Classify the triangle based on the side lengths 7. 15 and 21​

Answer:

y= 2/3x + 2

Step-by-step explanation:

Answer:

The equation of the line is y = 2x - 3

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

Let us take two points on the line to find its equation

∵ Points (3, 3) and (0, -3) lie on the line

∴ x1 = 3 and y1 = 3

∴ x2 = 0 and y2 = -3

→ Use the rule of the slope above to find m

∵ \(m=\frac{-3-3}{0-3}=\frac{-6}{-3}=2\)

∴ m = 2

→ Substitute its value in the form of the equation above

∴ y = 2x + b

∵ b is the value of y at x = 0

∵ y = -3 at x = 0

∴ b = -3

→ Substitute it in the equation above

∴ y = 2x + -3

→ Remember (+)(-) = (-)

∴ y = 2x - 3

∴ The equation of the line is y = 2x - 3

Answer:

descrease & increase

Step-by-step explanation:

Answer:

Decrease and increase.

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

divide both numbers to find how much in 1 min.

Answer: 2.5

Step-by-step explanation:

use a calculator to divide 50/20 = 2.5

to check your work, 2.5 * 20 = 50

The sample  should consist of  180 students at least in order for the dean take to ensure this is true.

since we are provided a standard deviation of 2.6 hours, we need to find the sample size at most of 0.5 hours. Since we know

E = z∗ σ/√n, where z is the score,σ is the standard deviation and n is the sample size. According to this case, z∗ will be 2.576 since the dean wants 99% confidence.  so the sample size will be

n=(z∗σ /E)^2

   = (2.57* 2.6/0.5)^2

  =  179.43 =  180

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Answer:

your answer is 8

hope this helped

Answer:

8

Step-by-step explanation:

|-7 - 1|

=> |-8|

=> 8

' | | ' represents absolute value

Absolute value of -ve number is +ve

Absolute value of +ve number is + ve

To find the point of intersection between the curves r1(t) = (t, 5 - t, 48 + t^2) and r2(s) = (8 - s, s - 3, s^2), we need to equate their respective components and solve for the common parameter.

Setting the x-component equal, we have t = 8 - s. Substituting this into the y-component equation, we get 5 - t = s - 3. Simplifying this equation gives t + s = 8.

Next, we equate the z-components: 48 + t^2 = s^2. Rearranging this equation gives t^2 - s^2 = -48.

We now have a system of equations:

t + s = 8

t^2 - s^2 = -48

Solving this system of equations yields two solutions: (t, s) = (4, 4) and (t, s) = (-4, -4).

Therefore, the curves intersect at two points: (4, 1, 64) and (-4, 7, 64).

To find the angle of intersection between the curves, we can calculate the dot product of their tangent vectors at the point of intersection and use the formula:

cos(theta) = (T1 · T2) / (||T1|| ||T2||)

where T1 and T2 are the tangent vectors of the curves.

The tangent vector of r1(t) is T1 = (1, -1, 2t), and the tangent vector of r2(s) is T2 = (-1, 1, 2s).

At the point of intersection (4, 1, 64), the tangent vectors are T1 = (1, -1, 8) and T2 = (-1, 1, 8).

Calculating the dot product: T1 · T2 = (1)(-1) + (-1)(1) + (8)(8) = 63.

The magnitude of T1 is ||T1|| = sqrt(1^2 + (-1)^2 + 8^2) = sqrt(66), and the magnitude of T2 is ||T2|| = sqrt((-1)^2 + 1^2 + 8^2) = sqrt(66).

Substituting these values into the formula, we get:

cos(theta) = 63 / (sqrt(66) * sqrt(66)) = 63 / 66 = 3 / 2.

Taking the inverse cosine of both sides, we find theta = arccos(3/2).

The angle of intersection between the curves is arccos(3/2).

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80 miles must be driven in a day to make the rental cost for company A a better deal than company B

according to the question

company A for $90 a day plus $0.30 per mile

company B charges $50 a day plus $0.80 per mile to rent the same truck

90+0.30m = 50 +0.80m

0.50 m= 40

m =40/0.50

m = 4000/50

m= 80 miles

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Answer:

Step-by-step explanation:

102

Given:

The piecewise function is

\(f(x)=\begin{cases}x+4 & \text{ if } -4\leq x<3 \\ 2x-1 & \text{ if } 3\leq x<6 \end{cases}\)

To find:

The range of given piecewise function.

Solution:

Range is the set of output values.

Both functions \(f(x)=x+4\) and \(f(x)=2x-1\) as linear functions.

Starting value of \(f(x)=x+4\) is at x=-4 and end value is at x=3.

Starting value: \(f(-4)=-4+4=0\)

End value: \(f(3)=3+4=7\)

Starting value of \(f(x)=2x-1\) is at x=3 and end value is at x=6.

Starting value: \(f(3)=2(3)-1=5\)

End value: \(f(6)=2(6)-1=11\)

Least range value is 0 at x=-4 and 0 is included in the range because -4 is included in the domain.

Largest range value is 11 at x=6 and 11 is not included in the range because 6 is not included in the domain.

So, the range of the given piecewise function is [0,11).

Therefore, the correct option is A.

Answer:

Every parabola has a turning point called the axis of symmetry,so for this question you just have to find the turning points

x turning point= -b/2a,and the y turning point is gotten by replacing the value of x in the equation

y=(x+1)(x-4)

=x^2-3x-4

a is 1,b is -3 and c is -4

x= -(-3)/2(1)

=1.5

and y=x^2-3x-4

=1.5^2-3(1.5)-4

= -6.25

therefore the axis of symmetry is (1.5,-6.25)

I hope this helps

Answer:

mdf= 90 degrees

Step-by-step explanation:

The required answer is the volume of the smaller solid is approximately 4.4.

we need to use the fact that the two solids are similar. This means that their corresponding sides are proportional.

The surface area of the smaller solid "S" and the surface area of the larger solid "L". We can set up the following proportion:

(Surface area of smaller solid) / (Surface area of larger solid) = (Side length of smaller solid)² / (Side length of larger solid)²

We can plug in the values we know:
49/169 = (Side length of smaller solid)² / (Side length of larger solid)²

Simplifying this equation gives us:
(Side length of smaller solid)² = (49/169) * (Side length of larger solid)²

Now we need to use the fact that the volume of a solid is proportional to the cube of its side length.
The volume of the smaller solid "V" and the volume of the larger solid "W". We can set up the following proportion:
(Volume of smaller solid) / (Volume of larger solid) = (Side length of smaller solid)³ / (Side length of larger solid)³

We can plug in the values we know:
V / 114 = ((49/169) * (Side length of larger solid)²)³ / (Side length of larger solid)³

Simplifying this equation gives us:
V / 114 = (49/169)³

Now we can solve for V:
V = 114 * (49/169)³
V ≈ 4.4
Therefore, the volume of the smaller solid is approximately 4.4.

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Using it's concept, the range of the function is given by:

All real numbers less than or equal to 4.

The range of a function is the set that contains all possible output values for the function.

For a concave down parabola, the range is from negative infinity to the y-value of the vertex, which in this problem is of 4, hence the correct option is given by:

All real numbers less than or equal to 4.

The graph of the function is given at the end of the answer, which corroborates our answer, as the range is composed by the values of y of the function.

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Answer:

(7,-3)

Step-by-step explanation:

y = -3

substitute in the first equation

3x - y^2 = 12

3x - (-3)^2 = 12

3x - 9 = 12

3x = 12 + 9

3x = 21

x = 7

coordinates of intersection (7,-3)

There will be 51 distinct pieces in the circle.

Formula: P = 1 + D/2, where P is the number of pieces and D is the number of dots.

In this case, D = 100. Therefore, P = 1 + 100/2 = 51. This means that there will be 51 pieces in the circle. Each dot will be connected to 99 other dots, so there will be 4950 individual lines in the circle. Since the points are chosen in such a way that three or more lines never meet at a single point, there will be no intersections and each of the 51 pieces will be distinct.

Therefore, there will be 51 distinct pieces in the circle.

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No, not all isosceles triangles are always similar. Two triangles are considered similar if their corresponding angles are congruent and their corresponding sides are in proportion. While all equilateral triangles are also isosceles triangles, not all isosceles triangles have congruent angles and proportional sides.

Any triangle with any two sides that have the same length is known as an isosceles triangle. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides. Triangles are three-sided polygons in geometry that can be divided into three groups based on their sides, such as:

For example, consider an isosceles triangle with base angles of 70 degrees and a third angle of 40 degrees, and another isosceles triangle with base angles of 80 degrees and a third angle of 20 degrees. These triangles have different angles and are therefore not similar, even though they are both isosceles triangles.

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The slope is -5/4 and the equation of the line in point-slope form is       y-5 = -5/4(x+4) + c.

The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.

For the given situation,

The points are  (x1,y1) is (−4,5) and (x2,y2) is (0,0)

The formula of slope is

\(m=\frac{y2-y1}{x2-x1}\)

⇒ \(m=\frac{0-5}{0-(-4)}\)

⇒ \(m=\frac{-5}{4}\)

The equation of the line in point-slope form is

\(y-y1=m(x-x1)\)

⇒ \(y-5=\frac{-5}{4} (x-(-4))\)

⇒ \(y-5=\frac{-5}{4} (x+4)\)

Hence we can conclude that the slope is -5/4 and the equation of the line in point-slope form is y-5 = -5/4 (x+4).

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Answer:

try -3

Step-by-step explanation:

The values of a and b in the equations are 100 each

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =

The given equations are

a. 5x²/2 when x = 10

By substitution, a= 5(10)²/2

This implies that a=( 5 * 100)/2

a= 200/2 = 100

b = [2x²(x-5)]/10x

Substituting x=10 in the equation we have

b = 2*10²(10-5)]/[10(10)]

200(5)/100

b= 10000/100

Therefore b = 100

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Answer:

4.  9  

5.    5x

Step-by-step explanation:

its an isocoles

Answer:

length of unknown side is 59

Answer:

\(P =5x-260\)

Step-by-step explanation:

Given

\(R = 3x^2 + 4x - 60\) --- Revenue

\(C = 3x^2 - x + 200\) --- Cost

Required

The expression for profit (P)

This is calculated as:

\(P =R - C\)

So, we have:

\(P =3x^2 + 4x - 60 - (3x^2 -x+200)\)

Open bracket

\(P =3x^2 + 4x - 60 - 3x^2 +x-200\)

Collect like terms

\(P =3x^2 - 3x^2+ 4x +x- 60-200\)

\(P =5x-260\)

If the profit is the difference between the revenue and the cost, 5x – 260  expression represents the profit. Correct option is 3.

The profit is calculated by subtracting the cost from the revenue. In mathematical terms, the profit (P) can be represented as:

Profit (P) = Revenue - Cost

Among the given options:

1. 3x - 260

2. 3x + 140

3. 5x - 260

4. 5x + 140

We need an expression where the first term represents the revenue and the second term represents the cost, so that when we subtract the cost from the revenue, we get the profit.

Option 3, 5x - 260, fits this pattern:

- Revenue: 5x

- Cost: 260

When we subtract the cost from the revenue:

Profit (P) = Revenue - Cost = 5x - 260

So, option 3, 5x - 260, is the expression that represents the profit.

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Complete question is:

If the profit is the difference between the revenue and the cost, what expression represents the profit?

1. 3x – 260

2. 3x + 140

3. 5x – 260

4. 5x + 140

Answer:

is nirvana considered indie? idrk--- but i listen to that band and a lot of rock songs :)

Step-by-step explanation:

when we evaluate the function f(x)=7000e^0.04x at x=4, the rounded result is approximately 8204.570.

To evaluate the function f(x)=7000e^0.04x at the given value x=4, we can substitute the value of x into the function and perform the necessary calculations.

First, let's substitute x=4 into the function:
f(4) = 7000e^0.04(4)

Next, we simplify the exponent calculation:
f(4) = 7000e^0.16

Now, we can evaluate the exponential term using a calculator or by using the approximation e≈2.71828:
f(4) ≈ 7000(2.71828)^0.16

Evaluating this expression, we find:
f(4) ≈ 7000(1.17351)

Multiplying these two numbers, we get:
f(4) ≈ 8204.57

Finally, we round the result to three decimal places as requested:
f(4) ≈ 8204.570
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Answer:

The cost of 10 bottles of water is $2.5.

Step-by-step explanation:

24/6=10/x

simplify 24/6 into 4,

4=10/x

x=10/4=5/2

The probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

The given data is

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

(a) calculate mean value of x:

μ = E(x)

  = ∑(xi.P(xi))

 = 4.13

(b)  calculate variance of x:

σ² = ∑(xi - E(x))².P(xi)

   = 1.81331

(c)  calculate standard deviation of x:

σ = √σ²

σ = √1.831

σ = 1.3539

The likelihood that the quantity of systems sold will be within one standard deviation of the its mean:

P(μ  - σ < x < μ  + σ ) = P(4.13 - 13539 < x < 4.13 + 1.3539)

                                = P(2.7761 < x < 5.4839)

                                = P(x = 3) + P(x = 4) + P(x = 5)

                                = 0.13 + 0.30 + 0.31

                                = 0.74

Thus, the probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

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The complete question is-

Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in one month is given by the following table.

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

What is the probability that the number of systems sold is within 1 standard deviation of its mean value?

The possible 5-digit numbers that are both divisible by 4 and 9 is 72252 and 77256.

The number 7_25_ is divisible by 4 and 9, which means that the last two digits must be divisible by 4 and the sum of all the digits must be divisible by 9.

For the last two digits to be divisible by 4, the possible options are 52 and 56.

For the sum of all the digits to be divisible by 9, the missing digits must add up to a multiple of 9. The sum of the digits must add up to 18 or 27 (multiple of 9), since the known digits already sums up to 14.

7 + _ + 2 + 5 + 2 = 18 ⇒ 7 + 2 + 2 + 5 + 2 = 18

7 + _ + 2 + 5 + 6 = 18 ⇒ 7 + 7 + 2 + 5 + 6 = 18

The missing digit is 2 and 7.

Therefore, the possible 5-digit numbers for 7_25_ that are divisible by 4 and 9 are 72252 and 77256.

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The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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Answer:

Hey dude, sry about earlier.

Anyways, 24%=24/100

24/100 simplified is 6/25

There we go :)

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