GEOMETRY-
Find the area of shaded portion

Step-by-step explanation:

it's mathematics or what I will help you.

The loans the finance company lent to each firm are:

The amounts lent for Firms A, B, and C can be determined using a system of equations, which are simultaneously solved by substitution.

The income from each firm is equated to the total income as demonstrated below.

Then the missing value of the Loan to Firm A is computed.

The interest rate for Firm A's loan = 7% (0.07)

The interest rate for Firm B's loan = 8% (0.08)

The interest rate for Firm C's loan = 8.5% (0.085)

Amount lent to Firm A = x

Amount lent to Firm B = x - 100

Amount lent to Firm C = x + 200

The total annual income = $126.50

126.50 = 0.07x + 0.08(x - 100) + 0.085(x + 200)

0.07x + 0.08x - 8 + 0.085x + 17 = 126.50

0.07x + 0.08x + 0.085x = 126.50 + 8 - 17

0.235x = 117.50

x = 500

Loan to Firm A = x = $500

Loan to Firm B = x - 100 = $400 ($500 - $100)

Loan to Firm C = x + 200 = $700 ($500 + $200)

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The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

Answer:

x = 4

y = 13

Step-by-step explanation:

x + 9 = y--------(1)

x + y = 17---------(2)

(1) ----> (2),

x + 9 + x = 17

2x + 9 = 17

2x = 8

x = 4

y = 13

Using translation concepts, it is found that the correct option is:

D. It is the graph of  translated 3 units up and 7 units to the right.

The parent function is:

\(f(x)=y=1nx\)

Shifting a function a units to the right is equivalent to finding f(x - a), thus:

\(f(x-7)=1n(x-7)\)

Shifting a function a units up is equivalent to finding f(x) + a, thus:

\(f(x-7)+3=1n(x-7)+3\)

Which means that the function was shifted 7 units to the right and 3 up, thus, option D is correct.

We are given two curves on a graph paper and we have to find the y values for the given x.

From the graph we can check for a value of x, what is the value of y from the curve.

x     -3     -2     -1    0      1         2        3

Exp  8      4      2    1      0.5  0.25  0.125

Lin.   7.5   6    4.5   3      1.5     0     -1.5

We find that the two have the same values where the two curves intersect.

From the graph we find that near to -3 and near to 2 both have the same values.

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The missing graph is attached below.

Answer:

A. 1.78cm².

B. 331.34 square meters.

Step-by-step explanation:

The area of the shaded region in a circle if the radius and central angle is given can be calculated using the following formula:

Area of shaded region = (θ/360) * πr²

Where:

A.

If the radius is 2 meters and the central angle is 51 degrees, then the area of the shaded region is:

Area of shaded region = (51/360)*π*2² = 0.357π m²

≈ 1.78 square meters

Therefore, the area of the shaded region is approximately 1.78square meters.

Therefore, the area of the shaded region is 1.78cm².

B.

If the radius is 12.5 meters and the central angle is 243 degrees, then the area of the shaded region is:

Area of shaded region = (243/360)*π*12.5² = 105.47π m²

≈ 105.47π square meters

Therefore, the area of the shaded region is approximately 331.34 square meters.

Answer:

a) x + 10 = 45

b) 3 = 6 - x

c) d = s * t

Step-by-step explanation: This is actually pretty simple. Let's put down one theorem.

SYMMETRIC THEOREM OF PROPERTIES: If a equals b, then b must equal a. Thus, a = b and b = a.

This is all we're really doing.

Take a) for example, 45 = x + 10. Let's label (45) as A, and (x + 10) as B. Thus we have A = B. Now we know by the Symmetric Property, we have B = A. Thus, substituting B and A again, we get x + 10 = 45.

Just keep doing this with all the equations.

Hope this helped!

Answer:

160 inches

Step-by-step explanation:

47+33+47+33=160inches

On July 20, the journal entry to record the reissuance of treasury stock is: Debit Cash for $4,140 and credit Treasury Stock for $4,140.

To record the reissuance of treasury stock on July 20, the company needs to make the following journal entry:

Date: July 20

Account Debit Credit

Cash $4,140

Treasury Stock $4,140

Explanation:

Debit to Cash ($46 per share * 90 shares) to record the cash received from the reissuance of 90 shares of treasury stock: $46 * 90 = $4,140.

Credit to Treasury Stock to remove the cost of the 90 reissued shares from the treasury stock account.

This journal entry reflects the cash inflow from the reissuance of treasury stock and reduces the balance in the treasury stock account, indicating a reduction in the number of shares held by the company as treasury stock.

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1 year insurance policy covering its equipment was purchased for 6,144. The date purchased was June 14 but it doesn't go into effect until June 16th, the amount paid for the month of June is approximately $252.75, and the amount paid for the entire year is approximately $6,144.

To calculate the amount paid for the month and the year, we need to consider the number of days covered by the insurance policy. Let's break it down step by step:

Step 1: Determine the number of days covered in June.

Since the policy doesn't go into effect until June 16th, there are 15 days remaining in June that will be covered by the insurance policy.

Step 2: Calculate the daily rate.

To find the daily rate, we divide the total cost of the insurance policy by the number of days in a year:

Daily rate = 6,144 / 365

Step 3: Calculate the amount paid for June.

The amount paid for June can be found by multiplying the daily rate by the number of days covered:

Amount paid for June = Daily rate * Number of days covered in June

Step 4: Calculate the amount paid for the year.

To calculate the amount paid for the year, we simply multiply the daily rate by 365 (the total number of days in a year):

Amount paid for the year = Daily rate * 365

Now let's perform the calculations:

Step 2: Daily rate

Daily rate = 6,144 / 365 ≈ 16.85 (rounded to two decimal places)

Step 3: Amount paid for June

Amount paid for June = 16.85 * 15 ≈ 252.75 (rounded to two decimal places)

Step 4: Amount paid for the year

Amount paid for the year = 16.85 * 365 ≈ 6,144 (rounded to two decimal places)

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Step-by-step explanation:

Two lines that are parallel have the same slope. If we make \(x - 3y = 15\) in to slope-intercept form it'll be like this:

\(x - 3y = 15 \\ -3y = 15 - x \\ y = \frac{15 - x}{-3} \\ y = \frac{1}{3}x - 5\)

Now we know \(y = \frac{1}{3}x - 5\\\) as its slope-intercept form we can see the slope is \(\frac{1} {3}\\\).

\(y = \frac{1}{3}x + 4\\\) has the same slope as \(y = \frac{1}{3}x - 5\\\) so they are both parallel.

\(y = \frac{1}{3}x + 4\\\)

Answer:

11:30am

Step-by-step explanation:

Answer:

Charlie and his friends should leave by 11:30 am at the latest.

There is no whole number by which you can multiply or divide 16087 to make it a perfect square.

To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.

In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.

To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.

A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.

Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.

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The trigonometric expression sin x = 3/5 can be used to find the value of x, and a = 0.6 for the expression x = sin⁻¹(a).

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

We use the trigonometric ratio of sine of the angle x, so that we make x the subject by finding the sine inverse of the fraction of the opposite side and the hypotenuse as follows:

sin x = 3/5

x = sin⁻¹(0.6)

x = 36.8699

Therefore, the trigonometric expression sin x = 3/5 can be used to find the value of x, and a = 0.6 for the expression x = sin⁻¹(a).

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Answer:

To find the numerator of the equivalent fraction with the denominator 12,

The given fraction is,

The equivalent fraction is given by,

Cancelling 11, we get

we get,

The required equivalent fractor is 5/12

The numer

Answer:

The car's average 18 number of miles per gallon

Step-by-step explanation:

The car has different efficiencies depending if its used on highway or city streets.

The efficiency on a highway is:

\(E_h=\dfrac{350}{15}\;\text{miles/gal}=23.33\;\text{miles/gal}\)

The efficiency for city driving is:

\(E_c=\dfrac{280}{18}\;\text{miles/gal}=15.56\;\text{miles/gal}\)

We now that the car uses twice as many gallons for city driving as for highway driving. This means that, for every gallon consumed, 2/3 are for city driving and 1/3 are for highway driving.

Then, we can calculate how many miles makes the car on average as:

\(E=\dfrac{1}{3}E_h+\dfrac{2}{3}E_c\\\\\\E=\dfrac{1}{3}\cdot 23.33+\dfrac{2}{3}\cdot15.56=7.78+10.37=18.15\;\text{miles/gal}\)

Answer:

120

Step-by-step explanation:

all you have to do is multiply 20*60

Answer:

The machine can blow up 300 balloons in 60 min.

Step-by-step explanation:

60 ÷ 4 = 15. 15 x 20 = 300. We know it takes 4 minutes to blow up 20 balloons. 4 minutes is only 1/15 of 60, so that means you have to blow up 20 balloons 15 times, which will take 60 minutes, and in that 60 minutes, you blew up 300 balloons.

Hope it helps!

Answer:

(A) 37.5 miles

Step-by-step explanation:

The trains x and y are travelling on tracks starting simultaneously from a from opposite ends of 100 miles roads.

Translate these information into a simple represention to visualize the problem. (Picture below)

■■■■■■■■■■■■■■■■■■■■■■■■■■

First let's calculate the velocity of both trains.

The velocity formula is:

● V = d/t

d is the distance travelled and t is the tile needed to do it.

● V(x) = 100/5 = 20 miles per hour

● V(y) = 100/3 = 33.33.. wich is approximatively 33 after rounding to the nearest unit.

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After calculateingboth velocities, Let's find when the trains meet.

First understand what does it mean matematically when both trains meet.

Go back to the representation and notice what happens when the trains meet.

Let t be that moment.

When x and y reches the meeting point at t, the sum of the distances they have travelled is equal to the total distance wich is 100 miles .

We khow that V = d/t so d = V×t

Let's find the expression of the distances both trains travelled when they have met each other.

● d = V(x) × t

● d' = V(y) × t

■■■■■■■■■■■■■■■■■■■■■■■■■■

So the equation will be:

● V(x) × t + V(y) × t = 100

Factor using t

● t (V(x) + V(y) ) = 100

Replace V(x) and V(y) by their values

● t (20+33) = 100

● 53 t = 100

Divide both sides by 53

● 53t /53 = 100/53

● t = 1.88

■■■■■■■■■■■■■■■■■■■■■■■■■

Replace t in the expression of the distance that train x has travelled when meeting y.

● d = V(x) × t

● d = 20 × 1.88

● d = 37.6 wich is approximatively 37.5 miles

Answer:

1/9

Step-by-step explanation:

Answer:

-84+(-11)= -95

-84 + (-11) = -84 - 11 = -95

By the commutative property, adding a negative number is the same as subtracting that number as a positive; therefore, something + (-11) = something - 11. After changing the equation from -84 + (-11) to -84 - 11, we use regular addition properties, adding the tens place and ones place to get -95.

Answer:

Options 2, 4 and 6 are True.

Step-by-step explanation:

Triangle MNO is dilated by a scale factor of \(\frac{3}{2}\) centered at M(0, 6).

Rule to be followed to dilate the vertices of the given triangle,

(x, y) → (kx, ky)

Here, k = scale factor

By this rule vertices of the new triangle M'N'O' will be,

M(0, 6) → M'(0, 6) [Coordinates of M' will remain same as M because center of dilation is point M]

N(-4, -4) → N'(-6, -6)

O(6, -2) → O'(9, -3)

Option 1

M'N' is shorter than MN

Distance between M and N = \(\sqrt{(0+4)^2+(6+4)^2}\)

                                              = 10.77

Distance between M' and N' = \(\sqrt{(0+6)^2+(6+6)^2}\)

                                                = 13.42

Therefore M'N' > MN

Therefore, Option A is False.

Option 2

ON is shorter than O'N'

True.

Option 3

OM is longer than O'M'

False

Option 4

ON is parallel to O'N'

Since OM and MN are dilated with the same scale factor, O'N' will be parallel to ON.

True.

Option 5

OM is parallel than O'M'

Since, O'M' is the dilated form of OM,

Therefore, all the points (O, M and M') will be in a straight line.

False

Option 6

M'N' coincide with MN

True.

Therefore, Options 2, 4 and 6 are True.

Answer:

see below

Step-by-step explanation:

7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".

Answer:

Area = 3.36 in²

Step-by-step explanation:

\(Area\space\ of \space\ trapezium = \frac{a \space\ + \space\ b}{2} h\) ,

where a and b are the two parallel sides, and h is the height.

\(Area = \frac{1.3 \space\ + \space\ 3.5}{2} (1.4)\\\\Area = 3.36 \space\ in^{2}\)

Answer:

Area of the shaded polygon= 372

For a curve to be a density curve, it must meet certain conditions such as it should be non-negative, and the area under the curve should equal 1. Furthermore, the curve should be continuous and smooth, and there should be no values outside the range of the data.

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Step-by-step explanation:

slope is the number before x so slope here is 3/1 always add the 1 if its a whole number if its a fraction leave it.

y=mx+b

the y-intercept is always be so graphing is now easy

put a dot on the y-intercept so in this case it is 3 on the y-axis. then use rise over run. rise being up and down and run being left and right. so go up 3 then right 1 and put a dot there and connect your 2 lines to make a graph. if the number was -3/1 you go down 3 and right one then but thats just hypothetical

now to make a equation for a point you put it in y=mx+b.

please mark me brainliest if this helped

Answer:

72 m²

Step-by-step explanation:

If you flatten the lateral surfaces, the combine to make a rectangle.

Length: 2 m + 1.5 m + 2.5 m = 6 m

Width: 12 m

Lateral Area = Length × Width

Lateral Area = 6 m × 12 m

Lateral Area = 72 m²

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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