Fina wants to use substitution to solve the system of equations. explain what she needs to do before using substitution. then solve the system of equations:

2x - y = 3
-1.5x + 3y = -18

Answers

Answer 1
Final answer:

To solve the system of equations using substitution, Fina needs to isolate one variable and substitute it into the other equation. The solution to the system of equations is x = -3 and y = -9.

Explanation:

To solve this system of equations using substitution, Fina needs to isolate one variable in one of the equations and then substitute that expression into the other equation.

Here are the steps:

Choose one equation and isolate one variable. Let's isolate x in the first equation: 2x - y = 3. Add y to both sides: 2x = y + 3 and divide by 2: x = (y + 3)/2.

Substitute the expression for x in the other equation. Replace x in the second equation with (y + 3)/2: -1.5((y + 3)/2) + 3y = -18.

Solve the equation for y. Simplify the equation: -1.5y - 4.5 + 3y = -18. Combine like terms: 1.5y - 4.5 = -18. Add 4.5 to both sides: 1.5y = -13.5. Divide by 1.5: y = -9.

Substitute the value of y back into the expression for x to find its value. Replace y in x = (y + 3)/2 with -9: x = (-9 + 3)/2 = -6/2 = -3.

Therefore, the solution to the system of equations is x = -3 and y = -9.


Related Questions

Find the volume of each figure

Answers

Cube volume (V) is equal to s^3 where s is the side of the cube, V=s^3.

Rectangular Prism volume (V) is equal to L times W time H, where L is the length, W is the width and H is the height, V = L x W x H.

Cylinder volume (V) is equal to (pi)r^2 times h, where r is the radius and h is the height, V = (pi)r^2 x h.

Sphere volume (V) is equal to 4/3(pi)r^3, where r is the radius, V = 4/3(pi)r^3.

Pyramid volume (V) is equal to 1/3Ah, where A is the area of the base and h is the height, V = 1/3Ah.

Cone volume (V) is 1/3(pi)r^2h, where r is the radius and h is the height, V = 1/3(pi)^2h.

Does 27/8 equal 2 7/8

Answers

No if you simplify 27/8 it equals 3 3/8.

please answer this, and HURRY I am giving away 20points.
Question: What is the measure of angle DBA?
____Degrees

Answers

Answer:

132

Step-by-step explanation:

65+67=132 || 180-132=48 || 180-48=132

Answer:

132 Degrees.

Step-by-step explanation:

The interior of any triangle is 180 degrees.

Solve for angle DBC

65 + 67 = 132

180 - 132 = 48 degrees

Since the sum of DBA and DBC is 180, and we already know what 180 - 48 is, there you have it.

The population of a species of fish in a river increased by a factor of 1.05 every day for the amount of days shown in the graph. The function shows the number of fish in the river f(x) after x days:

f(x) = 100(1.05)x

Answers

Answer: C: 0 < x < 31

Step-by-step explanation: Because the < sign shows the line is going up towards the top. It starts from 0 and travels to the top-right to 31

A reasonable domain for this function to have would be 0 ≤ x ≤ 31.

How to solve for the domain of the function

We have f(x) as the number of fishes that are present in this water. The month is October and October has 31 days.

The x values is the maximum of the number of days in October. The minimum value is given as 0 because it is the population in the beginning of the month.

Hence we have 0 ≤ x ≤ 31

Complete question

Which of the following is a reasonable domain for the function?

0 ≤ x ≤ 100

0 ≤ x ≤ 31

All positive integers greater than 100

All positive integers less than 100

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Graph the inequality x < 6
Please someone help now :(

Answers

Step-by-step explanation: To graph x < 6 on a number line, we start with an open dot at +6. The reason we use an open dot at +6 is that x is less than +6 but it is not equal to +6. Next we drawn an arrow going to the left to show that all numbers less than +6 are solutions to this inequality.

Image is attached below.

which expression is equivalent to 3/27x18?

a.3x3
b.3x6
c.9x3
d.9x6

Answers

Answer:

the answer is B

Step-by-step explanation:

give me brainly

what is the twin prime conjecture?

Answers

Answer:

It is a prime number which is either 2 less or 2 more than another prime number

Step-by-step explanation:

Final answer:

The twin prime conjecture posits the existence of an infinite number of twin prime pairs, which are pairs of prime numbers that are two units apart.

Explanation:

The twin prime conjecture is an unsolved question in mathematics that relates to the distribution of prime numbers. It specifically addresses the existence of pairs of primes that are only two numbers apart, such as (11, 13), (17, 19), and (41, 43), which are known as twin primes. The conjecture proposes that there are an infinite number of these twin prime pairs, even though prime numbers themselves become less frequent as numbers increase. Despite many efforts, a definitive proof of this conjecture has not yet been found.

(6x10^-6) (5.2x10^4 scientific notation

Answers

Step-by-step explanation:

[tex](6 \times {10}^{ - 6} )(5.2 \times {10}^{4} ) \\ = 6 \times 5.2 \times {10}^{ - 6} \times {10}^{4} \\ = 31.2 \times {10}^{4 - 6} \\ = 31.2 \times {10}^{ - 2} \\ = 0.312 \\ = 3.12 \times {10}^{ - 1} [/tex]

I need help with please ASAP but A is not the answer

Answers

Answer:

d

Step-by-step explanation:

[tex]-\frac{6}{5}[/tex] is rational

3.5 is rational

0.5 repeating is rational

[tex]\sqrt{4}[/tex] is rational

[tex]\sqrt{5}[/tex] is NOT rational

The answer correct answer is D.

A bag contains colored marbles. The ratio of red marbles to blue marbles is 1 : 4. The ratio of blue marbles to yellow marbles is 2 : 5. What is the ratio of red marbles to yellow marbles?

Answers

Final answer:

To find the ratio of red to yellow marbles, given the ratios of red to blue and blue to yellow, we equalize the blue part of both ratios and combine them, resulting in a red to yellow ratio of 2:5.

Explanation:

The question concerns finding the ratio of red marbles to yellow marbles given the ratios of red to blue marbles and blue to yellow marbles. To solve this, we use the given ratios: the ratio of red marbles to blue marbles is 1 : 4, and the ratio of blue marbles to yellow marbles is 2 : 5. Firstly, we make the number of blue marbles consistent in both ratios by finding a common value. Multiplying the first ratio by 2 gives us red to blue as 2 : 8, and keeping the second ratio as is (blue to yellow as 2 : 5), we can now combine these to find the ratio of red marbles to yellow marbles. The red to yellow ratio, through the intermediary blue, becomes 2 : 5.

find the rule solve for n please help me

Answers

y=3x. because when you multiply the numbers on the x side times 3 you get the y column answers

Answer:

Your answer is 9

Step-by-step explanation:

the answer is nine because if you look at the pattern, every number to the left is times 3 to the right. For example, 4 to 12 is times 3. this would work for n because 9x3 equals 27. the rule is times three.

Elsa can type 75 words per minute on a Keyboard

Answers

Elsa's rate of typing = 1.25 words per sec

Time is taken for typing each word = 0.8 a

What is unitary method used?

It is a method of solving by finding the value of one unit and the calculating the value of given unit by multiplying with the single value.

Step by step calculation

Numbers of words Elsa can type in 1 minute(the 60s)  = 75

Numbers of words Elsa can type in one second = 75/60

∴ Rate of typing = 1.25 words per sec

Time is taken to type one word = 60/75

                                                = 0.8 sec

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Question 3
Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of
4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?
$104.54
$378.21
$450.71
$1225.56

Answers

Answer:

The monthly payment, PMT = $450.71

Therefore the correct option is C.) $450.71

Step-by-step explanation:

i) Value of Loan, or Present value, PV = 24000

ii) Annual percentage rate , APR = 0.048

iii) number of periods, n = 12

iv) periodic interest, R = APR / n  = 0.048 / 12 = 0.004

v) number of years, t = 5

v) Monthly Payment, PMT =  [tex]\frac{PV\times R}{1 - (1 + R)^{(-1\times n \times t})} = \frac{24000 \times 0.004}{1 - ( 1 + 0.004)^{-60}}[/tex] = $450.71

prove the identity cos(x-y)-cos(x+y)=2sinx siny

Answers

Answer:

see explanation

Step-by-step explanation:

Using the Addition/ Subtraction formulae for cosine

Consider the left side

cos(x - y) - cos(x + y)

= cosxcosy + sinxsiny - (cosxcosy - sinxsiny) ← distribute

= cosxcosy + sinxsiny - cosxcosy + sinxsiny ← collect like terms

= 2sinxsiny = right side ⇒ proven

Mark is in training for a marathon race. He has been training by running 10 miles each day. He will
be increasing his running by this weekly formula: y = 10 (1.1), where y is the number of miles he
will run each day, x weeks from now.
What is the value of y if x = 0?
Round to the nearest mile.

Answers

Answer:

For x = 0, the value of y will be 10 miles.

Step-by-step explanation:

Mark is in training for a marathon race. Each day he runs 10 miles for this training purpose. He will  be increasing his running by this weekly formula: [tex]y = 10(1.1)^{x}[/tex], where y is the number of miles he  will run each day, x represents the number of weeks from now.

Now, for x = 0, the value of y will be [tex]y = 10(1.1)^{0} = 10[/tex] miles. (Answer)

Answer:

The Value of y is 10

Step-by-step explanation:

Kelly read 40% of a novel, and she now has 108 pages left. How many pages does the novel have?

Answers

Answer:

The novel has 180 pages.

Step-by-step explanation:

108 pages is 60% of the novel.

108 / 3 = 36.

20% of the novel is 36 pages.

36 * 5 = 180 pages

the base of parellogram is twice its height . if the area is 648msq find its base and height

Answers

Answer:

h=18m, b=2m

Step-by-step explanation:

Let the base be b and height be h

Condition 1:

b=2h ----(1)

Condition 2:

Area=b*h

b*h=648 -----(2)

Putting (1) into (2)

2h*h=648

2h^2=648

Dividing both sides by 2

h^2=324

Taking sq root on both sides

h=18 m

Now

Putting value of h in eq (1)

b=2(18)

b=36 m

A store offers a discount of 30 % on all refrence of books. If a dictionary cost $12 before the discount what is the dollar amount of the discount.

Answers

Answer:

3.6

Step-by-step explanation:

30%×12= 3.6

30%=0.3

A prism, bases of which are equilateral triangles, circumscribes a sphere of radius 6. What is the volume of the prism?

Answers

Answer:

  1296√3 cubic units

Step-by-step explanation:

The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.

The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...

  B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units

The volume of the prism is then ...

  V = Bh = (108√3)(12) = 1296√3 . . . cubic units

_____

Comment on the geometry

The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.

0.230769231 as a fraction

Answers

Final answer:

To express 0.230769231 as a fraction, the numerator is 230769231 and the denominator is 10^9.

Explanation:

To express the decimal 0.230769231 as a fraction, we need to determine the numerator and denominator. The numerator is the decimal without the decimal point, which is 230769231. The denominator is based on the number of decimal places, which is 9 because there are 9 digits in the decimal part. Therefore, the fraction is 230769231/10^9.

What is
2x-3y=-19
4x+3y=7
URGENT

Answers

Solve by elimination.

 2x-3y=-19

+(4x+3y=7)

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

6x=-12

x=-2

2(-2)-3y=-19

-3y=-15

y=5

Intersection Point: (-2,5)

Choose the correct simplification of (xy2z)3.

xy2z3
x3y6z3
x3y8z3
x4y5z4

Answers

Answer:

[tex]x^3y^6z^3[/tex]

Step-by-step explanation:

we have

[tex](xy^2z)^3[/tex]

Applying the property of exponents

[tex](x^m)^n=x^{m*n}[/tex]

[tex](xy^2z)^3=(x^3)(y^2)^3(z^3)=x^3y^{2*3}z^3=x^3y^6z^3[/tex]

The correct simplification of [tex]\((xy^2z)^3\) is \(x^3y^6z^3\).[/tex]

To simplify the expression [tex]\((xy^2z)^3\),[/tex] you need to raise each component within the parentheses to the power of 3.

[tex]\(x^3\)[/tex] represents \(x\) raised to the power of 3, [tex]\(y^{2 \times 3}\)[/tex] represents [tex]\(y^6\)[/tex] (since you multiply the exponents when raising a power to a power), and [tex]\(z^3\)[/tex]represents \(z\) raised to the power of 3.

So, [tex]\((xy^2z)^3\) simplifies to \(x^3y^6z^3\).[/tex]

The given options are:

[tex]a) \(x^3y^3z^3\)\\b) \(x^3y^6z^3\)\\c) \(x^3y^8z^3\)\\d) \(x^4y^5z^4\)[/tex]

Comparing the simplified expression [tex]\(x^3y^6z^3\)[/tex] with the options, the correct answer is option (b) [tex]\(x^3y^6z^3\).[/tex]

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How many square inches of wrapping paper will he need?

Answers

answer: 18.75 square inches

Miss Jacobs purchase 10.2 ounces of candy for her class. Each student gets 0.85 ounces. Right and solve an equation to determine how many students are in Miss Jacobs class.

Answers

Answer:

There are 12 students in Miss Jacobs class.

Step-by-step explanation:

Divided 10.2 and 0.85

If you check your answer. 0.85 multiplied by 12 is 10.2

Fill in the missing angle measures

Answers

Yo sup??

by angle sum property we know that the sum of all angles in a triangle is 180

let the unknown angle be x

then,

x+60+90=180

x=180-150

x=30

Hope this helps

The sum of the angles of a triangle is 180°.

The angle measures you know are 60° and 90° (because the box in the top right corner of the triangle means that it is a right angle, which equals 90°). So you can do this to find the missing angle:

60° + 90° + ? = 180°    Add 60 and 90

150° + ? = 180°     Subtract 150 on both sides

? = 30°  The missing angle is 30°

Find two nontrivial functions f(x) and g(x) so that f(g(x)) = (-6-3x)^6

Answers

Final answer:

Two nontrivial functions f(x) and g(x) that satisfy the equation f(g(x)) = (-6-3x)^6 are f(x) = x^6 and g(x) = -6 - 3x. These functions were found by assigning the inner function to g(x) and the outer function to f(x).

Explanation:

Looking at the expression [tex]f(g(x)) = (-6-3x)^6[/tex], we can see that it is a composition of two functions. A possible way to choose the functions f(x) and g(x) is to let g(x) be the inner function and f(x) be the outer function.

Let's choose g(x) = -6 - 3x. This function linearly transforms the input x. Now, let's choose the function [tex]f(x) = x^6[/tex]. This function takes any input (including results from the g(x) function) and raises it to the power of 6.

So, when we apply g to x (g(x)) and then f to the result (f(g(x))), we get the original equation[tex]f(g(x)) = (-6-3x)^6[/tex]. Therefore, the two nontrivial functions f(x) and g(x) that satisfy the equation are f(x) = x^6 and g(x) = -6 - 3x.

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Henry’s disability insurance pays 70% of his salary for up to 26 weeks if his salary is $450 and he is disabled for 20 weeks how much disability will he get?

Answers

Answer:

$1575

Step-by-step explanation:

70 % of his salary is 0.7 X 450 = 315

He gets it for 20 weeks

presuming the salary is monthly.

You do 315 X 5 = 1575   20 /4 = 5 months

Find the equation for the circle with center (-4,-5) and passing through (4,-2)

Answers

Answer:

(x + 4)² + (y + 5)² = 73

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) = (- 4, - 5), thus

(x - (- 4))² + (y - (- 5))² = r², that is

(x + 4)² + (y + 5)² = r²

The radius 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 ) = (- 4, - 5) and (x₂, y₂ ) = (4, - 2)

r = [tex]\sqrt{(4+4)^2+(-2+5)^2}[/tex]

  = [tex]\sqrt{8^2+3^2}[/tex]

 = [tex]\sqrt{64+9}[/tex] = [tex]\sqrt{73}[/tex] ⇒ r² = 73, thus

(x + 4)² + (y + 5)² = 73 ← equation of circle

Answer: [tex](x+4)^{2} +(y+5)^{2} = 73[/tex]

Step-by-step explanation:

the formula for finding equation of circle is given as :

[tex](x-a)^{2}+(y-b)^{2} = r^{2}[/tex]

where ( a,b) is the coordinate of the center and r is the radius

The radius is the distance between the point and the center , the formula for calculating the distance between two points is given by :

d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

d = [tex]\sqrt{(4-(-4))^{2}+(-2-(-5))^{2}}[/tex]

[tex]d = \sqrt{(4+4)^{2}+(-2+5)^{2}}[/tex]

[tex]d = \sqrt{8^{2}+3^{2}}[/tex]

[tex]d = \sqrt{73}[/tex]

since "r" is the distance , then

[tex]r = \sqrt{73}[/tex]

The the equation of the circle , using the formula [tex](x-a)^{2}+(y-b)^{2} = r^{2}[/tex] , will be

[tex](x+4)^{2} +(y+5)^{2} = 73[/tex]

solve x+3y=-28
y=-5x using substitution

Answers

Answer:

Step-by-step explanation:

x + 3y = - 28

y = -5x

x + 3(-5x) = -28

x -15x = -28

-14x=-28

x=2

y = -5(2)

y=-10

A rectangle has a perimeter of 25 meters. If the lengths of the sides of the rectangle are multiplied by 7 to make a new rectangle, what is the perimeter of the new rectangle?

Answers

Answer:

175 m

Step-by-step explanation:

We are given;

The perimeter of a rectangle as 25 m

We are required to determine the new perimeter if the sides of the rectangle are multiplied by 7.

We know that;

Perimeter of a rectangle = 2(L+W)

Therefore, initially;

2(L+W) = 25 m

Hence;

L + W = 12.5 m

if the sides are multiplied by 7, then;

New length = 7L

New Width = 7W

Thus;

New perimeter = 2(7L+7W)

                         = 14 (L + W)

but, L + W = 12.5

Thus;

New perimeter = 14 (12.5)

                         = 175 m

Therefore, the new perimeter will be 175 m

Answer:

The answer to the problem is 175

Step-by-step explanation:

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