write your answer in simplest radical form​

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:

-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

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.

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:

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:

A) Exponential growth

Step-by-step explanation:

Answer:

0.0698

Step-by-step explanation:

Given :

Population mean, μ = 20

Sample mean, xbar = 21.1

Sample standard deviation, s = 4.3

Sample size, n = 35

The hypothesis :

H0 : μ = 20

H0 : μ > 20

The test statistic :

(xbar - μ) ÷ (s/√(n))

T = (21.1 - 20) ÷ (4.3/√(35))

T = 1.1 ÷ 0.7268326

Test statistic = 1.513

Using the Pvalue calculator :

df = n - 1 = 35 - 1 = 34

Pvalue(1.513, 34) = 0.06976

Pvalue = 0.0698 (4 decimal places)

The p-value is 0.0698 if rounded to 4-decimal places.

It is given that students study an average of more than 20 hours each week and the random sample of 35 students was asked to keep a diary of their activities over a period of several weeks.

The average number of hours that the 35 students was 21.1 hours.

The sample standard deviation is 4.3 hours.

It is required to find the p-value.

It is defined as the measure of data dispersement, It gives an idea about how much is the data spread out.

We can test the hypothesis using the Z test, the formula for the Z-test is given below:

[tex]\rm Z= \frac{(x-u)}{\frac{S}{\sqrt{n} } }[/tex]

Where x is the sample mean

            u is the population mean

            s is the standard deviation

            n is the sample size.

The hypothesis are: H0 : μ = 20  V/s  H1 : μ > 20

We have x = 21.1

               u = 20

               s = 4.3

               n = 35

Putting these values in the above formula, we get:

[tex]\rm Z= \frac{(21.1-20)}{\frac{4.3}{\sqrt{35} } }\\\\\rm Z= \frac{(1.1)}{\frac{4.3}{\sqrt{35} } }\\\\[/tex]

Z = 1.513

difference or df = n -1 ⇒ 35-1 ⇒ 34

P-value at (1.513, 34) =  0.06976  (From the p-value calculator)

P-value = 0.0698 (Rounded to 4-decimal places)

Thus, the p-value is 0.0698 if rounded to 4-decimal places.

Learn more about the standard deviation here:

brainly.com/question/12402189

Answer:

12

Step-by-step explanation:

πr²h=πr²h

π(4.5)²*10=π(x/2)²4.9

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.

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:

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:

+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:

65% of 27.69 is 18.

Step-by-step explanation:

Formula = Number x 100

Percent = 18 x 100

65 = 27.69

Following shows the steps on how to derive this formula

Step 1: If 65% of a number is 18, then what is 100% of that number? Setup the equation.

18

65% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

65Y = 18 x 100

65Y = 1800

Y = 1800

100 = 27.69

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:

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.

Step-by-step explanation:

here's the answer to your question

Answer:

H0 : μ = 60000

H1 : μ ≠ 60000

Test statistic = 3.464

Step-by-step explanation:

Given :

Sample mean salary, xbar = 80000

Sample standard deviation, s = 10000

Population mean salary , μ = 60000

Sample size, n = 3

Hypothesis :

H0 : μ = 60000

H1 : μ ≠ 60000

The test statistic :

T = (xbar - μ) ÷ (s/√(n))

T = (80000 - 60000) ÷ (10000/√(3))

T = 20000 / 5773.5026

T = 3.464

The Decison region :

If Tstatistic >Tcritical

Tcritical at 10%, df = 2 ; two - tailed = 2.9199

Tstatistic > Tcritical ; He

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

Answer:

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

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:

I believe the answer is 4 37/50!

Answer:

y = 3x - 2

Happy Studying

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:

not similar

Step-by-step explanation:

32/26 = 16/13

18/12 = 3/2

16/13 is not equal to 3/2, so the rectangles are not similar.

Lets check

[tex]\\ \sf\longmapsto \dfrac{32}{18}\boxed{}\dfrac{26}{12}[/tex]

[tex]\\ \sf\longmapsto \dfrac{16}{9}\boxed{}\dfrac{13}{6}[/tex]

Hence

[tex]\\ \sf\longmapsto \dfrac{16}{9}\neq\dfrac{13}{6}[/tex]

Both rectangles are not similar

Answer:

Neal

Step-by-step explanation:

13.01 < 13.89

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:

5 miles per hour

Step-by-step explanation:

3¾ ÷ ¾ =

15/4 ÷ ¾ =

15/4 x 4/3 =

15/3 = 5

Answer:

C

Step-by-step explanation: