Question 2: 11A triangle has a base length of 6ac? and a height 3 centimeters more than the base length. Find the aroa of thetriangle if a = 2 and c = 3.O 5,994 cm?O 3,078 cm?O 11,988 cm?O2,025 cm?

Answer:

\( \frac{6 {x}^{2} - 12x - 48 }{3 {x}^{2} - 12x - 36 } = \frac{6( {x}^{2} - 2x - 8)}{3( {x}^{2} - 4x - 12)} = \frac{6(x + 2)(x - 4)}{3(x + 2)(x - 6)} = \frac{2(x - 4)}{x - 6} = \frac{2x - 8 }{x - 6} \)

Step-by-step explanation:

Proving by Vertex Form:Yes, if we put this equation in vertex form

\(a(x - h) {}^{2} + k\)

where h,k is vertex

we can find if it reaches 5.

First we do -b/2a.

\( \frac{ - 1}{10} \)

Is a solution, if we plug that in we get

Which gives

\(3.95\)

So the vertex form is

\(5(x + 0.1) {}^{2} + 3.95\)

Since the graph is facing upwards,because a is positive, the function will pass all values greater than 3.95, and 5 is one of them

Second Way: Watch if you want to see how long is reaches 5 meters.

Set the quadratic equation equal to 5.

\(5 {t}^{2} + t + 4 = 5\)

\( {5t}^{2} + t - 1 = 0\)

\(5 {t}^{2} + t - 1 = 0\)

Do quadratic formula, which is

\( - b± \frac{ \sqrt{b {}^{2} - 4ac} }{2a} \)

So a is 5 b is 1 and c is -1 so we get

\( - 1± \frac{ \sqrt{1 {}^{2} - 4( 5)( - 1)} }{2(5)} \)

\( - 1± \frac{ \sqrt{1 + 20} }{10} \)

\( - 1± \frac{ \sqrt{21} }{10} \)

\( \frac{ - 1}{10} + \frac{ \sqrt{21} }{10} \)

and

\( \frac{ - 1}{10} - \frac{ \sqrt{21} }{10} \)

are the solutions but since time is scalar, it can't be negative so qe take the positive solution

\( \frac{ - 1}{10} + \frac{ \sqrt{21} }{10} \)

which is approximate 0.358.

So if you wanted to know, it will take 0.36 seconds to reach a height of 5 meters.

Answer:

She already has 5 and the total is 32 so she has to make 28 friendship bracelets. Bracelets in packages of 4 and she buys 5 packages which is 20 so no, she doesn't have enough bracelets if she buys 5 packages.

Step-by-step explanation:

The minimum unit cost of the car is $12232.1

Given: cost function C(x)=0.9x² - 414x + 59,366

In order to find the minimum point, take the derivative of the cost function:

dC/dx = 2x - 414          (equate to zero and solve for x)

2x - 414 = 0                

2x = 414

x = 414/2 = 207

Thus, the minimum point is at x =207

The minimum unit cost can be obtained by substituting x = 207 into the cost equation:

C(x) = 0.9x² - 414x + 59,366

C(207) = 0.9(207)² - 414(207) +  59,366

          = 38564.1 - 85698 + 59,366

           = $12232.1

Therefore, the minimum unit cost is $12232.1

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Answer:

101.8 lb

Step-by-step explanation:

1760 sq ft are covered by 40 lb

4480 sq ft are covered by x

1760/40 = 4480/x

1760x = 40 × 4480

x = 179,200/1760

x = 101.818181...

Answer: 101.8 lb

Answer:

A

: hope this helps

The value of x is 32 degree.

The correct option is B.

According to the exterior angle theorem, the exterior angle that results from stretching a triangle's side is equal to the sum of the dimensions of the triangle's two opposed interior angles. The theorem can be used to determine a triangle's unknown angle's measurement. We must first determine the triangle's exterior angle and then its two remote inner angles in order to apply the theorem.

Using Exterior angle Property as

100 = 68 + x

x= 100 - 68

x = 32 degree.

Thus, the value of x is 32 degree.

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Cyclic redundancy checks work by using a generator polynomial to calculate a unique value (CRC) based on the original data. This value is then appended to the data and verified by the receiver to ensure data integrity.

Cyclic Redundancy Checks (CRC) work as an error-detecting method used to ensure data integrity during transmission or storage. The process involves the following steps:

1. A predetermined polynomial (called the generator polynomial) is chosen for the CRC algorithm.

2. Before transmitting data, the sender divides the original data by the generator polynomial, using binary division.

3. The remainder obtained from the division is treated as the CRC value.

4. The sender appends the CRC value to the end of the original data, forming the transmitted message.

5. The receiver, upon receiving the message, performs the same binary division using the same generator polynomial.

6. If the remainder from the receiver's division matches the CRC value sent by the sender, it is assumed that the data is error-free.

7. If the remainder does not match, the receiver knows that an error occurred during transmission and can request the sender to retransmit the data.

In summary, cyclic redundancy checks work by using a generator polynomial to calculate a unique value (CRC) based on the original data. This value is then appended to the data and verified by the receiver to ensure data integrity.

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Answer:

C

Step-by-step explanation:

In order to find the slope, you can use rise over run.

(y₂ - y₁) over (x₂ - x₁)

You can use the points (1, 1) and (2, -1). y₂ can be -1 and y₁ can be 1, but you could do either as long as you make x₁ and x₂ from the corresponding points (so y₁ and x₁ are one coordinate pair and y₂ and x₂ are the other). This way, you get -2 as your slope. Then, the table shows that y = 3 when x is 0, so that's your y-intercept, which is how you get +3. Hope this helps!

y = -2x + 3 will be the equation represents the data in the table shown.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, A data Set of the value of x and y that represents a linear equation.

From the slope intercept form of a linear equation,

y = mx + b,

where m is the slope

b is the y-intercept

y- intercept is point in line where the value of x will be 0.

From our data set,

y - intercept = b = 3 (since, at x = 0, y is 3)

And Slope, (m) = (y₂ - y₁)/(x₂ - x₁)

in our case,

m = (1-3)/(1-0)(from first two values of data set)

m = -2

Thus,

Equation of line:

y = -2x + 3

Therefore, The equation of line for the given data set will be y = -2x + 3.

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Answer:

m = -5 + 2b

Step-by-step explanation:

2b - m = 5

-2b    -2b

-m = 5 - 2b

-1         -1

5 ÷ -1 = 5

-2b ÷ -1 = 2b

m = -5 + 2b

The p-value can be found with the F-distribution table or statistical software. If the p-value is less than or equal to α, then answer is option (a),If the p-value is greater than α, then answer is option (b).

To determine the correct statistical decision based on the given F-statistic, F (3, 12) = 2.72, we need additional information such as the significance level (α) of the hypothesis test. The significance level is a predetermined threshold that is used to assess the statistical significance of the results.

The correct decision depends on whether the calculated p-value, which quantifies the strength of evidence against the null hypothesis, is less than or equal to the significance level (α).

To find the p-value, you would need the F-distribution table or statistical software.

Once you have the p-value, you can compare it to the significance level (α) to make a decision:

If the p-value is less than or equal to α, you would reject the null hypothesis, indicating a statistically significant mean difference.

If the p-value is greater than α, you would fail to reject the null hypothesis, suggesting that there is not a statistically significant mean difference.

Therefore, without the significance level or the p-value, it is not possible to determine the correct statistical decision.

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Answer:

The Bengal tiger's canine tooth is 10.16 cm long.

Step-by-step explanation:

1 inch = 2.54 cm   so 4 inches = ?cm

1/2.54 = 4/?               set up a proportional ratio : inch/cm = inch/cm and solve

? = 2.54(4)

? = 10.16cm. long

Answer:

x=60

Step-by-step explanation:

Answer:

A line traveling to the left with an open dot on x=1.

Explanation:

The inequality x < 1 basically means "less than 1." On number lines, the further left you go, the smaller the number becomes, and the further right you go, the larger the number becomes. So we know that because it's less or smaller than 1, then the line will be to the left. On the other hand, the inequality does not have a line under it to indicate a "less than or equal to 1," just "less than." Therefore, the dot is open. If there were a line under the inequality, then it would indicate "less than or equal to 1" and the dot would be closed.

The length of the bar is 10.5 foot and the width of the bar is 5.7 foot .

In the question ,

it is given that

the base area of the large chocolate bar is 59.85 square foot .

let the length of the chocolate bar be "l"

and the breadth of the chocolate bar be "b"

given that the length is 0.9 foot shorter than twice its width , means

l = 2w - 0.9

we have the area of rectangle = length \(\times\) width

Substituting the values of length , width and area we get

59.85 = (2w - 0.9 ) * w

59.85 = 2w² - 0.9w

2w² -0.9w -59.85 = 0

On solving the quadratic equation ,

we get w = -5.25 and w = 5.7

width cannot be in negative , so, the width is 5.7 foot .

and l = 2(5.7) -0.9 = 11.4 - 0.9 = 10.5

Therefore , the length of the bar is 10.5 foot and the width of the bar is 5.7 foot .

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Format:

{Expression} = {Rewritten} = {Value}

Answer:

3/8 * 24 = 72/8 = 9

5/9 * 18 = 90/9 = 10

11/12 * 36 = 396/12 = 33

The digits in millions period of the number is 468 as the digit 8 is in the ones million place, 6 is in the tens million place and 4 is in the hundred millions place.

Given the number is 21,468,127,471.

The digits in which are given in the large numbers are in groups of three places. The groups are called periods. Commas are usually used to separate the periods.

The groups of numbers are 3 digit group and which is starting from the right to left.

As we all know that we read the group of periods as ones, tens, hundreds, thousand, ten thousand, hundred thousand, million, ten million, hundred million, billion etc.

From  the above, we find that the given number 21,468,127,471 contains digit 1 is in the ones place, 7 is in the tens place, 4 is in the hundredth place, 7 is in the thousand place, 2 is in the ten thousand place, 1 is in the hundred thousand place, 8 is in the million place, 6 is in the ten million place, 4 is in the hundred million place , 1 is the billion place and 2 is in the ten bilion.

Hence, the digits in millions period of the given number 21,468,127,471 is 468 as the digit 8 is in the ones million place, 6 is in the tens million place and 4 is in the hundred millions place.

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Answer:

x = - 2

Step-by-step explanation:

Given

6 - 4x = 7x - 9x + 10, that is

6 - 4x = - 2x + 10 ( add 2x to both sides )

6 - 2x = 10 ( subtract 6 from both sides )

- 2x = 4 ( divide both sides by - 2 )

x = - 2

Answer: x = -2

Step-by-step explanation:

Answer:

The answer was C. 16ft on Edge 2022.

Step-by-step explanation:

Just think of Y as the height of the graph and X as the width.

With this in mind, it asks what's the length of the base of the graph.

In this case, the answer would be 16 since it goes from 0 or the origin to 16 on the X-axis.

Hence, the answer is C. 16ft.

Answer:

$1,489.88 (nearest cent)

Step-by-step explanation:

To calculate gross pay, multiply the number of hours worked by the pay per hour.

Warren worked 36.5 hours one week and 32 hours the week before.

Therefore, the total number of hours Warren worked was:

Multiply the total number of hours worked by Warren's rate of pay of $21.75 per hour:

Therefore, Warren's gross pay for the two weeks was $1,489.88 (nearest cent).

Answer:

$1489.875

Step-by-step explanation:

Warren's gross pay for 36.5 hours last week can be calculated as follows:

Gross pay for 36.5 hours = $21.75/hour * 36.5 hours = $793.875

Similarly, Warren's gross pay for 32 hours the week before can be calculated as follows:

Gross pay for 32 hours = $21.75/hour * 32 hours = $696

Adding the gross pay for the two weeks, we get:

Gross pay for 2 weeks = $793.875 + $696 = $1489.875

Answer:

  -25, 25

Step-by-step explanation:

Since the numbers have the same absolute value and the sum of their absolute values is 50, they both must have an absolute value of 50/2 = 25.

Unique numbers with the same absolute value will have opposite signs.

The numbers are -25 and 25.

The measure of ∠POX  = 160°  The length of XOA = 16.95 mm ,We know that PM¯, PN¯, and PO¯ are angle bisectors of triangle MNO, so they divide the opposite sides in two equal parts. Let x = MY, y = NY, and z = OY. Then, we have:

MX / NO = MY / NY (by the angle bisector theorem)

MX / (MX + XO) = x / (x + y)

MX(x + y) = x(MX + XO)

MXy = XOx

NO / OX = NY / OY (by the angle bisector theorem)

(OX + XO) / OX = y / z

1 + XO/OX = y/z

XO/OX = (z - y)/y

Now, we can use these equations to solve the problem:

To find PX¯, we need to find MX. Using the angle sum property of triangles, we have:

m∠M = 180 - m∠MON = 140°

m∠PMX = m∠M/2 = 70°

m∠PMO = m∠MON/2 = 20°

m∠XMO = m∠PMX + m∠PMO = 70° + 20° = 90°

Therefore, PX¯ is the altitude from M to XO¯, so we have:

tan(30°) = PX / MX

MX = PX / tan(30°)

= 23 / √(3)

= 13.31 mm

To find m∠PMX, we can use the fact that PM¯ is an angle bisector:

m∠PMX = m∠M + m∠PMO

= 140° + 20°

= 160°

To find m∠POX, we can use the fact that PO¯ is an angle bisector:

m∠POX = m∠O + m∠PNO

= 180° - m∠MON + m∠PNO

= 180° - 40° + 20°

= 160°

To find XO¯, we need to find y and z. Using the fact that PX¯ is an angle bisector, we have:

PY / OY = PM / OM

23 / z = 52 / (x + y + z)

y + z = 52z / 23

z = 23y / (52 - 23)

Using the equation XO/OX = (z - y)/y, we have:

XOA / 52 = (23y / (52 - 23) - y) / x

XOA= 52 * 23y / ((52 - 23) * x - 23y)

Substituting MX = 23/√(3) - PX = 23/√(3) - 13.31, we get:

y = NO * PY / (PM + PN + PO) = 56.17 mm

z = OY + PY = 79.17 mm

XOA = 16.95 mm

Therefore, the answers are:

Length of PX¯: 13.31 mm

Measure of ∠PMX: 160°

Measure of ∠PO

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Answer: 4310

Step-by-step explanation: Because it is a positive exponent instead of negative, you would move the decimal to the right 3 places

Answer:

D because when we multiply minus minus it became plus

Answer:

30

Step-by-step explanation:

gave 15 to his friend 30-15=15 his mom bought mom 60 candies so 30

Answer:

3x-7

Step-by-step explanation:

9x-6x=3x

12-19=-7

12+9x-6x-19=3x-7

The length of the addition to the room will be 8 feet.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Given that Teri has a living room that is 9 feet wide and has an area of 108 square feet. She is adding to the room. The remodelled living room will have a total area of 180 square feet.

The added length will be calculated as:-

TA = A₁ + A₂

180 = 108 + 9x

72 = 9x

x = 72 / 9

x = 8 feet

Therefore, the length of the room addition will be 8 feet.

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Answer: Yes you can use the HL theorem

Explanation:

HL = hypotenuse leg

The tickmarks tell us about the congruent hypotenuse sides. This takes care of the "H" from "HL".

The "L" portion is because BC = BC (reflexive property) which are the congruent legs.

So we have enough info to use the HL theorem to prove the triangles are congruent.

Note: The HL theorem only works for right triangles.

Answer:

I don't know. How much he wants I guess.

Step-by-step explanation:

The problem requires finding the volume of the solid when the region bounded by the curve \(y^2 = 2x\) and line x = 2y is rotated about x = -2.

Here, we need to make use of the formula for volume of solid obtained by rotating the curve:

y = f(x) from a to b, about x = L.

V =\(∏ ∫a^b (f(x))^2 dx.\)

In this case, we can rewrite \(y^2 = 2x as x = (y^2)/2 or y = (2x)^(1/2).\)

Also, x = 2y can be written as\(y = (1/2)x.\)

Rotating the curve y = \((2x)^(1/2)\)about the line x = -2 will give a solid of revolution that is symmetrical about the line x = -2.

Thus, to find the volume of the solid of revolution, we can integrate from -2 to 0 and multiply the result by 2.

So, the volume of the solid is given by:\(x = -2 is\)

\(V = 2∏ ∫0^2 ((y^2)/2 + 2))^2 dy = 2∏ ∫0^2 (y^4)/4 + 2y^2 + 4 dy\)

Simplifying:

 V =\(2∏ ((y^5)/20 + (2y^3)/3 + 4y)] from 0 to 2\)

 V =\(2∏ [(2^5)/20 + (2(2^3))/3 + 8]\)

 V = \(2∏ (16/5 + 16/3 + 8)\)

    = \((96/5)∏\)

So, the volume of the solid obtained by rotating the region bounded by the curves \(y^2 = 2x\) and x = 2y about the line

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