Challenge 1
A: Can you find the
area of the shape?
B:Can you find the
perimeter of the shape?

Answer:

The stone covers 36 m in the 5th second. Correct choice: A.

Step-by-step explanation:

Proportions

Two variables are said to be proportional if one of them can be calculated by multiplying the other by a constant of proportionality. If y and x are those variables, then:

y=k.x

There are other similar proportions where the relation is not linear. For example, if y is proportional to the square of x, then:

[tex]y=k.x^2[/tex]

According to the conditions of the question, the distance traveled by a stone dropped from a height of 5 Km varies directly with the square of the time taken to fall through that distance. If d is the distance and t is the time, then;

[tex]d=k.t^2[/tex]

To find the value of k, we use the given condition: The stone falls d=66 meters in t=4 seconds. Substituting:

[tex]64=k.4^2=16k[/tex]

Solving:

[tex]k=64/16=4[/tex]

Substitute the value of k into the equation to get the complete model.

[tex]d=4.t^2[/tex]

Now we calculate the distance when t=5 seconds:

[tex]d=4\cdot 5^2=4\cdot 25=100[/tex]

The stone has covered 100 m in 5 seconds. But we need to find the distance covered in the 5th second, that specific interval between 4 sec and 5 sec.

Since we already know the distance for t=4 sec (64 m), and the distance for t=5 sec (100 m), then:

distance in the 5th second = 100 m - 64 m = 36 m

The stone covers 36 m in the 5th second. Option A.

Answer:

sorry for my handwriting

i think this is the correct answer

Answer:

Step-by-step explanation:

Since the Tootsie Roll lollipop is a sphere

volume of sphere= [tex]\frac{4}{3}piR^3[/tex] = -0.25 [tex]in^3/min[/tex]

the negative sign indicates that the volume is decreasing

upon differentiating

as the diameter given is =0.75 so radius will be = 0.375

[tex]dV/dt = 4piR^2*dR/dt[/tex]

so [tex]dR/dt = 0.25/4*3.14 *(0.375)^2[/tex]

So the radius is decreasing at the rate of dR/dt= 0.142in/min

Answer:  A) The equation will be     x + 4x + x + 10 = 82   B) Paul's age is 12, Rebecca's age is 48  and Gemma's age is 22.

Step-by-step explanation:

We will represent Paul's age by    the equation  p= x  where p is Paul

We will represent Rebecca's age by the equation  r = 4x  Where r is Rebecca

We will represent Gemma's age by the equation g = x + 10  where g is also Gemma's age.

We given that the sum of their ages is 82 years so meaning that  x + 4x + x + 10  has to equal 82.

A) The equation will be     x + 4x + x + 10 = 82  

Solve for the x equation to find Paul age because his age is x.

B)  (x) + (4x) + (x+10) = 82   combine like terms on the left side

    6x + 10 = 82

           -10    -10

   6x = 72

   x= 12  

Paul age is 12.  

r= 4(12)

r = 48

Rebecca's age is 48.

g= 12 +10

g= 22

Gemma's age is 22.  

Answer:

96-49=47

Step-by-step explanation:

he goes down then up so 47

Answer:

-47

Step-by-step explanation:

-96 + 49

-47

Answer:

Tge answer:8k+25k-15

Answer:

0.016cm

Step-by-step explanation:

I would convert 2cm in terms of meters

2cm/1 = 1m/100cm

since there are cm on top and bottom it cancels out

2•1 /1m• 100 = 2m/100 = .02 m

now you solve using proportions

x/.8 = .02/1

x= (.8)(.02) cross multiples)

x= 0.016

Answer:

mB=46

Step-by-step explanation:

2x+30+7x-3=90

Combine like terms

9x+27=90

Subtract by 27 on both sides

9x=63

Divide by 9 on both sides

x=7

mB=(7x-3)

Substitute 7 for x

mB= 7(7)-3

mB= 49-3

mB=46

Answer:

The measure of B is 46°

Step-by-step explanation:

To solve this equation, you need to add the two equations, and set them equal to 90° since they are complementary angles

2x+30+7x-3=90

You also need to add like terms, so 2x+7x and 30+-3, or 30-3

9x+27=90

Then you need to isolate the variable by subtracting 27 from both sides

9x+27-27=90-27

=

9x=63

Then you need to divide both sides by 9 to get x=7

Since we know what x is, we plug x into the equation (7x-3) and we will now have 7(7)-3.

To solve this, we multiply 7 and 7, and subtract 3 to get 46.

So the answer is mB=46

I hope this helps!!

Answer:

96

Step-by-step explanation

4(x - 2)(x + 3) + 7(x - 2)(x - 5) - 6(x - 3)(x - 5)

4(5 - 2)(5 + 3) = 12(8) = 96

7(5 - 2)(5 - 5) = 0

- 6(5 - 3)(5 - 5)= 0

96+0-0 = 96

Answer:

B. They are not parallel because their slopes are not equal.

Step-by-step explanation:

Find the slope of the line that runs through points (6, 3) and (-1, 5):

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{-1 - 6} [/tex]

[tex] slope (m) = \frac{2}{-7} = -\frac{2}{7} [/tex]

Since the slope of the line that passes through points (6, 3) and (-1, 5) is not the same with line that has a slope of ¾, therefore, both lines cannot be parallel.

The answer is "B. They are not parallel because their slopes are not equal."

Answer: x=247

Step-by-step explanation:

1. Set up the equation

117/45=x/95

2. Cross multiply

117(95) = 11115

45(x)= 45x

3. Set both equal to each other

11115=45x

4. Divide 45 on each side

11115/45 = 45x/45

5. Solve for x

x=247

Hope this helps :)

-Morgan

Answer:

a2+b2=c2

Step-by-step explanation:

A right triangle is a triangle in which one of the angles is a 90∘ angle. A triangle can be determined to be a right triangle if the side lengths are known. If the lengths satisfy the Pythagorean Theorem (a2+b2=c2) then it is a right triangle.

Answer:

me

Step-by-step explanation:

Answer:

I do! Juicy do be kinda cute too tho. EddieVR though is probably the most funny. Especially his Horror VR videos.

Step-by-step explanation:

What about Narrator? He seems like he'd be really nice and he's funn-

when Mully cuts him off, it's golden lolololol

Answer:

32km

Step-by-step explanation:

Answer: 2.5

Step-by-step explanation: If you do 5/8 divided by 1/4 in the calculator it is 2.5.

Answer: .3330

Step-by-step explanation:

The proportion of exam scores are between 82 and 89.2 points is 0.3330.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

When comparing data sets that may have the same mean but a different range, it is helpful.

The mean of the two numbers 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30 for instance, is the same. The second, though, is obviously more dispersed.

Given:

mean = 83.2 points and

standard deviation = 8 points.

So, the proportion is

P(82 ≤ x ≤ 89.2)

=P( 82- 83.2 / 8 ≤ z ≤ 89.2 - 83.2/8)

=P (0.75) - P(-0.15)

=0.7734 -(0.4404)

= 0.3330

Learn more about standard deviation here:

https://brainly.com/question/13905583

#SPJ2

Answer:

x - y = 4

Step-by-step explanation:

Hope this helped! :)

Answer:1/2

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation: if each of you get part of the candy bar and you need to share it equally, both of you get 1/2 of it.

Answer: Maybe it is 2,4

Step-by-step explanation:

A fact family is a group of math facts using the same numbers. In the case of addition and subtraction, you use three numbers and get four facts.

For example, you can form a fact family using the three numbers 3, 10, and 13: 10 + 3 = 13, 3 + 10 = 13, 13 − 10 = 3, and 13 − 3 = 10.

Addition facts − Here the sum of two of the three given numbers is the remaining third number. This sum is expressed in two possible orders. Thus, there are two addition facts for any three given numbers

For 3, 10 and 13, the two addition facts are:

3 + 10 = 13;

10 + 3 = 13

Subtraction facts − Here the difference of two of the three given numbers is the remaining third number. There are two such differences. Thus, there are two subtraction facts for any three given numbers.

For 3, 10 and 13, the two subtraction facts are:

13 − 10 = 3;

13 − 3 = 10

We use fact families to reinforce the connection between addition and subtraction, and to help students learn and memorize the basic addition & subtraction facts.

Problem 1:

Make four related number sentences using each set of 3 numbers.

10, 7, 3:

There should be two additions and two subtractions.

Solution

10, 7, 3:

Step 1:

The addition facts using above three numbers are:

7 + 3 = 10;

3 + 7 = 10;

Step 2:

The subtraction facts using above three numbers are:

10 – 7 = 3;

10 – 3 = 7

Problem 2:

Make four related number sentences using each set of 3 numbers.

13, 8, 5

There should be two additions and two subtractions.

Solution

13, 8, 5

Step 1:

The addition facts using above three numbers are:

5 + 8 = 13;

8 + 5 = 13;

Step 2:

The subtraction facts using above three numbers are:

13 – 5 = 8;

13 − 8 = 5

Answer:

11.6 miles per gallon

Step-by-step explanation:

Answer:

11.6 miles per gallon

Step-by-step explanation:

just divide

Answer:

U = 1.6

Step-by-step explanation:

Divide 4.8 by 3.

Answer:

I believe [tex]\lim_{x \to a} f(x)[/tex] also equals 0.

Step-by-step explanation:

We know that g(x) has to be greater than or equal to 0. That means f(x) has to be smaller than g(x) or equal to 0.

If we plug in any value of x, f(x) will be positive because of the absolute value. The only way we are going to get f(x) smaller than g(x) or equal to g(x) is to have very small fractions.

Therefore, if [tex]\lim_{x \to a} g(x)=0[/tex], then [tex]\lim_{x \to a} f(x)=0[/tex] because f(x) must be smaller or equal to 0 as well.

Answer:

[tex]\displaystyle{ \lim_{x\to a}f(x)=0[/tex]

Step-by-step explanation:

The other user posted a great answer, but I would like to show you a more mathematical way!

We have [tex]|f(x)|\leq g(x)[/tex].

By the definition of absolute value, this is the same as saying:

[tex]f(x)\leq g(x)\text{ and } -f(x)\leq g(x)[/tex]

For the right, we can divide both sides by -1 to acquire:

[tex]f(x)\leq g(x)\text{ and } f(x)\geq- g(x)[/tex]

We can now combine them. This yields:

[tex]-g(x)\leq f(x)\leq g(x)[/tex]

Now, we can use the Squeeze Theorem (a.k.a. Pinch or Sandwich Theorem). The Squeeze Theorem posits that if we have:

[tex]g(x)\leq f(x)\leq h(x)[/tex]

And:

[tex]\displaystyle{ \lim_{x \to c} g(x)= \lim_{x \to c} h(x)=L}[/tex]

Then the following must be true:

[tex]\displaystyle{ \lim_{x \to c} f(x)=L[/tex]

We have:

[tex]-g(x)\leq f(x)\leq g(x)[/tex]

And we know that:

[tex]\displaystyle{ \lim_{x \to a} g(x)=0[/tex]

Then it follows that:

[tex]\displaystyle{ \lim_{x \to a} -g(x)=- \lim_{x \to a} g(x)=0[/tex]

Therefore, by using the Squeeze Theorem, we can conclude that:

[tex]\displaystyle{ \lim_{x\to a}f(x)=0[/tex]

And we're done!

Answer:

12

Just plug it in [the equation] to try it to

Draw out a vertical number line. Positive values are above 0, and negative values are below zero.

Answer:

24 = 2, 3 , 4, 6, 8, 12, 24

30 = 2, 3, 5, 6, 10, 15, 30

Step-by-step explanation:

Least common for both is 2

Greatest common factor for both is 6

Answer:

3.20

Step-by-step explanation:

Sorry i had the same question and i asked the teacher if he could help and he did but he sorta juts gave me the answer so cant really give an explanation so sorry.

Answer:

400 calories per hour in the first 3 hours

Step-by-step explanation:

The c.o.p for the first 3 hours is 400

Answer:

Horizontal asymptote: y = 0

Vertical asymptote: x = 3

Step-by-step explanation:

The vertical asymptote in this graph would be when x = 3 because it would make the denominator 0, which would make the equation undefined.

There will not be any holes in the graph, because there won't be any point undefined in the function except for when x = 3, but that's a vertical asymptote.

Now, for the horizontal asymptote, we see what value y approaches as x approaches plus and minus infinity. Since x is in the denominator, y will approach 0 when it's plus or minus infinity.

Horizontal asymptote: y = 0

Vertical asymptote: x = 3