Help with solving variable equations with variables on both sides.

Answer:

a)

[tex] {( \sqrt{5}) }^{2} \times {( \sqrt{3}) }^{2} = 5 \times 3 = 15[/tex]

b)

[tex]( { \sqrt[3]{9} )}^{3} \times ( { \sqrt{30} )}^{2} = 9 \times 30 = 270[/tex]

Um, I'm not directly sure what you mean but if its 5-2 then it makes 3.

I don't get this question. But, if its 5 - 2 it is 3.

Hope this helps! :)

Given that speed of the cyclist = 36 kilometers per hour.

Now question says to find the speed in meters per second.

We know that 1 kilometer = 1000 meter

and 1 hour = 3600 seconds

so to convert 36 kilometers per hour into meter per second, we will multiply 36 by 1000/3600

36*1000/3600

=36*10/36

=10

Hence final answer is speed = 10 meters per second.

That 10 meters per second means cyclist will travel 10 meters in 1 second.

Now to find distance travelled in 5 seconds, we just need to multiply 10 and 5

So the final answer will be 10*5 or 50 meters.

Since x=228 and the next age group count (men) is 309, expressed as a sum: x+81

-1 1/8 because -9/8 is equal to [tex]-\frac{9}{8}[/tex] so just make it a improper fraction, pretend the negative is not there then add the negative at the end

-hope this helps :D

Final answer:

To find the average speed of the big airplane that leaves after the small airplane, calculate the time the small airplane took to cover the distance and then use that to find the time the big airplane spent traveling to determine its speed. The average speed of the big airplane is 500 mph.

Explanation:

The average speed of the small airplane can be calculated using the formula:

Speed = Distance / Time

Given that the small airplane travels 625 miles at an average speed of 250 mph, the time taken is 625 / 250 = 2.5 hours. As the big airplane leaves 1.25 hours later and both planes arrive at the same time, the big airplane traveled for 2.5 - 1.25 = 1.25 hours. The average speed of the big airplane can be calculated as 625 miles / 1.25 hours = 500 mph.

no because the first five equals 5000

the second 5 equals 500

the third 5 equals 50

and the fourth 5 equals 5.

This is the distributive property because you are distributing the 9 into both terms of the parenthesis.

(10 + 7) x 9  = 10(9) + 7(9)

Answer: Distributive Property

i believe its distributive property

680*.0013=.884 because 6.8*10^2=680 and 1.3*10^-3=.0013 when you multiply them it'll give you .884

always move the decimal point the number of times that 10 is to the power to.

for example if its a negative number you move the decimal back and add zeros

if its a positive number move forward and add zeros

Answer:

8.84x10^-1

Step-by-step explanation:

Thankyou

To solve this problem, we set up equations based on the fact both boys cover the same distance in the given time. Taking Matthew’s speed as ‘x’, we find that 'x' equals 40 yards per minute, meaning Matthew’s speed is 40 yards per minute and Lowe’s is 120 yards per minute.

The scenario can be resolved by employing the concepts of rate, time, and distance. Here, we need to recognize that 'rate' stands for the speed at which each boy is moving, 'time' signifies the duration in which Lowe overtakes Matthew, and 'distance' represents how far Matthew was when Lowe started pursuing him.

In this instance, Lowe's speed is stated to be three times faster than Matthew's speed. Since both boys are present in the same place after 30 minutes (when Lowe overtakes Matthew), we can say that they've both traveled the same distance. We can state this mathematically as:

Matthew's speed * 30 minutes = 1200 yards, and Lowe's speed * 30 minutes = 1200 yards

As we know that Lowe's speed is three times Matthew's speed, let's consider Matthew's speed as 'x'. As a result,

Lowe's pace becomes '3x'.

Because both equations equal 1200 yards, we may set the two equations equal to each other and solve for 'x':

x * 30 = 3x * 30

Dividing both sides by 30 yields 'x' = 40 yards per minute. Therefore, Matthew's speed is 40 yards per minute, and Lowe's speed is 3x, or 120 yards per minute.

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Answer:

Step-by-step explanation:

Solution in given attachment.

The length of ribbon needed to make 9 bows is 9 times the amount of ribbon needed for one bow, expressed mathematically as 9*x given 'x' is the length of ribbon for one bow.

Based on your query, there appears to be a detail missing, which is the length of the ribbon needed to make one bow. Suppose we denote that length as 'x' units. To find the total length necessary for making 9 bows, we would simply multiply that length by 9. In mathematical terms, this would be expressed as 9*x. So if it takes x units of ribbon to make one bow, it will take 9*x units of ribbon to make 9 bows.

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Due to a typo, the exact length of ribbon per bow is unspecified. Assuming a length of [tex]\( x \)[/tex] per bow, for 9 bows the total needed would be [tex]\( 9x \)[/tex] This is akin to scaling up costs for making multiple items, similar to the production cost examples provided.

It seems there is a typo in the initial fraction of ribbon used per bow, as it is not provided in the question. Assuming the fraction provided is the one we would work with, let's say it takes [tex]\( x \)[/tex] of a ribbon to make one hair bow. To find out how much ribbon is needed to make 9 bows, we multiply [tex]\( x \)[/tex] by 9. Therefore, the total amount of ribbon required for 9 bows would be [tex]\( 9x \)[/tex].

Going by the example information given, if we compare it with the cost of manufacturing goods, we can draw on the parallel of calculating the cost to produce multiple items. For example, if pants finishing costs 49 cents for 7 pairs, and we want to calculate for 9 pairs, we would set up a proportion or use unit rate to find the answer. Though this example doesn't directly relate to the ribbon question, it illustrates the process of scaling up a unit quantity to a larger quantity, which is a common mathematical operation in both scenarios.

If you have to find x-intercept, then you have to equate y to 0. Thus,

when y=0, x+2·0=5 and x=5.

Point (5,0) is x-intercept.

Answer: (5,0)

The x-intercept of the graph is:

                                5

and the point where it is obtained is (5,0)

We know that the x-intercept of a graph is the x-value of the point where it's y-value is zero.

Similarly the  y-intercept of a graph is the y-value of the point where it's x-value is zero.

We are given a equation of a line as:

             [tex]x+2y=5[/tex]

Hence, when y=0 in the equation we get:

 [tex]x=5[/tex]

Hence, the point where the x-intercept is obtained is: (5,0)

and the x-intercept of the graph is: 5

x + (x + 1) = 75

2x + 1 = 75

2x = 74

x = 37

75 - 37 = 38

You can check by substituting the product for the value of x.

37 + 37 + 1 = 75

The two consecutive integers whose sum is 75 are; 37 and 38.

If two consecutive integers sum up to become 75.

We can represent the first number as = x and

the second number as = (x + 1).

The sum of both of the numbers = 75.

therefore, x + (x + 1) = 75.

Dividing both sides of the equation by 2; we have;

x = 37

x + 1 = 38.

Ultimately, the two consecutive integers are; 37 and 38.

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if ur saying 1 13/15 divided by 1 2/5 then the answer is

The exact form : 4/3

Decimal form : 1.3

Mixed number form : 1 1/3

10. Combine like terms 4w and -5w wich is -w.

Now I don't know if u have to solve or simplify but the simplified form is -w-29

Answer: 1)100ways and 2)90ways

Step-by-step explanation:

Given :-The 10 students who completed a special flying course are waiting to see if they will be awarded the one Distinction or the one Merit award for their efforts.

Ways can the two awards be given if the same student can receive both awards (i.e repetition is allowed)

=10×10=100ways

Ways can the two awards be given if the same student cannot receive both awards(i.e. repetition is not allowed)

=10×9=90ways

Final answer:

The number of ways two awards can be given out to 10 students is 100 when the same student can win both awards, and 90 when different students must win each award.

Explanation:

The student's question deals with the number of ways two awards can be given out to a group of 10 students under two different scenarios: one where the same student can receive both awards, and the other where the same student cannot receive both awards. This is a problem of permutations and combinations, a fundamental concept in probability and statistics.

Scenario 1: Same Student Can Receive Both Awards

In the first scenario, the same student can receive both the Distinction and the Merit award. Since there are 10 students and each student can potentially receive each of the two awards, we have 10 choices for the Distinction award and 10 choices for the Merit award. The total number of ways the two awards can be given out is simply the product of these two numbers:

10 (for Distinction) × 10 (for Merit) = 100 ways

Scenario 2: Different Students Receive Awards

In the second scenario, the same student cannot receive both awards. This means that once a student has been given one award, they cannot receive the other one. For the Distinction award, there are still 10 possible students. However, for the Merit award, there are only 9 remaining choices since the Distinction awardee cannot be considered:

10 (for Distinction) × 9 (for Merit) = 90 ways

Convert 7 1/8 to an improper fraction.

Simplify 7 * 8 to 56

-56 + 1/8 - (-9 1/2)

Simplify 56 + 1 to 57

-57/8 - (-9 1/2)

Convert 9 1/2 to an improper fraction.

-57/8 - (-9 * 2 + 1/2)

Simplify 9 * 2 to 18

-57/8 - (-18 + 1/2)

Simplify 18 + 1 to 19

-57/8 - (-19/2)

Simplify brackets

-57/8 + 19/2

Find the LCD

LCD = 8

Make the denominators the same as the LCD

-57/8 + 19 * 4/2*4

Simplify. Denominators are now the same

-57/8 + 76/8

Join the denominators

-57 + 76/8

Simplify

19/8

Convert to a mixed fraction.

2 3/8

Your answer is D.

You find the highest number that can divide into all of them without leaving any with a remainder.

Hope this helps.

u have to multiply the three numbers till u get the GCF

correct me if im wrong

have a blessed day!

Answer:

Adult ticket = $8

Child ticket = $5.5

a = 8 and c = 5.5

Step-by-step explanation:

2a + 4c = 38

3a + 3c = 40.5

To solve for the value of a and c in these equations. We solve the simulatenous equation by substitution method.

2a + 4c = 38 ..........eqn1

3a + 3c = 40.5 ............eqn2

Step 1, Find the value of a in eqn1

2a + 4c = 38

2a = 38 - 4c

a = (38-4c)/2

a = 19 - 2c

Step 2, subtitle the value of a in eqn2 to get the value of c.

3a + 3c = 40.5

3(19-2c) + 3c = 40.5

57 - 6c +3c = 40.5

57-40.5 = 6c -3c

16.5 = 3c

c = 16.5/3

c = 5.5

Step 3, subtitle the value of c in eqn1 to get the value of a.

2a + 4c = 38

2a + 4(5.5) = 38

2a + 22 = 38

2a = 38-22

2a = 16

a = 16/2

a = 8

Therefore:

Adult ticket = $8

Child ticket = $5.5

a = 8 and c = 5.5

(1)

we are given two points

A=(-3,-4)

B=(2,0)

and point P [tex](-1, -\frac{12}{5} )[/tex] partitions AB

Let's assume it partitions into m:n

so, we get

[tex]\frac{AP}{PB}=\frac{m}{n}[/tex]

so, we can write our point as

[tex](-1,-\frac{12}{5} )=(\frac{2m-3n}{m+n},\frac{0m-4n}{m+n})[/tex]

now, we can set x-value to x-value

and y-value to y-value

and then we can solve for m and n

[tex]-1= \frac{2m-3n}{m+n}[/tex]

[tex]-\frac{12}{5} =\frac{0m-4n}{m+n}[/tex]

now, we can solve for m/n

[tex]-m-n=2m-3n[/tex]

[tex]3m=2n[/tex]

[tex]\frac{m}{n} =\frac{2}{3}[/tex]

so, option-C.........Answer

(2)

we are given points as

J=(10, -2)

N=(-4 ,6)

Let's assume mid-point between J and N as M

so, we get

[tex]M=(\frac{10-4}{2},\frac{-2+6}{2})[/tex]

[tex]M=(3,2)[/tex]............Answer

area of square = 4ft²

a s area of square = length×lenght

let lenght =x

so area = x²

x²= 4ft²

taking square root

x=2 ftSo lebght of each side is 2 ft.

the answer is 10 that's my answer

Answer:

f(-3) =  -9

Step-by-step explanation:

We usually express quadratic functions graphs in the form of f(x) = ax^n + bx + c

So f(-3) means that the value of this graph in the y-axis where x = -3 is -9

f(-3) = -9

I hope this helped.

The value of f(-3) is -9 for the quadratic function graphed.

It is defined as a special type of relationship and they have a predefined domain and range according to the function.

We know that if we plot a quadratic function on the coordinate plane we will get a parabola graph and the standard expression for the parabola:

[tex]\rm f(x)=ax^2+bx+c[/tex]

Where a, b, c are real numbers and a ≠ 0

The value of f(-3) means the value of y on the coordinate plane when [tex]\rm x = -3[/tex]

From the graph, we can see the value of y when x = -3

Therefore,

f(-3) = -9

Thus, the value of f(-3) is -9.

Learn more about the function here:

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( - 6, 0).(2, 0 ) , vertex = ( - 2, - 16)

to find the x-intercepts set f(x) = 0

x² + 4x - 12 = 0

(x + 6)(x - 2) = 0 ( equate each factor to zero and solve for x )

x + 6 = 0 ⇒ x = - 6

x - 2 = 0 ⇒ x = 2

x- intercepts are ( - 6, 0),(2, 0)

given the quadratic in standard form : y = ax² + bx + c

the x-coordinate of the vertex = - [tex]\frac{b}{2a}[/tex]

here a = 1 , b = 4 and c = - 12

x- coordinate of vertex = - [tex]\frac{4}{2}[/tex] = - 2

substitute this value into the equation for y-coordinate

x = - 2 → y = 4 - 8 - 12 = - 16

vertex = ( - 2, - 16)

Answer: Our required decimal expansion would be[tex]1.\bar{240}[/tex]

Step-by-step explanation:

Since we have given that

[tex]1\dfrac{80}{333}[/tex]

We need to write in decimal form:

First we change the mixed fraction into improper fraction:

[tex]\dfrac{333\times 1+80}{333}=\dfrac{413}{333}\\\\=1.240240...............\\\\=1.\bar{240}[/tex]

Hence, our required decimal expansion would be[tex]1.\bar{240}[/tex]

The measure of angle 4 will be 42 degrees because corresponding angles are equal when two lines are cut by a transversal, and in this case, angle 5 and angle 4 are corresponding angles.

The concept involved here is that corresponding angles are equal when two lines are cut by a transversal. In the given problem, angle 5 and angle 4 are corresponding angles because they occupy the same relative position at an intersection of a transversal and two lines. Therefore, if the measure of angle 5 (m angle 5) is 42 degrees, then the measure of angle 4 (m angle 4) will also be 42 degrees.

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