Which set of angle measures could be measures of the interior angle of a triangle?

Answer:

Step-by-step explanation:

Plugin I = $ 500   ,   P = $2500 and t = 4 years in the mentioned formula and find the rate of interest 'r'

I = P*r*t

\(500 = 2500 *\dfrac{r}{100}*4\\\\\\ \dfrac{500*100}{2500*4}=r\\\\\\ \)

r = 5%

Answer:

The rate of interest is 5%.

Step-by-step explanation:

Here's the required formula to find the rate of interest :

\({\star{\underline{\boxed{\tt{I = \dfrac{PRT}{100}}}}}}\)

Substituting all the given values in the formula to find the rate of interest :

\({\implies{\tt{I = \dfrac{PRT}{100}}}}\)

\({\implies{\tt{I = \dfrac{P \times R \times T}{100}}}}\)

\({\implies{\tt{500= \dfrac{2500\times R \times 4}{100}}}}\)

\({\implies{\tt{500= \dfrac{10000R}{100}}}}\)

\({\implies{\tt{R = 500 \times \dfrac{100}{10000}}}}\)

\({\implies{\tt{R = \cancel{500} \times \dfrac{100}{\cancel{10000}}}}}\)

\({\implies{\tt{R =5 \times \dfrac{100}{100}}}}\)

\({\implies{\tt{R =5 \times \dfrac{1 \cancel{00}}{1\cancel{00}}}}}\)

\({\implies{\tt{R =5 \times 1}}}\)

\({\implies{\tt{R =5 \%}}}\)

\(\star{\underline{\boxed{\tt{\red{Rate =5 \%}}}}}\)

Hence, the rate of interest is 5%.

\(\rule{300}{2.5}\)

The solution is given below.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Remember that the Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

According to this, the correct answer is: given below.

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Answer:

156°

Step-by-step explanation:

each angle of a polynomial

\(=\frac{n-2}{n} \times 180\\here~n=15\\each~angle=\frac{15-2}{15} \times 180\\=\frac{13}{15} \times~180\\=13 \times 12\\=156 ^\circle\)

Answer:

63

Step-by-step explanation:

you divide and add then subtract

Answer:

1

Step-by-step explanation:

you asked to type 1

Answer:

x = -7

Step-by-step explanation:

The 2 horizontal lines are parallel as given ion the problem.

The x + 97 angle is congruent to the right angle.

x + 97 = 90

x = -7

The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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Answer:

Domain: [-2, infinity)

Range: [-4, infinity)

Step-by-step explanation:

There's only one graph I see.

Domain is how far the graph extends on the x axis.

Range is how far the graph extends on the y axis.

Answer:

a) y= 2x +3

b) y= ¼x +1

Step-by-step explanation:

Please see the attached picture for the full solution.

Further explanation:

b) y-intercept of A= 5

y-intercept of line= 5 -4= 1

Since the gradient of the line is equal to the gradient of line A, gradient of line= ¼.

Answer:

f=20

Step-by-step explanation:

each rectangle = 8in

8+8=16

36-16= 20

Answer:

-3,-1

Step-by-step explanation:

The point where they intersect is -3,-1

Hope this helps :D Please mark brainliest if correct :D

Answer:

it's going to be 3,3 is the answer

To calculate the area of the doughnut, we need to calculate the area of the larger circle and substract the area of the smaller circle.

The area of a circle can be calculated using its radius:

The diameter of the larger circle is 6cm which meand that its radius is half as large, so the radius is 3 cm and the area of the larger circle is:

Area of 9π cm².

The smaller one have a diameter of 2 cm, so its radius is half as large, radius of 1 cm.

So, the area of the smaller circle is:

Area of π cm².

The total shaded area is, then, the area of the larger minus the area of the smaller.

So, the shaded area is:

Answer:

Therefore, the interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.

Step-by-step explanation:

In statistics, the 68–95–99.7 rule, also recognized as the Empirical rule, is a shortcut used to recall that 68%, 95% and 99.7% of the values lie within one, two and three standard deviations of the mean, respectively.

Then,

P (µ - σ < X < µ + σ) = 0.68

P (µ - 2σ < X < µ + 2σ) = 0.95

P (µ - 3σ < X < µ + 3σ) = 0.997

he random variable X can be defined as the  amount of time a certain brand of light bulb lasts.

The random variable X is normally distributed with parameters µ = 1300 hours and σ = 90 hours.

Compute the interval of hours that represents the lifespan of the middle 68% of light bulbs as follows:

Thus, the interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.

Answer:

For the question, we are looking at two congruent triangles (as marked by ≅). They give us three lines and ask us to find the congruent segment on the opposite triangle.

Things to remember:

ΔBCD ≅ ΔUWV

This means UW is ≅ to BC.

VU is ≅ to DB and,

WV is ≅ to CD.

The next one is as follows.

ΔKML ≅ Δ LUS

This means MK is ≅ to SL

KL is ≅ to LU  and,

LM is ≅ US.

Step-by-step explanation:

hope this helps. . .<3

good luck!       UwU

Answer:

513.45

Step-by-step explanation:

use intelligence

Answer:

C. & D

Step-by-step explanation:

This would be the answer since countering the others it's 90 degrees. While the others are able to add up to 180 degrees. :)

Given

The objective is to solve for y, that is, isolate the y-term in one side of the expression.

The first step is to pass "-1/5y" to the left side of the expression by applying the inverse operation

Next pass "+2" to the right side of the expression

Finally multiply both sides by -5

Answer:

Mean = 59.1, Median = 61

(there might have been a mistake in calculation (a lot of numbers!))

Step-by-step explanation:

The sample size is 40,

Now, the formula for the mean is,

Mean = (sum of the sample values)/(sample size)

so we get,

\(Mean = (49+63+78+22+41+39+75+61+63+65+58+37+45+52+81+75+78+72+68+59+72+85+63+61+75+39+41+48+59+55+61+25+61+52+58+71+75+82+49+51)/40\\Mean = 2364/40\\Mean = 59.1\)

To find the median, we have to sort the list in ascending (or descending)order,

we get the list,

22,25,37,39,39,41,41,45,48,49,

49,51,52, 52,55,58, 58, 59, 59, 61,

61, 61, 61, 63, 63, 63, 65, 68, 71, 72,

72, 75, 75, 75, 75, 78, 78, 81, 82, 85

Now, we have to find the median,

since there are 40 values, we divide by 2 to get, 40/2 = 20

now, to find the median, we takethe average of the values above and below this value,

\(Median = ((n/2+1)th \ value + (n/2)th \ value )/2\\where, \ the\ (n/2)th \ value \ is,\\n/2 = (total \ number \ of \ samples) /2\\n/2=40/2\\(n/2)th = 20\\Hence\ the (n/2)th \ value \ is \ the \ 20th \ value\)

And the (n+1)th value is the 21st value

Now,

The ((n/2)+1)th value is 61 and the nth value is 61, so the median is,

Median = (61+61)/2

Median = 61

Step-by-step explanation:

12

Answer:

11

Step-by-step explanation:

11+12+13 =36

So  Kate would be 11. Bradley would be 12. And Cameron would be 13

Answer:

1 ÷ \(\sqrt{n\\}\) = x

Step-by-step explanation:

For the given, "the quotient of 1 and the square of a number", the expression is 1+√n

A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, Mathematicians have the ability to multiply, divide, add, and subtract. A mathematical operator, a number or variable, and an expression make up an expression.

The phrase "The quotient of 1 and the square of an integer" is presented.

The dividend and the amount being divided by the divisor are, respectively, referred to as the dividend and the amount being divided by it. The quotient is created by dividing the result.

If n is the number the expression can be written as,

=1+√n

Thus, for the given expression the expression is 1+√n.

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Answer:

(x+4)^2  -25

Step-by-step explanation:

x²+8x-9 in the form  (x+k)² +h.

We need to complete the square.

x^2 +8x   -9

Take the coefficient of x.

8

Divide by 2.

8/2 =4

Square it.

4^2 = 16

Add this then subtract i.

x^2 +8x+16    -16   -9

The x^2 +8x+16 becomes  (x+4) ^2  and we can simplify the remaining terms.

(x+4)^2  -25

Answer:

595.

Step-by-step explanation:

Take $2000 and subtract $810 from it. You now have the total of the two pieces of equipment without the extra pricing. You should get $1,190. Then divide that number by 2. You will get $595.

1st Piece of Equipment = $595

2nd Piece of Equipment = $1,405

2nd Piece is $810 more expensive and the two pieces combined is $2,000.

Answer:

Equation of line is given as y = mx + c, where m is the gradient/slope and c is the y-intercept.

First, rearrange 2y - x = 8 into y = mx + c form so that we can find out the gradient of the line.

2y - x = 8

2y = x + 8

y = 1/2x + 4

Since parallel lines have the same gradient, equation of line is y = 1/2x + c.

Substitute (14,3) into the equation to find c.

3 = 1/2(14) + c

3 = 7 + c

c = -4

Hence, equation of line is y = 1/2x - 4.

The domain of the quadratic function in this problem is given as follows:

All real values.

The domain of a function is the set of all the possible input values that can be assumed by the function.

On the graph, the domain of the function is given by the values of x of the function.

A quadratic function has no restrictions on the domain, hence it is defined by all the real values.

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The value of f(5) is positive

At f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, the values of x are [-2, 1]

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have

f(5) = 1

This means that f(5) is positive

Also, we have

When f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, we have the values of x to be

-2 ≤ x ≤ 1

When represented as an interval, we have

[-2, 1]

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The given polynomial is expressed as

P(x) = - 3x^2 + 9x

The domain values are the x values. To find P(-5), it means that we would substitute x = - 5 into the polynomial. It becomes

P(- 5) = - 3(- 5)^2 + 9(- 5)

P(- 5) = - 3 * 25 - 45

P(- 5) = - 75 - 45

P(- 5) = - 120

Answer:

The speed of the flying carpet in still air is 15.2 mph

Step-by-step explanation:

Answer:

15.2

Step-by-step explanation:

Do the math

Answer:

22x-12y

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THANK YOU.

Answer:

I think it's 27

because length is 3 times its width