Identify the x-intercept and y-intercept of the line 3x-5y=15

The surface area of the given rectangular prism is 148 square inches.

What is surface area ?

Surface area is the total area that covers the surface of a three-dimensional object. It is the sum of all the areas of the object's faces or surfaces. In other words, surface area is the measure of the amount of material required to cover the outside of a solid object.

Surface area is an important concept in mathematics and is used in various fields such as engineering, architecture, and construction. It helps in determining the amount of material needed to cover an object, the heat transfer rate between objects, and the strength of objects under different conditions.

According to the question:
To find the surface area of a rectangular prism, you need to add up the areas of all six faces.

The formula for the surface area of a rectangular prism is:

Surface Area = 2(lw + lh + wh)

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

Substituting the given values, we have:

Surface Area = 2(54 + 56 + 4*6)

Surface Area = 2(20 + 30 + 24)

Surface Area = 2(74)

Surface Area = 148 square inches

Therefore, the surface area of the given rectangular prism with height (h) of 6 inches, length (l) of 5 inches, and width (b) of 4 inches is 148 square inches.

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If you're just building a function, there's nothing stopping from simplify defining it as a function f : {1, 2, 3, 5, 7} -> {-1, 0, 1, 3} such that

\(f(x)=\begin{cases}3&\text{if }x=1\\1&\text{if }x=2\\-1&\text{if }x=3\text{ or }x=7\\0&\text{if }x=5\end{cases}\)

In case it's not familiar to you, the notation f : A -> B simply means f is a function that maps elements in the set A to a single element in the set B ; I emphasize "single", because otherwise f would not be a function.

Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

Answer: 94.2 cm

Step-by-step explanation:

C=2πr

2(3.14)(15)

2(47.1)

94.2

Answer:

12

Step-by-step explanation:

Given that,

f(x) = 2x² - 3x + 7

To find the value of f ( 2.5 ), replace x with 2.5 and solve the equation.

Let us solve it now.

f(2.5) = 2(2.5)² - 3×2.5 + 7

f(2.5) = 12.5 - 7.5 + 7

f(2.5) = 12

Answer:

\(f(x) = 2 {x}^{2} - 3x + 7 \\ f(2.5) = 2 {(2.5)}^{2} - 3(2.5) + 7 \\ f(2.5) = 12.5 - 7.5 + 7 \\ \boxed{f(2.5) = 12}\)

Answer:

Step-by-step explanation: To find the x let y=0

We substitute into the equation 3x+2y=15

3x+2 *0=15

3x=15

x=15/3=5

To find the y let x=0

we substitute into the equation x =0

3*0+2y=15

2y=15

y=15/2

Answer:

Area of a circle= π r square

22/7 × 6 ×6

22/7×36

= 792/7

=113.40

Answer:

rsgsadfg

Step-by-step explanation:

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A surveyor is estimating the distance across a river. The actual distance is 284.5 m. The surveyor's estimate is 300 m. Find the absolute error and the percent error of the surveyor's estimate. If necessary, round your answers to the nearest tenth.

(i) Absolute error = 15.5m

(ii) Percent error = 5.5%

Given:

Actual measurement of the distance = 284.5 m

Estimated measurement of the distance by the surveyor = 300 m

(i) The absolute error is the magnitude of the difference between the estimated value measured by the surveyor and the actual value of the distance across the river.

i.e

Absolute error = | estimated value - actual value |

Absolute error = | 300m - 284.5m | = 15.5m

(ii) The percent error (% error) is given by the ratio of the absolute error to the actual value then multiplied by 100%. i.e

% error = \(\frac{absoluteError}{actualValue}\) x 100%

% error = \(\frac{15.5}{284.5}\) x 100%

% error = 0.05448 x 100%

% error = 5.448%

% error = 5.5%  [to the nearest tenth]

The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.

Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:

the measure of angle Z is equal to 65°

the side EF corresponds to JK and side FG corresponds to KL, so:

8/20 = 11/x

x = (11 × 20)/8 {cross multiplication}

x = 27.5

the side EF corresponds to JK and EH corresponds to JM, so:

8/20 = y/30

y = (30 × 8)/20 {cross multiplication}

y = 12

Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

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The probability of getting 2 the same colour will be 39/100.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

The probability of getting 2 blue will be:

= 5/10 × 5/10

= 1/4.

The probability of getting 2 red will be:

= 2/10 × 2/10

= 1/25

The probability of getting 2 green will be:

= 3/10 × 3/10.

= 9 / 100

The probability of getting 2 the same colour is:

= 1/4 + 2/25 + 9 / 100

= 39/100

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Answer:

Step-by-step explanation:

3/40 is the correct answer

It takes 249hrs before trying them all.

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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Answer: d) Not in Col in Nul A

Step-by-step explanation: The definition of Column Space of an m x n matrix A is the set of all possible combinations of the columns of A. It is denoted by col A. To determine if a vector is a column space, solve the matrix equation:

A.x = b or, in this case, \(A.x=u\).

To solve, first write the augmented matrix of the system:

\(\left[\begin{array}{cccc}1&0&3&-4\\-2&-1&-4&-5\\3&-3&0&3\\-1&3&6&1\end{array}\right]\)

Now, find the row-echelon form of matrix A:

1) Multiply 1st row by 2 and add 2nd row;

2) Multiply 1st row by -3 and add 3rd row;

3) MUltiply 1st row by 1 and add 4th row;

4) MUltiply 2nd row by -1;

5) Multiply 2nd row by 3 and add 3rd row;

6) Multiply 2nd row by -3 and add 4th row;

7) Divide 3rd row by -15;

8) Multiply 3rd row by -15 and add 4th row;

The echelon form matrix will be:

\(\left[\begin{array}{cccc}1&0&3&-4\\0&1&-2&13\\0&0&1&-\frac{51}{15}\\0&0&0&-13 \end{array}\right]\)

Which gives a system with impossible solutions.

But if \(A.x=0\), there would be a solution.

Null Space of an m x n matrix is a set of all solutions to \(A.x=0\), so vector u is a null space of A, denoted by null (A)

Answer:

0.23

Step-by-step explanation:

Answer:

\({ \tt{12 {y}^{2} + 12y - 3 {y}^{3} = 124 - (y + 5)}} \\ 3 {y}^{3} - 12 {y}^{2} - 12y = - 124 + (y + 5) \\ {3y}^{3} - 12 {y}^{2} - 12y = - 124 + y + 5 \\ { \tt{3 {y}^{3} - {12y}^{2} - 11y + 119 = 0 }}\)

Answer:

4 1/10 when u have a inproper fraction like that every 10 is one whole number

The plane has intercepts

y = z = 0   ⇒   3x = 6   ⇒   x = 2

x = z = 0   ⇒   2y = 6   ⇒   y = 3

x = y = 0   ⇒   z = 6

and thus passes through the points (2, 0, 0), (0, 3, 0), and (0, 0, 6).

Parameterize the portion of the plane (call it P) by the vector function,

\(\vec r(s,t) = \left\langle 2(1-s)(1-t), 3s(1-t), 6t \right\rangle\)

where 0 ≤ s ≤ 1 and 0 ≤ t ≤ 1.

Compute the normal vector to P :

\(\vec n = \dfrac{\partial \vec r}{\partial t} \times \dfrac{\partial \vec r}{\partial s} = -\left\langle 18-18t, 12-12t, 6-6t \right\rangle\)

Then the flux of F through P is given by the surface integral,

\(\displaystyle \iint_P \vec F \cdot d\vec S = \int_0^1 \int_0^1 \left\langle 6s(1-s)(1-t)^2, 90st(1-t), 72t(1-s)(1-t) \right\rangle \cdot \vec n \, ds \, dt \\\\ = - \int_0^1 \int_0^1 \left(108(t-1)^3 s^2 + 108(t-1)^2(5t+1) s + 432t(t-1)^2\right) \, ds \, dt \\\\ = - \int_0^1 18(t-1)^2(41t+1) \, dt \\\\ = \boxed{-\frac{135}2}\)

Answer:

1.61

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.61

Answer:

x is 4.30 and 0.697

Step-by-step explanation:

Quadratic formular:

\(x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \\ \)

a » 1

b » -5

c » 3

\(x = \frac{ - ( - 5)± \sqrt{ {( - 5)}^{2} - (4 \times 1 \times 3)} }{(2 \times 1)} \\ \\ x = \frac{5± \sqrt{13} }{2} \)

Therefore, values of x :

\(x = \frac{5 + \sqrt{13} }{2} \: \: and \: \: \frac{5 - \sqrt{13} }{2} \\ \\ x = 4.30 \: \: and \: \: 0.697\)

The the length of LJ is approximately 3.5.OptionD) is correct.

To find the length of LJ, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides of the triangle.

Let's denote the length of JL as x. Then, we can set up the following proportion:

sin(23°) / LJ = sin(89°) / KL

where KL is given as 9.

We can simplify this proportion by using the fact that sin(89°) = cos(1°) (since the sine of the complement of an angle is equal to the cosine of the angle), and by using a calculator to find the values of sin(23°) and cos(1°):

0.3919 / LJ = 0.0175 / 9

Multiplying both sides by x and then dividing both sides by 0.0175, we get:

LJ = 0.3919*9/ 0.0175

x ≈ 3.5

Therefore, the length of LJ is approximately 3.5.OptionD) is correct.

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When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

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Note: the translated questions is

X = 13, which equation is true?

Answer:

1 Mile per hour = 1.60934 kilometers per hour = 0.44704 meters per second (SI base unit). 1 mph = 0.447 04 m/s.

Step-by-step explanation:

1 Miles Per Minute to Miles Per Hour = 60 70 Miles Per Minute to Miles Per Hour = 4200

Answer:

volume=60cm3, surface area=96cm2

Step-by-step explanation:

volume=1/3×(6×6)×5

=60cm3

surface area= 4(1/2×6×5)+(6×6)

=96cm2

Answer:

The answer is point A' (3, -2).