A history teacher is writing a test worth 100 points. She uses multiple-choice questions worth 6 points
each and true/false questions worth 2 points each. She wants the test to have three times as many
multiple-choice questions as true/false questions. Let m represent the number of multiple-choice
questions on the test, and let t represent the number of true/talse questions. Which system of
equations can be used to find how many each type of question she should write?
6m + 2t = 100
m=t+3
6m + 2t = 100
m = 3t
3m+t=100
m=31
6m + 2t = 100
t = 3m

Step-by-step explanation:

Given,

1. The given expression is [tex]\sqrt[10]{x^9}[/tex].

We need to write it into exponential form.

We know that,

[tex]\sqrt[a]{x} =x^{1/a}[/tex]

Here, a = 10

So,

[tex]\sqrt[10]{x^9}=(x^9)^{1/10}\\\\=x^{9\times \dfrac{1}{10}}\\\\=x^{9/10}\\\\=x^{0.1}[/tex]

2.

[tex](\sqrt[4]{3y} )^3\\\\=((3y)^3)^{1/4}\\\\=3^{3\times \dfrac{1}{4}}\times y^{3\times \dfrac{1}{4}}\\\\=3^{3/4}y^{3/4}[/tex]

Hence, this is the required solution.

Answer:

1) -3a + 24b

2) 5x^2 + 2x +1

Step-by-step explanation:

1) (-a + -a+ -a) + (6b + 8b + 10b)

(-3a) + (24b)

-3a + 24b

2) (2x^2 + 3x^2) + (4x - 2x) + (7-6)

(5x^2) + (2x) + ( 1 )

5x^2 + 2x + 1

Answer:

the other guy is correct

Step-by-step explanation:

mark him brainliest!! or me it does'nt matter

Answer:

360°

explanation:

the sum of interior angles of all quadrilaterals (polygons with four sides) is 360°. If you put a pen at any of the four corners and try to draw a line to any other corner, you'll find you can only make two triangles. And since the angle sum of triangles is 180°, 180 times 2 = 360

Answer:

A term can be a constant or a variable or both in an expression. ... Understanding how to solve math problems becomes easier as one learns ... Additive inverse The opposite of a number or its negative. ... The numbers a, b, and c are the coefficients of the equation and may be ... The arithmetic mean, denoted x, of a set of.

Step-by-step explanation:

Answer:

x²+y² = 64

Step-by-step explanation:

The standard form of writing the equation of a circle is expressed as;

(x-a)²+(y-b)² = r² where;

(a, b) is the centre of the circle

r is the radius of the circle

Given the diameter of the circle with endpoints (8,0) and (-8, 0)

d = √(x2-x1)²+(y2-y1)²

d = √(-8-8)²+(0-0)²

d = √(-16)²

d = √256

d = 16

radius r = 16/2

r = 8

The centre of the circle will be the midpoint of the coordinates

M = (8-8/2, 0+0/2)

M = (0/2, 0/2)

M = (0,0)

Hence the centre is at (0,0)

Get the required equation

Recall that (x-a)²+(y-b)² = r²

Substitute the centre and the radius

(x-0)²+(y-0)² = 8²

x²+y² = 64

This gives the required equation

Answer: If the frequency is 0, it does not repeat.

Step-by-step explanation: A relative frequency table is a chart that shows the popularity or mode of a certain type of data based on the population sampled. When we look at relative frequency, we are looking at the number of times a specific event occurs compared to the total number of events.

Please find the attached photograph for your answer

Answer:

bit.^{}

ly/3a8Nt8n

Step-by-step explanation:

DON'T GO HERE PLEASE ITS A SCAM IM WARNING YOU

Answer:

y = -a(x – 2)² – 4

a > 1

Example:

y = -2(x – 2)² – 4

Step-by-step explanation:

y = a(x – h)² + k

____________________

vetex: (h, k)

a: vertical reflection or stretch/compression

__________________________________

If it opens downward, has a vertex of (2, -4) and is narrower than y = x².

Then x² will have a negative coefficient of less than -1 and the input of x will be subtracted by the x value of the vertex which is 2, and the output will be added by the y value of the vertex which is -4.

Therefore y = -a(x – 2)² – 4 where a > 1

Answer:

C = 2πr

191.64 = 2 × 3.14 × r

r = 191.64/6.28

r = 30.51 yds

Answer:

$460.92

Step-by-step explanation:

First year monthly salary = $4,718

Second year annual salary = $62,147

Second year monthly salary = Annual salary / 12

= $62,147 / 12

= $5,178.92

How much more per month will you earn your second year?

Amount of increase in second year monthly salary = Second year monthly salary - First year monthly salary

= $5,178.92 - $4,718

= $460.92

Answer:

500 would be the answer of this question but it is also the standard form of this question

Answer:

I don't know but if it feels like you shouldn't be doing it then don't

Step-by-step explanation:

Answer:

You won't get in huge trouble but it probably wouldn't be the smartest thing to have them. if you think you can play good with them then you are fine! you should double check with the coach, because every school or team has different rules!

Answer:

160/9  or approx 17.78

Step-by-step explanation:

64-32=32

(32*5)/9

160/9 or approx 17.78

Answer: D) 0.55

Step-by-step explanation: good luck

Answer:

D) 0.55

Step-by-step explanation:

I got it correct on USATP.

Hope this helps!

From: Aug1e

Answer:

17x² + 2x – 3

Step-by-step explanation:

(9x2 + 3x – 5) + (8x2 – x + 2) →

(9x² + 3x – 5) + (8x² – x + 2) →

[Group like terms]

(9x² + 8x²) + (3x – x) + (2 – 5) →

[Simplify]

17x² + 2x – 3

Answer: bank owns smallest portion 1/20

Step-by-step explanation: Dave 1/4= 0.25 = 25 %. Delta 1/5 = 0.20 = 20%

And Alice 1/2 = 0.5 =50%. Bank owns 5% = 5/100 = 1/20

Answer:

It's a rectangle, but not a rhombus (or square).

Step-by-step explanation:

Let's see the vectors of each next vertex:

[tex]Q - P = (4, 5) - (-5, 2) = (9, 3)\\R - Q = (6, -1) - (4, 5) = (2, -6)\\S - R = (-3, -4) - (6, -1) = (-9, -3)\\P - S = (-5, 2) - (-3, -4) = (-2, 6)\\[/tex]

Firstly, we can notice that it's a parallelogram - because the Q-P side is parallel to the S - R side (if the x:y ratios are the same, the sides are parallel).

A rhombus needs the sides to be of the same length. But the length of a (x, y) vector is [tex]\sqrt{x^2 + y^2}[/tex] and [tex]\sqrt{9^2 + 3^2} > \sqrt{2^2 + (-6)^2}[/tex], we don't even have to compute it exactly. If it's not a rhombus, it's also not a square (every square is a rhombus).

The last thing left is to know if it's a rectangle - for it to be a rectangle, we need to check if the vectors are perpendicular.

We can compute the dot product of the vectors - perpendicular vectors always have a dot product equal to zero. The dot product of two vectors [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is equal to [tex]x_1x_2 + y_1y_2[/tex].

[tex](9, 3) \cdot (2, -6) = 9\cdot 2 + 3\cdot(-6) = 18 - 18 = 0[/tex]

So the sides are perpendicular, and as such - the figure is a rectangle.

Answer:

123.38

36+54+11.69+11.69

Make sure to round

Answer:

1/115

Step-by-step explanation:

there are 25 players on the team (10+6+9)

there are 6 infielders

They are picking without replacement

6/25 * 5/24 * 4/23

rearranging

6*4/24 *5/25 *1/23

1 *1/5 *1/23

1/115

Answer: 1/115

Answer: if you do length x width x height you should get 64 cm

Step-by-step explanation:

Answer:

[tex]\frac{17}{20}[/tex]

Step-by-step explanation:

Answer: The Answer is 11.

Step-by-step explanation: You line up the least to the greatest so in this case, 8, 6 , 10 , 13 , 14 , and 15, and than you divide that amount by however many numbers there are you are working with. Which would be 6. When all divided and done, it is all equal to 11

Answer:

10x^2 -623x +2

Step-by-step explanation:

the numbers were put in weird so im not sure if this is the answer you were looking for, but thats what i got

Answer:

I think the answer is C.

Step-by-step explanation:

A triangle inside always has to add up to 180. So of you subtract 78 and 41 from 180 it wil give you 61

Answer:

a

Step-by-step explanation:

3rd root of 64=4

3rd root of 125=5

=-4/5 since there's a negative inside

Answer:

x=180-(31+40)

Answer:

Step-by-step explanation:

Answer:

Is

[tex] - 5[/tex]

Step-by-step explanation:

(n÷3)-5= -5

Answer:

Final amount after 11 years = $4021.97

Step-by-step explanation:

We will use the formula to get the final amount after t years,

Final amount = [tex]a(1+\frac{r}{n})^{nt}[/tex]

here a = Initial amount

r = Rate of interest

n = Number of compounding in a year

For Initial amount 'a' = $1500

r = 9%

t = 11 years

n = 12 [Compounded monthly]

F = [tex]1500(1+\frac{9}{12})^{12\times 11}[/tex]

  = $4021.97