The angle measurement in the diagram are represented by the following expressions

The values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

√15/(y + 2) = y/√15 {opposite/adjacent}

y(y + 2) = (√15)² {cross multiplication}

y² + 2y = 15

y² + 2y - 15 = 0

by factorization;

(y - 3)(y + 5) = 0

y = 3 or y = -5

by Pythagoras rule:

(√15)² = x² + y²

15 = x² + 3²

x = √(15 - 9)

x = √6

z² = (√6)² + 2²

z = √(6 + 4)

z = √10

Therefore, the values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

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Answer:

6.7%

Step-by-step explanation:

cost: 75 cedis

sale price: 80 cedis

amount of profit: 80 cedis - 75 cedis = 5 cedis

Now we find what percent 5 cedis is of 75 cedis.

percent = part/whole * 100%

percent = 5/75 * 100%

percent = 0.06666 * 100%

percent = 6.6666%

percent = 6.7%

Answer:

109

Step-by-step explanation:

32.9 × 4 = 131.6

131.6 ÷ 1.2 = 109.6666666667

round down because you can seal 1 more box with .7 m of tape.

Answer:

The total number of boxes able to be sealed with this amount of tape is 109.6

Step-by-step explanation:

The equation of the tangent line in slope-intercept form is y = 67x - 40.

To find the point on the function when x = 1, we simply substitute x = 1 into the given equation:

y = (1+2)(2(1)^2+3)^3 = 27

So the point on the function when x = 1 is (1,27).

To find the slope of the tangent line when x = 1, we take the derivative of the given function and evaluate it at x = 1:

y' = (2x^2+7x+6)(2x^2+3)^2 + 3(x+2)(4x^3+18x^2+18x)

y'(1) = (2(1)^2+7(1)+6)(2(1)^2+3)^2 + 3(1+2)(4(1)^3+18(1)^2+18(1))

= 67

So the slope of the tangent line when x = 1 is 67.

Using the point-slope form of the equation of a line, we can write the equation of the tangent line when x = 1 as:

y - 27 = 67(x - 1)

Simplifying, we get:

y = 67x - 40

So the equation of the tangent line in slope-intercept form is y = 67x - 40.

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Answer:

the x is the horizontal axis and y is the vertical axis

Answer: X and Y are variables which means they represent some number that you don't know. When you are working with Graphs, X and Y could be coordinates. When it wants you to solve for x you have to do the inverse opperation until you isolate the variable you are trying to solve. Basically, inverse opperations are if it is -30 on one side you would add 30 to both sides to cancel it out. When you isolate the variable it is only that one letter with everything else on the other side.

Step-by-step explanation:

If this is confusing, let me know an example question and I can help you in the comments.

As a result of answering the given question, we may state that As a graphs result, assertion 1 is the only true statement: F(x) 0 over the intervals (-, -0.7) and (0.76, 2.5).

Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a relationship between two or more things. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential growth. a logarithmic graph shaped like a triangle.

Based on the information provided, we can deduce that the graph of f(x) is a curved line that crosses the x-axis at (-0.7, 0), (0.76, 0), and (2.5, 0) and the y-axis at (-0.7, 0). (0, 2). Its minimum value is (1.9, -5.7), while its maximum value is (0, 2).

As a result, statement 1 is correct: f(x) 0 over the intervals (-, -0.7) and (0.76, 2.5).

The curve intersects the x-axis at (-0.7, 0), (0.76, 0), and (0.76, 0). (2.5, 0). That is, f(x) is negative between -0.7 and 0.76 and positive outside of that range. As a result, statements 3 and 4 are both untrue.

As a result, assertion 1 is the only true statement: F(x) 0 over the intervals (-, -0.7) and (0.76, 2.5).

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In the image line segment SE is the tangent. The secant line making an angle with tangent line SE is NS. So the angle is ∠GSE. So option B is the correct answer.

Tangent is a line which intersect with only a single point on the curve. The point where the line meets is the point of tangency. Tangent line is always perpendicular to the radius drawn to the point of tangency. Here the tangent line is SE, point of tangency is S.

Secant lines are the lines which passes through two points of a curve. A chord drawn to the circle is a secant line. Here there are two secant lines NS and NA. Here only NS makes an angle with the tangent line.

So the angle made by a tangent and secant line is ∠GSE.

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The image for the question is attached below.

Because a 270° rotation around the origin and a subsequent reflection over the x-axis translate ABC onto LMN, the figures are congruent.

Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and form. Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another. In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

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9514 1404 393

Answer:

Step-by-step explanation:

The tangent of the angle can be found using the identity for the tangent of the difference of angles.

  tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(β))

The tangent of the angle of each vector is the ratio of the j coefficient to the i coefficient.

  tan(α) = -2/3

  tan(β) = 4/7

  tan(α-β) = (-2/3 -4/7)/(1 +(-2/3)(4/7))

  = (-14-12)/(21 -8) = -26/13 = -2

Then the magnitude of the angle between the vectors is ...

  arctan(2) ≈ 63.43°

Answer:

im going to go with A because you want to divide 6.60 by 2

Step-by-step explanation:

Subtract the third price by each of the answers until you get the second price for an answer. If you still don't get it can you comment down below and I'll tell you the answer.

Answer:

x = 7

y = 12

Step-by-step explanation:

To do this question you have to know your exponent rules, but also you need to know how to add fractions.

To multiply

6^(1/3) × 6^(1/4)

you can keep the 6 and just add the exponents.

That's why the answer is set up on the form 6^(x/y)

To add fractions, you need a common denominator, it is 12.

1/3 is 4/12.

1/4 is 3/12.

So 1/3 + 1/4

is the same as:

4/12 + 3/12

= 7/12

7/12 is the exponent you are looking for.

x = 7 and y = 12.

6^(1/3) × 6^(1/4)

=6^(7/12)

Answer:

3 3/4

Step-by-step explanation:

Based on the given sample, the economist reports a participation rate of approximately 33.00%.

To analyze the information provided, let's calculate the participation rate in the stock market for middle-income American households based on the given sample.

The economist reports that out of a sample of 2,100 middle-income American households, 693 actively participate in the stock market.

To determine the participation rate, we divide the number of households actively participating in the stock market by the total sample size and multiply by 100 to express it as a percentage:

Participation rate = (Number of participating households / Total sample size) * 100

Substituting the given values:

Participation rate = (693 / 2100) * 100

Calculating the participation rate:

Participation rate = 0.33 * 100

Participation rate ≈ 33.00%

Therefore, based on the given sample, the economist reports a participation rate of approximately 33.00% for middle-income American households in the stock market.

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The daily percent of increase in tourists from one month to the next is approximately 5.4% which is obtained through mathematical operations.

To calculate the daily percent of increase, we need to determine the difference in the number of tourists between the two months and divide it by the number of days in the second month. Then, we express this difference as a percentage.

In the given scenario, the increase in tourists from the first month to the second month is 6355 - 4500 = 1855. The number of days in the second month is 31. Dividing the increase by the number of days gives us

1855 / 31 = 59.8387.

To express this increase as a percentage, we multiply the result by 100, yielding 5983.87%. Rounding this to the nearest tenth of a percent gives us approximately 5983.9%.

Finally, to find the daily percent of increase, we divide the percentage by the number of days in the second month: 5983.9% / 31 = 5.4%.

Therefore, the daily percent of increase in tourists from one month to the next is approximately 5.4%.

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Answer:C

Step-by-step explanation:

Using percentages we know that the amount of the state tax which is paid by the Luce for no federal withholding allowances is $16.34.

Hundredths of any quantity are represented by a relative number called a percentage.

Since one percent is represented by the sign 1%, 100 percent, and 200 percent respectively imply the complete amount and double the amount.

A ratio or fraction can be changed into a percentage by multiplying by 100 and adding the "percentage sign"%.

So, Luce is unmarried and earns $763 twice per week.

She makes no claims for federal withholding benefits.

This sum falls between $760 and $780 in value.

The federal tax for this slab is $86 if we look at the table included in the issue.

State taxes now equal 19% of federal taxes.

Consequently, the $86 in federal tax at 19 percent is:

Tax = 86 * 19/100

Tax = 16.34

Therefore, using percentages we know that the amount of the state tax which is paid by the Luce for no federal withholding allowances is $16.34.

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Correct question:
Use the tax table to help answer the following question.

A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.

Luce is single and makes $763 biweekly. She claims no federal withholding allowances. If the state tax is 19% of the federal tax, how much in state tax does Luce contribute?

a. $12.92

b. $15.13

c. $15.77

d. $16.34

Answer:

137022 pounds

Step-by-step explanation:

At 4 weeks = 1114 pounds

At 16 weeks = 123 times more.

At 16 weeks = 1114 pounds * 123

At 16 weeks = 137022 pounds.

Please give brainliest, like, and rate 5 stars. i hope this helps. Thanks!

Answer:

Ivan biked a total of 6 2/3 hours.

Step-by-step explanation:

All you have to do is add up the hours. First, add up the full hours:

1+2+2=5

Now, add up the fractions.

2/3+1/3=3/3

+ 2/3

Now add everything together.

5 + 3/3 + 2/3= 6 2/3 hours

He biked 6 2/3 hours in total

Hope this helps!

Answer:

Step-by-

a =  0.58

b =  0.42

step explanation:

Answer:

A census was conducted that determined the land area and populations of towns in a certain region. The frequency table displays some of the results.

Rounded to the nearest hundredth, what values complete the conditional relative frequency table?

a =

0.58

b =

0.42

Step-by-step explanation:

Because her initial speed is already above the speed limit. So, the problem is not solvable under the given conditions.

Let's call Amanda's initial speed "s" (in mph). We know that she drove for 4 hours at speed s, and then for the remaining time (which is 6 hours), she drove at speed s - 20 mph.

The total distance of the trip is 400 miles. Using the distance formula:

distance = rate × time

we can write two equations:

First part of the trip:

400 = s × 4

Second part of the trip:

400 = (s - 20) × 6

Now we can solve for s. Starting with the first equation:

400 = s × 4

Dividing both sides by 4 gives:

s = 100

So Amanda's initial speed was 100 mph.

Checking with the second equation:

400 = (s - 20) × 6

Substituting s = 100, we get:

400 = (100 - 20) × 6

400 = 80 × 6

400 = 480

This equation is not true, which means that there must be an error in our calculations. The error is that Amanda cannot possibly have driven at 100 mph for 4 hours and then slowed down to 80 mph for the remaining 6 hours, because her initial speed is already above the speed limit. So, the problem is not solvable under the given conditions.

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Answer:

Step-by-step explanation:

Equations:

Subtract the second equation from the first:

Create equations

\(\\ \tt\Rrightarrow 8x+14y=254--(1)\)

\(\\ \tt\Rrightarrow x+14y=191--(2)\)

Substract eq(2) from eq(1)

\(\\ \tt\Rrightarrow 7x=63\)

\(\\ \tt\Rrightarrow x=\dfrac{63}{7}\)

\(\\ \tt\Rrightarrow x=9\)

The correct option is A. The volume is 6.77 cubic units

The function and interval given are f(x) = (x - 1)^-1/4 and the x-axis on the interval (1, 6].

We want to find the volume of the solid of revolution when the region is rotated about the x-axis.

Let's consider the graph of the function: graph{(x-1)^(-1/4) [-10, 10, -5, 5]}

To set up the integral to find the volume of the solid of revolution, we can use the disk method.

We need to integrate the area of each disk perpendicular to the x-axis from x = 1 to x = 6.

The area of a disk is given by the formula: A = πr²

where r is the radius of the disk and is equal to f(x) in this case.

Therefore, the area of a disk is: A = πf(x)²

Let's substitute f(x) into this formula and integrate from x = 1 to x = 6 to get the volume of the solid.

We have The integral that should be used to find the volume of the solid is given as:

V = ∫₁⁶ πf(x)² dx

We substitute f(x) = (x - 1)^(-1/4) into this expression and integrate to get the volume.

We have: V = ∫₁⁶ π(x - 1)^(-1/2) dx

Let u = x - 1, so that du/dx = 1 and dx = du.

When x = 1, u = 0, and when x = 6, u = 5.

Therefore, we have: V = ∫₀⁵ πu^(-1/2) du= 2π[u^(1/2)]₀⁵= 2π(√5 - 1) ≈ 6.77 cubic units.

The volume of the solid of revolution when the region is rotated about the x-axis is approximately 6.77 cubic units.

Thus, the correct option is A. The volume is 6.77 cubic units.

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The approximations of the solution at x = 1 using Euler's method with step sizes h = 0.25 and h = 0.1 are 9.625 and 9.997, respectively. Neither approximation matches the actual solution y₂ ≈ 5.987, but the approximation with h = 0.1 is closer to the actual value.

To approximate the solution to the initial value problem using Euler's method, we first need to express the problem in the form of a first-order differential equation. The given initial value problem is:

dy/dx = -3x²y,     y(0) = 10.

We can rewrite this equation as y' = -3x²y. The actual solution to this problem is given by y(x) = 10e^(-x³).

Now, let's apply Euler's method twice with two different step sizes to approximate the solution on the interval [0, 2].

1. Using step size h = 0.25:

We start at x = 0 with y = 10 (initial condition). The formula for Euler's method is:

yₙ₊₁ = yₙ + h * f(xₙ, yₙ),

where yₙ represents the approximation of y at the nth step, xₙ = nh represents the value of x at the nth step, and f(xₙ, yₙ) represents the value of the derivative at the nth step.

Applying Euler's method with h = 0.25, we get:

x₀ = 0, y₀ = 10.

x₁ = 0 + 0.25 = 0.25,

y₁ = y₀ + 0.25 * f(x₀, y₀) = 10 + 0.25 * (-3 * 0² * 10) = 10.

Now, for the second step:

x₁ = 0.25, y₁ = 10.

x₂ = 0.25 + 0.25 = 0.5,

y₂ = y₁ + 0.25 * f(x₁, y₁) = 10 + 0.25 * (-3 * 0.25² * 10) = 10 - 0.375 = 9.625.

2. Using step size h = 0.1:

Following the same process, we can calculate the approximations:

x₀ = 0, y₀ = 10.

x₁ = 0 + 0.1 = 0.1,

y₁ = y₀ + 0.1 * f(x₀, y₀) = 10 + 0.1 * (-3 * 0² * 10) = 10.

For the second step:

x₁ = 0.1, y₁ = 10.

x₂ = 0.1 + 0.1 = 0.2,

y₂ = y₁ + 0.1 * f(x₁, y₁) = 10 + 0.1 * (-3 * 0.1² * 10) = 10 - 0.003 = 9.997.

Comparing the approximations at x = 1 with the actual solution y₂ = 10e^(-1³) ≈ 5.987, we have:

For h = 0.25: Approximation = 9.625

For h = 0.1: Approximation = 9.997

As we can see, both approximations differ from the actual solution, but the approximation with a smaller step size (h = 0.1) is closer to the actual value.

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From the graph, the complex number with the greatest modulus is z1

From the question, we have the following parameters that can be used in our computation:

The complex numbers z1, z2, z3 and z4

The general rule of modulus of complex numbers is that

The complex number that has the greatest modulus is the complex number that is at the farthest distance from the origin

Using the above as a guide, we have the following:

From the graph, the complex number that is at the farthest distance from the origin is the complex number z1

Hence, the complex number with the greatest modulus is z1

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Answer:

No

Step-by-step explanation:

15^2+15^2=450 not 900=3^2

Hope this helps! ;-)

We need to know how to interpret a graph to solve the problem. (a) h is a function of t. (b) Approximate  height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.

(a) h is a function of t since the height of the projectile varies with time. The input values of the function is the time interval and the output values is the height of the projectile.

(b) The approximate height of the projectile after 0.5 second according to the graph is 20 feet and the height of the projectile after 1.25 second according to the graph is 30 feet.

(c)The domain of the function is [0,2.5] and the range of the function is [0,30].

(d) t is not a function of h.

Therefore a) h is a function of t. (b) Approximate  height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.

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To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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Answer:

200 students vote in the election

Step-by-step explanation:

We know

120 votes = 60%

1% = 2 votes

To find how many students vote in the election, we take

2 x 100 = 200 votes

So, 200 students vote in the election

Answer:

Refer to the attached image.

Step-by-step explanation:

Step-by-step explanation:

If they are similar, then 10 is to 3      as  x is to 15

10/3 = x/15    multiply both sides by 15

 50 mm = x