If , , and , then and .

we know the ratio of yellow and red tulips are 2 : 3, if there are 100 total, let's simply divide 100 by (2 + 3) and distribute accordingly.

\(\stackrel{\textit{\large yellow to red tulips ratio}}{\cfrac{\stackrel{\textit{yellow tulips}}{y}}{\stackrel{\textit{red tulips}}{r}} = \cfrac{2}{3}}\qquad \qquad \cfrac{2\cdot \frac{100}{2+3}}{3\cdot \frac{100}{2+3}}\implies \cfrac{2(20)}{3(20)}\implies \cfrac{\stackrel{yellow}{40}}{\underset{red}{60}}\)

Using exponential properties, it is found that the equivalent expression to the frequency of any pitch is given by:

\(f = 440\sqrt[12]{2^{10}}\)

It happens according to the following rule, with the denominator as the root and the numerator as the exponent:

\(a^{\frac{n}{m}} = \sqrt[m]{a^n}\)

The rule for the frequency is given by:

\(f = 440(2)^{\frac{10}{12}}\)

Hence the equivalent expression to f is given by:

\(f = 440\sqrt[12]{2^{10}}\)

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Answer:

-1/2

Step-by-step explanation:

The slope is always next to the x    :)

Answer:

Step-by-step explanation:

18 * 10 - 8 * 4    (remember pemdas)

180 - 32 =

148 cm²

The quadratic function for the path of the basketball as it is thrown indicates;

The path of the basketball will not make the shot

The height reached is about 5.24 meters

A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, c, are numbers.

The function for the path of the basketball is; b(x) = (-1/7)·x² + 1.36·x + 2

The function for the location of the basketball net is; n(x) = 3 and (8 < x < 8.5), where;

n(x) = The vertical height of the basketball

Plugging in the value of the n(x) = b(x), to check if equations have a common solution, we get;

b(x) = n(x) = 3 = (-1/7)·x² + 1.36·x + 2

(-1/7)·x² + 1.36·x + 2 - 3 = 0

(-1/7)·x² + 1.36·x - 1 = 0

(1/7)·x² - 1.36·x + 1 = 0

Solving the above equation, we get;

x = (119 - √(9786))/(25) ≈ 0.803, and x = (119 + √(9786))/(25) ≈ 8.717

Therefore, the x-coordinates of the height of the path of the basketball when the height is 3 meters are 0.803 and 8.717, neither of which are within the range (8 < x < 8.5), therefore, the baseketball will not go through the net and the path will not make the shot.

Bonus; The x-coordinates of the highest point of a quadratic function, f(x) = a·x² + b·x + c is; -b/(2·a)

Therefore, the x-value at the highest point of the equation, b(x) = (-1/7)·x² + 1.36·x + 2 is; x = -1.36/(2 × (-1/7)) = 1.36 × 7/2 = 9.52/2 = 4.76

The height of the highest point is; b(9.52) = (-1/7)·(4.76)² + 1.36·(4.76) + 2 ≈ 5.24 meters

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Answer:

the correct answer is -1/16 i believe

Answer: The blank is 112

Step-by-step explanation:

\(3^2 +b^2 =11^2 \\\\9+b^2 =121\\\\b^2 =112\\\\b=\sqrt{112}\)

Answer:

√112

Step-by-step explanation:

Answer:

The volume is about 1,128.88 cubic cm.

Step-by-step explanation:

\( \frac{1}{3} \pi( {7}^{2} )(22) = 1128.88\)

Answer:

(a+b)(a+b)

Step-by-step explanation:

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

tan x= -3/1

So, H = √1 + 9 = √10

sin x= -3/ √10 and cos x= 1/ √10

So, sin 2x= 2 sin x cos x =2 ( -3/ √10 )(1/ √10) = -3/10

and, cos 2x= 1- 2 sin²x

                  = 1- 2( 9/10)

                  = -8/10

and, tan 2x = sin 2x/ cos 2x =  -3/10 / ( -8/10) = 3/8

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After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.

From the label, we see that the serving size contains 3.5g of saturated fat.

To calculate the %DV for saturated fat, we use the equation:

%DV = (amount of nutrient per serving / DV) x 100%

Plugging in the values for saturated fat, we get:

%DV = (3.5g / 19g) x 100%

%DV = 0.1842 x 100%

%DV ≈ 18%

Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

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Answer:

b

Step-by-step explanation:

I think b is your answer if not I'm so sorry.

Answer:

a

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

The answer is 4

Step-by-step explanation:

I learnt this in 7th grade.

Answer: The answer is 1.

Step-by-step explanation: The entered points belong to an increasing, linear function.

Equation: y = 1x + 3.

The answer choice which must be true regarding the linear function is; The set must have a constant additive rate of change.

Since a linear function typically takes the slope-intercept form; f(x) = mx +c.

It therefore follows that the equation must have a constant slope m, which is the described additive constant rate of change.

It therefore follows that, the answer choice which is true regarding the linear function is therefore; The set must have a constant additive rate of change.

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Answer:

x=1 and y=3

Step-by-step explanation:

-2x1=-2

-2+3=1

So this answer makes sense

Answer:

y = 2x + 1

Step-by-step explanation:

Given: -2x+y=1

Add 2x to both sides: y=1+2x

Reorder: y = 2x + 1

I am not sure exactly what you need for this point, but here is the equation in y=mx+b form aka slope-intercept form

m = slope = 2

b = y-intercept = 1

Hope this helps, have a nice day :D

Answer:

1/6

Step-by-step explanation:

0.333 - 1/3

0.6667 - 1/6

0.2 - 2/10

0.2857 - 2/7

The dimensions of the rectangular slab are 16 meters in length and 2 meters in width.

Let's assume the length of the rectangular slab of concrete is L meters. According to the given information, the width is 14 meters less than the length, so the width would be L - 14 meters.

The formula for the area of a rectangle is A = length × width. In this case, the area is given as 32 m², so we can set up the equation:

32 = L × (L - 14)

Expanding the equation, we get:

32 = L² - 14L

Rearranging the equation, we have:

L² - 14L - 32 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. In this case, it's easier to use the quadratic formula:

L = (-b ± √(b² - 4ac)) / (2a)

Here, a = 1, b = -14, and c = -32. Substituting these values into the formula, we get:

L = (14 ± √((-14)² - 4 × 1 × (-32))) / (2 × 1)

Simplifying further:

L = (14 ± √(196 + 128)) / 2

L = (14 ± √324) / 2

L = (14 ± 18) / 2

Therefore, we have two possible values for L:

L₁ = (14 + 18) / 2 = 16

L₂ = (14 - 18) / 2 = -2

Since the length of the slab cannot be negative, we discard the negative value.

Thus, the length of the rectangular slab is 16 meters. To find the width, we subtract 14 meters from the length:

Width = 16 - 14 = 2 meters

Therefore, the dimensions of the rectangle are 16 meters by 2 meters.

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Answer:

-1

Step-by-step explanation:

\( - 2 \leqslant 0 < 1\)

g(x)=0-1=-1

The value of the function g(0) is -1.

A relation is a function if it has only One y-value for each x-value.

The given function g(x) = 3x-2,  -4≤x<-2

g(x) = -x-1,  -2≤x<1

g(x)=6, 1≤x≤3

We need to find value of g(0).

Let us check at which interval the value zero lies.

The zero lies in the interval  -2≤x<1.

So we have to use the function g(x)=-x-1

Now put x as zero

g(0)=-0-1

=-1

Hence, the value of the function g(0) is -1.

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Answer:

the product of the decimal equivalents of all discount in the series

Answer:

\(6\)

Step-by-step explanation:

\(1296^{0.17}\)

\(1296^{0.17}=3.38176\dots\)

\(=3.38176\dots\)

\(1296^{0.08}\)

\(1296^{0.08}=1.77422\dots\)

\(=1.77422\dots\)

\(\mathrm{Multiply\:the\:numbers:}\:3.38176\cdot \:1.77422=5.99998\dots\)

\(=5.99998\dots\)

\(=5.99998\)≈\(6\)

Answer:

D

Step-by-step explanation:

using the rules of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

\(a^{\frac{m}{n} }\) = \(\sqrt[n]{a^{m} }\)

\((1296)^{0.17}\) × \((1296)^{0.08}\)

= \(1296^{(0.17+0.08)}\)

= \(1296^{0.25}\) = \(1296^{\frac{1}{4} }\) , then

\(\sqrt[4]{1296}\)

= \(\sqrt[4]{6^{4} }\)

= 6

The result of the addition operation of 1204.2 + 4.72613 is approximately 1208.93.

An addition operation involves two addends added together to result in a number called the sum.

The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.

Mathematical operations combine numbers, variables, and values with mathematical operands to solve mathematical questions.

1204.2 + 4.72613

= 1208.92613

= 1208.93

Thus, the addition of 1204 and 4.72613 yields a total of 1208.93 approximately.

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Answer:

t = 1.2, -1.2

\(-2x+6=12\\2x=-6\\x=-3\)

Answer:

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

Find the differences in the sequence  -11, -7, -3, 1, ...

The difference is common, so the sequence is an AP.

The nth term is:

Find the 52nd term:

Find the 52nd term using the given formula:

Find the previous term:

Find the common difference:

Answer:

\(\begin{aligned}\textsf{34)} \quad d&=4\\a_n&=4n-15\\a_{52}&=193\end{aligned}\)

\(\begin{aligned}\textsf{35)} \quad d&=-4\\a_{52}&=-238\end{aligned}\)

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Given sequence:

To determine if the given sequence is arithmetic, calculate the differences between consecutive terms.

\(a_4-a_3=1-(-3)=4\)

\(a_3-a_2=-3-(-7)=4\)

\(a_2-a_1=-7-(-11)=4\)

As the differences are constant, the sequence is arithmetic, with common difference, d = 4.

The explicit formula for an arithmetic sequence is:

\(\boxed{a_n=a+(n-1)d}\)

where:

To find the explicit formula for the given sequence, substitute a = -11 and d = 4 into the formula:

\(\begin{aligned}a_n&=-11+(n-1)4\\&=-11+4n-4\\&=4n-15\end{aligned}\)

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=4(52)-15\\&=208-15\\&=193\end{aligned}\)

Therefore, the 52nd term is a₅₂ = 193.

\(\hrulefill\)

Given explicit formula for an arithmetic sequence:

\(a_n=-30-4n\)

To find the common difference, we need to compare it with the explicit formula for the nth term:

\(\begin{aligned}a_n&=a+(n-1)d\\&=a+dn-d\\&=a-d+dn\end{aligned}\)

The coefficient of the n-term is -4, therefore, the common difference is d = -4.

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=-30-4(52)\\&=-30-208\\&=-238\end{aligned}\)

Therefore, the 52nd term is a₅₂ = -238.

The wires are parallel lines. If you consider the floor to be a perpedicular line that crosses both parallel lines. Then angles m∠1 and m∠2 are corresponding angles (the lines form an F shaped line), this means, that they are equal, so:

m∠1=m∠2

If you replace ir with the given expressions you will determine a one unknown equation:

Solve for x

Using the value of x replace in the formulas to determine the measure of the angles

m∠1=2x+20=2*13+20=46º

m∠2=4x-6=4*13-6=46º

The angle og the guy wires are off the goverment regulations by one degree.