Consider triangle QRS. The legs each have a length of 10 units. Triangle Q R S is shown. Angle Q S R is 90 degrees. The length of Q X is 10 and the length of S R is 10. What is the length of the hypotenuse of the triangle?

Answer:

-6x^3 - x^2 + 2x

Step-by-step explanation:

We can first start with distributing the x using the distributive property

(3x^2 + 2x)(-2x+1) Remember that when x is multiplied with 3x, it increases the exponent to 3x^2)

Now we use FOIL to distribute (First, Outside, Inside, Last)

-6x^3 + 3x^2 - 4x^2 + 2x

We can combine the like terms (3x^2 and - 4x^2) into -x^2

-6x^3 - x^2 + 2x

Answer:

the answer is 5 if it was helpful please give 5 star

Answer:

1234

Step-by-step explanation:

Answer:

2625

Step-by-step explanation:

First let's see all the possible combinations.

(Even=E, Odd= O)

1) EEEO

2) EEOE

3) EOEE

4) OEEE

5) EEEE

Now let's see what E and O possibly could be

E = 0, 2, 4, 5, 6 and 8 (5)

O = 1, 3, 5, 7, 9 (5)

Now we are just simply gonna multiply

1) EEEO = 4*5*5*5

2) EEOE = 4*5*5*5

3) EOEE = 4*5*5*5

4) OEEE = 5*5*5*5

5) EEEE = 4*5*5*5

The even contains a 0, so you can't put 0 in, so (5-1=4), there are only 4 digits for the even.

500 times 4 = 2000

5⁴ = 625

2000+625= 2625

Answer: 2.12 seconds

Step-by-step explanation:

From the question, we are informed that Josie ran a lap in 45.23 seconds while Erica ran a lap in 43.11 seconds.

To calculate the extra amount of time it took Josie to complete the lap, we subtract Erica's time from Josie's time. This will be:

= 45.23 seconds - 43.11 seconds

= 2.12 seconds

Answer:

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

Step-by-step explanation:

Answer:

25/64

Step-by-step explanation:

ratio of perimeters = 15/24 = 5/8

ratio of areas = square of ratio of perimeters

ratio of areas = (5/8)^2 = 25/64

Answer:

22%

Step-by-step explanation:

Well if the ramp can hold 1000lbs and 6 people all weight 780 in total (they must be really fat lol, but anyway) we can make the following fraction.

780/1000

So now we simplify the fraction to 39/50.

And do 39 / 50 = .78

To make that a percent we move the decimal point 2 times to the right so 78% of the ramp‘s capacity is being used meaning there is stil 22% capacity left.

Answer:

See below.

Step-by-step explanation:

[tex](5x^2y^3)^0\div(-2x^{-3}y^5)^{-2}[/tex]

First, note that everything to the zeroth power is 1. Thus:

[tex]=1\div(-2x^{-3}y^5)^{-2}=\frac{1}{(-2x^{-3}y^5)^{-2}}[/tex]

Distribute using Power of a Power property:

[tex]=\frac{1}{(-2)^{-2}(x^{-3})^{-2}(y^5)^{-2})}[/tex]

Make the exponents positive by putting them to the numerator:

[tex]=\frac{(-2)^2(x^{-3})^2(y^5)^2}{1}[/tex]

[tex]=\frac{4x^{-6}y^{10}}{1}[/tex]

Make the exponent positive by this time putting it to the denominator:

[tex]=\frac{4y^{10}}{x^6}[/tex]

Answer/Step-by-step explanation:

Below are the steps to take in solving the given equation, as well as justification forf each step:

[tex] \frac{2}{3}y + 15 = 9 [/tex]  => Given

[tex] \frac{2}{3}y + 15 - 15 = 9 - 15 [/tex] => subtraction property of equality

[tex] \frac{2}{3}y = - 6 [/tex] => simplification

[tex] \frac{2}{3}y * \frac{3}{2} = - 6 * \frac{3}{2} [/tex] => multiplication property of equality

[tex] y = - 9 [/tex] => simplification

Answer:

Your answer is E

Step-by-step explanation:

To make sure, plug the values in the place of N

[tex]-2 <-1, 0, 1, 2, 3, 4, 5, 6, \\ -1, 0, 1, 2, 3, 4, 5, 6, \leq 6[/tex]

Answer:

6^2 is the answer

Step-by-step explanation:

just trust me ik

Answer:

Im pretty sure its B

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

180-(21+73+51)=25

Hey there! :)

Answer:

C. m∠x = 35°.

Step-by-step explanation:

Begin by finding the value of the third angle of the triangle. Recall that all interior angles of a triangle sum up to 180°:

180 - 73 - 51 = 56°.

Since the top angle is split into x and 21°, simply subtract to solve for x:

56 - 21 = 35°. Therefore:

m∠x = 35°.

Answer:

Hello!

____________________

Your answer would be (A) O point W.

Step-by-step explanation:  Intersection of the two lines is defined as the point where the two lines cross or meet each other.

It is given that the lines m and n intersect each other, which means that they must be intersecting each other at some point.

From the figure, it can be seen that in plane A, the lines m and n intersect each other at point W, thus point W is the point of intersection of the two line m and n.

Hence, option A is correct.

Hope this helped you!

Answer: point w hope this helped

Step-by-step explanation:

Answer:

the answer is below

Step-by-step explanation:

Demand seems to be based on price.

Therefore we must consider two things:

that "x" is equal to the price and that "y" is equal to the average attendance.

Thus:

the two points would be:

(x1, y1) = (10,27000)

(x2, y2) = (6.39000)

The slope of a straight line is given by:

m = (y2-y1) / (x2-x1)

we replace:

m = (39000 - 27000) / (6 - 10) = 12000 / -4 = -3000

The equation of a straight line can be expressed like this

y = m * x + b.

where

m is the slope and b is the y-intercept.

we replace

y = -3000 * x + b.

To solve for b, replace x and y with the value of one of the points on the line.

We choose (6.39000). and we replace:

39000 = -3000 * 6 + b

39000 = -18000 + b

39000 + 18000 = b

b = 57000.

if we replace we have:

the equation becomes y = -3000 * x + 57000

since it is the demand and * x is the price.

t = d (x), therefore the equation becomes

d (x) = -3000 * x + 57000.

d (x) = 57000 - 3000 * x.

when x = 0, the price is 0 and the demand will be 57000, which will be more than the stadium can contain because the stadium can only contain 50,000.

So:

when x = 6, the price is 6 and the demand is 57000 - 18000 = 39000.

when x = 10, the price is 10 and the demand is 57000 - 30000 = 27000.

Answer:

a) [tex]\frac{x^2}{16} +\frac{ y^2}{12} = 1[/tex]

b) [tex]\frac{x^2}{64} +\frac{ y^2}{16} = 1[/tex]

Step-by-step explanation:

a)

The vertices are located in the x-axis, so we have a horizontal ellipse.

The equation of an ellipse is given by:

[tex]\frac{(x - h)^2}{a^2} +\frac{ (y - k)^2}{b^2} = 1[/tex]

The coordinates of the foci and the vertices are given by:

Foci: [tex]F(h \pm c, k)[/tex]

Vertices: [tex]V(h\pm a, k)[/tex]

Comparing the coordinates with the values given, we have that:

h = 0, k = 0, c = 2, a = 4

To find the value of b we can use the following equation:

[tex]c^2 = a^2 - b^2[/tex]

[tex]4 = 16 - b^2[/tex]

[tex]b^2 =12[/tex]

So the equation of the ellipse is:

[tex]\frac{x^2}{16} +\frac{ y^2}{12} = 1[/tex]

b)

If the ellipse is centered at the origin, we have:

h = 0, k = 0

The major axis is 'a' and the other axis is 'b', so we have:

a = 8, b = 4.

So the equation is:

[tex]\frac{x^2}{64} +\frac{ y^2}{16} = 1[/tex]

Answer:

D

Step-by-step explanation:

The correct option is option D as 2cos²(x)cos²(x) simplifies as follows:

2cos²(x)cos²(x) = {3 + 4cos(2x) + cos(4x)} / 4

The given expression is : 2cos²(x)cos²(x)

The square identity for cosine is given by:

2cos²(x) -1 = cos(2x)

Thus,

2cos²(x) = {cos(2x) +1}

simplifying again,

cos²(x) = {cos(2x) +1}/2

Simplifying the above using squared identities:

2cos²(x)cos²(x) = {cos(2x) +1}cos²x

                         = {cos(2x) +1} {{cos(2x) +1}/2}

                         [tex]= \frac{\{cos(2x) +1\}^2}{2}\\\\=\frac{cos^2(2x)+2cos(2x)+1}{2}\\\\=\frac{\frac{cos(4x)+1}{2}+2cos(2x)+1}{2}\\\\=\frac{3+4cos(2x)+cos(4x)}{4}[/tex]

so,

2cos²(x)cos²(x) = {3 + 4cos(2x) + cos(4x)} / 4

Hence option D is correct.

Learn more about squared identities:

https://brainly.com/question/14613683?referrer=searchResults

Answer:

(2, -3)

Step-by-step explanation:

These are the steps I used:

(6x+2y=6) x3 -> 18x+6y=18

(7x+3y=5) x2 -> 14x+6y=10

When you subtract the equations you get:

4x=8

x=2

The solution to the system of equations is -3 and -2

The correct option is A

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one.

6x+2y=6 is equation (1)

7x+3y=5 is equation (2)

Multiplying equation (1) by (3)

18x+6y=18 is equation(3)

By multiplying (2) by 2

14x+6y=10 is equation (4)

Substrate equation (4) from (3)

4x=8 Now, divide both sides by 4

X=2

Substitute x=2 in (1)

6(2)+2y=6

12+2y=6

Substrate 12 from LHS and RHS

2y=-6

Divide both sides by 2

y=-3

Hence x=2 and y=-3

learn more about system of equations here;

https://brainly.com/question/25180086

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Answer:

The density of the final mixture is 1.012 g/cm³.

Step-by-step explanation:

To calculate the density of the final mixture we need to know the mass of each solution used is. We will also need to convert the volumes from litres to cm³, to do that we can just multiply 1000.

For the ethanol:

[tex]mass = volume*density\\mass = (80*1000)*1.09 = 87,200 \text{ g}\\[/tex]

For the propylene:

[tex]mass = (148*1000)*0.97 = 143,560 \text{ g}[/tex]

So the mass in the final mix is the sum of both:

[tex]mass_{final} = 87200 + 143560 = 230,760 \text{ g}[/tex]

Therefore the density is:

[tex]density_{final} = \frac{230760}{228000} = 1.012 \text{ }\frac{g}{cm^3}[/tex]

The density of the antifreeze is 1.01 g/cm³

Equations are used to show the relationship between two or more numbers and variables.

Let x represent the density of the antifreeze in g/cm^3.

1 cm³ = 0.001 L

80 L = 80000 cm³; 148 L = 148000 cm³, 228 L = 228000 cm³

Hence:

(1.09 * 80000) + (0.97 * 148000) = x * 228000

228000x = 230760

x = 1.01 g/cm³

The density of the antifreeze is 1.01 g/cm³

Find out more at: https://brainly.com/question/21667661

Answer:

4

Step-by-step explanation:

Converting 3kg to grams,

3 kg *  = 3000 g

If we divide 3000 g by 75, we will determine how many packets of butter there are.

3000 / 75 = 40.

40 packets of butter. If 10 go into a box, that means that

40 / 10 = 4 boxes.

Hence 4 such boxes can be made

Answer:

4 boxes can be made

Step-by-step explanation:

→ First work out the amount of small packets there are

3 kg = 3000g

3000 ÷ 75 = 40

→ Now we know that there are 40 small packets and one box can hold 10 packets so,

1 box  = 10 packets

?  boxes = 40 packets

40 ÷ 10 = 4

→ 4 boxes can be made

Answer:

D. 1/3

Step-by-step explanation:

Use the following equation to solve for the slope:

m (slope) = (y₂ - y₁)/(x₂ - x₁).

Let:

(x₁ , y₁) = (0 , 2)

(x₂ , y₂) = (3 , 3)

Plug in the corresponding numbers to the corresponding variables:

m = (3 - 2)/(3 - 0)

m = (1)/(3)

m = 1/3

D. 1/3 is your answer.

~

Answer:

The matched pairs are:

(A, 4), (B, 1), (C, 2) and (D, 3)

Step-by-step explanation:

The complete question is:

Match each description of an algebraic expression with the symbolic form of that expression :

A. 2 terms; variables = x and y

B. 3 terms; variables = x and y; constant = 3

C. 2 terms; variable = x; constant = 4.5

D. 3 terms; variables = x and y; constant = 2

1. x - 2y + 3

2. 4.5 - 2x

3. 4.5x + 2 - 3y

4. 4.5y - 2x

Solution:

A. 2 terms; variables = x and y  ⇒ 4. 4.5y - 2x

B. 3 terms; variables = x and y; constant = 3  ⇒ 1. x - 2y + 3

C. 2 terms; variable = x; constant = 4.5  ⇒ 2. 4.5 - 2x

D. 3 terms; variables = x and y; constant = 2 ⇒ 3. 4.5x + 2 - 3y

Answer:

[tex]\dfrac{6}{7}[/tex].

Step-by-step explanation:

It is given that the sum of first two terms of an infinite GP is 6.

nth term of a GP is

[tex]a_n=ar^{n-1}[/tex]

[tex]a+ar=6[/tex]     ...(1)

Each term is 5 times the sum of the succeeding terms.

[tex]a_n=5(a_{n+1}+a_{n+2}+...+\infty)[/tex]

[tex]ar^{n-1}=5(ar^n+ar^{n+1}+...+\infty)[/tex]

[tex]ar^{n-1}=5ar^n(1+r+r^2+...+\infty)[/tex]

Divide both sides by a.

[tex]r^{n-1}=5r^n(\dfrac{1}{1-r})[/tex]    [tex][\text{Sum of infinite GP}=\dfrac{a}{1-r}][/tex]

[tex]\dfrac{r^n}{r}=\dfrac{5r^n}{1-r}[/tex]

[tex]\dfrac{1}{r}=\dfrac{5}{1-r}[/tex]

[tex]1-r=5r[/tex]

[tex]1=6r[/tex]

[tex]\dfrac{1}{6}=r[/tex]

The common ratio is 1/6.

Put r=1/6 in (1).

[tex]a+a(\dfrac{1}{6})=6[/tex]

[tex]6a+a=36[/tex]

[tex]7a=36[/tex]

[tex]a=\dfrac{36}{7}[/tex]

Second term [tex]ar=\dfrac{36}{7}\times \dfrac{1}{6}=\dfrac{6}{7}[/tex]

Therefore, the second term is [tex]\dfrac{6}{7}[/tex].

Answer:

you can do the normal operation

or use a calculator

Answer:

Step-by-step explanation:

In this scenario, the probability of success, p is 28% = 28/100 = 0.28

Number of samples, n = 160

Probability of failure, q = 1 - p = 1 - 0.28 = 0.72

Mean,µ = np = 0.28 × 160 = 44.8

Standard deviation, σ = √npq = √160 × 0.28 × 0.72 = 5.68

Let x be the random variable representing the number of wood samples from long-leaf pine trees with a fungal disease. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

the probability that you’ll have at least 50 diseased samples to return to your boss is expressed as

P(x ≥ 50) = 1 - P(x < 50)

For P(x < 50)

z = (50 - 44.8)/5.68 = 0.91

Looking at the normal distribution table, the probability corresponding to the z score is 0.819

Therefore,

P(x ≥ 50) = 1 - 0.819 = 0.181

Answer:

6 bananas

Step-by-step explanation:

Divide the dollars by the price for bananas

15/2.45

6.12244898

Round down because she cannot buy part of a banana

6 bananas

Answer:

Step-by-step explanation:

=-3.875/7. (divided by 16)

Answer:

c       f(0)=6

Step-by-step explanation:

they match

Answer:

B. (2, 4)

D. (10, -1)

Step-by-step explanation:

The solution sets must be in the shaded region of the systems of inequalities. It cannot be on either lines because both lines are dotted. In that case, only B and D work because they are inside the shaded regions while the other points are not.

Answer:

B. (2, 4)

D. (10, -1)

Step-by-step explanation:

To be a solution, a point must be in the shaded part of the graph.

Answer: (2, 4), (10, -1)

Answer:

$1340.49

Step-by-step explanation:

From the attached image

Subtotal Cost of Purchased Items

[tex]= (20 \times 16.69)+(2 \times 20.78)+(2 \times 15.58)+(6 \times 21.38)\\+(118 \times 6.60)+(500 \times 0.22)+(10 \times 8.44)+(1 \times 150)\\\\=\$1658[/tex]

Since the builder receives a 20% contractor's discount, plus and additional 3% for paying in full within 30 days.

Discount = 23% of $1658 = 0.23 X 1658 =$381.34

Total (Less Discount) = 1658-381.34 = $1276.66

Tax on building materials is 5%.

Therefore:

Tax = 5% of $1276.66=0.05 X 1276.66

Tax=$63.83

Therefore, the total bill:

=$1276.66+63.83

Grand Total =$1340.49