If two angles are complementary, find the measure of each of angle.

Answer:

The numbers 3(pi)/2, 5(pi)/2 satisfy the conclusion of Rolle's Theorem

Step-by-step explanation:

1. The function must be continuous.  

Trigonometric functions are continuous.  

2.  It must be true that f(a) = f(b) = 0

For this case sin(pi) = sin(3pi) = 0

3. Therefore by Rolle's Theorem, there exist a point, x, such that f(x) = 0

For this case f(x) = cos(x)

And cos(x) = 0 at x = 3(pi)/2,5(pi)/2

Answer:

68.18

Step-by-step explanation:

→ Set up an equation

[tex]\frac{44x}{100} =30[/tex]

→ Times both sides by 100

44x = 3000

→ Divide both sides by 44

68.18

Answer:

5 miles per hour

Step-by-step explanation:

3¾ ÷ ¾ =

15/4 ÷ ¾ =

15/4 x 4/3 =

15/3 = 5

9514 1404 393

Answer:

  a. Definition of bisector.

Step-by-step explanation:

Line l is a line through the midpoint M. We can conclude it is a bisector, because, by definition, a bisector is a line through the midpoint.

The conclusion is justified by the definition of a bisector.

Given:

The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).

Transformation: Reflection over the x-axis and a translation of shifting right 10 units.

To find:

The image after glide reflection transformation.

Solution:

The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).

If a figure is reflected over the x-axis, then

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

Using this, we get

[tex]A(-1,-3)\to A'(-1,3)[/tex]

[tex]B(-4,-1)\to B'(-4,1)[/tex]

[tex]C(-6,-4)\to C'(-6,4)[/tex]

If a figure is shifting 10 units right, then

[tex](x,y)\to (x+10,y)[/tex]

Using this we get

[tex]A'(-1,3)\to A''(-1+10,3)[/tex]

[tex]A'(-1,3)\to A''(9,3)[/tex]

Similarly,

[tex]B'(-4,1)\to B''(-4+10,1)[/tex]

[tex]B'-4,1)\to B''(6,1)[/tex]

And,

[tex]C'(-6,-4)\to C''(-6+10,4)[/tex]

[tex]C'(-6,-4)\to C''(4,4)[/tex]

Therefore, the vertices of the image are A''(9,3), B''(6,1) and C''(4,4).

Answer:

Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.

4+z/y = 36/18

Step-by-step explanation:

a) Since both triangles are similar triangles, then the ratio of their similar sides is equal to a constant k. Therefore:

16/4 = 18/y

Note that the arrangement depends on which of the triangles sides cones first.

Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.

b) Same rule in (a) applies to the sum as well. Hence;

4+z/y = 16+20/18

4+z/y = 36/18

Answer:

I don't know the answer it is to hard.

Answer:

29/44

Step-by-step explanation:

[tex]\frac{4}{11} +\frac{5}{22} +\frac{3}{44} =\\[/tex]

-find the common denominator

[tex]\frac{4*4}{4*11} + \frac{2*5}{2*22} +\frac{3}{44} =[/tex]

[tex]\frac{16}{44} +\frac{10}{44} +\frac{3}{44} =[/tex]

-add the fractions and solve

[tex]\frac{16+10+3}{44} =[/tex]

[tex]\frac{29}{44}[/tex]

Answer:

C

Step-by-step explanation:

Answer:

682

Step-by-step explanation:

191,919 + 262,626

454545 ÷ 666 = 682.5

Thus meaning 682 bags will have 666 berries and one bag will have 333 berries.

Answer:

A) Exponential growth

Step-by-step explanation:

Answer:

m<1 = 55°

m<2 = 125°

m<3 = 55°

m<5 = 55°

m<6 = 125°

m<7 = 55°

m<8 = 125°

Step-by-step explanation:

m<4 = 125° (given)

✔️m<8 = m<4 (alternate exterior angles are congruent)

m<8 = 125° (substitution)

✔️m<1 = 180° - m<8 (supplementary angles/linear pair)

m<1 = 180° - 125° (substitution)

m<1 = 55°

✔️m<2 = m<8 (vertical angles are congruent)

m<2 = 125° (substitution)

✔️m<7 = m<1 (vertical angles are congruent)

m<7 = 55° (Substitution)

✔️m<3 = m<7 (alternate interior angles are congruent)

m<3 = 55° (substitution)

✔️m<5 = m<3 (vertical angles are congruent)

m<5 = 55°

✔️m<6 = m<4 (vertical angles)

m<6 = 125°

Answer:

The number is 30.

Step-by-step explanation:

Let the number be x

so

x + (130% of x) = 69

x + 13x/10 = 69

or, (10x + 13x)/10 = 69

or, 23x = 690

or, x = 690/23

so, x = 30

Answer: 30

Step-by-step explanation:

its correct on rsm

Answer:

X-intercept = -3 and y-intercept = 6

Step-by-step explanation:

We can start off by isolating the y term. To do that, we must add 2y to both sides to get

[tex]4x=2y-12[/tex]

Now, we must add 12 to both sides and the y term will be all alone on the right side:

[tex]4x+12=2y[/tex]

Now, to have only y on the right side, we must divide by 2 to get:

[tex]y=2x+6[/tex]

In slope-intercept form, b is the y-intercept, and 'b' in this equation is 6. We have our y-intercept.

To find our x-intercept, y must be equal to zero. We can plug in that value for y and solve for x:

[tex]0=2x+6[/tex]

We can start off by subtracting 6 from both sides to get:

[tex]2x=-6[/tex]

We can then divide both sides to get [tex]x=-3[/tex] when y is equal to 0. Thus, we have our x-intercept.

Answer:

y-intercept= -6

x-intercept= 3

Step-by-step explanation:

First, rearrange the equation to be in y=mx+b.

4x-2y=12

4x-12=2y

(1/2)(4x-12)=y

y=2x-6

From here, we know that the 'b' in an equation in form y=mx+b is the y-intercept, which is -6.

To find the x intercept make y=0 and solve.

You can also solve without rearranging the equation and simply making x=0 and solving to find the y-intercept. and making y=0 and solving to find the x-intercept.

Answer:

A, B, and E.

Step-by-step explanation:

A. 5^x * 5^x

= 5^x+x

=5^(2)(x)

=25^x

B. 5^2x

=5^(2)(x)

=25^x

C. 5*5^2x

=5^1+2x

D. 5*5^x

=5^1+x

E. (5*5)^x

=5^x*5^x

=5^(2)(x)

=25^x

F. 5^2*5^x

=5^2+x

Answer:

85 rounded to the nearest dollar would be $1. 73 rounded to the nearest dollar would also be $1

Step-by-step explanation:

Answer: C) (1,4)

Step-by-step explanation:

The intersection point is where f(x) = g(x)

x³ + 3x = x² + 3

x³ - x² +3x - 3 = 0

Answer:

Neal

Step-by-step explanation:

13.01 < 13.89

Answer:

U = 67.6 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos U = adj side / hypotenuse

cos U = sqrt(10)/ sqrt(69)

cos U = sqrt(10/69)

Taking the inverse cos of each side

cos ^-1( cos U) =  cos ^-1(sqrt(10/69))

U = 67.62335

To the nearest tenth

U = 67.6 degrees

Step-by-step explanation:

here's the answer to your question

Answer:

12

Step-by-step explanation:

πr²h=πr²h

π(4.5)²*10=π(x/2)²4.9

Answer:

-15 < x < -5

Step-by-step explanation:

-3 < x/5  < -1

Multiply all sides by 5

-3*5 < x/5 *5  < -1*5

-15 < x < -5

Answer:

a x^2/2 is a polynomial because the power of x is 2 which is a positive whole number but 2/x^2 is not a polynomial because the power of x is -2 which is negative whole number.

b.in

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

the power if x will be

[tex]x {}^{ \frac{1}{2} } [/tex]

which is not a whole number so it is not a polynomial.

but in

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

the power if x is a positive whole number.so it is a polynomial.

c.the greatest power of variable of the term is called degree of polynomial

Answer:

The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P =  1/32 = 0.03125

Step-by-step explanation:

There are up to 5 toppings, such that the toppings are:

caramel

whipped cream

butterscotch sauce

strawberries

hot fudge

We want to find the probability that,  If the server randomly chooses which toppings to add, she gets just caramel, butterscotch sauce, strawberries, and hot fudge.

First, we need to find the total number of possible combinations.

let's separate them in number of toppings.

0 toppins:

Here is one combination.

1 topping:

here we have one topping and 5 options, so there are 5 different combinations of 1 topping.

2 toppings.

Assuming that each topping can be used only once, for the first topping we have 5 options.

And for the second topping we have 4 options (because one is already used)

The total number of combinations is equal to the product between the number of options for each topping, so here we have:

c = 4*5 = 20 combinations.

But we are counting the permutations, which is equal to n! (where n is the number of toppings, in this case is n = 2), this means that we are differentiating in the case where the first topping is caramel and the second is whipped cream, and the case where the first topping is whipped cream and the second is caramel, to avoid this, we should divide by the number of permutations.

Then the number of different combinations is:

c' = 20/2! = 10

3 toppings.

similarly to the previous case.

for the first topping there are 5 options

for the second there are 4 options

for the third there are 3 options

the total number of different combinations is:

c' = (5*4*3)/(3!) = (5*4*3)/(3*2) = 10

4 toppings:

We can think of this as "the topping that we do not use", so there are only 5 possible toppings to not use, then there are 5 different combinations with 4 toppings.

5 toppings:

Similar to the first case, here is only one combination with 5 toppings.

So the total number of different combinations is:

C = 1 + 5 + 10 + 10 + 5 + 1 = 32

There are 32 different combinations.

And we want to find the probability of getting one particular combination (all of them have the same probability)

Then the probability is the quotient between one and the total number of different combinations.

p = 1/32

The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P =  1/32 = 0.03125

Step-by-step explanation:

x^2+2x+7y=15

7y=15-x^2-2x

y=15/7-1/7x^2-2/7x , x ∈ all real numbers

Answer:

+200 J

Step-by-step explanation:

The equally positive charges plates are placed at point x. Exponential lines are 100 V interval and therefore the charges on the potential line is positive. The potential for line c is +200 V which indicates that work required to move the third line is +200 J.

Answer:

I believe the answer is 4 37/50!

Answer:

Using 3.14   for pi  A = 113.0  ft^2

Using the pi button A = 113.1 ft^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

A = pi ( 6)^2

A = 36 pi

Using 3.14 for an approximation for pi

A = 36(3.14) = 113.04

To 1 decimal

113.0

Using the pi button

A = 113.0973355

A = 113.1

Answer:

The projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.

Step-by-step explanation:

The height of a projectile fired upward is given by the formula:

[tex]\displaystyle s = v_{0} t - 16t^2[/tex]

Where s is the height in feet, v₀ is the initial velocity, and t is the time in seconds.

Given a projectile with an initial velocity of 128 ft/s, we want to determine how long it will take the projectile to reach a height of 96 feet.

In other words, given that v₀ = 128, find t such that s = 96.

Substitute:

[tex](96) = (128)t-16t^2[/tex]

This is a quadratic. First, we can divide both sides by -16:

[tex]-6 = -8t+t^2[/tex]

Isolate the equation:

[tex]t^2 - 8t + 6 = 0[/tex]

The equation isn't factorable, so we can consider using the quadratic formula:

[tex]\displaystyle t = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]

In this case, a = 1, b = -8, and c = 6. Substitute:

[tex]\displaystyle t = \frac{-(-8)\pm\sqrt{(-8)^2-4(1)(6)}}{2(1)}[/tex]

Simplify:

[tex]\displaystyle t = \frac{8\pm\sqrt{40}}{2} = \frac{8\pm 2\sqrt{10}}{2} = 4\pm \sqrt{10}[/tex]

Hence, our two solutions are:

[tex]\displaystyle t = 4+\sqrt{10} \approx 7.16\text{ or } t= 4-\sqrt{10} \approx 0.84[/tex]

So, the projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.