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Problem: Construct a triangle with interior angle
measures of 60° and 75°.
What is the measure of the third angle?
O 30°
2C = 41°
O 45°
48°
9.2
10
50°
ZA = 49°
6.0 ZB = 90°

Answer:

[tex]radius = \sqrt{13}[/tex] or [tex]radius = 3.61[/tex]

Step-by-step explanation:

Given

Points:

A(-3,2) and B(-2,3)

Required

Determine the radius of the circle

First, we have to determine the center of the circle;

Since the circle has its center on the x axis; the coordinates of the center is;

[tex]Center = (x,0)[/tex]

Next is to determine the value of x through the formula of radius;

[tex]radius = \sqrt{(x_1 - x)^2 + (y_1 - y)^2} = \sqrt{(x_2 - x)^2 + (y_2 - y)^2}[/tex]

Considering the given points

[tex]A(x_1,y_1) = A(-3,2)[/tex]

[tex]B(x_2,y_2) = B(-2,3)[/tex]

[tex]Center(x,y) =Center (x,0)[/tex]

Substitute values for [tex]x,y,x_1,y_1,x_2,y_2[/tex] in the above formula

We have:

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

Evaluate the brackets

[tex]\sqrt{(-(3 + x))^2 + 2^2} = \sqrt{(-(2 + x))^2 + 3 ^2}[/tex]

[tex]\sqrt{(-(3 + x))^2 + 4} = \sqrt{(-(2 + x))^2 + 9}[/tex]

Eva;uate all squares

[tex]\sqrt{(-(3 + x))(-(3 + x)) + 4} = \sqrt{(-(2 + x))(-(2 + x)) + 9}[/tex]

[tex]\sqrt{(3 + x)(3 + x) + 4} = \sqrt{(2 + x)(2 + x) + 9}[/tex]

Take square of both sides

[tex](3 + x)(3 + x) + 4 = (2 + x)(2 + x) + 9[/tex]

Evaluate the brackets

[tex]3(3 + x) +x(3 + x) + 4 = 2(2 + x) +x(2 + x) + 9[/tex]

[tex]9 + 3x +3x + x^2 + 4 = 4 + 2x +2x + x^2 + 9[/tex]

[tex]9 + 6x + x^2 + 4 = 4 + 4x + x^2 + 9[/tex]

Collect Like Terms

[tex]6x -4x + x^2 -x^2 = 4 -4 + 9 - 9[/tex]

[tex]2x = 0[/tex]

Divide both sides by 2

[tex]x = 0[/tex]

This implies the the center of the circle is

[tex]Center = (x,0)[/tex]

Substitute 0 for x

[tex]Center = (0,0)[/tex]

Substitute 0 for x and y in any of the radius formula

[tex]radius = \sqrt{(x_1 - 0)^2 + (y_1 - 0)^2}[/tex]

[tex]radius = \sqrt{(x_1)^2 + (y_1)^2}[/tex]

Considering that we used x1 and y1;

In this case we have that; [tex]A(x_1,y_1) = A(-3,2)[/tex]

Substitute -3 for x1 and 2 for y1

[tex]radius = \sqrt{(-3)^2 + (2)^2}[/tex]

[tex]radius = \sqrt{13}[/tex]

[tex]radius = 3.61[/tex] ---Approximated

Answer:

t = 0.75n - 0.25

t represents your total

Step-by-step explanation:

So lets start by writing our total variable.

t =

Now each candy is 0.75 so lets write that down too.

t = 0.75

Since we don't know how much candy we buy, lets multiply 0.75 by n.

t = 0.75n

Now we have a $0.25 coupon so now subtract the 0.25 from the cost.

t = 0.75n - 0.25

There you go.

Answer: mr lee is 37 year .

Step-by-step explanation:32+5=37

Answer:

Mr. lee is 35 yrs old right now. his son 3

Step-by-step explanation:

after 5 yrs, his son will be 8 and lee 40, 8×5=40

Answer:

I believe the answer is d

Step-by-step explanation:

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers.

In this case, since [tex]\sqrt{81}[/tex] can be simplified to 9 and 9 can be written as a fraction (9/1) it is a rational number.

Answer:

[tex]3 \sqrt{2} [/tex]

Step-by-step explanation:

[tex] \frac{6}{ \sqrt{2} } = \frac{6}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{6 \sqrt{2} }{2} = 3 \sqrt{2} [/tex]

We can't have a fraction that has a number under square root as it's denominator. So we will have to rationalize it, which means we will multiply the numerator and also the denominator by the number that is under the square root.

Hope this helps ;) ❤❤❤

Answer:

[tex]\boxed{\sf 3\sqrt{2}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{6}{\sqrt{2} }[/tex]

[tex]\sf Multiply \ both \ numerator \ and \ denominator \ by \ \sqrt{2}[/tex]

[tex]\displaystyle \frac{6 \times \sqrt{2} }{\sqrt{2} \times \sqrt{2} }[/tex]

[tex]\displaystyle \frac{6\sqrt{2} }{2 }[/tex]

[tex]\sf Simplify[/tex]

[tex]3\sqrt{2}[/tex]

Answer: Density = 0.23 tons per cubic meter.

Step-by-step explanation:

Formula : [tex]Density=\dfrac{Mass(in \ ton)}{Volume (in\ m^3)}[/tex]

1 ton = 32000 ounces

⇒ 1 ounce = 0.00003125 ton

⇒  7 ounces = 7(0.00003125)=  0.00021875 ton

1 gallon = 0.00378541 cubic meter

2.5 gallons = 0.009475 cubic meter

Density= [tex]\dfrac{0.00021875}{0.009475}\text{ tons per cubic meter}[/tex]

[tex]\dfrac{21875}{94750}\text{ tons per cubic meter}\approx0.23\text{ tons per cubic meter}[/tex]

Hence, Density = 0.23 tons per cubic meter.

Answer:

0.02 tons per cubic meter

Step-by-step explanation:

Answer:

third option

Step-by-step explanation:

∠ E = 180° - (65 + 53)° = 180° - 118° = 62°, then

∠ A = ∠ F = 53° and ∠ C = ∠ E = 62° , thus

Δ ABC ~ Δ FDE by the AA postulate

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{BC}{DE}[/tex] = [tex]\frac{AB}{FD}[/tex] , substitute values

[tex]\frac{x}{z}[/tex] = [tex]\frac{w}{r}[/tex] ( multiply both sides by z )

x = z × [tex]\frac{w}{r}[/tex]

The expression to solve for x would be x = r × w/z Therefore, the correct option is 3.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Since,

∠ E = 180° - (65 + 53)°

= 180° - 118° = 62°,

then

∠ A = ∠ F = 53° and ∠ C = ∠ E = 62° ,

Thus, Δ ABC ~ Δ FDE are congruent by the AA postulate.

Since the triangles are similar then the ratios of corresponding sides are equal so,

BC / DF = AB / ED

Substitute;

x / r = w/ z ( multiply both sides by z )

x = r × w/z

Therefore, the correct option is 3.

Learn more about congruent triangles;

https://brainly.com/question/12413243

#SPJ2

Answer:

-3, -7, -5, 2, and -2

Step-by-step explanation:

When you are looking for opposites just think about a number line.

You are on the positive side

What is the opposite of a positive... negative

The same for the other way around

What is the opposite of a negative... positive

Answer:

Step-by-step explanation: The opposites are what you would imagine them to be, positive and negative.

the answer is -3, -7, -5 and 22

Answer:

9 in.

Step-by-step explanation:

Proportions:

1 in ⇔ 2 ft

R in ⇔ 18

R = 18*1/2

R = 9 in

Answer:

Step-by-step explanation:

a:b = 2:3

a = 2x    - first number

b = 3x   - second number

a³ + b³  =  945

[tex](2x)^3 + (3x)^3=945\\\\8x^3 +27x^3=945\\\\35x^3 = 945\\\\x^3=945:35\\\\x^3=27\\\\ x^3=3^3\\\\x=3\\\\\\a=2\cdot3 = 6\\\\b=3\cdot3=9[/tex]

Answer:

23.12 ounces

Step-by-step explanation:

Answer:

She bought 2 videos and 8 CDs.

Answer:

22, 29, 37

Step-by-step explanation:

There is a pattern to find the next number in the sequence. The sequence is taking the previous number and adding the number it is in the sequence.

Notice how the first number being added is the number of the previous sum and the second number being added is always increasing by one

1+0=1

1+1=2

2+2=4

4+3=7

7+4=11

11+5=16

16+6=22

22+7=29

29+8=37

22, 29, 37

Answer:

6×4p=24p

15a÷3=5a

3t×8y=24ty

24ef÷12e=2f

-4fx-5px-3 =-x(4f+5p)-3

-9abc÷3a=-3bc

Answer:

£13800

Step-by-step explanation:

1150*12=£13800

Answer:

The area of the shaded part is 36.53 cm²

Step-by-step explanation:

The dimension of the side of the square ABCD = 8 cm

The shaded part is seen to be the area of intersection of two quarter circles

The dimension of the radius of the quarter circles = The side length of the square

Therefore;

The dimension of the radius of the quarter circles = 8 cm

The figure can be taken as being formed by the two quarter circles with a square removed

The shaded area is the

Therefore, the area of the shaded part Sₐ, is given by the relation;

Sₐ = Area of first quarter circle + Area of second quarter circle - Area of the square

Given that the dimensions (radius) of the two quarter circles are the same, we have;

Area of first quarter circle = Area of second quarter circle = (π × 8²)/4 cm²

Area of the square = (Side length of the square)² = 8² = 64 cm²

Sₐ =  (π × 8^2)/4 + (π × 8^2)/4 - 64 = 36.53 cm²

The area of the shaded part = 36.53 cm².

Answer:

42.50

Step-by-step explanation:

bill + tip = total bill

The tip is based on the bill

tip = bill * 20%

tip = bill * .20

Replace in the original equation

bill + .20 bill = total bill

Combine like terms

1.20 bill = total bill

The total bill was 51 dollars

1.20 bill = 51

Divide each side by 1.20

1.20 bill / 1.2 = 51/ 1.2

bill =42.50

Answer:

$42.50

Step-by-step explanation:

If the total was $51 with the tip, and you know the tip was 20%, you can set up an equation and solve:

0.2x+x=51

1.2x=51

x=42.5

Therefore, the bill (w/o tip) was $42.50

p.s.Please give me brainliest. Thank you! :)

It depends on how b approaches 0

If b is positive and gets closer to zero, then we say b is approaching 0 from the right, or from the positive side. Let's say a = 1. The equation a/b turns into 1/b. Looking at a table of values, 1/b will steadily increase without bound as positive b values get closer to 0.

On the other side, if b is negative and gets closer to zero, then 1/b will be negative and those negative values will decrease without bound. So 1/b approaches negative infinity if we approach 0 on the left (or negative) side.

The graph of y = 1/x shows this. See the diagram below. Note the vertical asymptote at x = 0. The portion to the right of it has the curve go upward to positive infinity as x approaches 0. The curve to the left goes down to negative infinity as x approaches 0.

When you round 2.1 to the nearest whole number, the answer will be 2.

Answer:

2 is the answer

Step-by-step explanation:

to round 2.1 to the nearest whole number consider the tents value of 2.1 which is 1 end less than five therefore we have to round down the ones place value of 2.1 . 2 remains 2 and the decimal point is removed.

2.1 to the nearest whole number is 2

Answer:

76 degrees

Step-by-step explanation:

Let the angles be x, y and z

As per given:

Considering the first 2 equations in the third one:

So the third angle is:

Work Shown:

Solve for y. Then replace y with f(x).

[tex]680x + 10y - 1000 = 0\\\\10y - 1000 = -680x\\\\10y = -680x + 1000\\\\y = \frac{-680x + 1000}{10}\\\\y = \frac{-680x}{10} + \frac{1000}{10}\\\\y = -68x + 100\\\\y = 100 - 68x\\\\f(x) = 100 - 68x\\\\[/tex]

Effectively this involves adding 1000 to both sides and subtracting 680x from both sides, afterward we divide both sides by 10 to isolate y.

Answer:

choice B

Step-by-step explanation:

I did this problem like 6 months ago......

Answer:

-4 -5x

Step-by-step explanation:

4(1 – 3x) + 7x – 8.

Distribute

4 -12x +7x -8

Combine like terms

-4 -5x

Answer:

The simplified answer of this expression is -5x - 4

Step-by-step explanation:

4(1 - 3x) + 7x - 8

Distribute 4 to (1 - 3x)

4 - 12x + 7x - 8

Rearrange the terms so it'll be easier to combine them.

4 - 8 - 12x + 7x

Combine like terms.

-4 - 5x

Put the equation in standard form.

-5x - 4

Answer:

Option (2)

Step-by-step explanation:

To find the solution set of the given inequality we will follow the following steps.

1). Convert the inequality into an equation.

2). Find the solutions from the equation.

3). Check these solutions and intervals on a number line.

Given inequality is 5(x - 2)(x + 4) > 0

Step 1. Equation for given inequality is,

          5(x - 2)(x + 4) = 0

Step 2. Solutions for the given equation will be,

           (x - 2) = 0 ⇒ x = 2

           (x + 4) = 0 ⇒ x = -4

Step 3. Therefore, there will be two critical points on the number line,

           x = 2, x = -4

Now we will check the solutions of the given inequality in the given intervals,

x < -4, -4 < x < 2 and x > 2

For x < -4,

Let the solution is x = -5

5(x + 4)(x - 2) = 5(-5 + 4)(-4 - 2)

                     = 30 > 0

Therefore, x < -4 will be the solution area of the inequality.

For -4 < x < 2,

Let the solution is x = 0

5(x + 4)(x - 2) = 5(0 + 4)(0 - 2)

                     = -40 < 0

Therefore, -4 < x < 2 will not be the solution set for the given inequality.

For x > 2,

Let the solution is x = 3

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

                     = 35 > 0

Therefore, x > 2 will be the solution area of the inequality.

Summarizing all steps we find that the solution set of the inequality is,

{x | x < -4 Or x > 2}

Option (2) will be the answer.

Answer:

k=10BY DPING PROCESS IT BECOME

Step-by-step explanation:

Hey, there!!!

Let me explain you very simply,

The equation is;

y= -2/3 x +1/3

Now, we know the equation of a st.line in slope intercept form is,

y= m.x + c

now, comparing the given equation with y= m.x + c. we get,

m= -2/3

and y-intercept = 1/3.

Hope it helps...

Answer:

Clyde is 49.74 away from the harbor

Step-by-step explanation:

Here in this question, we are interested in knowing the distance of Clyde from the harbor.

The key to answering this question is having a correct diagrammatic representation. Please check attachment for this.

We can see we have the formation of a right angled triangle with the distance between Clyde’s ship and the harbor the hypotenuse.

To calculate the distance between the two, we shall employ the use of Pythagoras’ theorem which states that the square of the hypotenuse is equal the sum of the squares of the two other sides.

Let’s call the distance we want to calculate h.

Mathematically;

h^2 = 25^2 + 43^2

h^2 = 625 + 1849

h^2 = 2474

h = √2474

h = 49.74 miles

Answer:

The amount of money in Enid bank account can be written as a linear equation.

Ye = Xe + $4*m

where Ye is the money that Enid has in her account, m is the number of months that have passed since she opened it, and Xe is the initial deposit.

For Jim, the equation is similar:

Yj = Xj + $3*m

where Yj and Xj are similar as above.

Between May 15 and December 31 of the same year, we have 7 months (where i am counting December because the deposit is made in the first day of the month).

Then we have that:

Ye = $72 = Xe + $4*7 = Xe + $28

Xe = $72 - $28 = $44

So in May 15, Enid deposited $44.

For Jim we have:

Yj = $72 = Xj + $3*7 = Xj + $21

Xj = $72 - $21 = $51

So in May 15, Jim deposited $51.

Answer:

LM = 16

Step-by-step explanation:

From the question given:

L is the midpoint of NM

NL = 3x + 1

LM = 8x - 24

LM =?

Next, we shall determine the value of x.

This can be obtained as follow:

Since L is the midpoint of NM, it means that NL and LM are equal i.e

NL = LM

Thus, we can obtain the value of x as follow:

NL = 3x + 1

LM = 8x - 24

NL = LM

3x + 1 = 8x - 24

Collect like terms

3x - 8x = - 24 - 1

-5x = - 25

Divide both side by - 5

x = -25/-5

x = 5

Finally, we shall determine the length of LM as follow:

LM = 8x - 24

x = 5

LM = 8(5) - 24

LM = 40 - 24

LM = 16

Therefore, the length of LM is 16

Answer:

Length of diagonal = 6

Step-by-step explanation:

Given that

Diagonal of a rectangle makes an angle of [tex]30^\circ[/tex] with the longer side.

Kindly refer to the attached diagram of the rectangle ABCD such that diagonal BD makes angles of [tex]30^\circ[/tex] with the longer side CD and BA.

[tex]\angle CDB =\angle DBA =30^\circ[/tex]

Side AD = BC = 3 units

To find:

Length of diagonal BD = ?

Solution:

We can use the trigonometric ratio to find the diagonal in the [tex]\triangle BCD[/tex] because [tex]\angle C =90^\circ[/tex]

Using the sine :

[tex]sin\theta = \dfrac{Perpendicular }{Hypotenuse }[/tex]

[tex]sin\angle CDB = \dfrac{BC}{BD}\\\Rightarrow sin30^\circ = \dfrac{3}{BD}\\\Rightarrow \dfrac{1}2 = \dfrac{3}{BD}\\\Rightarrow BD =2 \times 3 \\\Rightarrow BD = \bold{6 }[/tex]

So, the answer is:

Length of diagonal = 6