2. Which of the following number is divisible by 6?
O. A. 672
O B. 813
O C. 7312
O D. 1234​

Answers

Answer 1

Answer:

A - 672

Step-by-step explanation:

Any number divisible by both 3 and 2 is divisible by 6.


Related Questions

A rectangular prism has a volume of 864 cubic units. How many cubic unit will fill the volume of the solid if they were packed without any gaps or overlaps

Answers

Answer: 864.

Step-by-step explanation:

The volume of a rectangular prism has a volume equal to:

V = W*L*H

W = width

L = length

H = height

We know that the volume is equal to 864 cubic units.

This means that if we want to fill the prism such that there is no gap or overlap, we should use exactly 864 unit cubes.

write a trinomial that has a factor of X +3 and a GCF of -5x

Answers

Answer:

it is - 15 please mark me brainliest

Determine the intercepts of the line.
-6x + 3y = -7
z-intercept:
y-intercept:

Answers

Answer:

(7/6, 0) and (0,-7/3)

Step-by-step explanation:

I think you mean x-intercept and y-intercept not z-intercept and y-intercept. The first step is to convert the equation to slope intercept form:

-6x+3y=-7

3y=6x-7

y=6/3x-7/3

y=2x-7/3

Now, to find the x-intercept we find the value of x when y is 0.

0=2x-7/3

7/3=2x

7/6=x so the x-intercept is (7/6,0)

Now, to find the y-intercept we find the value of y when x is 0.

y=2(0)-7/3

y=0-7/3

y=-7/3 so the y-intercept is (0,-7/3)

Sum and Product of zeroes of the quadratic polynomial 16s² - 16s + 4 respectively is:Sum and Product of zeroes of the quadratic polynomial 16s² - 16s + 4 respectively is:​

Answers

Answer:

The sum and product of zeroes are 1 and 1/4, respectively.

Step-by-step explanation:

To determine the zeroes of the quadratic polynomial, let equalize the polynomial to zero and solve in consequence:

[tex]16\cdot s^{2}-16\cdot s + 4 = 0[/tex]

By the General Quadratic Formula:

[tex]s_{1,2} = \frac{16\pm \sqrt{(-16)^{2}-4\cdot (16)\cdot (4)}}{2\cdot (16)}[/tex]

[tex]s_{1,2} = \frac{1}{2}[/tex]

Which means that zeroes are [tex]s_{1}=s_{2}=\frac{1}{2}[/tex].

The sum and product of zeroes are, respectively:

[tex]s_{1}+s_{2} =\frac{1}{2}+\frac{1}{2}[/tex]

[tex]s_{1}+s_{2} = 1[/tex]

[tex]s_{1}\cdot s_{2} = \left(\frac{1}{2} \right)^{2}[/tex]

[tex]s_{1}\cdot s_{2} = \frac{1}{4}[/tex]

The sum and product of zeroes are 1 and 1/4, respectively.

please this urgent!!​

Answers

Answer:

Step-by-step explanation:

1)First convert mixed fraction to improper fraction and them prime factorize

[tex]6\frac{1}{4} = \frac{25}{4}\\[/tex]

[tex]\sqrt{\frac{25}{4}}= \sqrt{\frac{5*5}{2*2}}= \frac{5}{2} = 2 \frac{1}{2} \\\\[/tex]

2)

[tex](2 \frac{1}{2}- 1 \frac{1}{2})*1 \frac{1}{7}=( \frac{5}{2}- \frac{3}{2})* \frac{8}{7}\\\\\\= \frac{2}{2}* \frac{8}{7}\\\\=1* \frac{8}{7}= \frac{8}{7}\\\\\\=1 \frac{1}{7}[/tex]

3) 0.00706 = 7.06 * [tex]10^{-3}[/tex]

4) 144 = 12 * 12

12 = 6*2

6 = 2*3

Prime factorization of 144 = 2 * 3 * 2 * 2 * 3 *2

                                          = 2⁴ * 3²

5) To find LCM, prime factorize 96 & 144

96 = 2 * 2 * 2 * 2 * 2 * 3 = 2⁵ * 3

144 = 2⁴ * 3²

LCM = 2⁵ * 3² = 32 * 9 = 288

6) HCF

105 = 7 * 5 * 3

135 = 5 * 3* 3 * 3

180 = 5 * 3 * 3 * 2 * 2

HCF = 5 * 3 = 15

7) 24 = 3 * 2 * 2 * 2 = 3 * 2³

   36 = 3 * 3 * 2 * 2 = 3² * 2²

   40 = 5 * 2 * 2 * 2 = 5 * 2³

LCM = 5 * 2³ * 3² = 5 * 8 * 9  = 360

HCF = 2² = 4

Difference = 360 - 4 = 356

8) Multiply each digit of the binary number by the corresponding power of 2, solve the powers and add them all

1111 = 1 *2³ + 1*2² + 1*2¹ + 1*2° = 8 + 4 + 2 + 1 = 15

Ans: 15

9) 36₇ = 102₅

10) 6.9163 = 6.916

I knew only this much

hope it's helpful

:)

CAN U PLS HELP ME OUT I WILL GIVE BRAINLIST AND A THANK YOU!!!!!! :)

Answers

Answer: X=25

Step by step: it is across from 25.

Answer:

Step-by-step explanation:

Vertically opposite angles are equal

x = 25°

Trevor thought there would only be 8 teams in the soccer tournament, but there were 17. What was his percent error?

Answers

Answer:

Around 52.94%

Step-by-step explanation:

We can use the percentage error formula, which is

[tex]\frac{|approx-exact|}{exact}\cdot100[/tex].

The approximated value was 8, however the exact value was 17, so we can substitute inside the equation.

[tex]\frac{|8-17|}{17}\cdot100 \\\\\frac{|-9|}{17}\cdot100 \\\\\frac{9}{17}\cdot100 \\\\0.5294...\cdot100 \\\\52.94[/tex]

Hope this helped!

FACTOR THIS EXPRESSION AS FAR AS POSSIBLE -385y IM GIVING THANKS AND BRAINLIST IF CORRECT. PLEASE HELP ME GUYS

Answers

Answer:

-385y

Step-by-step explanation:

This expression cannot be factored with rational numbers, so -385y is your answer.

Katherine's class is selling raffle tickets for $3 to raise money for charity. Katherine's class raised $504. Which equation would you use to find the number of tickets sold?

Answers

Hey there! I'm happy to help!

Let's represent each ticket with the variable t. For each ticket sold, there will be 3 dollars added to the total. So, if you multiply the number of tickets by 3, you will have your total.

This gives us the following equation.

3t=504

We could use this equation to find the number of tickets sold by dividing both sides of it by 3, which isolates the t, showing us that t=168.

Have a wonderful day!

Answer:

$504 / $3 = t

Step-by-step explanation:

t = total tickets sold

If each ticket cost $3 and the class raised $504, just divide the total amount by the cost.

I hope this helps you!  Please tell me if I am wrong!

Find the probability of drawing 3 Aces at random from a deck of 52 ordinary playing cards if the cards are:_________
A) Replaced
B) Not Replaced

Answers

Answer:

a. With replacement

1/2197

b. Without replacement

1/5,525

Step-by-step explanation:

Okay, here is a probability question.

The key to answering this question is by knowing the number of aces in a deck of cards.

There is 1 ace per suit, so there is a total of 4 aces per deck of cards.

So, mathematically the probability of picking an ace would be;

number of aces/ total number of cards = 4/52 = 1/13

a. Now since the action is with replacement; that means that at any point in time, the total number of cards would always remain 52 even after making our picks.

So the probability of picking three aces with replacement would be;

1/13 * 1/13 * 1/13 = 1/2197

b. Without replacement

what this action means is that after picking a particular card, we do not return the picked card to the deck of cards.

For the first card picked, we will be having a total of 4 aces and 52 total cards.

So the probability of picking an ace would be 4/52 = 1/13

For the second card picked, we shall be left with selecting an ace out of the remaining 3 aces and the total remaining 51 cards

So the probability will be 3/51 = 1/17

For the third and last card to be picked, we shall be left with picking 1 out of the remaining 2 aces cards and out of the 50 cards left in the deck.

So the probability now becomes 2/50 = 1/25

Thus, the combined probability of picking 3 aces cards without replacement from a deck of cards will be;

1/13 * 1/17 * 1/25 = 1/5,525

Using the binomial and the hypergeometric distribution, it is found that the probabilities are:

a) 0.0005 = 0.05%.

b) 0.0002 = 0.02%.

Item a:

With replacement, hence the trials are independent, and the binomial distribution is used.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.

For this problem:

In a deck, there are 52 cards, of which 4 are Aces, hence [tex]p = \frac{4}{52} = 0.0769[/tex]3 cards are drawn, hence [tex]n = 3[/tex].

The probability is P(X = 3), then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.0769)^{3}.(0.9231)^{0} = 0.0005[/tex]

0.0005 = 0.05% probability.

Item b:

Without replacement, hence the trials are not independent and the hypergeometric distribution is used.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.

In this problem:

Deck of 52 cards, hence [tex]N = 52[/tex].4 of the cards are Aces, hence [tex]k = 4[/tex].3 cards are drawn, hence [tex]n = 3[/tex].

The probability is also P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,52,3,4) = \frac{C_{4,3}C_{48,0}}{C_{52,3}} = 0.0002[/tex]

0.0002 = 0.02% probability.

To learn more about the binomial and the hypergeometric distribution, you can take a look at https://brainly.com/question/25783392

What is the justification for step 3 in the solution process?
0.8a - 0.1 a= a - 2.5
Step 1: 0.7a= a - 2.5
Step 2: -0.3a = -2.5
Step 3:
a= 8.3
OA.
the division property of equality
OB
B. combining like terms
O c. the subtraction property of equality
OD. the addition property of equality​

Answers

Answer:

c. the subtraction property if equality

Step-by-step explanation:

i just did this and got it right

The justification for step 3 in the solution process is the division property of equality option (A) the division property of equality is correct.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The equation is:

0.8a - 0.1 a =  a - 2.5

The above equation represents the linear equation in one variable.

Step 1: 0.7a = a - 2.5  (adding like terms)

Step 2: -0.3a = -2.5  ( subtraction property of equality)

Step 3: a =  8.3 (the division property of equality)

Thus, the justification for step 3 in the solution process is the division property of equality option (A) the division property of equality is correct.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ2

44) 93
O 2 remainder of 6
2 remainder of 7
2 remainder of 4
2 remainder of 5

Answers

2 with a remainder of 5

What is the process called?

Answers

Answer:

the distributive property. or distribution

hope this helps! :)

Rita got three colors of beads, half of them are pink. She used all her pink beads to make some bracelets. If the number of pink beads she used for each bracelet is one eighths of the total number of beads, how many bracelets did she make?

Answers

Answer: she made 4 bracelets.

Step-by-step explanation:

Let x, y, z are the number of three kinds of beads, where x= number of pink beads.

As per given, number of pink beads= half of total beads  

[tex]\Rightarrow\ x=\dfrac{1}{2}(x+y+z)\\\\\Rightarrow 2x= x+y+z\\\\\Rightarrow\ x= y+z\ \ \ ...(i)[/tex]

Also, She used all pink beads,  Number of pink beads she used for each bracelet= one eighths of the total number of beads

[tex]\dfrac{1}{8}(x+y+z)\\\\=\dfrac{1}{8}(x+x)\ \ \ [ {\text{From (i)}}][/tex]

[tex]=\dfrac{1}{8}(2x)\\\\=\dfrac{x}{4}[/tex]bracelets =

Number of bracelets = (Number of pink beads) ÷ (Number of pink beads used for each bracelet)

[tex]=\dfrac{x}{\dfrac{x}{4}}=4[/tex]

Hence, she made 4 bracelets.

For the rational equation,[tex]\frac{x^{2}+5x+6}{x+3}=1[/tex] , what is a valid value of x?

Answers

Answer:

-3 or -1 is a valid value for x

Step-by-step explanation:

We start by cross multiplying;

So the expression becomes;

x^2 + 5x + 6 = 1(x + 3)

x^2 + 5x + 6 = x + 3

x^2 + 5x -x + 6-3 = 0

x^2 + 4x + 3 = 0

x^2 + x + 3x + 3 = 0

x(x + 1) + 3(x + 1) = 0

(x + 3)(x + 1) = 0

x + 3 = 0 or x + 1 = 0

x = -3 or x = -1

solve for x 13(x-3)=39

Answers

Answer:

x=6

Step-by-step explanation:

13(x-3)=39

Divide each side by 13

13/13(x-3)=39/13

x-3 = 3

Add 3 to each side

x-3+3 = 3+3

x = 6

Answer:

x=6

Step-by-step explanation:

expanding we get

13x-39=39

13x=39+39

13x=78

x=78/13

x=6

ALGEBRAIC EXPRESSION 11. Subtract the sum of 13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7. 12. From the sum of x 2+ 3y 2 − 6xy, 2x 2 − y 2 + 8xy, y 2 + 8 and x 2 − 3xy subtract −3x 2 + 4y 2 – xy + x – y + 3. 13. What should be subtracted from x 2 – xy + y 2 – x + y + 3 to obtain −x 2+ 3y 2− 4xy + 1? 14. What should be added to xy – 3yz + 4zx to get 4xy – 3zx + 4yz + 7? 15. How much is x 2 − 2xy + 3y 2 less than 2x 2 − 3y 2 + xy?

Answers

Answer:

Explained below.

Step-by-step explanation:

(11)

Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).

[tex][(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z[/tex]

Thus, the final expression is (-11x + y - 12z).

(12)

From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).

[tex][(x^{2} + 3y^{2} - 6xy)+(2x^{2} - y^{2} + 8xy)+(y^{2} + 8)+(x^{2} - 3xy)] - [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[x^{2} + 3y^{2} - 6xy+2x^{2} - y^{2} + 8xy+y^{2} + 8+x^{2} - 3xy]- [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[4x^{2}+3y^{2}-xy+8]-[-3x^{2} + 4y^{2} - xy + x - y + 3]\\=4x^{2}+3y^{2}-xy+8+3x^{2}-4y^{2}+xy-x+y-3\\=7x^{2}-y^{2}-x+y+5[/tex]

Thus, the final expression is (7x² - y² - x + y + 5).

(13)

What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?

[tex]A=(x^{2} - xy + y^{2} - x + y + 3) - (-x^{2}+ 3y^{2}- 4xy + 1)\\=x^{2} - xy + y^{2} - x + y + 3 +x^{2}- 3y^{2}+ 4xy -1\\=2x^{2}-2y^{2}+3xy-x+y+2[/tex]

Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).

(14)

What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?

[tex]A=(4xy-3zx + 4yz + 7)-(xy - 3yz + 4zx) \\=4xy-3zx + 4yz + 7 -xy + 3yz - 4zx\\=3xy-7zx+7yz+7[/tex]

Thus, the expression is (3xy - 7zx + 7yz + 7).

(15)

How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?

[tex]A=(2x^{2} - 3y^{2} + xy)-(x^{2} - 2xy + 3y^{2})\\=2x^{2} - 3y^{2} + xy-x^{2} + 2xy - 3y^{2}\\=x^{2}-6y^{2}+3xy[/tex]

Thus, the expression is (x² - 6y² + 3xy).

Simplify 27^(-2/3) x 25^(1/2) x 5^0 9 5 9/5 5/9

Answers

Answer:

[tex]\frac{5}{9}[/tex]

Step-by-step explanation:

Using the rules of exponents/ radicals

[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex] , [tex]a^{0}[/tex] = 1

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

Given

[tex]27^{-\frac{2}{3} }[/tex] × [tex]25^{\frac{1}{2} }[/tex] × [tex]5^{0}[/tex]

= [tex]\frac{1}{27^{\frac{2}{3} } }[/tex] × [tex]\sqrt{25}[/tex] × 1

= [tex]\frac{1}{9}[/tex] × 5 × 1

=[tex]\frac{5}{9}[/tex]

shirley purchased a plot of land for $19,500. the land appreciates about 3.9% each year. what is the value of the land after 5 years

Answers

Answer:

$23,302.50

Step-by-step explanation:

Helpppppppppppppppp plzzz

Answers

Answer:

$0.56, or 56¢.

Step-by-step explanation:

According to the picture, there are two dimes, two nickels, a penny, and a quarter.

A penny is worth $0.01.

A nickel is worth $0.05.

A dime is worth $0.10.

A quarter is worth $0.25.

2(0.1) + 2(0.05) + (0.01) + (0.25) = 0.2 + 0.1 + 0.01 + 0.25 = 0.3 + 0.26 = 0.56.

So, Vivian is using $0.56, or 56¢, to buy a toy. That's a cheap one!

Hope this helps!

The answer is $0.56 or 56cents

How many significant figures does each value contain? 5.6803 kg has significant figures. 0.00047 seconds has significant figures. 0.240 miles has significant figures.

Answers

Answer:

5.6803 has five significant figures.

0.00047 has two significant figures.

0.240 has three significant figures.

What are Significant Figures?

Significant figures are numbers that are necessary to express a true value.

Place the values in scientific notation.

[tex]5.6803 * 10^{0} = 5.6803\\\\4.7 * 10^{-4} = 0.00047\\\\2.4 * 10^{-1}=0.240[/tex]

Explanation

5.6803

The zero that is within 5.6803 is "trapped," meaning it is in between two nonzero digits. Therefore, all five digits are significant figures.

This answer is also already in scientific notation because 5.6803 satisfies the inequality [tex]1 < x < 10[/tex], which decides if a number is correctly written in scientific notation or not.

0.00047

The zeroes that precede the 4 and the 7 are not significant because they are dropped in scientific notation and are not trapped by other nonzero digits. Therefore, only two digits of this value are significant.

0.240

Since the zero at the end of 0.240 is a trailing zero, it is significant along with the 2 and the 4. The zero that precedes these digits and the decimal point is not significant. Therefore, only three digits of this value are significant.

Therefore:

5.6803 has five significant figures.

0.00047 has two significant figures.

0.240 has three significant figures.

Figure a is a scale image of figure b. what is the value of x? please answer asap!

Answers

Answer:

[tex]\boxed{x = 20}[/tex]

Step-by-step explanation:

Hey there!

Well to find x we need to set up the following.

[tex]\frac{10}{12.5} = \frac{16}{x}[/tex]

Cross multiply

10x = 200

Divide both sides by 10

x = 20

Hope this helps :)

A laundry basket contains 18 blue socks and 24 black socks. What is the probability of randomly picking 2 black socks, with replacement, from the basket?

Answers

Answer:

144/441

Step-by-step explanation:

There are 18+24=42 total socks

There are 24 black socks

So the probability is (24/42)*(24/42)=12/21 * 12/21 = 144/441

Answer:

189

Step-by-step explanation:

what is the cost of paving a driveway that is 18m long and 4 m wide, if the paving costs $35 per square metre?​

Answers

Answer:

$2520

Step-by-step explanation:

→ Work out the area of the drive way

18 m × 4 m= 72 m²

→ Multiply the area by the cost per square metre

72 m² × $35 = $2520

The cost of paving a driveway that is 18m long and 4 m wide, if the paving costs $35 per square metre is $2520.

To calculate the cost of paving the driveway, you need to find the total area of the driveway and then multiply it by the cost per square meter.

The total area of the driveway can be calculated using the formula:

Area = length × width.

Given that the driveway is 18 meters long and 4 meters wide, the area would be:

Area = 18m × 4m

Area = 72 square meters.

Now,  find the cost of paving the driveway by multiplying the area by the cost per square meter:

Cost = Area × Cost per square meter

Cost = 72 square meters × $35/square meter

Cost = $2520.

So, the cost of paying the driveway would be $2520.

To learn more on Area click:

https://brainly.com/question/20693059

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Can u guys answer question 2 pls

Answers

Answer:

"2.93BAR

LET X=2.93BAR

10X=29.393BAR

100X=293.93BAR

NOW WE WILL SUBTRACT THE FIRST EQUATION FROM THIRD EQUATION

​100X=293.93BAR

X= 2.93BAR

99X=291.00BAR

IT CAN ALSO BE WRITTEN LIKE

X=291/99"

This was an answer from the same question someone else asked.

This answer was given by grvbundela008p3f6id

Step-by-step explanation:


How to do this question plz answer me step by step plzz plz plz plz ​

Answers

Answer: 25.6

First, notice that there is 1 adult and 2 children.

A normal adult ticket costs 24. But it's 1/3 off, so 24 * 1/3 = 8 off. That means with the Railcard, it only costs 24 - 8 = 16.

Next, one child ticket costs 12. But it's 60% = 3/5 off, so 12 * 3/5 = 7.2 off. That means with the Railcard, it only costs 12 - 7.2 = 4.8.

Remember there are 2 children, so we multiply by 2 to get 4.8 * 2 = 9.6 for the children.

Final answer: 1 adult + 2 children = 16 + 9.6 = 25.6.

Hope that helped,

-sirswagger21

Answer:

£25.60

Step-by-step explanation:

Adult tickets cost £24 and ⅓ is off the adult tickets according to the Family Railcard. That is:

24 × ⅓ = £8 is removed from the adult tickets. Therefore:

£24 - £8 = £16

Child tickets cost £12 and 60% is off the child tickets according to the Family Railcard. That is:

12 × 60/100 = £7.20 is removed from the child tickets. Therefore:

£12 - £7.20 = £4.80

To find the total cost of Mr. Brown spent:

1 child = £4.80

2 children = ?

4.80 × 2 = £9.60

1 adult = £16

£16 + £9.60

= £25.60

Mr. Brown spent £25.60 in total.

Let f (x) = x – 4 and g(x) = 6 - x
Evaluate g(f(10)).

Answers

G(f(10))

First solve f(x) by replacing x with 10:

F(x) = x-4 = 10-4 = 6

Now replace x in g(x) with 6

G(x) = 6-x = 6-6 = 0

So g(f(10)) = 0

is the square root of 2 between 1.4 and 1,5

Answers

Answer:

The square root is around 1.414, so yes, it is between 1.4 and 1.5.

Step-by-step explanation:

Find x. A. 22 B. 113–√ C. 222–√ D. 113√3

Answers

Answer:

x = 31.12

Step-by-step explanation:

First find the base (hypotenuse) of the smaller triangle (the isosceles triangle):  Its three sides are 11, 11 and b.  b can be found using the Pythagorean Theorem:  b^2 = 11^2 + 11^2 = 242.  Then b = √242, or b = approximately 15.56.

b (which is approximately 15.56) is the shorter leg of the large (right) triangle.  The trig function needed to solve for x is the cosine:

                               adjacent side

cos 60 degrees = ----------------------

                                  hypotenuse,

                                       15.56

which becomes (1/2) = ------------

                                            x

Solving this for x, we get:  x = 2(15.56) = 31.12

(x2 - 41)2 + (yz - Yı) to the find the length of the segment
62. Use the distance formula d =
from (6,0) and (-5, 4).

Answers

Answer:

√137

Step-by-step explanation:

[tex](x_1, y_1) = (6, 0)\\(x_2, y_2) = (-5, 4)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\d = \sqrt{(-5-6)^2+(4-0)^2}\\ d = \sqrt{(-11)^2+(4)^2}\\ d = \sqrt{121+16}\\ d = \sqrt{137}\: or \:11.7[/tex]

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