In ∆ABC, ∠A is a right angle and m∠B = 45°. Find BC.

[tex]4(4a+6b) =16a+24b[/tex]

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&2,625\\ P=\textit{original amount deposited}\dotfill & \$25,000\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years \end{cases} \\\\\\ 2625=(25000)(0.035)t\implies \cfrac{2625}{(25000)(0.035)}=t\implies 3=t[/tex]

Answer:

The  number of years = 3 years

Step-by-step explanation:

Points to remember

Simple interest

I = PNR/100

Where P - Principle amount

N - Number of years

R - Rate of interest

To find the number of years

Here P = 25,000

R = 3.5% and I = 2625

I = PNR/100

N = (I * 100)/PR

 = (2625 * 100)/(25000 * 3.5)

 = 3 years

Therefore number of years = 3 years

Answer:

-1/2

Step-by-step explanation:

The equation given is

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

Write it in form of y=mx+c where m is the gradient and c is the y-intercept

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

y-intercept is -1/2

Answer:

B. repeating

Step-by-step explanation:

An irrational number written in  decimal form will be nonterminating  and non-repeating  decimals.

For example we have √2 = 1.4142

This rational number is non-terminating and non-repeating.

Answer:

repeating

Step-by-step explanation:

Answer:

{f + c < 12

{7c + 4f < 100

-5⅓ < f

7⅓ > c

Step-by-step explanation:

The keyphrase is no more than, which tells you that the inequality symbol has to be less than.

I am joyous to assist you anytime.

Answer:

Johnny

Step-by-step explanation:

I don't think you put the whole question out

Answer:

352.8 feet

Step-by-step explanation:

The given triangle is drawn in the image attached with. Note that the image is not drawn to scale.

We can find the length of AB using the law of sines. According to which:

[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Since sum of angles in a triangle is 180, we can write:

A + B + C = 180

A + 102.9 + 18.6 = 180

A = 58.5

Using the values, in the law of sines, we get:

[tex]\frac{943}{sin(58.5)} = \frac{c}{sin(18.6)}\\\\ c = \frac{943 \times sin(18.6)}{sin(58.5)}\\\\ c = 352.8[/tex]

Thus, the measure of side AB would be 352.8 feet

Answer:

The length of AB is 352.8 feet

Step-by-step explanation:

* Lets revise some facts to solve the problem

- The sine rule: [tex]\frac{sinA}{BC}=\frac{sinB}{AC}=\frac{sinC}{AB}[/tex]

- The sum of the measures of the interior angles of a triangle is 180°

* Lets solve the problem

- In Δ ABC

∵ m∠ B = 102.9°

∵ m∠ C = 18.6°

∵ m ∠A + m∠ B + m∠ C = 180° ⇒ interior angles of a Δ

∴ m ∠A + 102.9 + 18.6 = 180

∴ m ∠A + 121.5 = 180 ⇒ subtract 121.5 from both sides

∴ m∠A = 58.5°

* Lets use the sine rule to find AB

∵ BC = 943

∵ m∠A = 58.5°

∵ m∠ C = 18.6°

∴ [tex]\frac{sin(58.5)}{943}=\frac{sin(18.6)}{AB}[/tex]

- By using cross multiplication

∴ AB × sin(58.5) = 943 × sin(18.6)

- Divide both sides by sin(58.5)

∴ AB = [943 × sin(18.6)] ÷ sin(58.5) = 352.76 ≅ 352.8

* The length of AB is 352.8 feet

Answer:

The answer is 3/5x^6y^6

Step-by-step explanation:

The given expression is:

-9x^-1 y^-9/-15x^5 y^-3

It can be written as:

= -9/-15 * x^-1/x^5 * y^-9/y^-3

As we know that [x^m/x^n = x^m-n]

= 3/5 * x^-1-5 * y^-9+3

= 3/5 * x^-6 * y^-6

= 3/5 * 1/x^6 * 1/y^6

= 3/5x^6y^6

The answer is  3/5x^6y^6....

The expression that is equivalent to the given expression is [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

(-9x^-1 y^-9)/(-15x^5 y^-3)

This can be written as

[tex](-9x^{-1}y^{-9} )\div (-15x^{5}y^{-3})[/tex]
[tex](-9\times \frac{1}{x} \times \frac{1}{y^{9} } )\div (-15 \times x^{5} \times \frac{1}{y^{3} } )[/tex]

[tex](\frac{-9}{xy^{9} } )\div (\frac{-15x^{5} }{y^{3} } )[/tex]

This becomes

[tex](\frac{-9}{xy^{9} } )\times (\frac{y^{3} }{-15x^{5} } )[/tex]

[tex]\frac{-9}{-15 } \times \frac{y^{3} }{xy^{9}\times x^{5} }[/tex]

[tex]\frac{3}{5 } \times \frac{1 }{y^{6}\times x^{6} }[/tex]

= [tex]\frac{3}{5x^{6}y^{6} }[/tex]

= [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]

Hence, the expression that is equivalent to the given expression is [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]

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Answer: The answer is A

Step-by-step explanation:

Its the only one that has the least amount of options and the highest probability chance

Answer:

[tex]1.02 \times 10^{13}[/tex]

Step-by-step explanation:

Speed of the sound = [tex]3.4 \times 10^{2}[/tex] meters per second

Time to calculate the distance traveled = [tex]3 \times 10^{10}[/tex] seconds

Since,

Distance = Speed x Time

Using the values we get:

[tex]Distance=3.4 \times 10^{2} \times 3 \times 10^{10}\\\\ = 3.4 \times 3 \times 10^{(2+10)}\\\\ = 10.2 \times 10^{12}[/tex]

Since the calculators show the final answer is scientific notation, the above answer in scientific notation would be:

Distance = [tex]1.02 \times 10^{13}[/tex]

Answer:

1.02 E 13

Step-by-step explanation:

The Answer is 1.02 E 13 because E means "time 10 to the power of". So 1.02 E 13 is basically just 1.02 time 10 to the power of 13.

Answer:

1) 32

2) 8 yards

Step-by-step explanation:

1. We must first subtract the base area of the pyramid from the total surface area to get the lateral surface area:

[tex]LA=2225-25^2=1600[/tex]

The lateral surface area is 4 times the area of one the congruent triangles.

[tex]LA=4\cdot \frac{1}{2}\cdot 25\cdot x[/tex]

[tex]\implies 1600=50x[/tex]

[tex]\implies \frac{1600}{50}=\frac{50x}{50}[/tex]

[tex]32=x[/tex]

Therefore the height of the slant surface is 32 yards

2) The surface area of a cone is [tex]S.A =\pi r^2+\pi r l[/tex], where l is the slant height.

We substitute the surface area S.A=151.58 and [tex]\pi=3.14,r=4[/tex] to obtain:

[tex]151.58=3.14\cdot 4^2+3.14\cdot 4 l[/tex]

[tex]151.58=50.24+12.56l[/tex]

[tex]101.34=12.56l[/tex]

[tex]\frac{101.34}{12.56}=l[/tex]

l=8.06

To the nearest whole number, the slant height is 8 yards

Answer:

[tex]\large\boxed{x^\frac{5}{3}y^\frac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \sqrt[n]{a^m}=a^\frac{m}{n}\ \text{and}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\\\\\\sqrt[3]{x^5y}=\sqrt[3]{x^5}\cdot\sqrt[3]{y^1}=x^\frac{5}{3}y^\frac{1}{3}[/tex]

Answer:

B

Step-by-step explanation:

edge 2021

Answer:

The equation would be x²/a² - y²/b² =1 , x²/9 - y²/40 = 1 ....

Step-by-step explanation:

The standard equation of hyperbola with a horizontal transverse axis is:

(x-h)²/a² - (y-k)² /b²  = 1

Use Pythagorean theorem to find the value of b.

c² = a²+b²

c= 7

a = 3

Put the value in the equation:

(7)² = (3)² +b²

49= 9+b²

49-9 = b²

40 = b²

Square root both sides:

√40 = √b²

√40 = b

Assume that the center of hyperbola is(0,0)

Thus

(x-0)²/a²  - (y-0)²/b² = 1

x²/a² - y²/b² =1

x²/(3)² - y²/(√40)² = 1

x²/9 - y²/40 = 1

Therefore the equation would be x²/a² - y²/b² =1 , x²/9 - y²/40 = 1 ....

Answer:

[tex]\dfrac{x^{2}}{9} - \dfrac{y^{2}}{40}} = 1[/tex]

Step-by-step explanation:

The standard form of the equation of a hyperbola with center (0,0) and horizontal transverse axis is

[tex]\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1[/tex]

and the distance c between the foci and the y-axis is given by

c² = a² + b²

1. Calculate b

7² = 3² + b²

49 = 9 + b²

40 = b²

b = √40

2. Write the equation

[tex]\dfrac{x^{2}}{3^{2}} - \dfrac{y^{2}}{(\sqrt{40})^{2}} = 1\\\\\mathbf{\dfrac{x^{2}}{9} - \dfrac{y^{2}}{40}}} = \mathbf{1}[/tex]

The figure shows your hyperbola with a horizontal transverse axis and c = 3.

[tex]\bf \stackrel{\textit{number divided by 4}}{(x\div 4)}\qquad \stackrel{\textit{then added to 17}}{+17}\qquad \stackrel{\textit{the result is}}{=}\qquad 25\implies \cfrac{x}{4}+17=25 \\\\\\ \cfrac{x}{4}=25-17\implies \cfrac{x}{4}=8\implies x=(4)8\implies x=32[/tex]

Answer:

Step-by-step explanation:

CPCTC: Corresponding Parts of Congruent Triangles are Congruent

If ΔLMN ≅ ΔXYZ, then:

B. LN ≅ XZ

C. ∠Y ≅ ∠M

E. MN ≅ YZ

Corresponding sides:

LN → XZ

LM → XY

MN → YZ

Corresponding angles:

∠L → ∠X

∠N → ∠Z

∠M → ∠Y

Answer:

C. MN=YZ; D. LN=XZ; and F. Y= M

[tex]8x=2^3\cdot x\\40y=2^3\cdot5\cdot y\\\\\text{gcf}(8x,40y)=2^3=8[/tex]

Answer:

The side length is 7 yds

Step-by-step explanation:

We know the formula for area of a square is

A = s^2 where s is the side length

49 = s^2

Take the square root of each side

sqrt(49) = sqrt(s^2)

7 =s

The side length is 7 yds

Final answer:

To find the side length of a square given its area, calculate the square root of the area. In this case, the side length of the square is 7 yards.

Explanation:

A square has an area of 49yd². To find the side length of each side, you need to take the square root of the area. In this case, the side length of each side would be 7 yards.

Answer:

7/5

Step-by-step explanation:

Slope intercept form is y=mx+b. It is called that because it tells us the slope,m, and the y-intercept, b.

So we can solve your given equation to find m the slope.

7x-5y=10

Subtract 7x on both sides:

-5y=-7x+10

Divide both sides by -5

y=(-7/-5)x+(10/-5)

Simplify:

y=(7/5)x+-2

m=7/5 so 7/5 is the slope.

Answer:

y = 2½x - 14

Step-by-step explanation:

You simply do this:

-29 = 5⁄2[-6] + b; -14 = b

-15

Now remember, parallel rate of changes [slopes] have SIMILAR slopes, so they remain the same.

**2½ = 5⁄2 [Do not worry]

I am joyous to assist you anytime.

Answer:

35 games.

Step-by-step explanation:

5 out of 8 is 5/8 of their  games which they have won.

So they should win (5/8) * 56

= 5*56 / 8

= 5*7

= 35 games.

Given the Rangers' current win rate of 5 wins out of 8 games, we can predict they would win about 35 games out of 56 if they continue at this rate.

The question you've asked is related to

ratios

and

proportions

. You're given that the Rangers won 5 out of 8 games. If we extend this winning rate to 56 games, we need to find a proportion that equals the same win rate. The setup is: 5/8 = x/56, where 'x' is the number of games we expect the Rangers to win. To solve for x, we multiply across the diagonal (5*56) and divide by 8. That results in a value of

35

, so the Rangers should win 35 games out of 56 if they continue their current winning rate.

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Answer:

[tex]\frac{\pi }{6}[/tex]

Step-by-step explanation:

[tex]\frac{7\pi }{6}[/tex] is in the third quadrant

To find the reference angle subtract π from it, that is

reference angle = [tex]\frac{7\pi }{6}[/tex] - π = [tex]\frac{\pi }{6}[/tex]

This was too long for me to write on the computer.

So I wrote it and took a picture.

If you have any questions, please don't hesitate to ask in the comments.

Step-by-step explanation:

Daquan's age = x

Juan's age = x

Phillipa's age = x + 3

x + x + x + 3 = 36

3x + 3 = 36

3x = 36 - 3

3x = 33

x = 33 ÷ 3

x = 11

the twins are 11 years old

Answer:

The equation is:

[tex]y=2500t+75000[/tex] where t is the number of years satisfying the inequality [tex]0\let\le5[/tex] and y is the population at that time.

Step-by-step explanation:

So it gives us the initial amount 75000; this is what happens at time 0.

So we have the point (0,75000) is on the function's graph.

(0,75000)

(1,77500)  -> It goes 2500 per year. So year 1 the population is 75000+2500.

So we have the y-intercept of the line which is (0,75000).

We just need the slope.

Our goal is to put into slope-intercept form: y=mt+b form where m is the slope and b is the y-intercept.

To find the slope, you line up the points vertically and subtract then put 2nd difference over 1st difference.

(  1   ,   77500 )

-( 0  ,    75000)

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

 1           2500

So the slope is 2500/1=2500 which we should have known earlier since the y's are increasing by 2500 while the x's are increasing by 1.

So while t is between 0 and 5 inclusive we have the following equation:

y=2500t+75000

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x=-y+6&(1)\\-4x+3y=8&(2)\end{array}\right\\\\(1)\\-y+6=2x\qquad\text{subtract 6 from both sides}\\-y=2x-6\qquad\text{change the signs}\\y=6-2x\\\\\text{substitute it to (2):}\\\\(2)\\-4x+3(6-2x)=8\qquad\text{use the distributive property}\\-4x+(3)(6)+(3)(-2x)=8\\-4x+18-6x=8\qquad\text{subtract 18 from both sides}\\-10x=-10\qquad\text{divide both sides by (-10)}\\x=1\\\\\text{put the value of x to (1):}\\\\y=6-2(1)\\y=6-2\\y=4[/tex]

Answer:

(1,4)

Step-by-step explanation:

i just did the quiz and it was correct

Answer:

[tex]\large\boxed{y=\dfrac{2}{5}x+\dfrac{24}{5}}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the slope [tex]m=\dfrac{2}{5}[/tex] and the point (-2, 4).

Put them in the equation of a line:

[tex]4=\dfrac{2}{5}(-2)+b[/tex]

[tex]4=-\dfrac{4}{5}+b[/tex]       add 4/5 to both sides

[tex]4\dfrac{4}{5}=b\to b=\dfrac{24}{5}[/tex]

Answer:

I think that the answer is C

Hello! What is this for?

Also, The answer is: The lead pattern would be in the shape of a circle.

Answer: The Circle!

Step-by-step explanation:

just took the test!

Answer:

Part 1) The area of the structure is [tex]2,453.25\ ft^{2}[/tex]

Part 2) The slab will contain  [tex]1,226.625\ ft^{3}[/tex] of cement

Step-by-step explanation:

Part 1) Find the area of the structure

we know that

The area of the structure is equal to the area of rectangle plus the area of semicircle

Find the area of rectangle

The area of rectangle is equal to

[tex]A=LW[/tex]

we have

[tex]L=70\ ft[/tex]

[tex]W=30\ ft[/tex]

substitute

[tex]A=(70)(30)[/tex]

[tex]A=2,100\ ft^{2}[/tex]

Find the area of semicircle

The area of semicircle is

[tex]A=\frac{1}{2}\pi r^{2}[/tex]

we have

[tex]\pi =3.14[/tex]

[tex]r=15\ ft[/tex]

substitute

[tex]A=\frac{1}{2}(3.14)(15)^{2}[/tex]

[tex]A=353.25\ ft^{2}[/tex]

Find the area of the structure

Adds the areas

[tex]A=2,100+353.25=2,453.25\ ft^{2}[/tex]

Part 2) If the structure is 6 in thick, how many cubic feet of cement will the slab contain?

Remember that

[tex]1\ foot=12\ inches[/tex]

Convert inches to feet

[tex]6\ in=6/12=0.5\ ft[/tex]

Find the volume of the structure

To obtain the volume , multiply the area by 0.5 ft (thick)

so

[tex]V=2,453.25*0.5=1,226.625\ ft^{3}[/tex]

Answer: 9 points

Step-by-step explanation:

The coefficient of determination is a number between 0 and 1 used to measure the level of precision with which the regression model  created fits the data. A measure of [tex]R ^ 2 = 1[/tex]   means that the model explains the entire variation between the two variables without error.

Therefore, in this case if [tex]R ^ 2 =1[/tex] means that the 9 points are on the line

Answer:

9 points

Step-by-step explanation:

Answer:

L ≅ P

Step-by-step explanation:

To prove congruence through ASA, we need the measures of two angles that are adjacent to a given side. If we are given that two angles are congruent to other angles in another triangle respectively and both of those angles are adjacent to one side (in which each side of each triangle is congruent) then the triangles are congruent through ASA.

To prove congruence using the ASA congruence theorem, we need to show that the angle measures of the triangles are equal. The additional information needed is that angle NM is congruent.

To prove that the triangles are congruent using the ASA congruence theorem, we need to show that the angle measures of the triangles are equal.

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