Given a function f(x)=|x+1|-|x -2|
How many solutions has f(x) = a, in respect of a?
If a E {-3, 3}, number of solutions is
if a E (-3, 3) number of solutions is
if a E (-infinity, -3) U (3,infinity) number of solutions is

Given A Function F(x)=|x+1|-|x -2|How Many Solutions Has F(x) = A, In Respect Of A?If A E {-3, 3}, Number

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]f(x)=/x+1/-/x-2/\\a=/x+1/-/x-2/\\\text{square both sides}\\a^{2}={(x+1)}^{2}+{(x-2)}^{2}-2(x+1)(x-2)\\a^{2}=x^{2}+2x+1+x^{2}-4x+4-2x^{2}+2x+4\\a^{2}=9\\a=\sqrt{9}\\a=+3\text{ or }-3[/tex]

[tex]\text{if }a \in \{-3, 3\},\text{the number of solutions is 2}[/tex]

[tex]\text{if }a \in \{-\infty, -3\}\bigcup\{\infty, 3\},\text{it is just like saying from infinity to infinity, which is still 2}[/tex]

Answer 2

Answer:

a=(x+1)-(x-2)

=x-x+1+2

a=3


Related Questions

Kya earned $630 per week. If she worked for 30 hours, what is her hourly rate?

Answers

Answer:

$21 per hour

Step-by-step explanation:

To find this answer you do the equation:

630/30 = ?

This equals 21.

Therefore, her hourly rate is $21 per hour.

Answer:

n 1 week, she worked 30 hours. So, she earned $630 for 30 hours. The hourly rate is then 630 / 30 = 21.

2: Solve for x:
2x 2= 4x + 8

Answers

Step-by-step explanation:

2x^2 - 4x - 8 = 0

x^2 - 2x - 8 =0

[tex]x = 2 ( - )(+) \sqrt{2 {}^{2} + 4.1.4 } \div 2.1 \\ x = 2( + )( - ) \sqrt{4 + 16} \div 2 \\ x = 2( - )( + ) \sqrt{20} \div 2 \\ x = 2( - )( + )2 \sqrt{5} \div 2 \\ x = 2(1( - )( + ) \sqrt{5} \div 2 \\ thefore \: x = 1 + \sqrt{5} \: or \: x = 1 - \sqrt{5} [/tex]

2x-4x=8-2
-2x=6
X=6/-2
X=-3

helppp i dont get it

Answers

Answer: Your answer will be 8 s = (8,3) but since there isn’t no 3 for your answers choice then it should be 8! Hope this help!

Use your plan of dividing both sides by five to solve the equation. What is the value of x?

Answers

where’s the equation

please help me guys I need your help

identify whether the figure labelled below is a triangle or quadrilateral

for example:

A.triangle
that's what I know​

Answers

Answer:

A. triangle, B. quadrilateral, C. triangle, D. quadrilateral, E. quadrilateral, F. triangle, G. triangle, H. quadrilateral, I. triangle, J. triangle

Step-by-step explanation:

triangles have 3 sides, quadrilaterals have 4 sides

Answer:

A-Triangle

B- Quadrilateral

C- Triangle

D- Quadrilateral

E- Quadrilateral

F-Triangle

G-Triangle

H-Quadrilateral

I- Triangle

J-Triangle

Step-by-step explanation:

If it has 3 sides it’s a triangle, if it has 4 it’s a quadrilateral.

5x – 3= 17
X=?
Find what x equals to.

Answers

Answer:

x=4

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

5x – 3= 17 add 3 to both sides

5x = 20 divide both sides by 5

x = 4

Based on the illustrations and the passage, which sentence tells how swifts and
sparrows are different?

Answers

Answer: Sparrows generally fly shorter distances than swifts do.

Step-by-step explanation: hope this right!

Answer:

What's the difference between a swallow and a swift?

=> Swifts fly in the upper part of the air column as they hunt; swallows pursue insects closer to the ground or water.

=> If the bird is perched on a nest box, power line, or branch, that's a giveaway: Only swallows have the wherewithal to sit upright. Swifts are just stage-five clingers.

=> The swift has a slightly forked tail, not as long as the swallow's.

[tex] \infty \infty [/tex]

_____X^2+10x+10_____

Answers

The problem in the picture would be
x^2+10x+21

help pleaseeeeeeeeeee i dont get it

Answers

Answer:

E=30H

Melissa earns $330 in 11 hours

Step-by-step explanation:

Answer:

Equation = 30h=E

Melissa's earnings for 11 hours : $363

If you need further explaination I'll be happy to help!!

~ PumpkinSpice1 ♥

Which describes the cross section of the square prism that passes through the vertices A, B, C, and D shown

Below

Answers

Answer:

first of all,

Step-by-step explanation:

In triangle ABC one side equal  and two sides equal  

Step-by-step explanation:

We are given a prism whose base is square with sides 8 in and height 12 in.

If we take cross section through vertices A, B and C

We will get a cross section as triangle.

In triangle ABC, sides are AB, BC and AC

AB is diagonal of top square whose side 8 in.

AC is face diagonal of front face.

BC is face diagonal of right face.

AC=BC≠AB

Hence, In triangle ABC one side equal  and two side equal  

Hope this helps!!

Unit 8 7th grade math

Answers

The mean is 9
First you add all the number then you divide by the amount of numbers

HELP PLEASE!! at a bale sale there was 42 raisin cookies sold. if the ratio of raisin cookies to oat meal cookies was 6 : 1, what is the combined amount of raisin and oatmeal cookies sold?

Answers

answer!

49 cookies were sold!

explaination!

42÷6= 7

42 plus 7 = 49

the amount of cookies sold was 49

(Sorry if it's wrong)

HELP PLZ MARKING BRAINLIEST 10 POINTS DONT ANWSER UNLESS U KNOW!!

Answers

Answer:

Y=13/4x-1/4

Step-by-step explanation:

Good luck

bir sayıyı 0,96 ile çarparsak bu sayıyı yüzde kaç azaltmış oluruz
A-96
B-40
C-9,6
D-4

Answers

I hope this helps you

Sayi 100A olsun

100A. 0,96=96A

100A-96A=4A

100A da 4A azaldiysa

100 de 4 azalir

The circumference of a circle is C centimeters. The diameter of the circle is 13 centimeters. Which expression best represents the value of π

Answers

Answer:

C6.5

Step-by-step explanation:

LOL B-)

Answer: Its C 6.5 I got it right on a test but not sure if its right for you but i think its B also like the other guy said

10
10
14
50
50
10
10
NOTE: Figure not drawn to scale.
Which statement can be used to prove that the triangles above are congruent?
A If two triangles have three pairs of corresponding sides that are congruent, then the triangles are congruent.
B If two triangles have three pairs of corresponding angles that are congruent, then the triangles are congruent
If two triangles have two pairs of corresponding sides that are congruent, and the included angles are congru
triangles are congruent.
D
If two triangles have to pairs of corresponding angles that are congruent, and the included sides are congru
triangles are congruent.

Answers

Answer:

do you have a picture or somthing beacuse i dont understand what your asking

Step-by-step explanation:

Answer: prove that two triangles with three congruent, corresponding angles are congruent, you would need to have at least one set of corresponding sides that are also congruent.

Step-by-step explanation:

City health officials will conduct a two-sample t-test for a difference in means to investigate whether
stray dogs in the city have more fleas, on average, than do stray cats. A random sample of 22 stray dogs
had a mean of 120 fleas and a standard deviation of 20 fleas. A random sample of 15 stray cats had a
mean of 100 fleas and a standard deviation of 30 fleas.
Assuming a null hypothesis of no difference, which of the following is a correct test statistic for the test?

Answers

Answer:

The calculated value     t =   2.366 > 2.0301 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means      

Step-by-step explanation:

Step(i):-

Given that the first sample size 'n₁' = 22

Given that the mean of the first sample x₁⁻ = 120

Given that the standard deviation of the sample (s₁) = 20

Given that the mean of the second sample x₂⁻ = 100

Given that the standard deviation of the second sample (S₂) = 30

Step(ii):-

T-test statistic

               [tex]t = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]

     where

             [tex]S^{2} = \frac{n_{1} S_{1} ^{2}+n_{2} S_{2} ^{2} }{n_{1} +n_{2}-2 }[/tex]

            [tex]S^{2} = \frac{22( 20)^{2}+ 15(30) ^{2} }{22 +15-2 }[/tex]

           S² =  637.1428

           S = √637.1428 = 25.24168  

The standard deviation of the sample 'S' = 25.24168   

Step(iii):-

Null Hypothesis:H₀:

There is no difference between the means

Alternative Hypothesis:H₁:

There is a difference between the means

         T-test statistic

               [tex]t = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]

              [tex]t = \frac{ 120 -100 }{\sqrt{637.14 (\frac{1}{22 }+\frac{1}{15 } ) } }[/tex]

             t =   2.366

Degrees of freedom

           γ = n₁+n₂ -2 = 22+15-2 = 35

     t₀.₀₅ = 2.0301

The calculated value     t =   2.366 > 2.0301 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means          

The correct test statistic for the test of the hypothesis for the considered situation is 2.2619 approximately.

How to perform two sample t-test?

If the sample sizes < 30, and we want to test the difference between the sample means, then we perform t-test.

Let we have:

[tex]\overline{x}_1[/tex] = mean of first sample[tex]\overline{x}_2=[/tex] mean of second sample[tex]s_1[/tex] = standard deviation of first sample[tex]s_2[/tex] = standard deviation of second sample.[tex]n_1[/tex] = first sample's size[tex]n_2[/tex] = second sample's size

Then, the value of t-test statistic is obtained as:

[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}[/tex]

If the level of significance is [tex]\alpha[/tex], then as we have:

the degree of freedom (d.f) = [tex]n_1 + n_2 - 2[/tex],

the critical value of t is found to be [tex]t_{\alpha/2}[/tex] , then if we get:

[tex]|t| < t_{\alpha/2}[/tex] we cannot reject the null hypothesis

and if we get [tex]|t| > t_{\alpha/2}[/tex] , then we may reject the null hypothesis and thus, accept the alternate hypothesis.

For this case, we're specified that:

For sample of stray dogs:

[tex]n_1 = 22[/tex] [tex]\overline{x}_1 = 120[/tex][tex]s_1 = 20[/tex]

For sample of stray cats:

[tex]n_2= 15[/tex][tex]\overline{x}_2 = 100[/tex][tex]s_2 = 30[/tex]

Thus, the t-test statistic for the difference of mean of these two samples is calculated as:

[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}\\\\t = \dfrac{120-100}{\sqrt{20^2/22 + 30^2/15}} = \dfrac{20}{\sqrt{200/11 + 60}}\\\\\\t \approx 2.2619[/tex]

Thus, the correct test statistic for the test of the hypothesis for the considered situation is 2.2619 approximately.

Learn more about two sample t-test here:

https://brainly.com/question/23797565

what can you conclude from the box-and-whisker plot?​

Answers

Answer:

that it is a cat :')

Step-by-step explanation:

remember, whisker = cat

Question is in image

Answers

Answer:

241.8 cm squared

Step-by-step explanation:

since this is a 5 sided pyramid, we would just need the triangle area calculating formula:

base X Height divided by 2

and then multiply it by 5

after you get the results, don't forget to add the area of the base too.

Please help meee! Math makes my brain hurt :(

Answers

The answer should be x=-2

The ratio of nonfiction books to fiction books on a shelf is 5:3. There are 12 fiction
books on the shelf. How many books are on the shelf?

Answers

Answer:

20

Step-by-step explanation:

the ratio is 5:3 the you divide the 12 fiction by 3 you get 4 so if the fiction is 4 then you times it by 5 and you get 20

The ratio of fiction books to nonfiction books on the shelf is 5:3, if there are 12 fiction books are on the shelf, then total number of books on the self, 32

What is the ratio?

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

The ratio of nonfiction books to fiction books on a shelf is 5:3

There are 12 fiction books on the shelf

Total number of books on the self  = ?

Suppose, the total number of books  = x

Nonfiction = x - 12

Ratio =   nonfiction/fiction

   5/3     =    x-12/12

   x      =    32

Hence, the total number of books is 32

To know more about Ratio check:

https://brainly.in/question/7996583

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can anyone explain to me how to find a locus of any point

Answers

Find the locus of a point P such that its ordinate is equal to the abscissa. Hence required equation of the locus of point P is y = 5x + 9. Hence required equation of the locus of point P is x = 2y + 3.

PLEASE HURRY THIS IS DUE IN 1 HOUR

Answers

Answer:

36

Step-by-step explanation:

Make a big square and a little one by cutting it. 6x5 is 30 and the small one is 3x2 which is 6....add then you get 36

someone help and PLEASE make sure it’s right plz

Answers

Answer:

So someone trolled me and deleted my answer. Don’t delete this please!! <3

Step-by-step explanation:

It is a right triangle because it has a 90º angle in it.

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!

Answers

y=3/4x-2

the y intercept is -2
and the slope is 3/4
slope= change in y/change in x

Will 100% give Brainiest to correct and help, please show work, needed answered asap

Answers

Answer:

x^6/2

Step-by-step explanation:

simplify the expression, 4x^4x^3/8x, you make it 4x^7/8x

and it simplifys to 4x^6/8 which then becomes x^6/2

extra note:

a^x * a^y = a^ x+y

(see attachment below)

I hope this helps :)

What is the alternative press?

Answers

Answer:

D. A news organization that is not owned by a corporation.

Step-by-step explanation:

your answer is i’ll be d hope this helps you

Solutions of a Two-Variable Equation Tell whether the given ordered pair is a solution of the equation. 1. 4y + 2x = 3; (1.5, 0) 2. y= 7x - 5; (0,5) 3. y = - 2x + 5; (2, 1)​

Answers

Answer:

1. yes     2. no   3. yes

Step-by-step explanation: (put this if you have to show your work)

1.  4*0+2*1.5 (solve with a calculator or by hand)

2 y*5=7*0-5(same as above solve with a calculator or by hand)

3. 1=-2*2+5(same as above solve with a calculator or by hand)

It doesn’t have the plus sign

Answers

+

there u go if that helps u can copy and paste it

Answer: +

Step-by-step explanation:

do exponential functions have a vertex?​

Answers

I second that. Yes, it does.

Exponential functions do not have a vertex.

What is an exponential function?

"Exponential function, as its name suggests, involves exponents. An exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

In mathematics, an exponential function is a function of form [tex]f(x) = a^{x}[/tex], where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0."

What is the vertex of a function?

"The standard form of a quadratic equation is y = ax² + bx + c and the vertex form of the same is y = a (x - h)² + k. Here, the vertex form has a square in it. So to convert the standard to vertex form we need to complete the square."

We know that, the graph of an exponential function consists of a horizontal asymptote. However, there is no quadratic function available that consists of a horizontal asymptote.

Hence, exponential functions do not have a vertex.

Learn more about an exponential function here: https://brainly.com/question/14355665

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