Mathematics Middle School

What is the domain of the function f(x) = 3|x + 4| + 1? all real numbers all real numbers less than or equal to −4 all real numbers greater than or equal to 1 all real numbers greater than or equal to −4

Answers

Answer 1
all real numbers..................
Answer 2

Answer:

The correct option is A.

Step-by-step explanation:

The vertex form of an absolute function is

[tex]g(x)=a|x-h|+k[/tex]

Where, (h,k) is vertex.

Domain is the set of input values.

The given function is

[tex]f(x)=3|x+4|+1[/tex]

It is the vertex from of an absolute function. Here h=-4 and k=1, so the vertex of the function is (-4,1).

These functions are defined for all real values of x. So, the domain of the given absolute function is all real numbers

Therefore the correct option is A.

Related Questions

Stuck on this problem

Answers

step 2 would be 10

step 4 would be 10x-x = 9x =7

 x = 7/9

Step 2: 10
Step 4: 9x
7/9

Hope this helps (;

How do variables help you model real-world situations? Give an example of a model that uses variables and explain how it helps people make predictions.

Answers

Variables are an integral part of the equations. 
With equations, you can simulate almost any process. For example, you can take the formula for payroll. (P)Payment=(T)the number of hours multiplied by the (R)rate per hour.P=T*R.In this formula, rate per hour (R) is constant (sometimes  revised, of course).And the Number of hours worked is variable. Every month the number of hours changes. So, to calculate the payroll helps modeling with the use of a formula.

Why cant you add the exponnents in the product 12 exponent 3 × 11 exponent 3

Answers

Because you are multiplying the bottom numbers and not adding it so it would be 132 in the exponent of 9

Barry orders a wallet for $12.99, a sweater for $20.99, and a watch for $66.49 from a mail-order catalog. He adds $12.06 for tax, shipping, and handling. What is the total cost of Barry’s order?

Answers

Hi!

To answer this, simply add all of the values together to get the final answer. 

12.99 + 20.99 + 66.49 + 12.06 = 112.53

The answer is 112.53

Hope this helps! :)

Bradley needs to paint a logo made using two right triangles. The dimensions of the logo are shown below. What is the total area of the two triangles that need to be painted?

Two right triangles are attached along their longest side. The smaller triangle has height 6 cm and base 2 cm. The height of the larger triangle is 7 cm, and its base is 3 cm.

Answers

The formula to find area of a triangle is (base × height) ÷ 2

The area of the first triangle = (6 × 2) ÷ 2 = 6
The area of the second triangle = (7 × 3) = 10.5

Total area of the logo is 6+10.5 = 16.5 cm²

Every integer is a divisor of itself. A proper divisor of an integer means a positive divisor other than the integer itself. For example, the divisors of $8$ are $1,$ $2,$ $4,$ and $8,$ but the proper divisors of $8$ are just $1,$ $2,$ and $4$.

What is the smallest positive integer whose proper divisors add up to more than the integer itself?

Answers

the answer is 12
1x12 2x6 3x4
1+2+6+3+4=16
Final answer:

The smallest positive integer whose proper divisors add up to more than the integer itself is 12. Its proper divisors are 1, 2, 3, 4, and 6, which sum up to 16.

Explanation:

To understand this problem, we need to find the smallest positive integer whose proper divisors add up to a sum greater than the integer itself.

When we examine numbers, we find that the number 12 fits this description. The proper divisors of 12 are 1, 2, 3, 4, and 6. If we sum these up, 1 + 2 + 3 + 4 + 6, it equals 16, which is more than the number itself, 12.

Therefore, the smallest positive integer that meets this condition is 12.

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The area of a square mirror is 256in^2. A rectangular mirror has a width the same as the square mirror's width. Its length is two inches longer than its width. What is the area of the rectangular mirror?

Answers

256 = l×w

l = 2 + w

substitute the "l" in the first equation with the second equation (2+w) and solve for "w". Once you find it, plug into the second equation to find "l". Use the area formula for rectangles to find the area. Hope this helps!

Which number makes this sentence true?
21:30=x:50

A. X=30
B. X=32
C. X=35
D. X=41

Answers

the answer is a) x=30

Devaughn's age is two times Sydney's age. The sum of their ages is 30

. What is Sydney's age?

Answers

D=2S

D+ S = 30

2s+S = 30

3S=30

S=30/3 = 10

Sydney is 10

Devaughn is 2*10 = 20

What is the value of the expression if z=27 7/9z-18+1/3z

Answers

The answer for this question would be: 4/81.

Answer:

The value of the expression is 12.

Step-by-step explanation:

Given :  Expression [tex]\frac{7}{9}z-18+\frac{1}{3}z[/tex] , where z=27

To find : The value of expression when z=27

Solution :

Given expression:

[tex]\frac{7}{9}z-18+\frac{1}{3}z[/tex]

Substitute value of z=27

[tex]=\frac{7}{9}(27)-18+\frac{1}{3}(27)[/tex]

[tex]=7\times 3-18+1\times 9[/tex]

[tex]=21-18+9[/tex]

[tex]=21-9[/tex]

[tex]=12[/tex]

Therefore, The value of the expression is 12.

You need to cut a 9 foot piece of plywood into 12 inch sections. Every cut also removes 1/8 inch. How much of the plywood will be left after cutting the 12 inch sections?

Answers

There are 9 feet so it would usually be nine 12" pieces but since each cut takes away 1/8, you can only cut 8 pieces equal to 12 inches. 

Considering this fact, each cut would take away 0.125 inches. If you're cutting 8 times, you would in all be taking away 1 inch.

So aside from the eight 12" sections, you would have a leftover of 11 inches.

11 inches of  the plywood will be left after cutting the 12 inch sections.

What is Fraction?

A fraction represents a part of a whole.

Given that we need to cut a 9 foot piece of plywood into 12 inch sections and every cut also removes 1/8 inch.

We are to find the quantity of plywood that will be left after cutting the 12 inch section.

We know that  1 foot = 12 inches.

So, 9 foot = 12 × 9 = 108 inches.  

Since each cut removes 1/8  inch at ever cut, so the number of 12 inch sections will be 8.

Quantity of plywood that remained after cutting the 12 inch sections will be 108-12×8-8×1/8=11

Hence, 11 inches of  the plywood will be left after cutting the 12 inch sections.

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Which expression could be used to determine the product of –4 and 3 1/4?

Answers

Final answer:

To determine the product of -4 and 3 1/4, multiply the whole numbers and the fractions separately, and then add the results together.

Explanation:

The product of -4 and 3 1/4 can be determined by multiplying the whole number part, -4, by the whole number part of the mixed number, 3, and then multiplying the fraction part, 1/4, by the whole number part of the mixed number and adding the result to the previous product.

So, -4 × 3 = -12

and (-4) × (1/4) = -1

Therefore, the product of -4 and 3 1/4 is -12 - 1/4 = -12 1/4.

Final answer:

To find the product of -4 and 3 1/4, convert the mixed number to an improper fraction and then multiply.

Explanation:

The product of -4 and 3 1/4 can be found using the expression:

-4 x 3 1/4

To multiply a whole number by a mixed number, you can convert the mixed number into an improper fraction and then multiply:

-4 x 13/4

Multiplying whole numbers and fractions can be done by multiplying the numerators and denominators separately:

-4 x 13 = -52

4 x 1 = 4

The final answer is -52/4, which simplifies to -13.

Which unit of measurement would Guatemalans typically use to measure milk for a recipe? a) milliliters b) grams c) ounces d) gallons

Answers

Guatemalans would use milliliters because they use the metric system which is common throughout Latin America and which is basically easier to use than the Imperial system because it is all divisible by 10 whether it be millitres,litres,meters, kilometers etc.

Find the 4th term if the sequend in which a1 = 2 and a n+1 = -4a n + 2.

Answers

The given sequence is
[tex]a_{1}=2 \\ a_{n+1}=-4a_{n}+2[/tex]

Write the first 4 terms.
When n=1, obtain
a₁ = 2
When n=2, obtain
a₂ = -4a₁ + 2
    = -4(2) + 2 = -8 + 2
    = -6
When n=3, obtain
a₃ = -4a₂ + 2
    = -4(-6) + 2 = 24 + 2
    = 26
When n=4, obtain
a₄ = -4a₃ + 2
   = -4(26) + 2 = -104 + 2
   = -102

Answer:  a₄ = -102

Television screens are measured along the diagonal. A certain 53-inch television is 45 inches wide. Which measurement represents the length of the hypotenuse?

Answers

the diagonal line. try visualizing the "sliced " into half. the diagonal line will be the side opposite the 90 degree angle, and being opposite of the right angle of the triangle proves that the hypotenuse of the is its diagonal line, which is 45-inch ((:

Answer:

Step-by-step explanation:

The right answer is 53in

2x+3y=-5
3x-5y=21

The value of y that satisfies the system of the equations above is
A) 2
B)7
C) -3
D)There is no solution

Answers

You have to find a way to eliminate either x and y. We'll eliminate x:

2x + 3y = -5
3x - 5y = 21

2x*3 + 3y*3 = -5*3
3x*-2 + -5y*-2 = 21*-2

6x + 9y = -15
-6x + 10y = -42

19y = -57

y = -3

How would I set this up?

(It's suppose to be a transformation.)

Answers

find the location of the points, multiply the y by 1/3

 draw the new triangle using the new points you calculated.

How much longer is the hypotenuse

Answers

x= sqrt(6^2 +8^2)

sqrt ( 100)

x=10

10-6 = 4

it is 4 feet longer than the shortest leg

AB² = 6² + 8² = 36 + 64 = 100
AB = √100 = 10 ft

Shorter leg is AC=6 ft

AB - AC = 10 - 6 = 4 ft

The hypotenuse is 4 ft longer than the shorter leg.

Write down three different improper fractions for the number four

Answers

1, 3, and 5 I think. You should maybe search it up 

Help me quick plz thanks

Answers

add 12-3 = 9

 the difference is 9

 

Can you help me solve both

Answers

#6) 232/15 = 15.4666

sqrt(15.4666) = 3.932

3.932 * 3.932 x 15 = 231.91

 so edge is approximately 3.9 m


#7) 232/2 = 116

sqrt(116)=10.770

10.77 * 10.77 * 2 = 231.99

so edge is approximately 10.8 m


Write in standard form 60000+80000+10=

Answers

To solve this problem to standard form means adding all those numbers together. 
600,000+80,000= 680,000680,000+10= 680,010
680,010 is your answer

What is the variance of the following data? If necessary, round your answer to two decimal places.
12, 13, 8, 13, 9, 11, 12, 9, 11
a)2.99
b)3.02
c)3
d)3.01

Answers

The formula of the variance, s^2, is

s^2 = sum [ value i - average]^2 for all the data i / (number of data)

Average = [12 + 13 + 8 + 13 + 9 + 11 + 12 + 9 + 11] / 9 = 98 / 9 = 10.889

data     value - average     (value - average)^2

12        12 - 10.889              1.2346

13        13 - 10.889              4.4568

8           8 - 10.889               8.3467

13         13 - 10.889             4.4568   

9           9 - 10.889               3.5679  

11         11 - 10.889              0.0123

12         12 - 10.889             1.2346

9           9 - 10.889               3.5679          

11         11 - 9.667              0.0123
                                         ------------
                      sum             26.8889

s^2 = 26.8889 / (n) = 26.8889 / (9) = 2.988 ≈ 2.99

Answer: 2.99

I've got two of these kinds of problems and no clue how to do them, help please!

Answers

Hello,

[tex]3x^3+2x^2-3x-2=0\\ 3x^3-3x+2x^2-2=0\\ 3x(x^2-1)+2(x^2-1)=0\\ (x^2-1)(3x+2)=0\\ (x-1)(x+1)(3x+2)=0\\ Sol=\{- \dfrac{2}{3}, -1,1 \} [/tex]
Doesn't X equal 0 because anything times 0 equals 0

square root of 16r raised to the 6

Answers

If you mean:  (√(16r)^6  that is the same as:

(16r)^(1/2)^6

relevant rule:  (a^b)^c=a^(b*c), in this case

(16r)^(6*1/2)

(16r)^3

4096r^3

Answer:

4r^3

Step-by-step explanation:

The trick is to look for squared value and then to take them outside the square root but not in squared form.

Chase answers 3/4 of his math questions correctly. There were 40 questions on the test.

a. How many did he get right?

b. How many did he miss?

Answers

Since there were 40 questions on a math quiz and he got 3/4 correct he got 30 correct and 10 incorrect.
A simple way to solve this is to add a zero to the end of each number in the fraction since there is 40 questions so it goes from 3/4 correct to 30/40 correct.
Hope this helps!!
Final answer:

Chase answered 30 questions correctly and missed 10 questions.

Explanation:

To find the number of questions Chase got right, multiply the fraction of questions answered correctly (3/4) by the total number of questions (40):

Number of questions answered correctly = (3/4) * 40 = 30

To find the number of questions Chase missed, subtract the number of questions he got right from the total number of questions:

Number of questions missed = 40 - 30 = 10

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The value of 34 + 6 ⋅ 5 = ___.

Answers

the answer is 64 because you have the multiply before you add
34+6×5=

multiply

34+30=

add

64

SOMEONE PLEASE GIVE ME THE RIGHT ANSWER!
The Baldwin family walked four over five of a mile in four over nine of an hour. What is their unit rate in miles per hour?

A.) four-ninths over four-fifths equals four over nine miles per hour
B.) four-fifths over four-ninths equals one and four-fifths miles per hour
C.) four-ninths over four-fifths equals one and four-fifths miles per hour
D.) four-fifths over four-ninths equals four over nine miles per hour

Answers

(4/5) / (4/9) = 4/5 * 9/4 = 36/20 = 9/5 = 1 4/5 miles per hour

so B.) one and four-fifths mph

Answer:

B.

Step-by-step explanation:

4/5 go over 4/9 because you are trying to find the unit rate of miles per hour. Since 4/5 is the mile, put that over 4/9. Then, simply divide the two fractions. Which is 1 over 4/5.

Mariah had owed her grandfather $2.25 but was recently able to pay him back $1.50. How much does Mariah currently owe her grandfather.

Answers

2.25-1.50=.75.He already paid 1.50 so he has only .75 left to pay

Thanks for the points! BTW, I have the same question.

Solve the system of equations.
13x+2y=1
5x-2y=-19

Answers

18x = -18
x = -1
13(-1) + 2y = 1
y = 7 
(-1,7)
18x=-18
x=-1
then find y
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