BONUS 1) You take the Math Time Machine into the past to save Julius Caesar and fix the calendar,
but you miss your timestamp and end up in Alexandria a few years early. You wander around before
ending up in front of the Great Library of Alexandria, which is guarded by a sphinx - known in
mythology for their tricky riddles. When you ask the sphinx what year it is, it refuses to answer
unless you solve a math problem. The sphinx shows you a right triangle with a base of 8 and a height
of 6, which you know has an area of 24. Then it tells you that if you that you can remove some
length x off of the 8 side, but if you do that you must add a rectangle under the 8 side with a height
equal to x, thus creating a trapezoid. How much length must you remove from the 8 side so the
trapezoid has the same area as the original triangle? X = 0 doesn't count.
a) X = 2
b) X = 3
c) X = 4
d) X = 5

Answer:

64 marbles

Step-by-step explanation:

The solution is, 24 is the total number of marbles in the bag.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

given that,

A bag of marbles only has red and blue marbles.

The bag has a ratio of blue marbles to red marbles of 3:5,

and there are 24 blue marbles in the bag.

we have to find the total number of marbles in the bag.

let, there are x red marbles .

we have,

blue marbles : red marbles = 3:5

so, we get,

blue marbles : red marbles = 24 : x

i.e. 3:5 = 24 : x

so, x = 24 * 5 / 3

or, x = 8*5

or, x = 40

so, there are 24 red marbles .

so, total = 24 + 40 = 64

Hence, The solution is, 24 is the total number of marbles in the bag.

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Answer:

b/3 = c - 6

Step-by-step explanation:

A number b divided by 3 is 6 less than a number c

b/3 = c - 6

Answer:

x = 28°

y = 23°

Step-by-step explanation:

5y - 4 + 3y = 180

solve for y

8y = 184

y = 23

3y and 2x + 13 are equal

solve for x now that we know y is 23.

3(23) = 2x + 13

69 = 2x + 13

56 = 2x

28 = x

Answer:

y=23 x=28

Step-by-step explanation:

5y-4 + 3y =180⁰

8y-4=180

8y=184

y=23

3y=2x+13

69=2x+13

-13 -13

56=2x

28=x

Hope this is helpful. good luck

Answer:

Hello! answer: 585

Step-by-step explanation:

This polygon can be split into 6 triangles so all you have to do is find the area of 1 then multiply by 6 to get the whole things area so...

15 × 13 = 195 195 ÷ 2 = 97.5 97.5 × 6 = 585 therefore the area is 585 hope that helps you!

Answer:

c. 4

Step-by-step explanation:

tan (30)/1 = x/7 *cross multiply*

x = 7 (tan(30))

x = 4.04

x = 4

Answer:

arc AB = 144°/360° x 2π x 10

= 2/5 × 20π = 8π

Answer:

A non-equilateral rhombus.

Step-by-step explanation:

We can solve this graphically.

We start with square:

ABCD

with:

A = (11, - 7)

B = (9, - 4)

C = (11, - 1)

D = (13, - 4)

Only with the vertices, we can see that ABCD is equilateral, as the length of each side is:

AB = √( (11 - 9)^2 + (-7 -(-4))^2) = √( (2)^2 + (3)^2) = √(4 + 9) = √13

BC =  √( (11 - 9)^2 + (-1 -(-4))^2) = √13

CD =  √( (11 - 13)^2 + (-1 -(-4))^2)  = √13

DA =  √( (11 - 13)^2 + (-7 -(-4))^2) = √13

And we change C by C' = (11, 1)

In the image you can see the 5 points and the figure that they make:

The figure ABCD is a rhombus, and ABC'D is also a rhombus, the only difference between the figures is that ABCD is equilateral while ABC'D is not equilateral.

Answer:

[tex] \frac{3}{5}x + 2 = \frac{2}{3} x[/tex]

[tex]2 = \frac{2}{3} x - \frac{3}{5} x[/tex]

[tex]2 = \frac{10}{15} x - \frac{9}{15} x[/tex]

[tex]2 = \frac{1}{15} x[/tex]

[tex]x = 2 \times 15[/tex]

[tex]x = 30[/tex]

Your answer is x=30

If you are helped with my answer pls tag me brianliest I really want it....... Plzz

THANK YOU......

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Work Shown:

Use the tangent ratio

tan(angle) = opposite/adjacent

tan(B) = AC/AB

tan(61) = AC/1

tan(61) = AC

AC = tan(61)

AC = 1.80404775527142

AC = 1.8

The river is about 1.8 miles wide between points A and C.

Make sure your calculator is in degree mode. One way to check is to type in tan(45) and you should get 1.

Answer:

Step-by-step explanation:

2(b+14)=-7(1-b)

2b+28=-7+7b

28+7=7b-2b

35=5b

35/5=b

7=b

Answer:

10.92

Step-by-step explanation:

136.5*(8/100)that is tax

Answer:10.92

Step-by-step explanation:

Answer:

the solutions of a function are the points where for some value of x the function becomes zero

thus the solns for this graph would be

that's option 1.

Answer:

Step-by-step explanation:

Calculate perimeter first

70 x 4 = 280

1 lap is 280m

Adil ran 5 laps so:

5 x 280m = 1400m

Answer:

[tex]y=-3x-8[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the midpoint of the line segment

When two lines bisect each other, they intersect at the middle of each line, or the midpoint.

[tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

Plug in the endpoints (5, -3) and (-7, -7)

[tex](\frac{5+(-7)}{2} ,\frac{-3+(-7)}{2} )\\(\frac{-2}{2} ,\frac{-10}{2} )\\(-1,-5)[/tex]

Therefore, the midpoint of the line segment is (-1,-5).

2) Determine the slope of the line segment

Recall that the slopes of perpendicular lines are negative reciprocals. Doing this will help us determine the slope of the perpendicular bisector.

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where the given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the endpoints (5, -3) and (-7, -7)

[tex]\frac{-7-(-3)}{-7-5}\\\frac{-7+3}{-7-5}\\\frac{-4}{-12}\\\frac{1}{3}[/tex]

Therefore, the slope of the line segment is [tex]\frac{1}{3}[/tex]. The negative reciprocal of [tex]\frac{1}{3}[/tex] is -3, so the slope of the perpendicular is -3. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-3x+b[/tex]

3) Determine the y-intercept of the perpendicular bisector (b)

[tex]y=-3x+b[/tex]

Recall that the midpoint of the line segment is is (-1,-5), and that the perpendicular bisector passes through this point. Plug this point into [tex]y=-3x+b[/tex] and solve for b:

[tex]-5=-3(-1)+b\\-5=3+b[/tex]

Subtract 3 from both sides

[tex]-5-3=3+b-3\\-8=b[/tex]

Therefore, the y-intercept of the line is -8. Plug this back into [tex]y=-3x+b[/tex]:

[tex]y=-3x-8[/tex]

I hope this helps!

Answer:

The null hypothesis is [tex]H_0: \mu = 16.1[/tex].

The alternate hypothesis is [tex]H_1: \mu < 16.1[/tex]

Step-by-step explanation:

A manufacturer claims that the mean amount of juice in its bottles is 16.1 ounces.

This means that at the null hypothesis, we test if the mean amount of juice is of 16.1, as claimed, that is:

[tex]H_0: \mu = 16.1[/tex]

A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this.

This means that at the alternate hypothesis, we test if the mean amount of juice is less than the claimed mean of 16.1 ounces. So:

[tex]H_1: \mu < 16.1[/tex]

Answer:

-9x+3

Step-by-step explanation:

See the steps below:)

Answer:

The distance is 11 units.

Step-by-step explanation:

First you look at the difference between the x values and then you look at the distance between the y values. Since the x values here are -5, and 6 then you count the distance between -5 and 6. This would be 11 since 6 is 6 units away from 0 and -5 is 5 units away from 0. Since the y values are the same then the distance will just be the distance between the x values.

Answer:

yes 8x is a coefficient

Step-by-step explanation:

because I know but if I'm wrong than sry

Lucy and Alicia should be planning to make 8 gallongs of lemonade.

If this helps, please mark brainliest!

Have a wonderful day!

Answer:

I probably think it's A..

Answer:

[tex]Pr(Odd\ or\ <4) = \frac{2}{3}[/tex]

Step-by-step explanation:

Given

[tex]S = \{1,2,3,4,5,6\}[/tex] --- roll of a die

[tex]n(S) = 6[/tex] ---- the sample size

[tex]Odd = \{1,3,5\}[/tex]

[tex]<4 = \{1,2,3\}[/tex]

Required

[tex]Pr(Odd\ or\ <4)[/tex]

First, list out the event of odd or <4

[tex]Odd\ or\ <4 = \{1,2,3,5\}[/tex]

So, the probability is:

[tex]Pr(Odd\ or\ <4) = \frac{n(Odd\ or\ <4)}{n(S)}[/tex]

[tex]Pr(Odd\ or\ <4) = \frac{4}{6}[/tex]

Simplify

[tex]Pr(Odd\ or\ <4) = \frac{2}{3}[/tex]

Answer:

1/3

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome. On a fair die, the number are 1 to 6 while 1 and 2 are the only numbers less than 3.

Hence the odds of getting  a number is the ratio of 6 to 6 while the odds of getting a number lower than 3 will be

= 2/6

= 1/3 (in the lowest term)

This is because the odd of getting 1 is 1/6 and the odd of hetting 2 is 1/6 9 recall that both numbers appear once on a die). Hence the odd of getting 1 or 2 will be

= 1/6 + 1/6

= 2/6

=1/3

Answer:

The hypotenuse measures 8.48 meters.

Step-by-step explanation:

Given that a right isosceles triangle has legs of 6 meters long each, to find the length of the hypotenuse to the nearest tenth of a meter the following calculation must be performed, through the application of the Pythagorean theorem:

6 ^ 2 + 6 ^ 2 = X ^ 2

36 + 36 = X ^ 2

√ 72 = X

8.48 = X

Therefore, the hypotenuse measures 8.48 meters.

Answer:

There is not enough evidence to reject the null hypothesis.

Their sum is greater than the probability value ,  the data does not fit the experiment and the null is  accepted.

Step-by-step explanation:

There are 3 colors so degrees of freedom = 3-1 = 2

The chi square value = 0.85

The p value for chi square =0.85 for 2 degrees of freedom for the left tailed test to be 0.34623 for 0.1,0.05 and 0.01 significance level.

There is not enough evidence to reject the null hypothesis.

The  p value for chi square =0.85 for 2 degrees of freedom for the right tailed test to be 0.65377 for 0.1,0.05 and 0.01 significance level.

There is not enough evidence to reject the null hypothesis.

Their sum is greater than the probability value ,  the data does not fit the experiment and the null is  accepted.

Answer:

y=5x+14

Step-by-step explanation:

Plug this into the equation y-y1=m(x-x1) where m is the slope. y1 is equal to 4, x1 is equal to -2, and m is equal to 5. This will make the equation y-4=5(x--2). This is equal to y-4=5(x+2). Use the distributive property to get y-4=5(x)+5(2). Simplify to get y-4=5x+10. We want to isolate y so we have to add 4 to both sides. This will be equal to y=5x+10+4. Combine like terms to get y=5x+14. Therefore, the equation is y=5x+14.

If this helps please mark as brainliest

Answer: the answer is 25

Step-by-step explanation: