A right triangle has a leg length of square root of 6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle. 3 36 square root of 39 square root of 43

Answer: 81y^4

Step-by-step explanation:

expand then calculate, -3 to the power of 4+81 then 81 added to y ^4 81y^4 is your finally power.

The solution to the system of linear inequalities -2x + y ≥ -3 and y > 1/3x + 2 is (3, 3)

In this case, the system of inequalities is given as

-2x + y ≥ -3

y > 1/3x + 2

Next, we plot the graph of the system of inequalities

In this case, the point of intersection of the inequalities represent the solution to the system

From the graph, the lines intersect at (3, -3)

Hence, the solution is (3, 3)

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For the given graph of quadratic function whose vertex is (4,2) , the domain  and the range in the interval notation is given by :

Domain = ( -∞ , ∞ )

Range = ( 2 , ∞ )

As given in the question,

For the given graph of quadratic function ,

Given graph represents the parabola.

Standard equation of the parabola with vertex ( h, k) is given by,

y = a ( x - h )² + k

Substitute the value ( h ,k ) = ( 4, 2 )

y = a ( x - 4 )² + 2

As it is a parabola in the first quadrant and faces in the upward direction,

Value of x tends to -∞ to ∞

Domain = ( -∞ , ∞ )

Minimum value of y coordinate is 2 and increases to ∞.

Range = ( 2, ∞ )

Therefore, for the given graph of quadratic function whose vertex is (4,2) , the domain  and the range in the interval notation is given by :

Domain = ( -∞ , ∞ )

Range = ( 2 , ∞ )

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The x - intercept (s) is x = [tex]\sqrt[3]{\frac{4}{5} }[/tex] and y - intercept (s) is -72

Given,

In the question:

The function is given as :

Consider f(x) = 3x² 30x - 72.

To find the x-intercept(s) and y-intercept of f(x).

Now, According to the question:

f(x) = 3x²× 30x - 72.

f(x) = 90[tex]x^{3}[/tex] - 72

Solve the equation:

90[tex]x^{3}[/tex] = 72

Make the leading coefficient of the variable one

[tex]x^3 = 72/90\\[/tex]

Cross out the common factor

[tex]x^3[/tex] = 4/5

Take the n-th root on both sides:

x = [tex]\sqrt[3]{\frac{4}{5} }[/tex]

To find the y - intercept(s)

f(x) = 3x²× 30x - 72.

Set x = 0

f(0) = 3 × 0 × 30 × 0 - 72

f(0) = - 72

Hence, The x - intercept (s) is x = [tex]\sqrt[3]{\frac{4}{5} }[/tex] and y - intercept (s) is -72

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Answer:

Step-by-step explanation:

1.935<2.5081<2.58<2.8

∵1.9350<2.5081<2.5800<2.8000

The mean age (nearest year) of all the people in the office is 22.4.

Using this formula to find the mean age

Mean age = Sum of men and women age / Number of men and women

Let plug in the formula

Mean age = ( 12 women × 22 years old)  + (3 men × 24 years old) / 12 women + 3 men

Mean age = 264 + 72 / 12 +3

Mean age = 336 /15

Mean age = 22.4

Therefore the mean age is 22.4.

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The value of the trigonometric function Cos61° + Cos45° is 1.192

The given expression is Cos61° + Cos45°

Now, we have :

Cos61° = 0.4848

and Cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] = 0.7072

Now, Cos61° + Cos45° = 0.4848 + 0.7072 = 1.192

Trigonometry is a branch of arithmetic that research relationships among side lengths and angles of triangles. the field emerged within the Hellenistic global at some stage in the third century BC from packages of geometry to astronomical research.

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosecant , cosine , cotangent , secant , sine , and tangent .

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Humberto's displacement is 2 miles due south far from his starting point.

We understand that displacement is a vector quantity with both magnitude and direction, while distance is a scalar quantity with only magnitude.

Displacement, unlike distance, shows the direction and position of an object from its original base.  This means that displacement refers to how far an object has traveled out of its original position with the direction included.

In other words, displacement shows the object's overall change in position and the direction of the new position from the former.

Starting point = 0

Distance covered toward the north = 3 miles

Distance covered toward the south = 5 miles

Displacement = 2 (0 - 3 + 5) miles

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We can see that there are 3,832 yes votes, we did that by using the given ratio.

We know that the ratio of yes votes to no votes was 4 to 3, so from each 7 votes, 4 are yes and 3 are no.

Then if we take the total number of votes, and we multiply it by (4/7), we will get the total number of yes votes.

In this case we know that the total number of votes is 6706, then the number of yes votes is:

(4/7)*6706 = 3,832

There are 3,832 yes votes.

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Answer:

AAS

Step-by-step explanation:

Two angles and two sides are marked as congruent.  Vertical angles are congruent, so the answer is  AAS

Using the confidence interval, a 95% confidence interval for the mean rate is (4.4206,4.2106).

In the given question, we have to construct a 95% confidence interval for the mean rate.

There is given  interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day.

It is reasonable to assume that the population is approximately normal.

4.754, 4.375, 4.173, 4.678, 4.425, 4.227, 4.126, 4.250, 3.951, 4.197

We find the mean

Mean=4.754+4.375+4.173+4.678+4.425+4.227+4.126+4.250+3.951+4.197/10

Mean=43.156/10

Mean=4.3156

Standard Deviation(S)=√(x−mean)^2/n−1

S=√(4.754−4.3156)^2/10−1

S=√(0.4384)^2/9

S=√0.1922/9

S=√0.02136

S=0.1462

95%=0.95 confidence interval for z is

Z= [tex]z_{\alpha /2,dt}[/tex]

dt=n−1

dt=10−1

dt=9

[tex]\alpha[/tex] = 1−0.95=0.05

[tex]\alpha /2[/tex]=0.05/2=0.025

Z= [tex]z_{0.025,9}[/tex]

Z= 2.262

Confidence interval

CI=Mean±Z× s/√n

CI=4.3156±2.262× 0.1462/√10

CI=4.3156±2.262× 0.1462/3.1623

CI=4.3156±2.262×0.0462

CI=4.3156±0.105

CI=(4.3156+0.105),(4.3156−0.105)

CI=(4.4206,4.2106)

Hence, a 95% confidence interval for the mean rate is (4.4206,4.2106).

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2 percentage of the students in the school are enrolled in health .

How do percentages work?

students are enrolled in health = 162

students are enrolled not  in  health = 38

162 + 38 = 200          Add

Total of 100 Students

then ,

200/100            

= 2%

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The measures of angles 5 and 3 is 100 degrees.

When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles, linear angles etc.

Therefore,

m∠7 = m∠5 (corresponding angles)

corresponding angles are congruent.

Therefore,

m∠5 = 100 degrees

m∠3 = m∠7(alternate angles)

m∠3 = 100 degrees.

Alternate angles are congruent.

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We could finish this question by applying the linar programming concept.

The profit function for the business is P(x) = 7x - 161

The number of units must be produced for the business to break even is

To find the formula of profit function, we have to understand first that profit is the remaining of revenue after being reduced by costs. Hence we could write this equation:

Profit = Revenue - Costs

Profit = R(x) - C(x)

If we create a new function P(x) that represent profit function, hence we could rewrite the profit function into:

P(x) = R(x) - C(x) ... (i)

Based on the question, we have both revenue and costs formulas as stated below:

R(x) = 24x ... (ii)

C(x) = 17x + 161 ...(iii)

We could subtitute equations (ii) and (iii) into equation (i) to get the profit formula:

P(x) = R(x) - C(x)

P(x) = 24x - (17x+161)

P(x) = 7x - 161 ... (iv)

To get the units must be produced, we have to understand that Break Even is a condition where the revenue is exactly the same of its costs, or when the profit is 0 (zero). Hence we could write the equation:

P(x) = 0 ...(v) --> Break Even

Then we would subtitute the equation (iv) into equation (v) to find the units must be produced (x) to achieve the break even.

P(x) = 0

7x - 161 = 0

7x = 161

x = 23 ... (vi)

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The  largest possible volume of the box is 108000cm^3.

The concept is the concept of

We can represent  the length of the square box as x

we can also represent the  surface of the box as S

we can represent the  height of the square box as y

we can represent the  volume as V= xy

Then since the top of the box is open  and we can equate the material of the box is equal  with surface area of box.

then  S=[x^2 +2xy +2xy]

= x^2 +4xy

Then substitute the value of S we have

10800= x^2 +4xy

y= [10800-x^2/4x]

V=2700 * 1/4X^2

V=2700 * 1/4X^2

Then substitute the value of y into

V= xy

= x[10800-x^2/4x]

V= 2700x - 3/4X^2

Differentiate the volume to 0

=3x^2 = 2700

X^2 = 3600

X = 60 and Y = 30

V=2700 * 1/4X^2

V= 270(60) - 1/4* (60)^2 = 108000cm^3

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Answer:

the 4th one

Step-by-step explanation:

because we determined by Pythagorean theorem (the square root of 11)2 + 7 the power of 2 =

(the square root of 60)2 .....square root cancelled by power of 2

11 + 49 = 60

60 = 60

Answer:

-1

Step-by-step explanation:

Take -1 as common form the denominator then cancel out the whole term i.e x²-x-1 and -1 remains.

Answer:

6

the recurring digit is 6

ANS: 0.6

Answer:

=======================

Equation of circle:

The center is the radius long distance from the x- axis to left and y-axis up same distance, this makes it in the second quadrant.

So the coordinates of the center are:

The equation is:

Answer:

[tex](x+8)^2+(y-8)^2=64[/tex]

Step-by-step explanation:

Required conditions:

If the circle is tangent to both axes, its center will be the same distance from both axes.  That distance is its radius.

If the center of the circle is in quadrant II, the center will have a negative x-value and a positive y-value → (-x, y).

Therefore, the coordinates of the center will be (0-r, 0+r) where r is the radius.

If the radius is 8 units, then the center is (-8, 8).

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Substitute the found center and given radius into the formula to create an equation for the circle that satisfies the given conditions:

[tex]\implies (x-(-8))^2+(y-8)^2=8^2[/tex]

[tex]\implies (x+8)^2+(y-8)^2=64[/tex]

Answer:

Bucket a would be a darker shade because the white makes bucket b lighter.

The expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.

First, let us understand the exponents or power:

A power, or index, is a little floating number that appears next to a number or letter.

It is denoted as a^m.

where a = base number

and m = power or index number.

Some laws of exponents are:

We are given:

8^-3

We can solve as;

8^-3 = 8^(3 * -1) = (8^3) ^ -1 = 1 / 8^3 [since a⁻¹ = 1 / a]

So, 8^-3 = 1 / 8^3.

Thus, the expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.

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The commission amount for sales totaling $15,000 is $600.

From the information, the advertising sales representative has sales totaling $4500 and for these sales, the representative earns a commission of $360.

Therefore, the commission fraction will be:

= Commission / Sales

= 360 / 4500

= 1/25

Therefore, the commission on $15000 will be:

= 1/25 × $15000

= $600

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Answer:

(1) where y = 18 when x = 2.

What is the value of x when y = 36?

= 4

(2) when x is 4, y is 11.

What is the constant of proportionality for this relationship?

= 2.75

(3) What is 34% of 650?

=4.875

(4) 28 7

    16 4

    12 3

=1/4x

(5) Last month 288 people attended the monthly bingo night. This month 243 people attended bingo night.

= 15.6

(6) Over 6.8 months, a tree grew 7.48 inches.

=1.1

(7) A party-size bag of chips contains 15 ounces. This is 750% of the amount in the snack-size bag.

=2

(8) An advertising sales representative has sales totaling $4500. For these sales, the representative earns a commission of $360.

Which proportion could be used to find the commission amount for sales totaling $15,000?

=360/4500=x/15,000

(9) Brad's dinner bill, including a 16% tip, is $10.44.

= 9

(10) Do the values in the table represent a proportional relationship?

x 2 4 6 8

y 3.2 6.4 9.6 12.8

Select from the drop-down menu to correctly complete the statement.

response - correct

All of the y-values are a constant multiple of the corresponding x-values, so the relationship is proportional.

(11) Molly estimated the width of a poster to be 21 inches. The actual width is 26 inches.

=19.2

(12) Solve for x.

x−9= −5/24

=1 7/8

(13) Each 1/2 inch on a scale model represents an actual length of 1/6 of a yard.

=3

(14) Landon is buying a shirt priced at $19.99. The sales tax is 8.5%.

= 21.69

(15) A sprinter ran 100 meters in 15 seconds.

=400

(16) Two gears are connected and rotating at the same time.  The smaller gear completes 3 2/3 rotations every time the larger gear completes 1/3  of a rotation.

=11

(17) Jasmine dumped her box of spare change and found out that she had saved 128 coins. She separated them and counted 48 dimes.

What percent of Jasmine's coins are dimes?

= 37.5

(18) A pair of boots costing $299 is marked down 45%.

= 164.45

(19) Figure 1 is dilated to get Figure 2.

What is the scale factor?

Enter your answer in simplest form in the box.

=5/8

(20) y=5/x Not proportional

       y=5(−2x) Proportional

       y=x/4 Proportional

       y=6x+4 Not proportional

Step-by-step explanation:

Hey here u go i so tired lol completely POOPED God bless  u have a great test

Answer: x=-y+9

y=-x+9

Step-by-step explanation:

The y-intercept for the given function is (0, -68).

The given function is f(x)=21x²-31x-68.

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (31/42,−6673/84)

Focus: (31/42,−556/7)

Axis of Symmetry: x=31/42

Directrix: y=−3337/42

Plot (0, -68) and (31/42, -6673/84)

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

y-intercept is (0, -68).

Hence, the y-intercept for the given function is (0, -68).

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The slope of the line that passes through the points (1, 6) and (1, 31) is, ∞

Slope is a ratio of change in y-coordinate w.r.t. change in x-coordinate. The net change in y coordinate is written as, Δy and the net change in x coordinate is written as, Δx.

So formula for the slope is,

m = change in y coordinate/change in x coordinate = Δy/Δx = y₂-y₁/x₂-x₁

Given that,

the line passes through the points, (1,6) and (1,31)

So, we can calculate slope for the line by using formula when two are given,

m =  y₂-y₁/x₂-x₁

x₁ = 1

y₁ = 6

x₂ = 1

y₂ = 31

m = 31-(6)/1-1

m ≈ ∞

Therefore, The line is parallel to y-axis

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Answer:

It's A.

Step-by-step explanation:

If you subtract from y, the graph moves to the right. If you add, it moves to the left.

Using the addition, the number that shows 2 more count from 6 is 8.

In the given question we have to write the number that shows 2 more.

We have to start counting from 6.

To write the number that shows 2 more we add 2 in 6, then again add 2 in the result of add of 2 and 6 and so on.

Hence the number that shows 2 more starting from 6 is

6+2=8

So the number that shows 2 more is 8.

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