Use technology, what is the solution to this system? 4x+8y=30

The linear equation that gives the height on the x-th month is:

y = 2.5*x + 74.5

This will be modeled with a linear equation of the form:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that for a line with the points (x₁, y₁) and (x₂, y₂), the slope is given by:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we have the two points (3, 82) and (7, 92). Where the first value is the number of months and the second value is the height.

So the slope is:

[tex]a = \frac{92 - 82}{7 - 3} = 10/4 = 2.5[/tex]

Then the linear equation is:

y = 2.5*x + b

To get the value of b, we use the fact that when x = 3, we have y = 82,

82 = 2.5*3 + b

82 = 7.5 + b

82 - 7.5 = b = 74.5

Then the linear equation is:

y = 2.5*x + 74.5

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Answer:

y = -x - 5

Step-by-step explanation:

The general structure of a line in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

Since you have been given the slope and y-intercept, you can substitute these values into the equation to find the answer.

m = -1                  

b = -5

y = mx + b

y = (-1)x + (-5)

y = -x - 5

Answer:

y = -x -5

Step-by-step explanation:

We can use y = mx + c to find the equation of the line.

Here,

m ⇒ slope of the line

c ⇒ y - intercept

They have already given that,

m ⇒ -1

c ⇒ -5

So, now we can write the equation of the line like this.

To write the equation of the line you can replace m and c with -1 & -5 respectively.

Let us write now.

y = m x + c

y = -1x - 5

Answer:

w + 10 = 40

Step-by-step explanation:

10 more than w is w + 10 is equal to 40 is =40

w + 10 = 40

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Answer:

Step-by-step explanation:

10 more than w is equal to 40 what is the expression

10 + w = 40                 is the expression

w = 40 - 10

w = 30                        is the solution

The compound interest when $7300 when interest is compounded semi annually is $2482.70.

The compound interest when $7300 when interest is compounded monthly is $1972.73.

An investment earns compound interest when both the amount invested and the interest accrued increases in value at predetermined time intervals.

The formula to represent compound interest is :

FV - amount invested

FV = P (1 + r)^nm

a. 7300 x [1 + (0.1/2)]^(3 x 2) = 9782.70

Compound interest = 9782.70 = 7300 = $2482.70

b. 7300 x [1 + (0.08/12)]^(12 x 3) = 9272.73

9272.73 - 7300 = $1972.73

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Answer: B

Step-by-step explanation:

Angles that measure 90 degrees, angles that measure 90 degrees are right angles, and perpendicular lines form right angles.

Since angle EAB is a right angle, and it is formed by segments EA and AB, B is the answer.

Answer: Hope this helps you.

-2

Step-by-step explanation:

y = mx+b (B is y-int)

y = 4^x-2

-2 is clearly replacing the b (y-int) meaning b, the y-int, is -2

[tex]y = {4}^{x} - 2 \\ for \: y \: intercept \: x \: s \\ is \: 0 \\ y = {4}^{0} - 2 \\ y = 1 - 2 \\ y = - 1 \\ [/tex]

Y intercept : (0,-1)

Hope it helps

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Answer:

Step-by-step explanation:

x divided by the sum of x and 5

x : (x + 5) =

x × (1/1x^-1 + 1/5) =

1 + 1/5x

Marcella won't be able to win the competition because the length of the rope is less than 162 feet.

How to find the sides of a right angle triangle?

The situation forms a right angle triangle.

The kite released rope is the hypotenuse side of the triangle formed.

The opposite side of the triangle is the height of the kite from the ground.

Therefore,

sin 28 = opposite / hypotenuse

sin 28 = 75 / h

h = 75 / sin 28

h = 75 / 0.46947156278

h = 159.754085116

h ≈ 160 feet

Therefore, she won't be able to win the competition because the length of the rope is less than 162 feet.

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Using Cavalieri’s Principle, the height of the oblique cylinder with the given volume and base radius is 6cm.

Option A) is the correct answer.

From Cavalieri's principle, the volume of an oblique cylinder is expressed as;

V = base area × h

V = πr² × h

Given that;

V = πr² × h

486πcm³ = π × ( 9cm )² × h

486πcm³ = π × 81cm² × h

486πcm³ = 81πcm² × h

h = 486πcm³ / 81πcm²

h = 6cm

Using Cavalieri’s Principle, the height of the oblique cylinder with the given volume and base radius is 6cm.

Option A) is the correct answer.

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The equivalent expression of [tex]\frac{7^5}{7^2}[/tex] is [tex]\frac{7*7*7*7*7}{7*7}[/tex]

The expression is given as:

[tex]\frac{7^5}{7^2}[/tex]

Expand the numerator and the denominator

[tex]\frac{7^5}{7^2} = \frac{7*7*7*7*7}{7*7}[/tex]

The above expression is represented by option (d)

Hence, the equivalent expression of [tex]\frac{7^5}{7^2}[/tex] is [tex]\frac{7*7*7*7*7}{7*7}[/tex]

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Answer:

StartFraction 7 times 7 times 7 times 7 times 7 Over 7 times 7 EndFraction

Step-by-step explanation:

Edge

Answer:

y = 130

Step-by-step explanation:

given that y varies directly with x and z then the equation relating them is

y = kxz ← k is the constant of variation

to find k use the condition y = 150 when x = 2.5 and z = 12 , then

150 = k × 2.5 × 12 = 30k ( divide both sides by 30 )

5 = k

y = 5xz ← equation of variation

when x = 4 and z = 6.5 , then

y = 5 × 4 × 6.5 = 20 × 6.5 = 130

Answer: (0,-1)

Step-by-step explanation:

Let's start with the first inequality, [tex]y < -x^{2}+x[/tex]. To check which points satisfy this inequality, we can substitute the x- and y-coordinates and see if they satisfy the inequality.

Once again, we can repeat this for the second inequality (but this time, we only need to check the points that satisfy the first inequality).

Therefore, the answer is (A) (0, -1).

Answer:

$46.272

Step-by-step explanation:

The each type of angle are discussed below

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

If the hours hand point to the hour 1 and minute hand at 12 then

angle will be acute.

If the hours hand point to the hour 2 and minute hand at 12  then

angle will be acute.

If the hours hand point to the hour 3 and minute hand at 12  then

angle will be right angle .

If the hours hand point to the hour 4 and minute hand at 12  then

angle will be obtuse.

If the hours hand point to the hour 5 and minute hand at 12  then

angle will be obtuse.

If the hours hand point to the hour 6 and minute hand at 12  then

angle will be straight angle .

If the hours hand point to the hour 7 and minute hand at 12  then

angle will be reflex.

If the hours hand point to the hour 8 and minute hand at 12  then

angle will be reflex.

If the hours hand point to the hour 9 and minute hand at 12  then

angle will be reflex.

If the hours hand point to the hour 10 and minute hand at 12  then

angle will be reflex.

If the hours hand point to the hour 11 and minute hand at 12  then

angle will be reflex.

If the hours hand point to the hour 12 and minute hand at 12  then

angle will be Complete angle.

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The domain and range of the functions sin x, cos x, and tan x will be (-∞, ∞) and [-1, 1], (-∞, ∞) and [-1, 1], and R - (2n + 1)π/2 and (-∞, ∞) respectively.

The domain means all the possible values of x and the range means all the possible values of y.

The three restricted functions are given below.

f(x) = sin (x)

f(x) = cos (x)

f(x) = tan (x)

Then the domain of the three restricted functions will be

The domain of sin x will be (-∞, ∞).

The domain of cos x will be (-∞, ∞).

The domain of tan x will be R - (2n + 1)π/2.

Then the range of the three restricted functions will be

The range of sin x will be [-1, 1].

The range of cos x will be [-1, 1].

The range of tan x will be (-∞, ∞).

The graph is given below.

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The y-intercept is 3.75, and the equation of the line of best fit is

y = 1.5x + 3.75, and after 13 months, 23 matches could be won.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

Part A:

As we can see in the graph, the line crosses the y-axis at a certain point between 3 and 4.5.

So the y-intercept lies between 3 and 4.5

We can take the middle of these two values to get the approximate value of the y-intercept.

b = (3+4.5)/2 = 3.75

We know the line of the best fit is:

y = mx + b

y = mx + 3.75

b is the y-intercept and m is the slope of a line

Plug the point (9, 18) in the equation to get the value of m:

18 = 9m + 3.75

m = 1.5

y = 1.5x + 3.75

Plug x = 13 months in the above equation:

y = 1.5(13) + 3.75

y = 23.25 ≈ 23 number of matches that could be won

Thus, the y-intercept is 3.75, and the equation of the line of best fit is

y = 1.5x + 3.75, and after 13 months, 23 matches could be won.

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i beleive the answer is 2610.4109589

Answer:

The percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.

What is a cylinder?

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the formula for the volume of the cylinder is given by:

We have r = 10 inches and h = 5 inches

V = 500π cubic inches

Percent change in volume from cylinder A to cylinder B:

= 50%

Thus, the percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.

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Step-by-step explanation:

Answer:

-3x

Step-by-step explanation:

its just like regular subtraction, 2-5= -3, and just add an X at the end and you get -3x.

Answer:

A.g, a.f ,a.b

Step-by-step explanation:

Answer:

First, multiply 5 and 8. That equals 40. Then you take the square root of 40, which doesn't result in a whole number, so you factor 40 and removing perfect squares. In which case the answer would be 2√10

Answer:

-13/20

Step-by-step explanation:

-0.65 can be written as -65/100. To simplify, divide both numerator and denominator with 5. 65/5=13.  100/5=20

And you get -13/20 for your answer.

Answer: 15 inches

Step-by-step explanation:

Answer:

In a right triangle, the hypotenuse, 2x, is equal to twice the length of the shortest leg, x, and the longer leg is equal to the product of the length of the shortest leg, x, and the square root of 3.

Hypotenuse: 10 in.

Shortest Leg:2x=10 , so x=5 in,

Longer Leg:   x sq rt 3 5 sq rt 3 in

area- 1/2 bh, 1/2 5*5 sq rt 3=

25t sq rt 3=21.65 sq inches

The approximate original price of the car is $23032

The given parameters are:

Rate, r = 8%

Price at 4 years old = 16,500

An exponential function is represented as:

y = a(1 - r)^x

Where a represents the initial value

This gives

y = a(1 - 8%)^x

Evaluate

y = a(0.92)^x

At 4 years old, we have:

16500 = a(0.92)^4

Divide both sides by (0.92)^4

a = 23032

Hence, the approximate original price of the car is $23032

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[tex]\textbf{Notation one:}~~ \dfrac 76\\\\\textbf{Notation two:} ~ \text{7 to 6}[/tex]

Answer:

D

Step-by-step explanation:

it shows the correct one