Make sure your answer is in
degrees. You should be able to
find this without a calculator.
-1
12/1/= = [?]°
sin-1

Answer:

y=13 degrees

Step-by-step explanation:

This is an isosceles triangle, we know this because NO and NM are equal.

In an isosceles triangle, the base angles are congruent. In this case, they are angle NOM and angle NMO.

We also know that the sum of the interior angles of a triangle are equal to 180.

With this information, we can make an equation by gathering all the interior angles:

8y+2(3y-1)=180

Solve for y.

8y+6y-2=180

14y-2=180

14y=182

y=13

Answer:

4 weeks

Step-by-step explanation:

First,, we should subtract the vacation price from her savings to get the base. That is 1835-1540=295. Then we can do 295/65,, and then we get 4  7/13. So,, she can only afford 4 weeks of these deductions in order to have enough money for her vacation.

Answer:

d = -2

Step-by-step explanation:

6 (d-4) = 18d

6d - 24 = 18 d

-24 = 18d - 6d

-24 = 12d

d = -24 / 12

d = -2

To Find: Value of (d) if,

6(d - 4) = 18 d.

6(d - 4) = 18d

→ 6d - 24 = 18d

(Simplified the LHS portion)

→ 6d - 18 d = 24

(Like terms are separated)

→ - 12d = 24

→ - d = 24/12

→ - d = 2

→ d = - 2

Verification:-

LHS:-

6(d - 4)

= 6d - 24

= 6(- 2) - 24

= - 12 - 24

= - 36

RHS:-

18d

= 18(- 2)

= - 36

Thus,

LHS = RHS.

Answer:

£16

the t-shirt increased by 0.25. let's convert that to percentage

therefore it increased by 25%

By using cross multiplication we can write as follows:

125%=£20

100%=£ x

(100×20)/125= £16

A. pyramid has only one base, B. The base of a pyramid is a polygon, C. If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height, F. The slant height is used to calculate the lateral area.

Let’s verify all the options:

A) A pyramid has only one base.

By definition, a pyramid has only one base

So, A is TRUE

B) The base of a pyramid is a polygon.

By definition, a pyramid is a polyhedron formed by a polygonal base.

So, B is TRUE

C) If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height.  

Given, the right pyramid and if the length of the base is known. Then, we can find the half distance of the base and it will form a right-angled triangle. Hence Pythagorean theorem can be used to find its slant height.

So, C is TRUE

D) The slant height is always the same length as the base of the pyramid.

No, the slant height is not always the same as the base of the pyramid.

So, D is FALSE

E) The lateral faces of a pyramid are rectangles.  

By definition, the shape of the lateral faces of the pyramids is triangular.

So E is FALSE

F) The slant height is used to calculate the lateral area.

The formula for the lateral surface area of the pyramid is given:

Lateral Surface Area = (P × L), where

P is the perimeter of the base

L is the slant height.

So F is TRUE

Hence the true options are A, B, C, and F.

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Disclaimer: The given question is incomplete. The complete question is mentioned below:

What information is true when calculating the surface area of a pyramid? Check all that apply.

A) A pyramid has only one base.

B) The base of a pyramid is a polygon.

C) If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height.

D) The slant height is always the same length as the base of the pyramid.

E) The lateral faces of a pyramid are rectangles.

F) The slant height is used to calculate the lateral area.

Your question was incomplete. Please refer the content below:

What information is true when calculating the surface area of a pyramid? Check all that apply.

A) A pyramid has only one base.

B) The base of a pyramid is a polygon.

C) If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height.

D) The slant height is always the same length as the base of the pyramid.

E) The lateral faces of a pyramid are rectangles.

F) The slant height is used to calculate the lateral area.

The options that are correct about a pyramid will include option (A), option (B), option (C) and option (F).

Now, we will see all the options one by one:

option (A) A pyramid has only one base.

Yes, it is true as it can only have 1 base.

option (B) The base of a pyramid is a polygon.

Yes, it is true as the base will always be a polygon only.

option (C) If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height.  

Yes, it is true as Pythagoras theorem can be used in a right angles triangle which will be formed by the slant height.

option (D) The slant height is always the same length as the base of the pyramid.

No, it is false as it can be different according to the pyramids.

option (E) The lateral faces of a pyramid are rectangles.  

No, it can be triangular also.

option (F) The slant height is used to calculate the lateral area.

Yes, it is true as the formula for the lateral surface area of the pyramid is given as:

Lateral Surface Area = (P × L), where

L represents the slant height.

Therefore, the options that are correct about a pyramid will include option (A), option (B), option (C) and option (F).

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The value of x is 4.47 units

In the given figure, there are two right angle triangle, to find the value of x we have to solve each triangle using the Pythagorean theorem.

Consider the bottom triangle

Base of the triangle = 6 units

The hypotenuse of the triangle = 9 units

Apply the Pythagorean theorem

The third side of the triangle = \(\sqrt{9^2-6^2}\)

= \(\sqrt{81-36}\)

= \(\sqrt{45}\) units

Similarly consider the top triangle

The base of the triangle = 5 units

The hypotenuse of the triangle = \(\sqrt{45}\) units

The third side of the triangle = \(\sqrt{\sqrt{45}^2- 5^2}\)

= \(\sqrt{45-25}\)

= \(\sqrt{20}\)

= 4.47 units

Hence, the value of x is 4.47 units

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The value of x when h(x) =-3 is 5.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

h(x) = -x + 2

Now, we have to find the value of x when h(x)= -3

So, h(x)= -3

-x+ 2= -3

Now, Subtracting 2 from both side

-x+ 2 -2= -3 -2

-x = -5

x= 5

Hence, the value of x is 5.

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Answer:

x = 19/3 or 6 1/3

Step-by-step explanation:

I solved for x using Algebra :)

The equation to represent the scenario is 3y - 38 = 10

Represent the given parameters as

x = Dominique

y = Roberto

From the question, we have

Dominique spent $38 less than 3 times what Roberto spent

This means that

x = 3y - 38

Also, Dominique spent $10

So, we have

3y - 38 = 10

Hence, the equation to represent the scenario is 3y - 38 = 10

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The y-intercept represents a. the maximum weight allowed in a shipment.

Given: The graph is between the Amount of allowed weight remaining Vs the Number of boxes included.

What is a graph?

A graph is a diagram or the representation of variations between two or more variables with respect to each other.

A graph consists of dependent and independent variables. We usually plot the response of the dependent variable with the change in the value of the independent variable.

What is y-intercept?

The y-intercept is the point on the y-axis that a given equation of line or a curve passes through when the value of x = 0. It can denote either the minimum value for a function is the function is increasing the the initial point is the y intercept or the maximum value for a decreasing function if the y-intercept is the initial point.

Let's solve the question:

It is given in the question that the graph is of  Amount of allowed weight remaining Vs the Number of boxes.

As it is "Amount of weight remaining", so we can interpret that it is a decreasing curve with the increase in the number of boxes or in simple words the value of y will keep decreasing with the increasing number of x value.

Therefore, for this graph the y-intercept will show the maximum weight remaining or as it is the y-intercept that is x = 0, which means when there are no boxes the maximum weight remaining is y-intercept. So it the maximum weight allowed in the shipment.

Hence the answer is a. the maximum weight allowed in a shipment.

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Disclaimer: The given question is incomplete. The complete question is mentioned below:

One manufacturer boxes screws so that each box weighs the same no matter what size the screws are. The graph shows the amount of allowed weight remaining in a given shipment depending on the number of boxes of screws already included. What does the y-intercept represent in this situation?

a. the maximum weight allowed in a shipment.

b. the minimum weight of a single box of screws.

c. the minimum number of screws in a single box.

d. the maximum number of single boxes for a shipment.

Answer:

normal force decreases

Step-by-step explanation:

N=mgcosθ, and cosine decreases as theta increases

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Answer:

A) decreases

Step-by-step explanation:

As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.

Answer:

\(y = 69\)

Step-by-step explanation:

Given the following question:

\(y=2x+9x+3\)
\(x=6\)

Substitute and solve using PEMDAS:

\(y=2x+9x+3\)
\(y=2(6)+9(6)+3\)
\(2\times6=12\)
\(y=12+9(6)+3\)
\(9\times6=54\)
\(y=12+54+3\)
\(12+54=66\)
\(66+3=69\)
\(y=69\)

Your answer is "y = 69."

Hope this

Answer:

3rd

C

Explanation:

Amit's mistake : The point (2, –2) doesn’t lie on the circle because the calculated distance should be the same as the radius.

The point (2,-2) is on the circle, and Amit's claim is wrong

The given parameters are:

Center = (-1,2)

Diameter = 10 units

Point = (2,-2)

Start by calculating the radius, r

r = diameter/2

r = 10/2

r = 5

Next, calculate the distance from the point to the center using:

\(r = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}\)

This gives

\(r = \sqrt{(2 + 1)^2 + (-2-2)^2}\)

Evaluate

r = 5

The distance from the center to the point equals the radius of the circle

Hence, the point is on the circle, and Amit's claim is wrong

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To find the probability that a plant chosen at random will be between and cm tall, we need to use the normal distribution formula. We know that the mean height of the plant is cm and the standard deviation is cm.

First, we need to standardize the values of and by subtracting the mean and dividing by the standard deviation:

Z1 = ( - ) / = ( - ) /
Z2 = ( - ) / = ( - ) /

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two Z-values. This area represents the probability that a plant chosen at random will have a height between and cm.

Alternatively, we can use the normal distribution function on a calculator or software to find the probability directly. The formula for the normal distribution function is:

P( < X < ) = 1/2[erf(( - )/sqrt(2)) - erf(( - )/sqrt(2))]

where erf is the error function.

Using either method, we can find that the probability that a plant chosen at random will be between and cm tall is approximately %.

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Graph the solution of the inequality 4.5k>18 is equal to  k > 4 ( see image), by using the inequality equation.

Based on the given conditions,

4.5k>18

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

a ≠ b says that a is not equal to b

a < b says that a is less than b

a > b says that a is greater than b

(those two are known as strict inequality)

a ≤ b means that a is less than or equal to b

a ≥ b means that a is greater than or equal to b.

To solve given graph,

We can write,

4.5k>18

4.5k - 18 > 0

4.5k > 18

k > 18/4.5

We can get the division,

k > 4   (We can see image)

Therefore,

4.5k>18 Graph the solution of the inequality is k > 4 ( see image ), by using inequality equation.

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To determine how many pills the patient should take every four hours, we need to calculate the dosage based on the patient's weight and the prescribed dosage formula.

Given:

Patient weight = 34 kg

Dosage formula = 48 mg/kg/day

First, let's calculate the total dosage the patient needs per day:

Total dosage = Dosage per kg * Patient weight

Total dosage = 48 mg/kg/day * 34 kg

Total dosage = 1,632 mg/day

Since the patient needs to take the medication every four hours, we need to determine the number of pills for each dose.

Let's calculate the number of pills for each four-hour dose:

Dosage per four hours = Total dosage per day / Number of four-hour intervals in a day

Dosage per four hours = 1,632 mg/day / (24 hours / 4 hours)

Dosage per four hours = 1,632 mg/day / 6

Dosage per four hours ≈ 272 mg

Since the drug is available in 300 mg tablets, we can calculate the number of tablets for each four-hour dose:

Number of tablets = Dosage per four hours / Tablet strength

Number of tablets = 272 mg / 300 mg

Number of tablets ≈ 0.91

Rounding up to the nearest whole number, the patient should take 1 tablet every four hours.

Therefore, the patient should take 1 pill every four hours.

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Answer:

1.(b) All angles are right angles

2.angle c and angle a are alternate exterior angles.

Answer:

1.(b) All angles are right angles

2.angle c and angle a are alternate exterior angles.

Answer: 2xy

Step-by-step explanation:

Answer:

slope = \(\frac{6}{7}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (8, 8)

m = \(\frac{8-2}{8-1}\) = \(\frac{6}{7}\)

Answer:

A. 10 cm

Step-by-step explanation:

Answer:3 necklaces

Step-by-step explanation:

6.6=0.6x+1.4y

6.6=0.6(4)+1.4y

6.6=2.4+1.4y

6.6-2.4=(2.4-2.4)+1.4y

4.2=1.4y

4.2/1.4=1.4/1.4y

y=3

Cora can make total of  3 necklaces with the leftover wire.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that,

Total length of wire that Cora has = 6.6 feet

Length of wire needed to make a bracelet = 0.6 feet

Length of wire needed to make a necklace = 1.4 feet

Cora has made 4 bracelets.

Length of wire used for 4 bracelets = 4 × 0.6 = 2.4 feet

Remaining length = 6.6 feet - 2.4 feet = 4.2 feet

Number of necklaces which can be made using the remaining wire is,

= 4.2 / 1.4

= 3

Hence Cora can make 3 necklaces with the remaining wire.

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The value of  h’(1) is = 22

How may the chain rule example be used?

Solution: Since f′(x)=ex, the exponential function with base e's derivative is simply the function itself. G′(x)=4 is the derivative of g. The chain rule states that h′(x)=f′(g(x))g′(x)=f′(4x)4=4e4x. It was crucial that we assessed f's derivative at 4x in this example.

Given that :

h(x) = 2f(x).g(x)

f(1) = 3, g(1) = 2, f’(1) = 4, g’(1) = 1

h’(x) = 2 f'(x)g(x) + g'(x)f(x) by chain rule

h’(1) = 2 f'(1)g(1) + g'(1)f(1)

= 2 * (4 * 2 + 1 * 3)

= 2* (11)

= 22

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The cell phone charges would be $104.95 if you use 4200 minutes and 88 text messages

a. Let's choose the following variables:

M: Number of minutes used

T: Number of text messages

b. The formula to express the cell phone charges would be:

C = 34.95 + 0.35(M - 4000) + 0.10(T - 100)

The flat monthly rate is $34.95, and for each minute after the first 4000 minutes, there is an additional charge of $0.35. Similarly, for each text message after the first 100, there is an additional charge of $0.10.

c. Using 6000 minutes and 450 text messages:

C = 34.95 + 0.35(6000 - 4000) + 0.10(450 - 100)

C = 34.95 + 0.35(2000) + 0.10(350)

C = 34.95 + 700 + 35

C = $769.95

So the cell phone charges would be $769.95 if you use 6000 minutes and 450 text messages.

d. The formula to express the cell phone charges with minutes at least 4000 and text messages less than 100 would be:

C = 34.95 + 0.35(M - 4000)

Since the number of text messages is less than 100, there would be no additional charge for text messages.

e. Using 4200 minutes and 88 text messages:

C = 34.95 + 0.35(4200 - 4000)

C = 34.95 + 0.35(200)

C = 34.95 + 70

C = $104.95

So the cell phone charges would be $104.95 if you use 4200 minutes and 88 text messages

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Answer:

25%

Step-by-step explanation:

$115 - $92 = $23 (first blank)

To do the fraction it is the new amount/the original amount

23/92

divide 23 and 92

23/92 = 0.25 (second and third blank)

0.25 x 100% = 25%

A question on a math quiz asks, "What is 175% of 72?" Petra calculates 12.6 as the answer. Is this a reasonable answer? ExplainAnswer:

Step-by-step explanation:

Formula for sphere = 4/3pi radius cubed.

So 4/3 (3.14) 12^3

=4/3(3.14)1728

=(4/3)5425.92

=7234.56

Answer is D.

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By applying Pascal's triangle concept for the f(n) as per given condition the value f(2) is 1.

To find f(2),  calculate the sum of the elements in the second row of Pascal's triangle

and subtract the sum of all the elements from the previous rows.

Pascal's triangle is formed by starting with a row containing only 1

and then each subsequent row is constructed by adding the two numbers above it.

The first row of Pascal's triangle is simply 1.

The second row of Pascal's triangle is 1 1.

To calculate f(2),  sum the elements in the second row and subtract the sum of the elements in the previous rows.

Sum of elements in the second row = 1 + 1 = 2

Sum of elements in the first row = 1

This implies, f(2) = 2 - 1 = 1.

Therefore, using Pascal's triangle the value f(2) is equal to 1.

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Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Answer:

The long fence, AC = 44 feet

4 shorter segments at 11feet each = 44 feet

Area = 484 ft^2

Step-by-step explanation:

The three pens will share one fence section parallel to the barn, we'll call it AB.  Each pen will need two side fence segments, from the front fence to the barn.  We'll call those portions AC.  We need four of them:  two for the outer sides and two more to divide up the space equally among the three pens.  The total area would be AB*AC.

We know that AC + 4AB = 88 feet.

or AC = (88feet - 4AB)

Area = AB(88feet - 4AB)

Area = 88AB - 4AB^2

To maximize the area, we can take the first derivative and set it equal to zero:

Area' = 88 - 8AB

0 = 88 - 8AB

AB = 11 feet

AC = (88 - 4AB)

AC = (88 - 44)

AC = 44 feet

The fours segments of fence:  

AC + 4AB = 88 feet

(44) + 4(11 feet) = 88feet

Area = 44' x 11 ft' = 484 ft^2