6. David bought 3 DVDs for 4 books for $40 at a yard sale. Anna bought 1 DVD and 6 books for
$18. How much did each DVD and book cost?

Answer:

A. 18

Step-by-step explanation:

the equation :

RF×RS = PR×RQ

16×9 = PR × 8

144 = PR×8

PR = 144/8

PR = 18

If the length of FR is 16 units then the length of PR is 18 units which is option A.

Circle is a figure whcih is having an arc showing points which are at equidistant from the centre point. The distance of arc from the centre point is known as radius.

From the rule of tangents and point outside the circle we can say that,

RF×RS = PR×RQ

16×9 = PR × 8

144 = PR×8

PR = 144/8

PR = 18 units

Hence if the length of FR is 16 units then the length of PR is 10 units.

Learn more about circle at https://brainly.com/question/24375372

#SPJ2

Answer:

96 ounces each day

Step-by-step explanation:

Divide the 24 bottles by 3

24/3 = 8

8bottles per day

8 bottles *12 ounces per bottle

96 ounces each day

Answer:

There are 104 nickels and 33 quarters

Step-by-step explanation:

Start of with the equation N = 3Q + 5. q is the amt of quarters n is the nickels. Then substitute Q with 33 since that is the amount of quarters and solve the equation for the amount of nickels that there are.

Answer: I'll solve A) since there is a lot of work to be shown.

Step-by-step explanation:

A)

(x−1)³+3x(x−4)+2=x³

Use binomial theorem to expand  (x−1)³

x³- 3x² + 3x - 1 + 3x(x-4) + 2=x³

Use distributive property on 3x(x-4)

x³- 3x² + 3x - 1 + 3x²-12x + 2=x³

Add like terms

x³ −9x + 1 =x³

Subtract x³ from both sides.

x³ −9x +1 -x³ = 0

Add x³ and -x³

−9x+1=0

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

−9x=−1

Divide both sides by -9.

x= 1/9

Answer:

the image/text is not there

Step-by-step explanation:

Answer:

a/9 - 4

Step-by-step explanation:

The expression will be (x/9) - 4.

It is given that a number x is the quotient of a number and 9 decreased by 4.

We have to find the variable expression for this.

What will be the expression for , 2 times of a number minus 4 ?

The expression will be 2x -4.

Quotient of a number and 9

= x / 9

Decrease this by 4 ; we get

= (x / 9 ) - 4

Thus , the expression will be (x/9) - 4.

To learn more about algebraic expression click here ;

https://brainly.com/question/2164351

#SPJ2

Answer:

Step-by-step explanation:

Triangle ABC is a 45-45-90 right triangle. That means that segment BC also measures 10.

The big triangle as a whole is a 30-60-90. The side length across from the 30 degree angle is 10, so the whole length of BD is 10√3. However, since we already have the length of BC as 10, then segment CD measures

10√3 -10 which is 7.32

The center of a triangle must always be found inside the triangle given that it is the concurrent point of the three median lines of the triangle all three of which are located only inside of the triangle

The examples of the properties of the center of a triangle are;

Given that the three medians are located inside the triangle therefore, based on the location of the center of the triangle on the medians of the triangle, the center of the triangle must always be found inside the triangle

Learn more about the centroid of a triangle here;

https://brainly.com/question/16482898

Multiply x and y by 2:

A. (-6, 4)

B. (2, 2)

C. (-2, -2)

Answer:

B. slope 1/4, y-intercept at ( 0, 5)

Step-by-step explanation:

slope m = change in y /chance in x = 5-4 / 0-(-4) = 1 / 4

the y-intercept is the point where the graph of the line intersects the y-axis so will have the coordinates (0 because x will be 0 if the point is on the y-axis, and y is a number) so is (0, a number)

we are given that one of the points is (x=0, y=5) so this is our y-intercept

OR

the slope intercept form equation of a line y= mx+b, where b is the y-intercept

y = (1/4)x +b, for the point (0, 5) we substitute x=0, and y=5

5 = (1/4)*0 +b

5 = b

[tex]{\huge\fcolorbox{blue}{black}{\pink{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: Solution\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}[/tex]

[tex]2(4 - 1) {}^{2} - 3 + 2(5) \\ \\ = 2(3) {}^{2} - 3 + 2(5) \\ \\ = 2 \times 9 - 3 + 2(5) \\ \\ = 18 - 3 +2(5)\\ \\ =>15-10 = 25[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{2(4 - 1)^2 - 3 + 2(5)}[/tex]

[tex]\mathsf{4 - 1 = \bf 3}[/tex]

[tex]\mathsf{= 2(3^2) - 3 + 2(5)}[/tex]

[tex]\mathsf{3^2}\\\mathsf{= 3\times3}\\\mathsf{= \bf 9}[/tex]

[tex]\mathsf{= 2(9) - 3 + 2(5)}[/tex]

[tex]\mathsf{2(9)}\\\mathsf{= \bf 18}[/tex]

[tex]\mathsf{= 18 - 3 + 2(5)}[/tex]

[tex]\mathsf{18 - 3}\\\mathsf{= \bf 15}[/tex]

[tex]\mathsf{= 15 + 2(5)}[/tex]

[tex]\mathsf{2(5)}\\\mathsf{= \bf 10}[/tex]

[tex]\mathsf{= 15 + 10}\\\mathsf{= \bf 25}[/tex]

[tex]\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf{25}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day! }[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Respuesta:

9 años

Explicación paso a paso:

Dado :

Capital = Principal, P = 8500 €

Rendimiento, tasa, r = 3,75%

Intereses, i = 2868,75 €

Para obtener el plazo, número de años que se necesitarán para devengar un interés de 2868,75 € sobre un capital de 8500 € al tipo del 3,75%;

Interés = principal * tasa * tiempo

2868,75 € = 8500 € * 0,0375 * t

2868,75 € = 318,75 billones €

t = 2868,75 € / 318,75 €

t = 9

Por lo tanto, tomará un período de 9 años.

Answer:

[tex]3\left(8-4x\right)<6\left(x-5\right)[/tex]

[tex]3(8-4x)=241-2x[/tex]

[tex]6(x-5)=6x-30[/tex]

[tex]24-12x<6x-30[/tex]

Subtract 24 from both sides

[tex]-12x<6x-54[/tex]

Now, subtract 6x from both sides

[tex]-18x<-54[/tex]

Multiply both sides by -1

[tex]18x>54[/tex]

Divide 18 from both sides

[tex]x>3[/tex]

OAmalOHopeO

$\sf\underline\bold{Question:1-}$

A ball is thrown upwards and it goes to the height of 100meter and comes down. What is the net displacement?

$\sf\underline\bold{Solution}$

$\sf{According \: to\:the\: question,}$

Displacement for the above situation is 0. As we know, that displacement is the shortest path from the initial to the final point. Here, the initial and the final points are the same, and henceforth, it takes no time to travel. So the displacement is 0.

$\sf\underline\bold{Question:2-}$

An athlete completes one round of a circular track of diameter 200m in 30 seconds. Find the distance covered by the athlete at the end of 30 second.

$\sf\underline\bold{Solution:}$

$\sf\bold{Given\:parameters:}$

$\sf\small{☆The\:diameter\:of\:the\:circular\:track:200m}$

$\sf{Radius=}$ $\sf\dfrac{200}{2}$ → $\sf\underline{Radius = 100m}$

☆Time taken by an athlete to complete one round : 30 seconds.

$\space$

$\sf\bold{To\:find:}$

❍Distance travelled by an athlete in 30 seconds.

$\space$

❍ AND,Distance travelled by the athlete will be equal to the cumference of the circle.

$\space$

$\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\sf{So,}$

$\mapsto$ $\sf{Circumference\:of\:the\:circle: 2 πr}$

$\space$

$\mapsto$ $\sf{Circumference=2\times}$ $\sf\dfrac{22}{7}$ $\sf{\times 100}$

$\space$

$\mapsto$ Circumference of the circle : $\sf\dfrac{4400}{7}$

$\space$

[tex]\sf\underline\bold{∴Circumference = 628.57m}[/tex]

$\space$

||Therefore,The distance travelled in 30 seconds, by the athlete is 628.57m.||

0 = 1st answer

628.57 m = Question 2 answer.

Answer:

51

Step-by-step explanation:

Answer:

(0, -2)

(-3, 1)

(3, -4)

Step-by-step explanation:

The constraints given as;

x + y ≥ -2

3x - y ≤ 2

x - y ≥ -4

Since we want to find vertices of the feasible region, we will ignore the less than or greater than sign and use the equal to sign to some simultaneously.

Let's add first and third constraint together to get;

2x = -6

x = -6/2

x = - 3

Put - 3 for x in equation 1 to get;

-3 + y = -2

y = 3 - 2

y = 1

Thus, vertex here is; (-3, 1)

Lets add first and third equations to get;

4x + 0 = 0

Thus, x = 0

Putting this for x in eq 1;

0 + y = -2

y = -2

vertex here is; (0, -2)

Lets subtract eq 3 from eq 2 to get;

2x = 6

x = 6/2

x = 3

Put 3 for x in eq 3;

x - y = -4

vertex here is; (3, -4)

Answer:

58%

Step-by-step explanation:

10*5=50

7*3=21

21/50 chance to choose inside small rectangle

21/50*2 = 42/100 chance to choose inside small rectangle

100-42=58%

Answer:

a^2 + b^2 = c^2

4+16 = c^2

20 = c^2

c = [tex]\sqrt{20}[/tex] = [tex]2\sqrt{5}[/tex]

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Cuz that’s the only graph that goes with the statement.

on this graph it’s saying the cost of 3 hair accessories is $10.

X = 3

Y = 10

Answer:

3

Step-by-step explanation:

Easy pythagorean theorum question.

The law states that "A squared plus B squared, equals C squared."

A and B are the two sides that border the 90 degree mark.

C is the hypotenuse or the longest side/diagonal.

Since we know C and A (I chose to use A because why not) we can fill in the equation with what we know

2^2 + ?^2 = [tex]\sqrt{13^{2} }[/tex]

So

4 + ?^2 = [tex]\sqrt{13^{2} }[/tex]

Since the 13 is already squared in side of a root, it stays as 13

4 + x^2 = 13

4 - 4 + x^2 = 13 - 4

x^2 = 9

x^2 root = root of 9

x = 3

The missing side is 3.

Or you could use an online calculator xD

Answer:

4th option, 5 5/6

Step-by-step explanation:

8 1/2 - 2 2/3

= 17/2 - 8/3

= (51-16)/6

= 35/6

= 5 5/6

Answered by GAUTHMATH

Answer:

is it 4.2626

Step-by-step explanation:

let me know if it right

Answer: The student is not correct

To reflect over the y axis, you use this rule

[tex](x,y) \to (-x,y)[/tex]

The x coordinate swaps in sign (from positive to negative, or vice versa) while the y coordinate stays the same.

So for a point like A(1,1), it should move to A ' (-1, 1) and not (-2,1) like the diagram shows.

B(3,1) should move to B ' (-3, 1)

C(1,4) should move to C ' (-1, 4)

It appears that the student applied a reflection over the y axis, and then they shifted the triangle 1 unit to the left.

Answer:

x = 4 and y = 8

Step-by-step explanation:

This is a special right triangle with angle measures 90-60-30 degrees

The side lengths are like the following :

The side length that sees 90 degrees is represented with a

The side length that sees 60 degrees is represented with a[tex]\sqrt{3}[/tex]

The side length that sees 30 degrees is represented with 2a

now, the angle measure that sees 60 degrees is given as 4[tex]\sqrt{3}[/tex] so we understand that a is = 4 that's how we find the value of x and y

Answer:

216

Step-by-step explanation:

π=3

r=3

h=8

so,

πr²h

= 3×3²×8

= 216

Answered by GAUTHMATH

Answer:

Step-by-step explanation:

Remark

The cos(60) = 1/2

The radii marked 6 is the adjacent side. You have to solve for the hypotenuse.

Why?

Because the hypotenuse is the distance from the center of the circle to the point of intersection of the angle. Once you have the hypotenuse, you can find the length of the tangent, which will lead to the area of the kite. Then take away 1/3 the area of the circle.

Hypotenuse

Cos(60) = 1/2

cos(60) = adjacent / hypotenuse        Multiply both sides by the hypotenuse

hypotenuse * cos(60) = adjacent       Divide by Cos(60)

hypotenuse = adjacent / cos(60)  

adjacent = 6

hypotenuse = 6/0.5

hypotenuse = 12

Tangent

tangent^2 = 12^2 - 6^2

tangent^2 = 144 - 36

tangent^2 = 108

tangent = sqrt(108)

tangent = 6sqrt(3)

Triangles

The area of the triangle = 1/2 6sqrt(3) * 6

The area of the triangle = 18 sqrt(3)

There are two triangles so the area = 36 sqrt(3) That's the area of the kite.

Circle sector.

Area of the circle sector = 1/3 * pi * r^2

r = 6

Leave pi as it is.

Area of the circle sector = 1/3 * pi * 6^2

area of the circle sector = 12 pi

Answer

Area of the red part = area of the triangles - the area of circle sector

Area of the red part = 36*sqrt(3) - 12* pi            

Answer:

Step-by-step explanation: