Suppose a and b are positive integers such that lcm(a,b) = 90 and gcd(a,b) = 3. If b is three more than a, then what are the values of a and b?​

Answer:

a = 10 and b = 6

Step-by-step explanation:

I am having a little trouble reading the numbers, but I think that I see

[tex]\frac{7^{2} 7^{8} }{7^{4} }[/tex]

If we wrote this in expanded form, it would look like:

[tex]\frac{7x7x7x7x7x7x7x7x7x7}{7x7x7x7}[/tex]  How many 7s are on the top?  10  That is the answer to a.  The product of powers principle tells us that if we are multiplying powers with the same bases we add the exponents 2 + 8 = 10

[tex]\frac{^{10} }{7^{4} }[/tex]

Now it looks like

[tex]\frac{7x7x7x7x7x7x7x7x7x7}{7x7x7x7}[/tex]  if we cross the 7's out in the top and the bottom, we are left with 6 7's on the top.  That is the answer to b.

The quotient of powers principle tells us that if we are dividing powers with the same bases, we can subtract the exponents (10 -4 = 6)

Answer:

The numbers are:

{-1, 0, 1, 2, 3}

Step-by-step explanation:

Note: I am assuming "between" does not include the endpoints.

Given the statement

'Four times a number, increased by one, is between negative seven and seventeen'

Let us break down the word statement into small pieces and then combine them to write it into an algebraic expression.

Let x be the number.

4 times a number = 4x

Increase by 1 = 4x+1

between negative seven and seventeen ⇒   -7 < 4x+1  < 17

Thus, the combined statement can be written in an algebraic expression.

-7 < 4x+1  < 17

solving the inequality expression

[tex]-7 < 4x+1 < 17[/tex]

Add -1 to all parts

[tex]-7+-1<4x+1+-1<17+-1[/tex]

[tex]-8<4x<16[/tex]

Divide all parts by 4

[tex]\frac{-8}{4}<\frac{4x}{4}<\frac{16}{4}[/tex]

[tex]-2<x<4[/tex]

Thus, the numbers are:

{-1, 0, 1, 2, 3}

i.e

[tex]-7<4x+1<17\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-2<x<4\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-2,\:4\right)\end{bmatrix}[/tex]

The graph is also attached below.

Answer:

x = 20/3 or x = -12/5

Step-by-step explanation:

Solve for x over the real numbers:

2 abs(x - 1) = x/2 + 8

Divide both sides by 2:

abs(x - 1) = 1/2 (x/2 + 8)

Split the equation into two possible cases:

x - 1 = 1/2 (x/2 + 8) or x - 1 = 1/2 (-x/2 - 8)

Expand out terms of the right-hand side:

x - 1 = x/4 + 4 or x - 1 = 1/2 (-x/2 - 8)

Subtract x/4 - 1 from both sides:

(3 x)/4 = 5 or x - 1 = 1/2 (-x/2 - 8)

Multiply both sides by 4/3:

x = 20/3 or x - 1 = 1/2 (-x/2 - 8)

Expand out terms of the right-hand side:

x = 20/3 or x - 1 = -x/4 - 4

Add x/4 + 1 to both sides:

x = 20/3 or (5 x)/4 = -3

Multiply both sides by 4/5:

Answer: x = 20/3 or x = -12/5

Answer:

1/2

Step-by-step explanation:

parallel slopes are exactly the same

Answer:

slope is 1/2

Step-by-step explanation:

the function y = 1/2 x+4 has the slope 1/2 because y=mx+b where m is slope

Tne slope of a parallel line to this function is the same m=1/2 because parallel lines have same slope

Answer:

$12.00

Step-by-step explanation:

Divide 504.00 by 42 hours

504/42 = 12

He earned $12 per hour

Answer:

The answer is B, sorry if I'm wrong.

Step-by-step explanation:

Answer:B=17.3 in2

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

n

Answer: D=[185]^1/2 or 13.6

(I think but idk... sorry if not correct)

Step-by-step explanation:

D=[(12-8)^2+(4-17)^2]^1/2

D=[(4)^2+(-13)^2]^1/2

D=[16+169]^1/2

D=[185]^1/2

Answer:

Step-by-step explanation:

[tex]d=\sqrt{(4-17)^2+(4-8)^2} =\sqrt{169+16} =\sqrt{185}[/tex]

around 44 or above

88+85+84+84+44= 385

385/5= 77

Answer:

The solution to the system of equations be:

[tex]y=4,\:x=0[/tex]

As the consistent system of equations has only one solution, it is independent.

Step-by-step explanation:

Given the system of equations

[tex]3y + 2x= 12[/tex]

[tex]36 - 9y = -6x[/tex]

solving the system of equations

[tex]\begin{bmatrix}3y+2x=12\\ 36-9y=-6x\end{bmatrix}[/tex]

Arrange equation variables for elimination

[tex]\begin{bmatrix}3y+2x=12\\ -9y+6x=-36\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}3y+2x=12\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:9y+6x=36[/tex]

[tex]\begin{bmatrix}9y+6x=36\\ -9y+6x=-36\end{bmatrix}[/tex]

so

[tex]-9y+6x=-36[/tex]

[tex]+[/tex]

[tex]\underline{9y+6x=36}[/tex]

[tex]12x=0[/tex]

[tex]\begin{bmatrix}9y+6x=36\\ 12x=0\end{bmatrix}[/tex]

solve 12x=0 for x

[tex]12x=0[/tex]

Divide both sides by 12

[tex]\frac{12x}{12}=\frac{0}{12}[/tex]

[tex]x=0[/tex]

[tex]\mathrm{For\:}9y+6x=36\mathrm{\:plug\:in\:}x=0[/tex]

[tex]9y+6\cdot \:0=36[/tex]

[tex]9y=36[/tex]

Divide both sides by 9

[tex]\frac{9y}{9}=\frac{36}{9}[/tex]

[tex]y=4[/tex]

Thus, the solution to the system of equations be:

[tex]y=4,\:x=0[/tex]

As the consistent system of equations has only one solution, it is independent.

Answer:

Step 1     z(c) = 2,323

CI = (  25 ;  30,2 )

Step-by-step explanation:

Normal Distribution:

Sample size  n = 25

Sample mean   μ  = 27,6

Sample standard deviation  s = 5,69

CI = 98 %   then  α  = 1 - 0,98     α = 0,02    α/2  = 0,01

From z-table we don´t  find z (score) for 0,01   directly, we need to interpolate between z = 2,32   and z = 2,33

For   0,0099           z score   is    2,33

for    0,0102            z score   is    2,32

Δ      0,0003                                  0,01

Then   by rule of three

for Δ        0,0003                ⇒      0,01

for Δ   (0,01- 0,0102)          ⇒        x

0,0003    0,01

0,0002      x

x = 0,0067

then  z (score for 0,01)   =  2,33 - 0,0067     z(c) = 2,3233

round to three decimal places z(c) = 2,323

Step 2:

CI =   μ  ±  z(c) * s/√n    ⇒   27,6  ± (2,323 * 5,69)/5

CI =  27,6 ± 2,6436

round to one decimal place

CI = 27,6 ± 2,6

CI = (  25 ;  30,2 )

Answer:

We kindly invite you to see the result in the image attached below.

The number in polar form is [tex]z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}[/tex].

Step-by-step explanation:

A complex number is represented by elements of the form [tex]a + i\,b[/tex], for all [tex]a[/tex], [tex]b[/tex] [tex]\in \mathbb{R}[/tex]. The first part of the sum is the real component of the complex number, whereas the second part of the sum is the imaginary component of the complex number. The real component is located on the horizontal axis and the imaginary component on the vertical axis.

Now we proceed to present the point on the graph: ([tex]a = 6[/tex], [tex]b = 3[/tex])  We kindly invite you to see the result in the image attached below.

The polar form of the complex number is defined by:

[tex]z = r\cdot e^{i\cdot \theta}[/tex] (1)

Where:

[tex]r[/tex] - Magnitude of the complex number, dimensionless.

[tex]\theta[/tex] - Direction of the complex number, measured in radians.

The magnitude and the direction of the complex number are defined by the following formulas:

Magnitude

[tex]r =\sqrt{a^{2}+b^{2}}[/tex] (2)

Direction

[tex]\theta = \tan^{-1} \frac{b}{a}[/tex] (3)

If we know that [tex]a = 6[/tex] and [tex]b = 3[/tex], then the polar form of the number is:

[tex]r =\sqrt{6^{2}+3^{2}}[/tex]

[tex]r = 3\sqrt{5}[/tex]

[tex]\theta = \tan^{-1} \frac{6}{3}[/tex]

[tex]\theta \approx 0.352\pi \, rad[/tex]

[tex]z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}[/tex]

The number in polar form is [tex]z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}[/tex].

Answer:

0.25(7x-6y)

Step-by-step explanation:

Answer:

71 degrees

Step-by-step explanation:

Use tangent to find x.

tantheta = opposite/adjacent

tan(x) = 130/45

x = tan^-1 (130/45)

x = 70.9

Round to nearest degree = 71 degrees

Answer:

x=17. I think.....

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation:

Since the two angles are vertical to each other they have the same measure.

x + 35 = 3x + 1 (subtract 1 on both sides)

x + 34 = 3x (subtract x on both sides)

34 = 2x (divide by 2 on both sides)

17 = x

Hope this helps ya!!

Answer:

2.5198421

Step-by-step explanation:

Answer:

1 and 3/5

Step-by-step explanation:

Answer:

360 tablespoons.

Answer:

id say 10 but im dumn if get wrong do not star me 5 only one star

Step-by-step explanation:

Answer: 6 of the flowers are pink

Step-by-step explanation:

If 3/5 of the flowers are yellow you would convert the 3/5 into a 9 because 1/5 of 15 is 3 so you would multiply 3 by 3 to get nine. By doing this you will find out the 2/5 or the remaining flowers are pink which makes 6 pink flowers.

Answer:

-4

Step-by-step explanation:

Answer:

the answer is -4. it's the same as dividing by a positive, except the number will be negative now :)

Answer:

I think it is 90 and 100

Step-by-step explanation:

I used this equation: x is the speed of the slower train

910 = (5x + 10) + 5x

Answer:

The answer is 86 and 96 mph

Step-by-step explanation:

Givens

Train A

Distance traveled = d

time taken = 5 hours

rate traveled = r

Train B

Distance traveled = 910 - d

time taken = 5 hours

rate = r + 10

Formula

basically d = r * t

Solution

Train A: d/r = 5 or d = 5*r

Train B = (910 - d)/(r + 10) = 5    or

Substitute d = 5*r   into Train B

(910 - 5*r)/(r + 10) = 5        Multiply both sides by r + 10

(910 - 5r) = 5 * (r + 10)       Remove the brackets on both sides

910 - 5r = 5r + 50             Add 5r to both sides

910 = 5r + 5r + 50

910 = 10r + 50                  Subtract 50 from both sides

910 - 50 = 10r                  Combine the left

860 = 10r

10r = 860                         Divide by 10

r = 860/10

r = 86

r + 10 = 96

Check

Train A distance: 5*r = 5 * 86 = 430

Train B distance: 5*r = 5 * 96 = 480

Total =                                         910

Step-by-step explanation:

Hey there!

See explanation in picture!

Hope it helps...

Answer:

x = -5

Step-by-step explanation:

If one draws a perfect verticle line at x = -5, one will have exactly 1/2 the parabola on each side. Then is one where to fold the parabola on that line, then there would be no overhang. Hence x = -5 is the axis of symmetry.

Answer:

$43.74

Step-by-step explanation:

will pay= $45

10% of =$45×10/100=$4.5

so, $45-$4.5= $40.5

8% tax= $40.5×8/100 =$3.24

total= $43.74

The speed of plane in still air will be 550 miles / hour and speed of wind will be 50 miles / hour.

It is given that a plane traveled 3900 miles in 6.5 hours with wind and 3250 miles in 6.5 hours against wind.

We have to find out the speed of plane in still air and speed of wind.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , division , etc.

As per the question ;

Distance travelled with wind in 6.5 hours = 3900 miles

Distance travelled against wind in 6.5 hours = 3250 miles

Let's assume speed of plane in still air be P and speed of wind be W.

So;

The total rate with the wind is the plane speed plus the wind speed and against the wind is speed of plane minus speed of wind.

i.e.,

d = rt

⇒ 6.5 ( P + W ) = 3900 miles  --- ---- --- --- -- ------- ----- --- Equation 1

and

⇒ 6.5 ( P - W ) = 3250 miles  --- ---- --- --- -- ------- ----- --- Equation 2

Let's solve the equations to get value of P and W ;

i.e.,

P + W = 3900 / 6.5

or

P + W = 600

and

P - W = 3250 / 6.5

or

P - W = 500

adding both equations ; we get ;

2P = 1100

or

P = 550 miles / hour

And

W = 50 miles / hour

Thus , the speed of plane in still air will be 550 miles / hour and speed of wind will be 50 miles / hour.

To learn more about algebra click here ;

brainly.com/question/26479183

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The length and midpoint of segment PQ, where the coordinate of P is (8, -15), and Q is (13, -10) are;

The given points are;

P(8, -15) and Q(13, -10),

Part A:

The distance between the points P and Q, which may be expressed as d(P, Q), is found as follows;

d(P, Q) = √((13-8)²+(-10-(-15))²) = √(50) = 5•√2

The length of PQ is therefore;

Second part;

The midpoint of segment PQ is obtained from the midpoint formula as follows;

[tex](x_m, y_m) = \left(\frac{x_1 + x_2}{2}, (\frac{y_1 + y_2}{2} \right)[/tex]

The midpoint, [tex](x_m, y_m) [/tex] of PQ is therefore;

[tex](x_m, y_m) = \left(\frac{8+13}{2}, \frac{(-15) + (-10)}{2} \right) = \left(11.5, -12.5\right) [/tex]

The coordinates of the midpoint of segment PQ is (11.5, -12.5)

Learn more about finding the midpoint of a segment here:

https://brainly.com/question/22835372

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Answer:

the amount after 5 years using compound continuously is $135.03

Step-by-step explanation:

The computation of the amount after 5 years using compound continuously is as follows

= Principal × e^(rate × time period)

= $110 × e^(4.2% × 5)

= $110 × 1.227525065

= $135.03

Hence, the amount after 5 years using compound continuously is $135.03

We simply applied the above formula so that the correct value could come

And, the same is to be considered