Solve the triangle using law of cosines. Round answer to the nearest tenth.

According to the diagram, angle JKL is

Adjacent angles are angles that share a common vertex and a common side, but do not overlap. In a trapezoid, adjacent angles can be any pair of angles that share a common vertex and a common side.

angle JKL and angle MKL are adjacent angels having same vertex at k

angle JKM = angle JKL  angle MKL

94 = angle JKL + 47

angle JKL = 94 - 47

angle JKL = 47

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The slope of the line containing (-1, 5) and (2, -4) will be negative 3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are (-1, 5) and (2, -4). Then the slope of the line is given as,

m = (5 + 4) / (- 1 - 2)

m = 9 / (-3)

m = - 3

The slope of the line containing (-1, 5) and (2, -4) will be negative 3.

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Answer:

Step-by-step explanation:

Straight line= 180 degrees

|_= 90 degrees

180-90=90

3s-2=52

2s+2=38

52+38=90

s=18

The vertical intercept of the graph is 100,000

A function whose value is a constant raised to the power of the argument, especially the function where the constant is e, is called an exponential function.

Given that, the population p of migrating butterflies satisfies the exponential function p = 100,000 (4/5)ⁿ, where n is the number of weeks,

So, we need to find the vertical intercept of the graph,

We know that, vertical intercept = intercept

To find the y-intercept of a line, we will put x = 0,

here x is n,

So, the y-intercept of the graph is = 100,000 (4/5)⁰ = 100,000×1 = 100,000

Therefore, the vertical intercept of the graph is 100,000

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The value of x is 5, while the value of y is 24

In order to get the value of x we would first have to find the value of y

The sum of angles on a straight line = 180

hence we would have:

5y + 2y + 12 = 180

7y = 180 - 12

7y = 168

y = 24 degrees

The angle that is made at R is 90 degrees

we would have

2y + 12 + 5x = 90

y = 24

2 * 24 + 12 + 5x = 90

60 + 5x = 90

5x = 90 - 60

5x = 30

x = 30 / 6

x = 5

Hence the value of x is 5

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The solution set for the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex] is (-4, -3) ∪ (-3, ∞).

What is inequality?

An inequality is a mathematical statement that describes a relationship between two values or expressions, where one is greater than, less than, or not equal to the other.

To solve the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex], we can use the concept of interval notation and test each interval to see if it satisfies the inequality. Here are the steps:

Find the critical points of the expression, which are the values that make the expression equal to zero. In this case, the critical points are -5, -4, and -3.

Use these critical points to divide the number line into four intervals: (-∞, -5), (-5, -4), (-4, -3), and (-3, ∞).

Test a value in each interval to see if the inequality is true or false. We can use the sign of the expression to determine this:

For x < -5, all three factors are negative, so the product is negative. Therefore, this interval does not satisfy the inequality.

For -5 < x < -4, the first factor is positive and the other two factors are negative. The product is therefore negative. This interval does not satisfy the inequality.

For -4 < x < -3, the first and third factors are positive and the second factor is negative. The product is therefore positive. This interval satisfies the inequality.

For x > -3, all three factors are positive, so the product is positive. Therefore, this interval satisfies the inequality.

Write the solution set using interval notation. We have found that the solution set is (-4, -3) union ( -3, ∞).

Therefore, the solution set for the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex] is (-4, -3) ∪ (-3, ∞).

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Answer:

Step-by-step explanation:

The sum of interior angles in a quadrilateral is 360°, from the picture we have a 90°, 160° and 70°.

so

take off from 360° the know angles and we will find the angle "?"

360 - 90 - 160 - 70 =

40° (your answer)

Answer:

Step-by-step explanation:

y = 2x - 6

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

Explanation:

If we plugged x = 4 into the expression, then we'll have 0 in the denominator. This causes a division by zero error.

Luckily the numerator factors to (x-4)(x-2)^2. This is found by using the Rational Root Theorem, along with either synthetic division or polynomial long division. I'll skip these steps unless you need me to write them out.

Once we know the numerator factors this way, we can then write the following steps:

[tex]L = \displaystyle \lim_{\text{x}\to4}\frac{\text{x}^3-8\text{x}^2+20\text{x}-16}{\text{x}-4}\\\\\\L = \displaystyle \lim_{\text{x}\to4}\frac{(\text{x}-4)(\text{x}-2)^2}{\text{x}-4}\\\\\\L = \displaystyle \lim_{\text{x}\to4}(\text{x}-2)^2\\\\\\L = (4-2)^2\\\\\\L = 4\\\\\\[/tex]

Therefore,

[tex]\displaystyle \lim_{\text{x}\to4}\frac{\text{x}^3-8\text{x}^2+20\text{x}-16}{\text{x}-4}=4\\\\\\[/tex]

You can use graphing software like Desmos or GeoGebra to confirm the answer is correct. WolframAlpha is another good choice.

Suppose that the functions q and r are defined as q(x) = 2x+2 and r(x) = x² +1, the function  (r * q)(4) =(q * r)(4) and they are equal to 170.

Which is the commutative law?

commutative law, in mathematics, is either of two laws relating to number operations of addition and multiplication that are stated symbolically as a + b = b + a and ab = ba. From these laws, it follows that any finite sum or product is unaltered by reordering its terms or factors.

Given the following functions:

q(x) = 2x+2

r(x) = x² +1

Taking the product

q(x)*r(x) = (2x + 2)(x² +1)

Note that according to the communatative law, (r * q)(x) = (q * r)(x)

(r * q)(4) =(q * r)(4)  = (2(4)+2)((4)² +1)

(r * q)(4) =(q * r)(4)  = (10)(16+1)

(r * q)(4) =(q * r)(4)= 10(17)

(r * q)(4) =(q * r)(4) = 170

Hence, the function  (r * q)(4) =(q * r)(4) and they are equal to 170.

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The numeric value of the marginal revenue at 33 units will be $336.

The sum of the units sold times the price per unit is the revenue. Multiply the output level by the pricing function to get the revenue function.

Revenue function is R(q) = - 8q ^ 2 + 600q

Differentiate with respect to q

R^ prime (q) = - 8(2q) + 600(1)

R' (q)=-16q+600 ...(1)

substitute q = 33 in equation

MR(113) = - 8(33) + 600

=-264 + 600

MR (113)= $336 per unit

The marginal revenue is $336.

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Answer:

35y^(10)z^(4)

Step-by-step explanation:

Solution Given:

(-5y^(4)z)(-7y^(6)z³)

Here while opening bracket

If their is like terms they can be multiplied ,divided,subtracted as well as added.

So

Here

opening bracket and keeping in serially

-5*-7*y^(4)*y^(6)*z*z^(3)

here if their is like terms their power is added.

And solving remaining one.

35y^(4+6)z^(1+3)

Here -5*-7=35

Again

Solving it.

35y^(10)z^(4)

Answer:

[tex]35y^{10}z^4[/tex]

Step-by-step explanation:

Given expression:

[tex](-5y^4z)(-7y^6z^3)[/tex]

Apply the rule:  (-a) · (-b) = ab

[tex]\implies 5y^4z \cdot 7y^6z^3[/tex]

Multiply the numbers:  5 · 7 = 35

[tex]\implies 35y^4zy^6z^3[/tex]

Collect like terms:

[tex]\implies 35y^4y^6z^3z[/tex]

[tex]\textsf{Apply exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 35y^{(4+6)}z^{(3+1)}[/tex]

Simplify the exponents:

[tex]\implies 35y^{10}z^4[/tex]

The angle measure m<T is equivalent to 78 degrees

Similar triangles are triangles that have similar sides and angles.

From the given triangle

<A = <R

<B = <S

<C = <T

Since the sum of angle in a triangle is 180 degrees, hence;

<A + <B + <T = 180

24 + 78 + <T = 180

102 + <T = 180

<T = 180 - 102
<T = 78 degrees

Hence the measure of m<T from the triangle is 78 degrees

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The conclusion is that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

The test statistic for this hypothesis test can be calculated as follows:

t = (μ1 - μ2) / sqrt(s1^2 / n1 + s2^2 / n2)

Plugging in the values, we get:

t = (1090 - 485) / sqrt(403^2 / 5 + 382^2 / 8) = 4.36

Next, we need to find the critical value for a two-tailed test at a significance level of 0.10 using a t-distribution table or using a t-distribution calculator.

Using a t-distribution table or calculator, we find the critical value for a two-tailed test at a significance level of 0.10 and df = 9.57 is ±1.833.

Since the calculated t-value (4.36) is greater than the critical value (1.833), we reject the null hypothesis and conclude that there is evidence to suggest that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

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The surface area of a horse with the mass  is 4.5 x 10^6 square centimeters,

From the question, we have the following parameters that can be used in our computation:

S = 10mi

Using the above as a guide, we have the following:

m =  4.5 x 10^5 grams

substitute the known values in the above equation, so, we have the following representation

S =10 * 4.5 x 10^5

So, we have

S =4.5 x 10^6

Hence, the surfave area is 4.5 x 10^6

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Answer:

30 mm

Step-by-step explanation:

just add the length of each side together

Note that the pattern in the table is that the perimeter of a square with area x is four times the square root of x. We can express this relationship as:

f(x) = 4 * √(x)

We know that the area of a square is calculated as the square of its side length, which means that the side length of a square with area x is the square root of x. Therefore, the length of the side of the square can be expressed as:

s = √(x)

To calculate the perimeter of the square, we simply add up the lengths of all four sides:

P = 4s = 4 * √(x)

So, the function f(x) in the table represents the perimeter of a square with area x, which can be calculated using the equation:

f(x) = 4 * √(x)

To verify this, let us take these examples:

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Mortgage B requires $27,336.60 more interest than mortgage A. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

There are four fundamental mathematical operations that can be used to express any real number; these are referred to as "arithmetic operations." The four operations are multiplication, division, addition, and subtraction.

We are given the principal amount as $80,000.

So, interest on Mortgage A = Total amount payable - principal amount

Interest = $110,158.20 - $80,000

Interest = $30,158.20

Similarly, interest on Mortgage B = Total amount payable - principal amount

So,

Interest = $137,494.80 - $80,000

Interest = $57,494.80

So, difference in interest = $57,494.80 - $30,158.20 = $27,336.60

Hence, mortgage B requires $27,336.60 more interest than mortgage A.

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The required angle of the elevation at point C to A is given as ∠C = 31°.

The angle of elevation is the angle between a horizontal line of sight and a line of sight that is directed upwards to an object or point. In other words, it is the angle between the horizontal and an observer's line of sight to an object above the observer

Here,
A figure has been shown, Consider triangle ABC, where ∠A = 59, ∠B = 90°,
Since the sum of the angle in the triangle should be 180°.
∠A + ∠B + ∠C = 180
∠C + 90 + 59 = 180
∠C = 90 - 59
∠C = 31°

Thus, the required angle of the elevation at point C to A is given as ∠C = 31°.

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Answer:

1.02n or 51/50n

Step-by-step explanation:

n + 2% raise = 1.02n and 50/51n

Answer:

There are 12 desktop computers and 20 laptop computers.

Step-by-step explanation:

32:2=16

8:2=4

16-4=12

16+4=20

Answer:

Step-by-step explanation:

Range: the difference between the highest and lowest values

Heights:

130

142

142

143

144

145

147

147

149

150

151

153

154

154

158

161

162

Formula to find the range

R= H-L

R = range

H = highest value

L = lowest value

    R = 160 - 130.

The range is 30.

The statement regarding the census in this problem is classified as a True statement.

Population: Collection or set of individuals or objects or events whose properties will be studied.

Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.

A Census is when a group of the population is chosen, that is, a sample is chosen, hence the statement for this problem is true.

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Answer: A) 6

Step-by-step explanation:

This is geometry. The two angles are corresponding angles, because they are both cut by the same **transversal line**. When that occurs, corresponding angles are created.

now importantly: corresponding angles are equal to each other, or **congruent**. Knowing this, we can set them equal to each other.

17x+11=19x-1

Solve...

11=2x-1

12=2x

x=6

hope this helps

MM

Answer: x=56

Step-by-step explanation: Question 2 shows a right angle that is equal to 90 degrees. Since you are already given 34, you just need to subtract 90-34.

Question 4 shows an 180 degree angle and so you need to do the same thing; 180-124

Answer:

Step-by-step explanation:

A) In a geometric sequence, t_(1)=625 and the common ratio is r=(1)/(5). For what value of n is t_(n)=(1)/(25)?

Step 1: Write the formula for the nth term

The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.

Step 2: Substitute the given values into the formula

t_n = 625 * (1/5)^(n-1)

Step 3: Solve for n when t_n = (1/25)

(1/25) = 625 * (1/5)^(n-1)

(1/25) / 625 = (1/5)^(n-1)

(1/5)^(n-1) = (1/25) / 625

(n-1) = log base (1/5) of ((1/25) / 625)

Step 4: Solve for n

n = 1 + log base (1/5) of ((1/25) / 625)

The value of n is the number of terms that have passed when t_n = (1/25).

B) (2)/(5),(3)/(6),(4)/(7),(5)/(8),...

Step 1: Determine the type of sequence

A sequence is an arithmetic sequence if the difference between any two consecutive terms is constant. Since this sequence does not have a constant difference, it is not an arithmetic sequence.

A sequence is a geometric sequence if the ratio between any two consecutive terms is constant. We can see that the ratio between any two consecutive terms is constant, so this sequence is a geometric sequence.

Step 2: Find the common ratio

To find the common ratio, we can divide any two consecutive terms. For example, the common ratio is (3/6) / (2/5) = (3/2) / (6/5) = 5/6.

Step 3: Write the formula for the nth term

The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.

Step 4: Substitute the given values into the formula

To use this formula, we need to know the value of t_1. We are given t_1 = (2/5), so:

t_n = (2/5) * (5/6)^(n-1)

This is the formula for the nth term of the sequence (2)/(5),(3)/(6),(4)/(7),(5)/(8),...

Using the equation of the arithmetic sequence given, the first four terms are 59, 52, 45 and 38 respectively

In the sequence given, the progression is an arithmetic progression since it increases by a common difference.

The first term of the sequence is 59 while the common difference is -7.

A = 59 - 7(n - 1)

n = 1

a = 59 - 7(1 - 1)

a = 59

n = 2

a = 59 - 7(2 - 1)

a = 52

n = 3

a = 59 - 7(3 - 1)

a = 45

n = 4

a = 59 - 7(4 - 1)

a = 38

The terms are 59, 52, 45 and 38

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Translation:  Find the first four terms of the sequence given the following

Answer:

He can eat 6 pies in 198 seconds.

Step-by-step explanation:

Divide

132÷4=33

Divide

198÷33=6 pies in 198 seconds