A.)List the 4 steps outlined in the lesson on solving equations. (1 points)

B.)Solve each equation and show all work (3 points each)

1.) 5x + 7 = 3x + 21

2.) 3x - 2(5 - x) = -3(x - 10) + 3x

3.) 5(x + 1) = 3(2x + 3) + 5

Answer:

The answer is A I just looked it up on mathaway and it is never wrong

Step-by-step explanation:

Standard form always has the largest coefficients first

Answer:

A

Step-by-step explanation:

When putting polynomials into standard form, the highest degree goes first.

(for example 5x³ + x² + 8x + 9)

Answer:

The correct option would be D, f(x)=2^x-3

Step-by-step explanation:

You can immediatly cross out options A and B because it cannot be negative. If it was negative, the graph would be going the opposite direction, it would curve closer to the negative numbers that the positive. We can cross out C because if it was -2, then it would cross the y-axis at -1 rather than -2.

hope this helps :)

Answer:

x=6

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

To evaluate the surface integral [tex]\( \iint_S xy \, dS \)[/tex] over the triangular region with vertices[tex]\((1,0,0)\), \((0,8,0)\), and \((0,0,8)\):[/tex]

1. **Equation of the plane**:

  8x + y + z = 8.

2. **Parametrize the surface**:

 [tex]\[   \mathbf{r}(x, y) = (x, y, 8 - 8x - y).   \][/tex]

3. **Normal vector**:

  [tex]\[   \mathbf{N} = (8, 8, 1), \quad |\mathbf{N}| = \sqrt{129}.   \][/tex]

4. **Surface integral setup**:

  [tex]\[   \iint_D xy \sqrt{129} \, dA, \quad \text{with} \quad D: \int_0^1 \int_0^{8(1-x)} xy \, dy \, dx.   \][/tex]

5. **Evaluate the integral**:

[tex]\[   \sqrt{129} \int_0^1 32x (1-x)^2 \, dx = \frac{8 \sqrt{129}}{3}.   \][/tex]

Thus, the value of the surface integral [tex]\( \iint_S xy \, dS \) is \( \frac{8 \sqrt{129}}{3} \).[/tex]

To evaluate the surface integral [tex]\( \iint_S xy , dS )[/tex], where ( S ) is the triangular region with vertices (1, 0, 0) ,  (0, 8, 0) , and  (0, 0, 8) , we can follow these steps:

1. Determine the equation of the plane containing the triangle:

  The vertices of the triangle are (1, 0, 0), (0, 8, 0), and (0, 0, 8). The equation of the plane can be found using these points.

  The general form of a plane equation is (Ax + By + Cz = D).

  Substituting the points:

[tex]- For \((1, 0, 0)\): \(A(1) + B(0) + C(0) = D \rightarrow A = D\).[/tex]

 [tex]- For \((0, 8, 0)\): \(A(0) + B(8) + C(0) = D \rightarrow 8B = D \rightarrow B = \frac{D}{8}\).[/tex]

[tex]- For \((0, 0, 8)\): \(A(0) + B(0) + C(8) = D \rightarrow 8C = D \rightarrow C = \frac{D}{8}\).[/tex]

  So, (D = A), [tex]\(B = \frac{A}{8}\), and \(C = \frac{A}{8}\).[/tex]

  Using (A = 8) (chosen for simplicity):

  - (A = 8),

  - (B = 1),

  - (C = 1),

  - (D = 8).

  Thus, the plane equation is (8x + y + z = 8).

2. Parametrize the surface:

  We can use (x) and (y) as parameters. From the plane equation, we get (z = 8 - 8x - y).

  Let ( (x, y) ) be the parameters. The surface can be parametrized as:

 [tex]\[ \mathbf{r}(x, y) = (x, y, 8 - 8x - y). \][/tex]

3. Find the normal vector and its magnitude:

  The normal vector [tex]\( \mathbf{N} \)[/tex] can be found from the cross product of the partial derivatives of [tex]\(\mathbf{r}\)[/tex] with respect to (x) and (y).

[tex]\[ \mathbf{r}_x = \frac{\partial \mathbf{r}}{\partial x} = (1, 0, -8), \][/tex]

 [tex]\[ \mathbf{r}_y = \frac{\partial \mathbf{r}}{\partial y} = (0, 1, -1). \][/tex]

 [tex]\[ \mathbf{N} = \mathbf{r}_x \times \mathbf{r}_y = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & 0 & -8 \\ 0 & 1 & -1 \\ \end{vmatrix} = (8, 8, 1). \][/tex]

  The magnitude of [tex]\( \mathbf{N} \)[/tex] is:

[tex]\[ |\mathbf{N}| = \sqrt{8^2 + 8^2 + 1^2} = \sqrt{64 + 64 + 1} = \sqrt{129}. \][/tex]

4. Surface integral:

  The surface integral is given by:

[tex]\[ \iint_S xy \, dS = \iint_D xy |\mathbf{N}| \, dA, \][/tex]

  where (D) is the projection of (S) on the (xy)-plane.

  From the vertices, (D) is a triangular region with vertices (1,0), ((0,8), and (0,0).

5. Set up the integral in (xy) coordinates:

  We can describe (D) as:

[tex]\[ \iint_D xy \, \sqrt{129} \, dA. \][/tex]

  The bounds for (x) and (y) are:

[tex]\[ \int_0^1 \int_0^{8(1-x)} xy \, dy \, dx. \][/tex]

6. Evaluate the integral:

 [tex]\[ \sqrt{129} \int_0^1 \int_0^{8(1-x)} xy \, dy \, dx. \][/tex]

  Evaluate the inner integral with respect to (y):

[tex]\[ \int_0^{8(1-x)} xy \, dy = x \left[ \frac{y^2}{2} \right]_0^{8(1-x)} = x \left( \frac{(8(1-x))^2}{2} \right) = x \left( \frac{64(1-x)^2}{2} \right) = 32x (1-x)^2. \][/tex]

  So the integral becomes:

[tex]\[ \sqrt{129} \int_0^1 32x (1-x)^2 \, dx. \][/tex]

  Let ( u = 1-x ). Then ( du = -dx ), and the limits change from ( x = 0 ) to ( u = 1 ), and ( x = 1 ) to ( u = 0 ):

[tex]\[ \sqrt{129} \int_1^0 32(1-u) u^2 (-du) = \sqrt{129} \int_0^1 32(1-u) u^2 \, du. \][/tex]

  Expand and integrate:

 [tex]\[ \sqrt{129} \int_0^1 32 (u^2 - u^3) \, du = 32 \sqrt{129} \left[ \frac{u^3}{3} - \frac{u^4}{4} \right]_0^1 = 32 \sqrt{129} \left( \frac{1}{3} - \frac{1}{4} \right). \][/tex]

  Simplify:

 [tex]\[ 32 \sqrt{129} \left( \frac{4}{12} - \frac{3}{12} \right) = 32 \sqrt{129} \left( \frac{1}{12} \right) = \frac{32 \sqrt{129}}{12} = \frac{8 \sqrt{129}}{3}. \][/tex]

Thus, the value of the surface integral[tex]\( \iint_S xy \, dS \) is \( \frac{8 \sqrt{129}}{3} \).[/tex]

(1, 22), (3, 18), (5,14), (6, 13), (8,5)

(1, 23), (3, 18), (5,14), (6, 11), (8,7)

you plot there on a graph. do you know how to place on a graph?

if not, the line going up and down is the x-axis and the line going side to side is the y-axis,

for example (4,7) it would be (x,y)

i really hope this helps :)

Answer:

x-axis

Step-by-step explanation:

The asymptote is a straight line that the curve gets closer and closer to but never touches it.

The given exponential function is [tex]f(x)=3^x[/tex].

The given graph has a horizontal asymptote,

The equation of this horizontal asymptote is y=0.

This is also refers to as the x-axis.

Therefore the asymptote is the x-axis.

Answer:

The answer is 225

Step-by-step explanation:

Setup a ratio saying 150:2/3

Next divide 2/3 by 1 to see how many times it can go into it which is 1 1/2

After that multiply 1 1/2 by 150

Answer is 225.

If a yogurt is 150 calories per 2/3 cup, how many calories is a full cup?

If we know that 150 calories are in 2/3 of a cup of yogurt, we can find out how many calories are in a full cup. If there are 150 calories in 2/3 of a cup, let’s first find out how many calories are in 1/3 of a cup by dividing 150 by 2.

150 ÷ 2 = 75 calories per 1/3 of a cup.

Now, we can multiply 75 by 3 to find out how many calories are in a full cup of yogurt.

75 x 3 = 225 calories per 1 cup of yogurt.

Therefore, there are 225 calories in 1 full cup of yogurt.

Answer:

The measure of angle DEF is ∠DEF=80°

Step-by-step explanation:

we know that

The incenter is constructed by taking the intersection of the angle bisectors of the three vertices of the triangle

The triangle DEF is an isosceles triangle

∠EDF=∠EFD

so

In the triangle DHF

∠HDF=∠HFD

∠HDF+∠DHF+∠HFD=180°

substitute the value

2∠HDF+130°=180°

∠HDF=25°

therefore

∠EDF=2*25°=50°

In the triangle DEF

∠EDF+∠DEF+∠EFD=180°

∠EDF=∠EFD=50°

substitute

50°+∠DEF+50°=180°

∠DEF=80°

Answer:

The answer would be 80?

That is correct!

Step-by-step explanation:

Once Im done with the question Ill come back and make sure its correct!

Find the product of 7 and 2/3.  When multiplying fractions, first multiply the numerators, and then multiply the denominators.

7/1*2/3

7*2=14

1*3=3

14/3 cups of lemonade

Hope this helps!!

To find the total amount of lemonade consumed by 7 people drinking 2/3 cup each, calculate the amount per person, then multiply by the number of people for the total to get 14/3 or 4 2/3 as the total lemonade consumed.

Saul threw a party for 7 people. Each person drank 2/3 cup of lemonade.

To find the total amount of lemonade consumed:

Calculate the amount of lemonade each person drank: 2/3 cup/person.

Find the total amount for all 7 people: 7 people x 2/3 cup/person = 14/3 cups.

Therefore, the total amount of lemonade consumed is 14/3 or 4 2/3 cups

The critical value for a two-tailed test of h0: β1 = 0 at α = .05 in a simple regression with 22 observations is 4.35.

A critical value can be calculated for different types of hypothesis tests. The critical value of a particular test can be interpreted from the distribution of the test statistic and the significance level.

Test of significance of linear regression between x and y.

Null hypothesis: There is no significant linear relationship between x and y.

Alternative hypothesis: There is a significant linear relationship between x and y.

Test statistic:

F0 = Mean square due to regression/  mean squared error ~ F(1, n-2)

Critical value: [tex]F_{\alpha}(1, n-2) = F_{0.05}(1,20) = 4.35[/tex]

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Answer:

  60.65

Step-by-step explanation:

The Law of Cosines can help you figure this out. Call the given sides "a" and "b" and the given angle "C". Then the third side, "c" will satisfy the relation ...

  c² = a² + b² -2ab·cos(C)

  = 33² +37² -2·33·37·cos(120°) = 3679

  c = √3679 ≈ 60.65476 ≈ 60.65

The length of the third side is about 60.65 units.

Answer:

601 square inches

Step-by-step explanation:

The wrapping is needed to cover a cubed gift box that is 9 inches high is 616 sq inches.

Calculation:-

The area of gift wrapping needed is equal to the total surface area of the box.

area of a bow =115

 ∴ side of bow =[tex]\sqrt{115}[/tex]

                       = 10.72

total surface area = 115+115+10.72+10.72

                                  =616 sq ft.

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Answer:

15%

Step-by-step explanation:

The population proportion can be estimated as the sample proportion.

6 / 40 = 0.15

Approximately 15% of the computers have viruses.

Answer: Hence, there are 15% of computers have viruses.

Step-by-step explanation:

Since we have given that

Total computers in an office = 500

Number of computers to be inspected = 40

Number of computers had viruses = 6

We need to find the percentage of the computers in the building that have viruses.

So, Percentage of computers in the buildings have viruses is given by

[tex]\dfrac{6}{40}\times 100\\\\=\dfrac{600}{40}\\\\=15\%[/tex]

Hence, there are 15% of computers have viruses.

Answer:

b

Step-by-step explanation:

(-2x³ - 4x²+ 9x² + 18x - 19x - 38 + 40)

÷ (x + 2)

[-2x²(x+2) + 9x(x+2) - 19(x+2) + 40]

÷ (x+2)

-2x² + 9x - 19 + 40/(x+2)

Answer:

Your answers are correct.

Step-by-step explanation:

The equality will be true for odd multiples of π/4, so the last two choices will not show the expression to be not an identity.

Answer:

11. (r+9)(r+3)

12.(g-3)(g+3)

13.(p+3)(2p^2+3)

Answer:

The system that models the situation is:

[tex]\left \{{{2x + y = 24} \atop {2x - y = 12}} \right.[/tex]

The solution is:

(9, 6)

Step-by-step explanation:

We must write the equations as indicated in the problem.

The sum of twice a number and another number is 24

a number:  x

other number:  y

Then

[tex]2x + y = 24[/tex]

The difference of twice the first number and the other number is 12

first number: x

other number:  y

Then:

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

The system that models the situation is:

[tex]\left \{{{2x + y = 24} \atop {2x - y = 12}} \right.[/tex]

To solve the system we add both equations to find the value of x

[tex]2x + y = 24\\\\2x - y = 12[/tex]

---------------------

[tex]4x +0 = 36\\\\x=\frac{36}{4}\\\\x=9[/tex]

[tex]2(9) +y = 24\\\\y=24-18\\\\y=6[/tex]

The solution is:

(9, 6)

Answer:

-2

Step-by-step explanation:

5x+45=35

Next step--> subtract 45 from 35 to start to get x by itself

5x= -10

Next divide by 5 on both sides so x is by itself to get

x=.  -2

Answer:

x = - 2

Step-by-step explanation:

5x + 45 = 35

5x = 35 - 45

x = - 10

x = - 10 ÷ 5

x = - 2

Answer:

A

Step-by-step explanation:

Opposite angles of a parallelogram are equal, so z = 96.

Alternate interior angles are congruent, so x = 31.

Angles of a triangle add up to 180, so y = 53.

Based on the parallelogram shown above, the values of the variables are: x = 31°, y = 53°, z = 96°.

In Mathematics, a parallelogram is a type of quadrilateral and two-dimensional geometrical figure that is composed of two equal and parallel opposite sides.

According to the opposite angles theorem, the opposite angles of a parallelogram are always congruent or equal and as such, we have the following:

m∠z = 96°

Based on the alternate interior angles theorem, angles on opposite of a line are congruent;

x = 31°.

Based on angle sum property, we have the following supplementary angles;

x + y + z = 180

31° + y + 96° = 180°

y = 180° - 127°

y = 53°.

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Answer:

Step-by-step explanation:

Essentially, what you have is a fraction divided by a fraction.  The rule there is to bring up the bottom fraction and then flip it to multiply.  That would look like this:

[tex]\frac{b^4}{2a^2}[/tex]×[tex]\frac{a}{b^3}[/tex]

Now you can do some canceling out of like terms.  There is a b^3 in the denominator and a b^4 in the numerator.  You can take 3 b's out of 4, so the b^3 cancels completely out with the b^4, leaving only one b behind.  The a in the numerator cancels with one of the a's in the a^2, leaving one behind.  So the answer to this is:

[tex]\frac{b}{2a}[/tex]

Answer:

B. 3 spaces to the right and 4 spaces up

Step-by-step explanation:

With both coordinates positive, we know that this point (3, 4) is in Quadrant I.

B. 3 spaces to the right and 4 spaces up

  is the correct choice.

Answer:

-5

Step-by-step explanation:

Sometimes f(x) can be a little confusing. You never quite know where which number goes where.

Start with the first part

f(6) means that wherever you see an x on the right you put a 6.

So do this.

f(6) = (3/2)(6) +b =

equals what

(3/2) * 6 + b = 7    That's because f(6) = 7 Now just solve it

(18)/2 + b = 7

9 + b = 7

9 - 9 + b = 7 - 9

b = - 2

================

The entire equation is

y = (3/2)x - 2

===============

What happens when you are given

f(-2)

The - 2 means that wherever you see an x, let it be - 2

f(-2) = (3/2)(-2) - 2

f(-2) = -3 - 2

f(-2) = - 5

===============

You could think of f(x) being y. You will not go wrong doing that. y = f(x)

Answer:

False

Step-by-step explanation:

we know that

1 yard= 36 inches

To convert 360 inches to yards

Multiply

(360)*(1/36)=10 yards

therefore

You would use the ratio 1 yard over 36 inches

Answer:

false

Step-by-step explanation:

[tex]\displaystyle\int_2^8g(x)\,\mathrm dx=12[/tex]

[tex]\displaystyle\int_6^8g(x)\,\mathrm dx=-3[/tex]

Use the fact that integrals are additive on their intervals. Mathematically, if [tex]c\in[a,b][/tex], then

[tex]\displaystyle\int_a^bg(x)\,\mathrm dx=\int_a^cg(x)\,\mathrm dx+\int_c^bg(x)\,\mathrm dx[/tex]

So we have

[tex]\displaystyle2\int_2^6g(x)\,\mathrm dx=2\left(\int_2^8g(x)\,\mathrm dx-\int_6^8g(x)\,\mathrm dx\right)=2(12-(-3))=30[/tex]

The value of 2 times the integral from 2 to 6 of g(x) dx is 30.

The integral from 2 to 8 of g(x) dx = 12

The integral from 6 to 8 of g(x) dx = -3

We want to find:

2 times the integral from 2 to 6 of g(x) dx.

First, we'll use the properties of integrals:

The integral from 2 to 8 of g(x) dx = The integral from 2 to 6 of g(x) dx + The integral from 6 to 8 of g(x) dx.

We know that the integral from 2 to 8 of g(x) dx is 12, and the integral from 6 to 8 of g(x) dx is -3:

12 = The integral from 2 to 6 of g(x) dx - 3.

Next, we'll isolate the integral we're interested in:

The integral from 2 to 6 of g(x) dx = 12 + 3

= 15.

Finally, we'll multiply this result by 2:

2 * 15 = 30.

So, 2 times the integral from 2 to 6 of g(x) dx is 30. The correct answer is 30.

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Answer:

24 and 12

Step-by-step explanation:

s=2d

s+d+52+4(3)=100

Answer:

son is 24 years old and daughter is 12 years old.

Step-by-step explanation:

Let the age of son = x years and age of the daughter = y years.

Now for equations

" The son is twice as old as the daughter "

x = 2y -------(1)

"After 4 years sum of all their ages will be 100."

56 + (x+4) + (y+4) = 100

x + y + 64 = 100

x + y = 100 - 64 = 36 ----------(2)

Now we substitute the values of x from equation (1) to (2)

2y + y = 36

3y    = 36

y = 12

Now from equation (1)

x = 2 × 12

x = 24 years

Therefore, son is 24 years old and daughter is 12 years old.

Answer:

4x² + 22x − 1 = 0

Step-by-step explanation:

Start off with the standard formula to finding area with polynomials and quadratic functions.

(2x + 5)(2x + 6)

Work out like a normal binomial.

4 + 22x + 30 - 31

(You're subtracting 31 to take out the minimum of what the frame has to be)

4 + 22x - 1 = 0

Answer:

4x² + 22x − 1 = 0

Answer:

B, C

Step-by-step explanation:

x-intercepts are when y=0.  f(x) has two x-intercepts at (1, 0) and (5, 0).  g(x) also has two x-intercepts; (-3, 0) and (5, 0).  So the first one is false, and the second one is true.

The maximum value of f(x) is 2.  The maximum value of g(x) is 4.  So the third one is true.

The y-intercept is the value of y when x=0.  So the y-intercept of f(x) is -1, and the y-intercept of g(x) is 3.  So the fourth one is false.

The statement which is true are f(x)​ and ​g(x)​ have a common x-intercept (B) and the maximum value of ​g(x)​ is greater than the maximum value of ​f(x)​ (C).

The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the x-axis. The value of y is equal to zero at x-intercept.

The function f(x) shown in the graph has two x intercept (5,0) and (1,0). The x intercept of g(x) are (-3, 0) and (5, 0).

Similarly, the y-intercept is the point on the coordinate at which a line, curve or plane intersect with the y-axis. The value of x is equal to zero at y-intercept.

The function f(x) shown in the graph has one y intercept (0,-1). The y intercept of g(x) is (0, 3). Here the maximum value of f(x) is 2 while g(x) is 4.

Thus, the statement which is true are f(x)​ and ​g(x)​ have a common x-intercept (B) and the maximum value of ​g(x)​ is greater than the maximum value of ​f(x)​ (C).

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Answer:

45.6 degrees

Step-by-step explanation:

First of all this needs to be recognized as a right triangle problem.  The angle of depression is the angle outside the triangle that is complementary to the vertex angle (the angle at the top).  Geometrically, this angle is congruent to the base angle inside the triangle (NOT the right angle).  So we need to find the measure of the base angle to find the measure of the angle of depression since they are the same.  A 500 foot cable describes the length of the cable, which serves as our hypotenuse.  The 350 is the base length of the triangle.  What we have then is a reference angle (x), the hypotenuse (500) and the side adjacent to the angle (350).  The ratio that relates the angle to the hypotenuse and the adjacent side is the cosine.  Setting up to find our angle gives us this equation:

[tex]cos\theta=\frac{350}{500}[/tex]

You find missing angles on your calculator by hitting the 2nd button and then the trig identity you want.  We want cosine, so hit 2nd then cos and you'll get cos^-1(     on your screen.  After the parenthesis, enter your 500/350 and hit enter.  This will give you your angle measure of 45.6.  Oh yeah!!! And make sure your calculator is in degree mode for this one!

The angle of depression  from the top of a 500-foot cable that runs from a tower to a point 350 feet away is 45.6 degrees

The situation forms a right angle triangle.

The length of the cable is the hypotenuse of the triangle formed.

The distance from the tower is the adjacent side of the right angle triangle.

Therefore, using trigonometric ratio,

let

∅ = angle of depression

cos ∅ = adjacent / hypotenuse

cos ∅ = 350 / 500

∅ = cos⁻¹ 0.7

∅ = 45.5729959992

∅ = 45.6°

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Answer:

The length of the longer side is 28 meters

Step-by-step explanation:

we know that

In a parallelogram,  the intersecting diagonals bisect each other;

The supplementary angle of 60° is 120°.

see the attached figure to better understand the problem

Let

a ----> the length of the longer side

b ----> the length of the shorter side.

Apply the Law of Cosines to the lower triangle.

[tex]a^2 = 20^2 + 12^2 - 2(20)(12) cos(120\°)[/tex]

[tex]a^2 = 784[/tex]

[tex]a=28\ m[/tex]

therefore

The length of the longer side is 28 meters

Answer:

   5 inches wider

Step-by-step explanation:

The given area expression factors as ...

  x² +2x -15 = (x -3)(x +5)

Apparently, we're to assume that these factors represent length times width, and the factor x-3 corresponds to a length that is 3 inches shorter than the old length (x). Then the width is (x+5), which is 5 inches wider than the old length.

Answer:

5 in wider is right

Step-by-step explanation: