(1,4) (3,10) what’s the slope, y-intercept and standard form [y=my+b]

Answer:

[tex]-\frac{7}{3}[/tex]

Step-by-step explanation:

To solve this, we are using the average rate of change formula:

[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]

where

[tex]m[/tex] is the average rate of change

[tex]a[/tex] is the first point

[tex]b[/tex] is the second point

[tex]f(a)[/tex] is the function evaluated at the first point

[tex]f(b)[/tex] is the function evaluated at the second point

We want to know the average rate of change of the function [tex]f(x)=0.5^x-6[/tex] form x = -3 to x = 0, so our first point is -3 and our second point is 0. In other words, [tex]a=-3[/tex] and [tex]b=0[/tex].

Replacing values

[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]

[tex]m=\frac{0.5^0-6-(0.5^{-3}-6)}{0-(-3)}[/tex]

[tex]m=\frac{1-6-(8-6)}{3}[/tex]

[tex]m=\frac{-5-(2)}{3}[/tex]

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

[tex]m=\frac{-7}{3}[/tex]

[tex]m=-\frac{7}{3}[/tex]

We can conclude that the average rate of change of the exponential equation form x = -3 to x = 0 is [tex]-\frac{7}{3}[/tex]

Answer:

C. $199.84

Step-by-step explanation:

The price of an upholstery fabric is $ 12.49 per yard.

This means that 1 yard costs $ 12.49

Now we want to find the cost of 16 yards of the upholstery fabric.

We just have to multiply $12.49 by 16.

We multiply to obtain:

[tex]12.49\times 16=199.84[/tex]

Therefore 16 yards will cost $ 199.84

The correct answer is C.

[tex]s = \frac{a + b}{2} \times h[/tex]

S = (19+23)/2×14

S = 42/2×14

S = 21×14

S = 294 cm^2

Answer294

Step-by-step explanation:

Answer:

Step-by-step explanation:

From first piece -6 < x ≤ 0.

From second piece 0 < x ≤ 4.

Therefore -6 < x ≤ 4 → x ∈ (-6, 4]

-7 ∉ (-6, 4]

-6 ∉ (-6, 4]

4 ∈ (-6, 4]

5 ∉ (-6, 4]

Answer:

18x + 27

Step-by-step explanation:

Distribute

-9(-2x-3)

18x + 27

Solution

18x + 27

Answer:

18x + 27

Step-by-step explanation:

- (8) * - (5 ) is = + 40

-----------------------------

-9( - 2x -3)

(-9*-2) + (-9*-3)

(18x )+(27)

18x + 27

Answer:

38.46%

Step-by-step explanation:

There are 91 students and 35 of them received a score of 90 or above.

So, there are 35/91 students with an A grade.

The probability to pick a random student that would be the same proportion that those who got the right score, so 35 / 91 = 0.3846 or 38.46%

38.46% of chances to pick someone who got an A (90 score or above), and, the opposite, 61.54% of chances to pick someone who didn't get an A.  That's a strong class!

Answer:

38.46% of the class received an "A"

Step-by-step explanation:

The Class has a total student count of 91 students. Out of those 91 students 35 of them received an "A" (90 or above). Meaning the percentage of students in the whole class who received a 90 or above is calculated by dividing the amount of students who received an "A" by the total amount of students in the class, as shown below.

[tex]\frac{35}{91} = 0.3846[/tex]

0.3846 * 100 = 38.46% ...... we multiply the decimal by 100 to get the percent

So 38.46% of the class received an "A"

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

The Volume is approximately 226

To find the volume of the cylindrical barrel with a height of 8 feet and a diameter of 6 feet, use the formula V = πr²h where r is the radius and h is the height. The approximate volume is approximately 226.08 cubic feet.

The approximate volume of the cylindrical barrel can be calculated using the formula V = πr²h.

Given that the diameter is 6 feet, the radius (r) would be half of the diameter, which is 3 feet. The height (h) is 8 feet.

Substitute the values into the formula to find the volume: V ≈ 3.14 × (3)² × 8 ≈ 226.08 cubic feet.

Answer:

The answer is 32.45

Step-by-step explanation:

Answer:

p = 80- 64 = 16

p = 16

Step-by-step explanation:

That's is the answer

Nandini needs to score at least 17 points to win.

To represent the number of points Nandini needs to win the game, we can use the inequality:

[tex]\( p > 80 - 64 \)[/tex]

Now, let's solve this:

[tex]\( p > 16 \)[/tex]

Therefore, Nandini needs more than 16 points to win the game.

Explanation:

1. Nandini needs more than 80 points to win the game, which means her total score should exceed 80 points.

2. She currently has 64 points, so to find out how many more points she needs, we subtract her current score from the total required points: \( 80 - 64 = 16 \).

3. Hence, the inequality representing the number of points she needs, denoted by \( p \), is \( p > 16 \), indicating that she needs more than 16 points to win the game.

This means Nandini needs to score at least 17 points to win.

Complete question:

Nandini needs more than 80 points to win a game. She has 64 points so far. which inequality represents p, the number of points she needs to win the game

Answer:

60√5

Step-by-step explanation:

(5√5)(6√4)

= (5√5)(12)

= 60√5

A random variable can be either discrete or continuous. It is discrete it can assume only a finite number of values, or a countable infinity of values at most.

It is continuous if it can assume values in an interval, or in general, an uncountable infinity of values.

That being said, we have:

Option A is a discrete random variable, because the number of heads in 5 throws can be 0, 1, 2, 3, 4 or 5. So, we have finitely many possible values.

Option B is a discrete random variable, because the number you roll on a die is either1, 2, 3, 4, 5 or 6. So, we have finitely many possible values.

Option C is a discrete random variable, because if there are n students in a class, the number of boys is an integer between 0 and n. So, we have finitely many possible values.

Option D is finally a continuous random variable, because the height of a 10-year-old can be any number (in a suitable range of course).

Final answer:

The example of a continuous random variable is D. Height of 10-year-olds, as height is a measured quantity that can have various values on a continuous scale.

Explanation:

When considering which of these is an example of a continuous random variable, it is important to understand the difference between discrete and continuous random variables. A discrete random variable consists of countable values, such as the number of heads when flipping a coin, whereas a continuous random variable includes values that are measured on a continuous scale, such as weight or height. Therefore, the correct answer to the student's question is D. Height of 10-year-olds because height is measured rather than counted, and it can take on a theoretically infinite number of values within a range.

Answer:

3 -1 > 1/4

Step-by-step explanation:

On the left hand side we have the expression;

3 - 1

3- 1 = 2

On the right hand side we have the value;

1/4

Therefore we are comparing 2 and 1/4

Since 2 is greater than 1/4 we have;

2 > 1/4

3 -1 > 1/4

The answers are:

Question 7:

154.29°

Question 8:

Yes, because the opposite sides are congruent.

For question 7:

We know that the sum of all interior angles of any polygon is determined by the following formula:

[tex]Angles=180*(sides-2)[/tex]

Therefore the sum of all interior angles of a 14-gon is equal to 2160°, so, the measure of each interior angle is given by the following calculation:

[tex]14-gon=(14-2)*180\°=2160\°[/tex]

Each interior angle is equal to:

[tex]\frac{2160\°}{12}=154.29\°[/tex]

For question 8:

We know that a quadrilateral is a parallelogram when the opposite sides are parallel or congruent.

From the statement we know that:

BE≅ED

and

AE≅EC

So, we can assume that the triangles formed by the sides BE and AE, and the sides EC and ED, are also congruent, meaning that the opposite sides BA and CD are congruent, so, the quadrilateral is a parallelogram.

Have a nice day!

Answer:

12

Step-by-step explanation:

Hi

H

Upggpugupgupgug0bjlblblibib,

Calculate half the base by multiplying the length of a side ( 60 cm) by the fraction of the ratio from the base to the vertex ( 5/12).

Then multiply that by 2 for the width of the base.

60 x 5/12 = 300/12 = 25 cm.

Full width = 25 x 2 = 50 cm.

Answer:

Full width = 25 x 2 = 50

Answer:

(x - 3), (x + 2), (x + 1) and (x + 3)

Step-by-step explanation:

Using synthetic division, I'd begin by testing various factors of -18 to determine whether any of them will divide into f(x)=x^4+3x^3-7x^2-27x-18 with no remainder.  Note that possible factors of -18 are ±1, ±2, ±3, ±6, ±18.

Let's arbitrarily start with -3.  In synthetic division, will the divisor yield a zero remainder ( which would tell us that -3 is a root of f(x)=x^4+3x^3-7x^2-27x-18 and that (x + 3) is a factor)?

-3   )   1    3    -7    -27    -18

              -3    0      21    +18

     ------------------------------------

         1      0    -7     -6      0  

Since the remainder is zero, -3 is a root and (x + 3) is a factor.  The coefficients of the quotient are shown above:  1  0  -7  -6.  Possible factors of 6 include ±1, ±2, ±3, ±6.  Arbitrarily choose 2.  Is this a root or not?

2    )    1     0     -7    -6

                 2     4     -6

      --------------------------

          1       2     -3    -12    

Here the remainder is not zero, so +2 is not a root and (x - 2) is not a factor.

Continuing to use synthetic division, I find that -1 is a root and (x + 1) is a factor, because the remainder of synth. div. is zero.  The coefficients of the quotient are 1, -1 and -6, which represents the quadratic y = x^2 - x - 6, whose factors are (x - 3)(x + 2).

Thus, the four factors of the original polynomial are (x - 3), (x + 2), (x + 1) and (x + 3).

Answer:

The third side is approximately 31.6 inches long.

Step-by-step explanation:

When given the lengths of two sides of a right triangle, you can easily use Pythagorean Theorem (a2+b2=c2; a or b being the legs, c being the hypotenuse) to find the length of the third side. Since the legs (10 in. and 30 in.) are already given to us, we can simply insert the numbers into Pythagorean Theorem and solve for the third side! It should look a little something like this: 102+302=c2, then solve for the squares to get 100+900=c2, then add the two side lengths to get to 1,000=c2, then find the square root of both sides (now, since the c is already being squared, they will cancel out to just c, but you will get the actual square root of 1,000). Should all go well, you should get an answer of 31.6227766017, which just so happens to round out to 31.6. And with that, we have our final no-longer-missing side length of 31.6 inches.

Hope this helped!

Answer:

$101.99

Step-by-step explanation:

She doesn't go over her 200 free miles.

If she drives 155 miles, then the amount she need to pay for the rental is:

                          $ 101.99

She got a special weekend rental deal for $101.99, with 200 free miles.

and $0.32 per mile after.

This means that for any mile covered less than or equal to 200 she just need to pay $ 101.99.

If she drives 155 miles, which is less than 200 miles then the amount she need to pay as a rent is:

             $ 101.99

Answer:

x>-3 is the answer hope it helps

Answer:

4 or up

Step-by-step explanation:

d ≅ 272ft. A car that is traveling at 70mph it will stop 272ft after the brakes are applied.

The key to solve this problem is using the equation d = k(r²), where d is the distance after the brakes are applied, k is the desaceleration constant and r is the speed of the car.

In order to maintain the consistency of the units, we have to convert mph to ft/s using the equation ft/s = mph x 1.467.

30mph x 1.467 ≅ 44ft/s

We know the speed of the car and the distance travelled after brakes are applied. The, clear k for the equation d = k(r²)

k = d/(r²)

Solving with d = 50ft and r = 44 ft/s

k = 50ft/(44ft/s)²= 0.0258 s²/ft

Then, is the same car now is traveling at 70mph, how many feet will it take to stop?

Convert 70mph to ft/s

70mph x 1.467 = 102.69ft/s

Using the equation d = k(r²), where k = 0.0258 s²/ft and r = 102.69ft/s

d = 0.0258s²/ft[(102.69ft/s)²] = 272.06ft

Equation A is linear and equation B is nonlinear

Answer:

Equation A is linear and equaiton B is nonlinear

Step-by-step explanation:

Equation A respresents a straight line with a x-intercept of x=-3/2 and a y-intercept of y = -2. This equation is linear because it is a first degree polynomical equation with x^1 = x

Equation A is not a linear equation and is written as :

[tex]y=3/(x+5)[/tex]  

This is a rational function but it is not linear because x is in the denominator and not numerator.

The correct option is C.

In an isosceles triangle ABC with base angles A and the sides b and c equal, you can use the Law of Cosines to find the length of the other side (a) in terms of b and c. The Law of Cosines is given by:

[tex]\[a^2 = b^2 + c^2 - 2bc \cos(A)\][/tex]

Given that A = π/4, b = c = 4, you can substitute these values into the equation:

[tex]\[a^2 = 4^2 + 4^2 - 2 \cdot 4 \cdot 4 \cos\left(\frac{\pi}{4}\right)\][/tex]

Simplify the expression:

[tex]\[a^2 = 16 + 16 - 32 \cos\left(\frac{\pi}{4}\right)\][/tex]

Now, you know that [tex]\(\cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}\)[/tex], so substitute that in:

[tex]\[a^2 = 16 + 16 - 32 \cdot \frac{\sqrt{2}}{2}\][/tex]

[tex]\[a^2 = 32 - 16\sqrt{2}\][/tex]

Now, factor out 16 from the expression:

[tex]\[a^2 = 16(2 - \sqrt{2})\][/tex]

So, the correct answer is:

[tex]\[a^2 = 4^2(2 - \sqrt{2})\][/tex]

Complete the question:

Suppose an isosceles triangle ABC has A= π /4 and b=c=4. What is the length of a^2 ？ A. 4^2sqrt(2) B. 4^2(sqrt(2)-2) C. 4^2(2-sqrt(2)) D. 4^2(2+sqrt(2))

Final answer:

By applying the Pythagorean theorem to the 45-45-90 isosceles triangle, we find that since both the sides a and b are 4, the square of side a is a² = 16.

Explanation:

In the context of an isosceles triangle with sides labeled a, b, and c, where side a is opposite angle A and side b equals side c, we can utilize the Pythagorean theorem to find the length of side a given that it's a right triangle. The Pythagorean theorem states:

a² + b² = c².

Given that angle A = π/4 radians (45 degrees), it implies that triangle ABC is a 45-45-90 right triangle, which tells us that sides a and b are equivalent in length. Under these conditions, the Pythagorean theorem simplifies to:

2a² = c².

We're given that b = 4, accordingly a would also be 4 (since a=b in an isosceles right triangle), and we're asked to find the length of a². Squaring side a, we get:

a² = 4² = 16.

Therefore, the length of a² is 16.

Answer:

[tex] g ( x ) * f ( x ) = ( x + 9 ) ^ 2 [/tex]

Step-by-step explanation:

We are given the following two functions and we are to find [tex]g(x) * f(x)[/tex]:

[tex]f(x)=x2-81[/tex]

[tex]g(x)=(x - 9)^{-1} ( x + 9)[/tex]

[tex]g(x)*f(x)=x^{-81} * \frac{x+9}{x-9}[/tex]

[tex]g ( x ) * f ( x ) =\frac{(x+9)(x-9)(x+9)}{x-9}[/tex]

[tex] g ( x ) * f ( x ) = ( x + 9 ) ( x + 9 ) [/tex]

[tex]  g ( x ) * f ( x ) =( x + 9 ) ^ 2 [/tex]

For this case we have the following fusions:

[tex]f (x) = x ^ 2-81\\g (x) = (x-9) ^ {- 1} * (x + 9)[/tex]

We can rewrite g (x) as:

According to the following power property:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Also:

If we factor f (x) we have:

[tex]f (x) = (x + 9) (x-9)[/tex]

We must find:

[tex]f (x) * g (x) = (x + 9) (x-9) * \frac {(x + 9)} {(x-9)}[/tex]

We simplify common terms in numerator and denominator:

[tex]f (x) * g (x) = (x + 9) ^ 2[/tex]

ANswer:

[tex]f (x) * g (x) = (x + 9) ^ 2[/tex]

Answer:

DATA GATHERING

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]|4r-2|>8\iff4r-2>8\ \vee\ 4r-2<-8\qquad\text{add 2 to both sides}\\\\4r>10\ \vee\ 4r<-6\qquad\text{divide both sides by 4}\\\\r>\dfrac{10}{4}\ \vee\ r<\dfrac{-6}{4}\\\\r>\dfrac{5}{2}\ \vee\ r<-\dfrac{3}{2}\\\\r>2.5\ \vee\ r<-1.5[/tex]

<, > - open circle

≤, ≥ - closed circle

<, ≤ - line to the left

>, ≥ - line to the right

Answer:

The value of 2 in 270,413 is 10,000x greater than the value of 2 in 419,427.

Step-by-step explanation:

The value of 2 in 270,413 is 200,000.

The value of 2 in 419,427 is 20

Divide the two numbers together to find your answer:

200,000/20 = 10,000

The value of 2 in 270,413 is 10,000x greater than the value of 2 in 419,427.

~

Hence ,value of 2  is [tex]10^{4}[/tex] time grater than value in 419,427

Place value of digit in number is  place at which it is placed .

Given

number one =  270413

Place value of 2= 200,000

number two =419,427

place value of 2= 20

Difference in place value of 2 in 200000 and 20 is of 2 x 10000

Hence  value of 2 is greater by [tex]10^{4}[/tex] in numbers .

Learn more about place value of numbers

https://brainly.com/question/12386995

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Answer:

The sum is [tex]S=\frac{16}{5}=3.2[/tex]

Step-by-step explanation:

To find the sum of the infinite geometric series we must first find the common ratio r.

The series is:

4-1 + 1 / 4-1 / 16 +

[tex]r =\frac{a_{n+1}}{a_n}[/tex]

[tex]r=\frac{-1}{4}=-\frac{1}{4}\\\\r=\frac{\frac{1}{4}}{-1}=-\frac{1}{4}[/tex]

Then the common ratio r is

[tex]r=-\frac{1}{4}[/tex]

The first term is: [tex]a_1=4[/tex]

By definition when [tex]0 <| r | <1[/tex] then the sum of the infinite sequence is:

[tex]S=\frac{a_1}{1-r}\\\\S=\frac{4}{1-(-\frac{1}{4})}\\\\S=\frac{4}{\frac{5}{4}}\\\\S=\frac{16}{5}[/tex]

Answer:

1.  6x

2. -3x + 2

3. -4x - 4

4. 4x + 11

5. -8x + 9

6. -14x - 18

Step-by-step explanation:

1. Finding sum of -3x+9x

As both the terms have different signs, the terms will be subtracted and the sign in the answer will be of the larger terms (the term with greater coefficient)

So the answer of -3x+9x is 6x

2. Finding the sum of -7x and 4x + 2

For sum,

-7x + (4x+2)

= -7x + 4x + 2

= -3x + 2

3. Finding the difference when 6x is subtracted from 2x - 4

= 2x - 4 - (6x)

= 2x - 4 - 6x

= 2x - 6x - 4

= -4x - 4

4. Finding the difference when -3x - 7 is subtracted from x + 4

= (x+4) - (-3x-7)

= x + 4 + 3x + 7

= x + 3x + 4 + 7

= 4x + 11

5. Finding the result when 13x + 2 is subtracted from 11 + 5x

= (11 + 5x) - (13x + 2)

= 11 + 5x - 13x - 2

= 5x - 13x + 11 - 2

= -8x + 9

6. Finding the result when -18x - 4 is added to 4x - 14

= (4x - 14) + (-18x - 4)

= 4x - 14 - 18x -4

= 4x - 18x - 14 - 4

= -14x - 18

..

AC would be the sum of ab plus bc.

AC = 9 + 12 = 21

Answer:

A.

9 centimeters

B.

12 centimeters

C.

15 centimeters

D.

18 centimeters

heres the answer choices, i need this too!!

Step-by-step explanation:

Answer:

The distance is 9 (Sorry if i'm wrong)

Answer:

square root of 85

Step-by-step explanation:

(7+2)^2 + (9-7)^2

(9)^2+(2)^2

81+4

Square root of 85