Find the length of the third side. If necessary, write in simplest radical form.
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2

By differentiation rules, the expression for the derivative of the function h(x) = u(x)^v(x), where u(x) = x² + 4 and v(x) = 5 · x is h'(x) = [(x² + 4)^(5 · x)] · [[(5 · x) / (x² + 4)] · (2 · x) + ㏑ (x² + 4) · 5].

In this question we find a differentiation rule for a function of the form h(x) = u(x)^v(x). Herein we find a function whose components are u(x) = x² + 4 and v(x) = 5 · x. First, determine the derivatives of u(x) and v(x):

u'(x) = 2 · x, v'(x) = 5

Second, substitute in the expression of the differentiation rule:

h'(x) = [u(x)^v(x)] · [[v(x) / u(x)] · u'(x) + ㏑ [u(x)] · v'(x)]

h'(x) = [(x² + 4)^(5 · x)] · [[(5 · x) / (x² + 4)] · (2 · x) + ㏑ (x² + 4) · 5]

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Answer:

Step-by-step explanation:

Answer:

70°

Step-by-step explanation:

Because line segment OB and OC are both straight lines, then the measure of angle fromed by this two segments is the same in different locations.

Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.

To determine which package is the better buy, we need to compare the cost per hook for each package.

For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:

Cost per hook = $9.95 / 25 = $0.398

Rounding to the nearest cent, the cost per hook is $0.40.

For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:

Cost per hook = $13.99 / 40 = $0.3498

Rounding to the nearest cent, the cost per hook is $0.35.

Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.

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the area of the region of points satisfying the inequalities x ≤ 0, y ≤ 0, and y ≥ |x + 4| − 5 is 12.5 square units.

With the help of a linear equation, we know that 182 gallons of water would be used to wash 14 loads.

So, gallons of water used to wash 14 loads are:

Therefore, with the help of a linear equation, we know that 182 gallons of water would be used to wash 14 loads.

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Answer:

170,700 words

Explanation:

Taking into account the table, if the size is 5.5 in x 6.5 in, the number of words that fit on this paper size is 300. Therefore, there will be an average of 300 words on each page. Then, if the book will have 569 pages, we can calculate the number of words of the story as:

569 x 300 = 170,700

So, the story will have 170,700 words.

According to the information we can infer that the parallel line would be AD or CF. Additionally, the perpendicular lines would be CB or FE.

To identify the parallel lines we must look at the figure and find the lines that have the same direction as the line BE and that would never intersect with the segment BE, according to the above, we can infer that the parallel lines would be:

On the other hand, the lines perpendicular to CF would be CB or FE because they make 90° angles with segment CF. Additionally, the face that would be parallel to ABC is DEF.

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Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

\(\\ \rm\rightarrowtail \dfrac{-6}{7}\div (\dfrac{-3}{8})\)

\(\\ \rm\rightarrowtail \dfrac{-6}{7}\times \dfrac{8}{-3}\)

\(\\ \rm\rightarrowtail \dfrac{-2}{7}(8)\)

\(\\ \rm\rightarrowtail -16/7\)

\(\\ \rm\rightarrowtail -2\dfrac{2}{7}\)

Answer:

7 1/2

Step-by-step explanation:

3/10x25

Answer:

Is this a workbook question?

Step-by-step explanation:

For me to help, I need a picture of the grid.

Answer:

x+2=1

Step-by-step explanation:

It is x=2=1

Answer:

The degrees of freedom is 6 for the chi square independence test.

Step-by-step explanation:

This is test hypothesis of independence. The test statistic under H0 is

χ²= ∑ (O - E)²/ E

where O is the observed and E is the expected frequency

which  has an approximate chi square distribution with ( r-1) (c-1) degrees of freedom, where r= rows and c= columns.

Here there are 4 rows and 3 columns

Hence the degrees of freedom will be

( 4-1) ( 3-1)= 3*2= 6

Answer:

C

Step-by-step explanation:

Sorry for the late response, but it's here if anyone else has this question later.

Answer: 7 x 551=3857 r  3

Step-by-step explanation:

Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.

According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.

Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.

Interest = Principal * Rate

= $13,250.00 * 0.10358

≈ $1,370.56

Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.

Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.

Calculating the interest with a credit score of 680:

Interest = Principal * Rate

= $13,250.00 * 0.09132

≈ $1,210.57

Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.

Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

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Answer:

=

You is welcome

Answer:

less than or equal

Step-by-step explanation:

I can put the actual inequality sign but the inequality is less than or equal to... if the sentence say no more than, then it would have to be less than or equal to.

f(4)=9*4-2 =34 & g(4)= -2*4 =-8 then,

f(4)- g(4) = 34+8= 42

Based on the mathematical problem given where 2/5 subtracts (-4/15) the solution would be 2/3

In order to be able to subtract fractions, they need to have the same base. If fractions have different basis, then use their lowest common multiple as the base and then convert the numerator.

When subtracting 2/5 - (-4/15), use the lowest common multiple of 15:
= 2/5 - (-4/15)

= 6 / 15 - (- 4/15)

= 6/15 + 4/15

= 10/15

= 2/3

In conclusion, the solution is 2/3 and it cannot be a mixed number or an improper fraction.

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Answer:

Divide them by 100 or use fraction

Answer:

D.

Step-by-step explanation:

Given: Dimensions of a rectangular prism are \(7.5\,\,inches,3\,\,inches\,,\,11.5\,\,inches\)

To find: total surface area of the rectangular prism in square inches

Solution:

Length of the rectangular prism (l) = 7.5 inches

Breadth of the rectangular prism (b) = 3 inches

Height of the rectangular prism (h) = 11.5 inches

Total surface area of the rectangular prism = 2(lb+bh+hl)

= \(2(7.5\times3+3\times11.5+11.5\times7.5 )\)

\(2(7.5\times3+3\times11.5+11.5\times7.5 )=2(22.5+34.5+86.25)\\=2(143.25)\\=286.5\,\,square \,\,inches\)

So, option D is correct

Answer:

D! I got it correcttt

Step-by-step explanation:

The point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0.

To graph the equation 2x + 3y = 6, we can rewrite it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Starting with the given equation, we isolate y to one side:

3y = -2x + 6

y = (-2/3)x + 2

Now, we have the equation in slope-intercept form, y = (-2/3)x + 2. The slope is -2/3, and the y-intercept is (0, 2).

To find the point where the graph intersects the x-axis, we need to determine the coordinates where y is equal to zero. This occurs when the line crosses the x-axis.

Setting y = 0 in the equation, we have:

0 = (-2/3)x + 2

(-2/3)x = -2

x = (-2)(-3/2) = 3

Therefore, the point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0, indicating the point of intersection with the x-axis on the graph.

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Answer:

Constant of variation = 5, y = 5x

Step-by-step explanation:

Answer:

1712

Step-by-step explanation:

Given arithmetic sequence is: -16,2,20

Here, a = - 16, d = 2 - (-16) = 2+ 16 = 18

n = 97, \( a_{97}=?\)

\(\because a_n = a + (n-1)d\\\\

\therefore a_{97}= - 16 + (97-1)\times 18\\\\

\therefore a_{97}= - 16 + 96\times 18\\\\

\therefore a_{97}= - 16 + 1728\\\\

\therefore a_{97}=1,712\\\\\)

Answer:

1712

Step-by-step explanation:

Formula of the sequence:

\(a_{n}=18n-34\\a_{97}=18(97)-34\\a_{97}=1712\)

So 1712 is the 97th term

Answer: $309

Step-by-step explanation:

The total earnings for Week 1 is \(75(5)+130=\$505\).

The total earnings for Week 2 is \(82(5)+115=\$ 525\).

Thus, the total earnings over both weeks is \(505+525=\$1030\).

30% of this is saved, which is equal to \((1030)(0.3)=\$ 309\).

[~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T by substituting the propositional variables.

A truth table is a table used to determine the truth values of a compound proposition, which is a logical statement made up of simpler propositions using logical operators such as "and" (represented by "&"), "or" (represented by "V"), "not" (represented by "~"), conditional (represented by "⊃"), and biconditional (represented by "≡").

Let's substitute the given truth values for the propositional variables in the given statement:

[~F & (F V F)] ≡ (T ⊃ F)

Using the truth table for conjunction (represented by "&") and disjunction (represented by "V"), we can simplify the left-hand side of the equivalence:

[T & F] ≡ (T ⊃ F)

Using the truth table for conditional (represented by "⊃"), we can simplify the right-hand side of the equivalence:

F ≡ F

Since both sides of the equivalence have the same truth value, the statement is true.

Therefore, [~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T.

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The correct answer is Option C. The graph represents the function f (x) = StartFraction 1 Over x EndFraction minus 1 is On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 0.

On a coordinate plane, the graph of a hyperbola is shown.

In quadrant 1, one curve opens up and to the right, while in quadrant 3, the other curve opens down and to the left.

The vertical asymptote is at x = -1, and the horizontal asymptote is at y = 0. This hyperbola is symmetrical across both the x and y axes.

The function f(x) = 1/x - 1 has a vertical asymptote at x = 0 because the denominator approaches zero as x approaches zero.

A fraction with a denominator of zero cannot exist.

The horizontal asymptote of this function is y = -1 because as x approaches infinity or negative infinity, f(x) approaches -1.

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