4. Use the graph below to answer the following questions. ​

Two sides are in same proportion and the included angle is common as per SAS. Therefore, both the triangles are similar.

Triangle:

A triangle is the three-sided polygon, which has three vertices. The three sides are interconnected with each other end to end at a point, which forms the angles of the triangle.

Here there are two triangles KLP and KMN. And the sum of all three angles of the two triangle is equal to 180 degrees.

Given,

Here we have the two triangle and we need to find that they are similar or not.

For that we have to calculate the total length of the sides of the triangle,

That,

KM = KL + LM

KM = 8 + 2 = 10

Similarly,

KN =  KP + PN

KN = 12 + 3 = 15

In triangles KLP & KMN,

KL/KP = 8/12 = 2/3

Similarly, for the triangle KMN,

KM/KN = 2/3

Here the angles have the same values so they are parallel. Which states that, Angle O is common in both the triangles.

Therefore, the two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.

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SOLUTION

We want to know which of the options would give us

y = 34,

Let's try A. 8y = 9

This becomes

We didn't get y = 34, hence A is incorrect.

Let's try B. y − 1= − 14

This becomes

B too is incorrect.

Let's try C. 4y = 6

C too is incorrect

Let's check D. 7 − y = 614

D too is incorrect

Answer:

q = -1

Step-by-step explanation:

We are given the inequality [tex]11-\frac{64}{q} > 60[/tex]

We want to find out which value of q is a solution to the inequality. In other words, which value of q makes the statement true?

We can substitute the values given for q into the inequality to see this.

Let's start with q=2.

Replace q with 2.

[tex]11-\frac{64}{2} > 60[/tex]

Divide 64 by 2.

64/2= 32

11 - 32 > 60

Subtract 32 from 60

11-32 = -21

-21 > 60

The inequality reads "-21 is greater than 60", which is false (negative numbers are less than positive ones).

This means q=2 is NOT an answer.

Next, let's try q=-2

[tex]11 - \frac{64}{-2 } > 60[/tex]

64/-2 = -32

11 - - 32 > 60

- - 32 means subtracting a negative, which is the same as adding 32 to 11.

11 + 32 > 60

43 > 60

This is also NOT true (it reads "43 is greater than 60").

So q=-2 is also NOT an answer.

Now, let's try q = -1

[tex]11-\frac{64}{q} > 60[/tex]

[tex]11-\frac{64}{-1} > 60[/tex]

64/-1=-64

11 - -64 > 60

11 + 64 > 60

75 > 60

This reads "75 is greater than 60".

This is a true statement, meaning q = -1 IS an answer.

We are technically done, but just to be sure, we can check q=1 as well.

[tex]11 - \frac{64}{q} > 60[/tex]

[tex]11 - \frac{64}{1} > 60[/tex]

11 - 64 > 60

-53 > 60

This reads "-53 is greater than 60", which is false.

So this confirms that q = -1 is the only option that is an answer.

Answer:

Option C,  [tex]f(x)=-3x^2-6xh-3h^2+2x+2h+1[/tex]

Step-by-step explanation:

Oooo the ol canvas quiz yeesh.

Anyway, for this sort of problem, anywhere in your second equation that you see an x, sub for (x+h).

[tex]f(x)=-3x^{2} +2x+1[/tex]

[tex]f(x)=-3(x+h)^{2} +2(x+h)+1\\[/tex]

You must foil the first part

[tex]f(x)=-3(x^2+h^2+2xh)+2(x+h)+1\\[/tex]

Now distribute to eliminate the parentheses

[tex]f(x)=-3x^2-3h^2-6xh+2x+2h+1[/tex]

As your answer choice has it:

[tex]f(x)=-3x^2-6xh-3h^2+2x+2h+1[/tex]

The perimeter of a triangle is given by the sum of all it is sides.

Now, we have the next measures:

- The longest side of a triangle is 5in longer than the shortest side.

- The medium side is 4 inches longer than the shortest side

Then, the perimeter is given by:

P = (s+5)+(s+4)+s

If the perimeter is P=21 inches:

21 = (s+5)+(s+4)+s

Solve for s:

21 = s+5+s+4+s

21 = 3s + 9

21-9 = 3s

12 = 3s

s = 12/3

s= 4

Therefore,

The shortest side of the triangle is 4 inches.

The medium side is s+ 4 = 4+ 4 = 8 inches

The longest side is s+5 = 4+5 = 9 inches

To find the time it takes the object to reach the maximum height we need to remember that this happens in the axis of symmetry of the parabola described by the function:

The axis of symmetry is given as:

in this case we have that a=-16 and b=64, then we have:

Therefore it takes 2 seconds to the object to reach its maximum height.

Now, to find the maximum height we plug this value of t in the equation, then we have:

therefore the maximum height is 144 ft.

The number of black bears in the national park is 36

Here, given the ratio of black bears to grizzly bears, and the number of grizzly bears, we want to find the number of blackbears the national park has

Let the number of black bears be x

what this mean is that the total number of bears in the park is (x + 12)

The total ratio of the two is 3 + 1 = 4

Matematically;

If the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.

It is given that, the first number is 2 and the last number is 18,

a = 2

L=18

n=5

a₅=5

a₅=a+(5-1)d

18=2+4d
4d = 18-2

4d = 16

d= 16 / 4

d=4

The terms of the sequence are,

a₁=2

a₂=2+4=6

a₃=6+4=10

a₄=10+4=14

a₅=14+4=18

Thus, if the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.

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Okay, here we have this:

Considering the provided data set, we are going to calculate the requested data, so we obtain the following:

Mean:

It corresponds to the result of adding all the data and dividing it by the amount of data, then we have:

Mean=(89+81+96+85+93+70+66+64+68+70)/10

Mean=782/10

Mean=78.2

Median:

First we will order the data from smallest to largest and the value that is in the center will be the median:

Sorted Data Set: 64, 66, 68, 70, 70, 81, 85, 89, 93, 96

Since 70 and 81 are in the middle, the median will be their average.

Median=(70+81)/2=151/2=75.5

Mode:

It is the data that is repeated the most, in this case it is 70 because it is twice

Range:

It is the difference between the smallest and largest value, then:

Range=96-64=32

Answer:

The length of the base is:

The resulting quadratic is

Step-by-step explanation:

Base = x

Height = 4x

Area, A = 1/2* base * Height

           A = (1/2) * (x) * (4x)

          A = 2x²           (1)

But,    A = 6              (2)

Since (1) = (2);

2x²= 6

x²= 3

Resulting quadratic:

x² - 3= 0

For the difference between 2 squares:

a² - b² = (a-b)(a+b)

Using that identity, we can factorize our quadratic:

(x-3)(x+3) = 0

So, we have 2 roots:

x = 3 and x = -3

Now, noting that length must take a positive value, we go for the first:

x = 3

The length of the base is:

The resulting quadratic is

the graph of a line passing through point

with gradient m

is given by

1) To find each unit price, let's find out the unit rate. Setting a proportion.

Option A

cupcakes price

12 ------------------- 29

1 --------------------x

Cross multiplying it:

12x = 29 Divide both sides by 12

x =2.42

Each cupcake costs $ 2.42

Option B

24 ------------ 56

1 ------------ y

24y = 56

y =$2.33 per cupcake.

2) The best deal for buying cupcakes is found in Option B. Since the price is lower per cupcake

3) Hence, the answers are:

Option A = $2.42 per cupcake

Option B =$2.33 per cupcake

Best Deal: Option B

we have

7 3/4 + 1 5/6​

step 1

Convert mixed number to an improper fraction

7 3/4=7+3/4=31/4

Remember taht

If you multiply 31/4 by (1.5/1.5) you obtain an equivalent fraction

so

(31/4)(1.5/1.5)=46.5/6

multiply by 10/10

465/60

1 5/6=1+5/6=11/6

multiply by 10/10

(11/6)(10/10)=110/60

step 2

Adds the fractions

465/60+110/60=575/60

simplify

Convert to mixed number

575/60=540/60+35/60=9+35/60

simplify the fraction 35/60

35/60=7/12

so

we have

9+7/12=9 7/12

In order to find how many pages can be typed, first let's convert 1.5 hours to minutes:

Then, to find the number of pages, let's do the following rule of three:

Therefore Chuck can type and spell check 52.5 pages in 1.5 hours.

Given the system of equations:

The two equations appear to be just the same, thus, we are only given one system of equations.

Therefore, the answer is letter B. It has infinite solutions because the two equations are just the same line.

Answer:

Question 1: 3

Question 2: $120

Step-by-step explanation:

Set up a proportion

[tex]\frac{inches}{miles}[/tex] = [tex]\frac{inches}{miles}[/tex]  fill in the numbers that you know and solve for the unknow.

[tex]\frac{5}{2}[/tex] =[tex]\frac{7.5}{m}[/tex]  Cross multiply

5x =7.5(2)

5x = 15  Divide both sides by 5

x = 3

If we take 40% off that means that we leave 60% on

Percent means per hundred

[tex]\frac{60}{100}[/tex]  When you divide by hundred, you move the decimal two places to the left.

200(.6)

$120.00

Given:

A diver starts at 342 feet below the surface, which means -342 feet.

Now, she swims 237 feet upward.

It shows that she is moving in a positive direction.

So, the current depth of diver is,

The depth is -105 feet, which shows that the diver is still 105 feet below the surface.

Solution

For this case since we want to verify if a circle can be circumscribed in the quadrilateral we can use the following Theorem:

Theorem: If a quadrilateral is incribed in a circle then the opposite sides are supplementary

And we cna verify:

105+ 98= 203

82 +75= 157

Then we can conclude that the answer is:

False

The given system of equation is:

Multiply through the first equation by 2:

Subtract the second equation from the first equation to get:

Therefore, the steps that will eliminate the variable x are:

Multiply the first equation by 2. Then subtract the second equation from the first.

Choice C

Given:

A bee produce 0.05 ml of honey per day

We will find how many liters of honey can the bee produce in its lifetime if they live for 28 days

Let it produces x ml

So, using the ratio and proportions

Solve for x:

Convert ml to liters

1 liter = 1000 ml

So, 1.4 ml = 0.0014 liters

So, the answer will be

The bee can produce honey in its lifetime = 0.0014 liters

Answer:

2x^2 + 12x

Step-by-step explanation:

The perimeter is the sum of all the sides of a geometric figure.

So x^2 + 6x - 3 + 5x + 3 + x^2 - x

Add like terms:

2x^2 + 12x

The reason I said 2x^2 + 12x here is that this is likely a misprint, and you'll have to ask your teacher about this. Since the 3s (3 and -3) cancel each other out, but there are only 10 x's, your true answer is 2x^2 + 10x.

However, it is more likely that the misprint concerns the x^2 - x, meaning it was meant to be x^2 + x, which would give you answer A. The idea that the problem is just missing a random 9 somewhere is much more farfetched.

I would select answer A.

This is a complicated and incorrectly formatted question. Hope this helps!

Answer:

D

Step-by-step explanation:

Given: A water tower has a volume of 874 m³

To Determine: How many liters of water it would take to completely fill the

water tower

Solution

Please note that 1 cubic meter (m³) = 1 kiloliter (KL)

Therefore

Also note that Kilo means 1000

Therefore

Hence, the water tower will be completely fill with 874000 liters(L)

Divide side R'O' (8) by th scale factor (2/3)

8 : 2/3= 12

The number line always goes from negative to positive :

It increases from left to right

SInce negative is always on the left side of the zero

Snumber greater than zero are always positive

i.e. x > o

Measures of center:

The mean is usually the better measure of center, however, this measure is greatly affected by extreme values (very low or very high values). If the data set is strongly skewed or has extreme values, the mean will be affected and won't reflect the true center of the said data set.

The median separates the data set in halves and is not affected by extreme values.

Given that this data set is strongly skewed to the left, the best measure of center will be the median.

Measures of dispersion:

The standard deviation is usually the most preferable measure of dispersion. But, one of

a) Given:

The length of the side of a square is,

To find:

The area of the square.

Explanation:

Using the formula of the area of the square,

Final answer:

The area of the square is,

We have to calculate the volume of the pyramid with the following dimensions:

We can express and calculate the volume as:

Answer: the volume is 128 dm³

to solve this, question, we would have to convert the percentage to fractions or decimals.

Let x represent the numbers of employees the had a year ago

a year ago, the company had 1224 empolyees

EXPLANATION

The measure that represent the most typical driving time is the mean.

GIVEN

The time left before the store closes is 3/4 h while the time taken to find one item is 1/8 h.

QUESTION A

Let the number of items that can be gotten before the store closes be N.

The number of items can be calculated using the formula:

Therefore, the equation to get the number of items will be:

QUESTION B

The solution can be obtained by division.

Apply the fraction rule:

Hence, the solution will be:

The answer is 6.

QUESTION C

Jane can find 6 items before the store closes.