Enter the correct answer in the box.
Simplify the expression (6²)4.

Answer:

-19

Step-by-step explanation:

Basically, plug in the values for x and y into the expression.

So, it is basically, (x = 5, y = -3)

5 × 5 + 4 + 6 × (-3) - 6 × 5 which is equals to 25 + 4 + (-18) -30.

Using PEDMAS or BODMAS, we get -19.

The answer when the expression 12.10² is multiplied is 1200. The right option is c. 1200

To multiply means to add equal groups. When we multiply, the number of things in the group increases.

To multiply 12.10², we use the technique below.

From the question,

Given:  12.10²

Change the . to multiplication.

From the law of indices,

Therefore,  12.10² = 12×100 = 1200.

Hence, the right option is c 1200

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The Surface Area of cylinders are: 100 yd² , 264 m², 226  mm²

The Surface Area of Can is 219 cm².

We know the formula for Surface Area of Cylinder

= 2πrh

1. Radius = 2 yd

Height = 8 yd

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 2 x 8

= 100 yd²

2. Radius = 7 m

Height = 6 m

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 6 x 7

= 264 m²

3. Radius = 3 mm

Height = 12 mm

So,  Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 3 x 12

= 226  mm²

4. Radius = 3.5 cm

Height = 10 cm

So, Surface Area of Can

= 2πrh

= 2 x 3.14 x 3.5 x 10

= 219 cm²

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The loss in percentage is 25%.

Given that,

Cost price of an article      = $28

Selling price of the article = $21

We know that,

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Now  loss can be calculated by subtracting selling price from  cost price,

Therefore,

28 - 21 = 7

Hence there are loss of $7 in business,

Now to calculate percentage loss,

Divide loss by cost price then multiply with 100,

Then,

⇒ (7/28)x100

⇒ 25%

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The key features of the dashed graph are

A graph is a pictorial representation of a function

To describe the key features of the dashed graph, we proceed as follows.

So, the key features of the dashed graph are

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Answer:

a corresponding side is a pair of matching sides that are in the same spot of two different shapes. The shapes must be either congruent or similar.

Step-by-step explanation:

a) The parametric equations of the line are: x(t) = −2 + 3t, y(t) = 4 − 2t, z(t) = 3 + 4t and The symmetric equation of the line are: (x + 2)/3 = (y − 4)/−2 = (z − 3)/4

b) The line intersects yz-plane at (0, 8/3, 17/3)

The given points on the line are:

(x₁, y₁, z₁) = (−2, 4, 3)

(x₂, y₂, z₂) = (1, 2, 7)

The direction ratios of this line are:

⟨a, b, c⟩ = ⟨x₂ − x₁, y₂ − y₁, z₂ − z₁⟩

             = ⟨1 + 2, 2 − 4, 7 − 3⟩

             = ⟨3, −2, 4⟩

a) Parametric equations of the line:

These are given by:

x(t) = x₁ + at = −2 + 3t

y(t) = y₁ + bt = 4 − 2t

z(t) = z₁ + ct = 3 + 4t

Symmetric equation of the line:

This is given by:

              (x − x₁)/a = (y − y₁)/b = (z − z₁)/c

              (x + 2)/3 = (y − 4)/−2 = (z − 3)/4

b) When a line intersects the yz-plane, its x-coordinate is zero.

Using the parametric equations of the part (a):

                                   x = 0

                          −2 + 3t = 0

                                  3t = 2

                                    t = 2/3

Substitute this in the parametric equations corresponding to y and z as well:

                                   y = 4 −2t

                                      = 4 − 2(2/3)

                                      = 8/3

                                   z = 3 + 4t

                                      = 3 + 4(2/3)

                                      = 17/3

Hence, the required point is: (x, y, z) = (0, 8/3, 17/3)

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Answer:

The answer is D

Step-by-step explanation:

Answer:

  total deposits: $35,100

Step-by-step explanation:

You have the value of an annuity earning 5% with payments of $65 a month for 45 years as $131,718.42. You want to know the total value of payments.

12 payments per year of $65 for 45 years will have a total value of ...

  12·65·45 = 35100

Total deposits will be $35,100.

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Step-by-step explanation:

therefore, the correct option is option number 1.

This is the simple form of the given equation \(\frac{(-4x^4z^3 - 5x^4z^5 + 8) }{(x^2z^2)}\)

What is the polynomial equation?

An algebraic equation, also known as a polynomial equation, in mathematics, is a formula of the form P=0, where P is a polynomial with coefficients in some field, typically the field of the rational numbers.

We have,

(32 x³ z² - 16 x⁷ z⁵ - 20 x⁷ z⁷) ÷ (4x⁵ z⁴)

(32 x³z² - 16 x⁷z⁵ - 20 x⁷z⁷) * 1/(4x⁵z⁴)

\(\frac{(32 x^3z^2 - 16 x^7z^5 - 20x^7z^7) }{(4x^5z^4)}\)

\(=\frac{(-4x^4z^3 - 5x^4z^5 + 8) }{(x^2z^2)}\)

Hence, this is the simple form of the given equation \(\frac{(-4x^4z^3 - 5x^4z^5 + 8) }{(x^2z^2)}\)

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Whwn the line of sight from the park ranger station, P, to the lifeguard chair, L, the length of PL is 0.76 miles.

It should be noted that since the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F, then the path from the park ranger station to the lifeguard chair is the hypotenuse of a right triangle with legs of 0.35 miles and 0.65 miles.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. Therefore, the length of PL is equal to:

= ✓(0.35² + 0.65²)

= 0.76 miles.

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Answer:

10/11

Step-by-step explanation:

Answer: The answer is 96 square units.

Step-by-step explanation:

(Because it's 8 square units long and 12 square units wide. L x W = Area)

So you have to do 12 x 8 and you should get the answer 96 square units.

Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.

I prefer Wills method because it is easier and less complicated.

Wills method:

(5x + 6x) - (2x - 1)

Subtract both 2x and -1

5x + 6x - 2x - - 1

5x + 4x + 1

In conclusion, Wills method is preferred when both methods are compared.

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Answer:

A

Step-by-step explanation:

The requried simplified value of x in the intersection of two lines is 6.

Opposite angles are a pair of angles that are formed when two lines intersect. The two angles are located on opposite sides of the point where the two lines intersect.

Opposite angles are also called vertical angles, and they have equal measures. This means that if we know the measure of one opposite angle, we can find the measure of the other opposite angle by setting them equal to each other.

Here,
When two lines intersect, opposite angles are equal. So, we can set the two opposite angles equal to each other and solve for x.

Given that the opposite angles are 3x + 2 and 20 degrees, we have:

3x + 2 = 20

Subtracting 2 from both sides, we get:

3x = 18

Dividing both sides by 3, we get:

x = 6

Therefore, the value of x is 6.

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Step-by-step explanation:

OUT of  35 spins   4 + 15 + 3  = 22   were blue or green or purple

 22/35 probability  = 63%

Answer:

x + 5y = -8

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Find b

y = -1/5x + b

0 = -1/5(-8) + b

0 = 8/5 + b

b = -8/5

Step 2: Rewrite equation

y = -1/5x - 8/5

Step 3: Isolate x and y

1/5x + y = -8/5

Step 4: Multiply everything by 5

x + 5y = -8

Answer:

Step-by-step explanation:

x² - 3x - 1 = 0

a = 1, b = -3, c = -1

x₁ = (3 + sqrt(-3² - 4(1(-1))))/(2(1))

x₁ = (3 + sqrt(9 + 4))/2

x₁ = (3 + sqrt(13))/2

x₁ = 3.302...

x₂ = (3 - sqrt(-3² - 4(1(-1))))/(2(1))

x₂ = (3 - sqrt(9 + 4))/2

x₂ = (3 - sqrt(13))/2

x₂ = -0.302...

The probability of pulling a spade or a four of hearts from a randomly shuffled deck is 0.288

To find the probability of pulling a spade or a four of hearts, we need to add the probabilities of pulling a spade to the probability of pulling a four of hearts and then subtract the probability of pulling both cards, which were included in both probabilities.

So, the probability of pulling a spade or a four of hearts can be calculated as

P(spade or four of hearts) = P(spade) + P(four of hearts) - P(spade and four of hearts)

P(spade or four of hearts) = 1/4 + 1/52 - (1/4 × 1/52)

Do the arithmetic operation

P(spade or four of hearts) = 0.288

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Answer:

x=1

Step-by-step explanation:

3x-15=17-x

3x-x=17-15

2x=2

x=1

Answer:

x=8

Step-by-step explanation:

3x-15=17-x  move variable to the left and change its sign

3x+x-15=17  collect like terms

4x=17 + 15 (3x=x=4x)

4x= 32  divide both sides by 4

x=8   (dividing 4x by 4 cancels the 4,s out and leaves x)

Answer:

are you realy a tutor?

Step-by-step explanation:

The height of the sand in the display container is 12 inches when the display container is right triangular prism.

What is right triangular prism ?

A right triangular prism is a three-dimensional geometric shape with two parallel triangular bases and three rectangular faces. The rectangular faces connect the corresponding vertices of the triangular bases.

To find the height of the sand in the display container, we need to use the fact that the volume of sand in the storage container is equal to the volume of sand in the display container.

The storage container has a length, width, and height of 6 inch, 6 inch, and 6inche, respectively. Then, the volume of the storage container is:

\(V_{storage} = L * W * H = 6 * 6 * 6 = 216 inch^3\)

Similarly, let's assume that the display container has a base of length 4 inch and height 9 inches and height of sand be H.

Then, the volume of the display container is:

\(V_{display} = (1/2) * b * h * H = (1/2) * 4 * 9 * H = 18H\)

where (1/2) is the area of the triangle base of the display container.

Since the volumes of sand in both containers are equal, we can set these expressions equal to each other and solve for h:

216 = 18H

H = 12 inches

Therefore, the height of the sand in the display container is 12 inches.

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Answer:

143 miles

Step-by-step explanation:

Let x = number of miles

Let y = total cost

150.55 = .92x + 18.99  Multiply all the way through by 100 to clear the decimal

15055 = 92x + 1899  Subtract 1899 from both sides

13156 = 92x  Divide both sides by 92

143 = x

The number of students who will be going on the trip is B. 40 students.

A mathematical expression is a rule-based set of numbers, variables, and mathematical operations performed to compute the output value.

The mathematical operations used to solve mathematical expressions include additions, subtractions, divisions, and multiplications.

The total of the weekend trip = $4,030

The cost of cleaning for the bus = $30

The cost of food and lodging per student = $60

The bus charge per student = $40

Total cost per student = $100 ($60 + $40)

The total cost, y = 4,030 - 30 - 100x

The number of students = x

x= (4,030 - 30)/100

= (4,000/100)

= 40.

Thus, the number of students who will be going on the trip is B. 40 students.

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Answer:

\((a)\ m = \frac{4}{3}\) --- slope of OA

\((b)\ y = \frac{4}{3}x\) --- the equation

Step-by-step explanation:

Given

The attached graph

Solving (a): Slope of OA

First, we identify two points on OA

\((x_1,y_1) = (0,0)\)

\((x_2,y_2) = (3,4)\)

So, the slope (m) is:

\(m = \frac{y_2 -y_1}{x_2 - x_1}\)

This gives:

\(m = \frac{4-0}{3-0}\)

\(m = \frac{4}{3}\)

Solving (b): The equation

This is calculated as:

\(y = m(x - x_1) + y_1\)

Recall that:

\((x_1,y_1) = (0,0)\)

\(m = \frac{4}{3}\)

So, we have:

\(y = \frac{4}{3}(x - 0) + 0\)

\(y = \frac{4}{3}(x)\)

\(y = \frac{4}{3}x\)

The graph is shifted right to 3 units, then the graph has a horizontal stretch by a factor of 2 and the graph is shifted up 4 units.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The function is:

f(x) = x²

First transformation:

x → (x- 3)

The graph is shifted right to 3 units.

F(x) = (x- 3)²

Second transformation:

F(x) → 2F(x)

The graph has a horizontal stretch by a factor of 2.

h(x) = 2(x- 3)²

Third transformation:

h(x) → h(x) + 4

The graph is shifted up 4 units.

g(x) = 2(x- 3)² + 4

Thus, the graph is shifted right to 3 units, then the graph has a horizontal stretch by a factor of 2 and the graph is shifted up 4 units.

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Answer:

C

Step-by-step explanation:

9x-4+5x+16=180

14x+12=180

14x=168

x=12

Answer:

  C)  12

Step-by-step explanation:

Consecutive interior angles are supplementary:

  (9x -4)° +(5x +16)° = 180°

  14x = 168 . . . . . . divide by °, subtract 12

  x = 12 . . . . . . . . divide by 14