Which number line represents the solution of 4 - 3x > 13?

Answer:

[tex]g(x)=\frac{1}{4}x-3[/tex]

Step-by-step explanation:

we have

[tex]f(x)=4x+12[/tex]

Find the inverse

step 1

Let

y=f(x)

[tex]y=4x+12[/tex]

step 2

Exchange the variables  (x for y and y for x)

[tex]x=4y+12[/tex]

step 3

Isolate the variable y

we have

[tex]x=4y+12[/tex]

Subtract 12 both sides

[tex]x-12=4y[/tex]

Divide by 4 both sides

[tex]y=\frac{x-12}{4}[/tex]

simplify

[tex]y=\frac{1}{4}x-3[/tex]

step 4

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{1}{4}x-3[/tex]

we have that

[tex]g(x)=f^{-1}(x)[/tex]

therefore

[tex]g(x)=\frac{1}{4}x-3[/tex]

Answer:

4.37%

Step-by-step explanation:

Given: Value of object in 1997 is $5000

            Value of object in 2012 is $4500.

             Number of years (2012-1997)= 15 years

∵We know that there is growth in value of object over multiple years.

∴Compound annual growth rate (CAGR)= [tex][(\frac{end\ value}{initial\ value} )^{\frac{1}{n} } ] -1[/tex]

Remember, n = number of years

∴ Growth rate=  [tex][(\frac{9500}{5000} )^{\frac{1}{15} } ]-1[/tex]

⇒Growth rate= [tex][(1.9)^{\frac{1}{15} } -1][/tex]

⇒Growth rate= [tex](1.9)^{0.0667} -1= 1.0437-1[/tex]

⇒ Growth rate= 0.0437

Now, finding percentage of growth rate

∴ [tex]0.0437\times 100= 4.37\%[/tex]

∴ Annual growth percent over the period of time is 4.37%

Answer:

△JKL ≅ △XYZ by HL congruency for right triangles

Step-by-step explanation:

If only given two sides and an uncontained angle, the triangles may not necessarily be congruent. However, since the given angle is a right angle, they are congruent.

When given that the hypotenuse and any "leg" of the right triangles are equal, the triangles are congruent.

Since one angle is 90°, the other two angles must be acute. This is unlike the ambiguous case when given an uncontained acute angle, where two possible triangles can be made by making another angle obtuse.

Imagine an isosceles triangle cut in half at the altitude, creating two right triangles (JKL and XYZ). They have the same angle measures. Each with a right angle, the angle that had an equal measure in the isosceles, and the unequal angle bisected. For the triangles' sides, the isosceles base was bisected by the altitude, and they have the same altitude.

Answer:

1) [tex]9\frac{1}{6}-8\frac{5}{6}=\frac{1}{3}[/tex]

2) [tex]10\frac{3}{4}-6\frac{4}{4}=3\frac{3}{4}[/tex]

Step-by-step explanation:

You can convert he mixed numbers to improper fractions:

1. Multiply the whole number part by the denominator of the fraction.

2. Add the product obtained to the numerator.

3. The denominator does not change.

Then:

[tex]9\frac{1}{6}=\frac{54+1}{6}=\frac{55}{6}\\\\8\frac{5}{6}=\frac{48+5}{6}=\frac{53}{6}\\\\10\frac{3}{4}=\frac{40+3}{4}=\frac{43}{4}\\\\6\frac{4}{4}=\frac{24+4}{4}=\frac{28}{4}[/tex]

Observe that, in each subtraction, the denominators are equal, then you can rewrite the denominator and subtract the numerators:

[tex]1)\ \frac{55}{6}-\frac{53}{6}=\frac{55-53}{6}= \frac{2}{6}=\frac{1}{3} \\\\2)\ \frac{43}{4}-\frac{28}{4}=\frac{43-28}{4}= \frac{15}{4}[/tex]

Divide 15 by 4. The quotient will be 3 and the remainder 3.

Then:

[tex]\frac{15}{4}=3\frac{3}{4}[/tex]

Final answer:

To find the product, multiply 400 by 9.460730473, then multiply the result by 2/3.

Explanation:

To find the product of 400 and 9.460730473 times 10/15, we need to multiply the three numbers together. First, let's simplify 10/15 to 2/3. Then, multiply 400 by 9.460730473 to get the product. Finally, multiply the result by 2/3 to find the final answer.

400 x 9.460730473 = 3784.2921892

3784.2921892 x 2/3 = 2522.8614595

The product of 400, 9.460730473, and 10/15 is approximately 2522.8614595.

Rena's answer is correct.

To evaluate whether Rena's answer is correct, we need to perform the division of the two fractions 3/4 and 2/5. To divide one fraction by another, you multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping its numerator and denominator.
Here is a step-by-step solution:
Step 1: Write down the problem.
\[ \frac{3}{4} \div \frac{2}{5} \]
Step 2: Find the reciprocal of the second fraction.
The reciprocal of \( \frac{2}{5} \) is \( \frac{5}{2} \).
Step 3: Multiply the first fraction by the reciprocal of the second.
\[ \frac{3}{4} \times \frac{5}{2} \]
Step 4: Multiply the numerators together and the denominators together.
\[ \frac{3 \times 5}{4 \times 2} \]
\[ \frac{15}{8} \]
Step 5: Simplify the fraction if necessary.
In this case, \( \frac{15}{8} \) is an improper fraction because the numerator is larger than the denominator. We can convert it into a mixed number.
The whole number part of the mixed number is obtained by dividing the numerator by the denominator:
\[ 15 \div 8 = 1 \text{ with a remainder of } 7 \]
So, the mixed number is \( 1 \frac{7}{8} \).
Conclusion:
Rena's answer of \( 1 \frac{7}{8} \) is correct. The statement about her answer is true; she correctly evaluated the division of \( \frac{3}{4} \) by \( \frac{2}{5} \).

Answer:

2.3 × [tex]10^{-4}[/tex] is 20,000 times greater than 1.15 × [tex]10^{-8}[/tex]

Step-by-step explanation:

Given as :

The first number= x = 2.3 × [tex]10^{-4}[/tex]

The second number= y = 1.15 × [tex]10^{-8}[/tex]

Let The first number is z times greater than second number

i.e x = z × y

Or, z = [tex]\dfrac{x}{y}[/tex]

Or, z = [tex]\dfrac{2.3\times 10^{-4}}{1.15\times 10^{-8}}[/tex]

Or, z = 2 × [tex]10^{4}[/tex]

∴  z = 20,000

So,The first number is 20,000 times greater than second number

Hence, 2.3 × [tex]10^{-4}[/tex] is 20,000 times greater than 1.15 × [tex]10^{-8}[/tex] . Answer

Step-by-step explanation:

2x²-4x=0

2x²=4x

[tex] \frac{2x {}^{2} }{x} = 4[/tex]

2x=4

x=2

Answer: 50%

Step-by-step explanation:

Answer: Nope it's 55%

Step-by-step explanation:

Answer:

36 more students of grade 7 went on a trip than students of grade 6

Step-by-step explanation:

60 % of 110 students= 60/100*110= 66 students

85 % of 120 students= 85/100 * 120= 102 students

No of students of grade 7th more than 6th grade students= 102-66= 36

60% of the 6th grade band members and 85% of the 7th grade band members went on a trip Disney World trip. Then 36 more 7th graders went on the trip than 6th graders

percentage, a relative value indicating hundredth parts of any quantity.

Given,

The number of students in 6th grade=100

The number of students in 7th grade=120

60% of the 6th grade band members

60%×110

60/100×110=0.6×110=66

85% of the 7th grade band members

85%×120=85/100×120

=0.85×120=102

We need to find how many more 7th graders went on the trip than 6th graders

For this we need to find difference of 7th and 6th grade

102-66=36

Hence 36 more 7th graders went on the trip than 6th graders

To learn more on Percentage click:

https://brainly.com/question/28269290

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Answer: One small box of oranges costs $7 and one large box of oranges costs $13.

Step-by-step explanation:

Let be "s" the cost in dollars of one small box of oranges and "l"  the cost in dollars of one small box of oranges.

Based on the data given in the exercise, you can set up the following System of equations:

[tex]\left \{ {{3s+14l=203} \atop {11s+11l=220}} \right.[/tex]

Use the Elimination Method to solve it:

- Multiply the first equation by 11 and the second one by -3.

- Add the equations.

- Solve for "l".

Then:

[tex]\left \{ {{33s+154l=2233} \atop {-33s-33l=-660}} \right.\\...............................\\\\121l=1573\\\\l=13[/tex]

- Substitute the value of "l" into any original equation and solve for "s":

[tex]3s+14(13)=203\\\\3s=203-182\\\\s=\frac{21}{3}\\\\s=7[/tex]

Answer:

 116 280

Step-by-step explanation:

number of combination = 20 x 19 x 18 x 17 = 116 280

HOPE THIS HELPED ;3

The number of different combinations are there if the numbers must be all different is 19380.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.

Given that, a combination lock has 20 numbers on it.

Different three-number combinations

= 20!/3!(20-3)!

= 20×19×18×17!/3!×17!

= 20×19×18×17/(3×2×1)

= 10×19×6×17

= 19380

Therefore, the number of different combinations are there if the numbers must be all different is 19380.

To learn more about the permutation and combination visit:

https://brainly.com/question/28065038.

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"Your question is incomplete, probably the complete question/missing part is:"

A combination lock has 20 numbers on it. How many different three-number combinations can be made? How many different combinations are there if the numbers must be all different?

Answer:

c=4

Step-by-step explanation:

Answer:

C=4

Step-by-step explanation:

when solving these equations you have to get the letter by itself and in this case the 4 is being multiplied by the c so you have to do the opposite and divide the 4 from the c and divide 16 by 4 because what you do to one side of the equal sign you have to do to the other side.

Step-by-step explanation: To determine whether the relation shown here is a function, it's important to understand that a function is a relation in which each x-term corresponds to exactly one y-term.

Each of the x-terms shown here 1, 2, 3, 4, and 5 appears only once so each x-term corresponds to only one y-term. So yes, this relation is a function.

The domain of a relation is the set of all the x-terms of the relation. So here, the domain will be the set of all the x-terms or {1, 2, 3, 4, 5}.

The range of a relation is the set of all the y-terms of the relation. SO here, the range will be the set of all the y-terms or {1, 2, 5, 10, 15}.

Since the sales tax is 6%, the object will cost 1.06 (100% + 6%) times the original value.

1.06 × $95.00 = $100.70

The object will cost $100.70.

Let me know if you need any clarifications, thanks!

Answer:

a. true

b. false

c. true

d. false

Step-by-step explanation:

a. A product raised to a power is equivalent to each of the multiplicand raised to that power as well. Example:

  (xyz)ⁿ = xⁿyⁿzⁿ

  (1·3·7)² = 1²(3²)(7²)

b. Is wrong. When you have addition/subtraction inside a parentheses, you have to foil. Example:

  (a + b)² = (a + b)(a + b)

               = a² + 2ab + b²

  (1 + 3)² = (1 + 3)(1 + 3)

               = 1² + 2(1)(3) + 3²

               = 16

c. Numbers with the same root can be merged when you're multiplying/dividing them. Example:

  √(a)√(b) = √(ab)

  √(2)√(3) = √(2·3) = √(6)

d. You can only merge or split the root when multiplying/dividing.

You CANNOT merge the root when adding/subtracting.

  √(a ± b) ≠ √(a) + √(b),    this is NOT allowed

e. I already gave examples in the previous parts.

Answer:

D

Step-by-step explanation:

For a function to be true, there cannot be the same x used for two different ys. D is the only table that follows this rule.

Answer:

46 and 47.

Step-by-step explanation:

If x is one of the integers then the other is x+1.

x + x + 1 = 93

2x = 92

x = 46.

Answer:

Step-by-step explanation:

3x+4y=5

6x+8y=10

---------------

-2(3x+4y)=-2(5)

6x+8y=10

----------------

-6x-8y=-10

6x+8y=10

------------------

0=0

Answer: Infinitely many solutions.

------------------------------------------------------

7x-2y=9

7x-2y=13

--------------

-1(7x-2y)=-1(9)

7x-2y=13

---------------------

-7x+2y=-9

7x-2y=13

-------------

0=4

Answer: NO Solution.

-------------------------------------

2x-y=-11

-2x+y=11

-----------------

0=0

Answer: Infinitely many solutions.

-----------------------

3x+6y=1

x+y=0

x=0-y=-y

3(-y)+6y=1

-3y+6y=1

3y=1

y=1/3

x=-y=-1/3

Answer: x=-1/3, y=1/3. (-1/3, 1/3).

Answer:69

Step-by-step explanation:

69

Answer: B. Adjacent

Step-by-step explanation: They share a common side and vertex

the answer is c

Step-by-step explanation:

12

23

34

56

512

the answer is c

Step-by-step explanation:

12

23

34

56

Answer:

2.15

×

10

−

3

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

The answer is 2.15 * 10^-3

Step-by-step explanation:

I got this answer from Khan Academy.

Hope this helps! :)

Answer:

16. Disagree because 0.1 0f 0.1 is 0.01

17. the whale swam for 19 to 21.7 hours. Because 152/8=19 and 152/7=21.7

18. Meg can use 15,000 / 50 because 14,270 rounded up to by the thousand will be 15,000.

19. 61.5 because 3016/7 = 430.8   430.8/7=61.5

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

2+1=3

3*3/2=4.5

it would not make sense if it was 2/3 cuz look what u get.......

3*2/3=2

Answer:

Step-by-step explanation:

If x and y are proporttional then

[tex]\dfrac{y}{x}=costant\to\dfrac{y}{x}=a\to y=ax[/tex]

From the table we have x = 2 and y = 3.

Substitute:

[tex]3=2a[/tex]          divide both sides by 2

[tex]\dfrac{3}{2}=\dfrac{2a}{2}\\\\\dfrac{3}{2}=a\to a=\dfrac{3}{2}[/tex]

Therefore we have:

[tex]y=\dfrac{3}{2}x[/tex]

We increase x by 1:

[tex]y_1=\dfrac{3}{2}(x+1)[/tex]             use the distributive property

[tex]y_1=\underbrace{\dfrac{3}{2}x}_{y}+\dfrac{3}{2}\Rightarrow y_1=y+\dfrac{3}{2}[/tex]

Answer:

The estimated population in 2025 will be 22261221.

Step-by-step explanation:

Let us assume that the annual growth rate is compounded annually on the population.

Now, in 2000, the population was 19169000 and the annual growth rate is 0.6%, the the population in the year 2025 will be given by  

[tex] 19169000(1 + \frac{0.6}{100} )^{25} = 22261220.7[/tex] ≈ 22261221

Therefore, the estimated population in 2025 will be 22261221. ( Answer )

Answer:

2 times

Step-by-step explanation:

Mai biked [tex]7\frac{1}{4} = \frac{29}{4}[/tex] miles today and Noah biked [tex]3\frac{5}{8} = \frac{29}{8}[/tex] miles  today.

We are asked how many times the length of Noah's bike ride was Mai's bike ride.

Therefore, the length of Mai's bike ride was [tex](\frac{29}{4} \div \frac{29}{8})  = 2[/tex] times the length of Noah's bike ride.  

Therefore, we will take option B will be correct. ( Answer )

Answer:

x  =    1

   ----------

     82V

Step-by-step explanation:

Answer:

No, we can't.

Step-by-step explanation:

Let x be the amount of time it takes each machine to make 1 cockpit, and y be the amount of time it takes each machine to make 1 propulsion system.

For machine A: 22 hours to produce 3 cockpits and 5 propulsion system.

For machine B: 44 hours to produce 6 cockpits and 10 propulsion system.

So, this will produce the following system of equations:

3x + 5y = 22  ⇒(1)

6x + 10y = 44  ⇒(2)

We can note that the second equation is two times the first equation.

So, the two equation are actually represent one equation.

OR, by another way the two equation have the same slope and y-intercept

So, the two equation are identical, therefore, we can't solve one equation with two variables.

Also, see the attached figure.

equation (1) with blue color and the second equation with red color.

Answer: 18%

Step-by-step explanation:

The percentage spent on book = cost of books / total cost x 100

% spent on book = 504/2800 x 100

= 18

Therefore , the percentage spent on book is 18