find the surface area of the triangular prism ​

Answer: To find out what grade the student must get on the next test, we can use the following formula:

(current total of scores + desired score) / (total number of scores) = desired average

We know that the student's current total of scores is 60 + 78 + 65 + 68 + 72 = 363, and the desired average is 70. We also know that the student has taken five tests, so there is one test remaining.

Therefore, we can plug in these values into the formula:

(363 + x) / 6 = 70

Where x is the grade the student must get on the next test.

We can solve for x by multiplying both sides of the equation by 6:

363 + x = 420

x = 57

Therefore, the student must get a grade of 57 on the next test in order to have an average of 70.

Step-by-step explanation:

Answer:

x = 48º

Step-by-step explanation:

x = 90 -42

x = 48º

Answer:

v(t)=2(t+1)(t-7)

7 months

Step-by-step explanation:

took the quiz

The number of months after its creation it will take the company to break even is; 7 months

We are given the net value of the company after t months to be represented by the equation;

v(t) = 2t² - 12t - 14

1) Now, we need to factorize this to get;

v(t) = 2[t² - 6t - 7]

When we factorize using the factors, we get;

v(t) = 2(t + 1)(t − 7)

2) Now, we are told that the company will break even when the net value is zero.

Thus;

2(t + 1)(t − 7) = 0

thus;

(t + 1) = 0 or t - 7 = 0

We have;

t = -1 or 7

t cannot be negative and so;

t = 7 months

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The plane will be at an altitude of 21,000 feet, 6 minutes after lift off.

For any equation, x = y + a, if we are given the value of any one of the variables, that is either x or y, we can find the value of the other.

Here, we are given an equation

a = 3400t + 600

where a = altitude of the plane in feet

and t = time (in minutes) passed after the plane's lift off

If the altitude of the plane is 21,000 feet

⇒ a = 21,000

Substituting this in the equation, we get

21,000 = 3400t + 600

21,000 - 600 = 3400t

20,400 = 3400t

3400t = 20,400

t = 20,400/ 3,400

t = 204/ 34

t = 6

Thus, the plane will be at an altitude of 21,000 feet, 6 minutes after lift off.

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The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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Answ

Step-by-step explanation:

Answer:

5 + 2 x 9

Step 1 = 7 x 9

Step 2 = 63

Step-by-step explanation:

= 5 + 2 x 9

= 5 + ( 2 x 9 )

= 5 + 18

= 23

Step 2 = 7 x 9

= 63

Step 3 = 63

C. jin did not make a mistake

Sorry i'm wrong :)

Answer:

621200000000000000

Step-by-step explanation:

(6.2×10^17 )+(1.2×10^15)

6.2×100000000000000000+1.2×10^15  ≈6.212⋅10^ 1  7

620000000000000000+1.2×10^15 ≈6.212⋅10^ 1  7

620000000000000000+1.2×1000000000000000≈6.212⋅10^ 1  7

620000000000000000+1200000000000000≈6.212⋅10^1  7

621200000000000000

Answer:

6.212×10^17

Step-by-step explanation:

\( = ( 6.2 \times {10}^{17} ) + (1.2 \times {10}^{15} )\)

\( = (620 \times {10}^{15}) + (1.2 \times {10}^{15} )\)

\( = 620 \times {10}^{15} + 1.2 \times {10}^{15} \)

\( = (620 + 1.2)\times {10}^{15} \)

\( = 621.2\times {10}^{15} \)

\( = 6.212 \times {10}^{17} \)

I hope it helped u :)

Answer:

domain : - ∞ < x < 1

Step-by-step explanation:

the function is increasing on the upward part of the curve. that is

from negative infinity to the vertex at (1, 3 )

domain : - ∞ < x < 1

The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Answer:

4x^2-22x+30

=2(2x^2 - 11x + 15)

=2(2x^2 -6x -5x +15)

= 2 { 2x(x-3) - 5(x-3) }

= 2 (x-3) (2x - 5)

Step-by-step explanation:

Hey, there!!!

The answer is option B

here, we have;

=4x^2-22x+30

=4x^2-(10+12)x+30

= 4x^2-10x-12x+30

now, taking common,

=2x(2x-5) -6(2x-5)

= 2(x-3)(2x-5).

Hope it helps

Answer:

y = 36

Step-by-step explanation:

given y varies directly  with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition when x = 5 , y = 15

15 = 5k ( divide both sides by 5 )

3 = k

y = 3x ← equation of variation

when x = 12 , then

y = 3 × 12 = 36

Answer:

He has 2 lbs. left over for cookies.

Step-by-step explanation:

I got this answer by first adding 1/2 + 1  1/2 = 2. Then subtracting 2 from 4 witch would be 2 lbs. left over.

Answer:

  B.  x = 1, y = 0, z = 3

Step-by-step explanation:

Systems of linear equations are readily solved by a suitable calculator or spreadsheet. The attached calculator display shows the solution to be ...

  x = 1, y = 0, z = 3

__

There are several ways a calculator can solve these equations. The method shown here is to input the equations as an augmented matrix of their coefficients, and reduce it to row-echelon form. The right-most column of the reduced matrix is the set of variable values in the same order as the coefficients.

A graphing calculator can also be used to graph the equations. You may have to write one variable in terms of the others. (Here, it is convenient to let z=3-y.) The second attachment shows the solution (x, y) = (1, 0). This is sufficient to choose the correct answer. Or, you can finish the solution by substituting into the expression for z: z = 3 -y = 3 -0 = 3.

Many calculators will solve the system of equations after you enter it as presented in the problem statement.

Using proportions, it is found that he bikes:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, the proportion is that he bikes 9.5 miles each half hour, hence:

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The angle formed by the two hands have a measure less than 1/4 turn

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

A clock with the hour hand at 12 and the minute hand at 2

The turn represented by the above is represened as

Turn = (2 * 30)/360

When simplified, we have

Turn = 1/6

Next, we have

Angle at the turn = 1/4

1/6 is less than 1/4

This means that the angle formed by the two hands have a measure less than 1/4 turn

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When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.

A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.

The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.

When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.

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Answer:

Step-by-step explanation:

Given

Simply

Solution

The coordinates of the turning point on the curve with the equation y = 9 + 18x - 3x² is (3,36).

Any equation of the form \(\rm ax^2+bx+c=0\) where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

It is given that:

The quadratic equation is:

y = 9 + 18x - 3x²

To find the turning point:

Graph the above quadratic equation;

From the graph:

The maximum point from where the graph starts to decrease is (3,36)

Thus, the coordinates of the turning point on the curve with the equation y = 9 + 18x - 3x² is (3,36).

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The critical value is 9.925, rounded to three decimal places.

To calculate the critical value for a 99.9% confidence level with a sample size of 4, we will use the t-distribution, since the population standard deviation is unknown.

The t-distribution is used when the sample size is small (usually n < 30) and the population standard deviation is unknown.

First, find the degrees of freedom (df) for the t-distribution, which is equal to the sample size (n) minus 1:

Next, we need to find the critical value (t) that corresponds to a 99.9% confidence level (or a 0.999 probability) and 3 degrees of freedom. We will look this up in a t-distribution table or use a t-distribution calculator.

Using a t-distribution calculator or table, the t-score corresponding to a 99.9% confidence level (two-tailed) and 3 degrees of freedom is approximately 9.925.

So, the critical value is 9.925, rounded to three decimal places.

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Answer:

The value of this game is $185

It would cost you $10 to play.

Step-by-step explanation:

Answer:

RST

Step-by-step explanation:

The question is asking you to complete the congruence statement. In a congruence statement, the corresponding angles must be in the same order they are in, in the first half of the statement. In the first triangle <M=79, <N=60, and <O=42. So the other half must be in this same order. In the other triangle <R=79, <S=60, and <T=52, which is why the answer is RST.