Solve and explain the question below

Roman has a certain amount of money. If he spends $15, then he has 1/4 of the original amount left. How much money did Roman have originally?

Rational number since a rational number is Any integer

Answer:

B) (4, 0)

C) (0, -1)

E) (2, 3)

Step-by-step explanation:

If we see the rule of function then it says that,

a function is a special relationship where each input, x,  has a single output, y.

It means that for every value of x there SHOULD be a different value of y.

A)

(-3,-2) Rejected

because when x = 3, y = -2  

D)

(1, 6) Rejected

because when x = 0, y = 6  

F)

(-5, 9) Rejected

because when x = 4, y = 9  

Answer:

The correct options are A, D and E.

Step-by-step explanation:

The given set of ordered pairs represents a function

[tex]f=\{(-5, 3), (4, 9), (3, -2), (0, 6)\}[/tex]

We need to find THREE ordered pairs that could be added to the set that would allow f to remain a function.

A relation is a function if there exist unique value of y for each value of x.

The x values for given function are -5, 4, 3 and 0.

If we add (-3,-2) in the given set, then we unique value of y for each value of x.  So, option A is correct.

If we add (4,0) in the given set, then we have y=0 and y=9 at x=4. Since the set have more than one value of y for same x-value, therefore option B is incorrect.

If we add (0,-1) in the given set, then we have y=-1 and y=6 at x=0. Since the set have more than one value of y for same x-value, therefore option C is incorrect.

If we add (1,6) in the given set, then we unique value of y for each value of x.  So, option D is correct.

If we add (2,3) in the given set, then we unique value of y for each value of x.  So, option E is correct.

If we add (-5,9) in the given set, then we have y=9 and y=3 at x=-5. Since the set have more than one value of y for same x-value, therefore option F is incorrect.

Therefore the correct options are A, D and E.

Answer:

I believe your problem is

"A baseball team won 10 games in the last 20 games, what percent of the games did the team win?"

In which case the answer is 50 % of the games

Step-by-step explanation:

The total amount of games played is equal to

20 games

If we apply a rule of three

20 games ------------------------100 %

10 games  ------------------------- x

x = (10 games / 20 games) * 100%

x = 0.5*100% = 50%

Answer:

[tex]\boxed{\bold{v=36}}[/tex]

Step-By-Step Explanation:

Switch Sides

[tex]\bold{\frac{7}{6}v=42}[/tex]

Multiply Both Sides By 6

[tex]\bold{6\cdot \frac{7}{6}v=42\cdot \:6}[/tex]

Simplify

[tex]\bold{7v=252}[/tex]

Divide Both Sides By 7

[tex]\bold{\frac{7v}{7}=\frac{252}{7}}[/tex]

Simplify

[tex]\bold{v=36}[/tex]

Answer:

360 points in total, Kevin needs 96 more.

Step-by-step explanation:

88 x 3 is  264

To get a mean of 90, Kevin needs 360 points in total because 90 x the 4 tests is 360.

360 - 264 is 96

so he needs 96 more points.

Answer:

0.875

Step-by-step explanation:

We know that

7/8

is the same as

7÷8

Then using

Long Division for 7 divided by 8

and rounding to a Max of 3 Decimal Places gives us

=0.875

hope this helps:)sorry if it doesnt

plz give brainliest

Answer:

0.875

Step-by-step explanation:

7/8 IS 0.875

you can round to hundredth

so 0.88

Answer:

A.) 64

Step-by-step explanation:

The first step is identifiying the original price of the shoes and the discount

Next you will decide what type of equation you will need. For this situation, you would need a subraction equation.

80 - 20% = ?

If you choose to slove with a calculator, don't put 0.2 in the place of 20%. We dont do this because it will result in a different answer. 80 - 0.2 = 79.8.

Now we solve the problem

80 - 20% = 64

Answer:

(-1,-3)

Step-by-step explanation:

The given system of equations is;

[tex]y=-5x-8...(1)[/tex]

and

[tex]y=4x+1...(2)[/tex]

Let us equate the two equations to get;

[tex]4x+1=-5x-8[/tex]

Group similar terms;

[tex]4x+5x=-8-1[/tex]

Simplify;

[tex]9x=-9[/tex]

Divide both sides by 9.

[tex]x=-1[/tex]

Put x=-1, into any of the equations, say (2);

[tex]y=4(-1)+1[/tex]

[tex]y=-4+1[/tex]

[tex]y=-3[/tex]

The solution is;

(-1,-3)

Answer:

The value of cosФ = -√5/3

Step-by-step explanation:

∵ sinФ = 2/3

∵ tanФ is less than 0

* Lets think about that:

 the value of sin is positive and the value of tan is negative

 according to ASTC rule:

 - All are positive in the first quadrant

 - sin only positive in the second quadrant

 - tan only positive in the third quadrant

 - cos only positive in the fourth quadrant

∴ Angle Ф lies on the second quadrant

∴ The value of cosФ is less than 0

∵ sin²Ф + cos²Ф = 1

∵ sinФ = 2/3

∴ (2/3)² + cos²Ф = 1

∴ cos²Ф = 1 - 4/9 = 5/9

∴ cosФ = ± √5/3

∵ Angle Ф lies on second quadrant

∴ cosФ = -√5/3

The cosine of the angle θ, given that sine θ is 2/3 and tangent θ is negative, is -√(5/9) since the angle is in the second quadrant.

If the sine of an angle (θ) is 2/3 and the tangent of that angle is less than zero, this indicates that the angle is in the second or fourth quadrant, where tangent values are negative. However, since sine is positive, the angle θ must be in the second quadrant. To find the cosine of θ, we can use the Pythagorean identity: sin² θ + cos² θ = 1. Substituting the sine value, we get (2/3)² + cos² θ = 1, which simplifies to 4/9 + cos² θ = 1. Solving for cosine gives us cos² θ = 1 - 4/9 = 5/9. The cosine value itself will be negative because cosine is negative in the second quadrant, so cos θ = -√(5/9).

Answer:

case 1) [tex]z=10[/tex]

case 2) [tex]z=5/32[/tex]

Step-by-step explanation:

case 1) we know that

Using proportion

[tex]\frac{1}{z}=\frac{(4/5)}{8}[/tex]

solve for z

[tex]\frac{1}{z}=\frac{(4/5)}{8}\\ \\z(4/5)=8\\ \\z=8*5/4\\ \\z=10[/tex]

case 2) we know that

Using proportion

[tex]\frac{1}{z}=\frac{4}{5/8}[/tex]

solve for z

[tex]\frac{1}{z}=\frac{4}{5/8}\\ \\4z=5/8\\ \\z=5/32[/tex]

Answer:

20cm or A

Step-by-step explanation:

pythagorean theorem

25^2=15^2+b^2

625=225+b^2

b^2=400

b=20

A because it is the number in between 15 and 25 because the line is shorter

Answer:

Yes

Step-by-step explanation:

The equation is y=2x+4

Andy's assertion is incorrect because the correct equation for the given data must include a y-intercept term. Hence, the equation would be of the form y = mx + b, with the slope m being 2 and the y-intercept b being 4. For this dataset, the equation would be y = 2x + 4.

Andy's statement that he can write an equation of the form y=mx for the given values is incorrect. If we look at the table, we see that as x increases by 1 unit, y increases by 2 units. This indicates that the slope of the line (m) is 2. However, the y-intercept is 4, not 0, hence our equation should have a form y = mx + b, where b ≠ 0. So, for this data, a correct equation would be y = 2x + 4.

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The complete question is here:

Andy uses the table below to write a linear equation.

x : -1, 0, 1, 2

y : 2, 4, 6, 8

He says he can write an equation of the form y=mx for the given values. Is he correct? Explain your reasoning.

Answer:

√23 - 4 , -√23 - 4

Step-by-step explanation:

By completing the square

half of 8 is 4

7+4^2= 23

(x+4)^2=23

Answer:

√23 - 4 , -√23 - 4

Step-by-step explanation:

Answer:

16.7%

Step-by-step explanation:

Total number of cases sold = 24

In order to find what percentage of cases were sold we first need to know the total number of cases that the merchant had.

Let the total number of cases the merchant initially had was x. After selling 24 cases, the number of cases he is left with is x - 24

According to the statement, the number of cases sold (i.e. 24) is 20% of the number of cases the merchant originally had (i.e. x - 24)

This can be written as:

24 is 20% of x - 24

In equation form this becomes:

24 = 20% of ( x - 24)

24 = 0.20(x - 24)

24 = 0.20x - 4.8

24 + 4.8 = 0.20x

28.8 = 0.20x

x = 144

This means the merchant initially had 144 cases of tapes. He sold 24 of them. So the percentage of cases he sold will be:

[tex]\frac{24}{144} \times 100\%\\\\ = 16.7%[/tex]

Therefore, the merchant sold 16.7% of the cases of tapes.

Answer:

B because it is close to 30

Step-by-step explanation:

Answer:

The correct answer is option A   17.8°

Step-by-step explanation:

From the figure attached with this answer,

We can see a perpendicular from B to side AC

To find BD

In triangle BDC, its angles are 30°, 60° and 90°

Therefore the sides are in the ratio 1 :√3 : 2

Here BC = 11

BD : DC : BC = 1 :√3 : 2 = 11√3/2 : 11/2 : 11

Therefore BD = 11/2

To find the value of  m<A

We have

Sin ∅ = Opposite side /Hypotenuse

AB = 18 and BD = 11/2

Sin A = BD/AB =(11/2)/18 = 11/36 = 0.3055

m<A = Sin⁻¹(0.3055) = 17.79 ≈ 17.8°

Therefore the correct answer is option A  17.8°

Answer:

option C

9 x 9 x 9 x 9 x 9  

Step-by-step explanation:

Given in the question the expression

[tex]9^{5}[/tex]

The exponent corresponds to the number of times the base is used as a factor.

in which base = 9

              exponent = 5

9 x 5

45

[tex]5^{9}[/tex]

[tex]9^{5}[/tex]

[tex]9^{5} x 5^{9}[/tex]

Answer:

y = 3x - 1

Step-by-step explanation:

We can manipulate the scatter plot feature in Ms. Excel then we simply add the linear trend line displaying the equation on the chart.

The excel output is attached below.

The relation exhibited by the data set is y = 3x - 1; given the value of x, the value of y is obtained by multiplying x by 3 and subtracting 1 from the result.

Answer: [tex]10\sqrt{2}units[/tex]

Step-by-step explanation:

You must apply the Pytagorean theorem, which is shown below:

[tex]a^2=b^2+c^2[/tex]

Where:

a is the hypotenuse and b and c are the legs of the triangle.

Then, if you know the lenght of the legs of the triangle, you can solve for the hypotenuse.

Therefore, keeping the above on mind, you obtain the following result:

[tex]a=\sqrt{b^2+c^2}[/tex]

[tex]a=\sqrt{(10units)^2+(10units)^2}\\a=10\sqrt{2}units[/tex]

The length of the hypotenuse of the triangle is 10√2 units

The triangle is a right angle triangle.

Right angle triangles are triangle that has one of its angles as 90 degrees.

Using Pythagoras theorem, we can find the length of the hypotenuse with the length of the two legs.

Therefore,

c² = 10² + 10²

c² = 100 + 100

c = √200

c = 10√2

learn more on right angle triangle here: https://brainly.com/question/2796771?referrer=searchResults

For 7A)

The sum of -4 can not be both positive as from the set of rules (+)(+) can only make postive and -4 is decleared as negative

For 7B)

The sum of -4 can not be both negative as both negative (-)(-) is equivalent to a positive and the integer is -4 meaning it can not be negative

The reasonable answer to this would be two different numbers

It could be negative and positive

Or positive and negative

Nothing else

Answer: =6x+ −6/5

Step-by-step explanation:

Let's simplify step-by-step.

6x−12/10 =?

= 6x + −6/5

* Hopefully this helps:) Mark me the brainliest:)  For a better a understanding I included the picture of what I exactly mean incase you didn't understand the work that I showed you :)

For this case we must simplify the following expression:

[tex]6x- \frac {12} {10}[/tex]

If we divide the numerator and denominator between "2", then we can rewrite the fraction as:

[tex]\frac {12} {10} = \frac {6} {5}[/tex]

So, we have:

[tex]6x- \frac {6} {5}[/tex]

Answer:

[tex]6x- \frac {6} {5}[/tex]

Answer:

C / (2 pi) = r

Step-by-step explanation:

C = 2 pi r

Divide each side by 2 pi

C / (2 pi) = 2 pi r/ (2 pi)

C / (2 pi) = r

Answer: 24 meters.

Step-by-step explanation:

The perimeter of a rectangle is given by the formula:

[tex]P=2l+2w[/tex]

Where l is the lenght and w is the width.

The perimeter of the original rectangle  is 88 m, then:

[tex]88=2l+2w[/tex]      [EQUATION 1]

Where l is the length of the original rectangle

 You know that if the width were doubled and the length were increased by 12 m, the perimeter would be 152 m. Therefore the new length is:

[tex]l+12[/tex]

The new width is:

[tex]2w[/tex]

Susbtitute into the equation of the perimeter and solve for w:

[tex]152=2(l+12)+2(2w)\\4w=152-(2l+24)[/tex]

 [tex]w=\frac{128-2l}{4}[/tex]      [EQUATION 2]

Substitute the Equation 2 into Equation 1 and solve for the length, as you can see below:

[tex]88=2l+2(\frac{128-2l}{4})[/tex]

[tex]88=2l+2(\frac{128-2l}{4})\\88-2l=\frac{128-2l}{2}\\\\176-4l=128-2l\\176-128=4l-2l\\\frac{48}{2}=l\\\\24=l[/tex]

Therefore, the length of the original rectangle is 24 m.

Answer:

Length  of original rectangle = 24 m

Step-by-step explanation:

Perimeter of rectangle

P = 2(l + b)

l - length and b - width

It is given that,the perimeter of a rectangle is 88 m. If the width were doubled and the length were increased by 12 m, the perimeter would be 152 m

Perimeter of original rectangle = 88 m

2(l + b) = 88

l + b = 44

b = 44 - l

To find length and width

length l = l + 12  and width = 2(44 - l) then,

Perimeter = 152 m

we can write,

2( l + 12 + 2(44 - l)) = 152

l + 12 + 88 - 2l = 152/2 = 76

100 - l = 76

l = 100 - 76 = 24

Therefore length = 24 m

width = 44 - l = 44 - 24 - 20 m

Answer:

This graph is reflected over the x-axis

Step-by-step explanation:

This is because the negative is a coefficient in front. This causes the graph to flip, which is the same as a reflection over the x-axis

Answer:

A

Step-by-step explanation:

Since we're dealing with the b value here, we are talking about an x axis reflection.

Answer: [tex]EF=15cm[/tex]

Step-by-step explanation:

You know that the triangle ABC and the triangle DEF are similar.

Therefore, if the lenght of AC is 12 centimeters and the lenght of DF is 10 centimeters, then you can find the ratio as following:

[tex]ratio=\frac{DF}{AC}\\\\ratio=\frac{10cm}{12cm}\\\\ratio=0.8333[/tex]

Then, the calculte the length of EF, you must multiply the lenght BC of the triangle ABC by the ratio obtained above.

Therefore, the lenght EF is the following:

[tex]EF=0.8333(18cm)\\EF=15cm[/tex]

Answer:

The length of EF = 15 cm.

Step-by-step explanation:

We are given that the two triangles, ABC and DEF, are similar to each other,

Given that the length of AC = 12 cm, BC = 18 cm and DF = 10 cm, we are to find the length of EF.

For this, we can simply use the ratio method.

[tex] \frac { EF } { BC } = \frac { DF } { AC } [/tex]

[tex] \frac { EF } { 18 } = \frac { 10 } { 12 } [/tex]

[tex] E F = \frac { 10 } { 12 } \times 18 [/tex]

EF = 15 cm

I think $18.50 would earn you the most money.

The first choice would earn you $33,350

The second choice would earn you $32,000

The third choice would earn you $33,670

I think the last choice would earn you $31,500

Hope this helps.

Answer:

Step-by-step explanation:

Givens

$17.50 per hour and $1,500 bonus at the end of the year, that is, at the ends of the 52 weeks.

If you work 35 hours per week for 52 weeks, with this plan, you gain

[tex]17.50 \times 35 = \$ 612.50[/tex]

Then, after 52 weeks: [tex]\$612.50 \times 52=\$ 31,850[/tex]

So, with the first plan, you make $31,850 + $1,500 = $33,350.

Just $32,000 per year. It's a little bit better than the first situation.

$18.50 per hour.

So, per week would be: [tex]18.50 \times 35 = \$647.50[/tex]

After 52 weeks you make: [tex]\$647.50 \times 52=\$33,670[/tex]

So, with the third plan, you make $33,670.

$30,000 per year with a 5% bonus, which mean

[tex]30,000 + 0.05(30,000)=30,000+1,500=31,500[/tex]

So, with this plane you make $31,500 a year.

Therefore, as you can deduct, the best option is the third plan, $33,670 per year.

Answer:

The area of the shaded region is [tex](77-4\pi)\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the rectangle minus the area of the circle

step 1

Find the area of the rectangle

[tex]A=(7)(11)=77\ cm^{2}[/tex]

step 2

Fin the area of the circle

[tex]A=\pi (2)^{2}=4\pi \ cm^{2}[/tex]

step 3

Find the area of the shaded region

[tex]77\ cm^{2}-4\pi \ cm^{2}=(77-4\pi)\ cm^{2}[/tex] -----> exact value

To find the approximate value use [tex]\pi=3.14[/tex]

[tex](77-4(3.14))=64.44\ cm^{2}[/tex] -----> approximate value

Yes this is true because if she can read 2 paragraphs every minute you would multiply 2 by 3 since that’s how many minutes she read for.

2 paragraphs x 3 minutes = 6 paragraphs

Hope this helps.

Answer:

Yes this is true because if she can read 2 paragraphs every minute you would multiply 2 by 3 since that’s how many minutes she read for.

2 paragraphs x 3 minutes = 6 paragraphs

Hope this helps.

Step-by-step explanation:

Answer: Christina weighs 98 pounds.

Step-by-step explanation: The formula to solve this problem is x + 17 + x = 179, where x equals Sarah’s weight.

X + 17 + x = 179

First you need to combine the x values:

2x + 17 = 179

Next, subtract 17 from both sides:

2x = 162

Finally, divide both sides by 2:

X = 81

Sarah’s weight is 81 pounds and Christina weighs 17 pounds more, which is 98 pounds. You can double check your work by adding both of their weights (98 + 81) to make sure that your answer is correct.

Final answer:

By setting up a system of equations with the given information, we can solve for Christina's weight. Christina weighs 125 pounds.

Explanation:

To determine how much Christina weighs, we can set up an equation based on the information given. Let's define Sarah's weight as 's' and Christina's weight as 'c'. According to the question, Christina weighs 17 pounds more than twice Sarah's weight. So we can write the equation as:

c = 2s + 17

The combined weight of Christina and Sarah on the freight scale is 179 pounds. We represent this with another equation:

c + s = 179

Now we have a system of two equations:

Substituting the expression for 'c' from the first equation into the second equation gives us:

(2s + 17) + s = 179

Combining like terms, we have:

3s + 17 = 179

Moving 17 to the other side by subtracting 17 from both sides:

3s = 179 - 17

3s = 162

Dividing both sides by 3 to find Sarah's weight:

s = 162 / 3

s = 54

Now that we know Sarah weighs 54 pounds, we can find Christina's weight using the first equation:

c = 2(54) + 17

c = 108 + 17

c = 125

So, Christina weighs 125 pounds.

Answer:

Step-by-step explanation:

Let the two numbers be x and y

x + y = 6

x - y = 36       Add the two equations.

2x = 42          Divide by 2

2x/2 = 42/2

x = 21

x + y = 6         Substitute for x

21 + y = 6        Subtract 21

21-21 + y = 6-21

y = - 15