You have violin lessons every fourth day and singing lessons every
fifth day. Today you have both lessons. In how many days will you
have both lessons on the same day again?
​

Answer:

2(3x + 7)(2x - 1)

Step-by-step explanation:

You can see it a little easier if you take out a common factor of 2

2(6x^2 + 11x - 7)

The 6 leaves you with a lot of factors, the 7 does not. It only has 2 factors.

Let 6 factor into 2 and 3 and the 7 into 7 and 1

2(3x - 1 )(2x + 7)

Now remove the brackets.

2(6x^2 + 21x - 2x - 7) This obviously does not work but we'll combine like terms anyway.

2(6x^2 + 19x - 7)

So we'll try it again

2(3x + 7)(2x - 1)

2(6x^2 + 14x - 3x - 7)    Looks like we have it.

2(6x^2 + 11x - 7)

So the right factors are

2(3x + 7)(2x - 1)

Answer:

1/64x^12

Step-by-step explanation:

Answer: x^12/64

Step-by-step explanation:

Apply exponent rule: a^-b = 1/a^b

(4x^-4)^-3 = 1/(4x^-4)^3 : 64/x^12

= 1/64/x^12

Apply the fraction rule: 1/b/c = c/b

=x^12/64

ANSWER

[tex]2 ( { \cos \: 56 \degree + i \sin \:56 \degree) }[/tex]

EXPLANATION

The complex number given to us is in the polar form,

32(cos 280° + i sin 280°)

The fifth root is

[tex] {32}^{ \frac{1}{5} } ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } [/tex]

This is equal to:

[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } [/tex]

According to the DeMoivre's Theorem,

[tex]( { \cos \theta \: \degree + i \sin\theta \degree) }^{ \frac{p}{q} } = ( { \cos \frac{p}{q} \theta \degree + i \sin \frac{p}{q} \theta \degree) }[/tex]

We now use the DeMoivre's Theorem to obtain:

[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } = 2 ( { \cos \: \frac{1}{5} \times 280 \degree + i \sin \:\frac{1}{5} \times 280 \degree) }[/tex]

[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } = 2 ( { \cos \: 56 \degree + i \sin \:56 \degree) }[/tex]

Answer:

g(x) has the greater max:  11 versus 6

Step-by-step explanation:

One can readily discern the max value of the graph; it is 6 and occurs at x =1.

Regarding the function g(x) = (-1/2)x^2 + 4x + 3:  Find the vertex, which also represents the max value:

Here the coefficients are a = -1/2, b = 4 and c = 3, so that the axis of symmetry is:

x = -b/(2a), which here is   x = -4 / ( 2·[-1/2] ) = -4 / (-1) = 4

At x = 4, the function (y) value is

g(4) = (-1/2)(4)² + 4(4) + 3, or

g(4) =    -8  +   16 + 3, or 11

This is greater than the max value of the graphed function.

To assess which function has a larger maximum value, analyze their critical points or endpoints, using the derivative and evaluating the function's values at those points, which reveal the function with the higher maximal value.

To determine which function has the larger maximum value, we must analyze the behavior of the functions and examine their critical points, endpoints, or any given constraints. For polynomial functions, the extreme value theorem ensures the existence of a maximum, provided the function is continuous over a closed interval. In many cases, finding where the derivative equals zero can indicate the location of a maximum. However, if the derivative does not equal zero at any real number, it suggests that the maximum may occur at the endpoints of the given interval.

When calculating the maximum, it's crucial to evaluate the function at the endpoints, which often reveal the highest value, especially when the turning points are not located within the interval of interest. This approach is validated through both algebraic manipulation, such as the application of the quadratic formula, and graphical analysis of the function.

In comparing two functions for their maximum values, we analyze each function similarly, derive their respective derivatives, solve for critical points, and evaluate the endpoints. Deductions are then made based on the calculated values to determine which function has the greater maximum value.

Answer:

YOur answer would be -1/5.

Step-by-step explanation

rise/run

-4--5/-2-3

=-1/5

For this case we have by definition, that the slope of a line is given by:

 the following formula:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

Having two points through which the line passes:

[tex](x_ {1}, y_ {1}): (- 2, -4)\\(x_ {2}, y_ {2}) :( 3, -5)[/tex]

Substituting:

[tex]m = \frac {-5 - (- 4)} {3 - (- 2)}\\m = \frac {-5 4} {3 2}\\m = \frac {-1} {5}[/tex]

Finally, the slope of the line is:

[tex]m = - \frac {1} {5}[/tex]

Answer:

[tex]m = - \frac {1} {5}[/tex]

Answer:

y ≥ 3x +4

Step-by-step explanation:

The line is solid, so the inequality will include the "or equal to" case. The shading is above the line, so values of y greater than or equal to those on the line are in the solution set. The only choice with the correct (≥) inequality symbol is ...

y ≥ 3x +4

Answer: Second Option

[tex]C = 16\pi[/tex]

Step-by-step explanation:

We are evaluating aarco lengths

The formula for the arc length is:

[tex]C = 2\pi r[/tex]

We want to know what is the arc length for a radius of r = 8

Then we substitute r = 8 in the equation and solve

[tex]C = 2 \pi * 8[/tex]

[tex]C = 16\pi[/tex]

The correct answer is the second option

Answer:

Correct choice is [tex]C=16 \pi [/tex].

Step-by-step explanation:

Given equation is [tex]C=2 \pi r[/tex].

Now we need to find the value of C using given equation [tex]C=2 \pi r[/tex] and [tex]r=8[/tex].

To find that, we just need to plug [tex]r=8[/tex] into [tex]C=2 \pi r[/tex] and simplify.

[tex]C=2 \pi r[/tex]

[tex]C=2 \pi \times 8[/tex]

[tex]C=16 \pi [/tex]

Hence correct choice is [tex]C=16 \pi [/tex].

16 flowers per arrangement

Answer:

2x2,2+2=4

Step-by-step explanation:

2*2=4

2+2=4

They can be described as a horizontal movement, a vertical movement, or a combination of the two (horizontal and vertical.)

Answer: 1/16=1/4*1/4

              125=5*5*5

               24= (2*6)*2

               125= 5*5*5

Step-by-step explanation:

the answer is A multiply 3x2 and multiply 4x3 then add hope that helps

Answer:

A

Step-by-step explanation:

It is asking for the total amount of miles the boys walked therefore addition for step 3.

Quick answer, it's B.

For this case we must rationalize the following expression:

[tex]\frac {2 \sqrt {5}} {- 3 \sqrt {50}}[/tex]

Multiply the numerator [tex]\sqrt {50}:[/tex]

[tex]\frac {2 \sqrt {5} * \sqrt {50}} {- 3 \sqrt {50} * \sqrt {50}} =\\\frac {2 \sqrt {5 * 50}} {- 3 (\sqrt {50}) ^ 2} =\\\frac {2 \sqrt {250}} {- 3 * 50} =\\\frac {2 \sqrt {250}} {- 150}[/tex]

Answer:

Option B

Answer:

[tex]a_n=a_{n-1}+16[/tex]

Step-by-step explanation:

The given arithmetic sequence is

14,30,46,62

The first term of this sequence is

[tex]a_1=14[/tex]

The common distance is obtained by subtracting a subsequent term from a previous term;

d=30-14

The common difference is

d=16

The recursive formula is given by:

[tex]a_n=a_{n-1}+d[/tex]

We now plug in the known value for the common difference to get;

[tex]a_n=a_{n-1}+16[/tex]

The recursive formula for the arithmetic sequence 14, 30, 46, 62 is an = aₙ₋₁ + 16 with the initial term a₁ = 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In this case, we have the sequence: 14, 30, 46, 62.

Step-by-Step Process

1. Determine the common difference (d) by subtracting the first term from the second term:

2. Using the first term (a1) and the common difference (d), we can now write the recursive formula.

Therefore, each subsequent term is obtained by adding 16 to the previous term.

Answer:

it is 11/6 and the second one I have no idea. sorry

Step-by-step explanation:

Answer:

The ratio of the perimeters is 11/6

The ratio of the areas is 121/36

Step-by-step explanation:

For the area, you need to do 11/6 squared which means 11 * 11 / 6 * 6 which = 121/36

And for the perimeter it's 11/6 = 11/6 because you cannot really do anything with that so it stays the same

if you are wondering why it is 11/6 is because the red = original and blue = image so since red is the original it goes on top.

I hope this helped  

Answer:

(6, -11)

Step-by-step explanation:

The translation (x-2,y+3) means "subtract 2 from x coordinate" and "add 3 to the y coordinate".

After the transformation, we have the point B'(4,-8). Which point, let it be (x,y), after being transformed is B'(4,-8)??

According to the transformation rule, we have to "subtract 2 from x coordinate" and "add 3 to the y coordinate", thus

x-2=4

x=4+2

x=6

and

y+3=-8

y=-8-3

y=-11

THe coordinate of B are (6,-11)

Answer:

A = 7552.866242 ft^2

Step-by-step explanation:

Circumference = 2 * pi *r

308 = 2 * pi *r

Divide each side by 2

154 = pi *r

Divide each side by pi

154/pi = pi *r/ pi

154/pi = r

The area of a circle is given by

A = pi r^2

A = pi * (154/pi)^2

A = pi * 154/pi * 154/pi

A = 154*154 /pi

A =23716/pi

Let pi be approximated by 3.14

A = 23716/3.14

A = 7552.866242 ft^2

Answer:

Area of circular platform is 7549.25 feet ².

Step-by-step explanation:

in the given question we have to find the area of Circle, where circumference of circle is given.

Area of Circle A = πr²

and Circumference of circle C = 2πr => r = C/2π

Putting value of r in area of circle:

A = π (c/2π)²

A = C²/4π

Putting value of C = 308 feet and π = 3.1415

A = (308)² / 4*3.1415

A = 7549.25 feet ²

So, Area of circular platform is 7549.25 feet ².

Answer:

P = 76%

Step-by-step explanation:

We look for the percentage of employees who are at least 25 years old.

We know that:

μ = 32 years

[tex]\sigma = 10[/tex] years

And we want to find

[tex]P(X\geq25) [/tex]

Then we find the z-score

[tex]Z =\frac{X - \mu}{\sigma}[/tex]

So

[tex]Z = -0.7[/tex]

Then

[tex]P (X\geq25) = P(\frac{X- \mu}{\sigma}\geq\frac{25-32}{10})\\\\\P (X\geq25) = P (Z\geq -0.7)[/tex]

By symmetry of the distribution

[tex]P(Z\geq -0.7)= 1-P(Z<-0.7)[/tex]

[tex]P(Z\geq -0.7)= 1-0.242[/tex]

Looking in the normal standard tables

[tex]P(Z\geq -0.7)= 0.758[/tex]

Finally P = 76%

solution

-4t < 12 3t-15<-3

-4 -4 3t<-3+15

t>-3 3t<12

3 3

t<4

therefore the numbers that makes both equations right is -3<t<4

Answer:

t<4

dont worry its right

Answer:

x = 5/3

Step-by-step explanation:

We have the fifth root of 8^3 and we want it equal to 8

(8^3) ^ (1/5) ^x = 8

We know that a^b^c = a^ (b*c)

8 ^ (3*1/5x) = 8

8 ^ (3/5x) = 8

We can rewrite 8 as 8^1

8 ^ (3/5x) = 8^1

The exponents must be the same

3/5 x = 1

Multiply each side by 5/3 to isolate x

5/3 * 3/5x = 1 * 5/3

x = 5/3

45% :) Step-by-step explanation:

In this diagram, there are a total of 20 squares, and 9 of them are shaded. This means that 9/20 of them are shaded, and to find what percent this is, divide 9 by 20 and multiply what you get by 100.

9 divided by 20 =0.45

0.45 x 100 = 45%.

45% is your final answer!

I hope this helps and have a great rest of your day!

Answer:

x = 5

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

15x-30=45

    +30 +30

 15x=75

15/15=1

75/15=5

x=5

Answer:

The arc PS would be a minor arc

Step-by-step explanation:

As a minor arc is one that is less that 180 degrees, it would be the only viable solution.

Line SO is not an arc, so it cannot be chosen

the measures of arcs SQ and PSR are each 180 degress, so they would not be minor.

The arc which is a minor arc  is:

                      Arc PS.

Minor arc--

A minor arc is a arc which subtend an angle of measure less than 180 degree in the center.

i.e. such a arc should be smaller than a semicircle.

1)

Arc SQ

This arc subtend an angle of 180 degree in the center,

This means it is a semicircle and not a minor arc.

2)

arc PSR

This is again a semicircle and not a minor arc.

Since  PR is the diameter of the circle and hence the arc so formed will be a semicircle.

3)

arc PS

The angle subtended at the center of the circle by this arc is less than 180 degree and hence it is a minor arc.

4)

Line SO

O is the center of the circle and S is a point on the circumference of the circle and hence it denotes the radius of the circle.

Answer:

The answer is C! I just took the quiz and got 100% shout out to all the cheaters out there, let's get this E2020 bread!

The percentage profit on a wheelbarrow is 512%

The percentage profit of an item is the amount of profit when the item is sold, expressed in terms of percentage

The selling price is given as:

SP = $42.50

The cost price is given as:

CP = $6.94

The percentage profit is then calculated as:

[tex]Profit = \frac{SP - CP}{CP} * 100\%[/tex]

This gives

P = (42.50 - 6.94)/6.94 * 100%

Evaluate the difference

P = 35.56/6.94 * 100%

Evaluate the quotient

P = 5.12 * 100%

Evaluate the product

P = 512%

Hence, the percentage profit on a wheelbarrow is 512%

Read more about percentage profit at:

https://brainly.com/question/19104371

Answer:

D. [tex]x>0[/tex]

Step-by-step explanation:

We have been given a quotient [tex]\sqrt{6x^2}\div\sqrt{4x}[/tex]. We are asked to find an inequality that represents all values of x for which the quotient below is defined.

We can rewrite our given expression as:

[tex]\sqrt{6x^2}\div\sqrt{4x}[/tex]

We know that a square root expression is defined for all values of x greater than or equal to 0. We also know that a fraction is defined when its denominator is greater than 0.

So our fraction will be defined for all values of x greater than 0.

[tex]4x>0[/tex]

Upon dividing both sides of our inequality by 4, we will get:

[tex]\frac{4x}{4}>\frac{0}{4}[/tex]

[tex]x>0[/tex]

Therefore, the inequality [tex]x>0[/tex] represents all values of x for which the given quotient is defined and option D is the correct choice.

Answer:

60x + 18

Step-by-step explanation:

8x - 4 [2x - 5 ( 3x + 1 )] - 2 [x - (x - 1)]

distribute

8x - 4 [2x - 15x - 5] - 2 [x - x + 1]

combine like-terms

8x - 4 [- 13x - 5] - 2 [1]

distribute again

8x + 52x + 20 - 2

combine like-terms again

60x +18

Answer:

320in^3

Step-by-step explanation:

V=lwh/3

V=(10)(8)(12)/3

V=960/3

V=320

For this case we have by definition, that the volume of a rectangular pyramid is given by:

[tex]V = \frac {a * b * h} {3}[/tex]

Where:

a, b: Are the sides of the rectangular base

h: It's the height of the pyramid

Substituting the values:

[tex]V = \frac {10 * 8 * 12} {3}\\V = \frac {960} {3}\\V = 320[/tex]

Thus, the volume of the pyramid is 320 cubic inches

Answer:

[tex]320 \ in ^ 3[/tex]

Answer:

Step-by-step explanation:

The equation of a circle in standard form:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the equation:

[tex]x^2+y^2=2[/tex]

Convert to the standard form:

[tex](x-0)^2+(y-0)^2=(\sqrt2)^2[/tex]

State the center and radius of x^2+y^2=2

Answer: The answer to the first question is C(20%)

Step-by-step explanation: 1. you need to find the absolute decrease which is subtracting 350-280= 70.

2. now you need to find the percent decrease which is dividing the absolute decrease by the whole price.. so.. 70/350= .20

3. now just multiply .20 *100 = 20%

Since we're trying to find out how much the price was reduced by, first you will do this

[tex]350 - 280 = 70[/tex]

The price was dropped by $70.

Then we find out how much $70 is of the original price which is 350

[tex]70 \div 350 = 0.2[/tex]

Then you convert 0.2 into a percentage which is 20%.

The price of the digital camera was reduced by 20%.

Answer:

Step-by-step explanation:

To find the equation of directrix of the parabola, we need to identify the axis of the parabola i.e, parabola lies in x-axis or y-axis.

We have 4 parts in this question i.e.

For each part the value of directrix will be different.

For x²  = 12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = -a

So, we need to find the value of a.

The general form of equation for y-axis parabola having positive co-efficient is:

x² = 4ay  eq(i)

and our equation in question is: x² = 12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

4ay = 12y

a= 12y/4y

a= 3

Putting value of a in equation of directrix: y = -a => y= -3

The equation of the directrix of the parabola x²= 12y is y = -3

For x²  = -12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = a

So, we need to find the value of a.

The general form of equation for y-axis parabola having negative co-efficient is:

x² = -4ay  eq(i)

and our equation in question is: x² = -12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

-4ay = -12y

a= -12y/-4y

a= 3

Putting value of a in equation of directrix: y = a => y= 3

The equation of the directrix of the parabola x²= -12y is y = 3

For y²  = 12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = -a

So, we need to find the value of a.

The general form of equation for x-axis parabola having positive co-efficient is:

y² = 4ax  eq(i)

and our equation in question is: y² = 12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

4ax = 12x

a= 12x/4x

a= 3

Putting value of a in equation of directrix: x = -a => x= -3

The equation of the directrix of the parabola y²= 12x is x = -3

For y²  = -12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = a

So, we need to find the value of a.

The general form of equation for x-axis parabola having negative co-efficient is:

y² = -4ax  eq(i)

and our equation in question is: y² = -12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

-4ax = -12x

a= -12x/-4x

a= 3

Putting value of a in equation of directrix: x = a => x= 3

The equation of the directrix of the parabola y²= -12x is x = 3