Solve each system of equations by constructing a table. Equation 1: y = 2x + 2
Equation 2: y = -x + 8

Answer:

The zeros of the function are x=-7 and x=2

Step-by-step explanation:

we have

[tex]A(x)=(x-2)(x+7)[/tex]

we know that

The zeros or roots of the function are the values of x when the value of the function is equal to zero (also is called the x-intercepts)

so

For A(x)=0

[tex](x-2)(x+7)=0[/tex]

Remember that

The Zero Product Property states that

if ab = 0, then either a = 0 or b = 0, or both a and b are 0

so

Let

[tex](x-2)=0[/tex] ----> [tex]x=2[/tex]

[tex](x+7)=0[/tex] ----> [tex]x=-7[/tex]

therefore

The zeros of the function are x=-7 and x=2

Answer:

The remaining wood will be 1.25 inches shorter.

Step-by-step explanation:

Only 10 cuts are required to cut the board into 11 equally sized lengths.  Thus, the length of the board after these cuts have been made will be

10(0.125 inches), or 1.25 inches, shorter.

By making 10 cuts, the total length of the board will be reduced by 1.25 inches due to the saw blade reduction. After converting this to feet, Michael will have approximately 15.896 feet of board left.

Michael has a 16-foot board that he plans on cutting into 11 equal lengths. This means he will need to make 10 cuts (as the 11th 'cut' is actually the end of the board not actually needing a cut). The saw blade will decrease the length of the board by -0.125 inches for each cut. To solve this, we multiply the number of cuts by the length that will be reduced by the saw blade. That gives us 10 x -0.125 = -1.25 inches. That means that the total usable length of the board will be reduced by 1.25 inches. We need to convert this to feet since the original length of the board is in feet. There are 12 inches in foot, so -1.25 inches is about -0.104 feet. Thus, the total length of the board after all the cuts will be 16 - 0.104, or approximately 15.896 feet.

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Answer:

28/8=3.5...so probably just 3

Step-by-step explanation:

Answer:

[tex]\large\boxed{x>2\to x\in(2,\ \infty)}[/tex]

Step-by-step explanation:

[tex]2x+3-x>5\qquad\text{subtract 3 from both sides}\\\\2x-x>5-3\\\\x>2[/tex]

Answer:

y<[tex]\frac{-1}{3}[/tex]x+1 is inequality shown on graph.

Step-by-step explanation:

The graph shows representation of inequality,

Here, Line passes through points say, A(3,0) and B(0,1)

The slope of line is given by m=[tex]\frac{Y2-Y1}{X2-X1}[/tex]

m=[tex]\frac{Y2-Y1}{X2-X1}[/tex]

m=[tex]\frac{1-0}{0-3}[/tex]

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

and Y-intercept is c=1

The equation of line is given by y=mx+c

y=[tex]\frac{-1}{3}[/tex]x+1 is equation of line in graph.

To decide which side you are going to shaded area on the graph

Take test of origin.

If (0,0) is statisfy the equation then, shaded the graph towards the origin.

Let suppose,

Take, y<[tex]\frac{-1}{3}[/tex]x+1

0<[tex]\frac{-1}{3}[/tex](0)+1

0<1

TRUE,

Therefore, y<[tex]\frac{-1}{3}[/tex]x+1 is inequality shown on graph.

Answer:

Step-by-step explanation:

1x117 = 117

3x39 = 117

9x13 = 117

The result of the division , 117 divided by 13 is 9.

Given the parameters which can be used in our calculation:

We can write the expression thus :

Now we have :

The result of the division operation is 9

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Answer:

I just did it and got it right so hoped it helped you ;)

1/2

1/2

1/4

Step-by-step explanation:

The probability that both coins will land heads up when Miranda flips them twice, assuming each coin is fair and has an equal chance of landing heads or tails, is 1/4. Each flip has a probability of 1/2 for heads, and these probabilities multiply for sequential independent events.

If Miranda flips a coin twice, the probability that both coins will land heads up needs to be calculated by multiplying the probability of the first coin landing heads up by the probability of the second coin doing the same. Since the chance of a coin landing on heads (assuming it is a fair coin) is usually 50%, that is 1/2 for each flip. Therefore, to find the probability of both coins landing heads up, we multiply these probabilities together: 1/2 × 1/2 = 1/4.

In a broader context, the more times you flip a coin, the closer you are likely to get to 50% heads due to the law of large numbers. Notably, in experiments such as one conducted by Karl Pearson, after 24,000 coin flips, the relative frequency of heads was 12,012/24,000 ≈ 0.5005, closely aligning with the theoretical probability of 1/2. An essential assumption in determining these probabilities is that the coin is fair and each flip is independent of the others.

Polynomials are in standard form when their terms are written in descending order of exponents. Choice B [tex](x^4 - 8x^2 - 16)[/tex] is in standard form. The correct answer is Choice B.

A polynomial is in standard form when its terms are written in descending order of their exponents. Let's evaluate each of the choices:

Therefore, the correct answer is Choice B.

Answer: Janessa has 10 Amari has 34

The number of blue berries with Janessa and Amari are 10 and 34 respectively.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Robert who has 20 blueberries such that he has 10 more blueberries than Janessa and 14 fewer blueberries than Amari.

Assume that the number of blue berries with Janessa and Amari are x and y respectively. We can write the following modelled equations as -

20 = x + 10

20 = y - 14

Solving, we get -

x = 10

y = 34

Therefore, the number of blue berries with Janessa and Amari are 10 and 34 respectively.

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Answer:

4/35

Step-by-step explanation:

5/7-3/5=

find common denominator =35

5/7*5/5=25/35

3/5*7/7=21/35

25/35-21/35=4/35

Answer:

[tex]x + \frac{3}{5} = \frac{5}{7}[/tex]

[tex] \times = \frac{5}{7} - \frac{3}{5} [/tex]

[tex]x = \frac{25}{35} - \frac{21}{35} [/tex]

[tex]x = \frac{4}{35} [/tex]

Answer:

20.397

Step-by-step explanation:

The expression below shows a number in expanded form:

[tex](2\times 10) + \left(3\times  \dfrac{1}{10}\right)+ \left(9 \times \dfrac{1}{100}\right) +\left (7 \times \dfrac{1}{1,000}\right)[/tex]

This expanded form tells you that the number has

Hence, this number is [tex]20.397[/tex]

Answer:

a) 21 nickels and 2 dimes

b) [tex]5x+10y=125[/tex]

c) There are 13 nickels and 6 dimes

d) The point (13,6) a solution to the equation you wrote

Step-by-step explanation:

Let x be the number of nickels and y be the number of dimes in Priya's pocket.

1 nickel = 5 cents

x nickels = 5x cents

1 dime = 10 cents

y dimes = 10y cents

b. Total amount in nickels and dimes is [tex]5x+10y[/tex] cents that is $1.25. Convert $1.25 into cents:

[tex]\$1.25=125\ cents,[/tex]

so the equation that describes the relationship between the number of dimes and number of nickels is

[tex]5x+10y=125[/tex]

a. To find one possible solution, substitute an arbitrary value of y and find x. Let y = 2, then

[tex]5x+10\cdot 2=125\\ \\5x+20=125\\ \\5x=125-20\\ \\5x=105\\ \\x=21[/tex]

21 nickels and 2 dimes

c. The point (13,6) means that there are 13 nickels and 6 dimes.

d. Substitute x = 13 and y = 6 intoe the equation and check whether it is true:

[tex]5\cdot 13+6\cdot 10=65+60=125[/tex]

True, so the point (13,6) a solution to the equation you wrote

Dependent variable: Hot chocolate sales

Independent variable: Outside temperatures

If it is 75°F I don't think people will be buying hot chocolate

But if it's 35°F more people will be buying hot chocolate. The sales of the hot chocolate depends on what the outside temperature is. While the temperature depends on nothing

Answer:

there are 2100 seconds in 35 minutes

There are 60 seconds in a minute, if you times 60 by how many minutes there are, you get how many seconds there are. Here is how I got the answer:

60 x 35 = 2100

I hope this helps you and you can use it for future reference! :)

Answer:

Step-by-step explanation:

y=mx+b is the formula for slope y-intercept form.

Answer:

9

Step-by-step explanation:

gave picture to explain

9 out of 400 phones are likely to be defective.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

If the probability of a phone being defective is 2.1%, we can use this probability to predict how many of the 400 new phones are likely to be defective.

The expected number of defective phones can be found by multiplying the probability of a phone being defective by the total number of phones ordered:

Expected number of defective phones = probability of a phone being defective × total number of phones ordered

In this case, the probability of a phone being defective is 2.1%, or 0.021 as a decimal.

The total number of phones ordered is 400.

So, we can write:

Expected number of defective phones = 0.021 × 400 = 8.4

We can't have a fractional number of defective phones, so we need to round to the nearest whole number.

Since 0.4 is greater than or equal to 0.5, we round up to 9. Therefore, we can predict that 9 of the 400 new phones are likely to be defective.

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Answer:

x=4

Step-by-step explanation:

-3x+4x=2*4-x

x=8-x

8=x+x

8=2x

x=8/2

x=4

Mrs. Bailey had a 75% decrease in the number of candies she had after giving away 9 out of the original 12 pieces.

To calculate the percent decrease of candy Mrs. Bailey had, we begin by identifying the initial amount and the final amount of candy. Mrs. Bailey started with 12 pieces and ended with 3 pieces, which means she gave away 12 - 3 = 9 pieces of candy. To find the percent decrease, we use the formula: “part over total, times one hundred, equals percent.” Here, the “part” is the amount of candy she gave away (9), and the “total” is the original amount she had (12).

The formula for the percent decrease is:

9 / 12 × 100 = 75%

So, the percent decrease in the number of candies Mrs. Bailey had is 75%.

Answer:

$12 per hour

Step-by-step explanation:

3600/6=600

600/50=12

Answer:

None of these choices are correct.

Step-by-step explanation:

The quoted value of 99.875, means that this bond is sold at 99.875%  of the face value and not at a price of  $99.875.

Therefore, calculate price;

Price = 0.99875 * 1000

Price = $998.75

Since brokerage fees is 5.5% of the selling price, Leona will pay additional cost to the quoted price making the total cost to be more than $998.75;

Brokerage fees = (0.055*998.75) = $54.93

Total cost = $998.75 +$54.93

= $1053.68

Therefore, none of the choices is correct.

Answer:

17% ?

Step-by-step explanation:

that seems like the most logical answer

Answer:

16.4

Step-by-step explanation:

this is right

Answer:education and training- speech Language pathologist And curriculum developer

Government and public administration- tax auditor and federal aid coordinator

Law, public safety corrections and security- attorney and paralegal

Step-by-step explanation:

The career clusters and some example careers within each cluster are Agriculture, Food, and Natural Resources (e.g. agricultural engineer, food scientist, forester), Business, Management, and Administration (e.g. accountant, human resources specialist, operations manager), and Health Science (e.g. medical doctor, nurse, medical laboratory technologist).

The career clusters and some example careers that fall under each cluster are as follows:

These are just a few examples, and there are many other careers within each career cluster.

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Answer:

1 meter is 100 centimeters

Henry misread the meters part and assumed his desk was 1 centimeter, which is why he thought his nametag was 7 cm longer.

In reality, his desk is 92 cm longer (100 cm - 8 cm = 92 cm)

Answer: The perimeter of the scale drawing is [tex]30[/tex].

Step-by-step explanation:

You need to analize the information provided in the exercise.

You know that the perimeter of rectangle is [tex]450[/tex] and the scale factor Natalie used to create the scale drawing, was:

[tex]scale\ factor=\frac{1}{15}[/tex]

From this you can identify that, in order to find the perimeter of the scale drawing of the triangle (Which can be represented with [tex]P_2[/tex]), you must multiply the original perimeter ((Which can be represented with [tex]P_1[/tex]), by the scale factor Natalie used.

Therefore, you get that the perimeter is:

[tex]P_{2}=\frac{1}{15}P_1\\\\P_2(\frac{1}{15})(450)\\\\P_2=30[/tex]

Answer:

(x^2-6)(x+2)(x-2)

Step-by-step explanation:

x^4-10x^2+24

(x^2-6)(x+2)(x-2)

The area swept by the minute hand in 12 minutes is 181.58 cm²

Step-by-step explanation:

In the circle clock

∵ The minute hand is swept by 12 minutes

∵ The central angle between each two consecutive minutes = 6°

∴ The central angle when the minute hand swept 12 minutes =

   6 × 12 = 72°

∵ The area of a sector of a circle = [tex]\frac{x}{360}*\pi r^{2}[/tex] ,

   where r is the radius of the circle and x is the central angle of

   the sector

∵ The radius of the circle is the length of the minute hand

∵ The minute hand in a clock is 17 cm long

∴ r = 17 cm

∵ The measure of the central angle is 72°

∴ x = 72°

- Substitute these values in the rule of the area of a sector

∵ Area = [tex]\frac{72}{360}*\pi (17)^{2}[/tex]

∴ Area = 181.58 cm²

The area swept by the minute hand in 12 minutes is 181.58 cm²

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Answer:

The number of number of bags of snacks = m  = 176

The number of beverages supplied = m + 19  = 176 +9 = 185

Step-by-step explanation:

Let us assume the number of bags of snacks = m

So, the number of beverages supplied = m + 19

Total number of items supplied  =  371

⇒ Number of (snacks + beverages) supplied=  371

⇒   m + (m +19)  = 371

or, 2 m = 371 - 19 =  352

or, m =  352 / 2 = 176  

⇒  m  = 176

Hence the number of number of bags of snacks = m  = 176

So, the number of beverages supplied = m + 19  = 176 +9 = 185

Answer:

The value of y is 5 , and The value of x is - 5

Step-by-step explanation:

Given as :

The line passes through point ( - 2, 5)

The slope of line is m =  [tex]\frac{2}{3}[/tex]

Equation of line is written as

y - [tex]y_1[/tex] = m × (x - [tex]x_1[/tex])

Since line passes through line ( - 2 , 5 ) and have slope [tex]\frac{2}{3}[/tex]

So, y - 5 =   [tex]\frac{2}{3}[/tex]  × (x + 2)

Or, 3 × ( y - 5 ) = 2 × ( x + 2 )

Or, 3 y - 15 = 2 x + 4

Or, 3 y - 2 x - 19 = 0 is the equation of line

Now points ( x , 3 ) lies on the line 3 y - 2 x - 19 = 0

So, 3 × 3 - 2 x - 19 = 0

or, 9 - 2 x - 19 = 0

or, 2 x = - 10

∴  x = - [tex]\frac{10}{2}[/tex]

I.e x = - 5

Again points ( - 2 , y )  lies on the line 3 y - 2 x - 19 = 0

So, 3 × y + 2 × 2 - 19 = 0

Or,  3 × y + 4 -19 = 0

or, 3 y = 15

∴  y = [tex]\frac{15}{3}[/tex]

I.e y = 5

Hence The value of y is 5 , and The value of x is - 5   .  Answer

Answer:

130°

Step-by-step explanation:

DEF is an isosceles triangle with base DE and DF = EF.

By definition, base angles of an isosceles triangle are equal.

Hence ∠FDE = ∠DEF = 25°

Angle F = 180° - ∠FDE - ∠DEF

= 180° - 25° - 25°

= 130°