Solve system of equation using elimination by addition.

Will give brainliest!!

Answer:

[tex]5^{10} \cdot 5^{-7} = 5^3[/tex]

[tex]\frac{5^{10}}{5^{-7}} = 5^{17}[/tex]

Step-by-step explanation:

You have two equations:

[tex]5^a \cdot 5^b = 5^3[/tex]

[tex]\frac{5^a}{5^b} = 5^{17}[/tex]

But since

[tex]x^a \cdot x^b = x^{a+b}[/tex]

you only need to solve a+b = 3 and a-b=17

Rewrite the second as a = 17+b and plug it into the first:

17+b + b = 3, then you find, 2b = -14, so b = -7.

Then a=3-b, so a = 10.

The point-slope form of the equation for the line is y - 3 =1/2(x - 2)

From the question, we are to determine the point-slope form of the equation for the line

The point-slope form of the equation of a line is given by

y - y₁ = m(x - x₁)

Where (x₁, y₁) is a point on the line

and m is the slope of the line

From the given information,

Slope, m = 1/2

and we have the point (2,3)

∴ The point-slope form of the equation for the line is

y - 3 =1/2(x - 2)

Hence, the point-slope form of the equation for the line is y - 3 =1/2(x - 2)

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Answer:

50 27.5

50.01 27.5055

50.02 27.511

50.03 27.5165

Step-by-step explanation:

Answer:

55 is 110% of 50

Step-by-step explanation:

Answer:

[tex]\displaystyle ME=\frac{z\cdot s}{\sqrt{n}}[/tex]

Step-by-step explanation:

[tex]z[/tex] represents the critical value, [tex]s[/tex] represents the sample standard deviation, and [tex]n[/tex] represents the sample size.

Answer:

-3

Step-by-step explanation:

Given equation:

[tex]\implies (x^4y^{-3})^n=\dfrac{y^9}{x^{12}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}:[/tex]

[tex]\implies (x^4y^{-3})^n=x^{-12}y^9[/tex]

Rewrite -12 as (4 × -3) and 9 as (-3 × -3):

[tex]\implies (x^4y^{-3})^n=x^{(4 \times -3)}y^{(-3 \times -3)}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c[/tex]:

[tex]\implies (x^4y^{-3})^n=(x^4)^{-3}(y^{-3})^{-3}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^c b^c=(ab)^c[/tex]

[tex]\implies (x^4y^{-3})^n=(x^4y^{-3})^{-3}[/tex]

Therefore, the missing value is -3

L = 2W

perimeter = 2( L + W ) = 20 .

2 ( 2W + W ) = 20

6 W = 20

W = 20/6

= 10/3

L = 20/3

Answer:

10/3

Step-by-step explanation:

Given properties of the rectangle:

Given this we want to find the width of the perimeter.

Creating a system of equation:

First off we know that perimeter = 2L + 2W

We also know that the perimeter of this rectangle is 20 cm

So we can say that 20 = 2L + 2W

We also know that the length of this rectangle is twice the width or in other words l = 2w

So we have the two equations, 20 = 2l + 2w and l = 2w

Solving the system:

We are going to use the substitution method to solve this system.

The substitution method works when you have two equations, one can be just a plain equation but the other must have one of the variables defined ( by itself on either side of the equal sign )

If you have one of the variables defined, you can plug it in ( substitute ) into the other equation and solve for the other variable.

Plugging in the defined variable into the other equation

Equation : 20 = 2l + 2w

Defined variable : l = 2w

==> plug in l = 2w

20 = 2(2w) + 2w ( now we solve )

==> multiply 2 and 2w

20 = 4w + 2w

==> combine like terms

20 = 6w

==> divide both sides by 6

20/6 = w

==> simplify fraction

10/3  = w

The width = 10/3

Checking our work:

First we must solve for length as well

Solving for length by plugging in width into either equation

l = 2w

==> plug in w = 10/3

l = 2(10/3)

==> multiply 2 and 10/3

l = 20/3

Now to check our we we plug in the length and width into both equations, if both are true then our answer is correct

Equation 1 : 2l + 2w = 20

==> plug in l = 20/3 and w = 10/3

2(20/3) + 2(10/3) = 20

==> simplify multiplication

40/3 + 20/3 = 20

==> add fractions

20 = 20

Equation 2 : l = 2w

==> plug in l = 20/3 and w = 10/3

20/3 = 2(10/3)

==> multiply 2 and 10/3

20/3 = 20/3

Both are correct so our final answer is correct as well! :)

Answer:

Part A:

In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.

Part B:Simply put, coterminal angles start at 0° and end at the same place, though in different directions and multiple times around (you're probably going to want to make that sound a little more formal). Since each time around is 360°, boom

Part C: 75° is in Quadrant II, right? If I go one more time around, 75 + 360 = 435°. I can also go "backward. Starting at 0 and going clockwise, I'm going 75 fewer degrees than all the way around, so 360-75 = 285° but since I'm going "backward" 75 - 360 = -285°. One more is on you.    

Step-by-step explanation:

The correct answer is option C which is 15 meters.

Unit conversion is a multi-step process that entails multiplying or dividing by a numerical factor, selecting the correct number of significant digits, and then multiplying or dividing by another numerical factor.

The unit conversion will be done as:-

1 km  =  1000 meters

0.0150 Km = 0.0150 x 1000 meters

0.0150 Km = 15 meters

Therefore the correct answer is option C which is 15 meters.

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Answer:

3

Step-by-step explanation:

Volume of prism = 0.5 times height times length times width

60 = (0.5)(8)(5)(x)

120 = 8(5)(x)

120 = 40x

x =  3

Let me know if its right

Length of another side of base x = 3 unit

A prism has a solid shape consisting of two identical ends (such as triangle, square, rectangle, etc.), flat faces or surfaces and uniform cross-section across its length. The cross-section looks like a triangle hence called triangular prism. The shape of the prism does not have any curve. Therefore, a prism can have square, rectangular, pentagonal and other polygon shapes but not the circular shape.

Height of the prism = 8units

Length of one side of base = 5 units

Length of another side of Base = x

Base is a right angle

Base Area = 5x/2

Volume of prism = 60 unit³

Volume of Prism = Base Area × Height

60 = (5x/2) × 8

60/8 = 5x/2

x = 120/40

x = 3 unit.

Hence,  x = 3 unit which is length of another side of base.

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Answer:

Should be 60°

Step-by-step explanation:

Since each interior angle in an octagon is 120°, you would subtract 120° from 180° (which is the angle of a line). This would get you 60 °.

Answer: 33

Step-by-step explanation:

Because corresponding sides of similar triangles are in proportion, [tex]\frac{x}{22}=\frac{39}{26} \longrightarrow x=\boxed{33}[/tex]

Step-by-step explanation:

length = 2×width + 6

84 = 2×length + 2×width

now using the first in the second equation :

84 = 2×(2×width + 6) + 2×width = 4×width + 12 + 2×width

84 = 6×width + 12

72 = 6×width

width = 12 cm

length = 2×width + 6 = 2×12 + 6 = 24 + 6 = 30 cm

Answer:

Angle 3 = 70

Step-by-step explanation:

This is a geometry property

"opposite angle theorem"

It's pretty easy to prove it as well
180-70 = 110
180-110 = 70

Answer:

(1.333, 0) and (3, 0)

Step-by-step explanation:

Use desmos to input your equations then click on the solutions (zeroes)

Answer:

Coordinates (0, -8/3)

Step-by-step explanation:

the area of a rectangular is

length × width

we know the area and one side, let's say it's the width (it does not matter, as multiplication are commutative, and a×b = b×a).

so,

7.5 = length × 0.3

length = 7.5 / 0.3 = 25 m

the perimeter of a rectangle is

2×length + 2×width = 2×25 + 2×0.3 = 50 + 0.6 = 50.6 m

Answer:

2.5

Step-by-step explanation:

The amplitude of a function is the amount by which the graph of the function travels above and below its midline.

The distance from the highest most point to the lowest point vertically is 5, meaning that the midpoint is 2.5 units from either end.

The car will be worth after one year is £ 5753.6.

An exponential function is defined by the formula f(x) = [tex]a^{x}[/tex], where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form

f(x) =  [tex]a^{x}[/tex]

Where a > 0 and a is not equal to 1.

x is any real number.

Given

Car cost when bought A =  £ 6200

Value of a car decreases by 7.2% each year.

n = 1

r = 7.2% or 0.072

The car will be worth after one year

[tex]y= A (1-r)^{n}[/tex]

⇒ [tex]y =6200(1-0.072)^{1}[/tex]

⇒ [tex]y = 6200(0.928)[/tex]

⇒ y = £ 5753.6

Hence, the car will be worth after one year is £ 5753.6.

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Using an exponential function, it is found that the value of David's Investment will be at least $415 after a period of 20 years.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, the initial value and the growth rate for his investment are given by:

A(0) = 230, r = 0.03.

Hence, the value after t years is given by:

[tex]A(t) = 230(1.03)^t[/tex]

Then, the value will be of at least $415 when:

[tex]A(t) \geq 415[/tex]

[tex]230(1.03)^t \geq 415[/tex]

[tex](1.03)^t \geq \frac{415}{230}[/tex]

[tex]\log{(1.03)^t} \geq \log{\frac{415}{230}}[/tex]

[tex]t\log{1.03} \geq \log{\frac{415}{230}}[/tex]

[tex]t \geq \frac{\log{\frac{415}{230}}}{\log{1.03}}[/tex]

[tex]t \geq 20[/tex]

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Implementing the LSA from your other question

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One can can paint 400ft²

Total cans

9cans you need

Answer:

12

Step-by-step explanation:

There are

16 cups = 1 gallon

3 gallons = 48 cups

48 divided by 4 = 12 batches of rice pudding

Answer

12

Step-by-step explanation:

4 cup of milk = 1 batch of rice pudding

1 gallon of milk= 16 cups of milk

3 gallon of milk = 3x 16

=48 answer

then, 48 cup of milk = 48 ÷ 4

= 12 answer

Hence, stacy can make 12 batch of pudding with 3 gallon of milk.

Answer:

isosceles

Step-by-step explanation:

▪︎ Isosceles triangle is a triangle that has two sides of equal length.

Answer:

x = - 1

Step-by-step explanation:

3(x + 1) = - 2(x - 1) - 4 ←  distribute parenthesis on both sides

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

3x + 3 = - 2x - 2 ( add 2x to both sides )

5x + 3 = - 2 ( subtract 3 from both sides )

5x = - 5 ( divide both sides by 5 )

x = - 1

The difference of the two numbers in scientific form is:

[tex]493*10^{-9} = 0.00000493[/tex]

Here we want to solve:

[tex](5*10^{-7}}) - (7*10^{-9})[/tex]

To solve this, we should have the same exponent in both sides, to get that, we can rewrite the first number as:

[tex]5*10^{-7} = 500*10^{-9}[/tex]

Replacing that, we will get:

[tex](500*10^{-9}) - (7*10^{-9}}) = 493*10^{-9}[/tex]

To write it in standard form, we need to move the decimal point 9 times to the left, so we get:

[tex]493*10^{-9} = 0.00000493[/tex]

The difference is equal to 0.00000493.

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The equation that relates x and y for the Fusion hybrid is y = k + x

So,

y = k + x

Therefore, the equation that relates x and y for the Fusion hybrid is y = k + x

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An equation is formed of two equal expressions. The number of rows in the original pattern will be 4.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of rows be represented by x. Now, the pattern has rows that are 5 tiles wide and an unknown number of rows. if you take these tiles and add one additional tile, you can create a pattern that has rows that are 3 tiles wide, with 3 more total rows than the original pattern. Therefore, we can write,

(Number of Tiles before) + 1 tile = (Number of Tiles afterward)

5x + 1 = 3(x+3)

5x + 1 = 3x + 9

5x - 3x = 9 - 1

2x = 8

x = 4

Hence, the number of rows in the original pattern will be 4.

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Answer:

Line s

Step-by-step explanation:

They are the same distance apart, so this makes them parallel.

By the definition of parallel lines, the line r is parallel to line s.

Arrangement of reference lines or curves used to identify the location of points in space is called as Coordinate System.

We have to find the line which is parallel to line r.

Parallel lines are the lines that do not intersect or meet each other at any point in a plane.

They are always parallel and are at equidistant from each other.

Parallel lines are non-intersecting lines.

We can also say Parallel lines meet at infinity.

As we observe the figure line s is parallel to line r and it is equidistant from r.

Hence, line s is parallel to line r.

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Answer:

it makes 15 gadgets in 5 minutes

Step-by-step explanation:

you take thw 1 gadget every 20 seconds there are 60 seconds in 1 minutes so 60 ÷ 20 is 3 so it makes 3 gadgets every minute so 3 x 5 is 15 so it makes 15 gadgets every 5 mins

Answer:

15 gadgets

Step-by-step explanation:

look above

hope ot helps

Answer:

-2, 1 or 3 only

Step-by-step explanation:

just did it