What is the solution to the system of equations?
5x – 4y = 6
-5x + 4y = -10
O (4,4)
0 (-2,-5)
O infinitely many solutions
O no solution

Answers

Answer 1

Hey there! I'm happy to help!

We have a 5x is one equation and a -5x in another equation. We can combine the two equations to cancel out the x and then solve! This is called solving by elimination.

5x-4y=6

+

-5x+4y=-10

0= -4

Since we lost our x and y while solving, there cannot be any solution.

Therefore, the answer is no solution.

Have a wonderful day!


Related Questions

The following sample contains the scores of 6 students selected at random in Mathematics and English. Use the scores in English as the dependent variable Y.

Mathematics score (X) 70 92 80 74 65 83
English score 74 84 63 87 78 90

Σx =464 Σy=476 Σx^2= 36354 Σy^2=38254 Σxy= 36926

Find the sample coefficient of determination and interpret.

a. 0.0575 and prediction accuracy is 5.75%
b. 0.2397 and prediction accuracy is 23.97%
c. 0.0575 and prediction accuracy is 94.25%
d. 0.2397 and prediction accuracy is 76.03%

Answers

Answer:

d the answer is d

Step-by-step explanation:

The length of a rectangle is twice its width. If the perimeter of the rectangle is 30m, find its area.

Answers

Answer:

If the perimeter of the rectangle is 30cm , find its area. W=5 FOR THE WIDTH. 5*10=50 FOR THE AREA.

Step-by-step explanation:

The area of the Rectangle is 50 sq.m

What is the formula of Area of Rectangle?

The area of rectangle for a rectangle of length L and width W is given by

                                              A =  L* W

It is measured in square units.

Let the length of the rectangle be L

The width of the rectangle is W

The length of a rectangle is twice its width

L = 2W

Perimeter of the Rectangle is 2( Length + Width)

30 = 2 (L +W)

15 = L + W

15 = 2W +W

15 = 3W

W = 5m

L = 10m

The area of the rectangle is Length * Width

Area = 10 *5

Area = 50 sq.m

To know more about Area of Rectangle

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What is 5% added to $194?

Answers

Answer:

203.7

Step-by-step explanation:

5% of 194 added to 194 =

= 5% * 194 + 194

= 0.05 * 194 + 194

= 9.7 + 194

= 203.7

Find the product of the roots of the equation
xl-5x - 36 = 0

Answers

Answer:

Step-by-step explanation:

Hello, I assume that you mean

[tex]x^2-5x-36[/tex]

The product is -36.

[tex]x_1 \text{ and } x_2 \text{ are the two roots, we can write}\\\\(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2[/tex]

So in this example, it means that the sum is 5 and the product is -36.

Thank you

simplify theta(sin theta) ²/2tan theta​

Answers

Step-by-step explanation:

When θ is very small, θ ≈ sin θ ≈ tan θ.

θ (sin θ)² / (2 tan θ)

θ³ / (2θ)

θ² / 2

Please answer! I am struggling with this question! Please show ALL work! <3 (the answer choices are provided on a separate image)

Answers

Answer:

The radius is 18 inches

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *r

36 pi = 2 * pi *r

Divide each side by pi

36 = 2r

Divide each side by 2

18 =r

Answer:

The answer is option C

Step-by-step explanation:

Circumference of a circle = 2πr

where

r is the radius of the circle

From the question

Circumference = 36π inches

To find the radius substitute the value of the circumference into the above formula and solve for the radius

That's

[tex]36\pi = 2\pi r[/tex]

Divide both sides by 2π

We have

[tex] \frac{36\pi}{2\pi} = \frac{2\pi \: r}{2\pi} [/tex]

We have the final answer as

r = 18 inches

Hope this helps you

Find the mass and center of mass of the solid E with the given density rho. E is the cube 0 ≤ x ≤ a, 0 ≤ y ≤ a, 0 ≤ z ≤ a; rho(x, y, z) = 9x2 + 9y2 + 9z2.

Answers

Answer:

mass = 9a^5

center of mass = [tex]\frac{7a}{12}, \frac{7a}{12}, \frac{7a}{12}[/tex]

Step-by-step explanation:

Finding the mass of the solid E

given density function : p ( x,y,z ) = [tex]9x^2 + 9y^2 + 9z^2[/tex]

Mass =   [tex]\int\limits^a_0 \int\limits^a_0 \int\limits^a_0 {9(x^2+y^2+z^2)} \, dx dydz[/tex]   [tex]= \int\limits^a_0 \int\limits^a_0 {9(\frac{a^3}{3}+ay^2+az^2 )} \, dydz[/tex]

         [tex]= \int\limits^a_0 {9(\frac{a^4}{3}+\frac{a^4}{3} +a^2z^2 )} \, dz[/tex]  [tex]= \int\limits^a_0 {9(\frac{2a^4}{3}+a^2z^2 )} \, dz[/tex]  [tex]= 9 ( \frac{2a^5}{3} + \frac{a^5}{3} )[/tex]  

( taking limits as a and 0 )

hence Mass = 9 [tex](a^5)[/tex]

finding the center of mass

attached below is solution

       

I require someone to answer this question for me ASAP please?

Answers

Answer:

x has to be less than 3

Step-by-step explanation:

Answer:

x < 3

I hope this helps!

Eliminate the parameter for the following set of parametric equations: x= t + 6 y= 3t – 1

Answers

Answer:

Solution : Option A

Step-by-step explanation:

What we want to do here is eliminate the parameter t. In order to do that, we can isolate t in our first equation x = t + 6 ----- ( 1 ) and then plug that value for t in the second equation y = 3t - 1. Our solution will be an equation that is not present with t.

( 1 ) x = t + 6, t = x - 6

( 2 ) y = 3( x - 6 ) - 1 ( Distribute the " 3 " in 3( x - 6 ) )

y = 3x - 18 - 1 ( Combine like terms )

y = 3x - 19

As you can see our result will be option a, y = 3x - 19.

Tierra's THR zone is 135-185 bpm (beats per minute). What might Tierra's heart rate be to
indicate that she was working too hard?
A. 145 bpm
B. 195 bpm
C. 175 bpm
D. 130 bpm​

Answers

The correct answer is B. 195 bpm

Explanation:

In health and related areas, THR or Target Heart Rate zone refers to the range of heart rate an individual should have including the maximum heart rate. In the case of Tierra, her THR zone indicates her maximum heart rate should be 185 beats per minute.

In this context, a heart rate above this number shows Tierra is working too hard or that his heart is doing too much effort, which is dangerous for her health. Thus, the heart rate that shows she is doing too hard is 195 bmp as this is the only one that is above the ideal rate.

How do u solve A/B + C/D = E

Answers

you cannot solve this, I don’t see how....

To measure Monarch butterfly migration,
scientist tag and release 100 butterflies in
Kansas and Missouri before traveling to
Mexico. While in Mexico, the same
scientist captured another 100 butterflies
of which 15 are tagged. Based on this
information, how many butterflies would
you predict start in Kansas and Missouri
and migrate to Mexico?

Answers

the answer is 667.

100/x = 15/100

it’s a proportion so you cross multiply. after cross multiplying you get 15x = 10,000. divided both sides by 15 and you get x = 66.6 (continuation of the 6). since it’s repeating, round it and you get 667.

by the way this is actually one of my homework questions for today ;)

The predicted number of butterflies that starts from Kansas and Missouri and migrate to Mexico is 667.

The Aim of the experiment is to measure the Monarch butterfly migration

number of butterflies tagged and released in Kansas and Missouri = 100 number of tagged butterflies captured in Mexico = 15 Let the number of butterflies that start from Kansas and Missouri and end in Mexico = x

Predicting the number of butterflies

= [tex]\frac{100}{x} = \frac{15}{100}[/tex]

= [tex]15x = ( 100 * 100)[/tex]

∴ x( predicted value ) = [tex]\frac{10000}{15 } = 667[/tex]

hence the approximate value of the number of butterflies that migrate to Mexico from Kansas and Missouri is  667

learn more about migration : https://brainly.com/question/23903333

What is the probability that a randomly selected individual on this campus weighs more than 166 pounds? (express in decimal form and round final answer to 4 decimal places)

Answers

Answer:

hello attached is the missing part of your question and the answer of the question asked

answer : 0.2951

Step-by-step explanation:

Given data:

number of persons allowed in the elevator = 15

weight limit of elevator = 2500 pounds

average weight of individuals = 152 pounds

standard deviation = 26 pounds

probability that an individual selected weighs more than 166 pounds

std = 26 ,  number of persons(x) = 15, average weight of individuals(u) = 152 pounds

p( x > 166 ) = p( x-u / std,  166 - u/ std )

                  = p (  z > [tex]\frac{166-152}{26}[/tex] )

                  = 1 - p( z < 0.5385 )

p( x > 166 ) = 1 - 0.70488 = 0.2951

g natasha is in a class of 30 students that selects 4 leaders. How many ways are there to select the 4 leaders so that natasha is one of the leaders

Answers

Answer:

3,654 different ways.

Step-by-step explanation:

If there are 30 students in a class with natasha in the class and natasha is to select four leaders in the class of which she is already part of the selection, this means there are 3 more leaders needed to be selected among the remaining 29 students (natasha being an exception).

Using the combination formula since we are selecting and combination has to do with selection, If r object are to selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

Sinca natasha is to select 3 more leaders from the remaining 29students, this can be done in 29C3 number of ways.

29C3 = 29!/(29-3)!3!

29C3 = 29!/(26!)!3!

29C3 = 29*28*27*26!/26!3*2

29C3 = 29*28*27/6

29C3 = 3,654 different ways.

This means that there are 3,654 different ways to select the 4 leaders so that natasha is one of the leaders

10 easy points!!!! What is the x-intercept of the line?

Answers

Answer:

Step-by-step explanation:

As x increases from -74 to -54 (a 'run' of 20), y decreases from 18 to 12 (a 'rise' of -6.  Thus, the slope of this line is m = rise/run = -6/20 = -13/10.

From y = mx + b we get     12 = (-13/10)(12) + b, or (after dividing all terms by 12)

1 = -13/10 + b/12, or

60 = -3(6) + 5b, or

42 = - 5b, or b = -42/5

The line is y = (-13/10)x - 42/5.

At the x-intercept, y = 0.  Setting y = 0, we get:

(13/10)X = -42/5,  or  13x = -84.

Thus, x = -84/13 =  -6.46

and so the x-intercept of the line is (-6.46, 0)

Find the doubling time of an investment earning 8% interest if interest is compounded continuously. The doubling time of an investment earning 8% interest if interest is compounded continuously is ____ years.

Answers

Answer:

8.66 years

Step-by-step explanation:

Given that:

Interest rate = 8%

Using the exponential growth function:

A = Ao * e^(rt)

Where A = final amount

Ao = Initial amount

r = growth rate

t = time

Here we are to calculate the time it takes an investment earning 8% interest to double;

rate (r) = 8% = 0.08

2A = A * e^(rt)

Divide both sides by A

2 = e^(rt)

2 = e^(0.08 * t)

2 = e^(0.08t)

In(2) = 0.08t

0.6931471 = 0.08t

Divide both sides by 0.08

0.6931471 / 0.08 = 0.08t / 0.08

8.6643397 = t

t = 8.66 years

Answer:

symbolically, the answer would be t= ln(2)/(.08)

Step-by-step explanation:

start by writing out your variables:

rate= .08

*dont forget the investment doubles too, thats where 2P is in the bottom equation

equation should look like:

[tex]2P=Pe^{.08t}[/tex]

then you solve, so divide P on the right and left:

[tex]\frac{2p}{p} = \frac{Pe^{.08t}}{p}[/tex]

now it looks like: [tex]2=e^{.08t}[/tex]

you can take the natural log (ln) of 2 to get the exponent by itself .08t

ln(2)=.08t

then divide .08 to get t by itself

[tex]\frac{ln(2)}{.08} =\frac{.08t}{.08}[/tex]

so symbolically, your equation should be:

[tex]t=\frac{ln(2)}{.08}[/tex]

to get t as your answer you can plug this equation into your calculator to get:

t=8.66 years so approximently 8 years

Find the measure of b. A. 63 B. 27 C. 31.5 D. 126

Answers

Answer:

126°

Step-by-step explanation:

If that angle is 27, so is angle a.

180-27-27=126

una compañía sabe que si produce "x" unidades mensuales su utilidad "u" se podría calcular con la expresión:


u(x)=-0.04x^2+44x-4000


donde "u" se expresa en dólares. Determine la razón del cambio promedio de la utilidad cuando el nivel de producción cambia de 600 a 620 unidades mensuales. Recuerde que la pendiente de la recta secante a la gráfica de la función representa a la razón de cambio promedio.


porfavor alguien que me explique el procedimiento :(

Answers

Answer:

Δf(u) /Δx  = 92,8    ( razón de cambio promedio)

Step-by-step explanation:

La expresión de la utilidad de la empresa u(x) en función de la cantidad de unidades producidas "x" es:

u(x) = 0,04*x² + 44*x  -4000

Entonces la razón de cambio promedio en un intervalo (a ; b)  en este caso ( 620 ;  600 ) viene dada por la expresión:

Δf(x)/ Δx  =  [ f(b)  -  f(a) ]/( b - a )

en donde  f(b)  y f(a) se obtienen por sustitución de los valores a y b es decir  600 y 620 respectivamente en la función f(x) = u(x) entonces

Δf(u) /Δx  =  [ u(b)  -  u(a) ]/( b -a )        (1)

u(b) =  0,04*(620)² + 44*(620) - 4000

u(b) = 15376 + 27280 -4000

u(b) = 2656 unidades

u(a)  = 0,04* (600)²  +  44* 600  - 4000

u(a)  = 14400  +  26400  - 4000

u(a) = 800

Sustituyendo esos valores en la ecuación 1

Δf(u) /Δx  =  2656 - 800 / 620 - 600

Δf(u) /Δx  = 92,8

The following shows the monthly sales in units of six salespersons before and after a bonus plan was introduced. At 95% confidence, determine whether the bonus plan has increased sales significantly.Monthly Sales Salesperson After Before1 94 902 87 853 90 844 86 815 80 806 85 80

Answers

Answer:

it is clear that at 95% confidence that the bonus plan has increased the sales significantly, because if we observe you will notice that sales after is greater than sales before in all six cases.

Step-by-step explanation:

A 95% confidence interval as we have above is the range of values that we can say with utmost certainty and confidence that 95% chance it contains the true mean of the population. in other words we can say that a  95% confidence interval defines a range of values that you can be 95% certain contains the population mean.

g Refer to the Number of Motorcycles Narrative} Are these probabilities true or false? ?a. P(X > 1)=0.35 b. P(X ≤ 2)=0.85 c. P(1 ≤ X ≤ 2)=.6 d. P(0 < X < 1)=0 e. P(1 ≤ X < 3)=.6 True False

Answers

Answer:

False.

Step-by-step explanation:

Probability distribution is the function which describes the likelihood of possible values assuming a random variable. The variance distribution is the squared value of each the difference by the mean. values of probability are squared and then their sum is taken to calculate variance deviation. The number of motorcycles greater than 1 has probability of 0.35 so the probability of x = 1 must also be 0.35.

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 3 percentage points with 99​% confidence if ​(a) he uses a previous estimate of 22​%?

Answers

Answer:

Sample size n [tex]\simeq[/tex] 1269.15

Step-by-step explanation:

From the information given ,

At 99% of confidence interval,

the level of significance ∝ = 1 - 0.99

the level of significance ∝ =  0.01

the critical value for 99% of confidence interval is:

[tex]\mathtt{\dfrac{\alpha }{2} = \dfrac{0.01}{2}}[/tex]

= 0.005

[tex]\mathtt {z_{\alpha/2} = z_{0.005/2} }[/tex]

The value for z from the standard normal tables

= 2.58

The Margin of error E= 3% = 0.03

The formula to  determine the sample size n used can be expressed as follows:

[tex]\mathtt { n = (\dfrac{z_{\alpha/2}}{E})^2 \ \hat p (1 - \hat p) }[/tex]

where;

[tex]\mathtt{\hat p }[/tex] = 22% = 0.22

Then:

[tex]\mathtt { n = (\dfrac{2.58}{0.03})^2 \ \times 0.22 \times (1 - 0.22) }[/tex]

[tex]\mathtt { n = (86)^2 \ \times 0.22 \times (0.78) }[/tex]

[tex]\mathtt { n = 7396 \ \times 0.22 \times (0.78) }[/tex]

n = 1269.1536

Sample size n [tex]\simeq[/tex] 1269.15

PLZ HELP ASAP (Algebra)

Answers

Answer:

Step-by-step explanation:

Whenever you add two number x and -x and it becomes 0 . IT is the identity property.

Ex:

-1/3 + 1/3 = 0

-1 + 1 = 0

-58 + 58 = 0

A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. A 95% confidence interval for the difference between the population means is (1.4, 8.7). If the hypothesis test is based on the same samples, which of the following do you know for sure:
A: The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
B: The hypothesis µ1 = µ2 would be rejected at the 10% level of significance.
C: The hypothesis µ1 = µ2 would be rejected at the 1% level of significance.
A) A and B
B) A and C
C) A only
D) A, B, and C

Answers

Answer:

C) A only

Step-by-step explanation:

In statistics, the null hypothesis is the default hypothesis and the alternative hypothesis is  the research hypothesis. The alternative hypothesis usually comes in place to challenge the null hypothesis in order to determine if the test is statistically significant or not.

Similarly,

In hypothesis testing, the confidence interval consist of all reasonable value of the population mean. Values for which the null hypothesis will be rejected [tex]H_o[/tex] .

Given that:

At 95% confidence interval for the  difference between the population means is (1.4, 8.7).

The level of significance = 1 - 0.95 = 0.05  = 5%

So , If the hypothesis test is based on the same samples, The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.

Suppose you do not know the population mean fee charged to H&R Block customers last year. Instead, suppose you take a sample of size n-8 and find a sample mean of 350. Assume that the distribution for fees is normally distributed with a sample standard deviation of $100.

i. Before conducting the survey, suppose you believed based on your previous observations, your best guess for population standard deviation of fee charged to H&R Block is $50. With this assumption in mind, What should your sample size n approximately be if you want:

Margin-of-Error of to be 2 % and confidence level to be 95 %?
Margin-of-Error of to be 4% and confidence level to be 95%?
Margin-of-Error of to be 4 % and confidence level to be 99%?

ii. 90% confidence interval for the population mean of fees H&R Block.

a. Calculate the margin of error (MOE) of x using a 10% significance level.
b. Calculate the 90 % confidence interval.
c. Suppose an analyst belief that the population mean fee is equal to $185. Using a 90% confidence level. can we conclude the analyst is right? Why or why not?

Answers

Answer:

i [tex]\to[/tex] a

    [tex]n = 96040000[/tex]

i [tex]\to[/tex] b

    [tex]n_1 =24010000[/tex]

i [tex]\to[/tex] c

    [tex]n_2 =41602500[/tex]

ii[tex]\to[/tex]a

     [tex]E = 58.16[/tex]

ii[tex]\to[/tex]b

    [tex]291.84 < \mu < 408.16[/tex]\

ii[tex]\to[/tex]c

    There is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval

Step-by-step explanation:

From the question we are told that

     The sample size is [tex]n = 8[/tex]

      The sample mean is  [tex]\= x = \$ 350[/tex]    

      The sample standard deviation is  [tex]\$ 100[/tex]

Considering question i

    i [tex]\to[/tex] a

         At   [tex]E = 0.02[/tex]  

given that the confidence level is 95%  =  0.95

         the level of significance would be  [tex]\alpha =1-0.95 = 0.05[/tex]

The critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

        [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

So  the sample size is mathematically evaluated as

            [tex]n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2[/tex]

=>        [tex]n =[ \frac{ 1.96 * 100}{ 0.02} ]^2[/tex]

=>         [tex]n = 96040000[/tex]

 i [tex]\to[/tex] b

  At  [tex]E_1 = 0.04[/tex]    and  confidence level  = 95%  =>  [tex]\alpha_1 = 0.05[/tex]   =>  [tex]Z_{\frac{\alpha_1 }{2} } = 1.96[/tex]

             [tex]n_1 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_1} ]^2[/tex]

=>           [tex]n_1 =[ \frac{ 1.96 * 100}{ 0.04} ]^2[/tex]

=>           [tex]n_1 =24010000[/tex]

 i [tex]\to[/tex] c

       At   [tex]E_2 = 0.04[/tex]     confidence level  = 99%  =>    [tex]\alpha_2 = 0.01[/tex]

The critical value of  [tex]\frac{\alpha_2 }{2}[/tex] from the normal distribution table is  

        [tex]Z_{\frac{ \alpha_2 }{2} } = 2.58[/tex]

=>    [tex]n_2 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_2} ]^2[/tex]

=>    [tex]n_2 =[ \frac{ 2.58 * 100}{ 0.04} ]^2[/tex]

=>    [tex]n_2 =41602500[/tex]

Considering ii

Given that the level of significance is  [tex]\alpha = 0.10[/tex]

Then the critical value  of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

           [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

Generally the margin of error is mathematically represented as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]E = 1.645 * \frac{100 }{\sqrt{8} }[/tex]

         [tex]E = 58.16[/tex]

Generally the 90% confidence interval is mathematically evaluated as

         [tex]\= x - E < \mu < \= x + E[/tex]

=>      [tex]350 - 58.16 < \mu < 350 + 58.16[/tex]

=>     [tex]291.84 < \mu < 408.16[/tex]

So the interpretation is that there is 90% confidence that the mean  fee charged to H&R Block customers last year is in the interval .So there is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval.

it is 235 miles from tulsa to dallas. it is 390 miles from dallas to houston. a) what is the total distance of a trip from tulsa to dallas to houston? b) what is the total distance from houston to dallas to tulsa? c) explain how you can tell whether the distances described in parts (a) and (b) are equal by using reasoning.

Answers

Answer:

a- tulsa to dallas to houston is 235+390 which is 625 miles

b - houston to dallas to tulsa is 390+235 miles which is 625 miles

c - by using reasoning both are same because they are just rewritten differently but the equation is same

please give me brainliest

hope it helps buddy

What is the slope of a line perpendicular to y=-7/4x
O A.
IN
O B.
7
O c.
4
-
O D.
7
4​

Answers

Answer:

y=4/7x

Step-by-step explanation:

perpendicular lines have opposite slopes. that means reciprocal and opposite sign.

Ellen is making jewelry sets that contain a bracelet and a pair of earrings. Each bracelet uses 3 times as many beads as one earring. Each bracelet uses 3 as times as many beads as one earring . Ellen uses 13 beads for each earring. How many beads does Ellen need to make one jewelry set?

Answers

So there are a pair of earrings and a Bracelet.

It's given that the Bracelet uses 3 times the number of beads that's used in making a single earring.

It's also given that one single earing has 13 beads. So a single bracelet would have (3×13) beads .... and that's equal to 39.

Making a single set of jewellery needs a pair of earrings and a Bracelet.

So total number of required beads will be =

39 + 13 + 13 = 65

3(x–6)=18 help plese

Answers

Answer:

x = 12

Step-by-step explanation:

3(x–6)=18

x-6 = 18:3

x-6 = 6

x = 6+6

x = 12

Answer:

x=12

Step-by-step explanation:

Given the polynomial, identify the coefficients and degree of each term:

Answers

Answer:

See below.

Step-by-step explanation:

The degree is simply the number of the exponent (or the sum) and the coefficient is simply the number in front of the term.

First Term: -7; Deg=0, Co=-7.

-7 is the same as saying -7x^0. Thus, the degree is 0.

Second Term: -x^4; Deg=4, Co=-1

-x^4 is the same as saying -1(x^4). Thus, the degree is 4 while the coefficient is -1.

Third Term: -5x^3; Deg=3, Co=-5

Again, this is the same as saying -5(x^3). Thus, the degree is 3 while the coefficient is -1.

Fourth Term: 7x; Deg=1, Co=7

7x is the same as saying 7x^1. Thus, the degree is 1 while the coefficient is 7.

Fifth Term: x^2; Deg=2, Co=2

x^2 is the same as 1(x^2). Thus, the degree is 2 while the coefficient is 1.

The leading coefficient is the first coefficient when the polynomial is placed in descending order based on degree number. First, arrange the polynomial into descending order based on the degree:

[tex]-x^4-5x^3+x^2+7x-7[/tex]

Thus, the leading coefficient is -1 (belonging to the x^4).

The degree of the leading term will always be the highest. In this case, it is 4.

The degree of the polynomial is the highest degree. In this case, it is 4.

A 20-foot ladder is placed against a tree. The bottom is located 5 feet from the base of the tree and the top of the ladder is 5√15 feet up the tree. Use tangent to find the angle created between the ladder and tree. Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest tenth of a degree.

Answers

Answer:

14.5°

Step-by-step explanation:

The sketch results in an angle of depression problem.

In this case, the opposite side of the triangle formed is 5 ft

The hypotenuse side is 20 ft

The adjacent side is the [tex]5\sqrt{15}[/tex] ft

Using tangent θ = opp/adj

tangent θ = 5/[tex]5\sqrt{15}[/tex] = [tex]\frac{1}{\sqrt{15} }[/tex] = 0.258

θ = [tex]tangent^{-1}[/tex] 0.258 = 14.5°

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