In the diagram below DE bisects ∠BAC. Answer the following questions.(a) If m∠BAC=80° then find m∠BAE and m∠BAD.(b) If m∠BAC= 2x then find an algebraic expression for m∠BAD that involves x.(c) If m∠DAC=122° find m∠CAB

Answer:

78

Step-by-step explanation:

The weight of one box is:

468 ÷ 6 = 78

Hi student, let me help you out!                            ✨

......................................................................................................................................

If 6 boxes of cookies weigh 468 grams, then we need to divide the total weight of the boxes by the total number of boxes, and we'll find the weight of one box: \(\mathtt{468\div6=78\:Grams}\).

∴ the weight of one box of cookies is ✨\(\bigstar\underline{\mathtt{78\:grams}}\).

Hope this helped you out, ask in comments if any queries arise. :)

Answer:

Step-by-step explanation:

= 13/20*100

= 60

David spent 60% of his money which was in his wallet.

Answer:

x = -15

Step-by-step explanation:

In fractional equations we cross multiply the expressions:

In cross multiplying the denominator of the first fraction is multiplied with the numerator of the second fraction and vice versa:

-2x = 30 divide both sides by -2

x = -15

Answer:

Let the number be x. Then, 4/5x - 3/4x = 4. Hence, The required number is 80.

Step-by-step explanation:

Let the number be x.

According to the question, lets form an equation

5

4x −4

3x +4

⇒ 5 4x − 4

3x =4

20

16x − 15x​ =4

⇒ 20x =4

⇒ x=4×20

⇒x=80

∴ The number is x=80.

Answer:

715000

Step-by-step explanation:

1300000 • 55%,

55% = 0.55

1300000 • 0.55 = 715000

Answer:

The scientific notation is a method of writing very large or very small numbers in a more compact and easy to read format. It is expressed in the form of a x 10^n, where "a" is a number between 1 and 10, and "n" is an integer.

To write 464000 in correct scientific notation, we need to move the decimal point to the left until we get a number between 1 and 10. We count the number of places we moved the decimal point, and that will be the exponent of 10.

So, we can write 464000 as:

4.64 x 10^5

Therefore, the correct scientific notation of 464000 is 4.64 x 10^5.

Step-by-step explanation:

Answer: 3/8 yard

Step-by-step explanation:

Since the beetle crawled 1/2 of a yard and the spider crawled 1/8 of a yard. To calculate how much farther the beetle crawl than the spider, we will have to subtract 1/8 from 1/2. This will be:

= 1/2 - 1/8

= 4/8 - 1/8

= 3/8 yard

Therefore, the beetle covered 3/8 yard more.

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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(49,5), (19,10), (9,20), (4,50), (1,100) are the only pairs of positive integers (a,n) such that n is greater than 2 and a + (a + 1) + (a + 2) + ... + (a + n - 1) = 100.

In mathematics, an integer is a number that can be written without a fractional or decimal component.

To start, we can use the formula for the sum of an arithmetic series to find the value of n.

The formula for the sum of n terms in an arithmetic series is given by

=> S = n/2 (a + a + n - 1),

where a is the first term and n is the number of terms. Substituting the values from the problem, we have:

=> 100 = n/2 (2a + n - 1)

Expanding the right side, we get:

100 = n/2 (2a + n - 1)

Multiplying both sides by 2 and rearranging, we get:

200 = n (a + n/2)

Dividing both sides by n, we get:

a + n/2 = 200/n

Since n is an integer greater than 2, we know that n must divide 200. To find all possible values of n, we can use the divisibility rule for 2, which states that an integer is divisible by 2 if and only if its last digit is 0, 2, 4, 6, or 8. Thus, we can list all possible values of n as follows:

=> n = 2, 4, 5, 8, 10, 20, 25, 40, 50, 100

For each value of n, we can use the formula for a to find all possible values of a that satisfy the conditions of the problem. Substituting n = 2 into the formula for a, we get:

=> a + n/2 = 200/n

=> a + 1 = 200/2

=> a = 199/2

Since a is a positive integer, we see that a = 199/2 is not an integer, so the pair (a,n) = (199/2,2) is not a solution. Continuing this process for each value of n, we find the following pairs of positive integers (a,n) that satisfy the conditions of the problem:

=> (a,n) = (49,5), (19,10), (9,20), (4,50), (1,100)

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The value of DP is 35.5.

Let's denote the radius of the circumcircle of AABC as R. Since P is the circumcenter of AABC, we know that PA = PB = PC = R. From the given information, we know that PC = 35, so R = 35.

Next, let's use the Pythagorean theorem to find DP. We have two right triangles: APD and BPD. Let's start with triangle APD. We know that PA = R = 35 and AD = 7x - 6. Using the Pythagorean theorem, we have:

DP² = PA² + AD²

DP² = 35² + (7x - 6)²

DP² = 1225 + 49x² - 84x + 36

Next, let's use the Pythagorean theorem on triangle BPD. We have PB = R = 35 and DB = 5x + 8. Using the Pythagorean theorem, we have:

DP² = PB² + DB²

DP² = 35² + (5x + 8)²

DP² = 1225 + 25x² + 160x + 64

Since DP is the same in both triangles, we can equate the two expressions for DP²:

1225 + 49x² - 84x + 36 = 1225 + 25x² + 160x + 64

24x = 128

x = 128/24

x = 5/2

Substituting x = 5/2 into the expression for AD or DB, we get:

AD = 7 × 5/2 - 6 = 15/2

DB = 5 × 5/2 + 8 = 25/2

Finally, substituting x = 5/2 into the expression for DP, we get:

DP² = 35² + (7 × 5/2 - 6)²

DP² = 35² + (15/2)²

DP² = 35² + 15²/4

DP² = 1225 + 225/4

DP² = 1225 + 56.25

DP = 35.5

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Answer:

1.)1804

2.)1827

3.)2286

4.)1473

5.)6489

6.)3448

7.)1122

8.)5467

9.)4755

10.)1524

Step-by-step explanation:

hope it helps:)

From matrix property it can be showed that A=B.

Given,

If A,B and x are matrices with x≠0 and AX=BX

Now,

X must be non-singular matrix because

A\(XX^{-1}\)=B\(XX^{-1}\)

AI = BI

= I( identity matrix )

⇒A = B

Hence Proved, A = B .

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Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.

We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.

Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.

Therefore,  y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.

Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.

Simplifying, we have :3x = $90000 + 75 = $90075.

Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.

Therefore, Jane received $30025 and Lydia received $60000.

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Answer: 17x - 39

Step-by-step explanation:

1) Find all sides of the hallway.

P = 4x-9 + x-2 + x+2 + 3x - 11 + x-2 + 3x - 11 + x+4 + 2x-9 + x-1

2) Add it together

P= 17x - 39

Answer:

three

Step-by-step explanation:

stem. is the tens place and the leaf is the. ones place

so you want to find 68 so you look in the stem column and look for six

in the row there are 6 numbers which mean:

60, 61, 67, 68, 68, 68

as you can see there is three 68 there for the answer ths 3

Answer:

a = 8

b = 2

c = 48

Step-by-step explanation:

3 cups of flour is needed to make 24 servings.

3:24

Simplify. First, divide 3 from both sides of the ratio.

(3)/3 : (24)/3

1:8

Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1

1 x 2 = b = 2

Finally, multiply 8 to 6 to get c.

8 x 6 = c = 48

~

The equation of the circle in standard form with a center at (-6, 5) and passing through the point (-11, 3) is (x + 6)² + (y - 5)² = 29.

The equation of a circle in standard form with a center at (h, k) and a radius r is:

(x - h)² + (y - k)² = r²

Center: (h, k) = (-6, 5)

Point on circle: (-11, 3)

Substituting these values into the standard form equation:

(x - (-6))² + (y - 5)² = r²

(x + 6)² + (y - 5)² = r²

Now we need to find the value of r, which is the radius of the circle.

The distance between the center (-6, 5) and the point (-11, 3) is equal to the radius of the circle.

Using the distance formula:

r = √((x₂ - x₁)² + (y₂ - y₁)²)

r = √((-11 - (-6))² + (3 - 5)²)

r = √((-5)² + (-2)²)

r = √(25 + 4)

r = √29

r² = 29

The equation of the circle:

(x - h)² + (y - k)² = r²

(x + 6)² + (y - 5)² = 29

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Answer:

$1.06 to thousendth is the tax

Step-by-step explanation:

13.30*2/25=Your answer

Answer:

2

Step-by-step explanation:

If he sells and makes x paintings, his expenses will he 10+45x and his revenue will be 50x.

The break-even point is the point at which total cost and total income are equal. For breakeven, Lamar needs to sell 2 paintings.

In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even."

Let the number of paintings that Lamar makes and sells at the break-even point be represented by x.

Given that Lamar bought some brushes for $10, and paint and canvas for each painting cost $45. Therefore, the total cost of making x number of paintings is,

Total cost of x painting = $10 + $45(x)

Also, the selling price of each painting is $50. Therefore, the revenue generated from x paintings is,

Revenue generated = $50(x)

Further, at the breakeven point, the total cost of production of any product is equal to the revenue generated by the product. Therefore, we can write,

Total cost of x painting = Revenue generated

$10 + $45(x) = $50(x)

10 + 45x = 50x

10 = 50x - 45x

10 = 5x

x = 10/5

x = 2

Hence, For breakeven Lamar needs to sell 2 paintings.

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Answer:

Step-by-step explanation:

As the problem is written, you have ...

  \(\dfrac{x}{4} =x+\dfrac{1}{5}\\\\5x=20x+4\qquad\text{multiply by 20}\\\\-15x=4\\\\x=-\dfrac{4}{15}\)

__

If you add parentheses to include x in the numerator, then you have ...

  x/4 = (x +1)/5

  \(5x=4(x+1)\qquad\text{multiply by 20}\\\\5x -4x = 4\qquad\text{eliminate parentheses, subtract 4x}\\\\x=4\)

__

Additional comment

We include the second working because it is a fairly common mistake to neglect to put parentheses around a numerator or denominator. The solutions to such problems are not often fractions, so we suspect you intend the latter form.

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \pounds 2200\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 2200[1+(0.10)(2)] \implies A = 2200(1.2)\implies A = 2640\)

Answer:

Your answer is every number is divided by 4

Step-by-step explanation:

so for the 4th term it would be 3/4, then divide that by 4, and then divide that by 4, and so on and so forth.

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

Brian is constructing figures inscribed in circle C.

Equilateral triangle MNQ inscribed in circle C:

This option is possible since the points M, N, and Q are labeled and they lie on circle C.

Equilateral triangle ANP inscribed in circle C:

This option is not possible. The points A and P are labeled, but the third vertex of the equilateral triangle is not specified.

Regular hexagon AMNBPQ inscribed in circle C:

This option is possible since the points A, M, N, B, P, and Q are labeled and they lie on circle C.

Square MNPQ inscribed in circle C:

This option is not possible based on the given information. The label points do not form a square.

Square ANBQ inscribed in circle C:

This option is not possible . The points A, N, B, and Q are labeled, but they do not form a square.

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

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The lake frontage of plot B is about 73.5 yds

To determine the lake frontage of lot B, we will apply similar shapes theorem

In similar shapes, the ratio of corresponding sides are the same.

The arrows with same colour represent corresponding sides

Considering the whole property:

192 yd corresponds to the length (45 + 62 + 55)

192 yd corresponds to 162 yd

Considering Lot B:

let the frontage of Lot B = B

th frontage corresponds to the length 62 yd

The ratio of corresponding sides:

cross multiply:

Answer:

The base = 24 in

The height = 16 in

Steps:

x(x-8)/2 = 192

(x²-8x)/2 = 192

x²-8x = 192 × 2

x²-8x = 384

x²-8x-384 = 0

by using the quadratic formula, the roots are: (24, -16)

hence

x = 24

The base = 24 in

The height = 16 in

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Answer:

\( x = 5 \)

Step-by-step explanation:

Given that segment EJ bisects angle DEF, it implies that angle DEF is divided into two equal angles, namely, angle DEJ = 5x + 7, and angle JEF = 8x - 8.

To find the value of x, let's derive an equation by setting m<DEJ equal to m<JEF, since both are equal parts of angle DEF bisected by segment EJ.

Thus:

\( 5x + 7 = 8x - 8 \)

Solve for x

\( 5x + 7 - 8x = 8x - 8 - 8x \) (subtracting 8x from both sides)

\( -3x + 7 = - 8 \)

\( -3x + 7 - 7 = - 8 - 7 \) (Subtracting 7 from both sides)

\( -3x = -15 \)

\( \frac{-3x}{-3} = \frac{-15}{-3} \) (dividing both sides by -3)

\( x = 5 \)

Answer: The radius of the circle is 5 3/8 inches.

Step-by-step explanation:

The radius of the circle is half of the diameter. We can start by converting the mixed number diameter to an improper fraction:

10 3/4 = (10 × 4 + 3)/4 = 43/4

So, the diameter of the circle is 43/4 inches. The radius is half of this, which we can find by dividing by 2:

r = (43/4) ÷ 2 = 43/8

To simplify the fraction, we can divide the numerator and denominator by their greatest common factor (GCF), which is 1:

r = 43/8 = 5 3/8

Therefore, the radius of the circle is 5 3/8 inches.

Answer:5 3/4

Step-by-step explanation:

10 3/4 * 1/2

1/2 * 43/4 = 43/8

8/43=5 3/4

Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.