How many solutions does the system of equations have?

y= -2x +9

6x + 3y =27

A) one
B) two
C) infinitely many
D) none

Answer:

Option D is correct.

[tex]\frac{4}{5}[/tex] is the ratio form a proportion with [tex]\frac{16}{20}[/tex]

Step-by-step explanation:

Proportion states that the two fraction or ratios are equal.

i.e, [tex]\frac{a}{b} = \frac{c}{d}[/tex]

Given the ratio [tex]\frac{16}{20}[/tex]

To find the proportion of this ratio forms.

[tex]\frac{16}{20}[/tex]

Divide top and bottom by 4 , we have;

[tex]\frac{\frac{16}{4} }{\frac{20}{4} }[/tex]

Simplify:

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

therefore, a ratio form a proportion with [tex]\frac{16}{20}[/tex] is, [tex]\frac{4}{5}[/tex]

Option D, 4/5 forms a proportion with 16:20.

To determine which ratio forms a proportion with 16:20, we must find a ratio equivalent to 16:20.

We start by simplifying 16:20. Both 16 and 20 can be divided by their greatest common divisor, which is 4:

16 ÷ 4 = 4

20 ÷ 4 = 5

This gives us the simplified ratio of 4:5. Now, we need to check which of the given options matches 4:5.

4/10: When simplified, 4:10 becomes 2:5, which is not equal to 4:5.

32/50: When simplified, 32:50 becomes 16:25, which is not equal to 4:5.

8/12: When simplified, 8:12 becomes 2:3, which is not equal to 4:5.

4/5: This ratio is already simplified and equal to 4:5.

Therefore, the ratio 4:5 forms a proportion with 16:20.

Correct Question

Which ratio forms a proportion with 16:20 ?      

A. 4/10    

B.  32/50  

C.  8/12    

D. 4/5

Answer:

Step-by-step explanation:

3-4i

The complex number is represented by the point graphed on the complex plane is 3-4i. Therefore, option C is the correct answer.

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.

Since the point (a, b) can be written in the form a + bi, where 'a' is the measurement along X-axis and 'b' is the measurement along Y-axis, so the point (3, -4) an be written in the following form:

(3, -4) = 3 + (-4)i = 3-4i.

Therefore, option C is the correct answer.

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Answer:

20,000

Step-by-step explanation:

We can create a proportion to find the total budget. A proportion is an equation where two ratios are set equal to each other. We create two fractions using the budget and percents.

[tex]\frac{13}{100} =\frac{2600}{x}[/tex]

We begin solving by cross multiplying numerator to denominator of each fraction.

[tex]13(x)=100(2600)\\13x=260000\\\frac{13x}{13}=\frac{260000}{13}  \\20,000=x[/tex]

Answer:

the company's total budget is 20,000

Step-by-step explanation:

A company spends 13% of its month budget on rent which total $2600

Let x be the month budget on rent

13% of the month budget is 2600

13% can be written as 13/100

[tex]\frac{13}{100} \cdot x=2600[/tex]

Now we solve for x

multiply both sides by 100

[tex]13x= 260000[/tex]

divide both sides by 13

x=20000

So, the company's total budget is 20,000

The population increase in the town is linear, and with a constant increase of 611 people per year, the population is projected to be 4855 in five years.

The population of a town described is increasing at a constant rate, therefore, this represents linear growth. Each year, the population increases by a fixed number, in this case, 611. This contrasts to exponential growth, where the population would increase by a fixed percentage.

To calculate the population in five years, we multiply the rate of increase (611) by the number of years (5) and add the starting population. So, 611*5 = 3055. Adding the current population of 1800 gives us 4855.

Therefore, the population of the town in five years will be 4855, given the linear growth rate holds steady.

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Answer:

24 photos per day

Step-by-step explanation:

Set up a chart.

x      y

1       24

2       48

3       72

4       96

5       120

6        144

The change between y is =24

The change in x is +1

change in y

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

change in x

24

----     =

1

24 photos per day

x = number of months

7*x = 7 times the number of months

7*x = total cost if you ignore the $100 fee

7x+100 = total cost with the fee of $100 included

y = total cost

y = 7x+100

Final Answer: y = 7x+100

note: the slope is 7 and the y intercept is 100

Answer: D) [tex]m+l=18\\\\1.25 m+0.75 l=19[/tex]

Step-by-step explanation:

Let 'm' represents the number of Mylar balloons  and 'l' represents the number of latex balloons.

Given : Mylar balloons cost $1.25 each l, and latex balloons cost $0.75 each.

i.e. cost of m Mylar balloons in dollars = 1.25 m

i.e. cost of l Latex balloons in dollars = 0.75 l

Then, the equations can be used to find the number of each type of balloon in a bunch of 18 balloons that costs $19 will be :-

[tex]m+l=18\\\\1.25 m+0.75 l=19[/tex]

Hence, the correct answer is Option D.[tex]m+l=18\\\\1.25 m+0.75 l=19[/tex]

The equations which can be used from the options given are :

(m + l) = 18

($1.25l + $0.75m) = $19

Cost per mylar balloon, m = $1.25

Cost per latex balloon, l = $0.75

Number of balloons in bunch = 18

Cost of bunch = $19

The cost can be expressed as :

(unit cost of each Ballon × number of each Ballon in a bunch) = total cost of bunch

($1.25l + $0.75m) = $19

Since the total Number of balloons in bunch = 18

And only mylar and latex balloons are present in the bunch ;

Then ;

(Number of mylar+number of latex) balloons = 18

(m + l) = 18

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Answer:

The equation is q + 10 = 20

The solution is q = 10

Step-by-step explanation:

"sum" means an addition.

"sum of q and 10" means "q + 10".

"is" means "="

That means you have the equation

q + 10 = 20

To solve the equation, subtract 10 from both sides.

q + 10 - 10 = 20 - 10

q = 10

Answer:

The equation is q + 10 = 20

The solution is q = 10

Answer:

q+10 = 20

Solving for q,

q=10

Step-by-step explanation:

Sum means addition and is means equals

q+10 = 20

We can solve for q by subtracting 10 from each side

q+10-10 = 20-10

q=10

Answer:

(1,7)

Step-by-step explanation:

You are given the system of two equations

[tex]\left\{\begin{array}{l}x-y=-6\\5x+3y=24\end{array}\right..[/tex]

Each equation represents straight line in the diagram. The point of intersection between these two lines represents the solution of the system of two equations. From the diagram  the best approximation of the solution of the system rounded to the nearest whole number is (1,7).

Or you can solve this system algebraically. Express x from the first equation

[tex]x=y-6[/tex]

and substitute it into the second equation:

[tex]5(y-6)+3y=24,\\ \\5y-30+3y=24,\\ \\8y=54,\\ \\y=\dfrac{54}{8}=\dfrac{27}{4}=6.75\approx 7.[/tex]

Then

[tex]x=6.75-6=0.75\approx 1.[/tex]

Answer:

see explanation

Step-by-step explanation:

MP = HP - HM = 22 - 10 = 12

MN = [tex]\frac{1}{2}[/tex] MP = 6 = NP

RN = RP + PN = 5 + 6 = 11

HN = HM + MN = 10 + 6 = 16

Answer:

-3 degrees per hour

Step-by-step explanation:

Temperature was [tex]0[/tex] degrees and it fell to [tex]-6\frac{3}{5}=-\frac{33}{5}[/tex] in [tex]2\frac{1}{5}=\frac{11}{5}[/tex] hours.

To get temperature change per hour, we divide the change by total number of hours. So:

So temperature changer per hour:

[tex]\frac{-\frac{33}{5}}{\frac{11}{5}}\\=-\frac{33}{5}*\frac{5}{11}\\=-\frac{33}{11}\\=-3[/tex] degrees per hour.

Answer:

The temperature change per hour was -3 degrees per hour.

Step-by-step explanation:

We know that the temperature fell from [tex]0[/tex] degrees to [tex]-6\frac{3}{5}[/tex] degrees in a time period of [tex]2\frac{1}{5}[/tex] hours.

So to find the rate of change of the temperature, we will divide the change in temperature by the number of hours.

For that, we will change the mixed number into improper fractions and then solve:

[tex]-6\frac{3}{5}=-\frac{33}{5}degrees[/tex]

[tex]2\frac{1}{5}=\frac{11}{5} hours[/tex]

Temperature change per hour = [tex]\frac{-\frac{33}{5}}{\frac{11}{5}} = \frac{33}{5}*-\frac{5}{11}=-3[/tex]

Therefore, the temperature change per hour was -3 degrees per hour.

Answer:

5/16

Step-by-step explanation:

We need to change the mixed number to an improper fraction to find the reciprocal

3 1/5 = (5*3+1)/5 = 16/5

The reciprocal of 16/5 is found by flipping the fraction

5/16

Answer:

5/16

Step-by-step explanation:

To find the reciprocal you have to make the fraction a mixed number by multiplying the denominator by the whole number then adding the numerator, in this case it would give you 16/5. Since the reciprocal is the number that you multiply to get one, if you switch the denominator and the numerator, you get 5/16.

You can check your work by multiplying the numbers together, if it equals one, your reciprocal is correct, if not, then you may have to do it again.

Answer:

10 five-point questions and 40 two-point questions

Step-by-step explanation:

Let x represent the total number of five-point questions and y represent the total number of two-point questions.

Equation 1:     5x+2y=130

Equation 2:     x+y=50

Multiplying Equation 2 by 2:     2x+2y=100     (Equation 3)

(Equation 1) - (Equation 3):     3x=30

                                                  x=10

Substituting x=10 into x+y=50:     10+y=50

                                                            y=40

Therefore, there are 10 five-point questions and 40 two-point questions.

Substituting x=10 and y=40 into Equation 1:

LHS=5x+2y=5(10)+2(40)=50+80=130

RHS=130

LHS=RHS

Substituting x=10 and y=40 into Equation 2:

LHS=x+y=10+40=50

RHS=50

LHS=RHS

Since in both cases the left-hand side is equal to the right-hand side, the answer is correct.

(LHS: left-hand side, RHS: right-hand side)

Final answer:

To find the number of five-point questions on the test, set up an equation using the given information and solve for x.

Explanation:

To find the number of five-point questions on the test, we need to first determine the total number of points available. The test is worth 130 points, and there are a total of 50 five-point and two-point questions. Let's denote the number of five-point questions as x.

The total points from the five-point questions would be 5x, and the total points from the two-point questions would be 2(50 - x) = 100 - 2x. Since the test is worth 130 points, we can set up the equation 5x + 100 - 2x = 130.

Simplifying the equation, we get 3x + 100 = 130. Solving for x, we subtract 100 from both sides, resulting in 3x = 30, and then divide both sides by 3, giving us x = 10. Therefore, there are 10 five-point questions on the test.

Answer:

the price is 6.75

Step-by-step explanation:

you deduct 25 from 16 what gives you 12.00

then deduct 25 from 12that gives you 9

then deduct 25 from 9 gives you 6.75

Answer:

see explanation

Step-by-step explanation:

the n th term of an arithmetic sequence is

[tex]t_{n}[/tex] = [tex]t_{1}[/tex] + (n - 1)d

given [tex]t_{1}[/tex] = 3 and [tex]t_{2}[/tex] = 10, then

[tex]t_{2}[/tex] = 3 + d = 10 ⇒ d = 10 - 3 = 7

[tex]t_{n}[/tex] = 3 + 7(n - 1) = 3 + 7n - 7 = 7n - 4

the sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex][2[tex]t_{1}[/tex] + (n - 1)d ]

                        = [tex]\frac{n}{2}[/tex][(2 × 3) + 7(n - 1) ]

                        = [tex]\frac{n}{2}[/tex](6 + 7n - 7 )

                        = [tex]\frac{n}{2}[/tex](7n - 1)

                        = [tex]\frac{7}{2}[/tex] n² - [tex]\frac{1}{2}[/tex] n

Answer:

The answer is y=20

Step-by-step explanation:

If you take a look at the attached picture you will notice that angles B and C are congruent, so that means they both are 25 degrees.

Next, add angles B and C together to get 50.

Then you take that 50 and add it to 70 in angle A's equation, and you will get 120.

Next, plug 120 into angle A's equation where the 70 was and you will have the equation 3y+120=180. (180 is there because that is what all the interior angles equal together.)

Next, slove the equation.

And theres your answer, I hope I helped. Put any questions in the comments.

The value of y in the isosceles triangle is 20. This was determined by making use of the angles sum property of a triangle and the specific properties of an isosceles triangle.

The subject of this question is geometry, specifically the properties of an isosceles triangle and the inner angles. An isosceles triangle is a triangle with at least two equal sides - in this case, sides AB and AC. Because it is an isosceles triangle, angles B and C are equal. Therefore, we know that the value of angle C in degrees is also 25 (5x = 25).

According to the angles sum property of a triangle, the sum of the inner angles of a triangle is always 180 degrees. Therefore, we have the equality: (3y + 70) + 25 + 25 = 180. If we subtract 70 from both sides, we have 3y = 180 - 120, which simplifies to 3y = 60. To solve for y, we divide both sides by 3. Concluding, y = 60/3 = 20.

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Answer:

Translation.

Step-by-step explanation:

Answer:

Transformation Shifted by 4 units right and 2 units down .

Step-by-step explanation:

Given  : Graph .

To find : Which type of transformation maps ABC to A'B'C.

Solution : We have given graph with  transformation maps ABC to A'B'C.

Coordinates of A ( -3 , 2) , B( -2 ,4) , C( -1 ,3) .

Coordinates of A' (1 , 0) , B'( 2 ,2) , C'( 3 ,1) .

We can see from given graph triangle ABC is shifted right ( x axis) by 4 units and move down by 2 units (y axis ).

Then

A ( -3 + 4 , 2 -2) →→A' (1 , 0)

B( -2+4 ,4 -2)  →→  B'( 2 ,2)

C( -1+ 4 ,3 -2)  →→ C'( 3 ,1) .

Therefore, Transformation Shifted by 4 units right and 2 units down .

The equation is linear because it is in the form y = mx+b, which is slope intercept form

m = 2 is the slope

b = -5 is the y intercept

Graphing y = 2x-5 produces a straight line.

The equation y=2x-5 is linear because it fits the form y = a + bx, with a straight-line graph and a direct relationship between x and y.

The equation y=2x-5 is a linear equation. In the form y = a + bx, a is the y-intercept, and b represents the slope.

Here, -5 is the y-intercept, and 2 is the slope of the equation, indicating how much y changes for each unit increase in x.

This linear equation can be graphed as a straight line.

The structure is similar to other linear equations like 7y = 6x + 8 and y + 7 = 3x, which are also represented by straight lines on a graph.

Linear relationships model a direct correlation between two variables, making them suitable for analysis with techniques like linear regression.

In practice, finding a relationship between an independent variable, such as hours worked on a car, and a dependent variable, like labor charges (y = 55x + 75), showcases a real-world example of linear equations.

Answer:

Shade in the first three rectangles

Step-by-step explanation:

1/4 of 12 is 3. So u fill in three

Answer:

3 boxes

Step-by-step explanation:

you would divide 12 by 4 and get 3 so shade in 3 boxes

Answer:

theta = 9/19 radians or  approximately .4737 radians

Step-by-step explanation:

The formula for arc length is

S = r theta  

where theta is in radians.  Lets put in what we know.  The radius would be 1.9 since the ropes would be the radius.

.9 = 1.9 theta

Divide by 1.9 on each side.

.9/1.9 = theta

theta = 9/19 radians

or in decimal form it is approximately  .4737 radians

Answer:

coefficient

Step-by-step explanation:

A coefficient is a number written with a variable to indicate the product of the number and the variable in a term.

In any of the algebraic expressions or an equation or a polynomial, a term contains at least one variable and a coefficient (numerical value). Thus, the coefficient of the term is one of the factors. So, the coefficient is indicated by the product of the number and the variable in a term.

The number written with a variable indicates the product of the number and the variable in a term is its coefficient. This is because it is a numerical value and it is the factor for the term.

E.g., 4xy - here 4 is the coefficient, and x y are the variables.

This can be written as 4 × x × y (product form).

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Answer: 7 and 8

Step-by-step explanation:

Let x represent the first number, then x + 1 is the other number.

(x)² + (x + 1)² = 113

x²  +  x² + 2x + 1 = 113    expanded (x + 1)²

2x² + 2x + 1 = 113          added like terms

2x² + 2x - 112 = 0        subtracted 113 from both sides

x² + x - 56 = 0           divided both sides by 2

(x + 8) (x - 7) = 0        factored polynomial

x + 8 = 0   x - 7 = 0    applied zero product property

x = -8     x = 7            solved for x

  ↓

not valid since the restriction is that x > 0 (a positive number)

So, x = 7     and     x + 1 = (7) + 1   = 8

Answer: It becomes 120% of original dough.

Step-by-step explanation:

Since we have given that

Jay is letting her bread dough rise,

After 3 hours, her bread dough is [tex]1\frac{1}{5}=\frac{6}{5}[/tex] of its original size.

We need to find the percent of its original size is Jay's bread dough.

So, Percentage will be

[tex]\frac{6}{5}\times 100\\\\=6\times 20\\\\=120\%[/tex]

So, it becomes 120% of original dough.

Answer:

Step-by-step explanation: For me, I would say C because it says Matt had 3 times as many stamps as Bria did and the other two isnt showing multiplying. They are mostly adding.

Answer,

= 4

Explanation,

So, basicly they want you to put the numbers (1/5) & (15) in place of the letters (c) & (d). Let's do that,

5 * 1/5 + 1/5 * 15

So, now that we have replaced the letters with numbers we simply simplify,

5 * 1/5 = 1

1/5 * 15 = 3

3 + 1 = 4

Hope this helps :-)

Answer:

y=6/5x+13

Step-by-step explanation:

6y=-5x+16

Divide by 6

y=-5/6x + 8/3

Slope: 6/5 (opposite reciprocal)

7=-5(6/5)+b

7=-6+b

b=13

Answer:

a. 19 degrees

Step-by-step explanation:

The angles of a triangle add up to 180 degrees.

This triangle is a right triangle, so it has a 90 degree angle.

The three angles are 90, 71, and x

90+71+x = 180

Combine like terms.

161+x=180

Subtract 161 from each side

161-161 +x =180-161

x =19

Answer:

Uranium-234 is an isotope of uranium. In natural uranium and in uranium ore, U-234 occurs as an indirect decay product of uranium-238, but it makes up only 0.0055% (55 parts per million) of the raw uranium because its half-life of just 245,500 years is only about 1/18,000 as long as that of U-238.

Step-by-step explanation: