Wite an expression in simplest form to represent the area of the shaded region

Answer:

answer D

Step-by-step explanation:

The person that is correct is; Calvin is correct because he correctly applied the quotient of powers rule.

The expression that Nadine and Calvin were trying to simplify is;

r⁻⁵s⁻³/(r⁸s⁻²)

Now, we are told that Nadine claims the first step is to simplify the expression is to raise the numerator and denominator to the given power.

Meanwhile, Calvin claims the first step to simplify the expression is to apply the quotient of powers.

We can conclude that Calvin is correct because he correctly applied the quotient of powers rule.

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The measure of the angle R in the right-angle triangle will be 22.62°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The measure of the angle R is given by the sine rule. The sine of angle R is the ratio of the perpendicular to the hypotenuse. Then we have

sin R = 5 / 13

R = sin⁻¹(5/13)

R = 22.62°

The measure of the angle R in the right-angle triangle will be 22.62°.

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The measure of angle R is 30 degrees.

To determine the measure of angle R, we can use the properties of special right triangles, specifically the 30-60-90 right triangle. In such a triangle, the angles are 30 degrees, 60 degrees, and 90 degrees, and the lengths of the sides opposite these angles are in the ratio 1:√3:2, respectively.

Given that side PR is the hypotenuse of the right triangle PQR and it is 2 units long, we can deduce that triangle PQR is a 30-60-90 triangle. The side QR, which is opposite the 30-degree angle at Q, is half the length of the hypotenuse. Since PR is 2 units, QR must be 1 unit.

The side PQ is opposite the 60-degree angle at P and is 3 times the length of QR. Since QR is 1 unit, PQ must be 3 units.

The angle R is opposite the side PQ, and since we have established that PQR is a 30-60-90 triangle, angle R must be the smallest angle, which is 30 degrees.

Therefore, the measure of angle R is 30 degrees.

answer should be 6

explanation: -5-(-3)-4 = -5 + 3 - 4 = -2 - 4 = -6 and the absolute value of -6 is 6

Answer:

The answer is 76

HOPE THIS HELPS!

Step-by-step explanation:

Answer:

The rectangular prism has the greatest surface area

Step-by-step explanation:

Verify the surface area of each container

case A) A cone

The surface area of a cone is equal to

[tex]SA=\pi r^{2} +\pi rl[/tex]

we have

[tex]r=6/2=3\ in[/tex] ----> the radius is half the diameter

[tex]l=10\ in[/tex]

substitute the values

[tex]SA=(3.14)(3)^{2} +(3.14)(3)(10)=122.46\ in^{2}[/tex]

case B) A cylinder

The surface area of a cylinder is equal to

[tex]SA=2\pi r^{2} +2\pi rh[/tex]

we have

[tex]r=6/2=3\ in[/tex] ----> the radius is half the diameter

[tex]h=10\ in[/tex]

substitute the values

[tex]SA=2(3.14)(3)^{2} +2(3.14)(3)(10)=244.92\ in^{2}[/tex]

case C) A square pyramid

The surface area of a square pyramid is equal to

[tex]SA=b^{2} +4[\frac{1}{2}bh][/tex]

we have

[tex]b=6\ in[/tex] ----> the length side of the square

[tex]h=10\ in[/tex] ----> the height of the triangular face

substitute the values

[tex]SA=6^{2} +4[\frac{1}{2}(6)(10)]=156\ in^{2}[/tex]

case D) A rectangular prism

The surface area of a rectangular prism is equal to

[tex]SA=2b^{2} +4[bh][/tex]

we have

[tex]b=6\ in[/tex] ----> the length side of the square base

[tex]h=10\ in[/tex] ----> the height of the rectangular face

substitute the values

[tex]SA=2(6)^{2} +4[(6)(10)]=312\ in^{2}[/tex]

Answer:

The rectangular prism has the greatest surface area

Step-by-step explanation:

mark me brainy plz!

Answer:

2 km/h

Step-by-step explanation:

Let x km/h be the speed of the current.

1. A tourist traveled on a motorboat against the current for 25 km (the current interfered), then it took him

[tex]\dfrac{25}{12-x}\ hours.[/tex]

2. Then he returned back on a raft (the speed of the current is the speed of the raft), then it took him

[tex]\dfrac{25}{x}\ hours.[/tex]

3. In the boat the tourist traveled for 10 hours less than on the raft, thus

[tex]\dfrac{25}{12-x}+10=\dfrac{25}{x}.[/tex]

Solve this equation:

[tex]25x+10x(12-x)=25(12-x),\\ \\25x+120x-10x^2=300-25x,\\ \\10x^2-170x+300=0,\\ \\x^2-17x+30=0,\\ \\D=(-17)^2-4\cdot 30=289-120=169,\\ \\x_{1,2}=\dfrac{-(-17)\pm\sqrt{169}}{2}=2,\ 15.[/tex]

The speed of the current cannot be greater than the speed of the boat, because then tourist was not able to travel against the current. Thus, the speed of the current is 2 km/h.

he should tip around this $24.83

Answer:

$24

Step-by-step explanation:

15 % of $165.56

15/100 x 165.56/100 =

245340/10000 = 24.534 ($24)

Answer:

D

Step-by-step explanation:

I'm assuming you're looking for area here.

The formula is b * h = A

So all you're doing is multiplying 30 by 18 to get 540.

Answer:

The length is 65 cm and the width is 12 cm

Step-by-step explanation:

A = lw = 780

P = 2 (l+w) = 154

The length is 5 more than 5 times the width

l=5w+5

P = 2 (l+w) = 154

Divide each side by 2

2 /2 (l+w) = 154/2

l+w = 77

Substituting l = 5w+5

5w+5 +w = 77

6w+5 = 77

Subtract 5 from each side

6w +5-5 = 77-5

6w = 72

Divide each side by 6

6w/6 = 72/6

w = 12

Now lets find l

l = 5w+5

l = 5(12)+5

l = 60+5

l = 65

Answer: 9,000 meters

Step-by-step explanation: There are 1,000 meters in one kilometer. 9 times 1,00p is 9,000.

Answer:

9000 Meters

Step-by-step explanation:

Check the picture below, well that picture is using feet, but is pretty much the same curve for meters.

notice, it hits the ground when y = 0, or h(t) = 0, thus

[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{12}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{1.8}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ 0=-4.9t^2+12t+1.8\implies -4.9t^2+12t+1.8=0[/tex]

There are several equations that can be used to find the time for a ball to reach the ground in projectile motion. The specific equation depends on the given information and scenario.

The equation that can be used to find the time it takes for the ball to reach the ground depends on the specific scenario and information given. There are several equations that can be used for projectile motion, including those that involve quadratic equations or simple equations of motion. It is important to analyze the given information and use the appropriate equation to solve for the time. For example, the quadratic formula can be used to find the time for projectile motion with vertical motion only, while the equation x = xo + vot + at² can be used to solve for the time when the initial and final positions and velocities are known.

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Answer:

(-1, -1) Let me know if the explanation didn't make sense.  

Step-by-step explanation:

If we graph the three points we can see what looks like a quadrilateral's upper right portion, so we need a point in the lower left.  This means M is only connected to N here and P is only connected to N.  So we want to find the slope of these two lines.

MN is easy since their y values are the same, the slope is 0.

NP we just use the slope formula so (y2-y1)/(x2-x1) = (-1-3)/(5-4) = -4.

So now we want a line from point M with a slope of -4 to intersect with a line from point P with a slope of 0.  To find these lines  weuse point slope form  for those two points.  The formula for point slope form is y - y1 = m(x-x1)

y-3 = -4(x+2) -> y = -4x-5

y+1 = 0(x-5) -> y = -1

So now we want these two to intersect.  We just set them equal to each other.

-1 = -4x -5 -> -1 = x

So this gives us our x value.  Now we can plug that into either function to find the y value.  This is super easy of we use y = -1 because all y values in this are -1, so the point Q is (-1, -1)

Answer:

43°

Step-by-step explanation:

From the diagram

∠xwy=∠xyw = isosceles triangle where base angles are equal

∠y= ∠w = (180-86)÷2 = 47°

if ∠xzy=90° and ∠xyz =47° then ∠d=?

∠d= 180°-(90°+47°)

∠d=180°-137° =43°

Answer:

  A ≈ 56.1°

Step-by-step explanation:

By the law of sines, ...

  sin(A)/a = sin(C)/c

  sin(A) = (a/c)·sin(C)

  A = arcsin((a/c)·sin(C)) = arcsin(5/6·sin(95°)) ≈ 56.1°

Answer:

80 HOPE THIS HELPED

Step-by-step explanation:

20+20+20+20=80

20 X 4 = 80

Answer: 55

Step-by-step explanation: The inside measure of a triangle should be 180 so knowing this subtract 43 and 82 and you get 55.

In the given triangle ∠E = 55° and side EF = 12.49 unit

As we know the sum of all three angles in a triangle is 180°

so ∠E = 180-43-82 = 55°

In a triangle ABC if BC = a, AC = b, AB = c

then [tex]\frac{Sin A}{a} = \frac{sin B}{b} = \frac{SinC}{c}[/tex]

From sine rule,

[tex]\frac{sin 43}{EF} = \frac{Sin 55}{15}[/tex]

[tex]EF = 15* \frac{Sin43}{Sin55}[/tex]

EF = 12.49

Therefore, in the given triangle ∠E = 55° and side EF = 12.49 unit

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Answer:

(3700)(1+.059/12)^4(1+.172/12)^8 is the corect answer -Apex

Step-by-step explanation:

Answer:

Option C is correct.

Step-by-step explanation:

Felipe transferred a balance of $3700 to a new credit.

The card had an introductory offer of 5.9% APR for the first 4 months and after that 17.2 % APR.

The card compounds interest monthly, that gives n = 12

So, the equation that represents Felipe's balance at the end of the year will be:

[tex]p(1+\frac{r}{n})^{a}\times (1+\frac{r}{n})^{b}[/tex]

Here a is the introductory rate number of months that is 4

And b is the rest of the standard months that is 8

So, the expression becomes:

[tex]3700(1+\frac{0.059}{12})^{4}\times (1+\frac{0.172}{12})^{8}[/tex]

Answer:

170 cm2

Step-by-step explanation:

Area of Parallelogram = Base x Altitude

Base = 10

Altitude = 17

10 x 17 = 170

Answer = 170 cm2

Answer:

KT = 60

OY = 11

Step-by-step explanation:

Remember that the tangent to a circle theorem states that if a line is tangent to a circle, it is perpendicular to the radius at the point of tangency. Which means angles OTK and OYK are right angles.

If OTK and OYK are right angles, triangles KOT and KYO are right triangles. Since KOT is a right triangle, we can use the Pythagorean theorem to find KT:

[tex]hypotenuse^2=leg^2+leg^2[/tex]

[tex]KO^2=KT^2+OT^2[/tex]

[tex]61^2=KT^2+11^2[/tex]

[tex]KT^2=61^2-11^2[/tex]

[tex]KT=\sqrt{3600}[/tex]

[tex]KT=60[/tex]

Now, remember that the "hat" theorem states that tangents to a circle from the same external point are congruent, so KT and KY are congruent.

The Hypotenuse-Leg theorem states that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg another right triangle, then the triangles are congruent. The hypotenuse, KO, of both right triangles are the same (therefore congruent) and legs KT and KY are congruent by the hat theorem, therefore triangles KOT and KYO are congruent. Since corresponding parts of congruent triangles are congruent, OY ≅ OT.

OY = OT = 10

OY = 10

Let's summary the above in a short proof:

1. ∠OTK and ∠OYK are ∟ angles       Tangent to a circle theorem

2. ΔOTK and ΔOYK are ∟ triangles   Definition of right triangles

3. KT ≅ KY                                             Hat theorem

4. KT = 60                                              Pythagorean theorem

5. OY ≅ OT                                            CPCTC

6. OY = 10                                               Definition of congruency  

Answer:

It is constant (10 gallons a minute)

120,000/10 = 12,000

12,000 minutes to fill the pool

120,000 - 10x

Step-by-step explanation:

Answer:

The pool holds 120,000 gallons of water.

Robert fills the pool at a rate of 10 gallons each minute.

That means for filling 120000 gallons, he will need = [tex]\frac{120000}{10}[/tex] = 12000 minutes

If we convert this to hour, then in 1 hour, [tex]10\times60[/tex] = 600 gallons  can be filled.

So, the rate in gallons per hour =  [tex]\frac{120000}{600}[/tex] = 200 gallons per hour.  

Therefore, the rate at which Robert will fill the pool is 200 gallons per hour.

Yes the rate is constant.

Answer:

9/7

Step-by-step explanation:

Since the pitch is found the same way as the slope of a line

Tangent= slope = pitch

But; Tangent = Opposite/Adjacent

Therefore;

Tan x = 9/7

Thus;

The pitch of the roof is 9/7

Answer:

Vertical angles

x =37

Step-by-step explanation:

Adjacent angles are next to each other and share one side

Vertical angles are across from each other and only share a vertex.

These angles are vertical angles.  Vertical angles are equal

3x-4 = 107

Add 4 to each side

3x-4 +4 =107+4

3x = 111

Divide by 3

3x/3 = 111/3

x=37

Answer:

The measure of angle EDC is [tex]60\°[/tex]

Step-by-step explanation:

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

so

[tex]m<EDC=\frac{1}{2}(arc\ EAB-arc\ EC )[/tex]

substitute the values

[tex]m<EDC=\frac{1}{2}(195\°-75\°)=60\°[/tex]

Answer:

6.375 or 6 3/8

Step-by-step explanation:

Just add 2 2/3+1 5/6+1 7/8 and that= 6.375 or 6 3/8

Answer:

2 in. by 3 in

Step-by-step explanation:

i think i could be totally wrong i probably am so so sorry

Zeros, roots, solutions, and solution sets are all 4 names

The solution of a quadratic function is also called as zeroes, roots and x - intercept.

Solving quadratic function means finding a value (or) values of variable which satisfy the equation. The value(s) that satisfy the quadratic function is known as its roots/ zeroes and x - intercept.

Example-

[tex]x^{2} -3x +2 = 0\\\\x^{2} -2x - x + 2 = 0\\\\x(x - 2) - 1(x - 2) = 0\\\\(x - 1)(x - 2) = 0\\\\x = 1 \, or \, 2[/tex]

Here, 1 and 2 are zeroes/ roots/ intercept of the quadratic function [tex]x^{2} -3x +2 = 0[/tex].

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Answer:

ab² - 9

Step-by-step explanation:

Given in the question an expression

(ab + 3)(ab - 3)

To product mentally we will use polynomial identity called

Difference of squares

here a = ab

        b = 3

(ab + 3)(ab - 3) = ab² - 3² = ab² - 9

Answer:

[tex]a^2b^2 - 9[/tex]

Step-by-step explanation:

We are given the following expression and we are to determine its product mentally:

[tex] ( a b + 3 ) ( a b - 3 ) [/tex]

For this, we can use the FOIL method, which stands for First, Outer, Inner, Last.

First means multiply the terms which come first in each of the binomial, Outer means multiply the outermost terms in the product. Inner means multiply the innermost two terms. Last means multiply the terms which occur last in each binomial.

So we get:

[tex]ab*ab +3*(-3)=a^2b^2 - 9[/tex]

Answer:

Part A: -3/7

Part B: y = -2

Step-by-step explanation:

Parallel lines have the same slope. Find the slope of CD. Then substitute it to find the value needed for AB.

The slope formula is

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{4-1}{-5-2} = \frac{3}{-7}[/tex]

Use the same formula and solve for y.

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\-\frac{3}{7}= \frac{y--5}{-6-1} \\\\\frac{3}{-7} =\frac{y+5}{-7}\\\\3 = y+5\\3-5 = y\\-2 = y[/tex]

Answer:

The correct answer is B.

Step-by-step explanation:

Kylie distributes the 4 into the first part of the equation by multiplying everything in the parenthesis by 4. She does the same with the second part of the equation multiplying 7 by everything in the parenthesis.

Answer:

[tex]\cos(\alpha +\beta)=\frac{2}{3}(1-\frac{\sqrt{5}}{5})[/tex]

Step-by-step explanation:

Let the hypotenuse of the smaller triangle be h units.

Then; from the Pythagoras Theorem.

[tex]h^2=4^2+2^2[/tex]

[tex]h^2=16+4[/tex]

[tex]h^2=20[/tex]

[tex]h=\sqrt{20}[/tex]

[tex]h=2\sqrt{5}[/tex]

From the smaller triangle;

[tex]\cos (\alpha)=\frac{4}{2\sqrt{5} }=\frac{2}{\sqrt{5} }[/tex] and [tex]\sin(\alpha)=\frac{2}{2\sqrt{5} }=\frac{1}{\sqrt{5} }[/tex]

From the second triangle, let the other other shorter leg of the second triangle be s units.

Then;

[tex]s^2+4^2=6^2[/tex]

[tex]s^2+16=36[/tex]

[tex]s^2=36-16[/tex]

[tex]s^2=20[/tex]

[tex]s=\sqrt{20}[/tex]

[tex]s=2\sqrt{5}[/tex]

[tex]\cos(\beta)=\frac{2\sqrt{5} }{6}=\frac{\sqrt{5} }{3}[/tex]

and

[tex]\sin(\beta)=\frac{4}{6}=\frac{2}{3}[/tex]

We now use the double angle property;

[tex]\cos(\alpha +\beta)=\cos(\alpha)\cos(\beta) -\sin(\alpha)\sin(\beta)[/tex]

we plug in the values to obtain;

[tex]\cos(\alpha +\beta)=\frac{2}{\sqrt{5} }\times \frac{\sqrt{5} }{3}-\frac{1}{\sqrt{5} }\times \frac{2}{3}[/tex]

[tex]\cos(\alpha +\beta)=\frac{2}{3}(1-\frac{\sqrt{5}}{5})[/tex]

Answer:

[tex]cos(\alpha + \beta)=cos(68.4\°) \approx 0.37[/tex]

Step-by-step explanation:

We know both legs, we can use the tangent trigonometric reason to find the angle.

[tex]tan\alpha =\frac{2}{4}\\ tan \alpha=\frac{1}{2}\\ \alpha=tan^{-1}(\frac{1}{2} )\\ \alpha \approx 26.6\°[/tex]

We know the hypothenuse and the opposite leg. We can use the sin trigonometric reason to find the angle

[tex]sin\beta =\frac{4}{6}\\ sin\beta=\frac{2}{3}\\ \beta=sin^{-1} (\frac{2}{3} )\\\beta= 41.8\°[/tex]

So, the sum of them is

[tex]\alpha + \beta = 26.6+41.8= 68.4\°[/tex]

Then,

[tex]cos(\alpha + \beta)=cos(68.4\°) \approx 0.37[/tex]

Therefore,

[tex]cos(\alpha + \beta)=cos(68.4\°) \approx 0.37[/tex]