In the figure, TU is tangent to the circle at point U. Use the figure to answer the questions.

(a) Describe the relationship among the lengths of the segments formed by the secant, RT, and the tangent segment, TU. You may used words and/or an equation.

(b) Suppose RT = 9 in. and ST = 4 in. Is it possible to find the length of TU? If so, show how to find the length. If not, explain why not.


Thanks in advance. I appreciate the help. I'm still not that good at questions like this one.

The possible dimensions for the rectangular carpet with an area represented by the trinomial 5x^2 - 3x - 14 are (5x + 7) and (x - 2). For the barnyard with area 6x^2 + 7x - 20, the dimensions are (2x - 5) and (3x + 4).

To find the possible dimensions of the rectangular carpet with area 5x^2 - 3x - 14, we need to factor the trinomial. Factoring the trinomial, it is evident that we need two numbers whose product is -70 (5 * -14) and whose sum is -3. Factoring the trinomial we get (5x + 7)(x - 2), so the possible dimensions of the carpet are (5x + 7) and (x - 2), which corresponds to option B.

Similarly, to determine the dimensions of a barnyard with area 6x^2 + 7x - 20, we again factor the trinomial. We are looking for two numbers that multiply to -120 (6 * -20) and add up to 7. Factoring yields (2x - 5)(3x + 4), so the possible dimensions of the barnyard are (2x - 5) and (3x + 4), which corresponds to option A.

It would be 2 + 1x. The y intercept is 2, and every unit, you would multiply those numbers together. For example, if the x axis is 6, then you would do 2 + 6 which is 8 on the y axis and etc.

Answer:

its D

Step-by-step explanation:

Answer:

The correct option is C.

Step-by-step explanation:

The given function is

[tex]F(x)=x^2[/tex]

The transformation of the function is defined as

[tex]G(x)=kF(x)[/tex]

If k>1, then the graph of function F(x) stretched vertically and If 0<k<1, then the graph of function F(x) compressed vertically.

It is given that the graph of F(x) can be stretched vertically, it means the value of k must be greater than 1.

The graph of F(x) is flipped over the x-axis, so the function G(x) is equal to the negative of k times of F(x).

[tex]G(x)=-kF(x)[/tex]

Where must be greater than 1.

In option 3, G(x) is equal to the negative of 4 times of F(x). Only in this option, there is negative relation between F(x) and g(x) with k>1.

[tex]G(x)=-4F(x)[/tex]

Therefore the correct option is C.

To solve the equation x^2+10x+12=36, subtract 36 from both sides and factor or use the quadratic formula to find the solutions. The solutions are x = -12 or x = 2.

To solve the equation x^2+10x+12=36, we need to bring all terms to one side of the equation and then factor or use the quadratic formula. Subtracting 36 from both sides gives us the equation x^2+10x-24=0. We can then factor this equation as (x+12)(x-2)=0. Setting each factor equal to zero, we find that x = -12 or x = 2.

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Answer:

A- The cabinets have the same base area.

C- The cabinets may have the same base dimensions.

D- The cabinets may have different base dimensions

Step-by-step explanation:

Answer:

A. C. D.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

The product of the polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)=25c^2-\frac{4}{9}[/tex]    

Step-by-step explanation:

given : The polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)[/tex]

We have to place the indicated product in the proper location o the grid.

Consider the given polynomial  [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)[/tex]

Apply identity of difference of square

[tex]\left(a+b\right)\left(a-b\right)=a^2-b^2[/tex]

We have,

[tex]=\left(5c\right)^2-\left(\frac{2}{3}\right)^2[/tex]

Simplify, we have,

[tex]=25c^2-\frac{4}{9}[/tex]

Thus, The product of the polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)=25c^2-\frac{4}{9}[/tex]

Location on gris shown below.

The correct answer is [tex]x = \frac{-4 + 2\sqrt{22}}{12}$ and $x = \frac{-4 - 2\sqrt{22}}{12}[/tex]

To find the exact solutions to the equation [tex]6x^2 + 4x - 3 = 0[/tex]using the quadratic formula, we can follow these steps:

Given quadratic equation: [tex]6x^2 + 4x - 3 = 0[/tex]

[tex]a = 6, b = 4, c = -3[/tex]

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]x = \frac{-4 \pm \sqrt{4^2 - 4(6)(-3)}}{2(6)}[/tex]

[tex]x = \frac{-4 \pm \sqrt{16 + 72}}{12}[/tex]

[tex]x = \frac{-4 \pm \sqrt{88}}{12}[/tex]

[tex]x = \frac{-4 \pm \sqrt{4 \cdot 22}}{12}[/tex]

[tex]x = \frac{-4 \pm 2\sqrt{22}}{12}[/tex]

Solution 1: [tex]x = \frac{-4 + 2\sqrt{22}}{12}[/tex]

Solution 2: [tex]x = \frac{-4 - 2\sqrt{22}}{12}[/tex]

Therefore, the two exact solutions to the equation [tex]6x^2 + 4x - 3 = 0[/tex] are:

[tex]x = \frac{-4 + 2\sqrt{22}}{12}$ and $x = \frac{-4 - 2\sqrt{22}}{12}[/tex]

Answer:

-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

You pay \blueD{\$6}$6start color blueD, dollar sign, 6, end color blueD for each box of strawberries. The number of dollars you spend depends on \goldD bbstart color goldD, b, end color goldD, the number of boxes of strawberries you buy.

To find the number of dollars you spend on strawberrries, we can use the equation \maroonD d=\blueD6\goldD bd=6bstart color maroonD, d, end color maroonD, equals, start color blueD, 6, end color blueD, start color goldD, b, end color goldD.

Answer:

Ok the answer is 565 but I'm going to break it down for those who wanna know how

Step-by-step explanation:

So first let's just assume the jar is a cylinder which means to use the formula

[tex]V=\pi r^{2} h[/tex]

They saved you time of having to finf the Radius and such

firstly, we're gonna solve before she eats all that salsa lol

r = 6

h = 11

we're gonna substitute 3.14 for pi

of course you'll solve for it which you'll get

v = 1243.44

now you need to find the volume after she eats the salsa which the only difference is that the height will be 6 instead of 11

substitute

solve and you'll get

678.24

now that you have the volume of before and after she eats the salsa all you need to do is subtract to find the difference

1243.44 - 678.24

which you'll get

565!

Hope this helps!

The union of A and B is {-1, 0, 1, 2, 3, 4, 6}, the intersection is {2, 4}, and the difference B - A is {0, 6}. The power set of B contains 16 subsets.

Set Operations: Union, Intersection, Difference, and Power Sets

Let's solve the given problems step by step:

a. The union of sets A and B (A ∪ B)

A ∪ B represents all unique elements that are in either set A or set B.

Given: A = {-1, 1, 2, 3, 4} and B = {0, 2, 4, 6}

A ∪ B = {-1, 0, 1, 2, 3, 4, 6}

b. The intersection of sets A and B (A ∩ B)

A ∩ B represents all elements that are present in both sets A and B.

A ∩ B = {2, 4}

c. The difference of sets B and A (B - A)

B - A represents all elements that are in set B but not in set A.

B - A = {0, 6}

d. The power set of B and its cardinality

The power set of a set is the set of all its subsets, including the empty set and the set itself. If a set has n elements, its power set will contain 2^n subsets.

B = {0, 2, 4, 6}

The power set of B is: { {}, {0}, {2}, {4}, {6}, {0, 2}, {0, 4}, {0, 6}, {2, 4}, {2, 6}, {4, 6}, {0, 2, 4}, {0, 2, 6}, {0, 4, 6}, {2, 4, 6}, {0, 2, 4, 6} }

The cardinality of the power set of B is 2^4 = 16.

In summary:

A ∪ B = {-1, 0, 1, 2, 3, 4, 6}

A ∩ B = {2, 4}

B - A = {0, 6}

The power set of B has 16 elements.

Answer:

-2

Step-by-step explanation:

In poker probability calculations, there are 2,598,960 possible five-card hands, various specific hand combinations such as those containing a king or four aces have their own probability, which can be determined using the formulas for combinations.

Calculations for Poker Probabilities

The subject of probability in a poker hand involves various combinations and permutations. Here's how the calculations are made:

Total number of five-card poker hands: The total number is calculated using combinations, as the order in which cards are drawn does not matter. This is given by the combination formula C(n, r) = n! / (r!(n-r)!), where n is the total number of available cards (52), and r is the number of cards drawn (5). Thus, there are 52! / (5!(52-5)!)= 2,598,960 possible hands.

Number of ways one king can be selected: There are four kings in a deck, so there are C(52, 5) - C(48, 5) ways to choose a hand with at least one king, as you subtract the number of hands without any kings from the total number of hands.

Number of ways four aces can be selected: There is only one way to choose all four aces, and then there are 48 remaining cards to choose the fifth card from, which gives 48 combinations.

Number of ways of getting four aces and one king: There are four kings to choose from and one specific combination of aces, so there are 4 ways to have a hand with four aces and one king.

we know that

An exterior angle is equal to the sum of the two non adjacent angles

so

In this problem

[tex](4n+6)\°=2n\°+60\°[/tex]

Solve for n

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](4n-2n)\°=(60-6)\°[/tex]

Combine like terms

[tex]2n\°=54\°[/tex]

[tex]n=27\°[/tex]

Find the measure of angle ABD

∠ABD=[tex](4n+6)\°[/tex]

Substitute the value of n

∠ABD=[tex](4*27+6)\°=114\°[/tex]

therefore

the answer is the option

[tex]114\°[/tex]

Answer:

the answer is 114

Step-by-step explanation:

hope i helped all of you guys and girls

Answer: 1.129

Step-by-step explanation:

In statistics, the slope of the line is given by :-

[tex]b=r\dfrac{\sigma_y}{\sigma_x}[/tex],

[tex]\text{where r is correlation coefficient,}\\\sigma_y\text{ is standard deviation of the y-coordinates,}\\\sigma_x\text{ is standard deviation of the x-coordinates,}[/tex]

[tex]\text{Given: }r=0.876\\\sigma_x=5.559\\\sigma_y=7.163[/tex]

Now, the slope of the line will be :-

[tex]b=0.876\times\dfrac{7.163}{5.559}\\\\\Rightarrow\ b =1.12876200756\approx1.129[/tex]

Hence, the lope of the line to three decimal places =1.129