Solve the equation for the given variable
2x - y = z ;x

Answer:

0.0625

Step-by-step explanation:

If the function f(x) varies inversely with x, then this function is of the form

[tex]f(x)=\dfrac{a}{x},[/tex]

where a is unknown number.

Since  f(x)=0.5 when x =0.3, then

[tex]0.5=\dfrac{a}{0.3},\\ \\a=0.5\cdot 0.3=0.15.[/tex]

Therefore, the function is

[tex]f(x)=\dfrac{0.15}{x},[/tex]

Now when x=2.4,

[tex]f(2.4)=\dfrac{0.15}{2.4}=\dfrac{15}{240}=\dfrac{1}{16}=0.0625.[/tex]

Answer:

3

Step-by-step explanation:

The zero at the point x=3 is a result of a factor of even degree, because the function does not change sign as the value of (x -3) changes sign. Since a cubic only has 3 factors, the even degree must be 2. That is, (x -3)² is a factor of f(x) and the root at x=3 has multiplicity 2.

Answer:

4/15

Step-by-step explanation:

Experimental probability is the actual times the event occurs divided by the number of trials

Actual times : 8

Number of trials: 30

Experimental probability of a 2: 8/30 = 4/15

Answer:

Short Answer: B

Step-by-step explanation:

You want to solve for x in

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

We have been given that our Einstein has baked a cake and cut it into 8 slices. So each slice will be equal [tex]\frac{1}{8}[/tex].

He hands out 3 slices to his guests. Let us find out part of the cake given to guests.

[tex]\text{The part of the cake given to guests}=\frac{1}{8}+\frac{1}{8}+\frac{1}{8}[/tex]

[tex]\text{The part of the cake given to guests}=\frac{1+1+1}{8}[/tex]

[tex]\text{The part of the cake given to guests}=\frac{3}{8}[/tex]

To find the fraction of left cake we will subtract [tex]\frac{3}{8}[/tex] from 1 as Einstein has 1 whole cake.

[tex]\text{fraction of cake is left}=1-\frac{3}{8}[/tex]

[tex]\text{fraction of cake is left}=\frac{8}{8}-\frac{3}{8}[/tex]

[tex]\text{fraction of cake is left}=\frac{8-3}{8}[/tex]

[tex]\text{fraction of cake is left}=\frac{5}{8}[/tex]

Therefore, [tex]\frac{5}{8}[/tex] of the cake is left.

Answer:

As per the given statement: Our Einstein has baked a cake and cut it into 8 slices.

⇒ Total slice of cake Einstein has baked = 8

Also, it is given that if he hands out 3 slices to his guests.

⇒ Number of slice he hands out to his guests = 3

Remaining slice of a cake Einstein left with = 8 -3 = 5.

We have to find the fraction of the cake is left.

Fraction states that a fraction is a number that represents a part of a whole. Also, It consists of a numerator and a denominator, where numerator represents the number of equal parts of a whole, while the denominator is the total number of parts.

Fraction of the cake is left = [tex]\frac{\text{Slices of cake left}}{\text{Total number of slices of a cake}}[/tex]

Substitute the given values we get;

[tex]\text{Fraction of the cake is left} =\frac{5}{8}[/tex]

therefore, the fraction of the cake is left is,  [tex]\frac{5}{8}[/tex]

If a, b and c are the lengths of the sides of a triangle then

if a ≤ b ≤ c, then a + b > c.

A: 4, 12, 15

4 + 12 = 16 > 15    CORRECT :)

B: 4, 13, 15

4 + 13 = 17 > 15   CORRECT :)

C: 4, 4, 15

4 + 4 = 8 < 15   INCORRECT :(

D: 4, 15, 15

4 + 15 = 19 > 15  CORRECT :)

E: 4, 11, 15

4 + 11 = 15   INCORRECT :(

F: 4, 15, 19

4 + 15 = 19  INCORRECT :(

Answer:

2. It can be solved by using the multiplication property of equality.

3. The equation should be: [tex]\frac{x}{18}=109.8[/tex]

6. The answer is 1,976.4.

Step-by-step explanation:

Let x be the number.  

We have been given that the quotient of a number and 18 is 109.8.

Since we know that in a division problem the number which is being divided called dividend and by which number we divide is called divisor.

[tex]\text{Dividend}\div \text{Divisor }=\text{ Quotient}[/tex]

We can represent our given information as:

[tex]\frac{x}{18}=109.8[/tex]

By using multiplication property of equality we will get,

[tex]18*\frac{x}{18}=18*109.8[/tex]

[tex]x=18*109.8[/tex]

[tex]x=1976.4[/tex]

Upon looking at our given choices we can see that 2nd, 3rd and 6th statements are correct choices.

Answer:

41

Step-by-step explanation:

We know that complex numbers are a combination of real and imaginary numbers

Real part is x and imaginary part y is multiplied by i, square root of -1

Modulus of x+iy = [tex]\sqrt{x^2+y^2}[/tex]

Here instead of x and y are given 9 and 40

i.e. 9+40i

Hence to find modulus we square the coefficients add them and then find square root

|9+49i| =[tex]\sqrt{9^2+40^2} =\sqrt{1681}[/tex]

By long division method we find that

|9+40i| =41

Answer:  Modulus of |9+40i| =41

Step-by-step explanation:

Since we have given that

[tex]z=\mid9+40i\mid[/tex]

Here,

[tex]z=a+bi\\\\where,\\\\a=\text{real number}=9\\\\b=\text{imaginary number}=40[/tex]

We need to find the modulus of z:

[tex]\mid z\mid=\sqrt{a^2+b^2}[/tex]

[tex]\mid z\mid=\sqrt{9^2+40^2}\\\\\mid z\mid=\sqrt{81+1600}\\\\\mid z\mid=\sqrt{1681}\\\\\mid z\mid=41[/tex]

Hence, Modulus of |9+40i| =41

Answer:

the answer is 3

Step-by-step explanation:

3 pizzas equal $9.00 so in order to know how much each pizza was, we will have to do division:

9 divided by 3

9/3

3

To find the total cost for the family to attend the baseball game, we substitute the given ticket prices into the expression 2a + 3c, where a is the cost of an adult ticket and c is the cost of a child ticket, resulting in a total cost of $70.

The student is asking about the cost for a family to attend a baseball game with the given prices for adult and child tickets.

Given the cost of an adult ticket as $17 and a child ticket as $12, we use the expression provided (2a + 3c) to calculate the total cost for the family.

Substituting the given values into the expression, we get 2(17) + 3(12), which equals 34 + 36.

Summing up these two products gives us a total of $70.

Therefore, it will cost the family $70 to attend the baseball game.

Answer:

Hence third choice RQ, RP, PQ is correct.

Step-by-step explanation:

We know that if A, B, C are the angles of the triangle and if ∠A > ∠B

a>b   {Where “a” is side created by angle A and “b” is side created by angle B }.

We will use same property to decide which side is bigger.

In triangle PRQ,

∠P = 30 degree

∠R = 85 degree

then ∠P + ∠R + ∠Q = 180 {since sum of all three angle of triangle is 180 degree}

30 + 85 + ∠Q = 180

115 + ∠Q = 180

∠Q = 180 - 115

∠Q = 65

Now we know measure of all angles so we can do comparison using above property.

Smallest angle is ∠P so side RQ will be smallest.

Largest angle is ∠R so side PQ will be largest.

Hence we get RQ < RP < PQ.

Hence third choice RQ, RP, PQ is correct.

Answer:

if you still need the answer, its C.

Step-by-step explanation:

Answer:

D) y = -1/3 x+6

Step-by-step explanation:

If we want to find a line parallel to 3x+9y=7, the slopes will have to be the same because parallel lines have the same slope.  Knowing y= mx+b we need to find the slope of the old line.

3x+9y=7

Subtract 3x from each side

3x-3x +9y = -3x+7

9y = -3x+7

Divide each side by 9

9y/9 = -3x/9 + 7/9

y = -1/3 x + 7/9

We know the slope of the  old line is -1/3, so the slope of the parallel line is -1/3.

If we know the slope of the line and a point, we can use the point slope form of a line

y-y1 = m(x-x1)

y-4 = -1/3(x-6)

Distribute the -1/3

y-4 = -1/3 x -1/3*-6

y-4 = -1/3x +2

Add 4 to each side

y-4+4 = -1/3x +2+4

y = -1/3x+6

A recursive rule for a geometric sequence:

[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]

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

[tex]a_1=3\\\\a_n=\dfrac{1}{2}a_{n-1}\to \boxed{r=\dfrac{1}{2}}[/tex]

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

Exciplit rule:

[tex]a_n=a_1r^{n-1}[/tex]

Substitute:

[tex]a_n=3\left(\dfrac{1}{2}\right)^{n-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot\left(\dfrac{1}{2}\right)^{-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot2\\\\\boxed{a_n=6\cdot\left(\dfrac{1}{2}\right)^n}[/tex]

Answer:

The answer is: a_n = 6*(1/2)^n

This problem deals with dependent events in probability. The probability of picking two good apples in a row from a bag containing 7 good and 3 bad apples, without replacement, is calculated as (7/10)*(6/9), which equals 0.467.

The subject of this question is Mathematics, specifically probability. When Nick picks two apples without replacement, we are dealing with dependent events, since the outcome of the second event depends on the outcome of the first event. Dependent events require a different calculation for the probability.

The total apples in the bag initially are 7 good + 3 bad = 10 apples. The probability of picking a good apple on the first draw is 7/10 or 0.7. When one apple is taken out, there are now 9 apples left in the bag. If the first apple was good, the probability of picking the second good apple is now 6/9 or 2/3.

Since these are dependent events, the total probability of picking two good apples in a row would be (7/10) * (6/9) which reduces to 14/30 or approximately 0.467.

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The first part of the proportion would be the known values of 32 people to 128 ounces.

The second part of the proportion is X ( the number of people) for 704 ounces.

This is written as 32/128 = X/704

To solve for X Cross multiply:

32 * 704 = 128x

Simplify:

22528 = 128x

Solve for X by dividing both sides by 128:

x = 22528 / 128

x = 176 people

Answer:

The author must sell 3000 books.

Step-by-step explanation:

The total amount earned  = advance + books sold * money per book

We know they want to make 7000

The advance is 2500

They earn 1.50 for each book sold

b= number of books sold

Substituting in

7000= 2500 + 1.5b

Subtract 2500 from each side

7000-2500 = 2500-2500 + 1.5 b

4500 = 1.5 b

Divide each side by 1.5

4500/1.5 = 1.5b/1.5

3000 = b

Answer: -2

=====================================================

Draw a vertical line through 4 on the x axis. This vertical line crosses the parabola at some point (which we'll call point A). Draw a horizontal line from point A to the y axis and note how it lands on y = 12. Therefore the point (4,12) is on this parabola.

Repeat the same steps as before to find that (8,4) is also on the parabola

We need to find the slope of the line through (4,12) and (8,4)

m = (y2 - y1)/(x2 - x1)

m = (4-12)/(8 - 4)

m = -8/4

m = -2

The slope of this line is -2 meaning that the average rate of change from x = 4 to x = 8 is -2.

The line goes down 2 units each time you move to the right 1 unit.

Answer: [tex]\bold{(A)\ \dfrac{\text{51 miles}}{\text{1 hour}}}[/tex]

Step-by-step explanation:

Consider the formula "distance (d) = rate (r) x time(t)" and solve for r.

d = r · t

÷ t  ÷ t  

[tex]\dfrac{d}{t}=r[/tex]

Now plug in the given d and t values from the table to solve for r:

[tex]r=\dfrac{\text{204 miles}}{\text{4 hours}}[/tex]

    [tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]   simplified the fraction

You can check this by plugging in the other 3 values from the table:

[tex]r=\dfrac{\text{306 miles}}{\text{6 hours}}[/tex]

    [tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]  

[tex]r=\dfrac{\text{408 miles}}{\text{8 hours}}[/tex]

    [tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]  

[tex]r=\dfrac{\text{510 miles}}{\text{10 hours}}[/tex]

    [tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]  

Answer:

f(x) = 2x

Step-by-step explanation:

Remark

What I'm about to do is probably not the best way to do this question, but it is right. The plan is to take out a common factor on the right of f(x - 2) and then derive f(x) from that.

Solution

Check

Final answer:

To find f(x), replace x - 2 with y to get f(y) = 2(y + 2) - 4, simplify to f(y) = 2y, then revert y back to x to find f(x) = 2x.

Explanation:

To find the function f(x) when you know that f(x - 2) = 2x - 4, you need to replace x - 2 with y so that x = y + 2. Therefore, f(y) = f(x - 2) = 2x - 4 becomes f(y) = 2(y + 2) - 4.

Simplifying this, we get:
f(y) = 2y + 4 - 4
f(y) = 2y.

Now, to revert back to the original function, replace y with x to get f(x) = 2x. This is the function we were looking to find.

Answer:

B

Step-by-step explanation:

The interior of the 4 triangles in the rhombus are right angle triangles. In addition AC is bisected by BD and BD is bisected by AC. Those form the sides of the right angle triangle.

So the sides of the right angle are

The area of one right angle is

The answer is B

Answer:

B. 125.5 square units

Step-by-step explanation:

The area of a rhombus is half the product of the diagonals.

If the diagonals have lengths a and b, then the are is:

area = ab/2

area = (17)(15)/2

area = 255/2

area = 127.5

Answer: B. 125.5 square units

Answer:

Option 3rd is correct

Step-by-step explanation:

Kevin takes a survey of the ages of people in the library at 10a.m and at 6p.m on a Wednesday.

He should talk at library to new drivers on the dangers of texting and driving at the time when there are more people with the car.

So, that he can convey messages to more people in less time.

Therefore, Option 3rd is correct that is  At 10 a.m., because there are more people with cars at the library at that time

Answer:

1 is correct.

Step-by-step explanation:

I had the same question and I tried the other answer and so it was wrong. And in the correction I had, it was the first one.

Answer:

143 miles

Step-by-step explanation:

Let the distance Karly biked be x

Then Dory biked 11x

So x+11x=156

x=156/12=13

So Dory biked 11 ⋅ 13= 143 miles

Is this correct?

Answer:

The numbers are 8 and 13

Step-by-step explanation:

In order to find this, we set the smaller number as x. Then we can set the larger one as x + 5, since it is 5 more than the smaller.

Given these two, we can then set them equal to 3x - 3, since the answer is three less than three times the larger.

x + x + 5 = 3x - 3

2x + 5 = 3x - 3

5 = x - 3

8 = x

Now to find the larger number, put into the larger number equation.

x + 5

(8) + 5

13

The numbers are 8 and 13.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''One number is five more than another and their sum Is there less than three times the smaller''.

Now,

Let the smaller number = x

Then, The another number = x + 5

Write the expression as;

x + x + 5 = 3x - 3

2x + 5 = 3x - 3

2x - 3x = - 3 - 5

- x = - 8

x = 8

And, The another number = x + 5

                                        = 8 + 5

                                        = 13

Thus, The numbers are 8 and 13.

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Answer: 10 cm

Step-by-step explanation:

Given: The volume of a solid piece of an aluminium cylindrical rod =[tex]200\cm^3[/tex]

The base area of cylinder = [tex]20\ cm^2[tex]

We know that the volume of cylinder is given by :-

[tex]\text{Volume]=\text{base area}\times \text{height}\\\\\Rightarrow200\=20\\times h\\\\\Rightarrow\ h=\frac{200}{20}=10[/tex]

Hence, the length of the piece of aluminium rod = 10 cm

To find the length of the aluminum rod with a volume of 200 cm³ and a base area of 20 cm², divide the volume by the base area. The length is 10 cm.

If a solid piece of an aluminum cylindrical rod has a volume of 200 cm3 and a base area of 20 cm2, to find the length of the aluminum rod, we can use the formula for the volume of a cylinder, which is Volume = Base Area  imes Height (or length in this case, since it's a rod). Given the volume (V) is 200 cm³ and base area (A) is 20 cm², the length (L) can be calculated as L = V / A.

When you divide 200 cm³ by 20 cm², the result is:

L = 200 cm³ / 20 cm² = 10 cm.

Therefore, the length of the aluminum rod is 10 cm.

Answer: 59/120 (choice D)

Add up the values in the "math" column and the "11th" row to find the total number of people who are either in 11th grade, in math, or in both.

So,

(12+10+8+7) + (14+5+3) = 59

represents the number of people who are in either category. This is out of 120 (given). This is where 59/120 comes from.

1 fence panel required 8 wooden slates and 8 fence panels required 64 wooden slates.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Wooden slates required to make 4 fence panels = 32

To find wooden required to make 1 panel, use ratio property,

4 fence panels = 32 wooden slates

1 fence panel = 8 wooden slates

Also, to find wooden required to make 8 panels, use ratio property,

4 fence panels = 32 wooden slates

8 fence panels = 64 wooden slates

1 fence panel required 8 wooden slates and 8 fence panels required 64 wooden slates.

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Final answer:

Gerard needs 64 slats to make 8 panels, as it is a proportional relationship.

Explanation:

To find out how many slats are needed for one panel, we simply divide the total number of slats by the number of panels. Since a builder uses 32 slats to make 4 panels, for one panel, Fatima would need:

Number of slats for one panel = Total number of slats \/ Number of panels

Number of slats for one panel = 32 / 4 = 8 slats

For Gerard's question, if 1 panel requires 8 slats, then to make 8 panels he would need:

Number of slats for 8 panels = Slats per panel x Number of panels

Number of slats for 8 panels = 8 x 8 = 64 slats

It's a straightforward example of a proportional relationship in mathematics, where the number of slats scales directly with the number of fence panels.

Answer:

the footballer's average pay would be $4 million/annum.