Rectangle A has a length of 2x + 6 and a width of 3x. Rectangle B has a length of x + 2 and an area of 12 square units greater than Rectangle A's area. What is a simplified expression for the width of Rectangle B? x + 2 x + 1 6x + 6 6(x + 2)(x + 1)

Answer:

[tex]a=9\ in\\b= 9\ in[/tex]

Step-by-step explanation:

This straight triangle has two angles equal to 45 ° and two equal sides.

We know that the side opposite the 90 degree angle is:

[tex]c =9\sqrt{2}\ in[/tex]

Since the triangle has two equal angles, then it is an iscoceles triangle.

This means that

[tex]a = b[/tex]

We use the Pythagorean theorem to find b

[tex]c^2 = a^2 + b^2\\\\c^2 = b^2 + b^2\\\\c^2 = 2b^2\\\\(9\sqrt{2})^2 =2b^2\\\\b^2=\frac{(9\sqrt{2})^2}{2}\\\\\sqrt{b^2}=\sqrt{\frac{(9\sqrt{2})^2}{2}}\\\\b=\frac{(9\sqrt{2})}{\sqrt{2}}\\\\b=a=9[/tex]

ANSWER

[tex]( - \frac{23}{5} , - 4)[/tex]

EXPLANATION

Given the points P(2,-1) and Q(-9,-6),the coordinates of the point that partition the directed line segment PQ in the ratio 3:2 is given by

[tex]x = \frac{ mx_2+nx_1}{m + n} [/tex]

[tex]y= \frac{ my_2+ny_1}{m + n} [/tex]

Where m=3 and n=2

[tex]x = \frac{ 3 ( - 9)+2(2)}{3+ 2} [/tex]

[tex]x = \frac{ - 23}{5} [/tex]

[tex]y= \frac{ 3( - 6)+2( - 1)}{3 + 2} [/tex]

[tex]y= \frac{ - 20}{5} = - 4[/tex]

The point is

[tex]( - \frac{23}{5} , - 4)[/tex]

The coordinates of the point on the directed line segment PQ that partitions it in the ratio 3/2 are (-21/5, -17/5).

To find the coordinates of the point on the directed line segment PQ that partitions it in the ratio 3/2, we can use the section formula. The section formula states that the coordinates of a point dividing a line segment with endpoints (x1,y1) and (x2,y2) in the ratio m:n are given by:

x = (m*x2 + n*x1)/(m+n)

y = (m*y2 + n*y1)/(m+n)

Plugging in the values from the given points P(2,-1) and Q(-9,-6) into the formula, we get:

x = (3*(-9) + 2*2)/(3+2) = -21/5

y = (3*(-6) + 2*(-1))/(3+2) = -17/5

So, the coordinates of the point are (-21/5, -17/5).

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5=(5 x 4)-3

Hope I helped! Sorry if I'm wrong!

~Potato

^^ What they said I think that’s right but I may be wrong

Answer:

f^-1 = 4(x-3)

Step-by-step explanation:

If f(x) = 1/4(x) + 3 we ned to find f^-1.

To find the inverse function, we need to solve the equation for "x", as follows:

f(x) = 1/4(x) + 3

y = 1/4(x) + 3

y-3 = 1/4(x)

4(y-3) = x

Now, change the "x" for an "y". And change the "y" for an "x":

4(x-3) = y

The solution is the last one.

Answer:  The correct option is

(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).

Step-by-step explanation:  Given that the segment AB is being dilated to A''B'' with the center at the origin. The image of A, point A" has coordinates of (3.2, 6.4).

We are to find the scale factor of the dilation and the co-ordinates of the point B''.

From the given graph, we note that

the co-ordinates of point A are (4, 8).

Now, If S is the scale factor of dilation, then we must have

[tex]S\times (4,8)=(3.2,6.4)\\\\\Rightarrow (4S,8S)=(3.2,6.4)\\\\\Rightarrow S=\dfrac{3.2}{4}=\dfrac{6.4}{8}=0.8.[/tex]

So, the scale factor is 0.8.

Now, the co-ordinates of point B are (-4, -6). So, the co-ordinates of B'' will be

[tex](-4\times 0.8,-6\times 0.8)=(-3.2,-4.8).[/tex]

Thus, the correct option is

(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).

Answer:

A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).

Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

Answer:

The answer is : Collision

Step-by-step explanation:

Alex would have to pay collision deductible before he receives a payment from the insurance company.

A deductible is any amount that you have to pay out of pocket when you make a claim.

Collision deductible comes to effect when your vehicle is damaged in an accident. This pays the cost of repairing the vehicle minus the amount of your deductible.

Answer:

C = 13

Step-by-step explanation:

C = 3(5) - 2

C = 15 - 2

C = 13

Answer:

C = 13

Step-by-step explanation:

Substitute x = 5 into the expression for C

C = (3 × 5) - 2 = 15 - 2 = 13

Answer:

$20,409.79

Step-by-step explanation:

First find John’s quarterly salary. ;$42,000 / 4 = $10,500 ;Total Contributions = John’s + Employer’s ;Total Contributions = $10,500 x 0.05 + $10,500 x 0.03 ;Total Contributions = $840 ;Find the interest rate per compounding period and the number of compounding periods. ;8% / 4 = 2% ;5 x 4 = 20 periods ;The factor from the table for 2% and 20 is 24.29737. ;Amount = $840 x 24.29737 ;Amount = $20,409.79

For this case we have to define trigonometric relations in a rectangular triangle that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle.

So, we have:

cos (Θ) = [tex]\frac {9} {15} = \frac {3} {5}[/tex]

Answer:

False

x - number of polio vaccinations

y - number of measles vaccinations:

x + y = 60    / * ( - 2 )

4 x + 2 y = 184

--------------------------

- 2 x - 2 y = - 120

+

4 x + 2 y = 184

--------------------------

2 x = 64

x = 64 : 2

x = 32

32 + y = 60

y = 60 - 32

y = 28

Answer: There were 32 polio and 28 measles vaccinations.

Answer:

32 and 28

Step-by-step explanation:

Answer:

The answer, using your equation is: 11 hours, 51 minutes and 44 seconds, that is  the number of daylight hours in that city

Step-by-step explanation:

Ok, in a normal year, the 220th day is the 8 of august, that is 08-08.

So, using x=220, we can estimate the number of daylight hours in that city:

[tex]y=2.15sin(\frac{2\pi }{12}x)+10= 2.15sin(\frac{2\pi }{12}(220))+10[/tex]

Then using a calculator in radians:

[tex]y=2.15(sin(0,524*220))+10[/tex]

[tex]y=2.15(sin(115.192))+10[/tex]

[tex]y=2.15(0,866)+10[/tex]

[tex]y=1.862+10[/tex]

[tex]y=11.862[/tex]

Then, you have that is 11 hours, but what about the 0.862 hours? We convert the to hours knowing that 1 hour has 60 minutes. Then 0,862*60 minutes= 51,72 minutes. And we do this for the 0,72 minutes as well, knowing that 1 minute has 60 seconds, then 0,72*60= 44 seconds.

The number of hours is 11 hours, 51 minutes and 44 seconds

Answer:

18 racks

Step-by-step explanation:

338/19=17.78 so if you round up you get 18 racks

Ms. Sanchez needs to buy 18 coat racks to accommodate 338 coats, as each rack holds 19 coats and we round up the result of the division 338/19 to the nearest whole number.

The question asks us to determine how many coat racks Ms. Sanchez should buy if she wants to hold 338 coats and each rack holds 19 coats. To find out the number of racks needed, we divide the total number of coats by the number of coats that one rack can hold, which is a straightforward division problem.

We calculate this by dividing 338 (the total number of coats the racks need to hold) by 19 (the number of coats each rack can hold):

338 / 19 = 17.7895...

Since we cannot have a fraction of a coat rack, we round up to the nearest whole number because Ms. Sanchez needs enough racks to hold all the coats, and you cannot purchase a fraction of a rack. Therefore, Ms. Sanchez should buy 18 coat racks to accommodate all 338 coats.

Final answer:

To find the length of a 90° arc with a circle radius of 10 miles, multiply the radius by π/2. The arc length is calculated to be approximately 15.71 miles.

Explanation:

The radius of a circle is 10 miles, and we're asked to find the length of a 90° arc. The length of an arc can be calculated using the formula arc length = (central angle in radians) × radius. Since there are 2π radians in a 360° circle, a 90° angle corresponds to π/2 radians. Therefore, the arc length for a 90° arc on a circle with a 10-mile radius would be (π/2) × 10 miles.

Calculating the arc length, we get:

arc length = (π/2) × 10 miles

arc length = 5π miles

Using the approximate value of π (3.14159), the arc length would be roughly:

arc length = 5 × 3.14159 miles

arc length = 15.70795 miles

Hence, the length of a 90° arc for a circle with a 10-mile radius is approximately 15.71 miles.

Answer:

Step-by-step explanation:

There are 6 letters all together. There 2 letters that if you draw them, you will be successful.

2/6 = 1/3

That means that 1 in 3 times you should draw an A or an E.

Answer:

D. The graph of d(x) is 25 units below the graph of f(x)

ANSWER

D. the graph of d(x) will be 25 units below the graph of f(x).

EXPLANATION

The graph of

[tex]f(x) = {x}^{2} [/tex]

is the base function.

The graph of

[tex]d(x) = {x}^{2} - 25[/tex]

is a vertical translation of the base function 25 units down.

This implies that, the graph of d(x) will be 25 units below the graph of f(x).

Therefore the correct answer is D.

The pentagon is translated 1 unit to the left, so the points move to the left by 1 unit. Moving left or right changes the x value, when you move right, the x value increases, when you move left, x decreases. Since x is going left 1 unit:

So x - 1

10 units down. Moving up down or up changes the y value, when you move down, y decreases, when you move up, y increases. Since the pentagon is going down 10 units:

y - 10

Your answer is A

The rule that describes the given transformation is (x, y) → (x - 1, y - 10). It is given that the pentagon is translated by 1 unit to the left and 10 units down.

The graph is transformed into a new graph by applying certain operations like,

It is given that a pentagon in the graph is translated as 1 unit to the left and 10 units to the down.

Here the translation is towards the negative axes.

So, the rule for this transformation we can write as (x, y) → (x - 1, y - 10)

Translating the points of the pentagon from the graph using this rule:

Actual coordinates                        Translated coordinates

(-1, 3)                                                 ((-1 - 1), (3 - 10)) = (-2, -7)

(1, 5)                                                  ((1 - 1), (5 - 10)) = (0, -5)

(2, 2)                                                 ((2 - 1), (2 - 10)) = (1, -8)

(4, 6)                                                 ((4 - 1), (6 - 10)) = (3, -4)

(5, 3)                                                 ((5 - 1), (3 - 10)) = (4, -7)

So, the new pentagon will be plotted in the graph with these translated coordinates.

The graph of the translated pentagon is shown below.

So, option A (x, y) → (x − 1, y − 10) describes the given transformation correctly.

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ANSWER

(-1,-1), (-4,-5), (-8,0)

EXPLANATION

We have a triangle with vertices:

(0,2), (-3,-2) and (-7,3).

The rule for the translation is

[tex](x, y) \to (x - 1,y - 3)[/tex]

The new vertices of the triangle will be;

[tex](0, 2) \to (0 - 1,2- 3) = ( - 1, - 1)[/tex]

[tex]( - 3, - 2) \to (- 3-1, - 2- 3) = ( -4, - 5)[/tex]

[tex]( - 7, 3) \to ( - 7 - 1,3- 3) = ( - 8, 0)[/tex]

The new vertices are:

(-1,-1), (-4,-5), (-8,0)

Answer:

ezpz false

Step-by-step explanation:

Answer:

34.7 degrees

Step-by-step explanation:

This is a right triangle trig problem. The angle in question, the angle of elevation, is the base angle that is NOT the right angle. The height of the tree is the side opposite the angle of elevation, and the distance away from the tree is the measure of the base of the right triangle. So the question, then, is "What is the angle that has a ratio equal to the side opposite the angle over the side adjacent to the angle?" This is the definition of the tangent of an angle. The equation will be set up as follows:

[tex]tan\beta =\frac{45}{65}[/tex]

Your calculator needs to be in degree mode when you do this operation. Press 2nd on your calculator then tan and you'll get tan^-1 on your display. This means you are looking for a missing angle. Enter the fraction as 45/65 inside the parenthesis and hit enter and you'll get an angle of 34.69515353. Round to the nearest tenth for 34.7

You will always use the 2nd and sin/cos/tan buttons to find missing angles.

The angle elevation is 34.6 9 degree.

When it lies between the horizontal line and the line of sight, the angle of elevation is formed. The angle that forms when the line of sight is above the horizontal line is referred to as the angle of elevation. The line of sight, however, is to the horizontal line downward in the angle of depression.

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

Given:

Height of tree= 45 foot

Distance= 65 feet

Now, Using Trigonometry

tan [tex]\theta[/tex] = P/ B

        = 45/65

        = 9/ 13

        = 0.6923

[tex]\theta[/tex] = 34.69 degrees.

Hence, the angle elevation is 34.6 9 degree.

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Answer:

C. [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

We have been given a table showing rates of time taken by Judy and Sam to complete a puzzle.

We can see from our given table that Sal's rate is r. We are told that Judy completes a puzzle by herself, it takes her 3 hours. working with Sal, it only takes them 2 hours.

Since Judy completes the puzzle in 3 hours, so part of puzzle completed by Judy in one hour would be [tex]\frac{1}{3}[/tex], therefore, correct choice is option C.

Answer:

C.

Step-by-step explanation:

Answer:

It's the first choice (20 degrees).

Step-by-step explanation:

These angles will be equal ( by The Alternate Angle Theorem).

5(x - 2) = x + 14

5x - 10 = x + 14

4x = 24

x = 6.

So the measure of each angle =  5(6 - 2) = 6 + 14 = 20 degrees.

The angles of elevation and depression are equal because they are alternate interior angles. Solving the given expressions yields x = 6. Therefore, both the angle of elevation and the angle of depression measure 20 degrees.

First, let's set up the problem:

In any scenario involving angles of elevation and depression, these angles are equal because they are alternate interior angles formed by a horizontal line and a transversal.

Therefore, we can equate the two expressions:

5(x-2) = (x+14)

Now, solve for x:

Now substitute x back into the expressions to find the angle measures:

For the angle of elevation: 5(x-2) = 5(6-2) = 5*4 = 20 degrees

For the angle of depression: (x+14) = (6+14) = 20 degrees

Therefore, both the angle of elevation and the angle of depression measure 20 degrees.

This confirms that our setup and calculation are correct.

Answer: 1 out of 5 for the first box and 1 out of 7 for the second box

( in simplest form)

Step-by-step explanation:

Answer:

c. 1 and 3

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot each equation.

Please see the attached image below, to find more information about the graph

s

The equations are:

1) y = sin (3x + π/6)

2) y = cos (3x - π/6)

3) y = cos (3x - π/3)

Looking at the graphs, we can see that the identical ones

are equations one and three

Correct option:

c. 1 and 3

Answer:

  you expect to win on average $1.33 per round

Step-by-step explanation:

The expected value is the sum of products of probability and value:

  2/6×$8 + 4/6×(-$2) = $8/3 - 4/3 = $4/3 ≈ $1.33

The expected value of the gambling game is calculated by taking into account the probability of winning $8 and losing $2. The final expected value is $1.33, which means on average, you would gain $1.33 per game played.

To calculate the expected value for the gambling game where you roll a die, you need to account for the different outcomes and their associated probabilities. In this game, rolling a 1 or 2 means you win $8, and there are two outcomes out of six that result in a win, giving a probability of 2/6 or 1/3 for each of these outcomes. Rolling any other number (3, 4, 5, or 6) results in losing $2, with a probability of 4/6 or 2/3 for each of these losing outcomes.

The expected value (EV) can be calculated using the formula:

EV = (Probability of Winning × Amount Won) + (Probability of Losing × Amount Lost)

Substituting the values into the formula:

EV = ‎‎(1/3 × $8) + (2/3 × -$2)

EV = ($2.67) + (-$1.33)

EV = $1.33

This means that the average gain per game, after many plays, is expected to be $1.33.

Answer:

The radius is 7, and the circumference is  43.96

Step-by-step explanation:

The radius is half of the diameter, and this would just be 14/2 which is 7. The circumference is found by C=pi(diamete) or 2pi(radius). This is found by 14*3.14 this is equals 43.96

The radius of the dartboard is 7 inches and the circumference is approximately 43.96 inches.

Radius:

The radius of a circle is half of its diameter. So, in this case, the radius is 7 inches.

Circumference:

The circumference of a circle can be found using the formula C = 2πr, where r is the radius. So, the circumference of this dartboard is 2π(7) = 14π inches, which rounds to 43.96 inches when rounded to the nearest hundredth.

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Answer:

Option A and Option C

Step-by-step explanation:

The surface area of a cone can be calculated with this formula:

[tex]SA=\pi r^2+\pi rs[/tex] (This matches with the option A)

Where [tex]\pi rl[/tex] is the lateral area of the cone (Being "s" the slant height) and [tex]\pi r^2[/tex] is the area of the base of the cone (which is a circle).

You know that BA the is the area of the base and LA the lateral area of the cone.

Then, substituting into the formula for calculate the surface area of a cone, you get:

[tex]SA=BA+LA[/tex]

This matches with the option C

Answer:

a and c

Step-by-step explanation:

a p e x

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

21.63

use the Pythagorean theorem.

a^2+b^2=c^2

Really hard to make it out, especially the upper limit of the sum, but I think it reads

[tex]\displaystyle\sum_{k=1}^n5k-42[/tex]

(not sure what [tex]n[/tex] is, but that's not very important)

Expand the sum as

[tex]\displaystyle5\sum_{k=1}^nk-42\sum_{k=1}^n1[/tex]

Recall that

[tex]\displaystyle\sum_{k=1}^n1=1+1+\cdots+1=n[/tex]

[tex]\displaystyle\sum_{k=1}^nk=1+2+\cdots+n=\dfrac{n(n+1)}2[/tex]

so that

[tex]\displaystyle\sum_{k=1}^n5k-42=\dfrac{5n(n+1)}2-42n[/tex]

Then just plug in whatever [tex]n[/tex] happens to be.