Find the coordinates of point D in the diagram below:​

Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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EXPLANATION

Mathematical expression:

2x4 + 5 + x

The function shown in the graph is f(x)=3x-2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the given graph let us take two points.

(0, -2) and (2,4)

m=6/2=3

Now let us find y intercept.

4=3(2)+b

4=6+b

-2=b

Hence, the function shown in the graph is f(x)=3x-2.

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Answer:

11.2

Step-by-step explanation:

Find the number in the tenth place  1  and look one place to the right for the rounding digit  8 . Round up if this number is greater than or equal to  5  and round down if it is less than  5 .

Hope this helps!

Answer and Explanation:

Since this is an isosceles right triangle, you can use the ratio of side lengths specific to this type of triangle where both legs are the hypotenuse over root 2:

u = v = 164√2 / √2 = 164

so:

u = 164

v = 164

Answer:

Step-by-step explanation:

We know that:

Let's solve this using Pythagoras theorem.

Hence, the measure of u and v is 164 units.

Answer:

\(SOLUTION:-\)

\( \rm{passed \: percent = { \displaystyle{33 \frac{1}{3} \%} = \frac{100}{3}\% }}\)

\({ \displaystyle{ \rm{failed \: percent = \left( 100 - \frac{100}{3} \right)}\%}}\)

\(\displaystyle{ \frac{3 \times 100 - 100}{3}\% }\)

\(\displaystyle{ \frac{200}{3}\% }\)

Let,x be the total number of examinees:-

We have,

\(\displaystyle{ \frac{200}{3}\% \: \rm{of \: x = 240} }\)

\(\displaystyle{ \frac{200}{3} \times \frac{1}{100} \rm \: x = 240}\)

\(\displaystyle{ \rm{x = \frac{240 \times 3 \times 100}{200} }}\)

\(\displaystyle{ \rm{x = 360}}\)

Hence,required number of examinees = 360 .

Answer:

\(3456\; \rm cm^{2}\).

Step-by-step explanation:

The diagram suggests that the length of a row of five cubes is \(40\; \rm cm\). Hence, the length of the edge of each cube would be:

\(\displaystyle \frac{40\; \rm cm }{5} = 8\; \rm cm\).

That would correspond to an area of \((8\; \rm cm)^{2} = 64\; \rm cm^{2}\) for each face of the cube.

Refer to the diagram attached.

Viewing from the front and from the rear each shows \(11\) faces of the cubes.

Viewing from the top and from the bottom each shows \(10\) faces of the cubes.

Viewing from the left and from the right each shows \(6\) faces of the cubes.

When viewed from the six perspectives, \(2 \times 11 + 2 \times 10 + 2 \times 6 = 54\) faces of the cubes are visible in total.

For this particular construction, all faces that need to be painted are visible when viewed from exactly one of the six perspectives: front, rear, top, right, left, right. Hence, Sam would need to paint \(54\) of such \(64\; \rm cm^{2}\) squares.

The area that Sam needs to paint would be \(54 \times (64\; \rm cm^{2}) = 3456\; \rm cm^{2}\).

Answer:

106.6273

Step-by-step explanation:

Answer:

106.6273 ft

Step-by-step explanation:

The volume of the pyramid  equals the one-third of the volume of the rectangular prism which is: 13 units³.

The volume of a rectangular prism is calculated as: V = (length)(width)(height).

The volume of a pyramid is calculated as one-third of the product of its height, width, and length. Thus, the formula is given as: volume = 1/3(length)(width)(height)..

If the height, width, and length of a pyramid are the same as the height, width, and length of a rectangular prism, then:

Volume of Pyramid = 1/3(volume of rectangular prism)

Volume of Pyramid = 1/3(length)(width)(height).

Given the following:

Dimensions of the pyramid and the rectangular prism are the same.

Volume of the rectangular prism = 39 units³.

Therefore, since the volume of pyramid = 1/3(volume of rectangular prism), we would have the following:

The volume of the pyramid = 1/3(39)

The volume of the pyramid = 13 units³

Therefore, the volume of the pyramid  equals the one-third of the volume of the rectangular prism which is: 13 units³.

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The equation x=0 represents the set of points (x,y) in the plane that have the form

(since x is zero). So its graph is a vertical line, the y axis to be precise

Answer: D

Step-by-step explanation: x is a variable, and so is the number of tractors he sells. he is going to get paid $1000 for sure each month.

So 150x(the number of tractors) + 1000(his pay each month)

Answer:

19 is 47.5% of 40.

Step-by-step explanation:

First, you have to use the formula is/of=%/100, so since 19 is closest to the word is, 19 will go on the top left, since 47.5% is a percentage it will go on top of 100, finally, 100 always goes on the bottom and x will be the of, since there is no given number for it (19/x=47.5/100). You cross multiply (19x100) then divide it by the remaining number (47.5) then you get your answer of 40.

Answer: 14π

Step-by-step explanation: The formula for circumference is 2 * pi * the radius. However, we are looking for the terms of pi, so we will multiply 2 times pi to get 2 pi. then we get 2 pi x 7 which gives us 14pi, the answer.

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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The child will have $9.92 in his piggy bank.

What is basic arithmetic operations?

Basic arithmetic operations are the foundation of mathematics and include addition, subtraction, multiplication, and division. These operations are used to perform mathematical calculations and are necessary for solving a wide range of problems, from simple arithmetic problems to more complex mathematical equations.

The child has $9.30 and spends $0.13 on a snow cone, so their piggy bank balance becomes $9.30 - $0.13 = $9.17.

After finding $0.75 to put in the piggy bank, the child now has $9.17 + $0.75 = $9.92 in their piggy bank.

Hence, the child will have $9.92 in his piggy bank.

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Answer:

Step-by-step explanation:

Solve:

       \(\rule{250}{2}\)

\(\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}\)

    Solve 2=2+g/4

\(\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\)

When solving an equation, we need to make sure all variables are on the left-hand side, and all numbers are on the right.

Since we have numbers on both sides, we need to move them to one side, as follows:-

\(\Longrightarrow\sf{2-2=g/4}\)

\(\longrightarrow\sf{0=g/4}\)

Now, we multiply by 4 on both sides to get rid of the fraction:-

\(\longrightarrow\sf{0\times4=g/4\times4}\)

\(\longrightarrow\sf{0=g}\)

So we conclude that g=0.

\(\rule{300}{3}\)

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Hello !

you made a typo with the c^-2 because otherwise it does not make a round result

\(a^{2} *b^{2} *c^{2} \\\\= 1^{2} *2^{2}* (-3)^{2} \\\\= 1*4*9\\\\\boxed{= 36}\)

Step-by-step explanation:

divide 62 by 100 and then multiply that number by 66. I don't have a calculator on me rn sorry

Answer:

Fraction:

\(\frac{1023}{25}\)

Decimal:

40.92

Mixed Number:

\(40\frac{23}{25}\)

Step-by-step explanation:

66% is the same this as \(\frac{66}{100}\). You can simplify \(\frac{66}{100}\) to \(\frac{33}{50}\). Then, find \(\frac{33}{50}\) of 62, which is the same thing as \(\frac{33}{50}\) x 62. You’ll get either of the three options, a fraction, decimal, or a mixed number, but all three are the same thing (you get to choose which one).

Hope this helps! :)

Answer:

The probability of getting someone who tests positive, given that he or she did not have the disease = P(P|No) = 0.041

Step-by-step explanation:

Complete Question

The data represents the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests positive, given that he or she did not have the disease.

P/N | Yes | No

+ve | 141 | 6

-ve | 11 | 142

Note that +ve and -ve l stands for testing positive and negative respectively.

Yes and No represents whether one has the disease or not respectively.

Solution

Let

- The event of testing positive be P.

- The event of testing negative be N.

- The event of having the disease be Yes.

- The event of not having the disease be No.

The probability of getting someone who tests positive, given that he or she did not have the disease = P(P|No)

The conditional probability of A given B is given mathematically as

P(A|B) = P(A n B) ÷ P(B)

Hence,

P(P|No) = P(P n No) ÷ P(No)

To solve these probabilities, we first define the probability of an event as the number of elements in that event divided by the Total number of elements in the sample space.

P(No) = n(No) ÷ n(Sample space)

n(No) = 6 + 142 = 148

n(Sample Space) = 141 + 11 + 6 + 142 = 300

P(No) = (148/300)

P(P n No) = n(P n No) ÷ n(Sample space)

n(P n No) = 6

n(Sample Space) = 300

P(P n No) = (6/300)

P(P|No) = P(P n No) ÷ P(No)

= (6/300) ÷ (148/300)

= (6/148)

= 0.0405405405 = 0.041 to 3 d.p.

Hope this Helps!!!

Answer:

2/3x + 7 = 10

Step-by-step explanation:

Due to your wording, I believe this is what you might be looking for when you ask "2/3 a number x."

Answer:

\(\sf \dfrac{1}{16}\)

Step-by-step explanation:

    In exponent multiplication, if bases are same, add the powers.

             \(\sf \boxed{a^m*a^n=a^{m+n}}\)

             \(\sf \boxed{a^{-m}=\dfrac{1}{a^m}}\)

      \(\sf 4^6 * 4^{-8}=4^{6+(-8)}\\\\\)

                   \(\sf =4^{-2}\\\\ =\dfrac{1}{4^2}\\\\=\dfrac{1}{16}\)

Answer:

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC2 = AB2 + AC2. Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.

Pythagoras Theorem Equation

The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

Answer:

Answer:

step 2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

step 2

The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.

According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.

Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.

Interest = Principal * Rate

= $13,250.00 * 0.10358

≈ $1,370.56

Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.

Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.

Calculating the interest with a credit score of 680:

Interest = Principal * Rate

= $13,250.00 * 0.09132

≈ $1,210.57

Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.

Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

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Answer:

(1,2)

Step-by-step explanation:

x+4y = 9

2x -4y= -6

Add the equations together

x+4y = 9

2x -4y= -6

-------------------

3x +0y = 3

3x=3

Divide by 3

3x/3 = 3/3

x=1

Now find y

x+4y = 9

1 +4y =9

Subtract 1 from each side

4y = 8

Divide by 4

4y/4 = 8/4

y =2

Answer:

Step-by-step explanation:

P(A) = 4/52 = 0.07692 which is bigger than 5%

5% = 0.05

0.07 is above 5% which is surprising.

The P(Spade A) = 1/52 = 0.01923 which is under 2% which meets your criteria.

Answer:

C. $11.55

Step-by-step explanation:

First, multiply 4 by $0.85 to get an answer of $3.40. Next, multiply 6 by $1.25 to get an answer of $7.50. Add up the cost of the pencils and pens by adding $3.40 and $7.50 to get $10.90. Next, we have to add the tax. Multiply $10.90 by 0.06 to get $.65. Add the $.65 to the $10.90 for a grand total of $11.55. Hope this helps!