Rewrite the following equation in exponential form.
log49 (7)=1/2

Answer:

y=2, x=1

Step-by-step explanation:

3x-6y=12(x2)

5x-2y=10(x6)

Eliminate y

6x-12y=12

30x-12y=60

-24x =-48

divide both sides by -24

-24x/-24=-48/-24

y=2

to get our x

3x-6(2)=12

3x-12=12

3x=12+12

3x=24(divide both sides by 3)

x=1

Answer:

27 bc he warms hard and should get a raise

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:25°

Step-by-step explanation:

tanθ= 35/72

Answer:

Length = 12 inches

Width = 14 inches

Step-by-step explanation:

Formula for perimeter of a rectangle is;

P = 2(L + W)

Where;

L is length

W is width

We are told that the length is 2 inches shorter than its width. Thus;

L = (W - 2)

Thus,perimeter is now;

P = 2(W - 2 + W)

P = 2(2W - 2)

P = 4W - 4

We are told that the perimeter is 52. Thus;

4W - 4 = 52

4W = 52 + 4

4W = 56

W = 56/4

W = 14 inches

From L = (W - 2) ;

L = 14 - 2

L = 12 inches

Answer:

c. 0.0498

Step-by-step explanation:

First of all, let us find the number of four digit numbers possible.

There are 4 digits and let us have a look at the possibility of each digit.

Number of possible options for Unit's digit = 10

Number of possible options for ten's digit = 10

Number of possible options for hundred's digit = 10

Number of possible options for thousand's digit = 9 (because 0 can not be there to make it a 4 digit number)

Total number of possible outcomes = [tex]10\times 10\times 10\times 9 = \bold{9000}[/tex]

As per the given condition, unit's digit is 7.

So, number of possible options for unit's digit = 1

Number of possible options for thousand's digit = 8 (7 and 0 can not be there to make it a 4 digit number)

Number of possible options for hundred's digit = 8 (7 and one digit used in thousand's place can not be there)

Number of possible options for ten's digit = 7 (7, two digits used at thousand's and hundred's places)

Number of possible outcomes as per given conditions = [tex]1\times 8\times 8\times 7 = \bold{448}[/tex]

Formula for probability of an event E can be observed as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

[tex]P(E) = \dfrac{448}{9000} =\bold{0.0498}[/tex]

Answer:

The rate of the interest for savings account is: 2%

Step-by-step explanation:

Simple interest is given by the formula

[tex]I = Prt[/tex]

Here

I is the interest,

P is the principal amount

r is the interest rate

and

t is the time period in years

Now, it is given that

P = $200

I = $8

t = 2 years

Putting the values in the formula

[tex]8 = 200 * r * 2\\8 = 400 * r\\r =\frac{8}{400}\\r = 0.02[/tex]

Converting into percentage

r = 2%

Hence,

The rate of the interest for savings account is: 2%

Answer:

0.02

Step-by-step explanation

Answer:

Step-by-step explanation:

Given angle - 610°

Coterminal angle is an angle in the interval 0°- 360° added or subtracted to multiples of 360°:

Correct option is 1.

Answer:

the margin of error for this interval is 0.049

Step-by-step explanation:

The computation of the margin of error for this interval is shown below;

Given that

n = 400

x = 200

Now

p = x ÷ n = 200 ÷ 400 = 0.5

Now the margin of error is

= [tex]z \times \sqrt{\frac{p(1-p)}{n}} \\\\1.96 \times \sqrt{\frac{0.5 \times 0.5}{400} }[/tex]

= 0.049

Hence the margin of error for this interval is 0.049

Answer:

let he takes x ride in total

1

$15 + 1.25x = $40

on solving

1.25x = 40 -15

1.25x=25

x=25/1.25 = 20

He can go on 20 rides.

Step-by-step explanation:

Answer:

The equation to find the cost of repairing a TV is:

y = 25x + 40

Step-by-step explanation:

We know that the slope-intercept form of the line equation is

[tex]y=mx+b[/tex]

where m is the slope or rate of change and b is the y-intercept

Given that the TV chairman charges $40 to come out to your house and check the TV  plus $25 per hour of labor.

It means $40 is the y-intercept because it represents the starting point/condition of the repairman.

Let 'x' be the number of hours and y be the cost.

The rate of change = 25$ per hour of labor

Thus, m = 25

Hence, the slope-intercept form of the line equation becomes

y = mx+b

substituting m = 25 and b=40

y = 25x + 40

Therefore, the equation to find the cost of repairing a TV is:

y = 25x + 40

Validation:

y = 25x + 40

putting x = 1 to determine the cost if labor works for 1 hour.

y = 25(1) + 40 = $65

putting x = 2 to determine the cost if labor works for 2 hours.

y = 25(2) + 40 = $95

Answer:

-4.834 / 73

Step-by-step explanation:

Two points: (2007, 84.134) and (2080, 79.300)

Use the slope formula.

m = y2-y1/x2-x1

m = 79.300 - 84.134 / 2080 - 2007

m = -4.834 / 73

Answer:

y = 2x - 5

I hope this helps!

Answer:

(a) Percentage of girls = 55[tex]\frac{5}{7}[/tex]

(b) Percentage of boys = 44[tex]\frac{2}{7}[/tex]

Step-by-step explanation:

To find percentage, we multiply the fraction out of the total by 100%.

Percentage of girls = [tex]\frac{780}{1400}[/tex] × 100%

                                = 55[tex]\frac{5}{7}[/tex]

Percentage of boys = [tex]\frac{1400-780}{1400}[/tex] × 100%

                                 = 44[tex]\frac{2}{7}[/tex]

Answer:

x^2 + 4x + 12 + [tex]\frac{30}{x-2}[/tex]

Step-by-step explanation:

idrk how to explain this one and im on a computer so i cant take a picture of my work but just divide lol

divide like you would with normal division kinda lol

hope this helps <3

Answer:

-4

Step-by-step explanation:

The equation for slope is as follows:

We can use point P and point V's coordinates to find the slope.

Point P is at (2,4)

Point V is at (3,0)

Let's define all the variables:

y2 = 0 (from point V)

y1 = 4 (from point P)

x2 = 3 (from point V)

x1 = 2 (from point P)

Now that we have all the variables we can plug it into the equation:

[tex]\frac{0-4}{3-2} = \frac{-4}{1} = -4[/tex]

Therefore, the slope of line PV is -4.

I hope this helps!!

Feel free to ask any questions!

- Kay :)

Answer:

you're going to get an A

Step-by-step explanation:

.............

Answer:

This describes a translation.

Answer:

x=-5

Step-by-step explanation:

f(x)=-8x

f(x)=40

substitute f(x) with 40 in the first equation

40=-8x

s=-5 (slove)

Answer:

Option A: Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = x2 + x + 1

Step-by-step explanation:

1) The axis of symmetry of quadratic graph is the vertical line that divides the graph curve into two congruent halves. In this case, it is: x = -0.5

2) Vertex is the point at which the graph curve changes direction or simply coordinates of the crest or trough of the curve.

The graph given has a trough with the coordinates: x = -0.5, y = 0.75. This is (-0.5, 0.75)

3) The roots of a quadratic equation are the points where the curve crosses the x-axis. In this case, it doesn't cross and so we have imaginary roots.

Now, formula for line of symmetry is; x = -b/2a

Thus; -b/2a = -0.5 or -b/2a = -1/2

Thus, b = 1 and a = 1

Our first and second terms will now be;

x² + x

Looking at the options, the only one with x² + x as it's first 2 terms is option A.

Thus, the complete equation will be x² + x + 1

Answer:

The discounted TV would cost $200 because the 20% discount takes off $50

Answer:

Option A Domain: all real numbers between –2.5 and 2.5 range: all real numbers greater than or equal to –5

Step-by-step explanation:

Domain corresponds to the values of x and Range corresponds to the value of y. If sketch the graph on an online calculator we can see that the domain lies between -2.5 and 2.5 for x and the range corresponds to y as in this case

range ≥ -5.

Answer:

a

Step-by-step explanation:

Answer: 49cm squared *tiney 2 above cm*

Step-by-step explanation:

Answer:

There are 36 scholars who have a sister.

Step-by-step explanation:

Given that:

Total number of scholars in classes = 90

Fraction of scholars who have a sister = 2/5

Fraction of scholars who have a brother = 1/2

Number of scholars who have sisters = 2/5 of 90

Number of scholars who have sisters = [tex]\frac{2}{5}*90[/tex]

Number of scholars who have sisters = 36

Hence,

There are 36 scholars who have a sisters.

Answer:

14400 $. do u need an explanation:

so if 6000 is 100 percent

then ??? is 2 percent

to find out that you need to 6000×2 and divide by 2=120$

so you get this monthly.

in ten years you will have 14400 because

10 year=120 month

120month×120$=14400.

btw I cant speak English well. I hope it will help

Answer: The expected value is $0.32

Step-by-step explanation:

The expected value can be calculated as:

EV = ∑xₙ*pₙ

Where:

xₙ is the n-th event.

pₙ is the probability of the n-th event.

First, let's see the events in this situation and the probability of each event.

Lossing $1.

This happens when you roll all different numbers.

To calculate the number of combinations where you roll all different values, we first need to count the number of possible options for each roll, this is:

First dice: you have 6 options

Second dice: You have 5 options, because we remove the option that was rolled in the first dice.

Third dice: You have 4 options, because we removed the two outcomes showed in the two previous rolls.

Then the number of combinations is:

c = 6*5*4 = 120.

And the total number of combinations for rolling 3 dice is equal to the product between the number of outcomes for each dice, each dice has 6 possible outcomes, then the total number of outcomes is:

C = 6*6*6 = 216

The probability of rolling all different numbers will be equal to the quotient between the number of combinations where you roll all different values and the total number of combinations:

P₁ = 120/216 = 0.56

In the other case, where you roll at least two equal outcomes, you win $2.

The probability for this case will be the complement of the previous one, then the probability can be calculated as:

P₂ = 1 - P₁ = 1 - 0.56 = 0.44

Then the expected value will be:

EV = -$1*0.56 + $2*0.44 =  $0.32

The expected value is $0.32