The measure of one of the small angles of a right triangle is 18 less than twice the measure of the other small angle. Find the measure of both angles. Use integers only

Answer:

g(-1) = 1

Step-by-step explanation:

Synthetic division is by far the fastest way to evaluate this function at x = -1.  Set up synth. div. as follows:

-1   )   1    6    12    8

              -1    -5    -7

     ----------------------

         1     5     7     1                

since the remainder is 1, g(-1) = 1

Answer:

8

Step-by-step explanation:

Use the Pythagorean theorem.

a^2 + 6^2 = 10^2

a^2 + 36 = 100

a^2 = 64

a = 8

The complete statements of the expression are

How to complete the statements in the expression

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

5x - 8(3y + 13) - 1

Consider an expression

Ax + b

Where x is the variable, we have

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

In the first term, 5 is a coefficient

In the second term, (3y+ 13) is a factor

In the third term, -1 is a constant

Question

Use the given expression to complete the statements.

5x– 8(3y + 13) – 1

In the first term, 5 is a _____

In the second term, (3y+ 13) is a ______

In the third term, -1 is a ______

Answer:

∠ACB==50°

b=15.6 units

c=11.9 units

Step-by-step explanation:

step 1

Find the measure of angle BCA

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

∠ABC+∠BAC+∠ACB=180°

substitute the given values

90°+40°+∠ACB=180°

∠ACB=180°-130°=50°

step 2

Find the measure of side b

Applying the law of sines

a/sin(∠BAC)=b/sin(∠ABC)

substitute the given values

10/sin(40°)=b/sin(90°)

b=10/sin(40°)

b=15.6 units

step 3

Find the measure of side c

Applying the law of sines

c/sin(∠ACB)=a/sin(∠BAC)

substitute the given values

c/sin(50°)=10/sin(40°)

c=[10/sin(40°)]*sin(50°)

c=11.9 units

ANSWER:

C=11.9

ABC=90 deg.

BAC=40 deg.

A=10

[tex]42_x+53_x=125_x\\4\cdot x^1+2\cdot x^0+5\cdot x^1+3\cdot x^0=1\cdot x^2+2\cdot x^1+5\cdot x^0\\4x+2+5x+3=x^2+2x+5\\x^2-7x=0\\x(x-7)=0\\x=0 \vee x=7[/tex]

There is no numeral system with base 0, so [tex]x=7[/tex].

-3y = -6/5

-3y(5) = (-6/5)(5)

-15y = -6

y = -6/-15

y = 6/15

y = 2/5

Answer:

Answer is 81y^4z^4

Step-by-step explanation:

The expression is (-3yz) (-3yz) (-3yz) (-3yz).

Since all the four terms have power 1:

(-3yz)^1 (-3yz)^1 (-3yz)^1 (-3yz)^1

We know that we can add the powers if the terms have same base

So,

=(-3yz)^1+1+1+1

=(-3yz)^4

=(-3)^4(y)^4(z)^4.

If the power is an even number than the negative sign changes into positive sign.

=3^4y^4z^4

=81y^4z^4

Thus the answer is 81y^4z^4....

Answer:

3619.11 cubic inches

Step-by-step explanation:

volume of a cylinder is [tex]V=\pi r^2h[/tex]

diameter is 16 in, so radius (r) is 8 in

plug in values: [tex]V=\pi 8^2(18) = 3619.11[/tex] cubic inches

The volume of a cylinder with a diameter of 16 inches and a height of 18 inches is calculated using the formula V = πr²h, which results in approximately 3617.3 cubic inches when rounded to the nearest tenths place.

To calculate the volume of a cylinder, we use the formula V = πr²h. Given that the diameter of the cylinder is 16 inches, which means its radius (r) is half of that, 8 inches. The height (h) of the cylinder is given as 18 inches. To find the volume, first square the radius, then multiply by π (approximated as 3.14 for this purpose), and then by the height.

So, the calculation looks like this:

Therefore, the volume of the cylinder, rounded to the nearest tenth place, is 3617.3 cubic inches.

Answer:

Option C. 15 cm

Step-by-step explanation:

The correct question is

A triangle has two sides that measure 8.7 cm and 12.3 cm. Which could be the measure of the third side?

A. 2.6 cm

B. 3.6 cm

C. 15 cm

D. 21 cm

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Analyze two cases

Let

x ----> the length of the third side

First case

x+8.7 > 12.3

x>12.3-8.7

x> 3.6 cm

Second case

12.3+8.7 > x

21 > x

Rewrite

x < 21 cm

For this case we must find an expression equivalent to:

[tex](2 \frac {1} {2} * 2 \frac {3} {2}) ^ 2[/tex]

So, we have:

[tex]2 \frac {1} {2} = \frac {2 * 2 + 1} {2} = \frac {5} {2}\\2 \frac {3} {2} = \frac {2 * 2 + 3} {2} = \frac {7} {2}[/tex]

Rewriting the expression:

[tex](\frac {5} {2} * \frac {7} {2}) ^ 2 =\\(\frac {35} {4}) ^ 2 =\\\frac {35} {4} * \frac {35} {4} =\\\frac {1225} {16} =\\76 \frac {9} {16}[/tex]

Answer:

[tex]76 \frac {9} {16}[/tex]

The answer to this question is that Julie weighs 210lbs, Ted weighs 420 (210 multiplied by 2 is 420). Mike weighs 630 (210 multiplied by 3 is 630). So, it would be "Julie weighs 210a0 pounds, Ted weighs 420 a1 pounds, and Mike weighs 630a2 pounds."

I hope this answer helps!

"Stay Brainly and stay proud!" - Zalgo

Answer:

Julie=35 lbs, Ted= 70 lbs, and Mike=105 lbs

Step-by-step explanation:

Julie=x ted=2x mike=3x

The sum of their weight all together is 210 pounds

Combine the x's

6x=210

Divide both sides by 6 to get 1x (Julies weight)

6x/6 = 210/6

1x= 35 (Julie weighs 35 lbs)

35 x 2= 70 ( Ted weighs 70 lbs)

35 x 3= 105 ( Mike weighs 105 lbs)

- Hope this helps!

Answer:

0.0072

Step-by-step explanation:

7.2 x [tex]10^{-3}[/tex]

=7.2 x 0.001

=0.0072

Answer:

0.0072

Step-by-step explanation:

The given expression is as follows:

7.2 * 10^(-3)

This expression is in scientific notation, We need to convert it to standard notation for which we will convert the power of 10 to 0.

The power of 10 here is -3. So we will move the decimal point 3 places to the left and get:

= 0.0072 x 10^0

= 0.0072 x 1

= 0.0072

Answer:

You'll get your answer as : 233

Answer:

Gary sold 5 paperback books

Step-by-step explanation:

each book is equal to $2 and $10 were made in Hardcover

So that only leaves us with ten unaccounted dollars

5x=10

Each book or (x) in this case is two dollars

so it will come out to be five books

Well, you can’t really divide a fraction because it is already a division problem. So we have to do the opposite.

9/4 divided by3/16

Leave the first fraction alone

Change the division sign into a multiplication sign.

Then switch the denominator and numerator of the second fraction, this new fraction is called a reciprocal.

Now multiply the numerators together and the denominators together and simplify.

You get: 144/12

Simplified the answer is : 12

Answer:

9 boxes are packed and 10 brownies are left over.

Step-by-step explanation:

Carrie made 127 brownies and packed 13 in each box.

The number of boxes packed are; [tex]\frac{127}{13}[/tex] = 9[tex]\frac{10}{13}[/tex]

Which means that 9 boxes were packed and 10 brownies were left over.

[tex]\text{Hey there!}[/tex]

[tex]\text{1(96) = 96}[/tex]

[tex]\text{2(48) = 96}[/tex]

[tex]\text{4(24) = 96}[/tex]

[tex]\text{6(16) = 96}[/tex]

[tex]\text{8(12) = 96}[/tex]

[tex]\text{The factors of 96 are: 1, 2, 3, 4, 6,8, 12, 16, 24, 32, 48, 96}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

Demand: q = -50p + 1200

Supply: q = 40p

Step-by-step explanation:

First let's define our variables.

q = quantity of T-shirts

p = price

We know that when p = 12, q = 600.  When p increases by 1, q decreases by 50.  So this is a line with slope -50 that passes through the point (12, 600).  Using point-slope form to write the equation:

q - 600 = -50 (p - 12)

Converting to slope-intercept form:

q - 600 = -50p + 600

q = -50p + 1200

Similarly, we know that when p = 9.75, q = 600 - 210 = 390.  When p increases by 1, q increases by 40.  So this is a line with slope 40 that passes through the point (9.75, 390).  Using point-slope form to write the equation:

q - 390 = 40 (p - 9.75)

Converting to slope-intercept form:

q - 390 = 40p - 390

q = 40p

Answer:

D

Step-by-step explanation:

we can use the formula of tan(A-B) to solve this equation .

The formula is

[tex]tan(A-B)= \frac{tanA-tanB}{1+tanA.tanB}[/tex]

In our question , A is x and B is [tex]\frac{\pi }{3}[/tex]

so when we apply these in the question we get

[tex]tan(x-\frac{\pi }{3} )=\frac{tanx-tan\frac{\pi }{3} }{1+tanx.tan\frac{\pi }{3} }[/tex]

Now since [tex]tan\frac{\pi }{3} = \sqrt{3}[/tex]

we get

[tex]tan(x-\frac{\pi }{3} )=\frac{tanx-\sqrt{3}  }{1+\sqrt{3} tanx.} }[/tex]

so correct option is

D

Answer:

<1 = 45

<2 = 50

Step-by-step explanation:

Let <1 = x

Let <2 = y

=============

x + y = 95

y = 2*x - 40

=============

I think the easiest way to do this is to substitute the second or bottom equation into the top equation. Substitute for y

x + 2x - 40 = 95                    Combine like terms on the left.

3x - 40 = 95                          Add 40 to both sides.

3x -40+40 = 95+40              Combine

3x = 135                                 Divide by 3

x = 45

=================

Now use the top equation to solve for y

x + y = 95

45 + y = 95                             Subtract 45 from both sides.

45 - 45 + y = 95 -45               Combine

y = 50

Answer:

C. 2π

Step-by-step explanation:

Given a wave of the equation y= a sin bx where a and b are constants, then the amplitude is a while the period is 360°/b.

360°= 2π radians  

For the provided function, the value of b =  

Thus period = 2π/1

=2π radians

Answer: 2 Pi

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

3 + 1 = 4

4 to the second power / 4 is 4

Hello There!

[tex]4^{2}[/tex] is multiplying 4 by itself twice, so we would get an answer of 16.

Finally, we divide 16 by 4 because 3+1=4 and when we do this, we get a quotient of 4

Your Answer Is 4

so the company has an overhead of $600, usually that involves premises leasing and industrial equipment for the manufacturing of the product, that's cost.  The cost to make each item is 50 cents, so if the company produces "x" items, their cost is 0.5x total.

so our cost equation C(x) = 0.5x + 600   <---- items' cost plus overhead.

the company sells the product for 85 cents, so if they sell "x" items, their total revenue or income will be 0.85x.

so our revenue equation is simply R(x) = 0.85x.

as you already know, the break-even point is when.... well, you break even, no losses but no gains either, how much you take in is the same amount that you shelled out, namely R(x) = C(x).

[tex]\bf \stackrel{R(x)}{0.85x}=\stackrel{C(x)}{0.5x+600}\implies 0.35x=600\implies x=\cfrac{600}{0.35} \\\\\\ x\approx 1714.285714285714\implies \stackrel{\textit{rounded up}}{x=1714}[/tex]

Answer:

[tex]\$30[/tex]

Step-by-step explanation:

we have

[tex]p(t)=3x+2x-4x^{2}+21[/tex]

Find the amount of money that each girl spent

For t= 2 hours

[tex]p(2)=3(2)+2(2)-4(2)^{2}+21[/tex]

[tex]p(2)=10-16+21[/tex]

[tex]p(2)=\$15[/tex]

Find the amount of money that they spend together

Multiply by 2 the amount of money that each girl spent

[tex](2)\$15=\$30[/tex]

Shawna and Keisha spent $30 together when each of them went shopping for 2 hours.

It seems there might be a typo in the function p(t) you provided. It should be[tex]\( p(t) = 3t + 2t - 4t^2 + 21 \)[/tex], where t represents the number of hours spent shopping.

To find out how much money Shawna and Keisha spent together when each of them went shopping for 2 hours, we need to evaluate the function p(t)  at [tex]\( t = 2 \)[/tex] and then add the results.

Let's plug in t=2 into the function p(t):

[tex]\[ p(2) = 3(2) + 2(2) - 4(2)^2 + 21 \][/tex]

[tex]\[ = 6 + 4 - 16 + 21 \][/tex]

[tex]\[ = 10 - 16 + 21 \][/tex]

[tex]\[ = 15 \][/tex]

Multiply by 2 since $15 is for each girl = 2*$15= $30

Answer:

Equation of line: y=3x-18

Step-by-step explanation:

Point: (4,-6) and slope = 3

[tex]y+6=3(x-4)[/tex]

y=3x-18

Answer:

y + 6 = 3(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 3 and (a, b) = (4, - 6), hence

y - (- 6) = 3(x - 4), that is

y + 6 = 3(x - 4) ← in point- slope form

Answer:

[tex]\large\boxed{21x^4-14y^2=7(3x^4-2y^2)=7(x^2\sqrt3-y\sqrt2)(x^2\sqrt3+y\sqrt2)}[/tex]

Step-by-step explanation:

[tex]21x^4-14y^2=7(3x^4-2y^2)\\\\=7\bigg((\sqrt3)^2x^{2\cdot2}-(\sqrt2)^2y^2\bigg)\qquad\text{use}\ (a^n)^m=a^{nm}\ \text{and}\ (ab)^n=a^nb^n\\\\=7\bigg((x^2\sqrt3)^2-(y\sqrt2)^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=7(x^2\sqrt3-y\sqrt2)(x^2\sqrt3+y\sqrt2)[/tex]

Answer:

0.0000000692

Step-by-step explanation:

We are given the following number in scientific notation and we are to express it in standard notation:

[tex] 6 . 9 2 \times 1 0 ^ - 8 [/tex]

We know that:

[tex] 6 . 9 2 \times 1 0 ^ { - 8 } = \frac { 6 . 9 2 } { 1 0 ^ { 8 } } = \frac { 6 . 9 2 } { 1 0 0 , 0 0 0, 0 0 0 } = 0 . 0 0 0 0 0 0 0 6 9 2 [/tex]

Therefore, the answer in standard notation is 0.0000000692.

Answer:

0.0000000692

Step-by-step explanation:

6.92 x [tex]10^{-8}[/tex]

= 6.92 x 0.00000001

= 0.0000000692

Answer:

D

Step-by-step explanation:

In a 30-60-90 triangle, if the short leg is x, then the long leg is x√3, and the hypotenuse is 2x.

Here, the hypotenuse is 10.  So the short leg is:

10 = 2x

x = 5

If the short leg is 5, then the long leg is 5√3.

Answer:

1) Are there 4 right angles? (90° angles)

2) Are there 2 sets of parallel lines?

3) Are there 2 sets of congruent lines?

4) Are there a set of congruent diagonals?

~

Answer:

3.0 cm

Step-by-step explanation:

The Law of Sines states the relationship between the sides and the angles of non-right (oblique) triangles.

In the given triangle,the following relation holds;

[tex]\frac{4.7}{sin(95)}=\frac{a}{sin(40)}\\\\a=\frac{4.7}{sin(95)}*sin(40)\\\\a=3.03[/tex]

Answer:

Option C. a = 3.0 cm

Step-by-step explanation:

We have to find the value of a from the given triangle ABC.

By applying sine rule in ΔABC

[tex]\frac{sin95}{4.7}=\frac{sin40}{a}[/tex]

Now we cross multiply in the given equation.

a(sin95°) = 4.7(sin40°)

a(0.9962) = 4.7(0.6428)

a = [tex]\frac{4.7(0.6428)}{0.9962}[/tex]

a = 3.03 cm ≈ 3.0 cm

Therefore, a = 3.0cm Option C. will be the answer.