What is the measure of 3?

To find the time for Car X to be 5 laps ahead of Car Y, we calculate the difference in laps completed per minute (0.25 laps) and divide the target difference (5 laps) by this rate, which gives us 20 minutes.

The question asks how long it will take for Car X to be 5 laps ahead of Car Y if Car X makes one lap every 60 seconds and Car Y every 80 seconds. To solve this, we need to find the difference in laps completed by the two cars over time, until Car X is 5 laps ahead. Since Car X is the faster car, it takes one lap less time than Car Y to complete a lap.

First, we find out how many laps Car X completes more than Car Y in one minute:

The difference in the number of laps per minute is 1 lap - 0.75 laps = 0.25 laps per minute for Car X compared to Car Y.

Next, we calculate the time it will take for Car X to be 5 laps ahead:

Therefore, it will take 20 minutes for Car X to be 5 laps ahead of Car Y.

Answer:

x = 1 is correct

Step-by-step explanation:

[tex]8 - 2x = - 8x + 14[/tex]

[tex]8x-2x + 8 = - 8x + 8x + 14 - 8[/tex]

[tex]6x = 6[/tex]

[tex]x = 1 [/tex]

yes a right triangle is and angle that is a angle at 90 degrees. A quick method if you don't ha protractor to measure is to measure the angle on a piece of paper like a posted note or note card since all the angles are 90 on them then see if they match up.

Answer:

Yes

Step-by-step explanation:

It is a right angle because it is 90 degrees.

Also,you can tell its a right angle because the variables a, b, and c

represent the Pythagorean Theorem which is used for finding missing lengths of a right triangle.

I didnt see the part at the bottom but the explanation for that would be

50+40> 30   True              40 squared + 30 squared= 50 squared

50+30> 40    True       or      1600+900=2500

40+30> 50    True                     2500=2500

Answer:

-6 ± √78\6 [0.47196014..., -2.47196014... = x]

Step-by-step explanation:

The roots [zeros] are the x-values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.

Answer:

x = 1 + √74/6 or x = 1 - √74/6

Step-by-step explanation:

Points to remember

Zeros of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

To find the zeros of given quadratic equation

It is given that,

6x² +12x - 7 = 0

Here a = 6, b = -12 and c = -7

x = [-b ± √(b² - 4ac)]/2a

 =  [-12 ± √(12² - 4*6*(-7))]/2*6

 = [12 ± √(144 +168 )]/12

 =  [12 ± √312]/12

 = [12 ± 2√74]/12

 = 1 ± √74/6

x = 1 + √74/6 and x = 1 - √74/6

Answer:

About 30

Step-by-step explanation:

1ST: see how many odd numbers are in 1-6 (which is 3)

2nd: Divide 64 by 3 (when rounded it equals around 30)

Answer:

The coordinates of her new position are (0 , -5) ⇒ answer B

Step-by-step explanation:

* Lets revise some translation

- If the point (x , y) translated horizontally to the right by h units

 then the new point = (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then the new point = (x - h , y)

- If the point (x , y) translated vertically up by k units

 then the new point = (x , y + k)

- If the point (x , y) translated vertically down by k units

 then the new point = (x , y - k)

* Now lets solve the problem

∵ Nancy start from position (2 , -3)

- She walks 5 blocks to the right and 3 blocks down

∴ Add x-coordinate by 5 and subtract y-coordinate by 3

∵ The starting position is (2 , -3)

∴ The new position is (2 + 5 , -3 - 3) = (7 , -6)

- She walks 7 blocks to the left and 1 block up

∴ Subtract x-coordinate by 7 and add the y-coordinate by 1

∴ The new position is (7 - 7 , -6 + 1) = (0 , -5)

* The coordinates of her new position are (0 , -5)

Answer:

b

Step-by-step explanation:

Answer:

There are 12 multiple choice

Step-by-step explanation:

Let m = multiple choice

f = free response

f+m = 15 since there are 15 questions

3m+5f = 51  since we have 51 minutes and 3 for multiple choice and 5 for free response

We have 2 equations and 2 unknowns

m+f = 15

3m+5f = 51

Multiply the first equation by -3

-3(m+f) = -3*15

-3m -3f = -45

Add this to the second equation

-3m-3f = -45

3m+5f = 51

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

        2f = 6

Divide by 2

2f/2 = 6/2

f = 3

There are 3 free response.

m+f = 15

m+3 = 15

Subtract 3 from each side

m+3-3=15-3

m=12

There are 12 multiple choice

Answer:

6cm

Step-by-step explanation:

[tex]A = \frac{h_b b}{2}[/tex]

[tex]38.4 = \frac{12.8_b b}{2}[/tex]

[tex]b = 2\frac{A}{h_b}[/tex]

[tex]b = 2\frac{38.4}{12.8}[/tex] = 6

The total space enclosed by the three boundaries of the triangle is called the area of the triangle.

The length of the base of the triangle is 6 cm.

A triangle has an area of 38.4 cm2.

The height of the triangle is 12.8 centimeters.

The total surface or space enclosed by the three boundaries of the triangle is called the area of the triangle.

The formula to calculate the area of the triangle is given by;

[tex]\rm Area \ of \ the \ rectangle = \dfrac{1}{2} \times Base \times Height\\\\[/tex]

Substitute all the values in the formula;

[tex]\rm Area \ of \ the \ triangle= \dfrac{1}{2} \times Base \times Height\\\\\rm 38.4 = \dfrac{1}{2} \times Base \times 12.8\\\\ Base = \dfrac{38.4 \times 2}{12.8}\\\\Base = 3 \times 2\\\\Base = 6 \ cm[/tex]

Hence, the length of the base of the triangle is 6 cm.

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For this case, we can discard options B and C because they do not have coefficients. Also, we discard option D because it has 4 roots given by -4.1, -1,2 each with multiplicity "1".

The multiplicity indicates the number of times a root is repeated.

Then, we have that the correct option is option A, we have a coefficient of "3", in addition to three roots (-4,1,2) with multiplicity "1", because they only repeat once.

Answer:

Option A

Answer: A

Step-by-step explanation:

Answer:

The statement most accurately describes the figure is AB > DB ⇒ A

Step-by-step explanation:

* Lets describe the figure

- AD intersect EC at point B

- There are two triangles ABE and DBC

- B is the mid-point of EC

- AD bisects EC

- EB = BC

- AE = DC

- m∠AEB = 30°

- m∠DCB = 27°

∵ The measure of angle AEB is greater than the measure of

   angle DCB

∴ The opposite side to the angle AEB is longer than the opposite

   side of angle DCB

∵ AB is the opposite side to angle AEB

∵ BD is the opposite side to angle DCB

∴ AB is longer than BD

∴ AB > DB

* The statement most accurately describes the figure is AB > DB

Answer:

The answer in the procedure

Step-by-step explanation:

Let

x ----> the number of gigabytes used in a month

C(x)------> the monthly cost in dollars

step 1

For the interval ----> [0,2]

[tex]0\leq x\leq 2[/tex]

[tex]C(x)=15[/tex]

step 2

For the interval ---->(2,6]

[tex]2< x\leq 6[/tex]

Find the equation of the line

Find the slope

we have

[tex](2,20),(6,40)[/tex]

[tex]m=(40-20)/(6-2)=5[/tex]

The equation of the line in to point slope form is equal to

[tex]y-20=5(x-2)\\ y=5x-10+20\\ y=5x+10[/tex]

therefore

[tex]C(x)=5x+10[/tex]

step 3

For the interval ----> (6,∞]

[tex]x> 6[/tex]

[tex]C(x)=50[/tex]

Answer:

C(x)=[tex]15, 0\leq x\leq 2[/tex]

        [tex]5x+10, 2<x\leq 6[/tex]

          [tex]50, [/tex] 6<x≤∞

Step-by-step explanation:

C(x) represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month

Lets find C(x) on each interval (for every line graph)

first interval 0 to 2

the value of y is 15 on the interval 0 to 2

Its horizontal line . So equation is c(x)=the constant y value

[tex]C(x)= 15, 0\leq x\leq 2[/tex]

Second interval 2 to 6

Pick two points to get the equation of that line

(3,25) and (6,40)

[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{40-25}{6-3} =5[/tex]

Equation of the line is using m=5 and (3,25)

[tex]y-y1=m(x-x1)[/tex]

[tex]y-25=5(x-3)[/tex]

[tex]y-25=5x-15[/tex]

[tex]y=5x+10[/tex]

[tex]C(x)= 5x+10, 2<x\leq 6[/tex]

Now we look at the third interval

6 to infinity

For the third graph , the value of y is 50 (constant)

It is a horizontal line

So [tex]C(x)= 50, [/tex] 6<x≤∞

We got three equations for C(x)

C(x) is a piecewise function

C(x)=[tex]15, 0\leq x\leq 2[/tex]

        [tex]5x+10, 2<x\leq 6[/tex]

          [tex]50, [/tex] 6<x≤∞

Answer: [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

We need to remember that equivalent fractions are  defined as fractions whose numerators and denominator are different but both fractions represent the same value.

To find an equivalent fraction, we must multiply the numerator and the denominator by the same number (Which must be a nonzero whole number).

In this case, to find a fraction equivalent to [tex]\frac{1.5}{9}[/tex],  with a whole number in both numerator and the denominator, we can multiply the numerator and the denominator by 2. Then you get:

[tex]\frac{1.5*2}{9*2}=\frac{3}{18}[/tex]

Reducing the fraction, you get:

[tex]=\frac{1}{6}[/tex]

the simplified whole number fraction equivalent is 1/6.

To find a fraction equivalent to 1.5 over 9 with a whole number in both the numerator and the denominator, first convert the decimal in the numerator to a fraction by expressing it as 1.5 or 15/10. Then, you can write the original fraction as (15/10)/9 which simplifies to 15/90 by multiplying the numerator and the denominator by 10. Finally, you simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 15 in this case. Thus, the simplified whole number fraction equivalent is 1/6.

Answer:

Domain of a geometric or arithmetic sequence is the counting numbers unless otherwise noted.

Answer: Set of Natural numbers.

Step-by-step explanation:

We know that the domain of a function is the set of all values for x for which the function must be defined.

The domain of the geometric sequence is always the set of natural numbers , since each term has a particular position in the sequence according to an order which can only represent by natural numbers.

Hence, the domain for the given geometric sequence = Set of natural numbers.

The expression that describes his father's age is A. 3x - 4

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Marcy determined that her father's age is four less than three times her age.

Assuming Marcy's age to be x.

∴ The equation that describes her father's age is (3x - 4).

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The correct expression that represents her father's age is A.[tex]\(3x - 4\).[/tex]

To arrive at this conclusion, let's analyze the given information:

Marcy determined that her father's age is four less than three times her age. Let's denote Marcy's age as x. According to the statement, her father's age can be expressed as three times Marcy's age minus four years.

Mathematically, this can be written as:

[tex]\[ \text{Father's age} = 3 \times \text{Marcy's age} - 4 \][/tex]

Substituting x for Marcy's age, we get:

[tex]\[ \text{Father's age} = 3x - 4 \][/tex]

Now, let's evaluate the other options to confirm that they are incorrect:

B. x - 4: This expression suggests that the father's age is four years less than Marcy's age, which does not match the given information that the father's age is four less than three times Marcy's age.

C. 4x - 3: This expression indicates that the father's age is three years less than four times Marcy's age, which again does not align with the given information.

D. 4 - 3x: This expression would imply that the father's age is calculated by subtracting three times Marcy's age from four, which is not the relationship described in the problem.

Therefore, the only expression that correctly represents the father's age based on the given information is A. [tex]\(3x - 4\).[/tex]

Answer:

240mg

Step-by-step explanation:

The patient takes 60mg the first day, 45mg the second and third day, 30mg the fourth and fifth day and 15mg the sixth and seventh day.

The amount of miligrams the patient will take is the following:

mg = 60mg + 2×45mg + 2×30mg and 2×15mg = 240mg

Then, the patient will take in total 240mg!

Answer: [tex]240 mg[/tex]

Step-by-step explanation:

We need to analize the information provided.

On day 1: [tex]60\ mg[/tex]

On day 2:  [tex]45\ mg[/tex]

On day 3:  [tex]45\ mg[/tex]

On day 4: [tex]30\ mg[/tex]

On day 5: [tex]30\ mg[/tex]

On day 6: [tex]15\ mg[/tex]

On day 7: [tex]15\ mg[/tex]

Then, to find the total mg the patient will take, we need to add the mg of each day. Therefore:

[tex]Total=60\ mg+45\ mg+45\ mg+30\ mg+30\ mg+15\ mg+15\ mg=240\ mg[/tex]

Answer:

$1.10

Step-by-step explanation:

1 ft = 0.3048 m

3 ft = 3 * 1 ft = 3 * 0.3048 m = 0.9144 m

$1.20/m * 0.9144 m = $1.09728

Answer: $1.10

Answer:

$ 1.08

Step-by-step explanation:

1 feet = 12 inches

so, 3 feet = 12 x 3 = 36 inches

1 metre = 40 inches

Cost of 1 m of fabric = $ 1.20

cost of 40 inches of fabric = $ 1.20

Cost of 1 inch of fabric = $ 1.20 / 40 = $ 0.03

Cost of 36 inches of fabric = $ 0.03 x 36 = $ 1.08

Thus, the cost pf 3 feet fabric is $ 1.08

Answer:

17 dimes, 21 quarters

Step-by-step explanation:

I suppose you want to know how many dimes and quarters she had in her jar.

Let's say x = dimes and y = quarters.

We can make the following 2 equations:

1) x + y = 38 (number of coins in the jar)

2) 10x + 25y = 695 (a number of dimes plus a number of quarters sum up to 695 cents)

From 1), we can isolate y: y = 38 - x, and place that value in the second equation:

10x + 25y = 695

10x + 25 (38 - x) = 695

10x + 950 - 25x = 695, then we subtract 950 on both sides and simplify

-15x = -255

x = 17

So, Jenna had 17 dimes.

y = 38 - x, so y = 38 - 17 = 21

And she had 21 quarters.

Answer:

$35.96

Step-by-step explanation:

19.72 divided by 3.4 = 5.8

5.8*6.2 =35.96

Answer:

Translation down 5 units.

Step-by-step explanation:

The - 5 results in a shift of the whole graph down 5 units.

Each value of g(x) is 5 units less f(x).

Answer:

a. Translate down 5 units

Step-by-step explanation:

So g(x) is the transformed function of f(x)

In this situation, only the parameter c affect the f(x) vertically to have g(x), if:

Here,  c= -5

So the function is Translate down 5 units  

Hope it will find you well.

Answer:

I would say the correct answer is 2^3 • 5 • 11

Step-by-step explanation:

To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 440 by 2

440 ÷ 2 = 220 -  No remainder! 2 is one of the factors!

220 ÷ 2 = 110 -  No remainder! 2 is one of the factors!

110 ÷ 2 = 55 - No remainder! 2 is one of the factors!

55 ÷ 2 = 27.5 - There is a remainder. We can't divide by 2 even anymore. Let's try the next prime number

55 ÷ 3 = 18.3333 - This has a remainder. 3 is not a factor.

55 ÷ 5 = 11 - No remainder! 5 is one of the factors!

11 ÷ 5 = 2.2 -There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number

11 ÷ 7 = 1.5714 - This has a remainder. 7 is not a factor.

11 ÷ 11 = 1 - No remainder! 11 is one of the factors!

If we put all of it together we have the factors 2 x 2 x 2 x 5 x 11 = 440. It can also be written in exponential form as 2^3 x 5^1 x 11^1.

here is also the factor tree method : -

Answer:

Fraction: 70/100

Decimal: 0.7

Percent: 70%

Answer:

The answer is:

Fraction: 7/10

Decimal: 0.7

Percent: 70

Step-by-step explanation:

There are 70 colored squares and 100 squares in total. The fraction is 70/100, which can be simplified to 7/10.

One way to convert the fraction 7/10 to decimals is to divide the numerator (7) by the denominator (10). That gives you the decimal 0.7.

A way you can convert the decimal to percent is to multiply 0.7 by 100. You get 70%. Also, there are 70 colored squares out of 100, so that equals 70%.

I hope this helped! :)

Answer:

The radius of the sphere is 5 units

Step-by-step explanation:

The volume of the sphere with radius r is given by the formula;

[tex]volume=\frac{4}{3}*\pi*r^{3}[/tex]

The volume of the sphere is given as;  500/3 π cubic units

We substitute this value into the formula and solve for r;

[tex]\frac{500}{3}\pi=\frac{4}{3}*\pi*r^{3}\\\\r^{3}=\frac{500}{4}\\\\r=\sqrt[3]{125}=5[/tex]

Answer:

The correct answer is second option

The radius of sphere = 5 units

Step-by-step explanation:

Points to remember

Volume of sphere = (4/3)πx³

Where 'x' is the radius of sphere.

To find the radius of sphere

We have volume is  500/3 π cubic units

(4/3)πx³ = 500/3 π

x³ = (500/3) * (3/4)

 = 500/4 = 125

x = ³√125

x = 5 units

The correct answer is second option

The radius of sphere = 5 units

Answer:

Yes

Step-by-step explanation:

It can be 6 units. The rule relating to the sides of the triangle is that you should be able to add two sides and get a length that is longer than the third side. You usually add the lower two numbers because it basically says that it will work for all sides but, if you're still in doubt you just have to compare the numbers.

For Example

3+5 is greater than 6

5+6 is greater than 3

6+3 is greater than 5.

All of these makes sense so 6 can be a possible answer.

In triangle EFG, it is not possible for segment GE to measure 6 units.

No, it is not possible for segment GE to measure 6 units in triangle EFG.

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Since segment EF measures 3 units and segment FG measures 5 units, the sum of these two sides is 8 units, which is less than 6 units. Therefore, segment GE cannot be 6 units long in triangle EFG.

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Answer:

18

Step-by-step explanation:

To find the number of adults required, take the number of students and divide by 15

270/15 =18

We require 18 adults

Answer:

18

Step-by-step explanation:

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Answer:

x = 6

Step-by-step explanation:

Since the line segment is an angle bisector then the following ratios are equal

[tex]\frac{42}{78}[/tex] = [tex]\frac{6x-1}{10x+5}[/tex] ( cross- multiply )

78(6x - 1) = 42(10x + 5) ← distribute parenthesis on both sides )

468x - 78 = 420x + 210 ( subtract 420x from both sides )

48x - 78 = 210 ( add 78 to both sides )

48x = 288 ( divide both sides by 48 )

x = 6

Answer:

Step-by-step explanation:

Write the explanation x-4

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Answer:

D.

Step-by-step explanation:

A term in a polynomial is a single number or a number multiplied by any number of variables. A polynomial is a sum of terms.

The only thing that can be done with variables in a polynomial is to multiply them by numbers or other variables. In a polynomial, you cannot: divide by a variable (have a variable in a denominator), have a root of a variable, have a log of a variable, have a variable as an exponent, etc.

All expressions are polynomials except for D. In D., the negative exponents mean division by variables.

When estimating the amount of paint needed, Janice should strive for an accurate estimate to avoid running out of paint or wasting excess. Factors to consider include the size of the apartment, the type of paint, and the need for multiple coats.

When estimating the amount of paint needed, Janice should strive for an accurate estimate to avoid running out of paint or wasting excess. Since the store sells paint in one-gallon cans, it is best to estimate in whole gallons. However, if Janice wants a more precise estimate, she can consider the following factors:

By considering these factors and making an accurate estimate, Janice can ensure that she buys the right amount of paint for her new apartment.

Answer: Volume is 628.32

              Surface Area is 408.41

Step-by-step explanation:

The formula for the surface area is A=2 π r h + 2πr*r

The formula for Volume is V=πr*rh

Good luck!

Step-by-step explanation:

1..take 2 common from given equation.

2.. then factories the obtained equation.

3.. separate the equation as

3x-5=0 and X+2=0

Answer:

x=-2

and

x=5/3

Step-by-step explanation:

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