Which expression has a base with an exponent of 4?

The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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We will investigate the application of mixed fractions with multiplication operator.

Terrell's snack shack consumes certain number of ketchup bottles:

The shack also consumes mustard. However, the number of bottles of mustard are expressed as fraction of the number of ketchup bottles consumed as follows:

We can express the number of mustard bottles consumed as follows:

We will convert the mixed fraction in the numerator as improper fraction as follows:

Next convert the division operator into a multiplication operator by reciprocating the denominator as follows:

Now completely express the number or mustard bottles:

Answer:

∠J = 115

∠N  = 65

∠M = 50

∠K = 130

Step-by-step explanation:

Sum of all the angles = 360

2x + 15 + x + 15 +x + 3x - 20 = 360

Combine like terms

2x + x + x + 3x + 15 + 15 - 20 = 360

               7x + 10 = 360

                      7x  = 360 - 10

                     7x = 350

                     x = 350/7

x = 50

∠J = 2x + 15 = 2*50 + 15 = 100+15 = 115

∠N = x +15 = 50 +15 = 65

∠M = x = 50

∠K = 3x - 20 = 3*50 - 20 = 150 - 20 = 130

The length of the fencing needed for the dog run will be 76 feet

The measure of the size of any object or the distance between the two endpoints will be termed the length.

Given that:-

Area of Dog Run = 240

Length of Dog Run = 30

The solution will be done as below:-

Width of Dog Run = 30 - x

Area of Dog Run:  30 * (30 - x) = 240

240 / 30 = 30 - x

8 = 30 - x

x = 24

Width of Dog Run = 8

How many feet of fencing will George need for the dog run?

Perimeter of Dog Run = 2Length + 2Width

Perimeter of Dog Run = (2 * 30) + (2 * 8)

Perimeter of Dog Run = 60 + 16

The perimeter of Dog Run = 76

Therefore the length of the fencing needed for the dog run will be 76 feet

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Answer:

C. 76 feet

Step-by-step explanation:

windows

The length of the field is greater than the width by the expression \((14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).\)

1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)

2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).

3. To find the difference between the length and width, we subtract the width from the length: (\(14x - 3x^2 + 2y) - (5x - 7x^2 + 7y\)).

4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)

5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)

6. Simplifying further, we add the coefficients of like terms:\((7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).\)

7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)

8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)

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The percentage of oil changes that take less than 60 minutes is 97.5% (rounded to the nearest tenth of a percent). Your answer: 97.5%.

To find the percentage of oil changes that take less than 60 minutes, we will use the information about the normal distribution provided:
Mean (µ) = 40 minutes
Standard Deviation (σ) = 10 minutes
X = 60 minutes.

Calculate the Z-score.
Z = (X - µ) / σ
Z = (60 - 40) / 10
Z = 20 / 10
Z = 2
Use a Z-table to find the percentage of oil changes taking less than 60 minutes.
Looking up a Z-score of 2 in the Z-table, we find that the area to the left of Z = 2 (which represents the percentage of oil changes taking less than 60 minutes) is approximately 0.9772, or 97.72%.

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Answer:

30 inches

Step-by-step explanation:

2 boards that were each 6 inches long

The key word is each because this represents multiplication

2 × 6 = 12

1 board that was 18 inches long

1 × 18 = 18

Now we add the two numbers together to find the total length of boards needed

12 + 18

30

Don't forget to include units in your final answer

30 inches

Answer:

4-. c = ±26

Step-by-step explanation:

c² = a² + b²

c² = 10² + 24²

c² = 100 + 576

c² = 676

√c² = √676

c = ± 26

Step-by-step explanation:

very unique nice speech for a number lol

Answer:

the volume of the toy house is 66cm3

Answer:

It contains 0 or 2 triangles.

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

((-10*15)-(-15*10))+(5–2)

((-10*15)-(-150))+(5–2)

((-10*15)+150)+(5–2)

(-150+150)+(5–2)

0+(5–2)

0+3

3

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

We need the graph of the function:

Comparing with the slope-intercept line function:

Where the slope is m and the y-intercept (the point where the line crosses the y-axis) is b.

In this case:

m=4 means that each step the graph advances 4 in y (vertical direction) and 1 in x (horizontal direction)

and b=0 means that the graph crosses the y-axis at y=0 --> the origin

The graph is as follows:

The required angle is 24.5°.

Given is a right triangle with perpendicular side 16 and the base = 35 we need to find an acute angle in it,

To find the acute angle in a right triangle given the lengths of the perpendicular side and the base, you can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the perpendicular side to the length of the base side.

In this case, the perpendicular side is 16 and the base is 35.

Let's denote the acute angle as θ.

Using the tangent function, we can set up the equation:

tan(θ) = perpendicular side / base

tan(θ) = 16 / 35

To find the value of θ, we can take the inverse tangent of both sides:

θ = tan⁻¹(16 / 35)

θ = 24.5°

Hence the required angle is 24.5°.

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Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Answer:

35 miles per hour is the answer

When the 2 graphs are the same. It'll be infinitely many solutions.

System Equations are to find the intercepts of graphs so just think that when 2 graphs are same, that means they both intercept each others infinitely.

So the answer is clearly C.

The number 100 would land in column 2

Given that we have the array of numbers

The length of each row in the array is 7

Dividing 100 by 7, we have

100/7 = 14 Remainder 2

This means that

Column = 2

In (a), we have

100/7 = 14 Remainder 2

This means that

Row = 14

Here, we have

The length of each row in the array is 6

Dividing 100 by 6, we have

100/6 = 16 Remainder 3

So, the location of 100 in rows of 6 numbers is row 16 and column 3

Let the length of each row in the array be n

Dividing 100 by n, we have

100/n = q Remainder r

This means that the location of 100 in rows of n numbers is row q and column r

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Answer:

Step-by-step explanation:

Given a + 1/a = 3, find its square:

Now find the square of (a - 1/a):

Substitute the value from the first square:

Since (a - 1/a)² = 5, its square root is:

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.

Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.

We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:

3 ml x 3 ml x 3 ml

-------- = ----------

728 ml total, 8 ml overall

If we cross-multiply, we obtain:

8(x) = 3(728)

To find x, we use the formula x = 3(728)/8 = 273

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

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273 milliliters of compound A are needed to make 728 milliliters of the drug.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.

Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:

3 : (3+5) or 3:8

This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.

To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:

3/8 = x/728

where x represents the amount of compound A needed.

To solve for x, we can cross-multiply:

8x = 3*728

8x = 2184

x = 273

Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.

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The differential of the function, f(x)=x^5 -8x is

df(x) = (5x^4 - 8) dx. That is dy = (5x^4 - 8) dx

From the question, we are to determine the differential of the given function

To find the differential of the function f(x), we use the formula:

df(x) = f'(x) dx

where f'(x) is the derivative of f(x) with respect to x, and dx is an infinitesimal change in x.

First, we need to find the derivative of f(x):

f'(x) = 5x^4 - 8

Now we can substitute this into the differential formula:

df(x) = (5x^4 - 8) dx

Hence, the differential of the function is

df(x) = (5x^4 - 8) dx

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The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

k = 6 and k = -4

Step-by-step explanation:

To determine two integral values of k (integer values of k) for which the roots of the quadratic equation kx² - 5x - 1 = 0 will be rational, we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -1) and q must be a factor of the leading coefficient (in this case, k).

Possible p-values:

Possible q-values:

Therefore, all the possible values of p/q are:

\(\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 1}{\pm k}=\pm 1, \pm \dfrac{1}{k}\)

To find the integral values of k, we need to check the possible combinations of factors. Substitute each possible rational root into the function:

\(\begin{aligned} x=1 \implies k(1)^2-5(1)-1 &= 0 \\k-6 &= 0 \\k&=6\end{aligned}\)

\(\begin{aligned} x=-1 \implies k(-1)^2-5(-1)-1 &= 0 \\k+4 &= 0 \\k&=-4\end{aligned}\)

\(\begin{aligned} x=\dfrac{1}{k} \implies k\left(\dfrac{1}{k} \right)^2-5\left(\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}-\dfrac{5}{k}-1 &= 0 \\-\dfrac{4}{k}&=1\\k&=-4\end{aligned}\)

\(\begin{aligned} x=-\dfrac{1}{k} \implies k\left(-\dfrac{1}{k} \right)^2-5\left(-\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}+\dfrac{5}{k}-1 &= 0 \\\dfrac{6}{k}&=1\\k&=6\end{aligned}\)

Therefore, the two integral values of k for which the roots of the equation kx² - 5x - 1 = 0 will be rational are k = 6 and k = -4.

Note:

If k = 6, the roots are 1 and -1/6.

If k = -4, the roots are -1 and -1/4.

Answer:

y = 2x^2 + 1

Step-by-step explanation:

Honestly I'm not too sure as I can only see one pair of coordinates, but if the next one is (2, 9) then this equation is right

To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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The answer is 6

If you divide 18 by 3 it's 6

The complition of flow chart is congruent by angle angle side property.

Two triangles are considered to be congruent if the three sides and the three angles of both the angles are equal in any orientation.

The three sides are equal Since, Two angles are the same and a corresponding side are the same (ASA: angle, side, angle).

We are given that;

BD bisects angle ABC

The figure ABCD

Now, In first column;

Statement is BD bisects angle ABC

Reason given

In second row first box: the statement is angle ABD congruent to angle DBC

reason is A segment bisects and divides a segment into two congruent segments.

In the second row second box statement is angleADB congruent to angle BDC

reason is given

In the second row second box;

statement is side AB congruent to side BC

reason is given

Therefore, by two pairs of congruent angles and one pair of congruent sides that are not between the angles, it is proven the triangles congruent by AAS.

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The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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