Use substitution to solve the linear system of equations.

y = 4x
3x + 5y = -46

(-8, -2)
(8, -2)
(-2, 8)
(-2, -8)

Answer:

3

Step-by-step explanation:

The number of dogs are 3 if the ratio of dogs to cats at the pet store's 1:3. If there are 6 more cats than Dogs.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

The ratio of dogs to cats at the pet stores is:

1:3

Let's suppose there are x dogs, then cats are 3x

3x = x + 6

2x = 6

x = 3

Thus, the number of dogs are 3 if the ratio of dogs to cats at the pet store's 1:3. If there are 6 more cats than Dogs.

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1, 3, 5

You can tell by looking that her science mean is greater than her math mean.

The higher range number means that her scores in math are more varied and spread out than her science scores.

You can tell by looking that the median scores are the same.

Answer:

A, C, E

Step-by-step explanation:

Answer:

a° = 118° , b° = 49° , c° = 144° , d° = 98°

Step-by-step explanation:

* Lets study the figure and take the information to solve the question

- There is a circle

- There is an inscribed triangle in the circle

- Each vertex of the triangle is an inscribed angle in the circle

- Each vertex subtended by an arc

- The measure of any inscribed angle is half the measure of its

  subtended arc

* Now lets solve the question

- The sum of the measures of the interior angles of a triangle is 180°

∵ The triangle has angle of measure 59° and another angle of

   measure 72°

∴ The measure of the third angle = 180° - (59° + 72°) = 49°

∵ b° is the measure of the third angle in the triangle

∴ b° = 49°

- The arc of measure a° is intercept the angle of measure 59°

∵ The measure of the angle is half the measure of the arc

∴ 1/2 a° = 59° ⇒ multiply both sides by 2

∴ a° = 118°

- The arc of measure c° is intercept the angle of measure 72°

∵ The measure of the angle is half the measure of the arc

∴ 1/2 c° = 72° ⇒ multiply both sides by 2

∴ c° = 144°

- The arc of measure d° is intercept the angle of measure 49°

∵ The measure of the angle is half the measure of the arc

∴ 1/2 d° = 49° ⇒ multiply both sides by 2

∴ d° = 98°

Answer:

None will be left.

Step-by-step explanation:

John needed 1000 Muffins a week for his party

Each person ate 100 Muffins

So there were [tex]\frac{1000}{100}[/tex] = 10 people in the party and they ate all the Muffins.

No Muffins were left over.

Answer:

Step-by-step explanation:

D is correct.  The area of the whole circle is (360/360)πr^2.  That of the unshaded sector is (theta/360)πr^2.

The expression which can be used to find the area of the shaded sector when the angle is measured in radians, is (θ/2)×r². Option A is correct.

Area of the circular sector is the space occupied by it. The area of the circular sector is the half of the product of angle of the sector and the radius of the circle.

When the angle is measured in degree it be given as,

Area of sector=(θπr²)/360

Here, r is the radius of the circle and θ is the angle of the sector.

When the angle is measured in radian it be given as,

Area of sector=(θ/2)×r²

Here, r is the radius of the circle and θ is the angle of the sector.

Hence, the expression which can be used to find the area of the shaded sector when the angle is measured in radians, is (θ/2)×r². Option A is correct.

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Answer:

5/36 (I won't repeat it 3 times :-) )

Step-by-step explanation:

We just have to calculate the ratio of times an action movie played in the las year, that should be a good indication of the chances for an action movie to be played next, since the reference data is quite large.  We're talking about a full year, no just a week or a month.

So, 15 action movies out of 108 movies...

The probability that next movie is an action movie is: 15 / 108 , or 5/36

That's roughly 1/7.

Answer:

15/108

Step-by-step explanation:

I did it and got it right.

Hope this helps:)

Answer:

The child has 6 dimes and 5 quarters.

Step-by-step explanation:

Let q and d represent the number of quarters and of dimes respectively.

Then q + d = 11 (Equation A), and ($0.25/quarter)q + ($0.10/dime)d = $1.85 (Equation B).

Multiply the 2nd equation by 100 to remove the decimal fractions:

25q + 10d = 185 (Equation C)

Now multiply the 1st equation by -10 to obtain -10q - 10d = -110 (Equation D), and combine this result with Equation C:

-10q - 10d = -110

25q + 10d = 185

--------------------------

15q         = 75, and so q = 75/15 = 5.

According to Equation A, q + d = 11.  Replacing q with 5, we get:

5 + d = 11, and so d = 6.

The child has 6 dimes and 5 quarters.

Answer:

y = 6x + 28

Step-by-step explanation:

We are to determine the equation of a line whose slope or gradient is 6 and passes through the point (-4, 4)

The slope-intercept form of the equation of the straight line would be given by;

y = mx + c

y = 6x + c

We proceed to use the given point to determine c;'

when x = -4, y = 4

4 = 6(-4) + c

4 = -24 + c

c = 28

The slope-intercept form of the equation of the straight line is thus;

y = 6x + 28

For this case we have that by definicon, the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

They tell us that the slope is 6, then:

[tex]y = 6x + b[/tex]

We substitute the given point, to find the cut point:

[tex]4 = 6 (-4) + b\\4 = -24 + b\\b = 4 + 24\\b = 28[/tex]

Finally:

[tex]y = 6x + 28[/tex]

Answer:

Option D

Answer:

b = ±3

Step-by-step explanation:

4b^2-45=-9

Add 45 to each side

4b^2-45+45=-9+45

4b^2 = 36

Divide by 4

4b^2 = 36/4

b^2 =9

Take the square root of each side

sqrt(b^2) = sqrt(9)

b = ±3

the approximate height

Answer:b

Step-by-step explanation: I took the test

$10.50 a $1.25 is $9.75 then you do $800 / $9.75 which is 82.05 so we round up with any decimal and he would need to sell 83 pies to start making a profit.

Answer:

0.75 I think

Step-by-step explanation:

Answer:

simple random sampling

Step-by-step explanation:

Simple random sampling is the fundamental sampling technique in which a group of subjects is selected for a particular study from a larger group, the population. Each subject is chosen purely by chance and each individual of the larger group (population) has an equal probability of being included in our sample.

Answer:

yes

Step-by-step explanation:

A rational number can be expressed in the form

[tex]\frac{a}{b}[/tex], where a, b are integers

6.610 can be expressed as

6 [tex]\frac{610}{1000}[/tex] = [tex]\frac{6610}{1000}[/tex] ← a rational number

6.610 is a rational number.

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Or in other words, any number that can be written as a ratio (or fraction) of two integers is a rational number.

Thus 6.610 is definitely a rational number as it satisfies the definition of a rational number.

We have, 6.610 = 661/100 which is expressed as the ratio of two integers.

Therefore, 6.610 is a rational number.

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Answer:

it measures spread around the mean. Because of its close links with the mean, standard deviation can be greatly affected if the mean gives a poor measure of central tendency. Standard deviation is also influenced by outliers one value could contribute largely to the results of the standard deviation.

Step-by-step explanation:

Answer with explanation:

Mean of a data set is defined as sum of all the observation divided by total number of observation.

For, example

Consider the Data set,the cost of five pens,={3,5,8,10,14}

Mean

      [tex]=\frac{3+5+8+10+14}{5}\\\\=\frac{40}{5}\\\\=8[/tex]

Now, Two pens having cost $ 47 and $ 53 is included in the Data set

New data set of Seven pens,={3,5,8,10,14,47,53}

   Mean

      [tex]=\frac{3+5+8+10+14+47+53}{7}\\\\=\frac{140}{7}\\\\=20[/tex]

So, you can see there is variation or Difference between two means.

We can conclude from above two results ,that mean is affected by outlier.

Thank you this is right

Answer:

10

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

I hope this helped it took so long to find.

Answer:

8

Step-by-step explanation:

13 - 0.75 (12) + 8 (0.5)

13 - 0.75 (12) + 4

13 - 9 + 4

4 + 4

8

Answer:

8

Step-by-step explanation:

Answer:

 - The scientist can use these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.

- The scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] and solve for the distance between the Sun and the shooting star (which would be the hypotenuse of the righ triangle).

Step-by-step explanation:

 You can observe in the figure attached that  "AC" is the distance between the Sun and the shooting star.

Knowing the distance between the Earth and the Sun "y" and the angle x°,  the scientist can use only these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.

 This is:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

In this case:

[tex]\alpha=x\°\\\\adjacent=BC=y\\\\hypotenuse=AC[/tex]

Therefore, the scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] , and solve for the distance between the Sun and the shooting star "AC":

[tex]cos(x\°)=\frac{y}{AC}[/tex]

[tex]AC=\frac{y}{cos(x\°)}[/tex]

The scientist can use the two measurements by applying the knowledge of trigonometry, particularly Cosine (cos).

[tex]cos x = \frac{adjacent (y)}{hypotenuse (AC)}[/tex]

AC = [tex]\frac{y}{cos x}[/tex]

where the distance between the shooting star and the sun is AC

and the distance between Earth and Sun is BC = y

the right angled triangle has three sides

cosine (θ) = [tex]\frac{adj}{hyp}[/tex]

sine (θ) = [tex]\frac{opp}{hyp}[/tex]

tan (θ) = [tex]\frac{opp}{adj}[/tex]

where (θ) =  angle of interest

This is the branch of mathematics that is concerned with angles of triangles as well as the length of it's sides.

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Answer:

  (-5, -8)

Step-by-step explanation:

The expression can be divided by 2 to give ...

  x² +13x +40

The solutions to this will have a product of 40 and a sum of -13, the opposite of the x-coefficient. All of the offered choices have a product of 40, but only (-5, -8) has a sum of -13.

Answer:

Option C) similar; SSS similarity; ΔABC

Step-by-step explanation:

we know that

The SSS similarity state : If the corresponding sides of two triangles are proportional, then the two triangles are similar

In this problem

80/30=56/21=72/27

2.67=2.67=2.67 -----> is true

therefore

The triangles STU and ABC are similar by SSS similarity

Answer:  The correct option is

(C)  similar; SSS similarity; ΔABC.

Step-by-step explanation:  We are given to check whether the pair of triangles in the figure are similar to each other or not.

If so, we are to complete the similarity statement.

From the figure, we note that

the lengths of the sides of triangle STU are

ST = 72, TU = 80 and SU = 56.

And, the lengths of the sides of triangle ABC are

AB = 27, BC = 30 and AC = 21.

So, we get

[tex]\dfrac{ST}{AB}=\dfrac{72}{27}=\dfrac{8}{3},\\\\\\\dfrac{TU}{BC}=\dfrac{80}{30}=\dfrac{8}{3},\\\\\\\dfrac{SU}{AC}=\dfrac{56}{21}=\dfrac{8}{3}.[/tex]

That is,

[tex]\dfrac{ST}{AB}=\dfrac{TU}{BC}=\dfrac{SU}{AC}=\dfrac{8}{3}.[/tex]

Therefore, the corresponding sides of the two triangles are proportional.

Hence, triangle ABC and STU are similar by SSS similarity.

Option (C) is CORRECT.  

Answer: 0.66 hours per mile

Step-by-step explanation:

You know that in 4 hours Addison walked 6 miles.

Now, you need to calculate the amount of hours she walked in 1 mile.

 Let be "x" the amount of hours she walked in 1 mile.

Then, to calculate the value of "x" you need to multiply 1 mile by 4 hours and divide by 6 miles:

[tex]x=\frac{(1mile)(4hours)}{6miles}\\\\x=\frac{2}{3}\ hours[/tex]

[tex]x[/tex]≈[tex]0.66\ hours[/tex]

Therefore, her walking rate in hours per mile was:

0.66 hours per mile

ANSWER

Yes, f is a function.

EXPLANATION

The domain of the relation is D = {xlx is a state in the United States}

The rule is that f(x) ="the state capital"

The relation will be a function if and only if no two elements in the first set have the same image in the second set.

Since no two states will have the same capital, the relation is a function.

Answer:

yes

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 3, 2), so

(x + 3)² + (y - 2)² = r²

r is the distance from the centre to a point on the circle

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (- 2, 9)

r = [tex]\sqrt{(-2+3)^2+(9-2)^2}[/tex] = [tex]\sqrt{1^2+7^2}[/tex] = [tex]\sqrt{50}[/tex], hence

(x + 3)² + (y - 2)² = 50 ← equation of circle

Substitute (- 10, 3) into the left side of the equation and if equal to the right side then the point lies on the circle

(- 10, 3) : (- 10 + 3)² + (3 - 2)² = (- 7)² + 1² = 49 + 1 = 50

Hence (- 10, 3) lies on the circle

Answer:

Simplify 23x

.

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2x3−12=13+56x

Simplify 56x

Step-by-step explanation:

For this case we must solve the following equation:

[tex]\frac {2} {3} x- \frac {1} {2} = \frac {1} {3} + \frac {5} {6} x[/tex]

Subtract [tex]\frac {5} {6} x[/tex] on both sides of the equation:

[tex]\frac {2} {3} x- \frac {5} {6} x- \frac {1} {2} = \frac {1} {3}[/tex]

We add [tex]\frac {1} {2}[/tex] to both sides of the equation:

[tex]\frac {2} {3} x- \frac {5} {6} x = \frac {1} {3} + \frac {1} {2}\\\frac {12-15} {18} x = \frac {2 + 3} {6}\\\frac {-3} {18} x = \frac {5} {6}\\- \frac {1} {6} x = \frac {5} {6}\\[/tex]

We multiply by 6 on both sides of the equation:

[tex]-x = 5[/tex]

We multiply by -1 on both sides of the equation:

[tex]x = -5[/tex]

Answer:

[tex]x = -5[/tex]

Answer:

Jameel is 13 and Laitfa is 13 x 2 - 10 = 16

16 + 13 = 29

Step-by-step explanation:

The equation has already been given to us, so we just have to solve it.

According to the question,

L + J = 29

L = 2J - 10

  L

2J - 10  +  J = 29

add 10 both sides

2J + J = 29 + 10 = 39

3J = 39

J = 39/3 = 13

Done!

After 2 months, the gym memberships at Gym A and Gym B will cost the same amount, based on the membership cost equations of each gym.

We need to determine after how many months the total costs of gym memberships at Gym A and Gym B will be the same. The cost of a gym membership at Gym A is described by the equation C = 12m + 36, where C represents the total cost and m represents the number of months. For Gym B, the cost is given by the equation C = 20m + 20.

To find the number of months where the costs are equal, we set the two equations equal to each other:

12m + 36 = 20m + 20

Subtracting 12m from both sides gives us:

36 = 8m + 20

Subtracting 20 from both sides gives us:

16 = 8m

Dividing both sides by 8 gives us:

m = 2

Therefore, after 2 months, the total costs for gym memberships at both Gym A and Gym B will be the same.

Answer:

40

Step-by-step explanation:

Just look up the conversion factor and set up the proportion.

1 dm = 1/10 th of a meter

x dm = 4 meters.                  Cross multiply.

1 dm * 4m = x * 1/10 of a meter. Change 1/10 to a decimal.

1 dm * 4 m = x * 0.1 m                  Divide by 0.1

1 dm * 4 m /0.1 m = x

x = 40 dm

Answer:

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]

[tex]\text{We have the equation}\ y=\dfrac{1}{3}x+6\to m_1=\dfrac{1}{3}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{3}}=-3.\\\\\text{We have the equation}\ y=-3x+b.\\\\\text{Put the coordinates of the point}\ (2,\ -3):\\\\-3=-3(2)+b\\-3=-6+b\qquad\text{add 6 to both sides}\\3=b\to b=3\\\\\text{Finally:}\\\\y=-3x+3[/tex]

given,

height of triangle(h)=3.5 in.

base of triangle (b)=4 in.

length of side of triangle(s)= 4 in.

length of prism(l)=9 in.

we have,

surface area of traingular prism( A)=bh+2ls+lb

=4×3.5+2×9×4+9×4

=14+72+36

=122 square inches

Answer:

They're right

Step-by-step explanation: