Which must be true?​

Answer:

inequality equation :3x ≤ 57

solution: x ≤ 19

Step-by-step explanation:

Length of all sides in  an equilateral triangle is same

thus, perimeter of  an equilateral triangle is 3x

where x is the side length of  an equilateral triangle.

_____________________________________

The perimeter of an equilateral triangle must be at most 57 feet.

It means that that

perimeter must be at most 57 or less that it.

Example perimeter can be 57, 56,52 or any number less than that but it cannot be 57.1, 58 and so on.

Thus, we can also say that

perimeter of an equilateral triangle must be less than or equal to 57 feet. perimeter of an equilateral triangle is give by 3x

where x is the side length

thus writing it in inequality form

3x ≤ 57

=>x ≤ 57/3

=> x ≤ 19

Thus,

inequality equation

3x ≤ 57

solution

x ≤ 19 ( it means length of side can be at-most 19 feet)

Answer:

B

Step-by-step explanation:

Answer:

1/9

Step-by-step explanation:

The probability of a bell ringing one day is 1/3. There is a 1/6 chance of the same bell ringing again.

Answer:

28 miles in 7 minutes, 240 miles in an hour

Step-by-step explanation:

We can first simplify the rate to miles per minute. Since the plane goes 12 miles in 3 minutes, we can divide it by 3 to find how much it travels in one minute. 12 divided by 3 is 4 and 3 divided by 3 is 1

The plane travels 4 miles a minute

To find how much it travels in 7 minutes, multiply by 7

4x7 is 28

28 miles in 7 minutes

To find an hour, multiply by 60

4x60= 240

240 miles in an hour

Answer:

9.3 × 10⁷ - 3.4 × 10⁶ = 89 600 000

Which is 8.96*10^7 in scientific notation

Hope this helps you

Answer:

Given the following information, the area of the triangle is x⁴+3x³+9x²+10x+12

Step-by-step explanation:

We must know the formula for finding the area of a triangle in order to begin.

Area = 1/2(b×h)

First we multiply the base and height together.

Base = x² + 2x + 4

Height = 2x² + 2x + 6

(x² + 2x + 4)(2x² + 2x + 6)

Use the foil method to solve this.

2x⁴ + 2x³ + 6x² + 4x³ + 4x² + 12x + 8x² + 8x + 24

Combine like terms.

2x⁴ + 6x³ + 18x² + 20x + 24

Now that we have our product, we have to divide this expression by 2 or 1/2.

(2x⁴ + 6x³ + 18x² + 20x + 24)/2

So, the area of the triangle is x⁴ + 3x³ + 9x² + 10x + 12

Answer:

however long it took him to run 200 meters x 2

Step-by-step explanation:

200 x 2 = 400

so

the ratio is 1:2

to keep this ratio you must multiply whatever he ran x 2 to get your answer

The time It will take Usain Bolt  to run 400 m is twice the time of 200 m.

The given parameters:

first distance of Usain Bolt= 400 meters

second distance Usain Bolt = 200 meters

To find:

Let the average speed of Usain Bolt in the 400 m = y

then, his average speed in the 200 m = y, since they are equal.

Average speed is calculated as;

[tex]Average \ speed = \frac{distance }{time} \\\\distance = average \times time[/tex]

Let the time taken by Usain Bolt to run 400 m = t₁

Let the time taken by Usain Bolt to run 200 m = t₂

To determine the time it takes him to run 400 m, we set up the following algebraic equations.

400 = yt₁ ---(1)

200 = yt₂  --- (2)

From the above equations, we solve for t₁ in terms of t₂

[tex]y = \frac{400}{t_1} = \frac{200}{t_2} \\\\\frac{400}{t_1} = \frac{200}{t_2} \\\\200t_1 = 400t_2\\\\t_1 = \frac{400t_2}{200} \\\\t_1 = 2t_2[/tex]

Thus, it takes Usain Bolt twice the time of 200 m to run 400 m

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Answer:

B = 61.75°

Step-by-step explanation:

The formula for the Law of Sines is given as:

a/ sin A = b/ sin B

In the question, we are given the following values

A = 56°, a = 16, b = 17

We are to solve for B

Hence,

16/ sin 56° = 17/sin B

Cross Multiply

sin B × 16 = sin 56° × 17

sin B = sin 56° × 17/16

sin B = 0.88

B = arc sin(0.88)

B = 61.74536°

Approximately B = 61.75°

Answer:

parabola

Step-by-step explanation:

This is the equation of a parabola, notice that only one of the variables (in this case the variable y) appears squared in the equation, and it satisfies the general form of a parabola with branches pointing horizontally.

Answer:

Perpendicular.

Step-by-step explanation:

8y=-x-1

y=-1/8x-1/8

-8x+y=-1

y=8x-1

Perpendicular

Answer:

2ab - 8a + 6

Step-by-step explanation:

(-3ab - 8a + 8) - (-5ab +2)

(-3ab - 8a + 8) -1(-5ab +2)

Distribute -1 to the brackets.

(-3ab - 8a + 8) + 5ab - 2

Remove the brackets.

-3ab - 8a + 8 + 5ab - 2

Rearrange.

5ab - 3ab - 8a + 8 - 2

Combine like terms.

2ab - 8a + 6

Step-by-step explanation:

Let the rhombus be $ABCD$, where $\angle DAB = 120^\circ$. Then $\angle ABC = 180^\circ - \angle DAB = 180^\circ - 120^\circ = 60^\circ$.

[asy] unitsize(1 cm); pair A, B, C, D; A = (0,1); B = (sqrt(3),0); C = (0,-1); D = (-sqrt(3),0); draw(A--B--C--D--cycle); draw(A--C); label("$A$", A, N); label("$B$", B, E); label("$C$", C, S); label("$D$", D, W); label("$6$", (A + D)/2, NW); [/asy]

Since $AB = BC$, triangle $ABC$ is equilateral. By the same argument, triangle $ACD$ is also equilateral. Each triangle has area

\[\frac{\sqrt{3}}{4} \cdot 6^2 = 9 \sqrt{3},\]so the area of the rhombus is $2 \cdot 9 \sqrt{3} = \boxed{18 \sqrt{3}}$.

Answer: kindly check Explanation

Step-by-step explanation:

The balance on card = $2000

Interest rate = 12.5%

Therefore, monthly rate = 12.5% / 12 = 0.0104167

Paying $75 of monthly balance :

Interest amount on 2000 = 0.0104167 × 2000 = $20.83

Therefore,

Principal amount payed = 75 - 20.83 = 54.17

Balance = ($2000 + $20.83) - $75 = 1945.83

Interest on balance = 0.0104167 × 1945.83 = $20.2691

Paying $100 of monthly balance :

Interest amount on 2000 = 0.0104167 × 2000 = $20.83

Therefore,

Repayment = 100 - 20. 83 = $79.17

Balance = ($2000 + $20.83) - $100 = 1920.83

Interest on balance = 0.0104167 × 1920.83 = $20.0087

Interest saved by paying $100 instead of $75

$20.27 - $20.00 = $0.27 = 27 cent

Answer:

$101

Step-by-step explanation:

Check link answer.

Answer: 19 ft

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:

c^2 = a^2 + b^2

Where c is the hypotenuse of the triangle (in this case the length of the ladder) and a and b are the other sides.

Replacing with the values given:

20^2 = (4 1/2)^2 + x^2

400=20.25 + x ^2

400-20.25 = x^2

379.75 = x^2

√379.75 = x

x = 19.48

x= 19 ft

Feel free to ask for more if needed or if you did not understand something.

The statement that is true is |-45| = 45 and |-96| = 96.

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

|-45| = 45

|-96| = 96

-|-45| = - 45  

-|-96| = - 96

|-45| = 45

|-96| = 96

|-45| = 45

|-96| = 96

Thus,

|-45| = 45 and |-96| = 96 is true.

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Answer:

310 balcony tickets were sold

Step-by-step explanation:

Part 1:

X=the number of orchestra seats sold

Y=the number of balcony seats sold

980=the total of tickets sold

X+Y=980

Part 2:

Orchestra seats cost $50

Balcony Seats cost $35

Total money collected $44,350

50X+35Y=44,350

X+Y=980

Y=980-X (substitute y in your second equation)

50X+35(980-X)=44,350

50X+34,300-35X=44,350

50X-35X=44,350-34,300

15X=10,050

X=670

Y=980-X

Y=980-670

Y=310

Check

50X+35Y=44,350

50(670)+35(310)=44,350

Answer:

Multiple Choice Answer: domain (-∞, ∞), range f(x) ≥ 3

Answer:

D

Step-by-step explanation:

4x^4+3x^2-3x^3-3x+1

Answer:

-2

Step-by-step explanation:

each number is being multiplied by -2 to get to the next number

A. -4/2 but if you factor it it will be -2

Answer: <MQR to be 15 degrees

The value of RQ = 9, from the given details, using the sine rule and other properties of triangles.

According to the sine rule, in a triangle ABC,

a/sin A = b/sin B = c/sin C

where a = BC, b = AC, and c = AB.

In the question, we are given a diagram and the following details:

∆PQR, m ∠R = 90° m ∠PQR = 75°, m ∠MQR = 60° M ∈ PR , MP = 18. We are asked to find the value of RQ.

Now, since m ∠PQR = 75° and m ∠MQR = 60°,

we can say that m ∠PQM = m ∠PQR - m ∠ MQR = 75° - 60° = 15°.

In Δ MQR,

m ∠R = 90°, m ∠Q = 60°.

∴ m ∠M = 180° - (m ∠R + m ∠Q) = 180° - (90° + 60°) = 30°. {using angle sum property of triangle}

At point M, m ∠RMQ + m ∠ QMP = 180° {Adjacent angles}

or, 30° + m ∠ QMP = 180° {∵ m ∠RMQ = 30°, calculated above}

or, m ∠ QMP = 180° - 30° = 150°.

Now, in ΔPQM,

m ∠P + m ∠Q + m ∠M = 180°.

or, m ∠P + 15° + 150° = 180°

or, m ∠P + 165° = 180°,

or, m ∠P = 15°.

Since, m ∠P = m ∠Q, Δ QPM is an isosceles triangle, with MP = MQ = 18 {Since, MP = 18 is given}.

Now in ΔRQM, by applying the sine rule, we can say that:

MQ/sin R = RQ/sin M,

or, 18/sin 90° = RQ/sin 30°,

or, RQ = (18*sin 30°)/sin 90° = (18*0.5)/1 {Since, sin 30° = 0.5 and sin 90° = 1},

or, RQ = 9.

Therefore, RQ = 9, using the sine rule.

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Answer:

60 min over 1 hour

Step-by-step explanation:

Answer:

IT IS A..

Step-by-step explanation:

100 % sure

[tex](x {}^{2} - x + 8) + (10x {}^{2} + 7)[/tex]

[tex]10x {}^{4} - 10x {}^{3} + 87x {}^{2 } - 7x + 56[/tex]

Answer:

C.

Step-by-step explanation:

Geometric sequences have an r difference, where r is the ratio/multiplying number. Choice C is correct because the numbers are multiplied by 2 each time, so r is 2.

Answer:

UV and WV

Step-by-step explanation:

Answer:

pretty sure it's A

Step-by-step explanation:

The problems don't add up so I'd say it's linear (you probably shouldn't take my advice I'm as bad at math as you are-)

Answer:

C. y + 4 = -1/2 (x - 1)

Step-by-step explanation:

The x values go up by 6 units each step, 1, 7, 13, 19.

Start with 1 and add 6 to get 7, then add 6 to get 13, then add 6 to get 19.

For each corresponding step in x, y becomes 3 less.

Start with -4, then subtract 3 to get -7, subtract 3 to get -10, subtract 3 to get -13.

For every change of 6 in x, you get a change of -3 in y. This means a linear relationship.

To find the equation, we can use any two of the given points and the point-slope equation of a line.

y - y1 = m(x - x1)

m = slope = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line, and m = slope.

Let's use the points (x1, y1) = (1, -4) and (x2, y2) = (7, -7)

y - y1 = (y2 - y1)/(x2 - x1) * (x - x1)

y - (-4) = (-7 - (-4))/(7 - 1) * (x - 1)

y + 4 = (-7 + 4)/(6) * (x - 1)

y + 4 = (-3/6)(x - 1)

y + 4 = -1/2 (x - 1)

Answer:

first answer is correct

Step-by-step explanation:

hello

as we can write

[tex]x^2-1=(x-1)(x+1)\\[/tex]

the least common denominator is

x(x-1)(x+1)

hope this helps

Answer:

x + 1

x - 1

x

Step-by-step explanation:

The denominators are as follows.

(x - 1)

x^2 - 1

x

=====

The second denominator is actually made of two factors.

x^2 - 1 =(x + 1)(x - 1)

So the least common denominator is

x + 1

x - 1

x

You do not count the x - 1 twice.

Answer:

figure ??????

Step-by-step explanation:

Answer:

The answer is -6p +1/7.

hope it helps...

Answer:

fkdoekenrnfrkdoki

Step-by-step explanation:

haha dokie