Write an expression to represent the total cost of paint at a rate of $5.75 per ft.? to paint a triangular-shaped mural where the base of the triangle is 22 feet longer than the height

Answer:

A) A = 200w - w²

B) w = 100 yards

C) Max Area = 10000 sq.yards

Step-by-step explanation:

We are told that Robert has available 400 yards of fencing.

A) we want to find the expression of the area in terms of the width "w".

Since width is "w", and perimeter is 400,if we assume that length is l, then we have;

2(l + w) = 400

Divide both sides by 2 gives;

l + w = 200

l = 200 - w

Thus, Area of rectangle can be written as;

A = w(200 - w)

A = 200w - w²

B) To find the value of w for which the area is largest, we will differentiate the expression for the area and equate to zero.

Thus;

dA/dw = 200 - 2w

Equating to zero;

200 - 2w = 0

2w = 200

w = 200/2

w = 100 yards

C) Maximum area will occur at w = 100.

Thus;

A_max = 200(100) - 100(100)

A_max = 10000 sq.yards

Answer:

5.75

Step-by-step explanation:

11.25 - 5.5 = 5.75.

So, Ana must take 5.5 more mL of Medicine A than Medicine B.

Hope this helps!

Answer:

[tex]\Huge \boxed{\mathrm{9}}[/tex]

Step-by-step explanation:

[tex]\Rightarrow \displaystyle \frac{18 \div 2 * 3}{5-2}[/tex]

Dividing first.

[tex]\Rightarrow \displaystyle \frac{9 * 3}{5-2}[/tex]

Multiplying and subtracting.

[tex]\Rightarrow \displaystyle \frac{27}{3}[/tex]

Division.

[tex]\Rightarrow 9[/tex]

Answer:

2.0

Step-by-step explanation:

Answer:

B. 2.0 miles

Step-by-step explanation:

Tony ran 1/2 of a mile for 1/4 of an hour.

First, to make it easier, change each fraction into decimals:

1/2 = 0.5

1/4 = 0.25

It takes Tony 0.25 hours to run 0.5 miles.

You are solving for 1 hours worth. Multiply 4 to both terms:

0.25 hr x 4 = 1 hr

0.5 miles x 4 = 2.0 miles

B. 2.0 miles is your answer.

~

Answer:

-3,-1,1,3,5

Step-by-step explanation:

__________

D = 4

__________

i blelieve this is it.

Answer:

Step-by-step explanation:

[tex]3\pi d = 12 \pi\\\\divide\:both\:sides\:of\:the\:equation\:by\: 3\:\pi\\\frac{3 \pi d}{3\pi} = \frac{12 \pi}{3\pi} \\\\d=4[/tex]

Answer:

Step-by-step explanation:

From the given information:

r = 10 cos( θ)

r = 5

We are to find the  the area of the region that lies inside the first curve and outside the second curve.

The first thing we need to do is to determine the intersection of the points in these two curves.

To do that :

let equate the two parameters together

So;

10 cos( θ) = 5

cos( θ) = [tex]\dfrac{1}{2}[/tex]

[tex]\theta = -\dfrac{\pi}{3}, \ \ \dfrac{\pi}{3}[/tex]

Now, the area of the  region that lies inside the first curve and outside the second curve can be determined by finding the integral . i.e

[tex]A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} (10 \ cos \ \theta)^2 d \theta - \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ 5^2 d \theta[/tex]

[tex]A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} 100 \ cos^2 \ \theta d \theta - \dfrac{25}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ d \theta[/tex]

[tex]A = 50 \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} \dfrac{cos \ 2 \theta +1}{2} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}[/tex]

[tex]A =\dfrac{ 50}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} {cos \ 2 \theta +1} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \dfrac{\pi}{3} - (- \dfrac{\pi}{3} )\end {bmatrix}[/tex]

[tex]A =25 \begin {bmatrix} \dfrac{sin2 \theta }{2} + \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{\dfrac{\pi}{3}} \ \ - \dfrac{25}{2} \begin {bmatrix} \dfrac{2 \pi}{3} \end {bmatrix}[/tex]

[tex]A =25 \begin {bmatrix} \dfrac{sin (\dfrac{2 \pi}{3} )}{2}+\dfrac{\pi}{3} - \dfrac{ sin (\dfrac{-2\pi}{3}) }{2}-(-\dfrac{\pi}{3}) \end {bmatrix} - \dfrac{25 \pi}{3}[/tex]

[tex]A = 25 \begin{bmatrix} \dfrac{\dfrac{\sqrt{3}}{2} }{2} +\dfrac{\pi}{3} + \dfrac{\dfrac{\sqrt{3}}{2} }{2} + \dfrac{\pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}[/tex]

[tex]A = 25 \begin{bmatrix} \dfrac{\sqrt{3}}{2 } +\dfrac{2 \pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}[/tex]

[tex]A = \dfrac{25 \sqrt{3}}{2 } +\dfrac{25 \pi}{3}[/tex]

The diagrammatic expression showing the area of the region that lies inside the first curve and outside the second curve can be seen in the attached file below.

Answer:

Remainder = (3145/8)x - 408

Step-by-step explanation:

We want to find the remainder when 6x^(5) + 4x⁴ - 27x³ - 7x² + 27x + 3/2 is divided by (2x² - 3)²

Let's expand (2x² - 3)² to give ;

(2x - 3)(2x - 3) = 4x² - 6x - 6x + 9 = 4x² - 12x + 9

So,we can divide now;

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

First of all, we'll divide the term with the highest power inside the long division symbol by the term with the highest power outside the division symbol. This will give;

3/2x³

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

We now subtract the new multiplied term beneath the original one from the original one to get;

3/2x³

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³+27x +3/2

We'll now divide the term in new polynomial gotten with the highest power by the term with the highest power outside the division symbol. This gives;

(3/2)x³ + (11/2)x²

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

We now subtract the new multiplied term beneath the immediate one from the immediate one to get;

(3/2)x³ + (11/2)x²

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³-7x²+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

(159/2)x³-(113/2)x²+27x+(3/2)

We'll now divide the term in new polynomial gotten with the highest power by the term with the highest power outside the division symbol. This gives;

(3/2)x³ + (11/2)x² + (159/8)x

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³-7x²+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

(159/2)x³-(113/2)x²+27x+(3/2)

(159/2)x³-(477/2)x²+(1431/8)x

We now subtract the new multiplied term beneath the immediate one from the immediate one to get;

(3/2)x³ + (11/2)x² + (159/8)x

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³-7x²+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

(159/2)x³-(113/2)x²+27x+(3/2)

(159/2)x³-(477/2)x²+(1431/8)x

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

182x²-(1215/8)x + (3/2)

We'll now divide the term in new polynomial gotten with the highest power by the term with the highest power outside the division symbol. This gives;

(3/2)x³+(11/2)x²+(159/8)x+(91/2)

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³-7x²+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

(159/2)x³-(113/2)x²+27x+(3/2)

(159/2)x³-(477/2)x²+(1431/8)x

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

182x²-(1215/8)x + (3/2)

182x²-545x + 819/2

We now subtract the new multiplied term beneath the immediate one from the immediate one to get;

182x² - (1215/8)x + (3/2) - 182x² + 545x - 819/2 = (3145/8)x - 408

Remainder = (3145/8)x - 408

Answer and Step-by-step explanation: The Trapezoidal and Simpson's Rules are method to approximate a definite integral.

Trapezoidal Rule evaluates the area under the curve (definition of integral) by dividing the total area into trapezoids.

The formula to calculate is given by:

[tex]\int\limits^a_b {f(x)} \, dx = \frac{b-a}{2n}[f(x_{0})+2f(x_{1})+2f(x_{2})+...+2f(x_{n-1})+f(x_{n})][/tex]

The definite integral will be:

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{9-4}{2.8}[2+2.\sqrt{5} +2.\sqrt{6} +2.\sqrt{7}+2.\sqrt{8}+3][/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{5}{16}[25.3193][/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = 7.9122[/tex]

Simpson's Rule divides the area under the curve into an even interval number of subintervals, each with equal width.

The formula to calculate is:

[tex]\int\limits^a_b {f(x)} \, dx = \frac{b-a}{3n}[f(x_{0})+4f(x_{1})+2f(x_{2})+...+2f(x_{n-2})+4f(x_{n-1})+f(x_{n})][/tex]

The definite integral will be:

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{9-4}{3.8}[2+4.\sqrt{5} +2.\sqrt{6} +4.\sqrt{7} +4\sqrt{8} +3][/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{5}{24}[40.7398][/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = 8.4875[/tex]

Calculating the definite integral by using the Fundamental Theorem of Calculus:

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \int\limits^9_4 {x^{\frac{1}{2} }} \, dx[/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{2.\sqrt[]{x^{3}} }{3}[/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{2.\sqrt[]{9^{3}} }{3}-\frac{2.\sqrt[]{4^{3}} }{3}[/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = 12.6667[/tex]

Comparing results, note that Simpson's Rule is closer to the exact value, i.e., gives better approximation to the exactly value calculated by the fundamental theorem.

By Thales' theorem:

[tex]\[\begin{array}{l}\frac{{18}}{{2x + 2}} = \frac{{24}}{{3x + 1}}\\18(3x + 1) = 24(2x + 2)\\54x + 18 = 48x + 48\\6x = 30\\x = 5\\A.\end{array}\][/tex]

Answer:

A. 2880 acres

Step-by-step explanation:

Formula: a = 640 s

Given information: s = 4.5

--> a = 640 x 4.5 = 2880 (acres)

Answer:

0

Step-by-step explanation:

16x2= 32 and 32x1=32 so 32-32=0

Answer:

the answer is 4.115 x 10^5

Step-by-step explanation:

hope that helps

Answer:

It´s rational

Step-by-step explanation:

27,14159 = 2714159/100000

Rational

Answer:

The length of the rectangle would be 4.

Step-by-step explanation:

We can start by naming the width x.

Therefore, the length would 3x-2.

The perimeter of the rectangle would then be:

2(3x-2+x)

We can set up the given equation

2(3x-2+x)=12

Solve for x.

Divide both sides by 2.

3x-2+x=6

Combine like terms.

4x-2=6

Add 2 to both sides.

4x=8

Divide both sides by 4.

x=2

The width would then be 2.

We can plug that into the expression for length.

3x-2

3(2)-2

6-2

4

The length of the rectangle would be 4.

Answer:

The z-score corresponding to an observed value of x of 2 is 0.215.

Step-by-step explanation:

We are given that a variable x has the possible observations shown below;

Possible observations of X: -3, -1, 0, 1, 1, 2, 4, 4, 5.

Firstly, we will find the mean and the standard deviation of X, i.e;

Mean of X, ([tex]\mu[/tex]) = [tex]\frac{\sum X}{n}[/tex]

                       =  [tex]\frac{(-3)+ (-1)+ 0+ 1+ 1+ 2+ 4+ 4+ 5}{9}[/tex]  

                       =  [tex]\frac{13}{9}[/tex]  = 1.44

Standard deviation of X, ([tex]\sigma[/tex]) =  [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]

                            =  [tex]\sqrt{\frac{(-3-1.44)^{2}+(-1-1.44)^{2}+......+(4-1.44)^{2}+(5-1.44)^{2} }{9-1} }[/tex]

                            =  2.603

Now, the z-score corresponding to an observed value of x of 2 is given by;

                  z-score =  [tex]\frac{X-\mu}{\sigma}[/tex]

                               =  [tex]\frac{2-1.44}{2.603}[/tex]  = 0.215.        

Answer:

W = 14

Step-by-step explanation:

7w=98

Divide

w=98/7

Done

w=14

Hope this helps! :)

(pls mark brainliest)

Answer:

w = 14

Step-by-step explanation:

98 = 7w

98/7 = 7w/7

14 = w

Hope this helps.

Answer:

this is wind turbine angular speed

Step-by-step explanation:

given data

angular speed ω = 64 rpm

time = 1 min = 60 seconds

solution

we know that angular speed ω is expess as

ω = [tex]\frac{2\pi }{T}[/tex]    .........................1

ω = 64 × [tex]\frac{2\pi }{T}[/tex]

ω  = 6.70 rad/s

so this is wind turbine angular speed

Answer: D. This variable is a discrete numerical variable that is ratio-scaled.

Step-by-step explanation:

A Discrete variables are variables which are countable in a finite amount of time. For example, you can count the amount of money in your bank wallet, but same can’t be said for the money you have deposited in eveyones bank account as this is infinite.

So the number of times an individual changes job in a five years period is a perfect example of  a discrete numerical variable that is ratio scaled because it can be counted.

The 3×3 Matrix is  [tex]B=\left[\begin{array}{ccc}1.2&1.4&3.1\\2.2&1.1&5.6\\3.7&4.2&6.7\end{array}\right][/tex]

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object

A 3 x 3 matrix is calculated for a matrix having 3 rows and 3 columns

Given,

B=

1.2 1.4 3.1

2.2 1.1 5.6

3.7 4.2 6.7

Then the 3×3 matrix is

[tex]B=\left[\begin{array}{ccc}1.2&1.4&3.1\\2.2&1.1&5.6\\3.7&4.2&6.7\end{array}\right][/tex]

Hence, The 3×3 Matrix is [tex]B=\left[\begin{array}{ccc}1.2&1.4&3.1\\2.2&1.1&5.6\\3.7&4.2&6.7\end{array}\right][/tex]

Learn more about Matrix and 3×3 Matrix here

https://brainly.com/question/12759849

#SPJ2

Answer:

Step-by-step explanation:

c11 =

⇒ 56.1  

c12 =

⇒ 12.1

c13 =

⇒ 236

Answer:

  H = M/(2A +2T)

Step-by-step explanation:

Factor out H and divide by its coefficient.

  M = 2HA +2HT

  M = H(2A +2T)

  M/(2A +2T) = H

  H = M/(2A +2T)

Answer:

The answer to the problem is 5.

Answer:

Step-by-step explanation:

[tex]-3-\left(-8\right)\\\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\=-3+8\\\\\mathrm{Add/Subtract\:the\:numbers:}\:\\-3+8\\=5[/tex]

Answer:

59.96

Step-by-step explanation:

when 67% if 89.5 is expressed in numbers,

[tex]\frac{67}{100}*89.5\\ \frac{5996.5}{100}\\ =59.96[/tex]

Answer:

the answer is 10.41. If you have a number 5 or more you round the nearest number on the left up 1 if it's 4 or less it stays the same it doesn't go up or down.

Answer:

9% of $1500 is $15 so she gains an extra $15 for each of the 18 years

$1500 in the bank each year for 18 years is $27000 after 18 years

$15 each year as well so that’s an extra $270 in the bank

The total in the bank is the sum of what she has invested and the interest so the total in the bank is $27270

Step-by-step explanation:

Answer:

[tex]\huge\boxed{Center= (-3,4) , Radius = 5\sqrt{2} }[/tex]

Step-by-step explanation:

Given equation is

[tex]x^2 + y^2 + 6x-8y - 25 = 0[/tex]

Adding 25 to both sides

[tex]x^2 + y^2 +6x-8y = 25[/tex]

Completing squares

[tex]x^2 +6x +y^2 - 8y = 25\\(x)^2-2(x)(-3) + (y)^2 - 2(x)(4) = 25[/tex]

Both of their "b" is -3 and 4 respectively

So, adding (-3)² => 9 and (4)² => 16 to both sides

[tex](x+3)^2 + (y-4)^2 = 25 + 9 + 16\\(x+3)^2 + (y-4)^2 = 50\\(x-(-3))^2 + (y-4)^2 = (5\sqrt{2)^2}[/tex]

Comparing it with [tex](x-h)^2+(y-k)^2 = r^2[/tex], where center = (h,k) and radius = r.

We get:

Center = (-3,4)

Radius = [tex]5\sqrt{2}[/tex]

Answer:

{-3, 2}U{2, 5}

Step-by-step explanation:

For an equation to be negative, it would need to be in a negative range (below the x-axis or the coordinates are negative y-values). Therefore, we can examine this question and see that the graph is negative when the function crosses the x-axis at -3 and it remains negative until you reach 2 on the x-axis.

Therefore, the first set of negative values is (-3, 2).

Secondly, applying the same logic as before, the function decreases at 2 and then touches the x-axis again at 5. Therefore, the second negative value would be (2, 5).

The negative values are {-3, 2}U{2, 5}.

Answer:

{-3, 2}U{2, 5}

Step-by-step explanation:

Answer:

1/46 is already in the simplest form.

Answer:

1/46 is already in its simplest form.

Answer:

The measure of angle RST = 120°

Step-by-step explanation:

Answer:

The measure of angle RST = 120°

hope this helps

Answer:

y = 1/5x - 6.4

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes, so the slope will be 1/5

Then, plug the slope and the point into the equation y = mx + b to find b

y = mx + b

-7 = 1/5(-3) + b

-7 = -0.6 + b

-6.4 = b

Then, plug this and the slope into the equation

y = 1/5x - 6.4 will be the equation