help please i have the answer on picture​

If FC bisects ∠ACD and ∠ACD is a straight angles, then proved that the ∠ACF is a right angle

The ∠ACD is a straight angles

We know the angles on a straight line add up to 180 degree

Therefore,

The measure of angle ACD = 180 degrees

Here it is given that the line FC bisects angle ACD

Therefore, The angle ACF is equal to Angel DCF

Angle ACF = Angel DCF

Angle ACF + Angle DCF = 180 degrees

Then,

Angle ACF = Angel DCF  = 90 degrees

Hence, if FC bisects ∠ACD and ∠ACD is a straight angles, then proved that the ∠ACF is a right angle

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Answer:

-14

Step-by-step explanation:

I might be wrong, but this is my interpretation of the problem.

To solve this problem, find the endpoints of the line in the interval. Then draw a line between those two points. Finally, find the slope of the line that passes between the two points.

The line is f(x) = -2x^(2) + 2x + 1

The interval (in standard notation) is (3 \(\leq\) x \(\leq\) 5)

So when x = 3,

-2x^(2) + 2x + 1

-2(3)^(2) + 2*3 + 1

-2 * 9 + 6 + 1

-18 + 7

- 11

One endpoint is: (3, -11).

When x = 5

-2x^(2) + 2x + 1

-2(5)^2 + 2*5 + 1

-2 * 25 + 10 + 1

-50 + 11

-39

The other endpoint is; (5, -39).

Find the slope of a line passing through these two points.

The formula to find the slope of a line is:

\(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

\(x_{1}\) = 3

\(y_{1}\) = -11

\(x_{2}\) = 5

\(y_{2}\) = -39

((-39) - ( -11))/((5) - (3))

Simplify

-28/2

-14

Answer:

x=2; the extraneous root x=42.

All the details are in the attached picture, the answer is marked with red colour.

The solution set is {2, 42} & the extraneous root is 42

If there are two roots in an equation, and one of them does not properly satisfy the equation, then the root is called extraneous root of that equation.

Given equation is,

\(2+\sqrt{2x-3}=\sqrt{x+7}\)

Squaring both sides we get,

\(2^{2} +2(2)(\sqrt{2x-3} )+(\sqrt{2x-3}) ^{2} = (\sqrt{x+7}) ^{2}\)

⇒ \(4+4\sqrt{2x-3} +2x-3=x+7\\\)

⇒ \(4\sqrt{2x-3} =6-x\)

Again, squaring both sides we get,

⇒ \((4\sqrt{2x-3}) ^{2} =(6-x)^{2}\)

⇒ \(16(2x-3)=6^{2} -12x+x^{2}\)

⇒ \(32x-48=36-12x+x^{2}\)

⇒ \(x^{2} -44x+84=0\)

⇒ \(x^{2} -42x-2x+84=0\)

⇒ \((x-42)(x-2)=0\)

So, x = 2 & 42

Here extraneous root is 42.

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Peter can have the electricity on for 18.5 hours if he wants to make a $49 profit.

We have,

Let's start by setting up an equation to represent the situation:

Profit = Revenue - Cost

We know that Peter's profit is $49, and we can find the revenue by multiplying the number of hours by the hourly rate:

Revenue = Hourly rate x Number of hours

The hourly rate is $4, and the cost includes the initial fee of $25 plus the hourly cost:

Cost = Initial fee + Hourly rate x Number of hours

Now we can substitute these equations into the profit equation and solve for the number of hours:

$49 = ($4 x Number of hours) - ($25 + $4 x Number of hours)

$49 = $4 x Number of hours - $25 - $4 x Number of hours

$49 + $25 = $4 x Number of hours - $4 x Number of hours

$74 = $4 x Number of hours

Number of hours = $74 / $4

Number of hours = 18.5

Thus,

Peter can have the electricity on for 18.5 hours if he wants to make a $49 profit.

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The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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Answer:

\(2x^{4} - 3x^{2} + 7x\)

Step-by-step explanation:

The value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the sine of angle 41°

sin 41° = 2.5/x {opposite/hypotenuse}

x = 2.5/sin 41° {cross multiplication}

x = 3.8106

Therefore, the value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

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Answer:

approx 26%

Step-by-step explanation:

you try find the multiplier

200000 * 1. ???? ^3= 400000

rearrange equation

\(\sqrt[3]{\frac{400000}{200000} }\)       =   multiplier

1.25992105

subract one

0.25992105

multiply by 100 to get percentage

25.9%

rounded to whole number = 26%

Answer:

It = 1

Step-by-step explanation:

25-24.75=0.25

0.25 / 25= 0.01

0.01 * 100 = 1

Using the monthly payment formula, it is found that the balance of the plan is of $26,731.23.

It is given by:

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which:

The parameters for this problem are given as follows:

A = 144, r = 0.06, n = (68 - 24) x 12 = 528.

Then:

r/12 = 0.06/12 = 0.005.

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

\(144 = P\frac{0.005(1 + 0.005)^{528}}{(1 + 0.005)^{528} - 1}\)

\(P = 144\frac{(1 + 0.005)^{528} - 1}{0.005(1 + 0.005)^{528}}\)

P = $26,731.23.

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The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.

The set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.

The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.

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9514 1404 393

Answer:

Step-by-step explanation:

The area of each triangular face is given by the formula ...

  A = 1/2bh

The triangular faces have a base of b=8 cm, and a height of h=6 cm. Their area is ...

  A = 1/2(8 cm)(6 cm) = 24 cm²

__

Each of the rectangular faces has a length of 20 cm. The width depends on which face is of interest. In each case, the area is given by ...

  A = LW

Bottom face: A = (20 cm)(8 cm) = 160 cm²

Back face: A = (20 cm)(6 cm) = 120 cm²

Sloped face: A = (20 cm)(10 cm) = 200 cm²

__

The total area is the sum of the areas of all of the faces and bases. There are two triangular bases, so the total area is ...

  (2×24 + 160 +120 +200) cm² = 528 cm²

The man still owes R87,726 in taxes.

To calculate the tax amount the man still owes, we need to determine his taxable income first.

Gross income: R500,000

Less: PAYE deductions (17% of gross income): R500,000 * 0.17 = R85,000

Taxable income: R500,000 - R85,000 = R415,000

Next, we can use the tax table information provided to calculate the tax owed based on the taxable income.

Tax owed: R93,135 + 36% of (taxable income - R393,200)

Tax owed: R93,135 + 0.36 * (R415,000 - R393,200)

Tax owed: R93,135 + 0.36 * R21,800

Tax owed: R93,135 + R7,848

Tax owed: R100,983

Finally, we subtract the rebate amount of R13,257 from the tax owed to find the amount the man still owes.

Tax owed - Rebate: R100,983 - R13,257 = R87,726

Therefore, the man still owes R87,726 in taxes.

The correct option is not provided among the given answer choices.

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According to the information, the missing number from the box is number 40.

To find the missing number of the table we must take into account different elements. In particular we must look at the totals and the columns and rows in which the empty space is. Once we identify the totals we can subtract the other values from the total and find the missing number in the table.

According to the above we can infer that the missing number is 40.

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In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:

its B :)

Step-by-step explanation:

i took the test

Answer:

sept one

Step-by-step explanation:

Properties of Exponential Function for Roots.

\(a^{\frac{m}{n}}=\sqrt[n]{a^m}\)

The first one is wrong as 4^1/2 would equal √4 = 2

The second choice is correct.

The third choice is correct because ∛8 = 2 and √4 also = 2

The fourth choice is wrong because √8 = 2√2

The fifth choice is also wrong because 2^1/2 would be √2 while √32 is 2^5

The sixth choice is 3^3/2 which would equal √27 = 3√3 which is correct.

Answer:

-3mn^3 and -5mn^3

Step-by-step explanation:

-3mn^3 and -5mn^3

Answer: -3mn^3 -5mn^3

Step-by-step explanation:

Answer:

f(x) = 3x2 + 5 and y = 3x2 + 5

Step-by-step explanation:

The value of expression (s - f) (- 7) would be,

⇒ (s - f) (- 7)  = 119

We have to given that,

Functions are defined as,

⇒ s (x) = 2x²

⇒ f (x) = 3x

Now, We can find the value of (s - f) (- 7) is,

⇒ (s - f) (- 7)

⇒ s (- 7) - f (- 7)

⇒ 2 (- 7)² - (3 × - 7)

⇒ 2×49 + 21

⇒ 98 + 21

⇒ 119

Therefore, The value of expression (s - f) (- 7) would be,

⇒ (s - f) (- 7)  = 119

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Using the integers −9 to 9 at most one time each, place a digit in each box (1, 3) and (9, 3) or (-9, 3) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3).

To find the endpoints of the longest possible line segment with midpoint (1, 3), we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).

In this case, we know the midpoint is (1, 3), so we can set up two equations using the variables for the endpoints (x and y) and solve for them:

(x₁ + x₂)/2 = 1

(y₁ + y₂)/2 = 3

We also know that the line segment must be as long as possible, so the endpoints should be as far away from each other as possible. To maximize the distance between the endpoints, we can choose one endpoint to be -9 and the other endpoint to be 9. This gives us:

(x₁ + x₂)/2 = 1 => x₁ + x₂ = 2

(y₁ + y₂)/2 = 3 => y₁ + y₂ = 6

Now we can solve for x₁ and y₁, since x₂ and y₂ will be 2-x₁ and 6-y₁ respectively:

x₁ + (2-x₁) = 2 => x₁ = 1

y₁ + (6-y₁) = 6 => y₁ = 3

So the endpoints of the longest possible line segment with midpoint (1, 3) are (1, 3) and (9, 3) or (-9, 3), and its length is 8 units.

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Step-by-step explanation:

The answer to the Q is=$49×5

$245

Answer:

No.

Step-by-step explanation:

Rounding to nearest ten.

66,687.232 ≈ 66,690.000.

You put a comma after rounding. There is a decimal point.

hope this helps.

904.32 is the volume.

Volume of sphere

= (4/3)πr³

= (4/3) × 3.14 × (6cm)³

= (4/3) × 3.14 × 6cm × 6cm × 6cm

= 4 × 3.14 × 2cm × 6cm × 6cm

= 904.32 cm³

Answer:

IT IS EASY FORMULAE OF SPHERE IS 4/3πr³ so,

Step-by-step explanation:

                                                    put the value,

                                              =   4/3 * 3.14 *  6³

                                              =  1.333 * 3.14 * 216

                                              =  4.18562 * 216

                                               =  904.09 cm³ ans

With the help of a linear equation, we know that 182 gallons of water would be used to wash 14 loads.

So, gallons of water used to wash 14 loads are:

Therefore, with the help of a linear equation, we know that 182 gallons of water would be used to wash 14 loads.

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Answer:

c. 30

Step-by-step explanation:

Reference angle = \( /theta \) = ?

Hypotenuse = 23

Adjacent side = 20

Thus, applying CAH:

\( Cos(/theta) = \frac{adj}{hyp} \)

\( Cos(/theta) = \frac{20}{23} \)

\( /theta = cos^{-1}(\frac{20}{23}) \)

\( /theta = 29.5918458 \) ≈ 30° (nearest degree)

We are asked to use trigonometric ratios to find the diagonal of a square whose area is 49 square feet.

Explanation

The area of a square is given by the formula below.

Therefore, we can then draw an image of the square below.