20. In the figure at right, ABDC lies in plane k and AD IDC.
AD is definitely perpendicular to k if which of the following is true?
(A) BDLDC (B) ADBC=AABC (C) ADBC is isosceles
(D) ADAB is similar to ADAC (E) none of these

Answer:

[tex]tan(2\theta) = -\frac{4}{3}\\[/tex]

Step-by-step explanation:

So cos is defined as: [tex]cos(\theta) = \frac{adjacent}{hypotenuse}[/tex], meaning we can tell that the adjacent side is 1, and the hypotenuse is 5, from the fraction you gave.

Using this we can solve for the opposite side.

[tex]1^2 + b^2 = \sqrt{5}^2\\1+b^2 = 5\\b^2=4\\b=2[/tex]

Now it's important to note, that b can be a negative number, so we have to use the information that sin(x) > 0, to determine the length of this side.

The sin is defined as: [tex]sin(\theta) = \frac{opposite}{hypotenuse}[/tex], and since we we're solving for the opposite side, this means that the value +\- 2, is in the top, and since the hypotenuse is positive, this means that the opposite side is also positive.

This also tells us one more thing, since both cos(x) and sin(x) are positive, we are dealing with a angle in the first quadrant.

So we can now define sin(x), using the opposite (2) and the hypotenuse (sqrt(5))

[tex]sin(\theta) = \frac{2}{\sqrt{5}}[/tex]

And we can rationalize the denominator for both the cosine and sine, by multiplying by the square root in the denominator so that

[tex]sin(\theta) = \frac{2\sqrt{5}}{5}\\\\cos(\theta) = \frac{\sqrt{5}}{5}[/tex]

Now we can define the value of tan(2 theta) using the double angle-identities such that:

[tex]tan(2\theta) = \frac{2\ tan(\theta)}{1-tan^2{\theta}}[/tex]

And we can also define tan(theta) using the definition that:

[tex]tan(\theta) = \frac{sin(\theta)}{cos(\theta)}[/tex]

So plugging in the values sin(theta) and cos(theta) we get the following:

[tex]tan(\theta) = \frac{\frac{2\sqrt{5}}{5}}{\frac{\sqrt{5}}{5}}\\\\tan(\theta) = \frac{2\sqrt{5}}{5} * \frac{5}{\sqrt{5}}\\\\tan(\theta) = 2[/tex]

Btw in the last step, I just canceled out the 5 and sqrt(5) since they were both in the denominator and numerator

So now let's plug this value, 2 as tan(theta) into the equation

[tex]tan(2\theta) = \frac{2\ *2}{1-2^2}\\\\tan(2\theta) = \frac{4}{-3}\\tan(2\theta) = -\frac{4}{3}\\[/tex]

Answer:

28

Step-by-step explanation:

Tangent is a line that touches the circle at one point and is perpendicular to the radius. Circle A has radius AB and tangent CB, so AB is perpendicular to CB. Therefore triangle ABC is a right angle, with angle B measuring 90 degrees. Since interior angles of a triangle add up to 180 degrees, measure of angle A is 180 - 90 - 62 = 28 degrees.

Answer:

1/2

Step-by-step explanation:

Since 50% is half the number of students it means that half of the students took the first bus which leaves the other half to take the 2nd bus

Answer:

84

Step-by-step explanation:

Multiply 35 by 2.5

Answer:

75 windows

Step-by-step explanation:

35 ---- 7

x ----- 15

[tex]x=\frac{(35)(15)}{7} =75[/tex]

Hope this helps

This means that after 0.5 hours, 259.81 milligrams of the medicine remain on the patient's body.

We know that the exponential function defined by:

[tex]m(h) = 300*(3/4)^h[/tex]

Represents the amount of a mediciene, in milligrams, after a number of hours h.

We want to see what does m(0.5) represent. This is the exponential function evaluated in h = 0.5

Then, it just represents the amount of medicine, in miligrams, in a patient's body present 0.5 hours after the medicine was administered.

Replacing h = 0.5 we get:

[tex]m(0.5) = 300*(3/4)^{0.5} = 259.81[/tex]

This means that after 0.5 hours, 259.81 milligrams of the medicine remain on the patient's body.

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[tex]d = \sqrt{ \frac{4h}{5} } \\ square \: both \: sides \\ d {}^{2} = \frac{4h}{5} \\ multiply \: both \: sides \: by \: 5 \\ 5d {}^{2} = 4h \\ divide \: both \: sides \: by \: 4[/tex]

[tex]h = \frac{5d {}^{2} }{4} [/tex]

There is only one statement that is true: B. The graph of the function is a parabola.

In this question we have a quadratic equation, whose characteristics have to be inferred and analyzed. We need to prove each of the five choices presented in the statement:

Choice A:

If we know that x = - 10, then we evaluated it at the function:

f(- 10) = (- 10)² - 5 · (- 10) + 12

f(- 10) = 162

False

Choice B:

By analytical geometry we know that all functions of the form y = a · x² + b · x + c always represent parabolae.

True

Choice C:

The quadratic function opens up as its leading coefficient is greater that 0.

False

Choice D:

If we know that x = 20, then we evaluate it at the function:

f(20) = 20² - 5 · (20) + 12

f(20) = 312

False

Choice E:

If we know that x = 0, then we evaluate it at the function:

f(0) = 0² - 5 · (0) + 12

f(0) = 12

There is only one statement that is true: B. The graph of the function is a parabola.

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The exponential function represented by the points (0, 2) and (3, 686) is y = 2(7)ˣ

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

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

The standard form of an exponential funtion is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

At point (0, 2)

2 = ab⁰

a = 2

At point (3, 686)

686 = 2b³

b = 7

The exponential function represented by the points (0, 2) and (3, 686) is y = 2(7)ˣ

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Answer:

y = 5x - 7

Step-by-step explanation:

y = mx + c

y = 5x + c

to find c, input given coordinates

8 = 5 x 3 + c

8 = 15 + c

-c = 15 - 8

-c = 7

c = -7

put that all together and you get:

y = 5x - 7

The equation of the line with a slope of 5 that contains the point (3,8) is

The equation of a line in slope-intercept form is given by y = mx + b, where m represents the slope and b represents the y-intercept.

Given that the slope is 5 and the line contains the point (3,8), we can substitute these values into the equation and solve for the y-intercept (b).

Using the point-slope form of the equation:

y - y₁ = m(x - x₁)

We have:

y - 8 = 5(x - 3)

Expanding and simplifying:

y - 8 = 5x - 15

Now, let's isolate y:

y = 5x - 15 + 8

y = 5x - 7

Therefore, the equation of the line with a slope of 5 that contains the point (3,8) is y = 5x - 7.

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∠ADB + ∠BDC = ∠ADC

39° + (3x - 4) = 8x + 5

3x - 4 = 8x + 5 - 39

3x - 4 = 8x - 34

34 - 4 = 8x - 3x

5x = 30

x = 6

∠ADC = 39° + (3(6) - 4) = 39 + 14 = 53°

Hope it helps!

The linear equation y = -x+45 models the scenario.

Solving the linear equation, it exists found that Hans will paint 16 snapdragons.

Since the rate of change exists always the exact, this question exists modeled by a linear equation.

Linear equation: y = mx + b

Where, m exists the slope and b exists the y-intercept.

To find the slope, we have to get two points (x, y), and the slope exists  given by the change in y divided by the change in x.

Points: (11, 34) and (12, 33).

Change in y: 33 - 34 = -1

Change in x: 12 - 11 = 1.

Slope: m = -1/1 = -1

The equation of the line exists y = -x + b

Replacing one of the points, the y-intercept can be found.

Point (11, 34) means that when x = 1, y = 34.

y = -x + b

34 = -1+b

b = 45

Therefore, the equation y = -x+45 models the scenario.

29 daisies mean that y = 29, we have to estimate the value of x for which y = 29.

y = -x+45

simplifying the equation,

29 = -x+45

x = 45 - 29 = 16

The value of x = 16

Therefore, Hans will plant 16 snapdragons.

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Answer:

The equation ✔ x = 45 – y models the scenario.

Hans will plant✔ 16 snapdragons

Step-by-step explanation:

Answer:

1025

Step-by-step explanation:

y=5x

y=5(205)

y=1025

The 205th term in the arithmetic sequence is 1025.

We have,

To find the 205th term in the sequence 5, 10, 15, 20, 25 ..., we can use the formula for an arithmetic sequence:

The nth term of an arithmetic sequence can be represented as:

[tex]a_n = a_1 + (n - 1) ~d[/tex]

Where:

[tex]a_n[/tex] is the nth term,

[tex]a_1[/tex] is the first term,

n is the position of the term we want to find, and

d is the common difference between consecutive terms.

In this sequence, the first term [tex]a_1[/tex] is 5, and the common difference (d) is 10 - 5 = 5.

Now, let's find the 205th term ([tex]a_{205}[/tex]):

= 5 + (205 - 1) * 5

= 5 + 204 * 5

= 5 + 1020

= 1025

Thus,

The 205th term in the arithmetic sequence is 1025.

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Answer:

20 L volume and 12.5 cm depth.

Step-by-step explanation:

See attached image.

Answer:

70

Step-by-step explanation:

8 choose 4: 8!/(4!*4!)=70

Answer:

1680

Step-by-step explanation:

the order matters so 8P4

The height of the rectangular prism. given its volume and base area is (3x³ + 16x² + 5x) / (x² + 5x) units.

Volume of a rectangular prism = Base area × height

Height = Volume of a rectangular prism ÷ Base area

3x³ + 16x² + 5x cubic units = (x² + 5x) square units × h

h = (3x³ + 16x² + 5x) cubic units ÷ (x² + 5x) square units

h = (3x³ + 16x² + 5x) / (x² + 5x) units

Therefore, the height of the rectangular prism. given its volume and base area is (3x³ + 16x² + 5x) / (x² + 5x) units.

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Using decimal multipliers, the correct statement is given by:

(iii) S1 = S2.

Increases of a% or decreases of a% re represented by decimal values, as follows:

Hence, in the context of this problem:

The options are given as follows:

They are equal, hence option (iii) is correct.

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The correct powers of x are not displayed in several of the goods.

Algebra tiles are mathematical manipulatives that help pupils better comprehend algebraic thinking and its ideas. These tiles have shown to give beginning algebra pupils in elementary, middle, high, and college concrete models.

Blocks called algebra tiles can be used to symbolize constant, linear, and quadratic terms. Small yellow squares stand in for constant blocks, green rectangles for linear blocks, blue squares for quadratic blocks, and red squares for negative sides for all other types of blocks.

Future:

The image shows,

3x(2x - 1) = 6x² - 3x

This should be the appropriate representation on the tile:

_____+x _____ +x _____ +x

+x _ +x² ______+x² ______+x²

|

+x__ +x² _____ +x² ______+x²

|

- __ -x ______ -x _______-x

+6x² - 3x

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The volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)

The complete question is added as an attachment

From the attached image, we have:

Length = 12 - 2x

Width = 7 - 2x

Height = x

The volume is calculated as:

Volume = Length * Width * Height

Substitute the known values in the above equation

Volume = (12 - 2x) * (7 - 2x) * x

This gives

Volume = x(12 - 2x)(7 - 2x)

Hence, the volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)

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The amount of Protein intake is 900 kilocalorie.

We have - 2000 Kilocalories of diet and 45 Percent of calories come from Proteins.

Wе have to find out the amount of protein intake.

Percentage of students affected are -  [tex]\frac{x}{n} \times 100[/tex]

In the question given -

Let the amount of Protein intake be y.

Then -

45 = y % of 2000

45 = [tex]\frac{y}{2000} \times100[/tex]

y = [tex]\frac{45\times2000}{100}[/tex]

y = 900 Kilocalorie

Hence, the amount of Protein intake is 900 kilocalorie.

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Check the picture below.

so the lateral area of the pyramid is really just the area of four triangles whose base is 10 and height is also 10, now, we're excluding the bottom because that's not lateral area.

[tex]\stackrel{\textit{area of four triangles}}{4\left[\cfrac{1}{2}(\stackrel{b}{10})(\stackrel{h}{10}) \right]}\implies 2(100)\implies \text{\LARGE 200}~ft^2[/tex]

Answer:

0.4

Step-by-step explanation:

4/10 is 4÷10 = 0.4

Answer:

(6, 1)

(1, 3)

(-7, 6)

Step-by-step explanation:

To have a function, each value used for x can appear only once.

The first set of points has as x: 1, -7, -3.

The only choice without 1, -7, or -3 for x is (6, 1)

The second set of points has as x: 2, 6, -7.

The only choice without 2, 6, or -7 for x is (1, 3)

The third set of points has as x: 1, -3, 6.

The only choice without 1, -3, or 6 for x is (-7, 6)

Answer:

 [tex]h(x)=7(1.3)^x[/tex]

Step-by-step explanation:

Since this is an exponential equation we will use

[tex]h(x)=a(b)^x[/tex]

[tex]a[/tex] Is your starting value, 7

[tex]b[/tex] Is your percentage of change, remember its not 0.3, as that would hint the population is decreasing by thirds exponentially, instead we will use 1.3 as our percent of change, as the 1 maintains the original value and the 0.3 adds 30%, now all we have to do is put it all together!

[tex]h(x)=7(1.3)^x[/tex]

Answer:

Hey stu132057, your the MAD for the data set given is

Step-by-step explanation:

Step 1: Find the mean of the data: (14+13+16+12+17+21+26)/7 = 17

Step 2: Find the difference between each data and mean:Difference between 14 and 17 is 3

Difference between 13 and 17 is 4

Difference between 16 and 17 is 1

Difference between 12 and 17 is 5

Difference between 17 and 17 is 0

Difference between 21 and 17 is 4

Difference between 26 and 17 is 9

Step 3: Add all the differences: 3+4+1+5+0+4+9 = 26

Step 4: Divide it by the number of data:26/7 = 3.7

So, the MAD = 3.7

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

Have a great day,

Nish

The value of the z score is 1.03.

According to the statement

we have given that the value of mean and standard deviation and we have to find the value of the z score.

So, For this purpose we know that the

Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.

And the given values are:

mean value = 69 inches

s.d value = 2.8 inches

And the value of x is 71.9 inches.

So, The Z score is

z = x - mean / standard deviation

substitute the values in it then

z = 71.9 - 69 / 2.8

then

z = 2.9 /2.8

z  = 1.03

So, The value of the z score is 1.03.

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Based on the stock price and its growth rate, the function that models the situation is 48 (1 + 8%) ^ n. The price of the stock 6 years from now is $76.17.

The value of a stock in future can be calculated using several types of formulas that take into account the various characteristics of the stock.

For this stock, the value of the stock at any given year is:

= Current price of stock x ( 1 + growth rate) ^ number of years from now

Assuming the number of years is n, the function becomes:

= 48 x ( 1 + 8%) ^n

In 6 years, the price will be:

= 48 x ( 1 + 8%) ⁶

= $76.17

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Step-by-step explanation:

abx^2-aby^2+xya^2-xyb^2

abx^2+xya^2-aby^2-xyb^2

ax(bx+ya)-yb(ay+xb)

ax(bx+ya)-yb(xb+ay)

(ax-yb) (bx+ya)