Mathematics College

The Picture above please do 4a and 4b I’m so lost. Thank you.

Answers

Answer 1

Answer:

First, we know that the function IxI works as follows:

IxI = x if x ≥ 0

IxI = -x if x < 0

So IxI is always positive.

then:

a) f(x) = Ix - 2I

this is:

f(x) = (x - 2) if (x - 2) ≥ 0

-(x - 2) if (x - 2) < 0

Then the graph of this function will be two lines (where the separation of the lines depends on the vale of x)

For the case of b we have

g(x) = -IxI + 1

then we have:

g(x) = -x + 1 if x ≥ 0

g(x) = -(-x) + 1 if x < 0

To graph the functions, you need to graph these lines for the given values of x. You also can see the graphs below. Where the red graph is the one for the point 4a, and the blue graph is the one for point 4b.

Now, let's find the domain and range:

4a) f(x) = Ix - 2I

The domain is the set of the possible values of x that we can input in that function. For this case, we do not have any value of x that generates a problem (like a zero in a denominator, for example) then the domain is the set of all real numbers: x ∈ R

The range is the set of the possible values of y.

f(x) = Ix - 2I is always equal or greater than zero (as you can also see in the graph) then the range will be:

R: y ∈ R, such that y ≥ 0.

4b) g(x) = -IxI + 1

Similar as the prior case, here the domain is the set of all real numbers:

D: x ∈ R

For the range, now we have:

y = -IxI + 1

if IxI is always equal or larger than zero, then -IxI is always equal or smaller than zero. If we add a + 1 to that, then the function will be always equal or smaller than 1.

Then the range is:

R: y ∈ R, such that y ≤ 1

Related Questions

Given the graph below, write the equation for the line in slope - intercept form.
1
2
A y = 22 + 2
B y = x + 1
C y= -2x - 2
D y= -2x +2

Answers

Answer:

Step-by-step explanation:

slope is -,y-intercept is 2

y=+mx+2

Each figure shows a triangle with one of its angle bisectors.

Answers

Answer:

x = 7

Step-by-step explanation:

XP bisects <X into two equal parts, <1 and <2. Therefore,

<1 = <2

<1 = 5x - 2

<2 = 4x + 5

Thus:

5x - 2 = 4x + 5

5x - 2 - 4x = 5 (subtraction property of equality)

x - 2 = 5

x = 5 + 2 (addition property of equality)

x = 7

What percent of 30 is 16.5

Answers

Answer:

Its 55

Step-by-step explanation:

hope this helps

Answer:

55%

Step-by-step explanation:

Hope this helps you :)

Have a great day!

If x < 0 and y > 0, determine the sign of the real number. (a) x y positive negative (b) xy2 positive negative (c) x − y xy positive negative (d) y(y − x) positive negative

Answers

Answer:

From the question it is given that x<0 and y>0 or in other words x is negative and y is positive.

(a)x y : x is negative and y is positive

⇒negative x positive = negative

Therefore, xy is negative

(b)x[tex]y^{2}[/tex] : x is negative and [tex]y^{2}[/tex] is positive

⇒negative x positive = negative

Therefore, x[tex]y^{2}[/tex] is negative

⇒(x − y) is negative and xy is negative {from (a)}

⇒negative x negative = positive

Therefore, (x-y)xy is negative

(d) y(y − x): x is negative and y is positive

here y - x is positive

⇒positive x positive = positive

Therefore, (y-x)y is negative

To decorate her bedroom, Lisa spent $62.89 on new bedding, $48.26 on paint, and $81.99 on accessories. About how much did she spend to decorate her bedroom? (1 point)

Question 3 options:

1)

$190

2)

$210

3)

$230

4)

$300

Answers

Answer:

3 because it makes a of sense

Step-by-step explanation:

expend log10 (x³y⁵)

Answers

Answer:

3log(x) + 5log(y)

Step-by-step explanation:

[tex] log({x}^{3} {y}^{5} ) \\ = log( {x}^{3} ) + log( {y}^{5} ) \\ = 3 log(x) + 5 log(y) [/tex]

Which order pairs are solution to the inequality Y-3x<-8

Answers

Answer:

your answer are c and d hope it helps .

If all of be the simple the side lengths of a triangle had a length of 1 what would be the simplified laws of sines be?

Answers

Answer:

sin A = sin B = sin C

Step-by-step explanation:

The sine rule is a law which relates all the three sides of a triangle with the sine of their opposite angles in the triangle. Given a triangle with a side of a and an opposite angle of A, side b with opposite angle B and side c with opposite angle C. The sine rule is given as:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

Given that all the side of the triangle have a length of 1, that is a = b = c = 1, hence the equation becomes:

[tex]\frac{sin(A)}{1}=\frac{sin(B)}{1}=\frac{sin(C)}{1}\\\\sin(A)=sin(B)=sin(C)[/tex]

Answer:

sin A = sin B = sin C

Step-by-step explanation:

edg

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
What is the solution set of this inequality?

Answers

Answer:

(-3,1) U (3,8) is the right answer.

Circle A has a circumference of B centimeters.

Circle C’s diameter is 3 times as long as circle A’s diameter.

What is the circumference of circle B?

Answers

Circle B has a diameter that is 1 1/2 times as long as Circle A's diameter. What is the circumference of Circle B? Solution. 4 m. If the diameter ...

How long should $1,000 be invested compounded
bimonthly to produce a final balance of $2,000 at
4.15%?
A. 16.70 years
B. 16.72 years
C. 16.76 years
D. 16.73 years

Answers

Answer: B. 16.72 years

Step-by-step explanation:

If interest is compounded bi-monthly, the formula to calculate the accumulated amount (A) is given by:-

[tex]A=P(1+\dfrac{r}{24})^{24x}[/tex] , where P = principal , r= rate of interest, x= time period(years).

[1 year =12 months, total periods in 12 months if period per month is 2 = 2 x 12 =24]

Given: P= 1000, A= 2000, r= 4.15% = 0.0415

Substitute all values in formula , we get

[tex]1000\times (1+\dfrac{0.0415}{24})^{24x}=2000\\\\\Rightarrow\ (1.00172916667)^{24x}=2\\\\\text{Taking log on both sides, we get}\\\\\Rightarrow \ln(1.00172916667)^{24x}=\ln2\\\\\Rightarrow 24x\ln(1.00172916667)=\ln2\\\\\Rightarrow\ x=\dfrac{\ln 2}{24\ln(1.00172916667)}\approx16.72\ years[/tex]

Hence, option B. is correct.

What value of x makes the equation true 7+2x=4x-5

Answers

Answer:

Step-by-step explanation:

Fact

Answer:

x=6

Step-by-step explanation:

1. 7+2x=4x-5

2. 7+2x-2x=4x-5-2x

7=2x-5

12=2x

x=12/2

x=6

Use this table to match the molecules with their estimated masses.

Atom Mass (in grams)
hydrogen 1.67 × 10-24
oxygen 2.66 × 10-23
carbon 1.99 × 10-23
nitrogen 2.32 × 10-23

Answers

Answer:

7.31 x 10^-23

Answer: CO2 (1 atom of carbon and 2 atoms of oxygen)

3.34 x 10^-24

Answer: H2 (2 atoms of hydrogen)

2.821 x 10^-23

Answer: NH3 (1 atom of nitrogen and 3 atoms of hydrogen)

7.64 x 10^-23

Answer: NO2 (1 atom of nitrogen and 2 atoms of oxygen)

Step-by-step explanation:

hope this helps :)

The matching is as follows;

7.31 x 10^-23 = CO2 i.e. 1 atom of carbon and 2 atoms of oxygen

3.34 x 10^-24 = H2 (2 atoms of hydrogen)

2.821 x 10^-23 = NH3 (1 atom of nitrogen and 3 atoms of hydrogen)

7.64 x 10^-23 = NO2 (1 atom of nitrogen and 2 atoms of oxygen)

Learn more: https://brainly.com/question/4804019?referrer=searchResults

what is the point slope form of a linear equation?

Answers

Answer:

y= m(x-x1) +y1

Step-by-step explanation:

that is point slope form

Answer:

answer 4 is correct

y-y1=m(x-x1)

putting value of m that is slope formula .

Jose has $20 and is saving $6 per week. Ana has $150 and is spending $4 per
week. When will they both have the same amount of money?

Answers

no they wont have the same amount of money ana has more than jose and he’s spending more and wont have enough for the whole week, while ana will have enough and she’s only wasting 4$....

Which decimal is less than 0.47
(0.38) (0.9) (0.64) (0.5)

Answers

Answer:

0.5

Step-by-step explanation:

just divide in a calculator

Answer:

0.38

Step-by-step explanation:

Look at the tenths decimal place to compare

3 is less than 4

9 is greater than 4

6 is greater than 4

5 is greater than 4

The only one less than 4 is 3 which corresponds to the decimal 0.38

What is the solution for the system of equations shown in this graph?

Answers

Answer:

[tex]\huge\boxed{\sf x = 2 , y = -2}[/tex]

Step-by-step explanation:

The common point where the lines of the two equations meet is exactly the solution of the system of equations.

So,

The common point is (x,y) = (2,-2)

This means that x = 2 and y = -2.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

What is the quotient of 63 and 0

Answers

Answer:

Step-by-step explanation:

Something divided OR multiplied by 0 always ends with 0

Answer:

63/7 = 9.

I think

Hope this helps

Roberto has run the first 18 miles of a race, which means he is 72% finished. How long is the race

Answers

Answer:

25 miles

Step-by-step explanation:

18 ÷ 72% =

18 ÷ (72 ÷ 100) =

(100 × 18) ÷ 72 =

1,800 ÷ 72 =

Use algebraic rules to show that n(n+1)+2n +2 is equivalent to (n+1)(n+2)

Answers

Answer:

This question is asking us to solve both of these equations, so let's do exactly that!

First equation:

[tex]n(n+1)+2n+2\\n^2+1n+2n+2\\n^2+3n+2[/tex]

Second Equation:

[tex](n+1)(n+2)\\n^2+2n+1n+2\\n^2+3n+2[/tex]

Both of the equations result with the same answer, therefore n(n+1)+2n+2 is equivalent to (n+1)(n+2).

Hope that helped! :)

Identify the equation of the parabola in vertex form if a = 1 and the vertex is (4, 6).

a) y = (x - 6)2 + 4

b) y = (x + 6)2 +
+4

c)y=(x + 4)² +6

d) y = (x - 4)2 + 6

Answers

Answer:

Step-by-step explanation:

Which statements are true? Check all that apply.

On a coordinate plane, point A is (2, 3), point B is (3, 2), point C is (negative 2, 2), point D is (negative 3, negative 3), point E is (0, 3), point F is (2, 0), and point G is (0, 0).
A is in Quadrant I.
B is on the x-axis.
C is in Quadrant I.
D is in Quadrant III.
E is on the x-axis.
F is on the x-axis.
G is on the y-axis. Please anwser quick!!!!

Answers

Given:

A(2, 3)B(3, 2)C(-2, 2)D(-3, -3)E(0, 3)F(2, 0)G(0, 0)

Let's first understand the different signs and different quadrants.

Quadrant I: (+, +)Quadrant ll: (-, +)Quadrant III: (-, -)Quadrant IIII: (+, -)

Verifying them with the given points,

A is in Quadrant I. - TRUEB is on the x-axis. - FALSEC is in Quadrant I. - FALSED is in Quadrant III. - TRUEE is on the x-axis. - FALSEF is on the x-axis. - TRUEG is on the y-axis. - FALSE

Hope it helps. :)

Answer:

A D F

Step-by-step explanation:

All credit to him

Given \qquad m \angle QPS = 107^\circm∠QPS=107 ∘ m, angle, Q, P, S, equals, 107, degrees \qquad m \angle RPS = 4x + 27^\circm∠RPS=4x+27 ∘ m, angle, R, P, S, equals, 4, x, plus, 27, degrees \qquad m \angle QPR = 9x - 115^\circm∠QPR=9x−115 ∘ m, angle, Q, P, R, equals, 9, x, minus, 115, degrees Find m\angle QPRm∠QPRm, angle, Q, P, R:

Answers

Answer:

20°

Step-by-step explanation:

4x+27°+9x-115°=107°

4x+9x + 27°-115°=107°

13x-88°=107°

add 88 on both sides

13x=195°

divide 13 on both sides

x=15

9(15°)-115°

135°-115° = 20

The answer is 20

Answer:

Step-by-step explanation:

A professor gives a test to a large class. The time limit for the test is 50 minutes, and the first student to finish is done in 35 minutes. The professor assumes that the random variable T for the time it takes a student to finish the test is uniformly distributed over [35, 50]. At what time T will 60% of the students be finished with the test?

Answers

Answer: at 44 minutes, 60% of the students will be finished with the test

Step-by-step explanation:

Given the data in the question;

we have a uniform distribution between 35 and 50

50 - 35 = 15

now, we simply multiply 15 by 60%; 15 × 0.6 = 9

so after 9 minutes, 60% percent of the students are done

Hence, 9min + 35 min = 44 minutes

Therefore at 44 minutes, 60% of the students will be finished with the test

The time T when 60% of the students will be finished with the test is 44 minutes.

What is the percentage?

The percentage is the value per hundred.

The time limit for the test = 50minute

The first student finishes in 35 minutes

The last student finishes in 50 minutes

So the difference between time = 15 minutes

It is given that the time it takes a student to finish the test is uniformly distributed over [35, 50].

So, the time T when 60% of the students will be finished with the test

T=35 + 60% of 15 minutes

T= 35 + 60*15/100

T= 44 minutes

Therefore, the time T when 60% of the students will be finished with the test is 44 minutes.

To get more about the percentage visit:

Can someone help please!

Answers

Answer:

650

Step-by-step explanation:

because it says that she earns 50 for each hour so if u multiple 50×13 u get =650

Sum of the radius of the base and height of a cylinder is 21 cm and the curved surface area of the cylinder is 616 sq.cm,find the total surface area of the cylinder.

Answers

Answer:

925.04cm²

Step-by-step explanation:

Curved surface area of a cylinder = 2πrh

r is the radius

h is the height

If the sum of the radius of the base and height of the cylinder is 21 cm, then;

r + h = 21

r = 21-h..... 1

Recall:

CSA = 2πrh

616 = 2πrh ....2

Substitute equation 1 into 2;

616 = 2π(21-h)h

616 = 2π(21h-h²)

616 = 42(3.14)h - 2(3.14)h²

616 = 131.88h - 6.28h²

98.09 = 21h - h²

h²-21h+98.09 = 0

h = 21±√21²-4(98.09)/2

h = 21±√441-392.36/2

h = 21±√48.64/2

h = 21±6/97/2

h = 21+6.97/2 and 21-6.97/2

h = 27.97/2 and 14.03/2

h = 13.985 and 7.015

Since r = 21-h

r = 21 - 13.985

Using r = 7.015

The total surface area = 2πrh + 2πr²

The total surface area = 616 + 2(3.14)7.015²

The total surface area = 616 + 309.04

The total surface area = 925.04

Hence the total surface area of the cylinder is 925.04cm²

I will give brainiest to whoever answers correctly !!

Answers

9514 1404 393

Answer:

a) interest: $215.33

b) proceeds: $3584.67

c) effective rate: 9.01%

Step-by-step explanation:

a) The problem statement tells you the loan was discounted 8.5%. The amount of interest paid is ...

I = Prt

I = $3800·0.085·8/12 ≈ $215.33

b) The proceeds of the loan are ...

$3800 -215.33 = $3584.67

c) The actual rate is found using the same formula as above, solving for r:

r = I/(Pt) = $215.33/($3584.67·2/3) ≈ 0.0901 = 9.01%

Given that XH bisects Answer choices
A.) 50
B.) 48
C.) 62
D.) none of the above

Answers

We know CXD form a 90 degree angle, plus 32 that is angle BXC
90+32=122
We also know XH bisects this angle, which means it cut it in half,
122/2= 61

Answer: 61

Please solve the question below

Answers

Answer:

AB = 14 units

∠F = 39°

Step-by-step explanation:

Given:

ΔABC ≅ ΔDEF

So,

AB = ED (By CPCT)

So,

AB = 14 units

∠C = ∠F (By CPCT)

∠F = 39°

What is the probability of rolling a multiple of 3 on a 6-sided die?

Answers

Answer:

33% or 1/3 ...............

1/3, 1:3, or simply about 33%

Let me know if you need help with anything else, I’ll be glad to help!

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