Are the triangles congruent using AAS?
True
False

During a basketball game, you made 11 shots of either 2 or 3 points. You scored a

total of 25 points. How many shots of each point value did you make?

Let

x -----> number of shots of 2 points

y -----> number of shots of 3 points

we have that

x+y=11

x=11-y -----> equation A

and

2x+3y=25 -----> equation B

substitute equation A in equation B

2(11-y)+3y=25

solve for y

22-2y+3y=25

y=25-22

y=3

Find the value of x

x=11-3

x=8

therefore

The length of AC is given by AE + EC

According to the Pythagorean Theorem, we know that:

AE² = AD² - ED²

AE² = 5² - 3²

AE² = 25 - 9

AE² = 16

AE = 4

EC² = DC² + ED²

Since DC = BC, we have:

EC² = BC² + ED²

EC² = 45 - 9

EC² = 36

EC = 6

Therefore, AC = 4 + 6 = 10

Answer: D. 10

Answer:

Step-by-step explanation:

Starting from tan x, you can find sec x, because of the trigonometric identity 1 + tan2 x = sec2 x.

1 + (-4/3)2 = 1 + 16/9 = 25/9 = sec2 x.

So sec x = ±√(25/9) = ±5/3.  But since x is in Quadrant II, sec x has to be negative.  That's because sec x has the same sign as cos x, because sec x = 1 / cos x.  We know that cos x is negative is Quadrant II, therefore so is sec x.  So sec x = -5/3.

Since sec x and cos x are reciprocals of each other, cos x = 1/sec x = -3/5.

Now use the identity sin2 x + cos2 x = 1, to find sin x:

sin2 x + (-3/5)2 = 1

sin2 x + 9/25 = 1

sin2 x = 16/25

sin x = ±4/5

Again, we know that sin x is positive in Quadrant II, so sin x = 4/5.

Now that we know sin x and cos x, we can use the double angle formulas to find sin 2x and cos 2x.

sin 2x = 2 sin x cos x = 2 (4/5) (-3/5) = -24/25

cos 2x = cos2 x - sin 2 x = (-3/5)2 - (4/5)2 = 9/25 - 16/25 = -7/25

Finally use the identity tan x = sin x / cos x to find tan 2x:

tan 2x = sin 2x / cos 2x = (-24/25) / (-7/25) = -24/-7 = 24/7

Let's call C the weight of the Cashews and B the weight of the Brazil nuts.

Since the professor wants to sel a 32 pound mixture, we have the following equation:

Now, since the price of the mixture will be $5.37 per pound, this means the price of the whole mixture will be

This leads us to the followin equation:

Now we have a system of equations:

To solve it, let's isolate one of the variables in the first equation by subtracting B from both sides of it:

Now, let's use this value of C in the second equation:

To solve this equation, let's subtract 198.4 from both sides of it:

Then, let's divide both sides by -1.9:

Using this value of B in the first equation will give us:

These would be the values of B and C round to two decimals. If we want, we can also write them as integer numbers. so the mix would need to have 18 pounds of cashews and 14 pounds of Brazil nuts.

Answer:

54 x 5

Step-by-step explanation:

the first figure out the brackets, then multiply by 5.

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Answer:

the answer is 6 ^ 15 you are very welcom

EXPLANATION

Let's see the facts:

The angles of symmetry in point A is 60 degrees because the plane in point A is divided in 6 parts, so dividing 360° by 6 give us 60°. The same reasoning applies for the point B dividing it by 3 parts.

The angles of symmetry in point B is 120 degrees.

Answer:

The answer is -23/2 or -11.5

Step-by-step explanation:

Given:

Set U: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

Set P: {2, 3, 5 7, 9, 11, 13, 17, 19}

Questin 7.

Complement of set P.

The complement of set P will be the set that contains the elements present in set U but not in P.

Hence, we have:

ANSWER:

P' = {1, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20}

She cannot afford to buy the car with monthly instalments of $350. She needs to make a downpayment of $856.44 to afford the car

The total amount of the car loan = 13456.44

Number of instalments = 36 monthly payments

Affordable installment per month = $350

EMI: A fixed payment is made by a borrower to a lender at a specific time each month, known as an equated monthly instalment (EMI). The loan is repaid in full over a predetermined period of time by making equal monthly payments to the principal and interest.

Total payment that can be made using the instalments = Monthly instalments * Number of instalments

= 350*36

Total payment that can be made using the instalments = 12600

The amount remaining after paying instalments = 13456.44 - 12600

= 856.44

Downpayment required = $856.44

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The amount of money should be invested to obtain interest of amount 50000$ is 34,000$(approximately)

The practice of adding interest to the principal amount of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. Reinvesting interest, or adding it to the lent capital rather than paying it out or seeking repayment from the borrower, results in interest being received on the principal amount plus interest collected previously.

[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]

Where,A is the total sum.

P equals the initial principal amount.

The nominal yearly interest rate is r.

The compounding frequency is n.

t is the total amount of time that the interest is charged (expressed using the same time units as r, usually years).

The final value less the beginning investment yields the entire compound interest.

On substituting the values we get that initial investment of approximately 34000$

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As we can see, there are 8 parts in our circle but 4 parts belong to wedge 2 and 5. Then, the probability of landing on 4 or 6 is given by

because part 4 and part 5 are disjoint sets. Since there are 8 parts in our circle, we have

which gives

which corresponds to option B

Based on the given equivalences, you have:

7 m = 7(100 cm) = 700 cm

700 cm = 700 (2.54 in) = 1,778 in

Hence, there are 1,778 inches in 7 meters

Answer:

{48, 55,73}

Explanation:

To determine if any three side lengths can form a right triangle, we check if it satisfies the Pythagorean Theorem.

Therefore, the side lengths that could form a right triangle are {48, 55,73}.

To make things easier to understand, let's see this figure, which represents the given situation:

According to this diagram, to find x, which is the length of the side of the triangle, we can use pythagorean theorem, this way:

The given function is increasing over these following intervals:

B. -2 ≤ x ≤ -1.

C. 0 < x < 1.

Considering the given definitions on the bullet points above, the behavior of the function can be separated as follows:

Items B and C have subsets of the interval -2.5 ≤ x ≤ 2.5, hence the function is increasing on those intervals, and they are the correct options for this problem.

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You have to find a line perpedicular to the line y=1/2x-3 that passes through the point (-5,2)

Given one line, to find another one perpedicular to it, you have to keep in mind that the slope of the perpedicular line is the negative inverse of the slope of the first one, that is:

Let the given line be:

And the perpendicular line

The slope of the perpendicular line will be:

So for the line

The slope is

For the perpedicular line it will be:

Now that the slope of the perpendicular is determined, use the point slope form to find the equation of the perpedicular line:

Replace the with m=-2 and (-5,2)

The equation perpendicular to

is

Now you can draw both lines:

The coordinate pair is between the third and fourth quadrants, on the y-axis.

Remember that the quadrants are:

First quadrant: x > 0, y > 0.

Second quadrant: x < 0, y > 0.

Third quadrant: x < 0, y < 0.

Fourth quadrant: x > 0, y < 0.

In this case our coordinate pair is (0, -1/2).

So it will be between the third and fourth quadrants.

And yes, because one of the variables is zero, it is on the y-axis (just between the two quadrants).

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Answer:

B

Step-by-step explanation:

if the number is x then 3 times the number is 3x

the difference is the subtraction of 3x and 4 , that is

3x - 4

Answer:

  (d)  Isosceles right

Step-by-step explanation:

You want to know the classification of a triangle with angles 45°-45°-90°.

The largest angle is 90°, a right angle. Any triangle containing a right angle is a right triangle.

Two of the angles have the same measure. This means the triangle is an isosceles triangle.

The triangle is classified as an isosceles right triangle.

__

Additional comment

A triangle whose largest angle is less than 90° is an acute triangle. If the largest angle is greater than 90°, it is an obtuse triangle.

If no sides are the same length, the triangle is scalene. If two sides are the same length, the triangle is isosceles. If all three sides are the same length, it is an equilateral triangle.

Larger angles are opposite longer sides, so if angles are the same, their opposite sides are the same.

It can be worthwhile to remember that the side length ratios in an isosceles right triangle are 1 : 1 : √2.

The years of education as per the given equation, for a person whose father had 14 years of education is 14.966 years.

What is education?

A planned activity, education has objectives like knowledge transmission or character and skill development. The development of understanding, reason, kindness, and honesty may be some of these goals.

As given in the question,

respondent's years of education is represented by y, and

respondent's father years of education is represented by x,

The equation for the least squares regression line for predicting a respondent's years of education is given as:

y = 9.996 + 0.355x

The year of education of respondent's father is given as 14

So putting the value of x in the given equation as 14:

we get,

y = 9.996 + 0.355(14)

y = 14.966

Hence, the years of education for a person whose father had 14 years of education is 14.966 years.

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The cost for 1 liter of premimum gasolinz is 1. 182 times greater

A ratio can be described as the ordered pair of numbers, like x and y, written in the form of a rational numbers, x/y with the denominator greater than zero.

It is also described as the number of times a number or element would contain another one.

It is also known to compare two quantities, elements or numbers.

From the information given, we have that;

To determine the value, we have;

Cost of 1 liter of 25 liters in permimum gasoline/Cost of 1 liter of 25 liters in regular gasoline

substitute the values

$69.73/ $58.98

Find the quotient

1. 182

Hence, the value is 1. 182

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The tanker has been filling the reservoir for 0.0288 minutes or 1.728 seconds as the rate of filling is 1212 gallons per minute using the estimation concept.

As per the question statement, A tanker truck fills the gas station’s reservoir at the rate of 1212 gallons per minute and the reservoir was empty and it is now 35 gallons full. We are supposed to find out for how long has the tanker been filling the reservoir. We will use the concept of estimation.

Rate of filling gas = 1212 gallons per minute

i.e., 1212 gallon of gas taken 1 minute for transfer.

1 gallon of gas will take = (1/1212) minutes

Hence 35 gallons of gas will take = (1/1212)*35 minutes = 0.0288 min.

So, the  tanker has been filling the reservoir for 0.0288 minutes or 1.728 seconds as the rate of filling is 1212 gallons per minute.

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Answer:

The expression is given below as

Concept:

We will have to explain the options so we can figure out what the final answer is

Sum:

The result is obtained by adding numbers

Quotient:

a quotient is a quantity produced by the division of two numbers.

Product:

A product is the result of multiplication,

Factor:

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.

Step 1:

We will then have to deal with the parenthesis

We will then have to multiply 7 by 16 before adding to 10

Hence,

7 in the expression above represents a factor because after adding 3 and 13, you would need to multiply 2 and 5. Then, you will multiply 7 and 16 which shows that 7 in the expression above represents a factor. 7 is a factor common to both 3 and 16

Therefore,

The final answer is OPTION A

The area of the square is 16 square inches.

The area of a square is calculated by multiplying a side by itself.

In this case, the side S is replaced by 4 in, then:

Answer:

first one is 80

Step-by-step explanation:

i did it

The total area for the parallelogram-shaped tiles Felix needs to buy exists 80cm² at the price of $40.

In calculating the area of a parallelogram, the base exists multiplied by the height, in an exact way as computing the area of a rectangle.

Given that, the base of one parallelogram-shaped tile exists 4cm with a height of 2 cm.

Area of one parallelogram shaped tile = 4cm × 2cm

Area of one parallelogram-shaped tile = 8cm²

Total area for the 5black and 5white tiles = 10 × 8cm²

Total area for the 5black and 5white tiles = 80cm²

Therefore, Felix must buy a total area of 80cm² of 10 parallelogram-shaped tiles.

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