The solution to the exponential equation 7^(3 – 2x) = 7^(-x) is 3
How to solve exponential equation?7^(3 – 2x) = 7^(-x)
Both equation has the same baseEliminate the base to remain the powers3 - 2x = - x
collect like terms
3 = - x + 2x
3 = x
Learn more about exponential equation:
https://brainly.com/question/9302810
#SPJ1
a car can travel 340 km with 17 litres of petrol. how much can I travel with 20 litres of petrol?
The car would travel a distance of 400 km using 20 litres of petrol
How to determine the distance travelled?The given parameters can be represented using the following scale ratio :
Scale = 340 km : 17 litres
For 20 litres of petrol, we have:
Distance : 20 = 340 km : 17
Express as fraction
Distance/20 = 340 km/17
Multiply both sides by 20
Distance = 400 km
Hence, the car would travel a distance of 400 km using 20 litres of petrol
Read more about scale ratios at:
https://brainly.com/question/12416132
#SPJ1
vehicle A has a final sale price of $25,000 at 5% interest and financing up to 60 months and vehicle B has a final sale price of $29,000 at 4% interest and financing up to 60 months
how do I solve this and do I have enough information to answer the question and what step would take to solve the problem and how do I calculate the results
The calculation of the interest based on the price given shows that vehicle B has a lower interest.
How to calculate the price?From the information given, vehicle A has a final sale price of $25,000 at 5% interest and financing up to 60 months. The interest will be:
= (25000 × 5 × 5)/100
= $6250
Vehicle B has a final sale price of $29,000 at 4% interest and financing up to 60 months. The interest will be:
= (29000 × 4 × 5)/100
= $5800
Therefore, the calculation of the interest based on the price given shows that vehicle B has a lower interest.
Learn more about price on:
brainly.com/question/1153322
#SPJ1
Write the equation of the line in slope-intercept form.
The equation of the line in slope-intercept form is ___
Answer:
y = 1/40x + 20
Step-by-step explanation:
Slope-intercept equation format:
y = mx + b
m = slope/ gradient/ constant of variation/ rate of change
b = y-intercept
To find the slope, use the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Find two random points:
1 - (0.5, 40) , 2 - (1, 60)
Plug in:
[tex]\frac{60-40}{1-0.5}[/tex]
Solve:
[tex]\frac{20}{0.5}[/tex]
Divide:
[tex]\frac{1}{40}[/tex]
The y-intercept is when the x-coordinate is equal to 0.
The y-intercept is always the beginning.
So observing the graph, the first point is (0, 20)
The x-coordinate is 0.
Y intercept = 20.
Plug in both slope and y-intercept:
y = 1/40x + 20
8. Simplify (+2) × (+6) (-3)
Step-by-step explanation:
= ( +2 ) × ( + 6 ) ( -3 )
= + 12 (- 3 )
[tex] = - 36[/tex]
hence - 36 is the answer...
Peter and Henry went to the movies Peter bought the two Movie tickets for 7 dollars each. How much did he spend for the movie tickets Henry bought two buckets of popcorn for 5 dollars each. How much did Henry spend on popcorn.
Answer:
Peter spent 14 dollars on movie tickets. Henry spent 10 dollars on popcorn.
Step-by-step explanation:
I hope this helps! :)
PLS HELP ME ASAP!!!!!
Answer:
c
Step-by-step explanation:
its just the dilate of the triangle which both add up to 180
Lucky Champ owes $204.00 interest on a 8% loan he took out on his March 17. The loan is due on August 17. What is the principal?
Answer:
2,550 dollars hope u get a good grade
Step-by-step explanation:
the andswer is 220.32
Step-by-step explanation:
when you take 204 times the 8percent interest
204 x .08
you get 16.32
now add 16.32 and 204 and thats what you owe for your loan
9. Which point is on the graph of 2x - 16y=-8?
OA (-4,0)
O B. (0,2)
O
c. (0,4)
O D.
D. (1.0)
Answer:
A. (-4,0)
Step-by-step explanation:
Solve the following equation by factoring.
y²-8y=0
Answer:
y=0, y=8
Step-by-step explanation:
y²-8y=0
y(y-8)=0
so either y=0 or y-8=0
so y=0, y=8
Given: x - 5> -2.
Choose the solution set.
OxIXER, x> -7}
OxIXER, x> -3}
OxIxER, x> 3}
Answer: [tex]\{x|x \exists \mathbb{R}, x > 3 \}[/tex]
Step-by-step explanation:
Adding 5 to both sides, we get x > 3.
Without using a calculator, determine the number of real zeros of the function
f(x) = x3 + 4x2 + x − 6.
PLEASE HELP!!!
The number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3
How to determine the number of real zeros?The equation of the function is given as:
f(x) = x^3 + 4x^2 + x - 6
Expand the function
f(x) = x^3 + 5x^2 - x^2 + 6x - 5x - 6
Reorder the terms of the function
f(x) = x^3 + 5x^2 + 6x - x^2 - 5x - 6
Factor the expression
f(x) = x(x^2 + 5x + 6) -1(x^2 + 5x + 6)
Factor out x -1
f(x) = (x^2 + 5x + 6)(x -1)
Expand
f(x) = (x^2 + 3x + 2x + 6)(x -1)
Factorize
f(x) = [x(x + 3) + 2(x + 3)](x - 1)
Factor out x + 2
f(x) = (x + 3)(x + 2)(x- 1)
The function has been completely factored;
And it has 3 linear factors
Hence, the number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3
Read more about functions at:
https://brainly.com/question/7784687
#SPJ1
What are the coordinates of the point on the directed line segment from (−3,8) to (6, -4) that partitions the segment into a ratio of 1 to 5?
let's say the segment is A(-3,8) and B(6,-4) and point C splits it on a 1:5 ratio from A to B, let's check for C coordinates.
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-3,8)\qquad B(6,-4)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:5} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{5}\implies \cfrac{A}{B} = \cfrac{1}{5}\implies 5A=1B\implies 5(-3,8)=1(6,-4)[/tex]
[tex](\stackrel{x}{-15}~~,~~ \stackrel{y}{40})=(\stackrel{x}{6}~~,~~ \stackrel{y}{-4})\implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-15 +6}}{1+5}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{40 -4}}{1+5} \right)} \\\\\\ C=\left(\cfrac{-9}{6}~~,~~ \cfrac{36}{6} \right)\implies C=\left( -\cfrac{3}{2}~~,~~6 \right)[/tex]
what is .3% written as a decimal
Since 0.3 is divided by 100, we will shift the decimal point backward in 2 places to have 0.003
What are decimal numbers?
Decimal numbers are numbers that includes the dot in between. Given the percentage value expressed as:
0.3%
This can be expressed as;
0.3% = 0.3/100
Since 0.3 is divided by 100, we will shift the decimal point backward in 2 places to have 0.003
learn more on decimal number here: https://brainly.com/question/703656
#SPJ1
5) Kerjakan perkalian dibawah ini
82
44
X
Answer:
1. 3608
2.3956
3. 714
Step-by-step explanation:
jap darab ke apa ni
find the measure of the missing angle
ASAP!! HELP!
A) Describe the relationship among the lengts of the segments formed by the secant (DB) and secant (CB) . You may use words and/or an equation.
B) Suppose DB = 18 ft, AB = 3 ft, and CB = 10 ft. Find the lengt of CE. Show all your work.
Given the following parameters DB = 18 ft, AB = 3 ft, and CB = 10 ft. Therefore, The length of the CE is 4.6 ft.
What is Secant-secant rule?The secant-secant rule states that if two secants are drawn from an external point to a circle, then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant.
Mathematically:
(BA + AD)BA = (BE + EC)BE
Given the following parameters
DB = 18 ft, AB = 3 ft, and CB = 10 ft.
Substitute to check if we can find CE
(BA + AD)BA = (BE + CE)BE
(3+ 15) x 3 = (10 + CE ) x 10
18 x 3 = 100 + 10CE
54 = 100 + 10CE
CE = 4.6
Therefore, The length of the CE is 4.6 ft.
Learn more on the secant-secant theorem here: brainly.com/question/10732273
#SPJ1
Graph: y+2=-3/4(x+4)
Use the drop down menus to correctly complete the statement.
1st-
-must be congruent
-Must not be congruent
-Can be either congruent or not congruent
2nd-
-must be perpendicular
-Must not be perpendicular
-Can be either perpendicular or not perpendicular
For a quadrilateral to be a square, the diagonals must be congruent and must be perpendicular.
Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places.
tan(π/5)
Answer: The answer is 0.7265.
Step-by-step explanation: I don't know how to explain. Put the tangent of pi / 5 into your calculator.
You get 0.726542528...
But you round to 4 decimal places.
This rounds to 0.7265.
[tex] \tan( \frac{\pi}{5} ) [/tex]
Calculate the approximate value
0.726543
Round the numberRound 0.726543 to the required place
0.7265
Answer:
0.7265
Height of a softball in feet h(t)=3+55+-+16+2
Answer:
18ft
Step-by-step explanation:
i can't lay out the formula
which choices are equivalent to the expression below? check all that apply (image provided)
Answer:
D, E, and A
Step-by-step explanation:
Because 4 is also equivelent to square root of 16 and square root of 16 times square root of 3 is equal to square root of 48 which is D, and E is also correct because square root 24 x square root 2 is also square root 48 and same concept with A.
the mean of the data set is 18. what number is missing? 21,11,_,27,22,13,16
The missing number given the mean of the data set is 16.
What is the missing number?Mean is the average of a data set. It is determined by adding all the numbers in the data set and dividing the sum by the numbers in the data set.
Missing number = (mean x total number in the data set) - sum of numbers in the data set
(18 x 7) - ( 21 + 11 + 27 + 22 + 13 + 16)
126 - 110
= 16
To learn more about mean, please check: https://brainly.com/question/25842202
#SPJ1
I need help with this problem
Answer:
sorry i can't see it properly I am very sorry
Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Which equation shows p, the price in dollars that she paid for her previous car?
22,500 = 2 p
2 (22,500) = p
22,500 = 2 p minus 8
2 (22,500) = p minus 8
An equation is formed of two equal expressions. The correct option is A.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Therefore, the equation shows p, the price in dollars that she paid for her previous car,
Price of new car = 2 (Price of the previous car)
22,500 = 2p
Hence, the correct option is A.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ1
Answer: a
Step-by-step explanation:
please help me with this
Answer:
10π (31.415926)
√101(10.0498756)
9.92749...
0.99853...
Step-by-step explanation:
For 10π, we can simplify π into 3.14 for an approximate amount. 3.14*10=31.4
For the square root of ten, we can estimate it's between 10 and 11 since 10 squared is 100 and 11 squared is 121.
Answer:
See explanation
Step-by-step explanation:
First, we have to put the expressions into numbers. For the square root of 101, it doesn't divide evenly into any whole number. We do know that 10^2 is 100, and 11^2 is 121. That means the square root of 101 is between 10 and 11. Pi is equal to 3.14, so we just multiply 10 by 3.14. If we do this, we get 31.4. From here we can rank the numbers in order from greatest to smallest.
31.4 (10pi) is greater than
The square root of 101 which is greater than
9.92749... which is greater than
0.99853...
Hope this helps!
This venn diagram shows sports played by 10 students let events A = the students plays basketball let event B = the students plays soccer What is P(A|B)
The probability of P(A|B) will be; P(A|B) = 2/5 = 0.4
How to deal with Venn Diagrams?
From the Venn diagram attached, it displays sports played by 10 students.
Let event A = The students play basketball.
Let event B = The student plays soccer.
Then the probability of P(A|B) will be;
P(A|B) = P(A ∩ B)/P(B)
P(A|B) = (2/10)/(5/10)
P(A|B) = 0.40
Read more about Venn Diagrams at; https://brainly.com/question/2099071
#SPJ1
Write the equation of the circle in general form. Show your work.
Answer:
x^2+2x+y^2−2y−7=0
Step-by-step explanation:
The method from converting to standard to general is very simple
this equation in standard form would be
(x+1)^2+(y-1)^2=9
This is because whatever the center of the circle is, you take the negative/positive version of that number
The center is at -1, 1. So it would flip to be put into the equation as 1, -1.
9 is the radius^2.
The radius is 3.
To convert to general form you just simplify
x^2+1+2x = (x+1)^2
y^2 + 1 -2y = (y-1)^2
x^2 - 2x + y^2 - 2y + 2 = 9
get the nine on the left side
x^2 -2x +y^2 - 2y 2 - 9 = 0
x^2+2x+y^2−2y−7=0
Give brainliest, please!
Hope this helps :)
Find the present value, using the future value formula and a calculator. Future value is $6,000 in two years at 9.5% simple interest. Round your answer to the nearest cent (two decimal places). Enter only the number without $ sign.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$6000\\ r=rate\to 9.5\%\to \frac{9.5}{100}\dotfill &0.095\\ t=years\dotfill &2 \end{cases} \\\\\\ A=6000[1+(0.095)(2)]\implies A=6000(1.19)\implies A=7140[/tex]
What are the solutions to this system of
equations?
x² + 2x - 8 = 0
y = x² + 3x + 5
y = x + 13
x = 2 and x = -4
A
(15, 2); (9,-4)
B
(2, 15); (-4, 9)
Answer:
B; because it has two points where x is once 2 and once -4
In a football tournament, each team plays exactly 19 games.
Teams get 3 points for every win and 1 point for every tie.
At the end of the tournament, team Olympus got a total of 28 points.
From the following options, how many times could team Olympus have tied?
Answer:16 ties
Step-by-step explanation:
there is 19 games if they tied 16 then that 16 points so 28 - 16= 12
then 4 games left so 4 times 3 is 12
At the end of the tournament, team Olympus have tied for 13,10,7,4,1 times
What is inequality?
A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
According to question
In a football tournament, each team plays exactly 19 games.
Points for every win (w) = 3
Points for every tie (t)= 1
Points for every loose = 0
Olympus got a total of 28 points
i.e 3w + t = 28 ---------(1)
And each team plays 19 games
T + W ≤ 19 --------------(2)
and T , W ≥ 0
from equation (1) and (2)
=> 2W ≥ 9
=> W ≥ 4.5
( match can be won in integers only )
=> W ≥ 5
W T Loose
5 13 1
6 10 3
7 7 5
8 4 7
9 1 9
Hence, Olympus have tied for 13,10,7,4,1 times
To know more about Inequality here :
https://brainly.com/question/15137133
# SPJ2