What is the change in elevation from -6 km to -14 km?

The measure of angle x in the right triangle is approximately 14.6 degrees.

The figure in the image is that of two right angles.

First, we determine the hypotenuse of the left-right angle.

Angle θ = 30 degrees

Adjacent to angle θ = 10 cm

Hypotenuse = ?

Using the trigonometric ratio.

cosine = adjacent / hypotenuse

cos( 30 ) = 10 / hypotenuse

hypotenuse = 10 / cos( 30 )

hypotenuse = \(\frac{20\sqrt{3} }{3}\)

Using the hypotenuse to solve for x in the adjoining right triangle:

Angle x =?

Adjacent to angle x = \(\frac{20\sqrt{3} }{3}\)

Opposite to angle x = 3

Using the trigonometric ratio.

tan( x ) = opposite / adjacent

tan( x ) = 3 / \(\frac{20\sqrt{3} }{3}\)

tan (x ) = \(\frac{3\sqrt{3} }{20}\)

Take the tan inverse

x = tan⁻¹(  \(\frac{3\sqrt{3} }{20}\) )

x = 14.6 degrees

Therefore, angle x measures 14.6 degrees.

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Answer:

- 11 < x < 8

Step-by-step explanation:

inequalities of the type | x | < a have solutions of the form

- a < x < a

then

| 2x + 3 | < 19

- 19 < 2x + 3 < 19 ( subtract 3 from each interval )

- 22 < 2x < 16 ( divide each interval by 2 )

- 11 < x < 8

The equation of parabola becomes y = -2/25(x-3)^2 + 4.

According to the statement

we have given a graph and from this graph we have to find the equation of parabola in the general form.

So,

we know that the equation of parabola in general form is

y = a(x-h)^2 +k - (1)

From the graph we have:

a point on the graph is (x,y) = (-2,2)

the vertex of the graph is (h,k) = (3,4)

Now, substitute these values in the equation number (1)

Then

y = a(x-h)^2 +k

2 = a(-2-3)^2 +4

2 = a(-5)^2 +4

2 = a(25) +4

25a = -2

a = -2/25.

Now put a = -2/25 and (h,k) = (3,4) in the equation(1).

Then

the equation of parabola becomes y = -2/25(x-3)^2 + 4

So, The equation of parabola becomes y = -2/25(x-3)^2 + 4.

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Answer:

Jada saved $40, Lin saved $60 and Elena saves $20

Step-by-step explanation:

Let the amount saved by Jada be x

Let the amount saved by Lin be y

Let the amount saved by Elena be z

If together they saved $120, then x+y+z = $120 ......... 1

If Jada saved $20 less than Lin, then x = y- 20 .....2

If Lin saved 3 times as much money as Elena, then y = 3z ...... 3

From equation 3, z = y/3 ....... 4

substitute equation 2 and 4 into 1;

x+y+z = $120

(y- 20)+ y + y/3 = 120

2y + y/3 - 20 = 120

2y + y/3 = 120+20

2y + y/3 = 140

multiply through by 3

6y + y = 420

7y = 420

divided through by 7

7y/7 = 420/7

y = 60

Since y = 3z

60 = 3z

z = 60/3

z = 20

From equation 2, x = y- 20

x = 60-20

x = 40

Hence Jada saved $40, Lin saved $60 and Elena saves $20

Answer:

(3x-1)

Step-by-step explanation:

\(6x^2+x-1\)

We need to find two numbers that multiply to get -6 and have a sum of 1...

3(-2)=-6

3+(-2)=3-2=1

We can use this information to split x into 3x and -2x...

\(6x^2+3x-2x-1\)

Factor the first and second half of the expression separately:

\(3x(2x+1)-1(2x+1)\)

Since both 3x and -1 are being multiplied by 2x+1, we can combine them to get...

\((2x+1)(3x-1)\)

Therefore the missing factor is...

(3x-1)

Answer:

pleas learn subtraction

Step-by-step explanation:

so it can make you better in math

Answer:

\(\large \boxed{\mathrm{Option \ A}}\)

Step-by-step explanation:

\({\mathrm{view \ attachment}}\)

Answer:

65+115=180

11x+ 48=180

Step-by-step explanation:

Answer:

Range could be 205000 to 214999. Any number in this range, when rounded to two signnificant digits will yield 210000.

Answer:

C) The sum of the first 2 terms after the fourth term.

Answer:

Letter C: 1188

Step-by-step explanation:

$1000 plus the interest earned the first year = 1000 x 9%

Calculated like this $1000  x ( 1.09  interest) = 1090

then

that amount 1090 plus the interest earned the second year on that already compounded amount:

1090 x 9% interest =

Calculated like this 1090  x ( 1.09  interest) = 1188.1

rounding down to 1188 to match the answers

The cost per minute of the plan is given by the following option:

$0.30 per minute.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The cost per minute of the plan is the slope of the function. From the table, we have that when the number of minutes increases by 5, the cost increases by $1.5, hence the cost per minute is given as follows:

1.5/5 = $0.30 per minute.

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Answer:

D

Step-by-step explanation:

Answer:

x<3

Step-by-step explanation:

4x<12

x<3

So Giselle worked as a blacksmith for 18 hours last week.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). Each part of the equation can contain variables, constants, and mathematical operations (such as addition, subtraction, multiplication, and division). The variables in an equation represent unknown quantities that we are trying to solve for, while the constants are fixed values.

Here,

Let x be the number of hours Giselle worked as a carpenter, and y be the number of hours she worked as a blacksmith. We know that:

Giselle earns $20 per hour as a carpenter, so her earnings from that job are 20x dollars.

Giselle earns $25 per hour as a blacksmith, so her earnings from that job are 25y dollars.

Giselle worked a total of 30 hours, so x + y = 30.

Giselle earned a total of $690, so 20x + 25y = 690.

We can use these equations to solve for x and y. One way to do this is to solve the first equation for y in terms of x, and substitute that expression for y in the second equation:

x + y = 30

y = 30 - x

20x + 25y = 690

20x + 25(30 - x) = 690

20x + 750 - 25x = 690

-5x = -60

x = 12

So Giselle worked as a carpenter for 12 hours last week. To find the number of hours she worked as a blacksmith, we can substitute x = 12 into the equation y = 30 - x:

y = 30 - x

y = 30 - 12

y = 18

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Answer:

The solution to both lines would be (0,4)

Answer:

Yes-

Step-by-step explanation:

It repeats .121212 infinitely... I assume. You didn't say if it repeated or not.

Answer:

Yes

Step-by-step explanation:

Every repeating decimal satisfies a linear equation with integer coefficients, and those equations have solutions that are always rational numbers.

Therefore, every repeating decimal is a rational number.

The probability that a point chosen at random on the segment satisfies the inequality x≤5 is 0.5.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is used in various fields, including mathematics, statistics, physics, and finance, among others.

Here,

The segment has a length of 8 units and starts at x = 1 and ends at x = 9. The portion of the segment where x ≤ 5 has a length of 4 units. Thus, the probability that a point chosen at random on the segment satisfies the inequality x ≤ 5 is:

Probability = Length of portion where x ≤ 5 / Total length of the segment

Probability = 4 / 8

Probability = 0.5 or 50%

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Complete question:

Find the probability that a point chosen at random on the segment satisfies the inequality: x≤5.

Answer:

8.8 feet per second

Step-by-step explanation:

1 mile = 5280 feet

3600 seconds = 1 hour

6 mph = 5280(6)/3600 = 528/60 8.8 feet per second

The expression for the function h(x) is h(x) = (x - 4)^2 + 2

The equation of the function f(x) is given as:

f(x) = x^2

From the graph, we have the following observations:

This translation is represented by

(x, y) = (x - 4, y + 2)

So, we have:

h(x) = (x - 4)^2 + 2

Hence, the expression for the function h(x) is h(x) = (x - 4)^2 + 2

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It looks like the recursive sequence is

\(a_n = \dfrac{a_{n-1}}2\)

By substitution, we have

\(a_{n-1} =\dfrac{a_{n-2}}2 \implies a_n = \dfrac{a_{n-2}}{2^2}\)

\(a_{n-2} = \dfrac{a_{n-3}}2 \implies a_n = \dfrac{a_{n-3}}{2^3}\)

\(a_{n-3} = \dfrac{a_{n-4}}2 \implies a_n = \dfrac{a_{n-4}}{2^4}\)

and so on, down to

\(a_n = \dfrac{a_1}{2^{n-1}}}\)

Given that \(a_1=64\), it follows that the 7th term in the sequence is

\(a_7 = \dfrac{64}{2^{7-1}} = \dfrac{64}{2^6} = \dfrac{64}{64} = \boxed{1}\)

The solutions to \((x+5)^(3/2) = (x-1)^3\)are x ≈ -4.65 and x ≈ 0.51, obtained by graphing the functions in Desmos.

To solve \((x+5)^(3/2) = (x-1)^3\) by graphing, we can plot both sides of the equation on the same graph using a tool like Desmos. The solution will be where the two curves intersect.

First, we can simplify the equation by cubing both sides:

\((x+5)^3 = (x-1)^6\)

Next, we can plot \(y1 = (x+5)^3 and y2 = (x-1)^6\) on the same graph in Desmos. The intersection of the two curves will give us the solutions to the equation.

By examining the graph, we can see that there are two real solutions: x ≈ -4.65 and x ≈ 0.51.

Therefore, the solutions to the equation \((x+5)^(3/2) = (x-1)^3\) are x ≈ -4.65 and x ≈ 0.51.

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To determine if the proportion of rats developing tumors has increased, we can perform a hypothesis test using the 0.05 level of significance.

Null Hypothesis (H₀): The proportion of rats developing tumors is equal to or less than 25%.

Alternative Hypothesis (H₁): The proportion of rats developing tumors is greater than 25%.

Since we are testing for an increase, it is a one-tailed test.

Next, we need to calculate the test statistic and compare it to the critical value. We will use the z-test for proportions.

The observed proportion of rats developing tumors in the repeated experiment is 16/48 = 0.333.

The expected proportion based on the null hypothesis is 25% or 0.25.

The sample size is 48.

The test statistic (z-score) can be calculated using the formula:

z = (p - P) / sqrt(P*(1-P)/n)

where p is the observed proportion, P is the expected proportion, and n is the sample size.

Substituting the values:

z = (0.333 - 0.25) / sqrt(0.25*(1-0.25)/48)

z = 0.083 / sqrt(0.25*0.75/48)

z ≈ 0.083 / 0.069

z ≈ 1.203

Looking up the critical value for a one-tailed test with a significance level of 0.05, we find that the critical value is approximately 1.645.

Since the calculated test statistic (1.203) is less than the critical value (1.645), we fail to reject the null hypothesis.

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Answer:

Step-by-step explanation:

The answer is Samples. A sample is a random selection of members of a population. It is a smaller group drawn from the people with the entire population's characteristics.

I hope I have helped.

Answer:

\(\frac{55}{16}\)

Step-by-step explanation:

\(550 \div 160\)

\( = \frac{550}{160} \)

\( = \bold{ \frac{55}{16} }\)

Answer:

550 DIVIDED BY 160 =3.4375

It would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

Dennis' reasoning is incorrect.

To determine the rate of picking apples per minute, Dennis correctly divided the total number of apples (24) by the time it took (6 minutes), resulting in 4 apples per minute. However, his approach to calculating the number of apples that could be picked in 8 minutes is flawed.

Dennis multiplied the rate of picking apples per minute (4 apples) by the given time (8 minutes), assuming that the rate remains constant. This approach would be valid if the rate of picking apples per minute were constant, but in this scenario, it is not necessarily the case.

The rate of picking apples could vary depending on factors such as fatigue, efficiency, or other variables. Therefore, it is not accurate to assume that the rate of picking apples per minute remains the same over a longer duration of time.

To determine the number of apples that could be picked in 8 minutes, it would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

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answer:

・x = 50

・y = 61

step-by-step explanation:

・first things you should know —

y + 8 + 2x + 11 = 180 ( supplementary angles equal to 180° )

・five sides add up to 540° ( pentagon! )

・therefore:

108 + 125 + 98 + 98 + 2x + 11 = 540

440 + 2x = 540

2x = 100

・x = 50

use what you know and plug in ;

y + 8 + 2x + 11 = 180

y + 8 + 2(50) + 11 = 180

y + 119 = 180

・y = 61

・you can always plug in or substitute to check your answers.ᐟ

Answer:

y = - 2x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =

with (x₁, y₁ ) = (4, - 6) and (x₂, y₂ ) = (0, 2 )

m =  =  =  = - 2

The line crosses the x- axis at (0, 2 ) ⇒ c = 2

y = - 2x + 2 ← equation of line

Answer:

672 had dark hair, 592 had blond hair, and 48 had red hair

Step-by-step explanation:

To solve this problem, we need to first find the total number of people for each hair color based on the given ratio.

Let's start by finding the common factor that we can use to scale the ratio up to the total number of people, which is 1,312:

42 + 37 + 3 = 82

We can then divide 1,312 by 82 to get the scaling factor:

1,312 ÷ 82 = 16

This means that for every 16 people, there are 42 with dark hair, 37 with blond hair, and 3 with red hair.

To find the actual number of people with each hair color in the town meeting, we can multiply the scaling factor by the number of people for each hair color in the ratio:

Dark-haired people: 42 × 16 = 672

Blond-haired people: 37 × 16 = 592

Red-haired people: 3 × 16 = 48

Therefore, there are 672 people with dark hair, 592 people with blond hair, and 48 people with red hair at the town meeting.

Answer:

A. The shape has perpendicular but not parallel lines.

Step-by-step explanation:

The shape is a right triangle, which has a 90 degree angle. This means that two of the sides are perpendicular because they meet each other at a right angle. None of the lines are parallel because if any of the sides were to never meet, there would not be a closed shape.