In ⊙C, DE≅FG. Select all the statements that must be true.

A. △DCE≅△FCE

B. arcDE arcFG

C. △FCE≅△FCG

D. ∠DCE≅∠GCF

E. EF≅ED

The length of XY in the congruent triangle is 8 units.

'

Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

Therefore, the triangle XYZ is congruent to the triangle MNL.

Hence,

ΔXYZ ≅ ΔMNL

Therefore,

XY = MN

XZ = ML

YZ = NL

Hence,

XY = MN = 8 units

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Answer:

x=3

Step-by-step explanation:

1.25/5.00=2/8=x/12=1/4

12=x×4

x=12÷4

x=3

Answer:

9a-2=7

Step-by-step explanation:

4a+ 5a-2=5+3-1

To simplify each side, combine like terms.

4a+5a = 9a

5+3-1 = 7

The equation becomes:

9a-2=7

A triangle with side lengths of 9, 40, and 41 is a valid right triangle.

The set of measurements 9, 40, and 41 could be the lengths of the sides of a right triangle. This is because these measurements satisfy the Pythagorean theorem,

which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, 9² + 40² = 41²,

which confirms that this set of measurements is valid for a right triangle. Additionally, 9 and 40 are both smaller than 41, which is consistent with the fact that the hypotenuse of a right triangle is always the longest side.

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The correct solution to the system of equations is (2, 0).

Looking at the data, we can observe the following coordinate pairs: (-4, -3), (0, -1), (2, 0), and (6, 2). We can calculate the slope using any two of these points. Let's take the points (0, -1) and (2, 0):

slope = (y2 - y1) / (x2 - x1)

= (0 - (-1)) / (2 - 0)

= 1 / 2

= 0.5

Therefore, the slope of the second line is 0.5, not -3/4 as previously mentioned.

Using the correct slope, we can find the equation of the second line using the point-slope form:

y - y1 = m(x - x1) (where m is the slope and (x1, y1) is a point on the line)

Using the point (2, 0):

y - 0 = 0.5(x - 2)

y = 0.5x - 1

Now, when we solve the system of equations:

y = -2x + 4 (equation 1)

y = 0.5x - 1 (equation 2)

Setting equation 1 equal to equation 2:

-2x + 4 = 0.5x - 1

Simplifying the equation:

-2.5x = -5

Dividing both sides by -2.5:

x = 2

Substituting x = 2 into equation 2:

y = 0.5(2) - 1

y = 1 - 1

y = 0

Therefore, the correct solution to the system of equations is (2, 0).

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The required total number of grams is 13.5 gram.

From figure we have,

The masses of 4 samples are the masses are 1.5 gram, 3.5 gram , 5 gram and 5 gram respectively.

To calculate the total number of grams of salt in the 3 samples with the most mass,

Add the masses of the three largest samples.

In this case,

The three largest samples are 3.5 grams, 5 grams, and 5 grams.

We have: 3.5 grams + 5 grams + 5 grams = 13.5 grams

Therefore, the total number of grams of salt in the 3 samples with the most mass is 13.5 grams.

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Answer:

[tex]\textsf{Area}=\dfrac{5\pi -3}{12} \approx 1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}[/tex]

Step-by-step explanation:

To find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector.

An isosceles triangle is made up of two congruent right triangles.

To find the height of the right triangles (and thus the height of the isosceles triangle), use the cosine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given values:

Substitute these values into the cosine ratio to calculate the height of the right triangles (and thus the height of the isosceles triangle):

[tex]\cos \left(\dfrac{5\pi}{12}\right)=\dfrac{x}{1}[/tex]

[tex]x=\cos \left(\dfrac{5\pi}{12}\right)[/tex]

[tex]x=\dfrac{\sqrt{6}-\sqrt{2}}{4}[/tex]

The base of one of the right triangles can be found by using the sine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given values:

Substitute these values into the sine ratio to determine the base of the right triangle:

[tex]\sin \left(\dfrac{5\pi}{12}\right)=\dfrac{y}{1}[/tex]

[tex]y=\sin \left(\dfrac{5\pi}{12}\right)[/tex]

[tex]y=\dfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]

The base of the isosceles triangle is twice the base of the right triangle, so the base of the isosceles triangle = 2y.

Therefore the area of the isosceles triangle is:

[tex]\begin{aligned}\textsf{Area of isosceles triangle}&=\dfrac{1}{2} \cdot \sf base \cdot height\\\\&=\dfrac{1}{2}\cdot 2y \cdot x\\\\&=\dfrac{1}{2} \cdot 2\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\dfrac{4}{16}\\\\&=\dfrac{1}{4}\sf \;square\;units\end{aligned}[/tex]

To find the area of the sector of the circle, use the area of a sector formula (where the angle is measured in radians).

[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]

Given values:

Substitute the values into the formula:

[tex]\begin{aligned}\textsf{Area of the sector}&=\dfrac{1}{2} \cdot (1)^2 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot 1 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{5\pi}{12}\;\; \sf square\;units\end{aligned}[/tex]

Finally, to find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector:

[tex]\begin{aligned}\textsf{Area of the shaded region}&=\sf Area_{sector}-Area_{isosceles\;triangle}\\\\&=\dfrac{5\pi}{12}-\dfrac{1}{4}\\\\&=\dfrac{5\pi}{12}-\dfrac{3}{12}\\\\&=\dfrac{5\pi -3}{12}\\\\&=1.05899693...\\\\&=1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}[/tex]

Therefore, the area of the shaded region is (5π - 3)/12 or approximately 1.06 square units (3 significant figures).

Answer:

[tex]\sqrt{844}=2\sqrt{211}=29.05[/tex]

[tex]\sqrt{900} =30[/tex]

[tex]\sqrt{650}=5\sqrt{26}=25.49[/tex]

[tex]\sqrt{784}=28[/tex]

[tex]\sqrt{699} =\sqrt{699}=26.43[/tex]

[tex]\sqrt{805}=\sqrt{805}=28.37[/tex]

[tex]\sqrt{729}=27[/tex]

Step-by-step explanation:

1.

[tex]\sqrt{844}[/tex]

[tex]\sqrt{2} *\sqrt{422}[/tex]

[tex]1\sqrt{422}[/tex]

[tex]1\sqrt{2} *\sqrt{211}[/tex]

[tex]1+1\sqrt{211}[/tex]

[tex]2\sqrt{211}[/tex]

[tex]29.05[/tex]

2.

[tex]\sqrt{900}[/tex]

[tex]\sqrt{9} *\sqrt{100}[/tex]

[tex]3\sqrt{100}[/tex]

[tex]3 \sqrt{25} *\sqrt{4}[/tex]

[tex]3*5*2[/tex]

[tex]30[/tex]

3.

[tex]\sqrt{650}[/tex]

[tex]\sqrt{25}*\sqrt{26}[/tex]

[tex]5\sqrt{26}[/tex]

[tex]25.49[/tex]

4.

[tex]\sqrt{784}[/tex]

[tex]\sqrt{4} *\sqrt{196}[/tex]

[tex]2\sqrt{196}[/tex]

[tex]2\sqrt{49}*\sqrt{4}[/tex]

[tex]2*7*2[/tex]

[tex]28[/tex]

5.

[tex]\sqrt{699}[/tex]

[tex]26.43[/tex]

(can't be simplified)

6.

[tex]\sqrt{805}[/tex]

[tex]28.37[/tex]

(Can't be simplified)

7.

[tex]\sqrt{729}[/tex]

[tex]\sqrt{9}*\sqrt{81}[/tex]

[tex]3*9[/tex]

[tex]27[/tex]

If the volume is 133 1/3 in³, the value of x is equal to 5 inches.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

133 1/3 = 10 × x ×  2 2/3

400/3 = 10 × x × 8/3

400/3 = 80x/3

80x = 400

x = 400/80

x = 5 inches.

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The solution of the expression, [tex](\frac{2}{3} )^{-4}[/tex] is 81 / 16.

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as multiplication, subtraction, addition etc.

Therefore, lets solve the expression as follows:

[tex](\frac{2}{3} )^{-4}[/tex]

Using exponential laws,

b⁻¹ = 1 / b

Let's apply the law to the expression as follows:

[tex](\frac{2}{3} )^{-4} = \frac{1}{(\frac{2}{3})^{4} }[/tex]

Therefore,

1 ÷ (2  / 3)⁴ = 1 × (3 / 2)⁴ = 3⁴ / 2⁴

Finally,

3⁴ / 2⁴ = 81 / 16

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Answer:

y=3x−9

Step-by-step explanation:

Answer: 4:20 and 13:65

Step-by-step explanation: First one is 4 x 5 and second one you would do 65/5

P(z<2.04) is approximately 0.9793 or 97.93% (rounded to two decimal places).

We can use a table or a calculator that offers the cumulative distribution function (CDF) of the standard normal distribution to determine the area under the standard normal curve below a specified value of z.

The chance that a standard normal random variable is less than or equal to a specified value is provided by the CDF.

In this case, we want to find the value of P(z<2.04), which represents the probability that a standard normal random variable is less than 2.04. Using a table or a calculator, we can look up the value of the CDF at z = 2.04, which is approximately 0.9793.

Therefore, we can say that the value of P(z<2.04) is approximately 0.9793, or about 97.93% (rounded to two decimal places).

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The area of Curtis's triangular frame is 36 square feet. The Option C is correct.

To get area of the frame, we will use formula for the area of a triangle which is [tex]A = 1/2 * b * h[/tex]

B = length of the base

H = perpendicular distance from the base to the vertex.

Substituting the values, we get:

A = 1/2 * 12 feet * 6 feet

A = 1/2 * 72 feets

A = 36 square feet

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Answer: 30.6 km away

Step-by-step explanation:

The main thing this problem requires is Pythagoras' theorem. So set the problem up by marking the airport as (0,0) on a graph. Then move 19 units to the right, and 24 units down and make a point. Now you have the two short lengths of a right-angle triangle, so all that's left is to solve for the hypotenuse. So using the formula [tex]a^{2} + b^{2} = c^{2}[/tex] you would end up with [tex]19^{2} + 24^{2} =c^{2}[/tex]. Then you get: 361+576=[tex]c^{2}[/tex]

solve for c and you get about 30.6 km!

Hope this helps!

The margin of error for the two-proportion 95% confidence interval is 0.0662.

The margin of error for a two-proportion 95% confidence interval can be calculated using the following formula:

ME = z√(p₁(1-p₁)/n₁ + p₂(1-p₂)/n₂)

where ME is the margin of error, z is the z-score corresponding to the level of confidence (in this case 1.96 for a 95% confidence interval), p₁ and p₂ are the sample proportions, and n₁ and n₂ are the sample sizes.

Using the given information, we have:

Sample 1: n₁ = 250, p₁ = 0.90

Sample 2: n₂ = 275, p₂ = 0.85

Level of confidence: 95%

Substituting these values into the formula, we get:

ME = 1.96√[(0.90×0.10 / 250) + (0.85 × 0.15 / 275)]

ME = 0.0662

Therefore, the margin of error for the two-proportion 95% confidence interval is 0.0662.

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Answer:

[tex]C = 11.3 \text{ cm}[/tex]

Step-by-step explanation:

We can find the circumference of the circle by using the formula:

[tex]C = 2\pi r[/tex]

↓ plugging in the given radius

[tex]C = 2\pi (1.8 \text{ cm})[/tex]

[tex]C = 3.6\pi \text{ cm}[/tex]

↓ rounding to the nearest tenth

[tex]\boxed{C = 11.3 \text{ cm}}[/tex]

The percent of sales tax on the food total is 6%.

We must first determine the 20% of the total amount of food that is the tip:

Tip = 0.2 * $32.50 = $6.50

The total cost of the meal before tax is:

Total cost before tax = food total + tip = $32.50 + $6.50 = $39.00

The cost of the lunch, including the sales tax of $1.95, is

Sales tax and the total cost before taxes = $39.00 + $1.95 =  $40.95.

The final price of the lunch, including tax and tip, is thus $40.95. You can compute the percentage of sales tax on the entire amount of food as follows:

Percent of sales tax on food = (sales tax / food total) * 100%

= ($1.95 / $32.50) * 100%

= 6%

So, the percent of sales tax on the food total is 6%.

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Answer:

[tex]\frac{13}{145}[/tex]

A bag of chips costs $0.95, a bottle of Water Costs 2*$0.95 = $1.90, and a gallon of milk costs 2*$0.95 + $1.90 = $3.80.

Let x be the cost of a bag of chips in dollars.

Since a bottle of water costs twice as much as a bag of chips, a bottle of water costs 2x dollars.

A gallon of milk costs $1.90 more than a bottle of water, so a gallon of milk costs 2x + $1.90 dollars.

Using the given information, we can set up the following equation to represent the total cost:

3(2x + $1.90) + 5(2x) + 8x = $28.50

Simplifying the equation, we get:

6x + $5.70 + 10x + 8x = $28.50

24x + $5.70 = $28.50

Subtracting $5.70 from both sides, we get:

24x = $22.80

Dividing both sides by 24, we get:

x = $0.95

Therefore, a bag of chips costs $0.95, a bottle of water costs 2*$0.95 = $1.90, and a gallon of milk costs 2*$0.95 + $1.90 = $3.80.

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Answer:

Measure of angle HEK is: 85°.

Step-by-step explanation:

Given that point E is the center of the protractor, we have:

angle HEJ = 55° (EH points to 55 degrees)

angle JEK = 30° (EK points to 30 degrees)

Since angle HEJ and angle JEK meets at a point E, then we can find angle HEK by summing up the two angles:

angle HEK = angle HEJ + angle JEK

angle HEK = 55° + 30°

angle HEK = 85°

The theorems that demonstrate that AC ⊥ BD are Angle Bisector Theorems and Perpendicular Bisector Postulate.

Recall that according to the angle bisector theorem, an angle bisector of a triangle divides the opposing side into two segments that are proportionate to the triangle's other two sides. An angle bisector is a ray that splits a given angle into two equal-sized angles.

In this case

∠1 ≅ ∠2 - Given

hence they is bisected by AX

Also ∠5 ≅ ∠6. This means that they are bisected by CX

Since AX and CX form AC, and

AC = CA (Reflexive Property)
Also

BD = DB  (Reflexive Property)

Then it means that AC ⊥ BC (QED)

Recall that the perpendicular bisector principle deals with congruent triangle segments, allowing for congruent diagonals from the vertices to the circumcenter.

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If 0 < θ < [tex]360^0[/tex] and sin θ = 0.3097, then θ is approximately [tex]24^0[/tex].

In order to find the value of θ given sin(θ) = 0.3907, we can use the inverse sine function, also known as arcsine or [tex]sin^{(-1)[/tex].

Using a scientific calculator or trigonometric tables, we can find the inverse sine of 0.3907:

θ= sin^(-1)(0.3907)

θ ≈ 23.576 degrees

Since 0 < θ < 360 degrees, we can conclude that θ is approximately 24 degrees.

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The equivalent value of the expression is A = four thousand two hundred and A = 4,200

Given data ,

Let the expression be represented as A

Now , the value of A is

A = four thousand two hundred

On simplifying the equation , we get

A = 4,200

And , when we write "four thousand two hundred," it is written in word form

Hence , the equation is A = 4,200

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1. The balances for each type of investment at the end of the third year are:

2. The total gain from all of the investments combined is $4,150.39.

a. Treasury bond:

Balance = Principal * (1 + (interest rate/100))^time

Balance = $12,000.00 * (1 + (5.35%/100))³

Balance = $13,964.18

CD:

Balance = Principal * (1 + (interest rate/100))^time

Balance = $3,000.00 * (1 + (4.75%/100))³

Balance = $3,429.57

Stock plan:

Principal = 0.3 * $30,000.00 = $9,000.00

Year 1: Increase of 9%, so balance = $9,000.00 * (1 + (9%/100)) = $9,810.00

Year 2: Decrease of 5%, so balance = $9,810.00 * (1 - (5%/100)) = $9,319.50

Year 3: Increase of 7%, so balance = $9,319.50 * (1 + (7%/100)) = $9,973.02

Savings account:

Balance = Principal * (1 + (interest rate/100))^time

Balance = $6,000.00 * (1 + (3.90%/100))³

Balance = $6,783.62

b. Treasury bond: Gain = $13,964.18 - $12,000.00 = $1,964.18

CD: Gain = $3,429.57 - $3,000.00 = $429.57

Stock plan: Gain = $9,973.02 - $9,000.00 = $973.02

Savings account: Gain = $6,783.62 - $6,000.00 = $783.62

Total gain from all investments combined = $1,964.18 + $429.57 + $973.02 + $783.62 = $4,150.39

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You saved $30,000.00 and want to diversify your monies. You invest 40% in a Treasury bond for 3 years at 5.35% APR compounded annually. You

place 10% in a CD at 4.75% APR for 3 years compounded annually. 30% you invest in a stock plan and the remainder is in a savings account at

3.90% APR compounded annually. The stock plan increases 9% the first year, decreases in value by 5% the second year, and increases by 7% the

third year.

1. What are the balances for each type of investment at the end of the third year?

2. What is your total gain from all of the investments combined?

Consignment cab be used as an option for selling the clothing

Consignment involves providing your goods to an established business, like a boutique or vintage store, which then sells the items on your behalf and takes a cut of the profits. This approach lets Drew benefit from the store's customer base and avoids the need to manage a storefront.

Mail order (option a) could also work if Drew is willing to manage shipping and handling, and has a method for advertising the products effectively without a physical or online storefront.

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(a) The sum of the interior angles of a regular octagon is 1,080⁰.

(b) The measure of one interior angle is 135⁰.

(c) The sum of the exterior angles of the octagon is 360⁰.

The sum of the interior angles of a regular octagon is calculated as follows;

The formula for sum of interior angles is given as;

sum of interior angles = (n - 2) x 180

where;

The number of sides of a regular octagon = 8

sum of interior angles = (n - 2) x 180

sum of interior angles = (8 - 2) x 180

sum of interior angles = 1,080⁰

The measure of one interior angle = 1,080 / 8 = 135⁰

The sum of exterior angles of a polygon = 360⁰, so the sum of the exterior angles of the octagon is 360⁰.

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