\(x^{2} +11x +24\)

Answer:

\(y=3x^2+12x+17\)

Step-by-step explanation:

The equation in vertex form is \(y=a(x+2)^2+5\).

We can use the point \((1,32)\) to solve for \(a\).

\(32=a(1+2)^2+5 \\ \\ 27=9a \\ \\ a=3 \\ \\ \\ \therefore y=3(x+2)^2 + 5 \\ \\ =3(x^2+4x+4)+5 \\ \\ =3x^2+12x+12+5 \\ \\ =3x^2+12x+17\)

Answer: 26.6 repeating number or 26 2/3

Step-by-step explanation:

The Great Wall of China is about 200 times longer then the Panama Canal

Scientific notation is used to compress large numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. An examples of 100 expressed in scientific notation is 1 x 10².

In order to determine the difference in the length of the great wall of China and the Panama Canal, divide the length of the Great wall of China by the length of the Panama Canal.

(1 x \(10^{4}\)) ÷ (5 x \(10^{1}\))

(1/5) x \(10^{4 - 1}\)

0.2 x \(10^{3}\)

2 x \(10^{3 - 1}\)

2 x10² = 200

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Answer:

-8

Step-by-step explanation:

\(\frac{x}{2} +6=2\\\)

\(\frac{x}{2} =2-6\)

\(\frac{x}{2} = -4\)

\(x=-4*2\)

\(x=-8\\\)

Hope this helps, have a great day:)

The AAS Triangle Congruence Theorem states that if two angles and the side between them of one triangle are equal to two angles and the side between them of another triangle, then the two triangles are congruent.

The AAS Triangle Congruence Theorem states that if two angles and the side between them of one triangle are equal to the two angles and the side between them of another triangle, then the two triangles are congruent. This theorem is an important tool in geometry that can be used to determine if two triangles are congruent and to find missing side lengths or angles. This theorem is based on the idea that if two sides and the included angle of one triangle are equal to the two sides and the included angle of another triangle, then the two triangles must be congruent. This is because the third side of the triangle, and the remaining angles must also be equal in order for the triangles to be congruent. Therefore, the AAS Triangle Congruence Theorem can be used to determine if two triangles are congruent, and to find missing side lengths or angles.

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Answer:

distance = 7.07 units

Step-by-step explanation:

x difference = 7

y difference = -1

using the Pythagorean theorem:

7² + -1² = d²

d² = 49 + 1 = 50

d = 7.07

Answer:

7.1

Step-by-step explanation:

distance between the x is 7 and y is 1

And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2

c=50

and take the square root, which is 7.071, rounds to 7.1

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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Step-by-step explanation:

Radius of circular track=r=0.75km

Circumference=2πr=2πkm

Speed of train=36 km\hr

Distance moved by train in 30 seconds =36×

3600

30

=

10

3

km

For 2π km, train turns 2π

c

∴ For

10

3

km, train turns

10

3

c

=

π

54

∘

1 minute of arc=

60

1

∘

Angle turned by train =(

π

54×60

) minutes of arc.

≃1031 minutes

Answer:

vận tốc22

chiềudai0.75

t=1/60

đ=111/30

Answer:

Princess is behind 2

Step-by-step explanation:

If all 3 hints are false, then the princess is not behind 1  ( so it must be 2 or 3)

The dragon is not behind 2 ( so it must be 1 or 3)  

The is no one behind 3  

That means the princess cannot be behind 3 and the dragon cannot be behind 3

The princess is behind 2 and the dragon is behind 1

Step-by-step explanation:

Sure, here's a step-by-step response you can use:

"Hey, that's a good question! Let me explain why (2x + 1)^2 is not equal to 4x^2 + 1.

When we see an expression like (2x + 1)^2, we know that it means we need to multiply (2x + 1) by itself. So let's do that first:

(2x + 1)^2 = (2x + 1) x (2x + 1)

Now we can use the FOIL method to multiply these two expressions together:

(2x + 1) x (2x + 1) = 4x^2 + 2x + 2x + 1

If we simplify the middle terms by adding them together, we get:

(2x + 1) x (2x + 1) = 4x^2 + 4x + 1

So the expression (2x + 1)^2 simplifies to 4x^2 + 4x + 1, not 4x^2 + 1.

I can see why you might have thought the answer was 4x^2 + 1, since that's the first term in the expression we got. But we can't forget about the two middle terms that come from multiplying 2x and 1 together twice.

I hope that helps clear things up! Let me know if you have any more questions."

Answer: Divide 276 by 12

276 divided by 12 is 23

Solution for 276 divided by 12

✍️See below how to solve this division manually.

276 divided by 12 - Long Division Solution

The solution below uses the "Long Division With Remainders Method". It is one of two existing methods of doing long division.

Start by setting the divisor 12 on the left side and the dividend 276 on the right:

   23 ⇐ Quotient

  ―――

12)276 ⇐ Dividend

  24

  --

   36

   36

   --

      ⇐ Remainder

276 divided by 12 is an exact division because the remainder is zero.

The equations of line of \(\triangle DEC\) is y=1, y=x-6 and y=4.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions

Here in \(\triangle DEC\) , the coordinate of D is (7,4) , E is (10,4) and C is (7,1).

Now to find line equation for DE,

\((x_1,y_1)=(7,4)\\(x_2,y_2)=(10,4)\)

Then slope m = \(\frac{y_2-y_1}{x_2-x_1} = \frac{4-4}{10-7}=0\)

Equation of line is \(y-y_1=m(x-x_1)\)

=> y-4=0

=> y=4.

Now line equation for EC ,

\((x_1,y_1)=(10,4)\\(x_2,y_2)=(7,1)\)

Then slope = \(\frac{1-4}{7-10} = \frac{-3}{-3}=1\)

Equation of line EC => y-4=1(x-10)

=> y-4=x-10

=> y=x-10+4

=> y = x-6.

Now line equation for CD,

\((x_1,y_1)=(7,1)\\(x_2,y_2)=(7,5)\)

Slope = \(\frac{5-1}{7-7}=0\)

Then equation is , y-1=0(x-7)

=> y-1=0

=> y=1.

Hence the equations of line of \(\triangle DEC\) is y=1, y=x-6 and y=4.

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Answer:

Rectangle 11.59 sqft

Rectangle 36 sqft

Polygon 47.59 sqft

Step-by-step explanation:

The amount the firm needs to deposit in the account now is 9,640.11. Given that the company has purchased a life truck with a useful life of 5 years, the maintenance costs for the truck during the first year are 2,000.

Also, maintenance costs are expected to increase at a rate of 300 per year over the remaining life, which is for four years. Assume that the maintenance costs occur at the end of each year.

The future maintenance costs for the truck can be calculated as shown below:

Year 1:\($2,000Year 2: $2,300Year 3: $2,600Year 4: $2,900Year 5: $3,200\)The maintenance account that earns 10% interest per year has to be set up, and all future maintenance expenses will be paid out of this account. The future value of the maintenance costs, i.e., the amount that the firm needs to deposit now to earn 10% interest and pay the maintenance costs over the next four years is given by:

\(PV = [C/(1 + i)] + [C/(1 + i)²] + [C/(1 + i)³] + [C/(1 + i)⁴] + [(C + FV)/(1 + i)⁵]\),where PV is the present value of the future maintenance costs, C is the annual maintenance cost, i is the interest rate per year, FV is the future value of the maintenance costs at the end of year 5, which is $3,200, and 5 is the total number of years, which is

5.Substituting the given values in the above equation:

\(PV = [2,000/(1 + 0.1)] + [2,300/(1 + 0.1)²] + [2,600/(1 + 0.1)³] + [2,900/(1 + 0.1)⁴] + [(3,200 + 3,200)/(1 + 0.1)⁵] = 9,640.11\)Therefore, the firm needs to deposit 9,640.11 in the account now. Hence, option (A) is the correct answer.

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A) The total annual dividend is $203.

B) annual yield (based on the low) = 2.46%

C) annual yield (based on the high) = 1.37%

To calculate the total annual dividend, we multiply the annual dividend per share by the number of shares:

(A) total annual dividend = annual dividend per share × number of shares

total annual dividend = $0.58 × 350

total annual dividend = $203

The total annual dividend is $203.

(B) annual yield (based on the low) = (annual dividend per share /low price) × 100

annual yield (based on the low) = $0.58 / $23.60) × 100

annual yield  ≈ 2.46%

(C) annual yield (based on the high) = (annual dividend per share / high price) × 100

annual yield (based on the high) = ($0.58 / $42.50) × 100

annual yield (based on the high) = 1.37%

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Answer:

the answer is c 4 hours because it's 75 per hour

The sign of the x-component and y-component of the vector will be negative and positive, respectively. The magnitude of vector A is approximately 8.944m, and the angle it makes with the positive x-axis is approximately 63.43 degrees.

(a) To calculate the magnitude of vector A with x-component 4m and y-component 8m, we can use the Pythagorean theorem. The magnitude (|A|) is given by the square root of the sum of the squares of the components: |A| = √(4^2 + 8^2) = √(16 + 64) = √80 ≈ 8.944m.

(b) To calculate the angle that vector A makes with the positive x-axis, we can use the inverse tangent function. The angle (θ) is given by the arctangent of the ratio of the y-component to the x-component: θ = tan^(-1)(8/4) ≈ 63.43 degrees.

In summary, the magnitude of vector A is approximately 8.944m, and the angle it makes with the positive x-axis is approximately 63.43 degrees.

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Answer:

C = 50°

X = 155°

X = 105°

Step-by-step explanation:

1. All angles inside the triangle add up to 180°

2. 180° - 25° = 155°

Supplementry angles are 180°

3. Opposite angles are the same

Answer:

C= 50 x= 155 x= 105

Step-by-step explanation:

Answer: Renata, \(416\ ft^2\)

Step-by-step explanation:

Given

The base of rectangular wood is \(b=32\ ft\)

The height of Renata frame is \(h_r=18\ ft\)

The height of the ben frame is \(h_b=5\ ft\)

The area of the rectangular frame is \(A=b\times h\)

The area of Renata frame is \(A_r=32\times 18=576\ ft^2\)

The area of the ben frame is \(A_b=32\times 5=160\ ft^2\)

Clearly, the area of Renata is more by  \(576-160=416\ ft^2\)

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

For this problem, we are given the graph of an ellipse, and we need to determine its expression in the standard form.

The standard equation of an ellipse is given below:

Where (h,k) is the center of the ellipse, a is the horizontal radius and b is the vertical radius.

The center of the ellipse on our problem is (-2,2), the vertical radius is 2 and the horizontal radius is 3. We have:

In order to calculate the Foci, we need to first find the eccentricity of the ellipse, which is given by the following formula:

The coordinates of the foci are given by:

The coordinates for the foci are: (-2-sqrt(5), 2) and (-2+sqrt(5), 2).

Given:

Number of green peas = 475

Number of yellow peas = 193

Let's find the 94% confidence interval to estimate the percentage of yellow peas.

Where:

Total number of peas = 475 + 193 = 668

For the sample proportion, we have:

For a 94% confidence interval, the significance level will be:

1 - 0.94 = 0.06

For the critical value, using the z-table, we have:

Now, to find the 94% confidence interval, apply the formula::

Where:

To find the margin of error E, we have:

Thus, we have:

Hence the confidence interval will be:

Lower limit = 0.2559 ==> 25.59%

Upper limit = 0.3219 ==> 32.19 %

The confidence interval does not contain 0.25, hence we can say that the true results contradicts the expectations.

ANSWER:

The confidence interval does not contain the expectation of 25%, hence, the true results contradicts the expectation.

Answer:

y=-1.25x-4.25

Step-by-step explanation:

I had the same assignment.

The equation of the line that passes through (0,-b) and (c,0) is

7y - 8x = 28

The formula for calculating the equation of a line in point-slope form is expressed as:

\(y-y_0=m(x-x_0)\)

m is the slope of the line

(x0, y0) is any point on the line

Given the coordinate points (0, -b) and (c, 0)

Since b  = -4 and c = -3.5

The required coordinate  points will be (0, 4) and (-3.5, 0)

Substitute the given parameters into the given formula for calculating the slope:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{0-4}{-3.5-0} \\m = \frac{4}{3.5}\\m = 8/7\)

Substitute m = 8/7 and the point (0, 4) into the expression \(y-y_0=m(x-x_0)\)

\(y-4=\frac{8}{7} (x-0)\\7(y-4)=8x\\7y-28=8x\\7y-8x=28\)

Hence the equation of the line that passes through (0,-b) and (c,0) is

7y - 8x = 28

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To find the equilibrium price, we need to determine the price at which the quantity demanded is equal to the quantity supplied. In other words, we need to find the price where D(p) = S(p).

Given the demand function D(p) = 1628 - 16p and the supply function S(p) = -4 + 8p, we can set them equal to each other:

1628 - 16p = -4 + 8p

Simplifying the equation, we combine like terms:

24p = 1632

Dividing both sides by 24, we find:

p = 68

Therefore, the equilibrium price is $68. At this price, the quantity demanded (D(p)) and the quantity supplied (S(p)) are equal, resulting in a market equilibrium.

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Answer:

A and C

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation: hope it helps ^w^

Answer:

A single outlier will make the value of the median to move slightly towards the outlier.

Step-by-step explanation:

Median simply means the middle number among a set of values when arranged in an ascending or descending order.

Now an outlier is a value that is much more smaller or much more larger than majority of other values in a given set of data.

Now, if the outlier is far greater than most other numbers in the set of data, it means that the median will slightly increase when we compare it to the median without the outlier.

Also, when the outlier is very small or far lesser than most other numbers in the set of values, it means the median will slightly decrease when we compare it to the median without the outlier.

Thus, in both cases, the median will move slightly towards the outlier.

well, let's take a peek at the pyramid, hmmmm it has a triangular face that has a height of 5 and a base of 4, wait a second! it reallyi has 4 of those, ooook, and then it has a bottom that is a 4x4 square.

\(\stackrel{\textit{\large Areas}}{\stackrel{four~triangles}{4\left[ \cfrac{1}{2}(4)(5) \right]}~~ +~~\stackrel{square}{(4\cdot 4)}}\implies 40+16\implies 56\)

$ (20b + 80) is the cost to buy a frame for the panting given that measures b meters by 4 meters and charges $10 per meter for a wooden frame. This can be obtained by finding the perimeter of the painting and multiplying with the cost of wood per meter.

Given that,

length of the painting (l) = b meters

width of the painting (b) = 4 meters

Perimeter of the painting = 2(l+b)

                                          = 2(b+4)

                                          = 2b + 8

Cost of the frame = (2b + 8)× $10 per meter

                             = $ (20b + 80)

Hence $ (20b + 80) is the cost to buy a frame for the panting given that measures b meters by 4 meters and charges $10 per meter for a wooden frame.

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The number of ball bearings that can be made based on the volume will be 10 ball bearings.

It should be noted that the volume based on the information given will be:

V = 4/3πr³

= 4/3 × 3.14 × 0.5³

= 0.524

From the information, it takes 5.24 cubic centimeters of molten steel to have a diameter of 1 centimeter.

Therefore, the number of ball bearings will be:

= 5.24/.0524

= 10

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