Which of the following graphs shows the solution to the system of inequalities? (Green representing the answer region)

Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

Let's multiply the following polynomial:

We get,

Answer:

80 degrees

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees so we can create the equation 70+30+x=180. This solves out to 80 so x=80 degrees.

Answer:

the actual amount of 24% of $94 is 11.28 so it compares to the estimated amount by 2.28

Step-by-step explanation:

2.28 is the difference between the actual amount and the estimated amount

Answer: Both $94 and 12% were rounded down, so the estimate will be less than the actual amount.

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

Given that:

Work required to stretch a string:

3 ft = 6ft - lb

The work required to stretch it 9 inches

Given that :

Work(W) = kx

Take the integral of W at 3 fts beyond its natural length;

W = ∫kx dx at 0 to 3

W = k ∫xdx at 0 to 3

W = 6

W = k[x²/2] at x =0 to x = 3

6 = k[3² /2] - 0

6 = k[9/2]

12 = 9k

k = 12/9 = 4/3 = 1.333

Converting inches to feet:

1 inch 0.0833 ft

9 inches = 0.75 ft

W = ∫kx dx at 0.75 to 0

W = 4/3 ∫xdx at 0 to 0.75 = 3/4

W = 4/3[x²/2] at x =0.75 to 0

W = 4/3[(3/4)²/2] at 0.75 to 0

W = 4/3[(9/16) / 2]

W = 4/3 * (9/16 * 1/2)

W = 36/96

W = 6/16 = 3/8 ft - lbs

Answer:

\(32000\ \text{cm}^3\)

Step-by-step explanation:

b = Length and breadth of base

h = Height of box

Surface area of box = \(4800\ \text{cm}^2\)

Volume is given by

\(V=b^2h\)

Surface area is given by area of base plus the area of the four sides

\(b^2+4hb=4800\\\Rightarrow h=\dfrac{4800-b^2}{4b}\\\Rightarrow h=\dfrac{1200}{b}-\dfrac{b}{4}\)

\(V=b^2h=b^2(\dfrac{1200}{b}-\dfrac{b}{4})\\\Rightarrow V=1200b-\dfrac{b^3}{4}\)

Differentiating with respect to the base dimensions we get

\(\dfrac{dV}{db}=1200-\dfrac{3}{4}b^2\)

Equating with 0

\(0=1200-\dfrac{3}{4}b^2\\\Rightarrow b=\sqrt{\dfrac{1200\times 4}{3}}\\\Rightarrow b=40\ \text{cm}\)

Finding the double derative

\(\dfrac{d^2V}{db^2}=-\dfrac{3}{2}b\)

at \(b=40\)

\(\dfrac{d^2V}{db^2}=-\dfrac{3}{2}b=-\dfrac{3}{2}\times 40=-60\\ -60<0\)

So, the maximum value of b is 40 cm

\(h=\dfrac{1200}{b}-\dfrac{b}{4}=\dfrac{1200}{40}-\dfrac{40}{4}\\\Rightarrow h=20\ \text{cm}\)

Volume is given by

\(V=b^2h=40^2\times20\\\Rightarrow V=32000\ \text{cm}^3\)

The largest possible volume of the box is \(32000\ \text{cm}^3\)

Answer:

its the same as 48

Step-by-step explanation:

Answer:

both sides are the same so it has to be also 48

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Answer:

5

step-by-step explanation:

it is congruent to 2.

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

17) The number of miles that the car will travel with 90%, 30%, and 50% probability on a full tank of gas is:

90% probability: 420.5 + (1.645 x 50) = 545.25 miles

30% probability: 420.5 - (1.645 x 50) = 295.75 miles

50% probability: 420.5 miles

18) The upper and lower values for the interval of miles traveled on a full tank of gas around the mean that includes approximately 68% of miles for this car is:

Upper value: 420.5 + (1 x 50) = 470.5 miles

Lower value: 420.5 - (1 x 50) = 370.5 miles

19) The upper and lower values for the interval of miles traveled on a full tank of gas around the mean that includes approximately 95% of miles for this car is:

Upper value: 420.5 + (2 x 50) = 520.5 miles

Lower value: 420.5 - (2 x 50) = 320.5 miles

20) The upper and lower values for the interval of miles traveled on a full tank of gas around the mean that includes approximately 99.7% of miles for this car is:

Upper value: 420.5 + (3 x 50) = 570.5 miles

Lower value: 420.5 - (3 x 50) = 270.5 miles

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.

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A third variable associated with two variables under study that results in a correlation between the two variables, falsely implying a causal relationship between the pair, is a) a lurking variable.

A lurking variable is an uncontrolled and unknown variable but significant effect on both independent and dependent variables.

A lurking variable creates a correlation between the independent and dependent variables without being intended by the researcher.

We can differentiate a lurking variable from a confounding variable.

A confounding variable is taken into account in research and can also influence the variables of interest but it is not credited with any relationship between the independent and dependent (response) variables.

Thus, the existence of a third variable resulting in a correlation between the independent and dependent variables is called a lurking variable.

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Answer:

6x + 25

Step-by-step explanation

Distribute 6 through the parenthesis

Then add 24 and 1 to get 25

then you end up with 6x + 25

Answer:

6x+25

Step-by-step explanation:

6x+24+1 first distribute 6 into (x+4)

then add all your constants 24+1

then u get 6x+25,ur answer

Answer:

m + (m + 15) + (m + 2)

Step-by-step explanation:

Even thought we don't know the value of m, we can use expressions to represent it.

Hope this helps.

The required expression is m + (m + 15) + (m + 2) which represents the total number of miles Marla, Lawrence, and Jerry drove in all.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers. Unknown variables, numbers, and arithmetic operators make up an algebraic expression.

Let's represent Marla drove "m" miles.

Since Lawrence drove 15 more miles than Marla.

So, this means the expression m + 15

Then Jerry drove 2 more miles than Marla.

So, this means the expression m + 2

Now, the total number of miles = m + (m + 15) + (m + 2)

This expression represents the total number of miles Marla, Lawrence, and Jerry drove in all.

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=========================================================

Explanation:

Use the rational root theorem to determine this list of possible rational roots: 1, -1, 1/2, -1/2

Plug each possible root one at a time into the original expression given. If the simplified result is 0, then that possible root is an actual root.

If we tried say a = -1, then,

2a³-a²+a-2​ = 2(-1)³-(-1)²+(-1)-2​ = -6

The result is not zero, so a = -1 is not an actual root.

But if we tried say a = 1, then,

2a³-a²+a-2​ = 2(1)³-1²+1-2​ = 0

We get 0 so a = 1 is an actual root. I'll let you try the other values, but you should find that a = 1 is the only rational root.

Since a = 1 is a root, this makes (a-1) to be a factor.

From here, use either synthetic or polynomial long division to determine the other factor. Refer to the diagram below for each method.

Regardless of which method you pick, the quotient is 2a² + a + 2 which is the other factor needed. The remainder of 0 tells us we have (a-1) as a factor. For more information, check out the remainder theorem.

Answer:

currently 1 £ = 1.10174 €

Answer:

The answer is zero.

Step-by-step explanation:

For the given function the value of limits are

\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\) is 5

\(\lim _{x\to 0^+}\left(f\left(x\right)\right)\) is 0

\(\lim _{x\to 0}\left x^2+5\)is 5

The given function is f(x)= x²+5, when x≤0

f(x)=2x when x>0

\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\)

Which is \(\lim _{x\to 0^-}\left x^2+5\)

The given limit is a left hand limit as there is minus in the limits

When we apply x as 0 we get the value 5

Now \(\lim _{x\to 0^+}\left(f\left(x\right)\right)\)

So \(\lim _{x\to 0^+}\left 2x\)

The given limit is a right hand limit as there is positive in the limits

When we apply x as 0 we get 0

Now \(\lim _{x\to 0}\left(f\left(x\right)\right)\)

Which is \(\lim _{x\to 0}\left x^2+5\)

We get 5

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Answer:

(y-5) ÷ 2

Step-by-step explanation:

Floyd needs 33 matches to make a rectangle with a length of 20 matches.

To find out how many matches Floyd needs to make a rectangle with a length of 20 matches, we can observe a pattern in the given information.

From the given data, we can see that as the length of the rectangle increases by 4 matches, the number of matches used increases by 8. This means that for every additional 4 matches in length, Floyd requires 8 more matches.

Using this pattern, we can calculate the number of matches needed for a rectangle with a length of 20 matches.

First, we need to determine the number of 4-match increments in the length of 20 matches. We can do this by subtracting the starting length of 3 matches from the target length of 20 matches, which gives us 20 - 3 = 17.

Next, we divide the number of 4-match increments by 4 to determine how many times Floyd needs to add 4 matches. In this case, 17 ÷ 4 = 4 with a remainder of 1.

Since Floyd requires 8 matches for each 4-match increment, we multiply the number of increments by 8, which gives us 4 × 8 = 32 matches.

Finally, we add the remaining matches (1 match in this case) to the total, resulting in 32 + 1 = 33 matches needed to reach a length of 20 matches.

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Answer:

C

Step-by-step explanation:

Formula to get the area

A = r^2π

A = 16^2π

A= 804.24 cm^2

As per the given data, the approximate area of the shaded sector is 283 square cm, which is option D.

Area is a measure of the amount of space inside a two-dimensional shape or a flat surface. It is typically measured in square units, such as square meters or square feet.

To find the area of the shaded sector, we need to first find the area of the whole circle, and then multiply it by the fraction of the circle that is shaded.

The area of a circle is given by the formula:

A = \(\pi r^2\)

Where r is the radius of the circle. In this case, we are given that the radius of the circle is 18 cm, so we can substitute this value into the formula:

A = \(\pi 18^2\)

A = 324π

So, the area of the whole circle is 324π square cm.

The shaded sector has a central angle of 100 degrees, which is a fraction of the total central angle of 360 degrees. So, the fraction of the circle that is shaded is:

100° / 360° = 5/18

Therefore, the area of the shaded sector is:

A = (5/18) * 324π

A = 90π

Using 3.14 as an approximation for π, we get:

A ≈ 90 * 3.14

A ≈ 283

Thus, the approximate area of the shaded sector is 283 square cm, which is option D.

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Answer:

In the A circle: 1,3,8

In the B circle: 2

In the middle: 4,9

In the outside: 5,6,7

Hope this helps!

Answer:

a number greater than any assignable quantity or countable number (symbol ∞).

Step-by-step explanation:

Answer:

A  =  139.25

Step-by-step explanation:

Answer:

\(5x+11\)

Step-by-step explanation:

Step 1: Distribute

\(3x+6+2x+5\)

Step 2: Add like terms

\(5x+11\) < your answer

Answer: The required ordered pairs are (–1,1) and (–6,–1),(0, 0) and (2, 5)  and (3, 0) and (8, 2)

Step-by-step explanation:

The estimate of 179% of 41 by rounding is about 73.19.

To find this estimate, first convert the percentage to a decimal by dividing it by 100: 179/100 = 1.79. Then, multiply this decimal by 41: 1.79 * 41 = 73.39.

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