63÷16 is
1. 3
2. 4
3. 3 R 15
4. 3 R 5

Answer:

5x = 8(x - 3)

5x = 8x - 24 → Expand the brackets

-3x = -24 → Collect like terms ,which simply means that you'll transfer 8x to the other side , which will make it -8x

x = 8 → Divide both sides by the coefficient of x (3) : minus cancels minus; then 24 ÷ 3 = 8.

Answer: True

Step-by-step explanation:

Based on the figure, the graph that shows the data on long distance calls on a 10-by-10 grid with appropriate scales is Graph C.

The data is to be shown on a 10-by-10 grid which means that the range of numbers on the x and y axis should be between 0 and 10.

The scales should also be appropriate which means that Time (hours) should represent the x axis and Cost (dollars) should be on the y axis.

Only Graph C has this which makes it the right one.

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The measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105

The diagram that completes the question is added as an attachment

From the diagram, we have

<1 + <2 = 180 degrees --- supplementary angles

Given that

<2 - <1 = 30 degrees

Add the above equations

So, we have

2<2 = 210

Divide both sides by 2

<2 = 105

Substitute <2 = 105 in <2 - <1 = 30

So, we have

105 - <1 = 30

Evaluate

<1 = 85

Also, we have

<3 = <1

<4 = <2

This means that

<3 = 85

<4 = 105

Hence, the measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105

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The area of the figure in the image is 800 square centimeters.

Here we have a square of sidelength of 30cm, such that in each corner we removed little squares of sidelength of 5cm.

Then the area of the figure will be the difference between the area of the first square and 4 times the area of the smaller square,

The area of a square of sidelength of 30 cm is:

A = 30cm*30cm = 900cm^2

The area of a square of sidelength of 5 cm is:

a = 5cm*5cm = 25cm^2

Then the area of the figure is:

area = A - 4a = 900cm^2 - 4*25cm^2 = 800cm^2

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The required equation for how many hours I have to work mowing lawns is f(x) = 10x + 200 and the required no. of hours is 30 hours.

A function can be thought of as an output for the given set of inputs.

According to the given question I work for 25 hours per week at the twist ice-cream shop and earn 8.00 dollars per hour.

∴ My total earning in a week will be (25×8) = 200 dollars.

But i want to earn 500 per week so need (500 - 200) = 300 dollars to reach my goal.

I also mow lawns in my neighbourhood for 10 dollars per hour.

∴  I need (300/10)  = 30 hours to earn the amount i need which is 500 dollars.

An equation can be written as

f(x) = 10x + 200, where x is the no. of hours and f(x) = 500.

500 = 10x + 200.

10x = 500 - 200.

10x = 300.

x = 300/10.

x = 30.

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Answer:

x = −2, 2

Step-by-step explanation:

[tex]f(x)=\frac{\left(x^{2}+3x+6\right)}{x^{2}-4}[/tex]

Find the horizontal asymptotes by comparing the degrees of the numerator and denominator.

Vertical Asymptotes:

x=−2,2Horizontal Asymptotes:

y=1

No Oblique Asymptotes

Full Explanation

The line x=L is a vertical asymptote of the function [tex] y=\frac{x^{2} + 3 x + 6}{x^{2} - 4}[/tex] if the limit of the function (one-sided) at this point is infinite.

In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.

So, find the points where the denominator equals 0 and check them.

x=−2, check: [tex] \lim_{x \to -2^+}\left(\frac{x^{2} + 3 x + 6}{x^{2} - 4}\right)=-\infty [/tex]

Since the limit is infinite, then x=−2 is a vertical asymptote.

x=2, check: [tex]\lim_{x \to 2^+}\left(\frac{x^{2} + 3 x + 6}{x^{2} - 4}\right)=\infty[/tex]

Since the limit is infinite, then x=2 is a vertical asymptote.

Vertical asymptotes: x=−2; x=2

Answer:

Solution

x= 2l  (2) 14+l

Step-by-step explanation:

Divide both sides

2l

2

2l

2

x

​

=

2l

2

14+l

​

The equation for the given description is 18 - 0.5x = 6

What is Equation?

A assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to symbol, or "=," is used to indicate it.

An identity, in which the variables can take on any value, or a conditional equation, in which the variables can only take on certain values, is a mathematical declaration that two expressions are identical (roots)

According to the given statement;

Since 18 less than half a number is 6

So here we assume the number be x

Now the equation is

18 - 0.5x = 6

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Answer:

2, 3

Step-by-step explanation:

The prime factorization of 6 is 2(3), so one possibility is 2 and 3.

[tex]{\huge\color{black}{\boxed{\fcolorbox{green}{red}{꧁ANSWER꧂}}}}[/tex]

Existence of an Inverse

There are two numbers that f takes to 4, f(2) = 4 and f(-2) = 4. If f had an inverse, then the fact that f(2) = 4 would imply that the inverse of f takes 4 back to 2. On the other hand, since f(-2) = 4, the inverse of f would have to take 4 to -2.

Option a: Broxton have a monthly savings of $0.18 if he purchases the brand that has the lowest price per ounce versus the highest price

Given,

Braxton’s average monthly usage of lotion = 8 ounces

The amount of two different brands of lotion are given:

Brand A: 24 ounces for $3.30

Brand B: 40 ounces for $4.60

We have to find the monthly savings of Braxton if he purchases the brand that has the lowest price per ounce versus the highest price:

We have to calculate amount for one ounce for the two brands given:

Brand A:

24 ounces for $3.30

Amount for one ounce = 3.30/24

Amount for one ounce = $0.1375

Brand B:

40 ounces for $4.60

Amount for one ounce = 4.60/40

Amount for one ounce = $0.115

Now, we have to calculate the amount for 8 ounces.

Brand A:

8 x 0.1375 = 1.1

$1.1 for 8 ounces of Brand A lotion.

Brand B:

8 x 0.115 = 0.92

$0.92 for 8 ounces of Brand B lotion.

Now, we have to calculate the savings:

Brand A – Brand B

1.1 – 0.92 = 0.18

That is, Broxton have a monthly savings of $0.18 if he purchases the brand that has the lowest price per ounce versus the highest price.

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Step-by-step explanation:

this is an exercise to take the logical definition of an operation and apply it.

we have first a triangle operation that simply stands for the sum of the 3 included values divided by 3.

in other words, FYI, it creates the mean value of 3 given numbers.

so, we need to calculate

mean value (7, 4, 4) + mean value (8, 2, 11).

(7 + 4 + 4)/3 + (8 + 2 + 11)/3 = 15/3 + 21/3 = 36/3 = 12

the second calculation is based on a table defining a new operation Delta :

2 Delta 2 = 20

2 Delta 5 = 5

2 Delta 3 = 5

5 Delta 2 = 3

5 Delta 5 = 10

5 Delta 3 = 23

3 Delta 2 = 3

3 Delta 5 = 2

3 Delta 3 = 50

so, now we need to use this to calculate

(5 Delta 2) Delta (2 Delta 3)

3 Delta 5

2

the result is 2.

Answer:

26

Step-by-step explanation:

The value equals 26

9 × 4 = 36

36 - 10 = 26

At random selection, there are 4, five-card selections possible.

Since there are only 20 cards in the deck so there are 4 sections of 5 cards each is possible as 4 × 5 = 20.

Therefore, there are 4, five-card selections possible.

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Answer:

Step-by-step explanation:

3TRWRRW

Answer:

Step-by-step explanation

t=2002-1992

t=10

p(10)=0.019(10)^3- 0.287(10)^3+ 3.073(10)+ 55.130

P(10)= 19- 287+ 30.73+ 55.130

p(10)= -182.14

Answer:

Natural number are the numbers: 1, 2, 3... (The ... means the pattern continues.  These were the first numbers that you learned about when you were little.

The whole numbers at the number 0 to the list.  0,1,2,3,...

Integers are the whole numbers and their opposites.  Zero is not positive or negative.  ...,-3, -2 -1 , 0, 1, 2, 3,....  The list does not include numbers like 1/2 or .75

Rational numbers are numbers that can be written as an integer/ integer.  This would include numbers like 1/2 and .75 because you can write .75 as 75/100(an integer over and integer.

Step-by-step explanation:

Do not get frustrated.  They are just asking for definitions of different classes of numbers.

The equivalent of 14.72 inches in centimeter is 37.3888 cm

An equation is an expression that shows the relationship between two or more numbers and variables.

The conversion from inches to cm is given by:

1 in = 2.54 cm

Hence:

14.72 in = 14.72 in * 2.54 cm per in = 37.3888 cm

The equivalent of 14.72 inches in centimeter is 37.3888 cm

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The speed of the fast plane is 490 mph while the speed of the slow plane is 400 mph

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the speed of the fast plane and y represent the speed of the slow plane.

Their speeds differ by 90mph, hence:

x - y = 90      (1)

The planes meet after 3 hours, hence:

3x + 3y = 2670    (2)

From both equations:

x = 490, y = 400

The speed of the fast plane is 490 mph while the speed of the slow plane is 400 mph

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The value of the given point after rotating the graph from the 270° clockwise around the origin is U(1,10).

According to the statement

We have to find that the value of the given points after rotation.

So, For this purpose, we know that the

The definition of a graph is a diagram showing the relationships between two or more things or equation.

From the given information:

The point U(–10,–1) after a rotation 270° clockwise around the origin.

Then

we have to rotate the graph about the clockwise

And when we rotate the graph clockwise the value of the x and y are interchanged and their signs also changed.

Thus, The value on the graph become 1,10.

So, The value of the given point after rotating the graph from the 270° clockwise around the origin is U(1,10).

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The probability of the event of a wafer to be conforming and from lot A are as follows;

(a) P(A) ≈ 0.15541

(b) P(C) ≈ 0.84

(c) P(AC) ≈ 0.159

(d) P(A|C) ≈ 0.86

(e) P(C|A) ≈ 0.185

(f) E1 and E2 are independent events

Probability is given by the ratio of the number of required outcomes divided by the number of possible outcomes.

(a) The number of wafers from lot A = 79 + 13 = 92

79+13+157+43+260+40 = 592

Which gives;

The probability that the wafer is from lot A is therefore;

(b) The conforming wafers = 79+157+260 = 496

Which gives;

(c) The conforming wafers in lot A are 79

Therefore;

The probability that the wafer is from lot A and conforming is therefore;

(d) The probability that the wafer is conforming, given that it is from lot A is therefore;

P(A|C) = 79/92 ≈ 0.86

(e) The number of conforming wafers = 496

The probability that the wafer is from lot A given that it is conforming is therefore;

(f) Independent events are events such that the occurrence of one does not impact the probability of the other.

Given that the occurrence of E1 changes the probability of event E2 if the wafer is not replaced, the events are not independent events.

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Answer:

[tex]3^{16/5}[/tex]

Step-by-step explanation:

[tex]3^3 \times \sqrt[5]{3} \\ \\ =3^3 \times 3^{1/5} \\ \\ =3^{16/5}[/tex]

The similarities between the expressions in all the three problems is that after opening brackets both of the expressions are the same.

Two expressions are similar if their values after solving are equal.

12. -3 and -(3)

Here, when we open the bracket for -(3), we obtain -3 which is the same as the first expression.

13. -1(7) and -(7)

Solving for the first expression, we get -1×7 = -7 and

-(7) = -7.

We can see that both expressions are similar.

14. -2(4) and -(2•4)

Solving -2(4), we get -2×4 = -8

And, -(2·4) = -(8) which is the same as -8

Hence, both expressions are similar.

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The graph that best describes the equations y = x + 1  y = −x − 1 is: A coordinate plane is shown with two lines graphed. One line passes through the y axis at 1 and the x axis at negative 1. The other line passes through the y axis at negative 1 and the x axis at negative 1. The lies intersect at negative 1 and 0.

A graph is a pictorial representation of data used in several disciplines. Graphs makes it easier to understand how a particular data relates with the other.

There many types of graphs, the type used here is the that of a straight line. The graph would have to cut through based on the signs that it has in the equation. That is if it is negative or positive.

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Distance between EF is 20.09 units.

By considering the given information

E=  (-4,2)

F= (16,4)

Distance between EF =

[tex]\sqrt{(16+4)^{2}+(4-2)^{2} } \\=\sqrt{400+4} \\=\sqrt{404} \\=20.09[/tex]

Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage. In coordinate geometry, the distance between two given points is calculated using the distance formula. The formula for calculating the separation between two points

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Check the picture below.

[tex]\stackrel{AC}{x}~~ + ~~\stackrel{CB}{2x}~~ = ~~\stackrel{AB}{33}\implies 3x=33\implies x=\cfrac{33}{3}\implies \boxed{x=11} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE AC}}{11}\hspace{10em}\stackrel{\textit{\LARGE CB}}{2(11)\implies 22}[/tex]

Answer:

6 push ups per day

Step-by-step explanation:

→  [tex]12 \div 2 = 6~push~ups[/tex]

Answer: 6 push-ups per day

Step-by-step explanation:

12 push-ups/2 days = 12/2 = 6 push-ups each day for 2 days to have 12 push-ups total.

Taking into account the definition of a system of linear equations, the number of box seats is 400, the number of bleacher seats is 1200 and the number of grandstand is 5400.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, the values ​​of the unknowns must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know that:

So, the system of equations to be solved is

Equation 1: B + G + BL= 7000

Equation 2: 6B + 4G + 2BL= 26400

Equation 3: B= 1/3BL

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, replacing equation 3 in equation 1 and isolating the variable G, you get:

1/3BL + G + BL= 7000

4/3BL + G= 7000

G= 7000 - 4/3BL

Substituting this expression and equation 3 into equation 2 you get

6×1/3BL + 4×(7000 - 4/3BL) + 2BL= 26400

Solving:

2BL + 4×7000 - 4×4/3BL + 2 BL= 26400

2BL + 28000 - 16/3BL + 2 BL= 26400

2BL - 16/3BL + 2 BL= 26400 - 28000

-4/3BL= -1600

BL= (-1600)÷ (-4/3)

BL= 1200

Remembering that B= 1/3BL and G= 7000 - 4/3BL and replacing the value of BL you get:

B= 1/3BL= 1/3×1200 → B= 400

G= 7000 - 4/3BL= 7000 - 4/3×1200 → G= 5400

In summary, the number of box seats is 400, the number of bleacher seats is 1200 and the number of grandstand is 5400.

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