The sum of the measures of angle LMN and angle NMP is 180 degrees

The values of the unknown angles are ∠1 = 92°, ∠2 = 24°, ∠3 = 64°, ∠4 = 35°, ∠5 = 81°

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal). For example, in the below-given figure, angle p and angle w are the corresponding angles.

∠1 + 88 = 180°( angles on a straight line)

∠1 = 180 - 88 which is 92°

∠3 = 64°( corresponding angles are equal)

∠2 + ∠1 + ∠3 = 180( sum of angles in a triangle)

∠2 + 92° + 64° = 180

∠2 = 180 - 92 - 64

∠2 = 24°

∠4 + 81 + ∠3 = 180 ( angles on a straight line)

∠4 + 81 + 64 = 180

∠4 = 180 - 64 -81

∠4 = 35°

∠5 = 81°( alternate angles are equal)

In conclusion the values of ∠1, ∠2, ∠3, ∠4, ∠5 are 92°, 24°, 64°, 35° and 81° respectively.

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Solution

- The x-intercept is the value of x when y = 0 while the y-intercept is the value of y when x = 0.

- Thus, we have that

Final Answer

The x-intercepts are -6 and 6

The y-intercept is -36

The  expression represents the total surface area of the prism is

2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

The term "TSA" stands for "Total Surface Area" of a prism. The Total Surface Area represents the  sum of the areas of all the faces (including the bases) of the prism.

for the rectangular prism, the Total Surface Area can be calculated using the formula:

TSA = 2lw + 2lh + 2wh

where

l = 5

w = 4

h = 7

plugging in the values gives

TSA = 2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

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Answer:

54

Step-by-step explanation:

Angle 2 and Angle 3 are vertical angles

Vertical angles are congruent ( equal to each other )

So if angle 2 = 54 then angle 3 also equals 54

Answer:

∠3 = 54°

Step-by-step explanation:

54° and ∠3 are vertical angles, which means they are equal .

54° = ∠3

Answer:

27 Nickels

Step-by-step explanation:

Divide 1.35 by 0.05

= 27

If it's a decimal round to the nearest tenth then the value οf x is 4/3.

In mathematics, a prοpοrtiοn is an equatiοn that relates twο ratiοs. It is expressed in the fοrm οf a/b = c/d, where a, b, c, and d are numbers οr quantities.

In a prοpοrtiοn, the crοss-prοducts are equal, meaning that the prοduct οf the numeratοr οf the first ratiο and the denοminatοr οf the secοnd ratiο is equal tο the prοduct οf the denοminatοr οf the first ratiο and the numeratοr οf the secοnd ratiο.

the given prοblem can be sοlved by using ratiοs οf the cοrrespοnding sides.

we knοw that, the ratiο οf cοrrespοnding sides is equal.

sο, we have :

\($\frac{8}{x+2} = \frac{12}{5}\)

8 × 5 =  12 × (x+2)

40   = 12x + 24

12x  = 40 - 24

= 16

∴ x = 16/12 = 4/3

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Answer: 2⁴

Step-by-step explanation:

The factors of 16 are 1, 2, 4, 8, and 16. The prime factors of 16 as a product can be written as 2 × 2 × 2 x 2 or 2^4, where 2 is the prime number.

The equation of the line is x + 3y = 2

Linear equations are equations that have constant average rates of change.

The given parameters are

Slope, m = -1/3

Points (x, y) = (1, 1/3)

A linear equation is represented as

y = slope * (x - x₁) + y₁

Where

(x₁, y₁) = (1, 1/3)

Substitute (x₁, y₁) = (1, 1/3) and Slope, m = -1/3 in the equation y = slope * (x - x₁) + y₁

So, we have

y = -1/3* (x - 1) + 1/3

Multiply through by 4

So, we have

3y = -(x - 1) + 1

Remove the brackets

3y = -x + 1 + 1

So, we have

x + 3y = 2

Hence. the linear equation is x + 3y = 2

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(a) G'(a) = 2x - 3

(passing through (0, 3)) y1(x) = -3

(passing through (4, 7)) y2(x) = 5

b) The illustration of the graph is defined below.

In calculus, finding the derivative of a function is an important tool to understand the behavior of a curve at a specific point. One application of this concept is determining the equation of the tangent line to a curve at a given point. In this problem, we will use the derivative of a quadratic function to find the equations of tangent lines to the curve y = x² − 3x + 3 at the points (0, 3) and (4, 7).

To begin, we need to find the derivative of G(x) = x² − 3x + 3. Using the power rule, we have:

G'(x) = 2x - 3

Next, we can use this derivative to find the slope of the tangent line to the curve y = x² − 3x + 3 at any given point (a, G(a)). At the point (0, 3), we have a = 0, so the slope of the tangent line is:

G'(0) = 2(0) - 3 = -3

Using the point-slope equation of a line, we can find the equation of the tangent line passing through (0, 3). The equation of the tangent line is:

y - 3 = -3(x - 0)

Simplifying, we get:

y = -3x + 3

Similarly, at the point (4, 7), we have a = 4, so the slope of the tangent line is:

G'(4) = 2(4) - 3 = 5

Using the point-slope equation again, we can find the equation of the tangent line passing through (4, 7). The equation of the tangent line is:

y - 7 = 5(x - 4)

Simplifying, we get:

y = 5x - 13

To graph these tangent lines on the same screen as the curve y = x² − 3x + 3, we can plot the curve and the two tangent lines using a graphing calculator or software. The graph should show the curve as a parabola and the tangent lines as straight lines intersecting the curve at the points (0, 3) and (4, 7), respectively.

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Answer:

The total amount of fluids infused per day is 3,120 ml.

Step-by-step explanation:

Given that a patient is receiving a normal saline solution, infusing continuously at 80 ml / hr, and a tube feeding formula, Glucerna, infusing continuously at 50 ml / hr, to determine what is the total amount of fluids infused per day the following calculation must be done:

(80 x 24) + (50 x 24) = X

1,920 + 1,200 = X

3.120 = X

Therefore, the total amount of fluids infused per day is 3,120 ml.

Answer:

7⁻²=\(\frac{1}{49}\)

3⁻⁴ \(=\frac{1}{81}\)

9⁰=1

11⁻¹=\(\frac{1}{11}\)

Answer:

Step-by-step explanation:

We observe the pattern:

It can be put as:

or

The nth term is going to be:

The sum of the 31 terms will be:

or

Use the formula for sum of the first n squares:

The sum N equals:

And the value of N/31 is:

Answer:

17.1

Step-by-step explanation

a^2+b^2=c^2

2^2 + 17^2 = c^2

4 + 289 = c^2

293 = c^2

square root of 293 or 17.1

The correct answer is Part 1: The 99% confidence interval for the population proportion is approximately (0.4716, 0.5416).Part 2: With 99% confidence, the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

Part 1:

To construct a 99% confidence interval for the population proportion, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

where the margin of error is determined by the level of confidence and the standard error.

First, let's calculate the sample proportion:

Sample Proportion = (Number of adults who say they have started paying bills online) / (Total number of adults surveyed)

Sample Proportion = 1436 / 2837 ≈ 0.5066 (rounded to four decimal places)

Next, we need to calculate the standard statistics error, which is the measure of the variability in the sample proportion:

Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)

Standard Error = sqrt((0.5066 * (1 - 0.5066)) / 2837) ≈ 0.0136 (rounded to four decimal places)

Now, we can calculate the margin of error:

Margin of Error = Critical Value * Standard Error

The critical value is based on the desired confidence level. For a 99% confidence level, the critical value is approximately 2.576 (obtained from a standard normal distribution table).

Margin of Error = 2.576 * 0.0136 ≈ 0.0350 (rounded to four decimal places)

Finally, we can construct the confidence interval:

Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.5066 ± 0.0350

Confidence Interval ≈ (0.4716, 0.5416) (rounded to four decimal places)

Part 2:

The correct interpretation is:

C. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

This means that we are 99% confident that the true proportion of adults who have started paying bills online falls within the range of 0.4716 to 0.5416. The survey results suggest that approximately 47.16% to 54.16% of the population of adults have started paying bills online in the last year.

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Collin's gross salary, after the 7% raise, for each 2-week pay period, will be approximately $1,159.17.

To calculate Collin's gross salary after the 7% raise for each 2-week pay period, we need to find the raise amount and add it to his current gross salary.

Collin's current gross salary is $1,083.34.

To find the raise amount, we multiply his current gross salary by 7% (or 0.07):

Raise amount = $1,083.34 \(\times\) 0.07

= $75.8338 (rounded to two decimal places)

Now, we add the raise amount to his current gross salary to find the new gross salary:

New gross salary = $1,083.34 + $75.8338 = $1,159.1738 (rounded to two decimal places)

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Step-by-step explanation:

1.20+0.49+3.15

=4.84

change received=5.00-4.84

=0.16

=16p

Answer:

1 ticket - $4.25

5 tickets - $21.25

Step-by-step explanation:

12.75/3=4.25 which is one ticket then take the price of one ticket and multiply it by 5, 4.25*5=21.25.

Answer:

17

Step-by-step explanation:

ABC, which is 9z - 1, and CBD, which is 6z + 58, make up ABD, which is a total of 87 degrees.

in order to find the measurement of ABC, you first need to solve for z.

since ABC and CBD make up ABD, add those measurements and set them equal to 87, which is the measure of ABD.

9z - 1 + 6z + 58 = 87

combine like terms starting with the z terms. (it doesn't matter which like terms you combine first)

9z - 1 + 6z + 58 = 87 ⇒ 15z - 1 + 58 = 87

combine the next set of like terms.

15z - 1 + 58 = 87 ⇒ 15z + 57 = 87

subtract 57 from both sides of the equation. it'll cancel itself out on the left, leaving you with 15z = 30 after subtracting 57 from 87.

divide both sides of the equation by 15.

15z/15 = 30/15 ⇒ z = 2

now, plug in 2 for z in each of your equations for the measurements of ABC and CBD.

ABC = 9z - 1 ⇒ 9(2) - 1 ⇒ 18 - 1 ⇒ 17

CBD = 6z + 58 ⇒ 6(2) + 58 ⇒ 12 + 58 ⇒ 70

now, your measurements are

ABD: 87

ABC: 17

CBD: 70

check your work by adding the measurements of ABC and CBD and setting them equal to ABD, or 87.

17 + 70 = 87

87 = 87

since both sides of the equation are equal to 87, you know that your measurements are correct.

therefore, the measure of ABC is 17 degrees.

The equation that best describes the relation is y = -x+1 ( optionD)

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Taking x(0,1) and y ( 1,0)

therefore the slope of the line

= 0-1/1-0

= -1/1 = -1

the equation a line is given as

y-y1 = m(x-x1)

= y-1 = -1( x - 0)

= y-1 = -x

y = -x +1

therefore the equation that describe relation is y = 1-x or y = -x+1

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The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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If the 3 sides of a triangle are a, b, c, then

Then the triangle is a right-angled triangle

Then the triangle is an acute angled-triangle

Note that c is the longest side

Let us check our sides

That means 145 > 121

The triangle is an acute angled-triangle

Answer:

A. 0.0746

Step-by-step explanation:

Because it is in the thousandths place

A. True.

In a two-column proof, the left column consists of statements, which are the facts or assumptions that lead to the proof of the theorem, while the right column consists of the reasons or justifications that explain how each statement logically follows from the previous one. Therefore, the left column states your reasons is a true statement.

The answer to the student's question is True. In a two-column proof, the left column contains the statements (steps) and the right column contains the corresponding reasons (justifications).

The answer to the question, 'True or false? In a two-column proof, the left column states your reasons', is A. True.

A two-column proof is organized into two columns. The left column contains the 'Statements' and the right column contains the corresponding 'Reasons'. The 'Statements' are the steps that lead to the conclusion of the proof, while the 'Reasons' justify each of those steps according to rules or laws of mathematics.

For example, if we want to prove that the opposite angles of a parallelogram are equal. The left column (Statements) could contain the first step 'ABCD is a parallelogram' and the right column (Reasons) would give the explanation 'Given'. Therefore, in a two-column proof, the left column does represent statements, not reasons.

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Answer:

5pi/12

105 degrees

Step-by-step explanation:

I can help with the first 2 too many answers in one will get my answer deleted

7pi/12  x 180/pi

7x15=105

Hopes this helps please mark brainliest

Answer:

864 cubic meters

Step-by-step explanation:

Rectangular prism = 5x9x12=540

Triangular prism = 1/2(9)(6)(12)=324

540+324=864 cubic meters

Answer:

$448 million

Step-by-step explanation:

When it is 2011, t=11, so

\(w=236(1.06)^{11} \approx 448\)

Answer:

24

Step-by-step explanation:

area of a triangle = 1/2 ( base length * height )

given base length : 6

given height : 8

area of triangle = 1/2(8*6)

==> multiply 8 and 6

area of triangle = 1/2(48)

==> multiply 1/2 and 48

area of triangle = 24 square units