Which equation will create a system of equations with infinitely many solutions?
A) 3x - y=5
B) -3x +y=5
C) 12x + 4y = 20
D) 12x - 4y= 20

Given:

The figure of a triangle.

To find:

The missing length.

Solution:

Let x be the missing length.

Basic proportionality theorem(BPT): According to this theorem, if a line is parallel to the one side of a triangle then that the line intersects the other two sides of the triangle in the same ratio.

Using Basic proportionality theorem, we get

[tex]\dfrac{6}{8-6}=\dfrac{12-x}{x}[/tex]

[tex]\dfrac{6}{2}=\dfrac{12-x}{x}[/tex]

[tex]3=\dfrac{12-x}{x}[/tex]

[tex]3x=12-x[/tex]

Adding x on both sides, we get

[tex]3x+x=12[/tex]

[tex]4x=12[/tex]

[tex]x=\dfrac{12}{4}[/tex]

[tex]x=3[/tex]

The missing length is 3 Therefore, the correct option is D.

Answer:

450 students

Step-by-step explanation:

Answer:

15 ml

Step-by-step explanation:

Find the volume of the tank which is 1.8m*0.6m*0.5m=0.54m^3

For every 0.18m^3,5ml of treatment is added,what of 0.54m^3

(0.54m^3*5ml)/(0 18m^3)=15ml

Answer:

xxyy2578

Step-by-step explanation:

This is in contrast to theoretical probability where it's what we think would happen, or predict to happen.

For example, the theoretical probability of getting heads on a coin is 1/2 = 0.50 = 50%. If you flip a coin say 1000 times and get 400 heads, then the empirical or experimental probability of getting heads is 400/1000 = 0.40 = 40%. The experimental probability is what actually happens when you do the experiment. The theoretical probability is what you predict what would happen given some list of assumptions and rules about the object.

According to the law of large numbers, the experimental probability should get closer and closer to the theoretical one assuming the theoretical probability has been calculated properly (and all assumptions are correct). If we got say 475 heads instead of 400, then we might have fairly good evidence that we have a fair coin (since 475/1000 = 0.475 is fairly close to 0.500); however, if we got something like 300 heads then we might suspect that the coin is biased toward tails than it is toward heads. The more trials you do, the better a picture you can get of it.

Answer:

2,3,4, and 5

Step-by-step explanation:

#1

So all are positive

#2

In Q3

Hence all are negative

#4

Yes anything left to or bottom to zero us negative

#6

option A,B,D,F are correct

Bert, Camille, and Etsuko.

Answer:

Bert, Camille, and Etsuko has the solution as x = 4.

Step-by-step explanation:

Bert:

2x - 9 = -1

Camille:

-2x + 12 = 4

Etsuko

[tex]2(x - 10) = - 12[/tex]

Answer:

95

Step-by-step explanation:

a cardinal number is anything that is to 70 and the rest of the numbers above 70 are counting by 10s

Answer:

[tex]f^{-1}(6) = 50[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \sqrt{2x} - 4[/tex]

Required

Find [tex]f^{-1}(6)[/tex]

First, we calculate the inverse function

[tex]f(x) = \sqrt{2x} - 4[/tex]

Express f(x) as y

[tex]y = \sqrt{2x} - 4[/tex]

Swap the positions of x and y

[tex]x = \sqrt{2y} - 4[/tex]

Solve for y: Add 4 to both sides

[tex]4 + x = \sqrt{2y} - 4+4[/tex]

[tex]4 + x = \sqrt{2y}[/tex]

Square both sides

[tex](4 + x)^2 = 2y[/tex]

Divide both sides by 2

[tex]y = \frac{(4 + x)^2}{2}[/tex]

Express y as an inverse function

[tex]f^{-1}(x) = \frac{(4 + x)^2}{2}[/tex]

Next, solve for: [tex]f^{-1}(6)[/tex]

Substitute 6 for x

[tex]f^{-1}(6) = \frac{(4 + 6)^2}{2}[/tex]

[tex]f^{-1}(6) = \frac{(10)^2}{2}[/tex]

[tex]f^{-1}(6) = \frac{100}{2}[/tex]

[tex]f^{-1}(6) = 50[/tex]

Answer: B

Step-by-step explanation: So that you know you are only getting the best for what YOU PAID for.

Answer:

Harper's age = 18

Miguel age = 16

Step-by-step explanation:

Given:

Miguel age = [2/3][Harper's age] + 4

Sum of their age = 34

Computation:

Assume;

Harper's age = a

So,

Miguel age = [2/3][a] + 4

Sum of their age = 34

So,

Miguel age + Harper's age = 34

[2/3][a] + 4 + a = 34

[2a / 3] + a = 34 - 4

[2a + 3a] / 3 = 30

5a / 3 = 30

5a = 90

a = 18

So,

Harper's age = 18

Miguel age = [2/3][a] + 4

Miguel age = 16

Answer:

A

Step-by-step explanation:

f(x) = x

x = 3

->

f(3) = 3

A

Given:

The point (5,-2) is translated 3 units to the left.

To find:

The new location of the point.

Solution:

If a point is translated 3 units to the left, then

[tex](x,y)\to (x-3,y)[/tex]

Using this rule of translation, we get

[tex](5,-2)\to (5-3,-2)[/tex]

[tex](5,-2)\to (2,-2)[/tex]

Therefore, the new location of the point is (2,-2). Hence, the correct option is C.

Answer:

178.2 ft

Step-by-step explanation:

[tex] \sin(60) = \frac{x}{200} \\ \frac{ \sqrt{3} }{2} = \frac{x}{200} \\ x = 100 \times \sqrt{3}[/tex]

So,

[tex]h = 5 + x = 5 + 100 \times \sqrt{3} = 178.2[/tex]

Answer:

Step-by-step explanation:

19 of 22 participants (86.36%) from the high-power posing group took a gambling risk to double their money, while 12 of 20 (60%) from the low-power posing group took the gambling risk. Use a calculator tool from Module 10 to determine the p-value associated with the hypothesis test examining if there is a statistically significant difference between the proportion of people willing to take risks in the two groups. Round to 3 decimal places

H0 : P1 - P2 = 0

H1 : P1 - P2 ≠ 0

P1 = 0.8636

P2 = 0.6

q1 = 1 - P1 = 0.1364

q2 = 1 - P2 = 0.4

Tstatistic = (p1 - p2) ÷ √(p1q1)/n1 + (p2q2)/n2]

Tstatistic = (0.8636-0.6) ÷ √0.01735432]

Tstatistic = 0.2636 ÷ 0.1317357

Test statistic = 2.0009761

Test statistic = 2

The Pvalue from t statistics :

Tscore = 2 ; df = 20 + 22 - 2 = 40

Answer:

She needs a time of 61 min on her 8th ride

in order to average 51 min for the 8 rides

Step-by-step explanation:

+%28+46+%2B+48+%2B+50+%2B+43+%2B+54+%2B+54+%2B+52+%2B+t+%29+%2F+8+=+51+

+347+%2B+t+%29+%2F+8+=+51+

+347+%2B+t+=+408+

+t+=+61+

Use the binomial theorem:

[tex]\displaystyle (2x-9)^5 = \sum_{k=0}^5 \binom5k (2x)^{5-k}(-9)^k = \sum_{k=0}^5 \frac{5!}{k!(5-k)!} 2^5 \left(-\frac92\right)^k x^{5-k}[/tex]

The x ³ terms occurs for 5 - k = 3, or k = 2, and its coefficient would be

[tex]\dfrac{5!}{2!(5-2)!} 2^5 \left(-\dfrac92\right)^2 = \boxed{6480}[/tex]

Answer:

Step-by-step explanation:

n+37=180

n=180-37=143°

Answer:

B) 143°

Step-by-step explanation:

Since n° is supplementary to 180°, then n°=180°-37°=143°.

Answer: 10%

Step-by-step explanation:

Since the shopkeeper purchased 60 pencil boxes for 4,500, he purchased them at the rate of:

= 4500 / 60

= 85 per pencil box

If the shopkeeper sold them at the rate of 4,125 for 50 pencil boxes, then he sold them at the rate of:

= 4125 / 50

= 82.50 per pencil box.

Therefore the percentage profit will be:

= Gain / Cost price × 100

= (82.50 - 75) / 75 × 100

= 7.5/75 × 100

= 10%

Answer:

[tex](-2,8)[/tex]    [tex](7,5)[/tex]      [tex](1,7)[/tex]

Step-by-step explanation:

Given

[tex]x + 3y = 22[/tex]

Solving (a): The possible coordinates

We have:

[tex](x,y) = (-2,8)[/tex]

This gives:

[tex]x + 3y = 22 \to -2 + 3 * 8[/tex]

[tex]x + 3y = 22 \to -2 + 24[/tex]

[tex]x + 3y = 22 \to 22[/tex]

(-2,8) is a point on the grid

[tex](x,y) = (7,5)[/tex]

This gives:

[tex]x + 3y = 22 \to 7 + 3 * 5[/tex]

[tex]x + 3y = 22 \to 7 + 15[/tex]

[tex]x + 3y = 22 \to 22[/tex]

(7,5) is a point on the grid

[tex](x,y) = (-5,5)[/tex]

This gives:

[tex]x + 3y = 22 \to -5 + 3 * 5[/tex]

[tex]x + 3y = 22 \to -5 + 15[/tex]

[tex]x + 3y = 22 \to 10[/tex]

(-5,5) is a not point on the grid

[tex](x,y) = (1,3)[/tex]

This gives:

[tex]x + 3y = 22 \to 1 + 3 * 3[/tex]

[tex]x + 3y = 22 \to 1 + 9[/tex]

[tex]x + 3y = 22 \to 10[/tex]

(1,3) is a not point on the grid

[tex](x,y) = (1,7)[/tex]

This gives:

[tex]x + 3y = 22 \to 1 + 3 * 7[/tex]

[tex]x + 3y = 22 \to 1 + 21[/tex]

[tex]x + 3y = 22 \to 22[/tex]

(1,7) is a point on the grid

So, we plot the following on the grid

[tex](-2,8)[/tex]    [tex](7,5)[/tex]      [tex](1,7)[/tex]

See attachment

Answer: B. 183 cm^3

V = pi r^2 h/3

V = pi (5^2) (7/3)

V = pi (25) (2.33)

V = 183

Answer:

B.183 [tex]cm^{3}[/tex]

Step-by-step explanation:

Volume of cone is [tex]V=\pi r^{2} \frac{h}{3}[/tex]

where h=7 and r=5 (because r=d/2, where d=10)

V=[tex]5^{2}\frac{7}{3}\pi[/tex]

V=25·[tex]\frac{7}{3} \pi[/tex]

V=175/3[tex]\pi[/tex]

V=183.2595715 or 183 [tex]cm^{3}[/tex]

Answer:

I would maybe say 34% im in sixth grade and this hard for me atleast i tried

Step-by-step explanation:

Answer:

1 out of 27,636,336,000

Step-by-step explanation:

40 · 39 · 38 · 37 · 36 · 35 = 27,636,336,000

Answer:

true

false

true

false

true

false

Step-by-step explanation:

Answer: 3n - 12

Product means multiplication. So the 3 and n are being multiplied. If 12 is less than, then that means it is being subtracted from 3n, not the other way around.