Simplify each equation, then solve. 1) log 2 128=x

Answers

Answer 1

Answer: $\log _( 2 ){ 128 } =x\n \n \log _( 2 ){ \left( { 2 }^( 7 ) \right) } =x\n \n 7\cdot \log _( 2 ){ 2 } =x$

$\n \n 7\cdot 1=x\n \n \therefore \quad x=7$

Answer 2

Answer: $l[tex]log_(2)128=x\n\n Formula\ for\ log:\nlog_(a)c=b\ \ \ =>\ a^b=c\n\n2^x=128\n\n 2^x=2^7\n\n x=7\n\nSolution\ is\ x=7.$ [/tex]

Related Questions

Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After running for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable. Which equation can be used to represent k, the number of kilometers Julissa runs in t minutes? How does this work i cant really figure it out
A TV that normally cost $800 is on sale for 33% off. There is a 6% sales tax on the purchase. What is the final cost of the TV?
Lim -> 0 sin(2x) /(x*cos(x) )help
Tom drives a truck. His regular trip is a distance of 280 km. He drives at an average speed of 80 km/h. For safety reasons Tom’s boss puts a speed limiter on his truck. This reduces Tom’s average speed by 10 km/h. How much longer will it take Tom to drive his regular trip?
If a man can run p miles in x minutes, how long will it take him to run q miles at the samerate?

One yardstick for measuring how steadily—if slowly—athletic performance has improved is the mile run. In 1958, the local record for the running of a certain distance was 3 minutes, 59.3 seconds, or 239.3 seconds. In the half-century since then, the record has decreased by 0.5 seconds per year.

Answers

Answer:

They will hit 180 seconds in 118.6 year

Step-by-step explanation:

Let M be the record for the mile (in seconds)

Let x be the year after 1958

So, x=(year)-19548

We are given that In the half-century since then, the record has decreased by 0.5 seconds per year

So, slope = m = 0.5

Now we will use point slope form

y = mx+c

So, we can express M as,

$M=239.3-0.5 * x$

Now we are supposed to find when they will hit 180 seconds

Substitute M = 180 in equation

180=239.3-0.5x

x=118.6

So, they will hit 180 seconds in 118.6 year

Final answer:

You can model the decreasing record time with the linear equation y=239.3-0.5x, where x is years since 1958 and y is the run time in seconds. By using this model, you can find the record time for any given year.

Explanation:

The subject of this question is Mathematics, specifically linear equations. The question mentions an initial record of 239.3 seconds for a run which decreases by 0.5 seconds every year. We are tasked to find the running time after a certain number of years.

Let's let x represent the number of years since 1958 and y represent the number of seconds to run the race. Based on the information provided:

The starting time (y-intercept) in 1958 was 239.3 seconds.
The rate of decrease (slope) is 0.5 seconds per year.

Therefore, the relationship between x and y can be expressed by the linear equation: y=239.3-0.5x

To find a certain year's running time, we substitute the number of years passed since 1958 into x in the equation above and solve for y. For example, to find the running time in 50 years after 1958 (2008), we replace x with 50: y = 239.3 - 0.5(50) = 214.3 seconds.

Learn more about Linear Equations here:

brainly.com/question/32634451

#SPJ3

What is the equation of the line that passes through (-3, -1) and has a slope of 3/5 ? Put your answer in slope-intercept form. A y = 3/5x + 4/5
B y = 3/5x - 4/5
C y = -3/5x - 4/5

Answers

y +1 = 3/5(x+3)

y + 1 = 3/5x + 9/5

y =3/5x + 9/5 - 1

y = 3/5x + 9/5 - 5/5

y = 3/5x + 4/5

answer:A y = 3/5x + 4/5

Deanna collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected:Favorite Sport
Swimming Running Volleyball Row totals
Grade 8 0.14 0.18 0.22 0.54
Grade 9 0.17 0.24 0.05 0.46
Column totals 0.31 0.42 0.27 1

Based on the data, which statement is most likely correct?
In Grade 8, 14 students liked swimming.
In Grade 9, 31% of students liked swimming.
In Grade 8, 22% of students liked volleyball.
In Grade 9, 5 students liked volleyball.

Answers

Answer:

In Grade 8, 22% of students liked volleyball.

Step-by-step explanation:

Given:

The table representing the relative frequencies of different sports in different grades among the students.

Swimming Running Volleyball Row totals

Grade 8 0.14 0.18 0.22 0.54

Grade 9 0.17 0.24 0.05 0.46

Column totals 0.31 0.42 0.27 1

Relative frequency givesthe ratio of the number of quantities of a particular kind and the total number of quantities.

$\textrm{Relative frequency}=\frac{\textrm{Number of students in a particular sport}}{\textrm{Total students}}$

From the above table, we can conclude the following points:

Grade 8:

14% liked swimming, 18% liked running and 22% liked volleyball. So, a total of 54% students liked playing sports.

Grade 9:

17% liked swimming, 24% liked running and 5% liked volleyball. So, a total of 46% students liked playing sports.

Combining students of grade 8 and 9:

31% liked swimming, 42% liked running and 27% liked volleyball.

From all the options available, we observe that, third option is only correct.

In Grade 8, 22% of students liked volleyball.

Mr. Levine corrects 7 tests in 25 minutes. At this rate, how long would it take him to correct 120 tests?

Answers

Answer:

428 4/7ths minutes

Step-by-step explanation:

Answer: 7 hours and 8 minutes

Step-by-step explanation:

7 tests in 25 minutes

7 divided by 25= 3.57

3.57 minutes per test times 120 tests= 428.57 minutes

428.57 divided by 60 (60 minutes in an hr) = 7 hours and 8 minutes (and 57 seconds if u want to count those too)

Write 5.2 as the quotient of two integers A...11/3
B...21/5
C...26/5
D...51/10

Answers

Answer:

C) $(26)/(5) = 5.2$ .

Step-by-step explanation:

Given : Number 5.2

To find : write 5.2 as the quotient of two integers.

Solution : We have given Number 5.2

For $(11)/(3) = 3.666$ .

For $(21)/(5) = 4.2$ .

For $(26)/(5) = 5.2$ .

For $(51)/(10) = 5.1$ .

So, 5.2 is quotient of 26 and 5 integers.

Therefore, C) $(26)/(5) = 5.2$ .

it would be C because what i did A. 11 divided by 3=3.666666666666666666
B.21 divided by 5=4.2 C. 26 divided by 5= 5.2 D. 51 divided by 10=5.1 we want 5.2 and C = 5.2

Solve the equation using the quadratic formula : x^2-10x+25=18

Answers

$x^2-10x+25=18 \n \nx^2-10x+25-18 = 0\n \n x^2-10x+ 7 =0 \n \na=1 , b = -10 , c= 7 \n \n \Delta = b^(2)-4ac = (-10)^(2)-4*1*7=100-28 = 72 \n \n√(\Delta )=√(72)= √(2*36) =√(36)*√(2) =6√(2)$

$x_(1)=(-b-√(\Delta ))/(2a) =(10- 6√(2))/(2)=(2(5-3√(2)))/(2)= 5-3√(2)\n \nx_(2)=(-b+√(\Delta ))/(2a) =(10+ 6√(2))/(2)=(2(5+3√(2)))/(2)= 5+3√(2)$

$Answer : \ x= 5-3√(2) \ \ or \ \ x = 5+3√(2)$

Other Questions

Alberto is heating a solution in his chemistry lab. The temperature of the solution starts at 17°C. He turns on the burner and finds that the solution's temperature increases by 5°C every minute. This graph shows the temperature change.

Choose the correct product of (5x + 4)2.25x2 + 40x + 1625x2 − 1625x2 + 1625x2 − 40x + 16

54+(x-4)=x ............

PLEASE HELP WORTH 15 PTSUsing the scatterplot below, can you estimate the salary of something working for 11 years?