how many boys are in the choir​

Given:

[tex]x = 1, y = 7,z = 15[/tex]

A number is added to x, y, and z yields consecutive terms of a geometric sequence.

To find:

The number which is added to  x, y, and z, then find the first three terms in the geometric sequence.

Solution:

Let the unknown number be k.

After adding k to x, y, and z, we get

[tex]x = 1+k, y = 7+k,z = 15+k[/tex]

These are the consecutive terms of a geometric sequence. So,

[tex](7+k)^2=(1+k)(15+k)[/tex]

[tex]49+14k+k^2=15+k+15k+k^2[/tex]

[tex]49+14k=15+16k[/tex]

Isolate the variable terms.

[tex]49-15=16k-14k[/tex]

[tex]34=2k[/tex]

[tex]\dfrac{34}{2}=k[/tex]

[tex]17=k[/tex]

The unknown number is 17.

Now,

[tex]x=1+k[/tex]

[tex]x=1+17[/tex]

[tex]x=18[/tex]

Similarly,

[tex]y=7+k[/tex]

[tex]y=7+17[/tex]

[tex]y=24[/tex]

And

[tex]z=15+k[/tex]

[tex]z=15+17[/tex]

[tex]z=32[/tex]

Therefore, the three terms in the geometric sequence are 18, 24, 32.

Answer:

2y bigger or same -12-4y is correct

Step-by-step explanation:

Y=1

2=-12-4×1

2=-16

2 is bigger

Y=-2

-4=-12-4×(-2)

-4=-4 it's same

Answer:

A = 907.46 [tex]m^{2}[/tex]

Step-by-step explanation:

C = πd

34π = πd

d = 34

r = 17

A = [tex]\pi r^{2}[/tex] = 3.14([tex]17^{2}[/tex]) = 3.14(289) = 907.46 [tex]m^{2}[/tex]

Answer:

6

Step-by-step explanation:

The formula to find the area of a triangle is length times height (12) and divide by 2.

Answer:

y=2x-14

Step-by-step explanation:

Answer:

I think it's [tex]\frac{7}{10}[/tex].

Why 7/10?

Well, the probability of pulling out a blue marble + pulling out a green marble is also written as [tex]\frac{2}{10} +\frac{5}{10}=\frac{7}{10}[/tex]

Answer:

2  3/4 hours

Step-by-step explanation:

We see from the figure that 2 students spent 1/4 hours and 3 students spent 3/4 hours.

So the total time spent is

2* (1/4) + 3(3/4) hours

= 1/2 + 9/4

=(2+9)/4  taking l.c.m

= 11/4

= 2 3/4 hours

The total time spent by 5 students on 1/4 hours and 3/4 hours is 2 and 3/4 hours.

Answer:

12 dollars

Step-by-step explanation:

29+12=41 or 12-49=29

Given:

The function is:

[tex]f(x)=\dfrac{2x}{3}-4[/tex]

To find:

The inverse of the given function, i.e., [tex]f^{-1}(x)[/tex].

Solution:

We have,

[tex]f(x)=\dfrac{2x}{3}-4[/tex]

Step 1: Substitute [tex]f(x)=y[/tex].

[tex]y=\dfrac{2x}{3}-4[/tex]

Step 2: Interchange x and y.

[tex]x=\dfrac{2y}{3}-4[/tex]

Step 3: Isolate y.

[tex]x+4=\dfrac{2y}{3}[/tex]

[tex]3(x+4)=2y[/tex]

[tex]\dfrac{3x+12}{2}=y[/tex]

[tex]\dfrac{3}{2}x+6=y[/tex]

Step 4: Substitute [tex]y=f^{-1}(x)[/tex].

[tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex]

Therefore, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex].

Answer:

She can make 55 bracelets

Step-by-step explanation:

We have the correct question as follows;

Ariel bought a 15 1/6 foot long string, and a 12 1/3 foot long string. If each bracelet requires 1/2 of a foot long string, how many bracelets can Ariel make

we have the solution as follows

Firstly, we need to find the total length of the strings bought

We can get this by adding what was bought

That would be;

15 1/6 + 12 1/3

= 91/6 + 37/3

= (91 + 74)/6 = 27 1/2 ft

From the question, each bracelet requires 1/2 ft long

so the number of 1/2 ft long bracelets we can find will be;

27 1/2 divided by 1/2

= 55/2 * 2/1

= 55

Answer:

C Minor

Step-by-step explanation:

Answer:

ΔABC ≈ ΔDEF

∡B ≅ ∡E

x = 4.5

BC is similar to EF

Step-by-step explanation:

to find 'x':

6/16 = x/12

16x = 72

x = 4.5

Answer:

1) tri ABC ~ tri DEF

2) angle B ~ angle E

3) x= 4.5

4) ?= BC

Step-by-step explanation:

hi! a note: pls let me know if any of the answers are wrong ! i want anyone to have a wrong answer because of me thank u vm! (obviously, my explanations are not the official mathematical explanations)

1) I just matched up the letters, A to D, B to E, C to F

You can also use ratios, but if you dont need an explanation then ignore it.

2) matched up the angles: B corresponds to E

3) Ratio: 6/16 = x/12

              16x = 72   cross multiply

                 x = 4.5

4) Again, just match up the sides

BC corresponds to EF

hope this helps :D best of luck

Answer:

The equation of the line is;

3y = 2x-8

Step-by-step explanation:

Firstly, we need the to get the slope of the given line

To do this, we will write the equation of the line in the standard form

the standard form

is;

y = mx + b

where m is the slope and b is the y-intercept

y -4 = 2/3(x-3)

y -4 = 2x/3 - 2

y = 2x/3 -2 + 4

y = 2x/3 + 2

with respect to the given equation, the slope of the line is 2/3

Mathematically, when two lines are parallel, the slopes of the line are equal

So now, we want to find the equation of the line that has a slope of 2/3 and passes through the point (1,-2)

so;

y = 2x/3 + b

So substitute the values of (1,-2)

1 for x and -2 for y

-2 = 2/3(1) + b

-2 = 2/3 + b

b = -2 - 2/3

b = (-6-2)/3 = -8/3

So the equation of that line is;

y = 2/3x - 8/3

Multiply through by 3

3y = 2x - 8

Answer:

$11.52

Step-by-step explanation:

18% of 64 is 11.52

Answer:

Percentage

Step-by-step explanation:

The higher the probability number or percentage of an event, the more likely is it that the event will occur. If an event has only one possible outcome, the probability for this outcome is always 1 (or 100 percent).

Answer:

61, 63, 65

Step-by-step explanation:

n + n+2 + n+4 = 189

3n = 183

n = 61

Answer:

The three consecutive odd integers are 61, 63, and 65

Step-by-step explanation:

Let the three consecutive odd integers be:

n + 1, n + 3 and n + 5

Therefore:

n + 1 + n + 3 + n + 5 = 189

3n + 9 = 189

3n = 180

n = 60

n + 1 = 61

n + 3 = 63

n + 5 = 65

Answer:

1/6

Step-by-step explanation:

if you want to roll a 2 from a six sided dice then you have six different outcomes. If you want a two then you have a 1 out of six chance of getting the two

Answer:

thats id correct 1/6

Step-by-step explanation:

the possible out come of rolling a 2 out of six is 1/6

Answer:

B) 16/20

Step-by-step explanation:

sin∅=opposite/hypotenuse

sin∅=16/20

Therefore, your answer is B.

Answer:

(12/16)

Step-by-step explanation:

Answer:

57

Step-by-step explanation:

1+2=180

123+2=180

2=180-123

2=57

2=6=57 ( because 2 and 6 are 2 isotopic angles)

Answer:

He can ride the bus 20 times

Step-by-step explanation:

35-5=30

3=2x1.5

mental gymnastics helped me lol

Answer:

78.5°

Step-by-step explanation:

We solve for the above question, using the formula for the Trigonometric function of Cosine

cos θ = Adjacent/Hypotenuse

Adjacent = The distance between the house and the base of the ladder = 4 feet

Hypotenuse = Length of the Ladder = 20 feet

Hence,

cos θ = 4/20

θ = arc cos(4/20)

θ = 78.463040967°

Approximately = 78.5°

Therefore, the angle that the ladder makes with the ground is 78.5°

9514 1404 393

Answer:

  222 cm²

Step-by-step explanation:

The surface area can be found using the formula ...

  A = 2(LW +H(L+W))

To minimize fraction nonsense, we'll let H be the fraction.

  A = 2(12·8 +(3/4)(12 +8)) = 2(96 +15) = 222

The surface area of the prism is 222 square centimeters.

[tex] \frac{19}{6} \pi \times \frac{360}{75} = \frac{19}{6} \pi \times \frac{24}{5} = \frac{76}{5} \pi[/tex]

[tex] {x}^{2} \times \pi = \frac{76}{5} \pi[/tex]

[tex]x = \frac{2 \sqrt{95} }{5} = 3.9[/tex]

Answer:

there is not enough info to answer this

Step-by-step explanation:

Answer: There is not enough information given to answer. You need to include how fast Jose and Edwin were jogging/walking.

Answer: 135 hamburgers

540 divided by 4 (ratio of hamburgers to cheeseburgers is 3 to 1) = 135. 135 burgers and (135 times 3) 405 cheeseburgers = 540.

Step-by-step explanation: Hope this helps! :)

Answer: 180 hamburgers were sold on Saturday

Step-by-step explanation:

I’m pretty sure this is the answer

what do i choose? because all i see is a lot of numbers and words lol

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation: