On a coordinate plane, a triangle is shown. It has points (1, 4), (5, negative 2), and (negative 3, negative 2).
Mary thinks the triangle is equilateral. How would you support or dispute her conjecture?

Calculate the slope of all three sides, and check whether the slopes are equal.
Calculate the slope of all three sides, and check whether any slopes are reciprocals.
Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.
Use the distance formula to calculate the length of all three sides, and check whether any two sides are congruent.

Answer:

C) Yes, because 1 and 5 are congruent

Step-by-step explanation:

Same-side congruent angles prove this to be true

Answer:

The answer is C

Step-by-step explanation:

Answer:

10.5 gallons are equal to 48000 cm3

Step-by-step explanation:

Step-by-step explanation:

A) as you can see there is no current flowing in a bar magnet so (incorrect)

B) Lines of magnetic field is going in A-->B direction so it have starting and ending points.(incorrect)

C) Yes whenever a magnetic object is placed near the another magnetic object they either attract or repell so they have a force in a form of push and pull [correct]

D)No because magnetic field lines goes from North--> South so A is the South pole [ incorrect]

E) Yes it will point always towards North pole of the magnet [correct]

F) yes it depends upon the density of field lines[correct]

G)No the near the magnet is it becomes more stronger as compared to magnet kept far.(incorrect)

So option C E F are correct

Hope this helps

Have a great day

[tex]~~~~~~150\times x\% = 35\\\\\implies 150 \times \dfrac{x}{100} = 35\\\\\implies \dfrac{3x}{2}=35\\\\\implies 3x = 35\cdot 2\\\\\implies 3x = 70\\\\\implies x = \dfrac{70}{3}\\\\\implies x =23.\overline{3}\\\\\text{So, 35 is}~ 23.\overline{3}\%~ \text{of} ~150.[/tex]

Step-by-step explanation:

[tex] = ( - 3c + 6) + ( - c + 8)[/tex]

[tex] = - 3c + 6 - c + 8[/tex]

[tex] = - 3c - c + 6 + 8[/tex]

= -4c + 14

hence -4c + 14 is the answer ...

hope it helped !!

Answer: Solve for Y

y = -16x - 38

And then y intercept is

(0, -38)

Step-by-step explanation:

Answer:

Point C

Step-by-step explanation:

The correct answer would be about 2.2 so C is the closest.

Answer:

9

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 ) then the discriminant is

Δ = b² - 4ac

x² + 5x + 4 = 0 ← is in standard form

with a = 1, b = 5 , c = 4 , then

b² - 4ac = 5² - (4 × 1 × 4) = 25 - 16 = 9

Answer:

9

Step-by-step explanation:

8 3/4 to the nearest whole number is 9

Answer:

25/6

Step-by-step explanation:

a²=6 -> a=✓6 (a must be positive so reject negative solutions)

ab=5 -> b = 5/✓6

thus area of C is b² = 25/6

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: a = \pi {r}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: a = 3.14 \times {3}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: a = 3.14 \times 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: a = 13.26 \: \: ft {}^{2} [/tex]

Answer: 28.26

Step-by-step explanation:

D = 6

R = 3

3.14 x 3 x 3 = 28.26

Answer:

a)   x² + 6x + 9

Step-by-step explanation:

When we square something, we multiply it by itself:

⇒ (x + 3)² = (x + 3)(x + 3)

Using the FOIL method:  (a + b)(c + d) = ac + ad + bc + bd

⇒ (x + 3)(x + 3) = x² + 3x + 3x + 9

                        = x² + 6x + 9

a.

[tex]\huge{{x}^{2} + 6x + 9}[/tex]

Step-by-step explanation:

Using Binomial Theorem:

[tex]\boxed{{(a+b)} ^n= \sum_{k=0}^{n}\binom{n}{k} a^{n-k}b^{k}}[/tex]

.

.

.

[tex](a+b) ^2 =a^{2} + 2ab +b^{2} [/tex]

The answer seems to be [tex]x^{2} + 6x + 9[/tex]...

The required value of the x in the expression of angle is 19.

An expression of angle is given as 7x + 2 = 135°, the value of the x is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
7x + 2 = 135
Simplifying,
7x = 135 - 2
7x = 133
x = 133 / 7
x = 19

Thus, the required value of the x in the expression of angle is 19.

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Answer:

There are 525 chairs in the hall.

Step-by-step explanation:

35 x 15 = 525

An example to learn this:

35 is the amount of all the chairs in ONE row, when you times 35 by 15, it is DUPLICATING those chairs by 15, equaling to an equal 35 chairs in EACH row! hope this helped.

Quadratic equation has a leading degrees of 2. The correct equation in vertex form is (x - 3)^2 + 5

Quadratic equation has a leading degrees of 2.

Given the quadratic function expressed as:

f(x) = x^2 - 6x + 14

Complete the square

x^2 - 6x + (-3)^2 - (-3)^2 + 14

(x- 3)^2 - 9 + 14
(x - 3)^2 + 5

Hence the correct equation in vertex form is (x - 3)^2 + 5

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Answer:

$5

Step-by-step explanation:

$5 appeared more in the prices

Answer:

5 dollars

Step-by-step explanation:

cuz I just know

Answer:

[tex]m = \boxed 7[/tex]

Combine like terms

[tex]21=33\cdot \mathrm{m}-21-27\cdot \mathrm{m}[/tex]

Group like terms

[tex]21=\left(33\cdot \mathrm{m}-27\cdot \mathrm{m}\right)-21[/tex]

Simplify the arithmetic

[tex]21=6\cdot \mathrm{m}-21[/tex]

Swap sides

[tex]6\mathrm{m}-21=21[/tex]

Answer:

[tex]\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \boxed{ \frac{1}{4} }[/tex]

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \lim_{x \to c} x = c[/tex]

Special Limit Rule [L’Hopital’s Rule]:
[tex]\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]

Differentiation

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:

Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify given limit.

[tex]\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3}[/tex]

Step 2: Find Limit

Let's start out by directly evaluating the limit:

When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:

∴ we have evaluated the given limit.

___

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___

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Without using l'Hopitâl's rule, we can instead rationalize the numerator.

[tex]\dfrac{\sqrt{x+1} - 2}{x-3} = \dfrac{\left(\sqrt{x+1}-2\right)\left(\sqrt{x+1}+2\right)}{(x-3)\left(\sqrt{x+1}+2\right)} = \dfrac{(x+1)-4}{(x-3)\left(\sqrt{x+1}+2\right)} = \dfrac1{\sqrt{x+1}+2}[/tex]

We've removed the discontinuity at [tex]x=3[/tex], so the limand is continuous and

[tex]\displaystyle \lim_{x\to3} \frac{\sqrt{x+1}-2}{x-3} = \lim_{x\to3} \frac1{\sqrt{x+1}+2} = \frac1{\sqrt{3+1}+2} = \boxed{\frac14}[/tex]

Answer:

income tax=13% of total salary

Step-by-step explanation:

Here,

let salary be 'x'

Now,

13%of x = $10 000

13/100 × x = $10 000

13x = 1000000

x=10 00000/13

Therefore x =76,923.0769

His salary that year was 76,923.0769

The probability of rolling the die once to get a four is 1/6

So we do 1/6*1/6*1/6 which is 1/216 since it's combined probabilities

Hope this helped

The standard deviation of the population dataset is 9.35

The dataset is given as:

18, 14, 35, 34, 11, 26

Start by calculating the mean using:

Mean = Sum/Count

This gives:

[tex]\bar x = (18+ 14+ 35+ 34+ 11+ 26)/6[/tex]

Evaluate

[tex]\bar x = 23[/tex]

The standard deviation is then calculated using:

[tex]\sigma = \sqrt{\frac{\sum (x - \bar x)^2}{n}}[/tex]

This gives

[tex]\sigma = \sqrt{\frac{(18 - 23)^2 + (14- 23)^2 + (35- 23)^2 + (34- 23)^2 + (11- 23)^2 + (26- 23)^2}{6}}[/tex]

Evaluate

[tex]\sigma = \sqrt{\frac{524}{6}}[/tex]

This gives

[tex]\sigma = 9.35[/tex]

Hence, the standard deviation of the population is 9.35

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When a circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base, a pair of intersecting lines is formed.

The right circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base.

This means the intersecting line forms a right angle with the base of the right circular cone.

Therefore, what is produced from this interaction is a pair of intersecting lines. The intersecting lines also have a point.

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Answer:

a) 11/100

b) 60 times

Step-by-step explanation:

a)

We want to find the probability that a 3 will be rolled.

Probability = # of favorable outcomes / total # of outcomes.

Here the number of favorable outcomes will be the number of times a 3 was rolled and the total number of outcomes will simply be the # of times that the dice was rolled which can be calculated by finding the sum of the frequencies of each number.

So # of favorable outcomes = 11 ( as the dice was rolled on a 3 11 times.)

And the total number of outcomes would be 100 ( the sum of the frequencies , 12 + 35 + 11 + 23 + 7 + 12 = 100 )

So the probability of rolling a 3 would be 11/100

b)

For this part we want to find the expected times that a 6 would be rolled if we rolled the die 500 more times.

To calculate this we simply find the probability of rolling a 6 and then multiply that by 500.

So again probability = # of favorable outcomes / total # of outcomes.

Here # of favorable outcomes is frequency of rolling a 6 which would be 12 and the total number of outcomes is 100 as we found out during the last part.

So the probability of rolling a 6 is 12/100 or 3/25

We then multiply this by 500 to find the expected number of times a 6 would be rolled if the dice was rolled 500 more times

So our answer = 3/25 × 500 = 60 times

Answer:

[tex]-\frac{8}{4}[/tex]

Step-by-step explanation:

To find slope from 2 points: [tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{-2-6}{2-(-2)} =-\frac{8}{4}[/tex]

Answer:

Step-by-step explanation:

Discussion

You haven't given us any choices. Always do that it you have them. Look for the graph that looks like the one below. It has the following characteristics

Answer:

A. 4.

Step-by-step explanation:

The scale factor is 4.

If you multiply 8, 5, and 2 by 4, you get 32, 20, and 8.

For the spinner with 3 sectors, the total number of outcomes for 3 spins is 27.

A combination is a mathematical technique that determines the number of possible arrangements.

Let's we have to define

A, B, and C, as the regions in the spinner.

So, we spin it 3 times, and for each of these times there are 3 outcomes, so the outcomes will be of the form:

The outcome of spin 1, the outcome of spin 2, outcome of spin 3.

The total number of  different outcomes will be:

3^3 = 27

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Answer:  480 and 253.2

Step-by-step explanation:

For the first one we want to do (12 x 5 / 2) x 16 which equals 480.

For the next question, the answer is 253.2 because 2πrh is the formula of lateral area. If we just plug in the numbers it's (2 x 3.14 x 4.8 x 8.4) = 253.2cm

Answer:

66$

Step-by-step explanation:

1/3 of 99 is 33

so 99 - 33 = 66

Based on the relationship between the ratings and cost, the association is a positive correlation. The data point that affects the appropriateness of using linear regression is $4,200 and 15 rating.

A car that is cost effective and rated highly is the data point (3,500,100).

In general, the cost of cars shown is higher when the customer reviews are high as well. This shows a positive correlation between cost and customer ratings.

The car at (4,200, 15) is an outlier because it is expensive and yet has low ratings. It would therefore affect a linear regression model if one is used to fit the data shown.

The car at (3,500, 100) is cost-effective and rated high because it is not as expensive as a lot of other cars, and yet has the highest customer rating of 100.

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