Using the diagram on the right, find the length of GT and TA.

In thinking about what number each term may be multiplied by to eliminate the fractions, we can take one of two courses:

1) Find the lowest common multiple, ie. the lowest value that each of the fraction denominators have in common as a multiple.

Now a multiple is basically that number multiplied by an integer - for example, multiples of 2 are 2, 4, 6, 8, 10, etc.

So, let us write out the first few multiples for each of the denominator values:

4 (from 3/4): 4, 8, 12, 16, 20

3 (from 1/3): 3, 6, 9, 12, 15, 18

2 (from 1/2): 2, 4, 6, 8, 10, 12, 14, 16

Looking at the values above, we can see that the lowest value that occurs in all three sets of numbers is 12, thus 12 is the lowest common multiple.

Therefor, in order to eliminate the fractions before solving, each term must be multiplied by 12.

2) You could alternatively try multiplying the equation (or simply each fraction) by each of the possible answers and seeing if that will eliminate all of the fractions - this may seem quicker at first but it is always worthwhile understanding how to calculate this question without having possible answers, and as you complete more questions, the process of finding the lowest common multiple will become more natural and even quicker in the end. Nonetheless, let us try this method:

a) Multiplying each fraction by 2

(3/4)*2 = 3/2

This does not eliminate the fraction, therefor 2 is not the answer.

b) Multiplying each fraction by 3

(3/4)*3 = 9/4

This does not eliminate the fraction, thus 3 is not the answer.

c) Multiplying each fraction by 6

(3/4)*6 = 9/2

This does not eliminate the fraction, therefor 6 is not the answer.

d) Multiplying each fraction by 12

(3/4)*12 = 9 (this works so far)

(1/3)*12 = 4 (this also works so far)

(1/2)*12 = 6 (this also works)

Since multiplying each fraction by 12 will eliminate the fractions, 12 is the answer.

Answer:

D is the answer

Step-by-step explanation:

Answer:

9√3in^2 hope this helps. found an answer...

Answer:

9 sqrt 3

Step-by-step explanation:

It was correct on my quiz

1/4 x 6 squared x sqrt 3

Answer:

2.2

2.20

Explanation

You can add zeros or take them away and the number will still have the same value.

namely, how many times does 3/4 go into 3½?  Let's firstly convert the mixed fraction to improper fraction.

[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{2}\div \cfrac{3}{4}\implies \cfrac{7}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{3}\implies \cfrac{14}{3}\implies 4\frac{2}{3}[/tex]

Answer:

Danika signed up to work for 3.5 hours at the science fair, if each work shift is 3/4 hour = 0.75 hours, the amount of shifts will be:

Shifts = 3.5/0.75 = 4,66 ≈ 5 shifts. Given that shifts have to be an integer number, we need to round the result to the nearest integrer.

Therefore, Danika will work 5 shifts.

Answer:

A and E

Step-by-step explanation:

A line has a slope of -4/5, then a perpendicular line has a slope 5/4, because

[tex]-\dfrac{4}{5}\cdot \dfrac{5}{4}=-1[/tex]

Find the slopes of the lines in all options:

A. True

[tex]\dfrac{5-0}{2-(-2)}=\dfrac{5}{4}[/tex]

B. False

[tex]\dfrac{-5-5}{4-(-4)}=-\dfrac{5}{4}[/tex]

C. False

[tex]\dfrac{0-4}{2-(-3)}=-\dfrac{4}{5}[/tex]

D. False

[tex]\dfrac{-5-(-1)}{6-1}=-\dfrac{4}{5}[/tex]

E. True

[tex]\dfrac{9-(-1)}{10-2}=\dfrac{5}{4}[/tex]

Answer:

C

Step-by-step explanation:

=(0-4)/(2+3)

=-4/5

Answer:

7

Step-by-step explanation:

This operation is identical to subtracting 6 from 13.  The correct result is 7.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 2 and (a, b) = (10, - 9), hence

y - (- 9) = - 2(x - 10), that is

y + 9 = - 2(x - 10) ← in point- slope form

Answer: [tex]y+9=-2(x-10)[/tex]

Step-by-step explanation:

We know that the equation of a line in point slope form passing through point (a,b) and having slope 'm' is given by :-

[tex](y-b)=m(x-a)[/tex]

Given : Point : (10,-9)

Slope :  m=-2

Then , the equation of a line in point slope form passing through point (10,-9) and having slope '-2' is given by :-

[tex](y-(-9))=-2(x-10)\\\\\Rightarrow\ y+9=-2(x-10)[/tex]

Answer:

61300000000000000

Step-by-step explanation:

Multiplying 20,000,000,000,000 by 3,065 results in 61,300,000,000,000,000.

Write down the numbers in standard form:

2 x[tex]10^{13}[/tex] for 20,000,000,000,000 and

3.065 x 10³ for 3,065.

Multiply the two standard forms:

(2 x [tex]10^{13}[/tex]) * (3.065 x 10³).

Combine the powers of 10:

2 * 3.065 = 6.13 and

[tex]10^{13}[/tex] * 10³ = [tex]10^{16}[/tex]

The result is 6.13 x [tex]10^{16}[/tex]

In standard numerical form, this is 61,300,000,000,000,000.

So, 20,000,000,000,000 x 3,065 equals 61,300,000,000,000,000.

Complete Question:

Multiply 20000000000000 x 3065.

The congruence theorems that will be used to prove that both triangles are congruent are: C. LL E. SAS.

The LL theorem is a triangle congruence theorem that states that if the two pairs of legs of two right triangles are congruent, then the triangles are congruent.

The SAS theorem is a triangle congruence theorem that states that if the two pairs of sides and a pair of included angles of two triangles are congruent, then the triangles are congruent.

Based on the information given, the theorem that can be used to show both triangles are congruent are: C. LL E. SAS

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Triangle DEF can be proven congruent to triangle KLM using the Leg-Leg (LL) Theorem, Side-Angle-Side (SAS) Theorem, and Hypotenuse-Leg (HL) criterion .

The correct answer is option B, C and E.

In geometry, a congruence theorem is a statement that two geometric figures are congruent, meaning that they have the same size and shape. There are many different congruence theorems, but the most common ones are the Side-Angle-Side (SAS) Theorem, the Angle-Side-Angle (ASA) Theorem, and the Leg-Leg (LL) Theorem.

The LL Theorem is a special congruence theorem that applies to right triangles. It states that if two right triangles have two congruent legs, then the triangles are congruent. This means that all of their corresponding sides and angles are congruent.

In the diagram provided, we have two right triangles, DEF and KLM. We are given that DE = KL and DF = LM. Since these are the legs of the two triangles, we can use the LL Theorem to conclude that DEF = KLM.

Hypotenuse-Leg (HL): This criterion applies specifically to right-angled triangles. If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. Here, the right angles at D and K establish the triangles as right triangles, and the equal side lengths ED = KL and DF = KM complete the congruence conditions.

We cannot use the HL Theorem because the diagram does not explicitly show that the two triangles are right triangles.

Therefore, from the given options the correct one is B , C and E.

For more such information on: congruent

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Answer:

L=9 ft

W=28 ft

Step-by-step explanation:

LW=252

L=10+2W

Plug 2nd into 1st

(10+2W)W=252

Distribute

10W+2W^2=252

Divide both sides by 2

5W + W^2=126

Reorder using commutative property

W^2+5W =126

Subtract 126 on both sides

W^2+5W-126=0

What are two numbers multiply to be -126 and add to be 5?

My scratch paper:

-126=-2(63)

-126=-2(7)(9)

-126=-14(9)

So 14(-9) is -126 and 14+(-9)=5 so these are our magic numbers

(W+14)(W-9)=0

W=-14 or W=9

So W=9 is what makes sense here sense length can't be negative

Now let's go back and find L...

L=10+2W=10+2(9)=10+18=28

The problem can be solved by setting up a quadratic equation based on the given information. By solving the equation, we find that the width is 7 feet, and the length is 24 feet.

In this problem, we are given that the area (A) of the rectangular wall is 252 square feet, and the length (L) of the wall is 10 feet longer than twice its width (W). We need to find both the length and width of the barn. The formula for the area of a rectangle is A = L × W.

From the problem, we know that L = 2W + 10. Substituting this into the formula gives us A = W × (2W + 10). Set this equal to 252 to get 252 = W × (2W + 10). Solving this quadratic equation, we find that the width of the barn is 7 feet. Substituting this value into L = 2W + 10, the length of the barn is 24 feet.

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x-3y= 1

The equation needs to be rewritten in proper Slope intercept form ( y = mx+b) where m is the slope and b is the y-intercept.

x-3y = 1

Subtract x from each side:

-3y = 1-x

Divide both sides by -3:

y = 1/-3 - x/-3

Simplify:

y = 1/3x - 1/3

The slope is 1/3

Answer:

The area of the circle is [tex]A=6.25\pi\ units^{2}[/tex]

Step-by-step explanation:

step 1

Find the diameter of circle

we know that

The diameter of the circle is equal to the distance AB

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute the values

[tex]AB=\sqrt{(5-1)^{2}+(5-2)^{2}}[/tex]

[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]

[tex]AB=\sqrt{25}[/tex]

[tex]AB=5\ units[/tex]

therefore

the diameter of the circle is

[tex]D=5\ units[/tex]  

step 2

Find the area of the circle

The area of the circle is equal to

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

[tex]r=5/2=2.5\ units[/tex]  ----> the radius is half the diameter

substitute

[tex]A=\pi (2.5)^{2}[/tex]

[tex]A=6.25\pi\ units^{2}[/tex]

Answer:

Option 4 is correct.

Step-by-step explanation:

Given the following options

we have to choose the difference of cubes.

Option 1:

[tex]9w^{33}-y^{12}[/tex]

[tex]9(w^{11})^{3}-(y^4)^3[/tex]

which is not the difference of cubes

Option 2:

[tex]18p^{15}-q^{21}[/tex]

[tex]18(p^5)^3-(q^7)^3[/tex]

which is not the difference of cubes

Option 3:

[tex]36a^{22}-b^{16}[/tex]

[tex](6a^{11})^2-(b^8)^2[/tex]

which is the difference of square

Option 4:

[tex]64c^{15}-a^{27}[/tex]

[tex](4c^5)^3-(a^9)^3[/tex]

which is the difference of cubes.

Answer:

C. $150 :)

Step-by-step explanation:

If Annabell works 4 hours and earns $100 that means for every hour she earns $25 so 25×4=100 so then multiply 25×6=15]

Answer:  C. $150.

Step-by-step explanation:

When two quantities x and y are directly proportional ,then the equation of direct proportion is given by :-

[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]

Given : Annabelle's total pay varies directly with the number of hours she works. If she works 4 hours, she earns $100.

Let [tex]x_1=100\ ;\ y_1=4 \ :\ x_2=x,\ y_2=6[/tex], then we ahve

[tex]\dfrac{100}{4}=\dfrac{x}{6}\\\\\Rightarrow\ x=\dfrac{100\times6}{4}=150[/tex]

Hence, Annabelle earns $150 if she works 6 hours.

Answer:

r(-1) = 6.31 and r(2) = -16.88

Step-by-step explanation:

* Lets read the problem and solve it

- Evaluate means find the value, so evaluate r(x) means find the value

 of it at the given values of x

∵ r(x) = -0.21x³ + x² - 8.1x - 3

∵ x = -1 and x = 2

- Then find r(-1) by substitute x by -1 and find r(2) by substitute x by 2

# At x = -1

∴ r(-1) = -0.21(-1)³ + (-1)² - 8.1(-1) - 3  

∴ r(-1) = -0.21(-1) + (1) - 8.1(-1) - 3

∴ r(-1) = 0.21 + 1 + 8.1 - 3

∴ r(-1) = 6.31

# At x = 2

∴ r(2) = -0.21(2)³ + (2)² - 8.1(2) - 3  

∴ r(2) = -0.21(8) + (4) - 8.1(2) - 3

∴ r(2) = -1.68 + 4 - 16.2 - 3

∴ r(2) = -16.88

* r(-1) = 6.31 and r(2) = -16.88

Answer:

Option A is the correct answer.

Step-by-step explanation:

Let the work plow a field be x.

Annmarie can plow a field in 240 minutes.

   Rate at which Annmarie can plow[tex]=\frac{x}{240}[/tex]

Gladys can plow a field 80 minutes faster

Time taken by Gladys = 240 - 80 = 160 minutes.

   Rate at which Gladys can plow[tex]=\frac{x}{160}[/tex]

If they combine time taken to plow [tex]=\frac{x}{\frac{x}{240}+\frac{x}{160}}=\frac{240\times 160}{240+160}=96\texttt{ minutes}[/tex]

Option A is the correct answer.

the time taken for Annmarie and Gladys to plow the field together is 96 minutes. The correct answer is A) 96 min.

Annmarie can plow a field in 240 minutes, and Gladys can do it in 160 minutes (since she is 80 minutes faster). To find out how long it would take for them to plow the field together, we can use the formula for combined work rates:

Let A be Annmarie's work rate and G be Gladys's work rate. Annmarie's work rate is 1 field per 240 minutes, or 1/240 fields per minute. Gladys's work rate is 1 field per (240 - 80) minutes, or 1/160 fields per minute.

Combined work rate of Annmarie and Gladys: A + G = 1/240 + 1/160.

Now, to find the time it would take them working together, we take the reciprocal of the combined work rate.

The combined work rate is:

1/240 + 1/160 = 1/240 + 1/160 = (1x160 + 1x240) / (240x160) = (160 + 240) / (240x160) = 400 / (240x160)

The time it takes for them to work together is the reciprocal of 400 / (240x160), which is (240x160) / 400.

Calculate: (240x160) / 400 = 38400 / 400 = 96

Therefore, the time taken for Annmarie and Gladys to plow the field together is 96 minutes. The correct answer is A) 96 min.

Answer:

5.

Step-by-step explanation:

What you require is the area of the rectangle  whose base is between 210 and 215.

The number having levels between 210 and 214

= 20 * the relative frequency

= 20 * 0.25

= 5 (answer).

Answer:

rotate 180 degrees ccw from (0,0)

Answer:

We get Rectangle A'B'C'D' by rotating the Rectangle ABCD by 180° about origin.

Step-by-step explanation:

We are given a graph which Rectangle ABCD and A'B'C'D'

To find : Set of transformation

From the graph,

Vertex of the Rectangle ABCD,

A( -4 , 2 ) , B ( -4 , 1 ) , C ( -1 , 1 ) and D ( -1 , 2 )

Vertices of Rectangle A'B'C'D'

A( 4 , -2 ) , B ( 4 , -1 ) , C ( 1 , -1 ) and D ( 1 , -2 )

Clearly from above,

we get that coordinates of the vertices of Rectangle A'B'C'D' is negative of the coordinates of the vertices of Rectangle ABCD .

That is if Coordinates of A( x , y ) then A'( -x , -y )

This transformation is done when we rotate the given figure by 180° about origin.

Therefore, We get Rectangle A'B'C'D' by rotating the Rectangle ABCD by 180° about origin.

[tex]9-(4^2-(3+20)=9-(16-23)=9-(-7)=16[/tex]

Answer:

0.2

Step-by-step explanation:

[tex]\text{f(x) = }\dfrac{90}{9+\frac{50}{e^x}}[/tex]

[tex]\text{f(-2) = }\dfrac{90}{9+\frac{50}{e^{-2}}}[/tex]

[tex]\text{f(-2) =} \dfrac{ 90 }{9 + 50*e^2}[/tex]

Now we can work out the denominator separately.

9 + 50*e^2

9 + 50*7.389

9 + 369.45

378.45

Now use this number to get the final answer.

f(-2) = 90 / 378.45

f(-2) = 0.237   To the nearest tenth

f(-2) = 0.2

There was a lot of movement for that e^x factor make sure you study carefully how that moved around and why. It's a good question. Get what you can from it.

Answer:

Step-by-step explanation:

it will have no sol. when a1/a2=b1/b2!=c1/c2

!= means not equal to

kx+3y=k+2

kx+3y-(k+2)=0 equation 1

12x+ky=0

taking a1/a2=c1/c2

k/12=3/k

k^2=36

k=6

when k= 6 it will have no sol

it's r because it does not sit on the same plane as the rest of the points that are given.when looking at the diagram c,d and e are all connected to the square on the bottom of the pyramid. The same goes for points u,s and a. The point R is different by sitting on one of the triangles of the pyramid.

The point R is not coplanar with C, D, and E. This is because point R is not lying in the plane of C, D, and E.

The points which lie on the same plane are said to be coplanar points.

The given points are R, A, S, and U

The considered pane is w.r.t the points C, D, and E.

So, point A is forming a square with the points C, D, and E. So, it is coplanar with these points.

Point S is on the surface of the plane formed by ACDE. So, it is coplanar.

Point U is also in the plane w.r.t point C, D, and E. So, it is a coplanar point.

But point R does not lie in the plane w.r.t C, D, and E. So, it is not coplanar with points C, D, and E.

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Answer:

10

Step-by-step explanation:

x=2

f(2)=5x3-2=15-2=13/2=6.5=f

g(2)=2+1=3/2=1.5=g

(6.5-1.5)(2)=(13-3)=10

Answer:

5x³ - x - 3

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 5x³ - 2 -(x + 1) = 5x³ - 2 - x - 1 = 5x³ - x - 3

Check the picture below.

Answer:

Your answer is 56.

Step-by-step explanation:

To solve this problem, we simply need to plug in the given numbers into the expression.

If we do this, we get the following:

u + xy

2 + (9*6)

Using PEMDAS, we know that we have to perform the multiplication in this problem before the addition.  Thus the first step in simplification is multiplying 9 and 6 together.  If we do this, we get:

2 + 54

Next, we simply add together the two remaining terms.

54 + 2 = 56

Therefore, your answer is 56, the first option.

Hope this helps!

Answer:

y=−x−1/3x−8

Step-by-step explanation:

y=8x−1/3x+1

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables: y=8x−1/3x+1 becomes x=8y−1/3y+1.

Now, solve the equation x=8y−1/3y+1 for y.

y=−x−1/3x−8

Sorry I was in a rush and couldn't do the fractions as formulae. Hope it helped anyways.

Answer:

Step-by-step explanation:

[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\(x_1,\ y_1)-point\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\============================[/tex]

[tex]\text{We have the points:}\ (-1,\ 2)\ \text{and}\ (3,1).\\\\\text{Substitute:}\\\\m=\dfrac{1-2}{3-(-1)}=\dfrac{-1}{4}=-\dfrac{1}{4}\\\\y-2=-\dfrac{1}{4}(x-(-1))\\\\y-2=-\dfrac{1}{4}(x+1)\qquad\text{convert to the standard form}\ Ax+By=C\\\\y-2=-\dfrac{1}{4}(x+1)\qquad\text{multiply both sides by 4}\\\\4y-8=-(x+1)\\\\4y-8=-x-1\qquad\text{add 8 to both sides}\\\\4y=-x+7\qquad\text{add x to both sides}\\\\x+4y=7[/tex]

The equation of a line passing through points (-1, 2) and (3, 1) can be determined using the slope formula, which is (y2 - y1)/(x2 - x1). The resulting slope is -1/4 or -0.25. Unfortunately, none of the provided options match this description.

The subject of the question is about finding the equation of a line that passes through the points (-1,2) and (3,1). To find the correct equation, we need to use the formula for the slope of a line which is: (y2 - y1) / (x2 - x1). Plugging in the coordinates (-1,2) and (3,1) will give us a slope of -1/4 or -0.25. This slope should be the coefficient of 'x' in the correct equation. None of the provided choices A, B, C, D have a coefficient of -0.25 for x, therefore, unfortunately, none of these equations represent a line that passes through the points (-1,2) and (3,1).

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Answer:

A.

(x - 3)(x - 3)

Step-by-step explanation:

x^2 – 6x + 9

What 2 numbers multiply to 9 and add to -6

-3*-3 =9

-3+-3 = -6

(x-3) (x-3)

Answer:

103

Step-by-step explanation:

Evaluate 4k2 + 3

To evaluate 4k² + 3, when k = 5, which means when you sees k, put 5 in replacement

4k² + 3 = 4(5)² + 3

4(5×5) + 3

4(25) + 3

open the bracket

4 × 25 = 100

∴ 100 + 3 = 103

Please mark me brainliest  

[tex]\text{Hey there!}[/tex]

[tex]\text{If k = 5 the replace the 'k' value with 5}[/tex]

[tex]\text{4(5)}^2+3[/tex]

[tex]\text{(5)}^2=5\times5=25[/tex]

[tex]\text{4 (25)+ 3 = ?}[/tex]

[tex]\text{4 (25) = 25 + 25 + 25 + 25 = 100}[/tex]

[tex]\text{100 + 3 = 103}[/tex]

[tex]\boxed{\boxed{\bf{Your\ answer: 103}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

The game’s expected value of points earned for a turn is 71.

Step-by-step explanation:

Here we know that:

Points     Frequency

50           55

75            32

150          13

Here points earned is a random variable.

We need to find its expected value,

Finding Expected value:

Expected value of a random variable is its mean value. So we will first find the mean value of points earned per turn from the table we are given.

Total number of turns = sum of frequencies

= 55 + 32 + 14 = 100

Total points earned = 50(55) + 75(32) + 150(13)

= 7100

Expected value of points earned for a turn = Mean value of points

= Total points/no. of turns

= 7100/100

= 71