Evaluate the expression 7x^2y, when x = 5 and y=3

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-7})\qquad \stackrel{center}{(\stackrel{x_2}{-6}~,~\stackrel{y_2}{-4})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[-6-1]^2+[-4-(-7)]^2}\implies r=\sqrt{(-6-1)^2+(-4+7)^2} \\\\\\ r=\sqrt{(-7)^2+3^2}\implies r=\sqrt{58} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{-4}{ k})\qquad \qquad radius=\stackrel{\sqrt{58}}{ r}\\[2em] [x-(-6)]^2+[y-(-4)]^2=(\sqrt{58})^2\implies (x+6)^2+(y+4)^2=56[/tex]

To find the equation of the circle with a given point (1,-7) and center (-6,-4), calculate the radius using the distance formula to find that the radius is √58, then substitute the center coordinates and radius into the standard circle equation to get (x + 6)² + (y + 4)² = 58.

To write the equation of the circle given a point on the circle at (1,-7) and the center at (-6,-4), we will use the standard form of the circle's equation (x-h)² + (y-k)² = r², where (h, k) is the center of the circle and r is the radius. First, we calculate the radius of the circle using the distance formula: r =
√[(x_2-x_1)² + (y_2-y_1)²]. Plugging in our values, we get r = √[(1 - (-6))² + (-7 - (-4))²] = √[49 + 9] = √58. Therefore, the equation of the circle with center (-6,-4) and passing through the point (1,-7) is (x + 6)² + (y + 4)² = 58.

Answer:

x = 11

Step-by-step explanation:

Given the 2 equations

y = [tex]\frac{1}{4}[/tex] x → (1)

5x - 8y = 33 → (2)

Substitute y = [tex]\frac{1}{4}[/tex] x into (2)

5x - 8( [tex]\frac{1}{4}[/tex]x ) = 33

5x - 2x = 33

3x = 33 ( divide both sides by 3 )

x = 11

Answer:

11

Step-by-step explanation:

Given that ,

⇒ y = 1/4x and

⇒ 5x - 8y = 33

We can write 1st equation as ,

⇒ 4y = x

Put x = 4y in 2nd Equation ,

⇒ 5*4y - 8y = 33

⇒ 20y - 8y = 33

⇒ 12y = 33

⇒ y = 33/12

Put this in 1st ,

⇒ 33/12 = 1/4 x

⇒ x = 33/12 × 4

⇒ x = 33/3

⇒ x = 11 .

Answer:

m = 1/3

Step-by-step explanation:

When you multiply by a fraction it's actually dividing.

:)

The variable m equals 1/3 for the equation 2 = 6m obtained by dividing both sides by 6.

The given equation is 2=6m.

m is the variable in the equation.

To determine the value of m in the equation 2 = 6m, we need to isolate the variable m.

Divide both sides of the equation by 6:

2/6 = (6m)/6

1/3 = m

Therefore, m equals 1/3.

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Answer:

The top-right graph.

Step-by-step explanation:

Because f(-2) = 0.

The graph which represents the non-linear function with power 1/3 is similar graph in right side of upper option. Thus, the option B is correct.

When the graph of the function represents the straight line, then it is called the linear function.

The graph of a function in which the power of variable is more than one is called the non-linear graph.

The function given in the problem is,

f(x)=∛(x+2)

It is a non-linear function. This function can be written as,

[tex]f(x)=(x+2)^\dfrac{1}{3}[/tex]

The graph of this function is attached below. This graph passes from the point (-2,0) and (0,1.26) and looks similar to the option B (right side of upper option).

Hence, the graph which represents the non-linear function with power 1/3 is similar graph in right side of upper option. Thus, the option B is correct.

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Answer:

it would be b

Answer:

B

Step-by-step explanation:

This quadratic factors.

x^2 - 15x + 56

= (x - 7)(x - 8)

x - 7 = 0

x = 7

=====

x - 8 = 0

x = 8

====

{7,8}

Answer:

Step-by-step explanation:

[tex]\log_ab=c\iff a^c=b\\\\Domain:\ x+2>0\to x>-2\\\\\log_3(x+2)-8=-2\qquad\text{add 8 to both sides}\\\\\log_3(x+2)=6\iff x+2=3^6\\\\x+2=729\qquad\text{subtract 2 from both sides}\\\\x=727\in D[/tex]

The answer is is x=727 ^^

Answer: 40 per square mile

Step-by-step explanation: 800/20

Answer:

1) y = 12

2) x = 4

3) w = -3

4) k = -35

Step-by-step explanation:

Answer:

Question 1: y = 12

Question 2: x = 4

Question 3: w = -3

Question 4: k = -35

Answer: [tex]tan(x)=\±\frac{3}{4}[/tex]

Step-by-step explanation:

You know that [tex]sin(x)=\frac{3}{5}[/tex] and you can identify that. Then:

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

[tex]sin^2(x)=\frac{9}{25}[/tex]

Remember that:

[tex]cos^2(x)=1-sin^2(x)[/tex]

Then [tex]cos^2(x)[/tex] is:

[tex]cos^2(x)=1-\frac{9}{25}\\\\cos^2(x)=\frac{16}{25}[/tex]

Apply square root to both sides to find cos(x):

[tex]\sqrt{cos^2(x)}=\±\sqrt{\frac{16}{25}}\\cos(x)=\±\frac{4}{5}[/tex]

Remember that:

[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

Then, this is:

[tex]tan(x)=\frac{\frac{3}{5}}{\±\frac{4}{5}}[/tex]

[tex]tan(x)=\±\frac{3}{4}[/tex]

Answer:

1/7

Step-by-step explanation:

Answer: -1/7

Step-by-step explanation: Since the fractions have the same denominator you can add them together without trying to have to change it

Answer: A) y = -4

Step-by-step explanation:

The midline is usually at y = 0.  In the given equation, the graph is shifted down 4 units so the new midline is at -4.

Answer:

The remainder is 0 ⇒ 3rd answer

Step-by-step explanation:

* In the synthetic calculation we use the coefficient of the dividend

  with the value of x when the divisor = 0

∵ x - 1 = 0 ⇒ add 1 to both sides

∴ x = 1  

Step 1 : Write down the coefficients of the f(x) , put x = 1 at the left  

                         1        1     0     -1     1     -1    

                                ________________

Step 2 : Bring down the first coefficient to the bottom row.

                        1         1      0    -1     1    -1    

                               ________________

                                   1

Step 3 : Multiply it by 1, and carry the result into the next column.

                       1         1      0    -1     1    -1    

                               ____ 1_________

                                  1  

Step 4 : Add down the column

                       1        1       0    -1     1    -1    

                                ____1__________

                                 1      1

Step 5 : Multiply it by 1, and carry the result into the next column

                       1        1      0     -1     1     -1    

                              _____1___1_______

                                 1       1

Step 6 : Add down the column

                      1         1       0    -1      1     -1    

                                ____1___1______

                                 1       1      0

Step 7 : Multiply it by 1, and carry the result into the next column

                    1        1       0    -1      1     -1    

                               ___1___1___0______

                              1      1      0

Step 8 : Add down the column

                    1         1     0      -1      1      -1  

                          _____1____1__0_____

                              1      1       0      1

Step 9 : Multiply it by 1, and carry the result into the next column

                  1         1     0      -1       1      -1  

                          ____1____1___0___1___

                            1     1        0      1        

Step 10 : Add down the column

                  1         1     0      -1       1      -1  

                          ____1____1___0___1___

                            1     1        0      1         0

∴ The quotient is (x³ + x² + 1 ) and the remainder is 0

* The remainder is 0

Answer:

B

Step-by-step explanation:

So, we know that this inequality has an "at most" in its phrase, therefore signifying the sign x ≤ 5. Since the x is in the left side without any negatives, so the arrow goes left, and the circle is filled. So, B.

Answer: Associative property of addition.

Step-by-step explanation:

The rule for the Associative property of addition is:

[tex]a + (b + c) = (a + b) + c[/tex]

Therefore, this property establishes that it does not matter how you group the numbers, the sum will not change.

You can observe that, in this case, the numbers of the given addition can be grouped as [tex]6 + (14 + 70)[/tex] or [tex](6 + 14) + 70[/tex], and the sum will be the same.

Then, you get:

[tex]6 + (14 + 70) = (6 + 14) + 70 = 20 + 70 = 90[/tex]

ANSWER

(f.g)(x)

EXPLANATION

From the table we can observe the following patterns:

f(-6)=12

g(-6)=-6

h(-6)=-72=12×-6

f(0)=3

g(0)=0

h(0)=0=3×0

f(6)=-6

g(6)=6

h(6)=-36=-6×6

Hence the h(x) is obtained by multiplying f(x) by g(x).

h(x)=(f.g)(x)

Answer:

- 13

Step-by-step explanation:

To evaluate h(j(2)) substitute x = 2 into j(x) then substitute the value obtained into h(x)

j(2) = - 2 × 2 = - 4, then

h(- 4) = (3 × - 4) - 1 = - 12 - 1 = - 13

Hence h(j(2)) = - 13

Answer:

14 five-dollar bills

Step-by-step explanation:

Let

x-----> the number of five-dollar bills

y----> the number of twenty-dollar bills

we know that

x+y=32 ----> y=32-x ----> equation A

5x+20y=430 ----> equation B

Substitute equation A in equation B and solve for x

5x+20(32-x)=430

5x+640-20x=430

20x-5x=640-430

15x=210

x=14 five-dollar bills

Find the value of y

y=32-x ----> y=32-14=18 twenty-dollar bills

Answer:

Option A

Step-by-step explanation:

The parent function [tex]y=x^2[/tex] has a minimum [tex](0,0)[/tex].

If we map [tex]x\mapsto x-1[/tex] we get [tex]y=(x-1)^2[/tex]. This is a horizontally translated copy of the parent function, so the minimum is still 0.

Then if we map [tex]f(x)\mapsto f(x)-4[/tex] we have [tex]y=(x-1)^2-4[/tex]

This is a vertical translation 4 units down, so now the minimum is -4, which appears in the equation.

The required equation which includes the minimum or maximum of f is given as f(x) = (x - 1)² - 4. Option A is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,

First of all, all the function mentioned does not have a maximum,  but have the same minimum, at (1, -4).
But, as of the appearance equation f(x) = (x - 1)² - 4 includes the minimum. because when terminating x it gives minimum y and when terminating it gives x minimum.

Thus, The required equation which includes the minimum or maximum of f is given as f(x) = (x - 1)² - 4. Option A is correct.

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Answer:

9

Step-by-step explanation:

Answer: D or 36 just answered on apex

Step-by-step explanation:

To find the constant in an equation with a graph, examine the graph's features such as slope, intercept, or specific data points and compare them with theoretical constants provided, like k1, k2, k3, k4, and K3.

The value of the constant in the equation being discussed is related to graphing functions and the characteristics of lines and curves on a graph. In general, when determining a constant from a graph in mathematics, it is essential to look at certain features such as the slope, the intercept, or specific data points depending on the context of the problem. For instance, if we are trying to find a constant of proportionality (k), we might use a linear fit of data points to determine the slope, which then gives us the value of k. Similarly, other constants may be deduced by comparing the theoretical values with the actual data points on the graph.

To determine the value of a constant such as k in a force (F) versus displacement (x) graph, one would label the transition region of the graph and use the given constants (e.g., k1, k2, k3, k4, K3) to measure the force. The slope (m) of the line on the graph is representative of how the value changes along the graph and is calculated using the change in y over the change in x. In situations where the graph does not display a constant force, the value may be represented by the area under the force versus distance graph.

(e) is the homogeneous mixture

Answer:

it is E

Step-by-step explanation:

Just finished the test

Answer:431⁄500

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\csc B=\dfrac{1}{\sin B}\\\\-1\leq\sin B\leq1,\ \text{therefore}\ \csc B\leq-1\ or\ \csc B\geq1\\\\-1.75\leq-1\\\\0.5\to \bold{ANSWER}\\\\1\geq1\\\\1.05\geq1[/tex]

By definition, the cosecant is the inverse of the sine:

[tex]\csc(x) = \dfrac{1}{\sin(x)}[/tex]

Since the sine is never more than 1, the cosecant can never be smaller than 1.

So, the only impossible option is 0.5.

Answer:

350

Step-by-step explanation:

Answer:

350

Step-by-step explanation:

First, do 7 x 5

7 x 5 is 35

Now just add a zero to the end to get 350

I hope this helps! :)

h= k/j

Multiply by j for the left and right hand side

(h)(j)= k/j(j)

Cross out j and j for the right hand side.

hj= k

answer is : k= hj

I think this is the answer

ANSWER

[tex]k = hj[/tex]

EXPLANATION

The given formula is:

[tex]h = \frac{k}{j} [/tex]

We want to solve this formula for k.

Let us multiply both sides by j.

[tex]h \times j = \frac{k}{j} \times j[/tex]

Cancel the common factors.

[tex]hj = k[/tex]

Or we rewrite to obtain,

[tex]k = hj[/tex]

k is now isolated on one side of the equation.

Answer:

y = -1/2 x + 1

Step-by-step explanation:

Lines that are perpendicular to each other have slopes that are negative reciprocals. You get the negative reciprocal of a number by flipping the fraction for the slope, then changing the positive/negative.

The lines are written in slope-intercept form, y = mx + b.

"x" and "y" are points on the line.

"m" is the slope.

"b" is the y-intercept.

In y = 2x + 8, the slope is 2. Find its negative reciprocal.

Write the slope as a fraction.

[tex]m=2=\frac{2}{1}[/tex]

Flip the fraction.

[tex]m=\frac{1}{2}[/tex]

Change the negative/positive.

[tex]m=-\frac{1}{2}[/tex]    This is the slope of the perpendicular line.

Now we need to find the y-intercept, "b", for our line. We know m = -1/2, and we know a random point (6, -2). Points are written (x, y), which mean x = 6 and y = -2. Substitute the values of the point and the slope into y = mx + b.

[tex]y = mx + b[/tex]

[tex]-2 = -\frac{1}{2}*6 + b[/tex]      Multiply (-1/2)(6) by combining into the numerator

[tex]-2 = -\frac{6*1}{2} + b[/tex]      Simplify numerator

[tex]-2 = -\frac{6}{2} + b[/tex]       Reduce fraction

[tex]-2 = -3 + b[/tex]         Isolate "b" now

[tex]-2 + 3 = -3 + b + 3[/tex]      Add 3 to both sides

[tex]1 = b[/tex]        Solved for "b"

[tex]b=1[/tex]         Write the variable on the left side for standard formatting

b = 1 and m = -1/2

Substitute them into slope-intercept form for the final answer.

y = -1/2 x + 1

To find the equation of a line perpendicular to a given line and passing through a specific point, use the negative reciprocal of the original line's slope. Applying this to the point-slope form of the line equation gives y = -(1/2)x + 1, which is the correct answer as per the given options.

The subject of the question is about writing the equation of a line that is perpendicular to another line, specifically y = 2x + 8, and passes through a specific point (6, -2). The concept involved here is the slope of the lines. The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. Since the slope of our given line is 2, the slope of the line that is perpendicular to this would be -1/2.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point through which the line passes, we can substitute m = -1/2 and (x1, y1) = (6, -2). Therefore, the equation of the line is y = -(1/2)x + 1.

The correct answer from the given options is (D) y = -(1/2)x + 1.

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Answer:

Step-by-step explanation:

The answer is 1.5 ft i just took the test

Answer:

The correct option is 4.

Step-by-step explanation:

The volume of a cylinder is

[tex]V=\pi r^2h[/tex]

where, r is radius of the base and h is height of the cylinder.

It is given that the radius of the cylindrical sandbox is 2 ft and the volume of cylindrical sandbox is 18.84.

[tex]18.84=(3.14)\times (2)^2\times h[/tex]        [tex][\because \pi=3.14][/tex]

[tex]18.84=(3.14)\times 4\times h[/tex]

[tex]18.84=12.56\times h[/tex]

[tex]\frac{18.84}{12.56}=h[/tex]

[tex]1.5=h[/tex]

The height of the sandbox is 1.5 ft. Therefore the correct option is 4.

Answer: $92.53

Step-by-step explanation:

95 x 0.026 = 2.47

95 - 2.47 = $92.53