ABCD is a rhombus. If AB = 2x + 12 , AC = 7x - 3, ∠=12°, and ∠ = (4y - 1)°.m ∠BAC = __ . (FIND BAC NOT CD)

Answer: Anna got 30

Step-by-step explanation: 2x+3y=25

15+10=25

Answer:

m∠DBC = 51°

Step-by-step explanation:

Circle Theorem vocabulary

Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of the intercepted arc.

Therefore:

[tex]\sf \implies \angle DBC=\dfrac{1}{2}\:\overset{\frown}{BC}[/tex]

[tex]\sf \implies \angle DBC=\dfrac{1}{2}\:(102^{\circ})[/tex]

[tex]\sf \implies \angle DBC=51^{\circ}[/tex]

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[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

To determine ∠DBC, we will apply the theorem relating the inscribed angle to the intercepted arc:

[tex]\longrightarrow \sf{Intercepted \: arc= (inscribe \: angle)}[/tex]

[tex]\longrightarrow \sf{Intercept \: arc= 102^\circ}[/tex]

[tex]\longrightarrow \sf{Inscribed \: angle= \angle DBC }[/tex]

[tex]\longrightarrow \sf{102=2( \angle DBC)}[/tex]

[tex]\longrightarrow \sf{\angle DBC= \dfrac{102}{2} }[/tex]

▪ [tex]\longrightarrow \sf{\angle DBC = 51^\circ}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\boxed{\bf{\large m \: \angle DBC= 51^\circ}}[/tex]

Answer:

8

Step-by-step explanation:

I belive what they mean is how many dots thier are i am not complety sure though but just by counting them up i came up with 8.

hope this helped

The answer is y = -5.5x - 52.

First, let's find the slope of the line.

m = Δy/Δx

Now, substitute the slope and one of the given points in the point slope equation.

y - y₁ = m (x - x₁)

Answer: y=-5,5x-52.

Step-by-step explanation:

                        Equation of a straight line

                               [tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

[tex](-10;3)\ \ \ \ \ (-8;-8).\\\displaystyle\frac{x-(-10)}{-8-(-10)} =\frac{y-3}{-8-3}\\ \frac{x+10}{-8+10}=\frac{y-3}{-11} \\ \frac{x+10}{2}=\frac{y-3}{-11} \\-11*(x+10)=2*(y-3)\\-11x-110=2y-6\\2y=-11x-104\ |:2\\y=-5,5x-52.[/tex]

Answer:

36

Step-by-step explanation:

Honestly, I'd work this out visually (see image) by drawing a rectangle and dividing it up. But if you need to show the math, here's how to do it:

Let x = the number of students in the homeroom

1/3 x have drama

1/4 (x - 1/3x) have band, and we are told 6 students have band, so

1/4 (x - 1/3 x) = 6

1/4 (2/3 x) = 6    

2/12 x = 6          

1/6 x = 6            

6 × 1/6 x = 6 × 6

1 x = 6 × 6            

x = 36

Answer:

36

Step-by-step explanation:

Let n be the total number of students in Mr. Short's homeroom. Then, working backward, we see that 

6 = 1/4(1 - 1/3)n = 1/4(2/3)n = 1/6n,$

so n = 6 x 6 = 36 students.

Answer: 80% of the 10 people saw the show.

Step-by-step explanation:

8/10 = 0.8, which is 80%.

I hope this helped!

The statement that the equation has no solutions because the constant is the same is true

The equation is given as:

3x - 8 = 7x- 8

Add 8 to both sides

3x - 8 + 8= 7x-  8 + 8

Evaluate the like terms

3x = 7x

Divide both sides by x

3 = 7

The above equation is false, because 3 and 7 are not equal

This means that the statement that the equation has no solutions because the constant is the same is true

Hence, I agree with Kiran

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The value of x is 11 1/2 OR 11.5

From the question, we are to determine the value of x

In the given diagram, we have two isosceles triangles

Since base angles of isosceles triangles are equal,

Then, each of the base angles of the isosceles triangle is 68°

Then, we can write that

m ∠2 + 68° + 68° = 180° (Sum of angles in a triangle)

From the given information,

m ∠2 = 4x - 2

Then,

4x -2 + 68° + 68° = 180°

4x = 180 - 68 - 68 +2

4x = 46

x = 46/4

x = 11 1/2 OR 11.5

Hence, the value of x is 11 1/2 OR 11.5

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The surface integral of the given surface [tex]z=\frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2})[/tex] in the intervals 0 ≤ x ≤ 4, 0 ≤ y ≤ 1 is 7.36615.

To evaluate the surface integral, the formula applied is

[tex]S=\int\limits^b_a\int\limits^d_c {f(x,y)} \ dy\ dx[/tex]

⇒ S = [tex]\int\limits^b_a \int\limits^d_c {\sqrt{1+(\frac{dz}{dx})^2+(\frac{dz}{dy})^2 } } \, dy \, dx[/tex]

Where the differentiation is partial differentiation and f(x, y) = z.

The given function is

f(x, y) = [tex]z=\frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2})[/tex]

Then, applying the partial differentiation w.r.t x and y respectively,

dz/dx = [tex]\frac{2}{3}(\frac{3}{2})x^{1/2}[/tex] = [tex]x^{1/2}[/tex]

dz/dy = [tex]\frac{2}{3}(\frac{3}{2})y^{1/2}[/tex] = [tex]y^{1/2}[/tex]

Then,

we have surface integral  formula as

S = [tex]\int\limits^b_a \int\limits^d_c {\sqrt{1+(\frac{dz}{dx})^2+(\frac{dz}{dy})^2 } } \, dy \, dx[/tex]

On substituting,

⇒ S = [tex]\int\limits^4_0 {\int\limits^1_0 {\sqrt{1+(x^{1/2})^2+(y^{1/2})^2} \, dy } \, dx[/tex]

⇒ S = [tex]\int\limits^4_0 {\int\limits^1_0 {\sqrt{1+x+y} \, dy } \, dx[/tex]

On integrating w.r.t y

⇒ S = [tex]\int\limits^4_0 {\frac{2}{3}(1+x+y)^{3/2}} \,|_0^1 dx[/tex]

Applying limits,

⇒ S = [tex]\int\limits^4_0 {\frac{2}{3}[(1+x+1)^{3/2}-(1+x+0)^{3/2} } \, dx[/tex]

⇒ S = [tex]\frac{2}{3} \int\limits^4_0 {[(x+2)^{3/2}-(x+1)^{3/2}}] \, dx[/tex]

Again applying the integration w.r.t x

⇒ S = [tex]\frac{2}{3}[\frac{2}{5}(x+2)^{5/2}-\frac{2}{5}(x+1)^{5/2}]|_0^4[/tex]

Applying the limits and simplifying,

⇒ S = [tex]\frac{4}{15}[(4+2)^{5/2}-(4+1)^{5/2}-(0+2)^{5/2}+(0+1)^{5/2}][/tex]

⇒ S = [tex]\frac{4}{15}[1+36\sqrt{6}-25\sqrt{5}-4\sqrt{2}][/tex]

∴ S = 7.36615

Therefore, the surface integral of the given function is 7.36615.

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3 /10 foot³ packing material is required to fill the box.

What is meant by volume of prism?

Volume =  base area × height

             = 9/10 × 1/3

             =  3 /10  foot³

Therefore, 3/10  foot³ packing material is required to fill the box.

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The complete question is-

An empty box is shaped like a rectangular prism. The box has a base area of 9/10 square foot and a height of 1/3 foot. How much packing material is required to fill the box?

The height of the taller building is 18.6 meters

A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

Therefore, the height of the taller building is the sum of the height of the smaller building and upper part of the taller building.

tan 53 = opposite / adjacent

tan 53 = x / 10

cross multiply

x = 10 tan 53

x = 10 × 1.32704482162

x = 13.2704482162

x = 13.3 m

tan 28 = y / 10

y = 10 tan 28

y = 5.31709431661

y = 5.3

Therefore, the height of the taller building is 13.3 + 5.3 = 18.6 meters.

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Answer:

y=(1/-4)(x+4)^2 +4

Step-by-step explanation:

Don't ask

720 cubic inches of soil will be in the flower box.

Cuboid Definition: Cuboid shaped objects surround us in our day-to-day life. From television sets, books, carton boxes to bricks, mattresses, and shoeboxes, cuboid objects are all around us. In Geometry, a cuboid is a three-dimensional figure with six rectangular faces, twelve edges, and eight vertices.

Volume of Cuboid = Length x Width x Height

∴ The volume of the soil box = 15 x 8 x 8 = 960 inch³

Since 3/4 is occupied by the soil, the volume of the soil becomes

= 3/4 x 960

= 720 inch³

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Each element in the range of g(x) is 3 less than the corresponding element in the range of f(x).

Answer:

See below.

In short, by having vertical shift will affect range from -1 ≤ y ≤ 1 to -1 + a ≤ y ≤ 1 + a

Step-by-step explanation:

Generally, a cosine function without vertical shift will always have range equal to -1 ≤ y ≤ 1

If there is given vertical shift, our range will change to -1 + a ≤ y ≤ 1 + a

An example is if we are given the function of cos(x), this always has range of -1 ≤ y ≤ 1 because there is no vertical shift.

But if we have cos(x) + 1, we have vertical shift which is 1. Then the range will be -1+1 ≤ y ≤ 1+1 which equals to 0 ≤ y ≤ 2.

Hence, the function of -5cos(2x) has only range of -1 ≤ y ≤ 1 but the function of -5cos(2x) - 3 will have range of -1-3 ≤ y ≤ 1-3 which equals to -4 ≤ y ≤ -2

The identity for addition for rational numbers is zero which is the option b.

Given addition of rational numbers.

We are required to find the identity for the addition of rational numbers.

Rational numbers are those numbers which can be written in the form of p/q and q cannot be equal to zero because if q is equal to zero the whole fraction will become infinity. The numbers whih cannot be written as p/q are known as irrational numbers.

From the all option zero is the identity for addition for rational numbers. This  means if a is a rational number. Then a+0=0+a=a.

Hence the identity for addition for rational numbers is zero which is the option b.

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The discount to be increased so that he can gain only 15% is 8%.

How much is the discount to be increased so that he can gain only 15%:

The cost price of the goods - y.

The selling price of the goods - x.

The selling price is

1.2y (100% + 20% = 120%).

The refrigerator was sold at 13% VAT at Rs. 10848:

=> 1.2y + 13%(1.2y) = 10848

=> 1.2y + 0.156y = 10848

=> 1.356y = 10848

=> y = 8000

Thus, the cp is Rs 8000.

The selling price is:

=> 0.96x = 1.2y

=> 0.96x = 1.2(8000)

=> x = 10000

The selling price is Rs. 10000

For a profit of 15%, that is 1.15(8000) = 9200, the discount is:

(1 - discount)10000 = 9200

1 - discount = 0.92

Discount = 1 - 0.92 = 0.08 or 8%

How much is the discount to be increased so that he can gain only 15%: Discount=8%

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Answer: [tex]\Large\boxed{a_n=6n-4}[/tex]

Step-by-step explanation:

Given sequence

2, 8, 14, 20, 26

Determine the pattern

2 + 6 = 8

8 + 6 = 14

14 + 6 =20

20 + 6 = 26

For each term, add 6 to get the next term

Determine the type of sequence

Since it continuously adds 6, the common difference is 6, which means it is an arithmetic sequence

Given the arithmetic sequence formula

aₙ = a₁ + d (n - 1)

Substitute values into the formula

aₙ = (2) + (6) (n - 1)

aₙ = 2 + 6 (n - 1)

aₙ = 2 + 6n - 6

aₙ = 2 - 6 + 6n

[tex]\Large\boxed{a_n=6n-4}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Given sequence :-

Solution :-

We need to calculate the nth term of the given sequence.

We know that,

Applying the values here.

>> tn = 2 + (n - 1) 6

>> tn = 2 + (n - 1) × 6

>> tn = 2 + 6n - 6

>> tn = 6n - 4

Therefore, nth term of the sequence is (6n - 4).

The area of the given parallelogram is 8 square units

A parallelogram is a 2 dimensional figure with 4 sides and angles. From the given diagram, the opposite sides are equal and the sum of the adjacent angles are supplementary

The formula for calculating the area of a parallelogram is expressed as:

A = base * height

From the given diagram

Base = (4, 0) = 4 units

Height. = (2, 0) = 2 units

Substitute the given values into the formula to have:

A = 4 units * 2 units

A = 8 square units

Hence the area of the given parallelogram is 8 square units

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Using the Fundamental Counting Theorem, it is found that there are 1024 ways of delivering the letters.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem, each house has a correct letter, however the letter cannot be used for the house, hence the parameters are given as follows:

n1 = n2 = n3 = n4 = n5 = 5 - 1 = 4.

Thus the number of ways is:

N = 4 x 4 x 4 x 4 x 4 = 4^5 = 1024.

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Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.

At the null hypothesis, it is tested if the average cost is still of $50,000, that is:

[tex]H_0: \mu = 50000[/tex]

At the alternative hypothesis, it is tested if the average cost is decreasing, that is:

[tex]H_1: \mu < 50000[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are:

[tex]\overline{x} = 49450, \mu = 50000, \sigma = 2500, n = 100[/tex]

Hence:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{49450 - 50000}{\frac{2500}{\sqrt{100}}}[/tex]

z = -2.2.

Using a z-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with z = -2.2, the p-value is of 0.0139.

Since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.

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Answer:

6 children passes

Step-by-step explanation:

a = adult and c = children

25a + 15c = 440           and          a + c = 20

                                                     c = 20 - a

25a + 15(20-a) = 440

25a + 300 - 15a = 440

25a - 15a = 440 - 300

10a = 140

a = 140/10

a = 14 and this is 14 adult tickets

Now we plug the a value into the equation to find the c value

14 + c = 20

c = 20 - 14

c = 6

Verify answer:

25(14) = 15(6) = 440

350 + 90 = 440

440 = 440

Answer: x =   -1

Step-by-step explanation:

To remove the radical on the left side of the equation, square both sides of the equation.

√1−3x2=(x+3)2

Simplify each side of the equation.

1−3x=x2+6x+9

Solve for x

x=−1−8

Exclude the solutions that do not make true

√1−3x=x+3

x=−1

The length of the rectangle is 77cm.

According to the statement

we have given that the area of a painting is 4081 c m squared. and width of the painting is 53 cm.

And we have to find the Length of the painting.

So, For this purpose

Area of rectangle is the region occupied by a rectangle within its sides. It depends on its sides.

So, the formula to find the area of rectangle is

Area = Length*Breadth

4081 = L*53

L = 4081/53

L = 77 cm.

So, The length of the rectangle is 77cm.

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The value of dividing x^2-3x+9 by x-2 is x + 3

There are several ways to divide polynomial functions; some of these ways include

The expression for the polynomial division is given as:

x^2-3x+9/x-2

To divide polynomial functions, we make use of the division by factorization method

Start by expanding the numerator of the polynomial division

x^2-3x+9/x-2 = x^2 + 3x - 6x + 9/x-2

Factorize the equation

x^2-3x+9/x-2 = x(x + 3) - 2(x + 3)/x - 2

Factor out x + 3 from the numerator

x^2-3x+9/x-2 = (x- 2)(x + 3)/x - 2

Cancel out the common factors

x^2-3x+9/x-2 = x + 3

Hence, the value of dividing x^2-3x+9 by x-2 is x + 3

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Answer:

See image

Step-by-step explanation:

Using a graphing calculator, first press the Y= button at the top left.

Then enter the equation given in the question.

Next, press 2nd then graph, and you will get the table. Put in whatever values for x to get y.

So your answer is 48, 18, 0, -6, 0, -18, 0, 48

The mean of the data set A is 4.58 while the mean of data set B is 5.

An equation is an expression that shows the relationship between two or more numbers and variables.

The mean of a set of numbers is the average of that group of number. It is the ratio of the sum of the data to the total number of data.

Mean of data set A = [(3 * 1) + (4 * 3) + (5 * 2) + (6 * 2) + (7 * 3) + (8 * 1)] / (1 + 3 + 2 + 2 + 3 + 1) = 4.58

Mean of data set B = [(4 * 2) + (5 * 2) + (6 * 2)] / ( 2 + 2 + 2) = 5

The mean of the data set A is 4.58 while the mean of data set B is 5.

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Answer:

[tex]4\ln \left| \dfrac{1}{3}\sqrt{9+(\ln x)^2} + \dfrac{1}{3}\ln x \right|+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

[tex]\displaystyle \int \dfrac{4}{x\sqrt{9+(\ln(x))^2}}\:\:\text{d}x[/tex]

Rewrite 9 as 3²:

[tex]\implies \displaystyle \int \dfrac{4}{x\sqrt{3^2+(\ln(x))^2}}\:\:\text{d}x[/tex]

Integration by substitution

[tex]\boxed{\textsf{For }\sqrt{a^2+x^2} \textsf{ use the substitution }x=a \tan\theta}[/tex]

[tex]\textsf{Let } \ln x=3 \tan \theta[/tex]

[tex]\begin{aligned}\implies \sqrt{3^2+(\ln x)^2} & =\sqrt{3^2+(3 \tan\theta)^2}\\ & = \sqrt{9+9\tan^2 \theta}\\ & = \sqrt{9(1+\tan^2 \theta)}\\ & = \sqrt{9\sec^2 \theta}\\ & = 3 \sec\theta\end{aligned}[/tex]

Find the derivative of ln x and rewrite it so that dx is on its own:

[tex]\implies \ln x=3 \tan \theta[/tex]

[tex]\implies \dfrac{1}{x}\dfrac{\text{d}x}{\text{d}\theta}=3 \sec^2\theta[/tex]

[tex]\implies \text{d}x=3x \sec^2\theta\:\:\text{d}\theta[/tex]

Substitute everything into the original integral:

[tex]\begin{aligned} \implies \displaystyle \int \dfrac{4}{x\sqrt{9+(\ln(x))^2}}\:\:\text{d}x & = \int \dfrac{4}{3x \sec \theta} \cdot 3x \sec^2\theta\:\:\text{d}\theta\\\\ & = \int 4 \sec \theta \:\: \text{d}\theta\end{aligned}[/tex]

Take out the constant:

[tex]\implies \displaystyle 4 \int \sec \theta\:\:\text{d}\theta[/tex]

[tex]\boxed{\begin{minipage}{7 cm}\underline{Integrating $\sec kx$}\\\\$\displaystyle \int \sec kx\:\text{d}x=\dfrac{1}{k} \ln \left| \sec kx + \tan kx \right|\:\:(+\text{C})$\end{minipage}}[/tex]

[tex]\implies 4\ln \left| \sec \theta + \tan \theta \right|+\text{C}[/tex]

[tex]\textsf{Substitute back in } \tan\theta=\dfrac{1}{3}\ln x :[/tex]

[tex]\implies 4\ln \left| \sec \theta + \dfrac{1}{3}\ln x \right|+\text{C}[/tex]

[tex]\textsf{Substitute back in } \sec\theta=\dfrac{1}{3}\sqrt{9+(\ln x)^2}:[/tex]

[tex]\implies 4\ln \left| \dfrac{1}{3}\sqrt{9+(\ln x)^2} + \dfrac{1}{3}\ln x \right|+\text{C}[/tex]

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Using a quadratic regression equation, it is found that the prediction of volunteers in year 10 is of:

A. 47.

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, we have that the function initially increases, then it decreases, which means that it is a quadratic function. The points (x,y) to  be inserted into the calculator are given as follows:

(1, 20), (2,17), (3, 16), (4,16), (5,18), (6,21), (7,25), (8,31)

Inserting these points into the calculator, the prediction of y for a value of x is given as follows:

y = 0.702x^2 - 4.726x + 23.857

Hence, when x = 10, the prediction is:

y = 0.702 x 10² - 4.726 x 10 + 23.857

y = 47.

Hence option A is correct.

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