For what values of x does 25^x = 5^x^2-3?
Answers
The values of x that satisfy the given equation are -1 and 3
What is an indical equation?From the question, we are to determine the values of x that satisfy the given equation
The given equation is
25^x = 5^x^2-3
The can be written as
[tex]25^{x} =5^{x^{2} -3}[/tex]
Expressing 25 in index form, we get
[tex]5^{2x} =5^{x^{2}-3 }[/tex]
Now, equate the powers (since the bases are equal)
[tex]2x =x^{2}-3[/tex]
Then, we have that
[tex]x^{2} -2x-3 =0[/tex]
Solve quadratically
Using the factorization method, we get
[tex]x^{2} -2x-3 =0[/tex]
[tex]x^{2} -3x+x-3 =0[/tex]
[tex]x(x-3)+1(x-3)=0[/tex]
[tex](x+1)(x-3) =0[/tex]
∴ x+1 = 0 OR x-3 = 0
x = -1 OR x = 3
Hence, the values of x that satisfy the given equation are -1 and 3.
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Related Questions
Identify the hypothesis of the statement below.
If the sum of the measures of two angles is 180°, then the angles are supplementary angles.
Answers
What is Indegree and Outdegree of a graph?
Answers
Outdegree-The number of outward directed graph edges from a given graph vertex in a directed graph.
Solve the inequality. -2/3x – 10 < 1/3
Answers
Hope this helps
-2/3x-10<1/3
add 10 to both sides
-2/3x<10 1/3
divide -2/3 (which means to flip the numbers and multiply!)
since you divide by a negative, you flip the sign!
x> -31/2, -15.5, -15 1/2
If b= the number of boys, which algabraic expression represents the phase?
Answers
math help easy will give brainliest
Answers
y = 8x + b because the slope is same = 8.
using point slope form
y - -3 = 8(x - - 2)
y + 3 = 8x + 16
y = 8x + 13 Answer
Answer: the equation will be of the form
y = 8x + b because the slope is same = 8.
using point slope form
y - -3 = 8(x - - 2)
y + 3 = 8x + 16
y = 8x + 13 Answer
I hope that this helps! :3
A clearance rack is marked as 35% off the regular price. A shirt on the clearance rack has a regular price of $45.99. If there is 7.25% sales tax, what will the shirt ring up for at the register?
a.
$17.26
b.
$21.67
c.
$29.89
d.
$32.06
Answers
The shirt ring-up at the register will be $32.06. Then the correct option is D.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A clearance rack is marked as 35% off the regular price. A shirt on the clearance rack has a regular price of $45.99. If there is a 7.25% sales tax.
The shirt ring up for at the register will be given as,
⇒ $45.99 x (1 - 0.35) x (1 + 0.0725)
⇒ $45.99 x 0.65 x 1.0725
⇒ $32.06
The shirt ring-up at the register will be $32.06. Then the correct option is D.
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PLEASE HELP! 15 POINTS
Answers
she earns 550 per week
so that is one one side of the equation 550w
the other side would be the 4500 she spent plus the 200 per week' so 4500 +200w
equation is 550W> 4500+200W
Your business borrowed 10 bitcoins on May 1, when 1 bitcoin was worth $1,418.86. On June 1, 1 bitcoin was worth $2,441.29. Not counting the 1 month of interest, what is the total amount, including the principal, your business owed on June 1, in dollars?
Answers
The business owed a total of $24,464.43, including the principal, on June 1.
Explanation:To calculate the total amount your business owed on June 1, we need to find the value of the borrowed bitcoins in dollars on that date.
Step 1: Convert the number of borrowed bitcoins to dollars on May 1 by multiplying it by the value of 1 bitcoin in dollars: 10 bitcoins * $1,418.86/bitcoin = $14,188.6.
Step 2: Convert the value on May 1 to the value on June 1 by multiplying it by the change in the value of 1 bitcoin:
$14,188.6 * ($2,441.29/$1,418.86)
= $24,464.43.
Therefore, your business owed a total of $24,464.43, including the principal, on June 1.
The total amount owed on June 1, not counting the 1 month of interest, is $24,412.90.
To calculate the total amount owed on June 1, we need to multiply the number of bitcoins borrowed by the value of one bitcoin on that date.
On May 1, the business borrowed 10 bitcoins, and the value of one bitcoin on June 1 was $2,441.29. Therefore, the total amount owed on June 1, excluding interest, is calculated as follows:
Number of bitcoins borrowed = 10
Value of one bitcoin on June 1 = $2,441.29
Total amount owed on June 1 (in dollars) = Total amount owed on June 1 (in dollars) = [tex]10 \times $2,441.29[/tex]
Total amount owed on June 1 (in dollars) = $24,412.90
Thus, the total amount owed on June 1, not counting the 1 month of interest, is $24,412.90.
Which function is negative for the interval [–1, 1]?
The answer is the second graph
Answers
Answer:
the answer is the 2nd graph your welcome:)
Step-by-step explanation:
A function is the relationship between two variables such that each input has exactly one output
The function which is negative for the interval [-1, 1] is the function represented by the second graph
The reason the second graph is the correct option is as follows:
The output values of a function are the y-values of the function. A function is negative over an interval if its y-values are negative in the interval
The given interval is [-1, 1], which is the interval from x = -1, to x = 1
From the given graphs, the graph of the function that is negative over the interval [-1, 1] which is the second graph
a·x² + b·x + c = 0
At x = 0, y = -2
At x = 1, y = 0
At x = -1, y = 0
At x = 2, y = 2
Solving the above gives; The equation of the function is f(x) = x² - 2
The graph of the function is attached
Learn more about graphs of function here:
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There are 14 dogs in a particular class at a dog show. Blue, red, yellow, and white ribbons will be awarded to the first through fourth place finishers, respectively. In how many different ways can the ribbons be awarded?
1001
6006
24024
38416
Answers
There are 13 possibilities for second place, since a dog can't get both first and second place.
There are 12 possibilities for third place, since a dog can't get both first, second, and third place.
There are 11 possibilities for fourth place, since a dog can't get both first, second, third, and fourth place.
Multiply them together and get 24024 possibilities.
Hope this helps!
Answer:
24,024
Step-by-step explanation:
on god
Lima is constructing a square in which two of its vertices are points A and B. He has already used his straightedge and compass to construct the lines and arcs shown.
Answers
The equation below describes a proportional relationship between x and y. What is the constant of proportionality? y=2/7x
Answers
is the constant of proportionality is : 2/7
Jill is 7 kilometers away from joe. both begin to walk toward each other at the same time. jull walks at 1.5 kilometers per hour. they meet in 2 hours. how fast is joe walking?
Answers
The inverse of x y is: x y x y y x x y y x
Answers
Answer:
The inverse of xy is yx.
Step-by-step explanation:
Given: xy
We need to find the inverse of xy.
To find inverse of an expression, we need to replace the variable x by y and y by x.
Given xy.
Now replace x by y and y by x, we get
yx
Therefore, the inverse of xy is yx.
Let me show you an example.
y = x - 2
To find the inverse function, replace x by y and y by x, we get
x = y - 2
It is an equation, to write the equation in terms of y, add 2 from both sides, we get
x + 2 = y -2 + 2
x + 2 = y
Therefore, y = x + 2
will give award to whoever answers!
justify each step in solving 4x - 3 = 9
4x - 3 + 3 = 9 + 3
4x = 12
4x/4 = 12/4
x = 3
Answers
4x = 9 + 3
4x = 12
x = 3
hope that helps, God bless!
x=3is this right?
are the lines the same if the right line is a translation of the left line 4 units to the right
Answers
A new hybrid car has a 18-gallon gas tank. On one tank of gas, the owner can drive 540 miles. The number of miles traveled varies directly with the number of gallons of gas the car uses.
a. Write an equation that relates the number of miles traveled with the number of gallons of gas used.
b. How many miles can the owner travel on 12 gallons of gas?
Answers
What is the answer for 623 divided by 20?
Answers
i. e 31 3/20
=
31.15........
Divide. Write your answer in simplest form.
4 ÷ 5/6
Answers
4 x (6/5) - flip the fraction and flip the second number
4 x (6/5) = 4.8
4.8 is your answer
hope this helps
In a certain sequence, each term, starting with the 3rd term, is found by multiplying the previous two terms. what is the difference between the 6th and 3rd terms in the sequence? (1) the 1st term is equal to 8 times the 2nd term. (2) the 4th term is equal to 1.
Answers
Again, consider the series 2, 1/4, 1/2, 1/8, 1/16, 1/(8*16). Clearly, the difference of the 6th and the 3rd term is different for them. Insufficient.
From F.S 2, let the series be a,b,ab,ab2,a2b3,a3b5a,b,ab,ab2,a2b3,a3b5. Now we know that ab2=1ab2=1. The required difference =a3b5−ab=ab(a2b4−1)=ab[(ab2)2−1]a3b5−ab=ab(a2b4−1)=ab[(ab2)2−1]= 0.Sufficient.
Write the equation for the vertical line that contains point E (10,-3)
Answers
This means it eventually crosses the x axis.
Undefined equations are represented by x= (wherever it crosses the x axis)
So since this point is (10 , -3), it crosses the x axis at 10 and goes up and down forever.
The equation of the line is x = 10.
Hope this helped C:
Write programs with loops that compute
a. the sum of all even numbers between 2 and 100 (inclusive).
b. the sum of all squares between 1 and 100 (inclusive).
c. all powers of 2 from 20 up to 220.
d. the sum of all odd numbers between a and b (inclusive), where a and b are user inputs.
e. the sum of all odd digits of an input. (for example, if the input is 32677, the sum would be 3 + 7 + 7 = 17.)
Answers
<3
tysm
Which unit rate is the lowest price per ounce? choice
a.25 ounces of potato chips for $3.49 choice
b.45 ounces of potato chips for $4.79 choice a choice b the unit rates are equal. the unit rates cannot be determined?
Answers
= $ 0.1396 / ounce < ---- unit rate
b. 45 ounces of potato chips for $4.79 => $ 4.79 / 45 ounces =
= $ 0.1064 / ounce. <---- unit rate
So, the answer is the unit rates are different, being the choice b, the lowest price per ounce.
Answer:
choice b
Step-by-step explanation:
im smart
Find equations in standard form of the lines through point P that are A.) parallel to, and B.) perpendicular to, line L. P(0,-4); L: 2y=x. I've tried solving it and looking at examples, but no examples in my book are like this problem.
Answers
y = 1/2x....the slope of this line is 1/2.
A parallel line will have the same slope.
y = mx + b
slope(m) = 1/2
(0,-4)....x = 0 and y = -4
now we sub and find b, the y int
-4 = 1/2(0) + b
-4 = b
so ur equation is : y = 1/2x - 4...but we need it in standard form Ax + By = C
y = 1/2x - 4....subtract 1/2x from both sides
-1/2x + y = -4...multiply both sides by -2
x - 2y = 8 <== standard form of parallel line
==========================
the slope of the line was 1/2. A perpendicular line will have a negative reciprocal slope. All that means is flip the slope and change the sign. So our perpendicular line will have a slope of -2...see how I flipped 1/2 making it 2/1...and changed the sign, making it -2.
y = mx + b
slope(m) = -2
(0,-4)...x = 0 and y = -4
sub and find b
-4 = -2(0) + b
-4 = b
so this equation is : y = -2x - 4....but we need standard form
y = -2x - 4....add 2x to both sides
2x + y = -4 <== standard form of perpendicular line
0.74 as a fraction in simplest form
Answers
74/100 reduces to 37/50 <==
Sadie's ice cream shop sold 11 sundaes with nuts and 1 sundae without nuts. what is the ratio of the number of sundaes without nuts to the number of sundaes with nuts?
Answers
1:11
1:11
Are the graphs of the lines in the pair parallel? Explain. y = 3/7 x + 11 and –3x + 7y = 13
Answers
Which figure shows how a shape can be rotated about an axis to form a cone?
A. Triangle
B. Circle
C.Square
D. right triangle
Answers
The figure that shows how a shape can be rotated about an axis to form a cone is (d) right triangle
How to determine the figure?The shapes are given as:
A. Triangle
B. Circle
C.Square
D. right triangle
Rotating a circle about its axis would form a sphere, while a square would be rotated to form a cylinder.
However, when a right triangle is rotated, it forms a cone
Hence, the figure is (d) right triangle
Read more about rotation at:
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Guys please help! 15 points and brainliest! In triangle CDE, the measure of angle C is 90 degrees, side CD is 15 and DE is 3 more than CE. Find the length of the longest side of CDE.
Answers
your triangle is
CD=15=a
CE=?=b
DE=CE+3=b+3=c
and C=90°
-> insert those values, with c substituted with b+3 to remove c
c^2=a^2+b^2-2*a*b*cos(C)
(b+3)^2=15^2+b^2-2*15*b*cos(90)
cos(90)=0->
(b+3)^2=15^2+b^2
b^2+2*3*b+3^2=225+b^2
6b+9=225
6b=216
b=36=CE
DE=CE+3=36+3=39
BRAINLIESTTTT!!!
1. Which of the following statements best describes the graph of x + y = 4?
It is a line which intersects the x-axis at (4, 4).
It is a line which intersects the y-axis at (4, 4).
It is a line joining the points whose x- and y-coordinates add up to 8.
It is a line joining the points whose x- and y-coordinates add up to 4.
Answers
A is false because any point on the x axis will have y = 0
B is false because any point on the y axis will have x = 0
C is false; the coordinates add up to 4
D is the only thing left. It's true since x+y = 4 indicating that the coordinates add up to 4
Answer: choice D
==============================================================
Problem 2
You're close but the answer is actually choice C. The shaded region is below the slanted line so we'll have a "less than or equal to" sign instead of a "greater than or equal to" sign for the first inequality.
=================================================================
Problem 3
Using geogebra (see attached image) I'm getting the graph that matches with choice A
So it looks like you have the correct answer. Nice job.