an equation to find how much money they will save after the 3 weeks. Will they have enough money to buy the gift?

(B) 8n  (C) -6y (A) 23x  (D) -17w

Evaluation:

B. 10 + (-2) is the same as 10 - 2, the answer is 8.

C. 8 - 14 could be rewritten as -14 + 8, depending on which is easier to comprehend. The answer is -6

A. 9 + 14 = 23.

D. -6 - 11 is the same as -11 + (-6), which is -17.

Cheers,

qxxi

The amount that Riley paid for the hair dryer is $225.37.

Given the information in the question, the dryer is depreciating in value. Depreciation is when the value of an asset declines with the passage of time.

The formula that can be used to determine the amount paid for the hair dryer is:

p = FV / (1 - r)^n

Where:

p = $100 / (1 - 0.15)^5

p = $100 / 0.85^5

p = $225.37

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For the obtuse triangle with 16 and 21 as two sides of the triangle there are 18 possible lengths for the third side

An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.

With the obtuse triangle we have the following rule:

a^2 + b^2 < c^2

a + b > c

So, lets called the third side (c)

c + 16 > 21 =  c > 5

c+21 > 16 = c > - 5

21 + 16 > c =  37 > c

The third side must be:  5 < c < 37

To be an obtuse triangle we have:

c^2 > 21^2 +16^2

c^2 > 697

c > 26 (positive integer)

Calculating if the other angles are obtuse:

21^2 > c^2 + 16^2

c^2 < 185

c < 14

16^2 > c^2 + 21^2

c^2 < a negative integer, not possible

This means that for the angle opposite the third side to be obtuse should be:

26 < c < 37

27,28,29,30,31,32,33,34,35,36 = 10 possible lengths

And for the angle opposite the side 21 to be obtuse, should be:

5 < c < 14

6,7,8,9,10,11,12,13 = 8 possible lengths

Total possible lengths = 10 + 8 = 18 possible lengths

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[tex]\huge\begin{array}{ccc}f(x)=\dfrac{4}{5}x-5\end{array}[/tex]

We have:

[tex]f(5)=-1\\\\f(0)=-5[/tex]

therefore we have two points on the line:

[tex](5,-1),\ (0,-5)[/tex]

Use the two points-slope formula:

[tex]A(x_a,\ y_A),\ B(x_B,\ y_B)\\\\y-y_A=\dfrac{y_B-y_A}{x_B-x_A}(x-x_A)[/tex]

Substitute:

[tex](5,-1)\to x_A=5,\ y_A=-1\\(0,-5)\to x_B=0,\ y_B=-5[/tex]

[tex]y-(-1)=\dfrac{-5-(-1)}{0-5}(x-5)\\\\y+1=\dfrac{-5+1}{-5}(x-5)\\\\y+1=\dfrac{-4}{-5}(x-5)\\\\y+1=\dfrac{4}{5}(x-5)\\\\y+1=\dfrac{4}{5}x-4\\\\y+1-1=\dfrac{4}{5}x-4-1\\\\\boxed{y=\dfrac{4}{5}x-5}[/tex]

Answer:

f(x) = 0.8x - 5

Step-by-step explanation:

the equation of a linear function is of the form

f(x) = ax + b

to find  a and b use the given points

f(5) = - 1 ⇒ (5, - 1)

f(0) = - 5 ⇒ (0, - 5 )

substituting into the standard form , (0, - 5 )

- 5 = a(0) + b

- 5 = b

then

f(x) = ax - 5

substitute the other point (5, - 1 )

- 1 = 5a - 5 ( add 5 to both sides )

4 = 5a ( divide both sides by 5 )

[tex]\frac{4}{5}[/tex] = a

f(x) = [tex]\frac{4}{5}[/tex] x - 5

or

f(x) = 0.8x - 5

Answer:

70x+44y

Step-by-step explanation:

step 1: distribute

84x+82y−(14x+38y)

84x+82y−14x−38y

step 2: combine like terms

84x+82y−14x−38y

84+82−14−38

70x+44y

A management conundrum is an issue or difficulty that a manager faces that necessitates a choice. This difficulty or challenge frequently defines the study question and motivates researchers to conduct research to discover a solution that is the given statement is true.

Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Student research also has the following characteristics: Students create questions, tactics, and outcomes that are, at least for them, unique. Students employ the same broad techniques as research mathematicians. They go through data collection, visualization, abstraction, conjecture, and proof cycles.

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An extraneous solution is not part of the solution set because it is not valid in the original problem context and may not satisfy the problem's constraints.

The scenario in problem 14 generates an extraneous solution because it is a solution obtained by squaring both sides of an equation, which can lead to extraneous solutions. These extraneous solutions may not satisfy the original equation, and hence, cannot be considered as a valid solution. To determine if a solution is extraneous, we must check if it satisfies the original equation. If it does not, then it is considered extraneous and should not be used.

In other words, an extraneous solution is an extraneous or unintended answer that is obtained as a result of an error in the solution method, but it may not satisfy the original equation or problem. This can occur when using algebraic methods that involve squaring, square roots, or other operations that can cause the equation to change in such a way that some solutions are no longer valid. To ensure that a solution is valid, it is always important to check that the solution satisfies the original equation, and not just the simplified or transformed equation.

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Answer:

[tex]x_1 + x_2 = \boxed{-5}[/tex]

Step-by-step explanation:

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]

[tex]x_{1,\:2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\implies x_{1,\:2}=\dfrac{-b}{2a}\pm\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]

Let's have

[tex]x_{1}=\dfrac{-b}{2a}+\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]\

[tex]x_{2}=\dfrac{-b}{2a}-\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]

[tex]x_1 + x_2 =\dfrac{-b}{2a}+\dfrac{\sqrt{b^{2}-4ac}}{2a} + \dfrac{-b}{2a}-\dfrac{\sqrt{b^{2}-4ac}}{2a}\\[/tex]

[tex]\dfrac{\sqrt{b^{2}-4ac}}{2a} - \dfrac{\sqrt{b^{2}-4ac}}{2a} = 0\\\\[/tex]

Leaving us with
[tex]\dfrac{-b}{2a} + \dfrac{-b}{2a}\\\\\implies 2 \cdot \left(\dfrac{-b}{2a}\right)\\\\\implies -\dfrac{b}{a}\\\\[/tex]

The given equation is
[tex]3x^2+15x+9=0[/tex]

Here a = 3, b = 15

So
[tex]-\dfrac{b}{a} = --\dfrac{15}{3} = -5\\[/tex]

Answer:
[tex]x_1 + x_2 = \boxed{-5}[/tex]

Therefore , the solution of the given problem of unitary method  comes out to be total cost for to make 15 jars is  12,386.25 euroes.

After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.

Here,

Given :

cost of blackberry = 88 euroes

cost of sugar = 650 euroes

Jam bottles costs =87.75

total cost for to make 15 jars is

=> 15 * (87.75+650+88)

=> 15 * 825.75

=>  12,386.25 euroes

Therefore , the solution of the given problem of unitary method  comes out to be total cost for to make 15 jars is  12,386.25 euroes.

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The image of △ABC is the triangle with vertices (-1, -6), (1, -2) and (3, -2)

The image of point (x,y) after reflecting across the x-axis is (x, -y) and after the translation it is (x + 4, -y).

Applying these transformations to each vertex of △ABC:

So, the image of △ABC is the triangle with vertices:

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The ratio of the areas of the rectangles will be 4:9.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

We know that the sides cannot be the same because it is a rectangle, therefore there is a width and length.

For the width, which is the shortest side, we will keep the radius as it is, that is, for rectangle 1 it will be 2 and for rectangle 2 it will be 3.

For the length, which is the longest side, we multiply the radius by two, which means that rectangle 1 will be 4 (2 x 2) and for rectangle 2 it would be 6 (2 x 3)

If we calculate the area it would be:

Rectangle 1:

2 x 4 = 8

Rectangle 2:

3 x 6 = 18

This means that the radius is 8/18 = 4/9

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The mean duration of the game will be 70%.

The likelihood of not receiving any color will be equal to the likelihood of receiving one fewer ball of each hue:

P(green) = 2/5 P(red after green) = 3/6

P(green after yellow after red) = 1/4 0.5 x 0.4 x 0.25 = 0.05

Suppose we follow a different order:

Yellow has the following probabilities: P(yellow) = 1/6, P(red after yellow) = 3/5, and P(green after red after yellow) = 2/4.

As you can see, we also get denominators of 4,5,6, and numerators of 1, 3, and 2!

Therefore, the result probably will be 0.05 for any feasible combination (believe me on this one)!

How many possible combinations exist?

RGY\sRYG\sYGR\sYRG\sGRY\sGYR

6 combinations are thus feasible. The likelihood of each at 0.05 times 6 equals 0.3.

6 combinations are thus feasible. The likelihood of each at 0.05 times 6 equals 0.3.

The likelihood of all outcomes minus the ones we discovered, or 1 - 0.3 = 0.7, is the probability of not receiving distinct colors.

So 70% is the answer.

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The solution to the system of equations is (-2, -2)

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

The graph

On the graph, we have two lines that intersect at the point (-2, -2)

The point of intersection represent the solution

This means that the solution to the system of equations is (-2, -2)

Hence, the required solution is (-2, -2)

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Answer:

(5, 42)

Step-by-step explanation:

22 + 4x= 42

There is only one that will work.

42 - 22 = 20

4x = 20

x= 5

"  X is the number of weeks they have gotten the allowance "

Answer: D. (5,42)

Step-by-step explanation:

If x is representing the weeks that she received her allowance, this means that we would need to add 4 to her starting amount (22) for every week.

So, if she got an allowance for 5 weeks, we would need to multiply her earning amount (4 per week) by the number of weeks (5).

5 x 4 = 20

But, we aren't done just yet! We still need to add this amount to her starting balance, which is $22. So, 20 + 22 = 42.

So, if x is 5, y would be 42, just like in the answer!

Another way of solving this answer would be 22 + 4x = 42.

I hope this helped you :)

Cheers!

Answer:

Below

Explanation:

y = 1/2 x + 1

y = 3/2x + 4        Use first equation to sub in for y  ( equate the equations)

1/2 x + 1  = 3/2 x + 4    solve for 'x'

-3 = x      then use this value in one of the equations to calculate 'y'

y = 1/2 x + 1

y = 1/2 (-3) + 1 =  - 1/2

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 3000e^{0.06\cdot 2} \implies A \approx 3382.49~\hfill \underset{interest~only}{\stackrel{3382.49~~ - ~~3000}{\approx\text{\LARGE 382.49}}}[/tex]

The required image of (−4,−4) after dilation by a scale factor of 5 centered at the origin is (-20, -20).

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

A dilation with a scale factor of k, centered at the origin, will take a point (x,y) in the pre-image to the point (kx,ky) in the image.

Given the required image of (−4,−4) after dilation by a scale factor of 5 centered at the origin.

For x-coordinate:

- 4 × 5 = -20

For y-coordinate:

- 4 × 5 = -20

Thus, the required coordinates are (-20, -20).

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Answer:

The third angle is 60

Step-by-step explanation:

The interior angle of a triangle is equal to the 180 minus the exterior angle.

[tex]180-80=100[/tex]

So one of the interior angles is equal to 100

All of the interior angles of a triangle add up to 180

[tex]180=100+20+x[/tex]

[tex]x=60[/tex]

the answer is in the picture.. if you have any questions feel free to ask

Answer:

No, the following ratios are not proportional, because they are not equal, nor can be reduced.

Step-by-step explanation:

Hope it helps! =D

Answer:

Yurrrr Tha answer to your question is 2.8

Step-by-step explanation:

now tha full Answer is 2.88571429

but hope this help and hope you pass type xhii

Answer: Yes

Step-by-step explanation: The value of x is 3 therefore the equation is balanced.

If the mean arrival rate is 6 customers per hour, then the mean inter-arrival time is calculated to be 10 minutes.

The mean arrival rate of customers = 6 customers/ hour.

Therefore, the mean inter-arrival rate is given as:

Mean inter-arrival rate = 1/ mean arrival rate = 1/6 hour = 1/6 * 60 minutes = 10 minutes.

The inter-arrival time is the time between two consecutive arrivals and is often modeled as an exponential random variable. The exponential distribution has a mean equal to the reciprocal of the rate parameter, which in this case is 6 customers per hour. So, the mean inter-arrival time is 1/6 hour or 10 minutes.

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The area of the triangular prism is calculated as; 170 cm²

The given triangular prism when broken down is made up of;

2 triangles (top and bottom)

2 side rectangles

1 back rectangle

Formula for area of triangle = ¹/₂ * base * height

Formula for area of rectangle = length * width

Thus;

Area of trapezoid = 2(¹/₂ * 5 * 4) + 3(10 * 5)

Area = 20 + 150

Area = 170 cm²

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The average speed of aircraft to dry dock on the trip is given by the equation S₁ = 8 km/h

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the average speed to dry dock be represented as S₁

The time for aircraft for dry docking = 10 hours

Now , the equation will be

The average speed on the return trip S₂ = 20 km/h

The time for aircraft for the return trip = 11 hours

So , Speed = Distance / Time

Substituting the values in the equation , we get

The distance = average speed on the return trip S₂ x time

On simplifying the equation , we get

The distance D = 20 x 11 = 220 km

And , the average speed to dry dock S₁ = 220 km / 10 hour

On simplifying the equation , we get

The average speed to dry dock S₁ = 22 km/hr

Hence , the average speed is 22 km/hr

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The equations that can verify the solution.

-48 = -35 - 13

-48 = 7(-5) - 13

-48 = -7(5) - 13

Options B, C, and D are the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 6 is an equation.

We have,

-48 = -7x P - 13

-48 + 13 = -7P

-35 = -7P

P = 5

The solution is 5.

This means,

-48 = - 7 x 5 - 13

-48 = -35 - 13

-48 = -48

Verified.

Now,

A.

-48 = -7(-5) - 13

-48 = 35 - 13

-48 = 22

Not true.

B.

-48 = -35 - 13

-48 = -48

Verified.

C.

-48 = 7(-5) - 13

-48 = -35 - 13

-48 = -48

Verified.

D.

-48 = -7(5) - 13

-48 = -35 - 13

-48 = -48

Verified.

E.

48 = 35 + 13

48 = 48

True.

F.

48 = 7(5) + 13

48 = 35 + 13

48 = 48

True.

Thus,

-48 = -35 - 13

-48 = 7(-5) - 13

-48 = -7(5) - 13 equations can verify the solution.

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The degree and leading coefficient of each polynomial in one variable is given below :- (2). degree 3; leading coefficient 8 | (4). degree 6; leading coefficient | (6). not a polynomial

The "leading coefficient" is the coefficient of the highest-degree term in the sum of terms that makes up a polynomial.

These expressions all have one variable, so the number of variables is not an issue in any case. All of the exponents are positive integers, so that is not an issue in any case. However, the variable appears in the denominator in the expression of problem 6, so that sum is not a polynomial.

______

(2). In order to put this into the form we recognize as a polynomial, the expression must be "simplified' by performing the multiplication of the two factors:

= 8x³ -4x² +6x -3

The leading coefficient is the coefficient of the highest-degree term, which is the product of the highest-degree terms of the factors. That product is ...

 (2x)(4x²) = 8x³

so the leading coefficient is 8. The variable is to the 3rd power, so the degree is 3.

______

(4). The expression is already written as a sum, so we only need to find the term of highest degree. That is the last one: 7y^6. Its degree is 6 and its leading coefficient is 7.

_____

(6). Variables are not allowed in the denominator of a polynomial. This expression is not a polynomial.

Hence the degree and leading coefficient of each polynomial in one variable is given below :-

(2). degree 3; leading coefficient 8 | (4). degree 6; leading coefficient | (6). not a polynomial

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----------- Correct format of the question is given below --------

(Q). State the degree and leading coefficient of each polynomial in one variable. if it is not a polynomial in one variable, explain why?

*equations of each polynomial is given below in image.*

If you divide $320 by 40 your answer is 8, so Mary probably earns 8 dollars an hour.

The constant variation rate is given as follows:

62.5 miles per hour.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Hence we can solve for the constant as follows:

k = y/x.

In the context of this problem, the constant variation rate is the constant of the proportional relationship, obtained dividing one output by it's respective input, hence:

k = 375/6

k = 62.5 miles per hour.

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