For what values of x does 25× - 5ײ-3?
O x = -3, x = 1
O x = -1, x = 3
3
0 X=-²2/₁X-2
Ox
3
O x= -2, x=-2/
Answers
Answer:
X = 3, -1; B
Step-by-step explanation:
Use log properties, log 5 on both sides, log 5 of 25 is 2 that times the exponent, so 2*x = 2x, and on the other side, log 5 and base of 5 cancels. So 2x = x^2 -3, which can be solved using factoring:
x^2 -2x -3 = (x-3)(x+1) = 0, x=3,-1
The value of x in 25ˣ = 5ˣ²⁻³ is x =3 or x = -1.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given that the equation is 25ˣ = 5ˣ²⁻³.
To solve the equation, take logs on both sides, we get,
x log(25) = (x²- 3)log5
2x log 5 = (x²- 3) log5
2x = x²-3
x²- 2x -3 = 0
Now, factorize the quadratic equation,
we get,
x² - 3x + x - 3 = 0
x(x- 3) + 1(x - 3) = 0
x = 3 or -1.
Therefore, x = 3 or x = -1.
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Related Questions
Can someone answer this as soon as possible.
Answers
find the positive square root of 217.05 and 100.2001......with division method
Answers
The square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.
How to depict the square root?It should be noted that square root is factor of a number that when multiplied by itself will give the original number.
In this case, the square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.
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please help me with this
Answers
The range of possible heights is given by the inequality:
d ≥ 300.125 m
How to find the possible heights of the building?
We know that the time that it takes for an object to fall from a distance d is:
[tex]t = \frac{\sqrt{2d} }{4.9}[/tex]
In this case, we know that t ≥ 5s.
Then we can solve for the minimum distance, which is given when t = 5s.
[tex]5 = \frac{\sqrt{2d} }{4.9}\\\\(5*4.9)^2/2 = d = 300.125[/tex]
So the minimum height of the building is 300.125 meters, then the range of possible heights is:
d ≥ 300.125 m
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WILL GIVE BRAINLIEST!!!! *20 points*
Answers
Answer:
g(-0.0001) = -9
g(0.0001) = -1
g(0) = -1
g(9) undefined
Step-by-step explanation:
g(9) undefined .because the graph have an empty circle
at (9 , 0) which means g is not defined at 9.
Which of the following equations demonstrate the multiplication property of equality for the equation x = 2? Check all
that apply.
✔x(3) = 2(4)
x(5) = 10
x(1.5) = 2(2)
x(0.5) = 2(0.5)
x(12) = 12
Intro
Done
3 of 12
Answers
Answer: x(5) = 10 has the multiplication property.
Step-by-step explanation:
To verify the multiplication property of equality , We need to put the value of x= 2
1. x(5) = 10
Solution = 2(5) = 10 ✔
2. x(1.5) = 2(2)
Solution = 2 (1.5) = 3 X
3. x(0.5) = 2(0.5)
Solution = 2 (0.5) = 1 X
4. x(12) = 12
Solution = 2 (12) = 24 X
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Answer:
Step-by-step explanation:
answer B and D
I got it right and didnt spell the entire constitution
There are 12 ducks and 11 geese in a certain park. Find the ratio of geese to ducks.
Answers
Answer:
11:12
Step-by-step explanation:
You first have to put the number of geese to ducks in a ratio form and since 11 and 12 have no common factors one cannot reduce the ratio
Which is equivalent to 3√8* ?
O x √8^3
O 8 ^3/x
O 8 ^x/3
O 8^3x
Answers
Answer:
O 8 ^x/3
Step-by-step explanation:
Remember that :
[tex]\sqrt[n]{x} = x^\frac{1}{n}[/tex]
………………………………
Then
[tex]\sqrt[n]{8^x} = (8^{x})^{\frac{1}{3}}[/tex]
[tex]= 8^{x\times\frac{1}{3}[/tex]
[tex]=8^{\frac{x}{3}[/tex]
A sequence is defined by the recursive function f(n + 1) = one-half(n). If f(3) = 9 , what is f(1) ?
Answers
The value of f(1) is 81
What is Recursive function?Recursive Function is a function that repeats or uses its own previous term to calculate subsequent terms and thus forms a sequence of terms
Given:
f(n + 1) = 1/3* f(n)
f(3) = 9
let n=0
f(0+1) = 1/3 * f(0)
f(1) = 1/3 * f(0)
Let n=1
f(1+1) = 1/3 * 1/3*f(0)
f(2) = 1/9 * f(0)
let n=2
f(2+1) = 1/3 * 1/9* f(0)
f(3) = 1/27 * f(0)
Also, f(3) =9
So,
9 = 1/27 * f(0)
f(0) = 27 * 9
f(0) = 243
Now,
f(1) = 1/3 * f(0)
f(1) = 1/3/ 243
f(1) = 81
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In one class, homework is worth 10% of the final grade, each of 3 projects is worth 20%, and a final exam is worth 30%.
(a) If a student has an 81 homework average and a 95 on the first project, what is the student's grade at this point?
(b) If the same student from part (a) gets a 72 on the second project and a 71 on the third project, what is the lowest grade the student can get on the final exam to get an 80 overall in the course?
(a) The grade at this point is_____
(Simplify your answer. Round to the nearest tenth as needed.)
(b) The lowest possible grade is____
(Simplify your answer. Round to the nearest integer as needed.)
Answers
a) At this point, the grade is 27.1
b) The lowest possible grade is 81
How to get the grades of the student?
a) At this point the student has 81 in homework and 95 on the first project.
Remember that the homework is worth 10% of the final grade, and each project is worth 20%, then at this point the final grade is:
F = 0.10*81 + 0.20*95 = 27.1
b) The student gets 72 on the second project and 71 on the third project, at this point the final grade is:
F = 27.1 + 0.20*72 + 0.20*71 = 55.7
Now the student wants to get a final grade of 80, then if we define x as the grade on the final exam (which is worth 30%) we must have that:
55.7 + 0.30*x = 80
Now we can solve this for x:
x = (80 - 55.7)/0.30 = 81
The lowest possible grade that he must get is 81.
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Which of the following is correct for determining the length of x to the nearest tenth of a metre?
cos 42 = x/6
tan 48 = x/5
sin 48 = x/5
tan 42 =x/6
Answers
My square patio is tiled with square tiles, all the same size. All the tiles are gray, except the tiles along the two diagonals, which are all yellow. (The corners are yellow, the center is yellow, and all the tiles along the diagonal in between are yellow.) If there are $89$ yellow tiles, how many gray tiles are there
Answers
Answer:
1936
Step-by-step explanation:
We can start by removing the center tile, because all four diagonals over lap on that tile. We'll add it back later. 88/4=22. which means there are 22 tiles per half, 44+1(the center tile) total tiles per side, which means there are a total of 1936 tiles.
AOPS ANSWER:
Suppose that we have a square with dimensions [tex]$e \times e$[/tex]. The diagonals each have [tex]$e$\\[/tex] tiles. If [tex]$e$\\[/tex] is even, the number of yellow tiles is [tex]$2e$[/tex], because the [tex]2[/tex] diagonals don't intersect. If [tex]$e$[/tex] is odd, then the number of yellow tiles is [tex]$e+e-1=2e-1$[/tex]. (We have to subtract [tex]1[/tex] because the center tile is counted [tex]2[/tex] times). We know that there are [tex]89[/tex] yellow tiles, which is an odd number, so [tex]$89=2e-1$[/tex]. This implies that [tex]$e = 45$[/tex]. So the dimensions of the floor are [tex]$45 \times 45$[/tex], or [tex]2025\\[/tex] square units. Since all of the other tiles are gray, there are [tex]$2025-89=\boxed{1936}$[/tex] gray tiles.
Jacob is calculating the amount of time it takes a rocket to get to the moon. the moon is around 239,000 miles from earth. how many hours would it take a rocket that can travel at 250 miles per minute to travel to the moon? round to the nearest hour.
Answers
Answer:
16hr
Step-by-step explanation:
distance= time x speed
250mi/min=250x60mi/hr =15000mi/hr
239000/15000≈15.9333hr
Round up to 16hr
Polygon C and polygon D are similar. The perimeter of polygon C is 60 inches,
and the perimeter of polygon Dis 12 inches. If one side of polygon C is 4
inches, what is the length of the corresponding side in polygon D?
A. 0.3 in
OB. 20 in
OC. 4 in
OD. 16 in
k
Answers
Answer:
Using the method of ratio and proportion, we find that the length of the side of Polygon D is 0.8in.
Step-by-step explanation:
Given that Polygon C and Polygon D are similar. This means that the ratio of the length of one side of Polygon C to the length of corresponding side of Polygon D will stay same even if we change the lengths.
Perimeter of polygon C = 60in
Perimeter of polygon D = 12in
Length of side of polygon C = 4in
Let us take the number of sides of both the polygons same. Let the length of the side of polygon D x inches. Let the number of sides be n.
First equation, 4n = 60
Second equation, xn = 12
Dividing second by first
(xn) / (4n) = 12 / 60
x / 4 = 1 / 5
x = 4 / 5 = 0.8in
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what is the length of the base? help me please thank u ;)
Answers
=============================================================
Explanation:
a = 26 and b = 26 are the congruent legs
angle C = 60 degrees is between sides 'a' and b
c = unknown base which is opposite angle C
We'll use the law of cosines to find this missing side.
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 26^2 + 26^2 - 2*26*26*cos(60)
c^2 = 676
c = sqrt(676)
c = 26
It turns out that all three sides are the same length (26), which means this isosceles triangle is really equilateral. Consequently, it means all three interior angles are 60 degrees each.
---------------
Here's another way to see why we have an equilateral triangle.
The vertex angle is 60 degrees. Let x be the measure of each base angle. Those two base angles add to the 60 degrees to get 180
x+x+60 = 180
2x+60 = 180
2x = 180-60
2x = 120
x = 120/2
x = 60
Each base angle is 60 degrees, so all three angles are 60 degrees. This points us to the triangle being equilateral and we can say all three sides are 26 units long.
If we didn't have an equilateral triangle, then we'd have no choice but to use the law of cosines mentioned earlier.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:base \:\:side = 26 \:\: units [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
As the two sides of the triangle are equal, the corresponding angles opposite to the the sides are equal as well.
[tex] \textsf{let each of those angles measure ' x ' } [/tex]
[tex]\qquad \tt \rightarrow \:x + x + 60 = 180[/tex]
[ sum of all interior angles of a triangle ]
[tex]\qquad \tt \rightarrow \:2x + 60 = 180[/tex]
[tex]\qquad \tt \rightarrow \:2x = 180 - 60[/tex]
[tex]\qquad \tt \rightarrow \:2x = 120[/tex]
[tex]\qquad \tt \rightarrow \:x = \cfrac{120}{2} [/tex]
[tex]\qquad \tt \rightarrow \:x = 60 \degree[/tex]
Therefore, all angles of the triangle are equal. that being the case we can conclude that it's an equilateral triangle.
henceforth, all its sides are equal to one another.
[tex]\qquad \tt \rightarrow \:base \: \: side = \: \: 26 \: \: units[/tex]
Need help (pic included)
Answers
Answer:
a = 1Step-by-step explanation:
We have the expression:
12x² + ax - 20
3x + 4 is a factor. Therefore:
12x² + ax - 20 = (3x · 4x) + ax + (4 · (-5))
12x² + ax - 20 = (3x + 4)(4x - 5)
(3x + 4)(4x - 5) = (3x)(4x) + (3x)(-5) + (4)(4x) + (4)(-5)
= 12x² - 15x + 16x - 20 = 12x² + x - 20
a = 1Other method:12x² + ax - 20 = (3x + 4)(bx + c)
12x² + ax - 20 = (3x)(bx) + (3x)(c) + (4)(bx) + (4)(c)
12x² + ax - 20 = 3bx² + 3cx + 4bx + 4c
12x² + ax - 20 = 3b² + (3c + 4b)x + 4c
therefore
3b = 12
a = 3c + 4b
4c = -20
3b = 12 ⇒ b = 4
4c = -20 ⇒ c = -5
substitute to a:
a = 3 · (-5) + 4 · 4
a = -15 + 16
a = 1How tall is the tree?
5ft
35°
-20ft-
[? ]ft
Answers
Answer:
[tex]\boxed{\bf 19ft}[/tex]Step-by-step explanation:
[tex]\bf tan\:\theta =\cfrac{opp}{adj}[/tex]
[tex]\bf tan(35^o)=\cfrac{x}{20}[/tex]
[tex]\bf 20\;tan (35^o)=x[/tex]
[tex]\bf 14ft=x[/tex]
The height of the tree:-
[tex]\bf x+5ft[/tex][tex]\bf 14ft+5ft[/tex][tex]\bf 19ft[/tex]Answer:
19.00 ft to the nearest hundredth.
Step-by-step explanation:
tan 35 = h / 20
h = 20 tan 35
Now we add the man's height
Total height of the tree
= 20 tan 35 + 5
= 19.00 ft to the nearest hundredth.
please answer I've got 10 mins
100 POINTS FOR BRAINLIEST
Determine if the two expressions are equivalent and explain your reasoning.
3(4n) + 2 + 6n and 13n + 2
Answers
Answer:
3(4n) + 2 + 6n
12n + 2 + 6n
12n + 6n + 2
18n + 2 is not equal to 13n + 2
hence both the expression are not equivalent
Need help simple explanation if possible
Answers
Answer: 21 sqrt(43)/43
Step-by-step explanation: The tangent identity states that tanx = sinx/cosx. Thus, we get 21/22 / sqrt(43)/22. We can simplify this to 21 sqrt(43)/43
Please mark my answer as brainliest if this helped you.
What is the function written in vertex form? f(x) = 4(x 6)2 10 f(x) = 4(x 6)2 – 26 f(x) = 4(x 6)2 – 134 f(x) = 4(x 6)2 154
Answers
The required vertex form of the given equation is a) [tex]4(x-6)^2 +10[/tex] is correct
the function [tex]y=4x^2+24x+154[/tex] is given,
vertex form of a equation [tex]y=ax^2+bx+c[/tex] is given by [tex]y=a(x-h)^2+k[/tex].
since [tex]y=4x^2+24x+154[/tex]
Now h = - b/2a
h = -N
Now at x = 0
k = 10
vector form can be given by [tex]4(x+6)^2 +10[/tex]
The question is incomplete. The question could be:
what is the correct vertex form of equation [tex]y=4x^2+24x+154[/tex]?
a)[tex]4(x+6)^2 +10[/tex]
b)[tex]4(x-6)^2 -26[/tex]
c)[tex]4(x-6)^2 -134[/tex]
d)[tex]4(x-6)^2 +154[/tex]
Thus, the vector form of the given function is [tex]4(x+6)^2 +10[/tex]
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The distance on a map between a student’s house and her job is 6 cm. On the same map, the distance between her house and her school 8 cm. The actual distance from her house to school is 12 km. If d represents the approximate distance in km between her house and her job, what is d? A. 4 km B. 9 km C. 48 km D. 16 k
Answers
The approximate distance in km between her house and her job is 9 km.
What is the approximate distance?The map is a scale drawing of the places mentioned. A scale drawing is a smaller image of a larger place or diagram.
The scale of the map = 8cm : 12km
Distance between the house and the job = (12 x 6) / 8 = 9m
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The formula for the surface area of a
sphere that has a radius 7 is shown in
the box below.
SA = 4tr-2
A sphere and one of its dimensions are
shown in the diagram below.
5 in.
What is the surface area, in square
inches, of the sphere?
Answers
Step-by-step explanation:
hope you can understand
Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base perimeter. Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y.
The figures
and
have the same volume.
Answers
The figures Сone Z and Cylinder Y have the same volume.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Where:
h is the height.r is the radius.Similarly, the volume of a cylinder can be calculated by using this formula:
V = πr²h
In this context, we can infer and logically deduce that Сone Z and Cylinder Y have the same volume because they both have the same base area, while the cone's height is three (3) times the height of Cylinder Y.
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Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs.
x + y = 3,500
x – y = 2,342
Answers
Step-by-Step Explanation:
I am assuming that we just have to Solve for ‘x’ and ‘y’.
‘x’ = No. Of Contemporary Titles
‘y’ = No. Of Classic Titles
=> x + y = 3500 (Eq. 1)
=> x - y = 2342 (Eq. 2)
Adding Eq. 1 and Eq. 2, we get :-
2x = 3500 + 2342
2x = 5842
x = 5842/2
=> x = 2921
Therefore, x = 2921
Substitute value of ‘x’ in Eq. 1 :-
x + y = 3500
(2921) + y = 3500
y = 3500 - 2921
=> y = 579
Therefore, y = 579
Hence,
No. Of Contemporary Titles = 2921
No. Of Classic Titles = 579
Solve for x..........
[tex]5x - x - 8 = 15 + 3x[/tex]
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 23 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 5x - x - 8 = 15 + 3x[/tex]
[tex]\qquad \tt \rightarrow \: 4x - 8 = 15 + 3x[/tex]
[tex]\qquad \tt \rightarrow \: 4x - 3x = 15 + 8[/tex]
[tex]\qquad \tt \rightarrow \: x = 23[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
x = 23
Explanation:
⇒ 5x - x - 8 = 15 + 3x
collect like terms
⇒ 5x - x - 3x = 15 + 8
add or subtract like terms
⇒ x = 23
Checking:
5(23) - 23 - 8 = 15 + 3(23)
115 - 23 - 8 = 15 + 69
84 = 84
What type of association does the following scatterplot represent?
Answers
Answer:
Positive Linear Association
Step-by-step explanation:
A positive/negative association can be determined by seeing if the slope of the line of best fit is positive or negative. A positive slope indicates a positive relationship and a negative slope indicates a negative relationship.
If y increases as x increases => positive
If y decreases as x increases => negative
In the graph, the line of best fit clearly has a positive slope. I.e. as x increases, y also increases. Therefore, the association is positive.
Next determine if the relationship is linear or nonlinear. A linear relationship can be modeled strongly with a straight line. Anything else is nonlinear. In the graph, a straight line can be draw through the points with a strong correlation, therefore the association is linear.
Therefore, the best answer is Positive Linear Assosciation
In 1990, the average monthly bill for cellular telephone service was $80.90. From 1990-1997, the monthly bill decreased by 8.6% per year (in other words, each year the bill is 91.4% of
what is was the previous year (Source: Statistical Abstract of the United States).
Part a: Write a formula for the average monthly cellular telephone bill in terms of the year. Let n = 1 represent 1990.
Part b: What was the average monthly bill in 1993
Answers
A)The formula for the average monthly cellular telephone bill in terms of the year will be A = 80.90(0.914)ⁿ⁻¹
B)The average monthly bill in 1993 willl be $ 61.77
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.
The formula for the average monthly cellular telephone bill in terms of the year willl be,
A=P(R/100)ⁿ
A = 80.90(0.914)ⁿ⁻¹
The average monthly bill in 1993 is found as ;
n=4 for 1993
A=P(R/100)ⁿ
A = 80.90(0.914)³⁻¹
A=$ 61.77
Hence the formula for the average monthly cellular telephone bill in terms of the year will be A = 80.90(0.914)ⁿ⁻¹ and the average monthly bill in 1993 willl be $ 61.77.
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Jithu is curating Christmas hampers for his neighbours.
A minimum of 6 cupcakes are to be included in a hamper box.
If he wants to pack 665 cupcakes evenly into hamper boxes, what could be the smallest number of cupcakes that can be included in one hamper box?
Answers
1 hamper box, curated by Jithu can be contained 5 cupcakes.
Calculation:The total amount of cupcakes =665 nos.
Jithu wants to create a gift box, each of which contains 6 cupcakes.
We have to see first, whether 665 could be equally distributed or not.
Hence, 665/6= 110.84 unit
It is seen that the number is in a fraction.so, It can be said that 665 cakes cannot be equally distributed to each gift pack carrying 6 cakes.
Hence, 110*6=660 cupcakes.
∴665-660= 5 cupcakes in one box
So, it is concluded that Jithu could be prepared 110 gift boxes containing 6 cakes each & 1 box containing 5 cupcakes.
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Question 11 of 25
What is an equation of the line that is perpendicular to y + 1 = -3(x-5) and
passes through the point (4, -6)?
Ay-6--(x+4)
OB. y-6=3(x+4)
C. y+6=(x-4)
D. y+6=-3(x-4)
SUBMIT
Answers
Answer: y+6 = 1/3(x-4
The equation of line perpendicular to the given line and passes through the point P ( 4 , -6 ) is y + 6 = ( 1/3 ) ( x - 4 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y + 1 = -3 ( x - 5 )
So , the slope of the line is m = -3
Now , the lines are perpendicular , so the slope of the line m₂ is
m₂ = 1/3
Let the first point be P ( 4 , -6 )
And , the equation of line is y - y₁ = m ( x - x₁ )
On simplifying , we get
y - ( -6 ) = ( 1/3 ) ( x - 4 )
y + 6 = ( 1/3 ) ( x - 4 )
Hence , the equation of line is y + 6 = ( 1/3 ) ( x - 4 )
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solution.
5(4x + 7)-2x = ________+ 21
Answers
Answer:
18x + 14
Step-by-step explanation:
First, we need to distribute the 5:
5(4x + 7) - 2x = __ + 21
20x + 35 - 2x = __ + 21
Now, we can combine like terms:
20x + 35 - 2x = ___ + 21
18x + 35 = ___ + 21
> subtract 21 from both sides to isolate "___"
18x + 35 = __ + 21
-21 -21
18x + 14 = ___
now that we have a solution, we should check that it works:
5(4x + 7) - 2x = ____ + 21
5(4x + 7) - 2x = 18x + 14 + 21
{simplify both sides:}
20x + 35 -2x = 18x + 35
18x + 35 = 18x + 35
(TRUE)
So, we know our solution is 18x + 14
hope this helps!!
Does this graph show a function? Explain how you know.
Answers
Answer:
No, the graph fails the vertical line test
Step-by-step explanation:
To determine if the graph is a function, we can use the vertical line test.
Use a vertical line, if the vertical passes through two or more points, the graph is not a function
Looking at the y axis ( which is a vertical line), it passes through two points
This means the graph is not a function
No, the graph fails the vertical line test
