Use this diagram to answer the questions
4b. 3
Part A
Which expression represents the area of the rectangle?
B. 6+ (40 - 3)
A6(4-3)
D. 2 x 6 x (40 - 3)
C
6+ (40 - 3) + 6 + (40 - 3)


Part B
Which expression is equivalent to the expression you chose in Part A?
B. 246 - 18
A
240-3
D859
C. 80+ 6

Find the area of the rectangle if = 4 Enter your answer in the box
square units

The customer wants to leave 15% tip, if the bill is $35, then the tip is

Therefore, the customer should leave $5.25 as a tip.

A bookstore spent $241 to send a group of students to a reading

competition. Each student who won was given a $5 gift certificate. And

a personalized bookmark that cost $2. Included in the $241 was $45 for

the salary of a staff member who accompanied the students to the

competition. How many students won prizes?

Let

x -----> number of students that won prizes

we have that

the equation that represents this situation is

241=(5+2)x+45

241=7x+45

solve for x

7x=241-45

7x=196

x=28

therefore

A chemist is using 383 milliliters of a solution of acid and water.

If 17.3% of the solution is acid, how many milliliters of acid are there?

We basically need to calculate 17.3% of 383 milliliters.

Therefore, the solution has 6.3 milliliters of acid.

Answer:

Explanation:

The area of the rectangle with the given coordinates is:

We can apply trigonometric ratios, on this case we ned to use sine

Where alpha is th reference angle, O the opposite side from the reference angles and H the hypotenuse of the triangle

On our case O is b and H is c, then replacing

then sinB is b/c, then right option is first

Statement 1:

ΔABC ≅ ΔCBD ≅ ΔACD

Reason: Given

_________________________________

Statement 2:

b/c = y/b; a/x = x/a

Reason: corresponding sides of similar triangles are proportional

(we want to have to have in the next statement that b² = cy; a² = cx

and proportionality is usually represented as fractions, if we observe the figure, the fractions of this statement correspond to the division of similar sides of the triangles)

________________________

Statement 3:

b² = cy; a² = cx

Reason: cross product property

(if we multiply both sides of b/c = y/b by b, we obtain b² = cy, and if we do the same for a/x = x/a we obtain a² = cx, since we are multiplying, it is called product, then, the option that best fit this field is cross product property)

_______________________________

Statement 4:

a² + b² = cx + cy

Reason: addition property of equality

(we want to prove that a² + b² = c², from the previous statement we can add both equalities so we obtain a² + b² , which is nearer to the conclusion we want to prove)

____________________

Statement 5:

a² + b² = c(x + y)

Reason: factor

(we find the common factor of cx and cy, it is c, then cx + cy = c(x + y))

___________________________

Statement 6:

c = x + y

Reason: Segment addition postulate

(we almost have the conclusion in the previous statement except for the (x + y) of the right part of the equality, since in the figure we observe that c = x + y, then we can use it to replace (x + y))

___________________________

Statement 7:

a² + b² = c²

Reason: substitution

(we substitute c by (x + y) of the statement 5)

⊕

We have the following expression

In our case x is equal to 4, then, we will evalute the given function h(x) when x is 4. It yields,

which gives

Therefore, the asnswer is h(4)=24

The median is the middle of a sorted list of number. So, we need to place the number in value order, that is,

then, the middle is between the 5th and 6th number:

then, we need to find the mean value of these numbers. So, the median is

Therefore, the answer is option C.

To find the confidence interval for a proportion, we use the following formula:

Where:

p is the sample proportion

z the chosen z-value

n sample size

Since we want to make a confidence interval of 95%, we need to use z = 1.96. The sample size is n = 879.

We can use cross multiplication to find p, which is the percentage of the total sample size that preferred foreign cars:

p is the proportion in decimal, we need to divide by 100:

Now, we can use the formula:

Thus, the answer is:

Lower endpoint: 0.297

Upper endpoint: 0.359

Answer:

Im taking the test ill give the answers in 5 minutes

Step-by-step explanation:

Given data:

The given growth rate is r=7.8%=0.078.

The final number of bacteias in terms of initial is P'=2P.

The expression for the bacterias growth rate is,

Substitute the given values in the above expression.

Thus, after 9.23 hours population of the bacterias doubled.

We need to find the first five numbers of a sequence determined by the expression:

Notice that each time we increase the value of x by 1 unit, we add 12 to the previous result. Thus, subsequent terms in the sequnce differ by 12 units.

From the options, the only one with all the terms differing by 12 units is the beginning at x=1:

Therefore, the answer is: C. 18, 30, 42, 54, 66

Height is 5 feet 8 inches.

1 feet is 12 inches. So,

(5*12) + 8 = 68 inches

Now, let's convert to meters.

We know:

1 inch = 0.0254 meters

So, 68 inches would be:

68 * 0.0254 = 1.7272 meters

We would need to convert the fractional part (excess of 1, which is 0.7272) to cm.

We know:

1 m = 100 cm

So,

0.7272 m is:

0.7272 * 100 = 72.72 cm

Hence,

The answer is:

Solution

What is the end behavior of the graph of the function?

The end behaviors of the function describe the functions of x as it approaches +∝ and as x approaches -∝

Therefore the correct answer is

Option D

Final answer = Down and Up

Turning points = 2

The range of the given data set will be 15.

So, the range of the given data:

The range will be:

Therefore, the range of the given data set will be 15.

Know more about the range here:

https://brainly.com/question/2264373

#SPJ1

Correct questions:

Work out the range 51,38,48,36,39,40,39,47

Given the function:

Let's graph the function.

Let's find the following:

• (a). x-intercepts:

The x-intercepts are the points the function crosses the x-axis.

To find the x-intercepts substitute 0 for f(x) and solve for x.

Factor the left side using AC method.

Find a pair of numbers whose sum is 4 and product is -12.

We have:

6 and -2

Hence, we have

Equate the individual factors to zero and solve for x.

Therefore, the x-intercepts are:

x = -6 and 2

In point form, the x-intercepts are:

(x, y) ==> (-6, 0) and (2, 0)

• (b). The y-intercept.

The y-intercept is the point the function crosses the y-axis.

Substitute 0 for x and solve f(0) to find the y-intercept:

Therefore, the y-intercept is:

y = -12

In point form, the y-intercept is:

(x, y) ==> (0, -12)

• (c). What is the maximum or minimum value?

Since the leading coefficient is positive the graph will have a minimum value.

To find the point where it is minimum, apply the formula:

Where:

b = 4

a = 1

Thus, we have:

To find the minimum values, substitute -2 for x and solve for f(-2):

Therefore, the minimum value is at:

y = -16

Using the point form, we have the minimum point:

(x, y) ==> (-2, -16).

• (d). Use the points to plot the graph.

We have the points:

(x, y) ==> (-6, 0), (2, 0), (0, -12), (-2, -16)

Plotting the graph using the points, we have:

Given

To find the value of x.

Explanation:

It is given that,

Then,

Hence, the value of x is 16.22.

Answer: $1161

Step-by-step explanation: The equation for compound interest is A=P(1+r/n)^n*t. P is the principal, in this case, being $480 originally invested, r is the rate, in this case being 15% or 0.15, and n is 4 because it is compounded quarterly. t is 6 because the period invested is 6 years. A=480(1+0.15/4)^4*6. This can simplify to 480(1.0375)^24, which equals approximately $1161 dollars. If the question requires to the tenths, it is $1161.3, and for the hundredths, $1161.33.

Explanation

From the image, angle x and 65 degrees form angles on a straight line. We will recall that the sum of angles on a straight line sums up to 180 degrees.

Therefore,

Angle y and 65 degrees form alternate angles, we will recall that alternate angles are equal

Therefore,

Angle x and angle z form corresponding angles, we will recall that corresponding angles are equal.

Therefore,

Answer:

Solution:

To find the appropiate trigonometric formula.

we know that,

for the right angle triangle, we have that,

The side opposite to the right angle is hypotenuse, the side opposite to the angle theta is opposite side and the other side is adjacent side.

Also we have,

Using this we get,

Answer is:

Transform equation form Ax + By = C

to y = ax + b

THen

4x + 2y = -6

A= 4. B= 2. C= -6

y = (-A/B)•x +(D/B)

y= (-4/2)•x + (-6/2)

y = -2x -3

Therefore in new equation

Slope a = -2

Y intercept b = -3

We want to calculate the following quotient

Note that using properties of radicals, given non zero numbers a,b we have that

So, using this fact, our quotient becomes

As we are taking the square root, this opearation is only valid if and only if the expression inside the square root is a non negative number. That is, we must have that

As this is a quotient, we should also that the quotient is defined.

To understand this last point, we should make sure that we are not dividing by 0. So first, we want to exclude those value s of 0 for which the denominator becomes 0. So we have the following auxiliary equation

which implies that x=0.

So, the second quotient is always defined whenever x is different from 0. However, assuming that x is not 0 we want to find the value of x for which

To start with this problem, we solve first the equality. So we have

since x is not 0, we can multiply both sides by 8x², so we get

If we divide both sides by 28, we have that

now, by adding 1 on both sides we get that

so, whenever x=1, we have that the quotient inside the radical becomes 0.

Now, we will solve the inequality, that is

Note that on the left, we are mostly dividing two expressions. Recall that the quotient of two expressions is positive if and only if both expressions have the same sign.

Note that the expression

is the product of number 8 (which is positive) with the expression x², which is also always positive for any value of x. This means that the expression 8x² is always positive.

So, taking this into account, we should focus on those values of x for which the numerator is positive, as the denominator is always positive. So we end up with the following inequality

If we divide both sides by 28 we get

So, if we add 1 on both sides, we get

So, whenever x is greater than 1, the expression inside the radical is positive.

This means that the original quotient is defined whenever x=1 and whenever x>1. Thus, we would have

The original function is f(x) = 4x - 12...

to find the inverse function, we need to solve it for x:

f(x) = 4x - 12

f(x) + 12 = 4x

(f(x) + 12)/ 4 = x

f(x)/4 + 3 = x

if we change now f^-1(x) for x and x for f^-1(x):

x/4 + 3 = f^-1(x)

f^-1(x) = x/4 + 3

f^-1(x) = (1/4)x + 3

Answer:

we know that

the equation in slope intercept form is equal to

y=mx+b

In this problem

we have

b=-4 ------> because the y-intercept is (0,-4)

Find the slope

we need two points

we take

(-2,0) and (0,-4)

so

m=(-4-0)/(0+2)

m=-4/2

m=-2

therefore

The quotient is 113/21.

It is formed by combining three parts a whole number, a numerator and a denominator. Here, the numerator and denominator are  a part of the proper fraction that makes the mixed number. These are also known as mixed fractions. It contains both an integer or a whole number. A mixed fraction or number is therefore a product of a whole number and a proper fraction.

2 5/6 = (2·6 +5)/6 = 17/6

1 3/4 = (1·4 +3)/4 = 7/4

Here 17/6 is dived by 7/4,we get

(17/6) ÷ (7/4) = (17/6) × (4/7) = (17×4)/(6×7) = (17×2)/(3×7) = 34/21

Here 34/21 is converted into a mixed number.

34/21 = (21 +13)/21 = 1 13/21

Therefore, the quotient is 113/21

To know more about mixed number, visit:

brainly.com/question/24137171

#SPJ1

The petrified stump is 4 ft tall and cast a shadow that is 2 ft long .

2 ft shadow has a 4 ft height

5 ft shadow will have ? height

cross multiply

The number of groups of 4 magazines can she choose from the 7 magazines is 35

Total number of magazines that school librarian would like to buy subscription = 7 magazines

The number of subscription that she can afford = 4 new subscription

The different groups of 4 magazines can she choose from the 7 magazines = [tex]7C_4[/tex]

The combination is the method of selecting a particular items or objects from the group of collection. The combination can also be defined as the number of possible arrangement from the collection.

Then the value of

[tex]7C_4[/tex] = 7! / 4!(7 - 4)!

= 7! / (4! × 3!)

= (7 × 6 × 5 × 4!) / (4! × 3!)

= (7 × 6 × 5) / 3!

= (7 × 6 × 5) / 3 × 2 × 1

= 210 / 6

= 35

Hence, the number of groups of 4 magazines can she choose from the 7 magazines is 35

Learn more about combination here

brainly.com/question/28720645

#SPJ1

The y-intercept is at the point where the line cut the y-axis.

Hence, the y-intercept is 1

Hence, the slope is -3

Comparing the values to the equation y = =-3x +1, the equation is valid for the line.