Answers
Given :[tex] 2log_{5} x^{2} =log_{5} 2^{2} [/tex]
To solve for x we use the logarithm rule for powers.
The log rule for powers states:
[tex] mlog_{a}n =log_{a} n^{m} [/tex]
We apply this rule to the left side of the equation.
[tex] log_{5} x^{2} =log_{5} 4
Both sides have log with same base so it can be eliminated.
Eliminating log from both sides we have:
[tex] x^{2} =4
To solve for x we take root of both sides
x=2,-2.
Related Questions
Valerie drives to and from work 5 days a week. The distance from her home to work is 6 miles. Over the course of 5 days, her car uses 14 of a tank of gas. Complete each sentence.
Answers
______________
The correct answer is
A round trip is 12 miles.
In a 5 day week she drives 60 miles (5 · 12)
Now we need to know how much gas she uses.
_________________
Hope this helps you
According to these three facts, which statements are true?
Circle M has center (1, 10) and radius 12.
Circle N is a translation of circle M, 1 unit left.
Circle N is a dilation of circle M with a scale factor of 3.
Select each correct answer. (can be more than one)
The radius of circle N is 12.
Circle N and circle M have equal diameters.
The center of circle N is (0, 10).
Circle M and circle N are similar.
Answers
Answer:
The center of circle N is (0, 10).
Circle M and circle N are similar.
Step-by-step explanation:
It is given circle N is translation of circle M 1 unit left .The radius of circle M is (1,10) when it is translated 1 units left the circle N will have the center (0,10).The y value will remain same while the x coordinated is reduced by 1 that is 1-1=0.The center of circle N is (0, 10)
As the circle N is a dilation of circle M by scale factor 3 so the radius of the two circle will not be same and hence the diameter will also be different.
In translation we have a similar figure ,So circle M and N will be similar.
1. What is the value of w? 7 3.5 7(sqrt)of 3 14
Answers
1. You have:
Cos(α)=Adjacent/Hypotenuse
α=30°
Adjacent=7√3
Hypotenuse=w
2. When you substitute this values into Cos(α)=Adjacent/Hypotenuse, you obtain:
Cos(α)=Adjacent/Hypotenuse
Cos(30°)=(7√3)/w
3. When you clear "w", you obtain:
wCos(30°)=7√3
w=(7√3)/Cos(30°)
4. Then, the result is:
w=14
The answer is the last option: 14
In "how to eat an ice cream cone" what does the author compare a melting ice cream cone to?
A runaway train
A machine gun
An atomic bomb
A hand grenade
Answers
I hope this helps:)
The author compare a melting ice cream cone to c. an atomic bomb.
In the essay ""How to Eat an Ice Cream Cone"" by Eugene Field, the author humorously compares the act of eating a melting ice cream cone to an atomic bomb.
The comparison is used to illustrate the chaotic and uncontrollable nature of trying to consume the ice cream before it melts, much like the destructive and rapid spread of an atomic bomb's explosion.
The author does not compare the melting ice cream cone to a runaway train, a machine gun, or a hand grenade, as these are not mentioned in the context of the essay.
The atomic bomb metaphor is used to emphasize the urgency and potential mess that can result from not eating the ice cream cone quickly enough, likening it to a catastrophic event that is difficult to contain once it starts."
if you reflect fgh across the y-axis, what will be the coordinates of the vertices of the image f'g'h'
Answers
The correct answer is b.
Hope this helps =)
Therefore option B is correct.
What is reflection of coordinates?When a point is reflected across the line y = x, the x-coordinates and y-coordinates change their place. Similarly, when a point is reflected across the line y = -x, the x-coordinates and y-coordinates change their place and are negated. Therefore, The reflection of the point (x, y) across the line y = x is (y, x).
We have,
Coordinate of the vertex of the ΔFGH is F( -2 , -1 ) , G( 2 , 2 ) and H( 4 , -3 )
According to the question,
We know that when a point ( x , y ) reflected over y-axis , the y-coordinate remains the same but the x-coordinate is transformed into its opposite .i.e., ( -x , y )
So, Image of the Vertex F( -2 , -1 ) = F'( -(-2) , -1 ) = F'( 2 , -1 )
Image of the Vertex G( 2 , 2 ) = G'( -2 , 2 )
Image of the Vertex H( 4 , -3 ) = H'( -4 , -3 )
Hence, the image of the vertexes is F'( 2 , -1 ) ,G'( -2 , 2 ) and H'( -4 , -3 )
To learn more about reflection of coordinates from here
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1000p for an answer please
Answers
A rectangular pool contains 920 cubic meters of water. the pool is .4 meter deep and 100 meters wide. How long is the pool?
Answers
To find the length of the pool, divide the volume (920 m³) by the product of the width (100 m) and depth (0.4 m), which gives a pool length of 23 meters.
Explanation:The question asks to find the length of the pool given the volume, width, and depth of the pool. The volume of a rectangular prism (which is the shape of the pool) can be found using the formula Volume = length × width × depth. We can rearrange this formula to solve for the length by dividing the volume by the product of the width and depth.
Therefore, the length of the pool is calculated as follows:
Volume = 920 cubic metersWidth = 100 metersDepth = 0.4 metersLength = Volume / (Width × Depth)Length = 920 m³ / (100 m × 0.4 m)Length = 920 m³ / 40 m²Length = 23 metersSo, the length of the pool is 23 meters.
Simplify the expression 6√2/√3
B. 6√3
C. 2√3
D. 2√6
Answers
I am going to say your answer is D. 2 squar6
What is the value of k?
Answers
Value of k = 10
Further explanationTriangles are flat fields bounded by 3 intersecting sides and 3 angles
This side can be the same length or different.
There are two angles that can form:
Supplementary Angles: if both angles are added = 180 ° Complementary Angles: if both angles are added = 90 °From picture: ∠Y = Supplementary Angles:
115 ° + ∠Y = 180 °
∠Y = 180 ° - 115 °
∠Y = 65 °
As we know, the sum of angles in a triangle = 180 °
So from the picture, the sum of ∠Y + ∠X + ∠Z = 180 °
65 ° + 6k + 10 ° + 4k + 5 ° = 180 ° (combine like terms)
65 ° + 10 ° + 5 ° + 6k + 4k = 180 °
80 ° + 10 k = 180 °
10 k = 180 ° -80 °
10 k = 100 °
k = 10
Learn more
the Sin rule
https://brainly.com/question/3324288
trigonometric ratios
https://brainly.com/question/10782297
the triangle angle
https://brainly.com/question/1611320
Answer:
The value of k is 10.
Step-by-step explanation:
Triangles are flat fields bounded by 3 intersecting sides and 3 angles
This side can be the same length or different.
There are two angles that can form:
Supplementary Angles: if both angles are added = 180 °
Complementary Angles: if both angles are added = 90 °
From picture: ∠Y = Supplementary Angles:
115 ° + ∠Y = 180 °
∠Y = 180 ° - 115 °
∠Y = 65 °
As we know, the sum of all interior angles of a triangle = 180 °
So from the picture, the sum of ∠Y + ∠X + ∠Z = 180 °
65 ° + 6k + 10 ° + 4k + 5 ° = 180 ° (combine like terms)
65 ° + 10 ° + 5 ° + 6k + 4k = 180 °
80 ° + 10 k = 180 °
10 k = 180 ° -80 °
10 k = 100 °
k = 10
For more information:
https://brainly.com/question/13672217?referrer=searchResults
(03.07)
Graph with a line going through points zero comma two point five and four comma two point five.
Select the equation of the line that passes through the point (3, -1) and is parallel to the line on the graph.
y = -1
y = 3
y = x -1
y = 3x - 1 @ankitshaw
Answers
The slope of a line is m=(y2-y1)/(x2-x1 )
For the given line, x1=0, y1=2.5, x2=4, y2=2.5
Substituting the values in the formula,
m=(2.5-2.5)/(4-0)
m=0/4
m=0
Another line passes through (3,-1).
The line passes through (3,-1) is parallel to the line that passes through
(0,2.5) and (4,2.5).
Therefore the slopes of these two lines are equal.
m=0 and the line passes through (3,-1)
The formula is y-y1=m(x-x1)
X1=3 and y1=-1 m=0
Substituting these values in the formula,
y+1= 0(x-3)
y+1=0
y=-1
find the interest due on $5,000 at 11% for 3 years.
a. 136.36
b. 165.00
c. 1,363.63
d. 1,650.00
Answers
I hope I helped!
solve this problem for N
N - (2 x 7) = 7
A.20
B.21
C.22
Answers
n-14=7
n+(14-14)=7+14
n=21
B. 21
which ordered pairs lie on the graph of the exponential function f(x)=-3^2x+5
select each correct answer
(3,724)
(-2,76)
(0,4)
(1,-4)
(-2,76)
Answers
It must be -3^(2x) + 5 In that case 0,4 works. That gives (-3)^0 = -1
-1 + 5 = 4
Unfortunately so does 1,-4 because -3^2 = - 9
- 9 + 5 = - 4
If (-2,76) is the answer, then the question should be written (-3)^(2x) - 5
Until the ambiguity is gone, we're not sure.
Answer:
1,-4
0,4
3,-724
Step-by-step explanation:
If the circumference of a circle is 10 pie inches, what is the area, in square inches, of the circle?
Answers
therefore 2r=10, r=5
Area, A=pi r ^2=78.54 square inches
Find the directional derivative of f(x, y, z) = xy2z3 at p(4, 1, 1) in the direction of q(0, −7, 9).
Answers
Answer:
Step-by-step explanation:
Since we have been given two points, P(4,1,1) and Q(0,-7,9), we can take the vector between the two toget the directional vector.
So, vector PQ = v = <-4, -8, 8>. Now, we find its UNIT VECTOR.
Since the UNIT VECTOR is just the vector divided by its magnitude, we get that the unit vector u = v / |v|
|v| = [tex]\sqrt{(-4)^2+(-8)^2+(8^2)}[/tex] = [tex]\sqrt{144}[/tex] = 12
Dividing each part of the original vector v by 12 gives us the unit vector.
Now, we take the partial derivatives, Fx, Fy, and Fz.
Fx = [tex]y^2z^3[/tex]
Fy = [tex]x(2y)z^3[/tex]
Fz = [tex]xy^2(3z^2)[/tex]
plugging in the original point P(4,1,1) gives us the following values for the gradient, which is just the vector of the partial derivatives.
ΔF = <1,8,12>
Now we just use the equation Duf = ΔF * u, where we take the DOT PRODUCT of the gradient at the given point with the direction unit vector.
This gives us <1,8,12> * <-1/3, -2/3, 2/3> = 7/3
The directional derivative of [tex]\( f \)[/tex] at point [tex]\( P(4, 1, 1) \)[/tex] in the direction of [tex]\( Q(0, -7, 9) \)[/tex] is [tex]\( \frac{7}{\sqrt{6}} \).[/tex]
To find the directional derivative of the function [tex]\(f(x, y, z) = xy^2z^3\)[/tex] at the point [tex]\(P(4, 1, 1)\)[/tex] in the direction of [tex]\(Q(0, -7, 9)\)[/tex], we'll use the formula for directional derivative:
[tex]\[ D_{\mathbf{u}} f(x, y, z) = \nabla f \cdot \mathbf{u} \][/tex]
where [tex]\( \nabla f \)[/tex] is the gradient vector of [tex]\( f \)[/tex] and [tex]\( \mathbf{u} \)[/tex] is the unit vector in the direction of [tex]\( Q \).[/tex]
First, let's find the gradient vector [tex]\( \nabla f \):[/tex]
[tex]\[ \nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z} \right) \][/tex]
[tex]\[ = \left( y^2z^3, 2xyz^3, 3xy^2z^2 \right) \][/tex]
Now, evaluate [tex]\( \nabla f \)[/tex] at the point [tex]\( P(4, 1, 1) \):[/tex]
[tex]\[ \nabla f(P) = \left( (1)^2(1)^3, 2(4)(1)(1)^3, 3(4)(1)^2(1)^2 \right) \][/tex]
[tex]\[ = (1, 8, 12) \][/tex]
Next, find the unit vector in the direction of [tex]\( Q \):[/tex]
[tex]\[ \mathbf{u} = \frac{\mathbf{Q} - \mathbf{P}}{\|\mathbf{Q} - \mathbf{P}\|} \][/tex]
[tex]\[ = \frac{(0 - 4, -7 - 1, 9 - 1)}{\sqrt{(0 - 4)^2 + (-7 - 1)^2 + (9 - 1)^2}} \][/tex]
[tex]\[ = \frac{(-4, -8, 8)}{\sqrt{16 + 64 + 64}} \][/tex]
[tex]\[ = \frac{(-4, -8, 8)}{4\sqrt{6}} \][/tex]
[tex]\[ = \left( -\frac{1}{\sqrt{6}}, -\frac{2}{\sqrt{6}}, \frac{2}{\sqrt{6}} \right) \][/tex]
Now, calculate the dot product [tex]\( \nabla f \cdot \mathbf{u} \):[/tex]
[tex]\[ D_{\mathbf{u}} f(P) = \nabla f(P) \cdot \mathbf{u} \][/tex]
[tex]\[ = (1, 8, 12) \cdot \left( -\frac{1}{\sqrt{6}}, -\frac{2}{\sqrt{6}}, \frac{2}{\sqrt{6}} \right) \][/tex]
[tex]\[ = -\frac{1}{\sqrt{6}} + \left(-\frac{16}{\sqrt{6}}\right) + \frac{24}{\sqrt{6}} \][/tex]
[tex]\[ = \frac{7}{\sqrt{6}} \][/tex]
Therefore, the directional derivative of [tex]\( f \)[/tex] at point [tex]\( P(4, 1, 1) \)[/tex] in the direction of [tex]\( Q(0, -7, 9) \)[/tex] is [tex]\( \frac{7}{\sqrt{6}} \).[/tex]
According to the national center for health statistics in 1990 28% of babies in the United States were born to parents who were not married. Throughout the 1990s this increased by approximately 0.6% per year. If this trend continues, in which year will 43% of babies be born out of wedlock?
Answers
If the trend continues, 43% of babies will be born out of wedlock in the year 2015.
Explanation:To find the year in which 43% of babies will be born out of wedlock, we can use the information given. In 1990, 28% of babies were born to unmarried parents. And throughout the 1990s, there was an increase of approximately 0.6% per year. So, we can set up an equation: 28 + 0.6x = 43, where x represents the number of years after 1990.
To solve for x, we can subtract 28 from both sides of the equation: 0.6x = 15. Then, divide both sides by 0.6 to isolate x: x = 15 ÷ 0.6. Using a calculator, we find that x is approximately 25. Therefore, if the trend continues, 43% of babies will be born out of wedlock in the year 1990 + 25 = 2015.
Final answer:
If the trend continues, 43% of babies will be born out of wedlock in the year 2015.
Explanation:
To find the year when 43% of babies will be born out of wedlock, we need to calculate how many years it will take for the percentage to reach 43% based on an initial value of 28% and an annual increase of approximately 0.6%.
Calculate the difference between the target percentage and the initial percentage: 43% - 28% = 15%Divide the difference by the annual increase rate to find the number of years: 15% ÷ 0.6% = 25 yearsAdd the number of years to the initial year (1990) to determine the year when 43% of babies will be born out of wedlock: 1990 + 25 = 2015Therefore, if the trend continues, 43 of babies will be born out of wedlock in 2015.
please help me thank you I will give you brainly
Answers
The point slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y-1- 1-12). What is the standard form of the equation for this line?
Answers
.. y -1 = (1/4)(x -12)
Multiply by 4 and subtract the left side to put into general form.
.. x -12 -4(y -1) = 0
.. x -4y -8 = 0
Add 8 to put into standard form
.. x -4y = 8
AB and AD are tangents of the circle with the center at C. The measure of BDC = 45o, and the circle has a diameter of 4. Which is the length of AB?
help needed!!
Answers
ABCD is a diamond.
Let's D' the intersection of the circle and DC.
m∠BCD'=2*m∠BDC=2*45=90°
m∠BCD=90°
The diagonals of ABCD are perpendicular==>ABCD is a diamond and AB=BC=CD=DA=2
a^9*8a^4 will mark as brainiest
Answers
Final result :
23a13
Step by step solution :
Step 1 :
Equation at the end of step 1 :
23a9 • a4
Step 2 :
Multiplying exponential expressions :
2.1 a9 multiplied by a4 = a(9 + 4) = a13
Final result :
23a13
A town plans to make a triangular park. The triangle has a base of 120 feet and a height of 115 feet. What will the area of the park be?
A)13,800 ft2
B)27,600 ft2
C)6,900 ft2
D)6,612.5 ft2
Answers
The answer would be 6,900 ft2. The equation to find the area is "a=1/2bx"
a= area b=base h=height. Hope this helps :D
Given that, a town plans to make a triangular park. The triangle has a base of 120 feet and a height of 115 feet.
We know that area of a triangle = [tex] \frac{1}{2} [/tex] x base x height
Given that base of triangle is 120 feet and height is 115 feet. From the given data, we calculate the area of the triangular park.
Area = [tex] \frac{1}{2}*120 *115 = 6900 [/tex]
Hence , Area of triangular park is 6900 square feet.
which of the following is the best definition of three-dimensional drawing? A. a three-dimensional drawing represents, on a three-dimensional plane, the length and width of a solid figure.B. a three-dimensional drawing uses graph paper to show the length and width of a solid figure in such a way that it looks realistic.C. a three-dimensional drawing represents on a two-dimensional plane the length, width, and depth of a three-dimensional figure.D. a three-dimensional drawing uses at least one vanishing point to create the illusion of width.
Answers
If a girl were going up a escalator how many steps would she have to take if it was not moving/10929120/99020363?utm_source=registration
Answers
72 steps!
It took me like an hour to figure it out but I got it!
Hope this helps!
@SamSamySamantha
HELP IF YOU'RE GOOD AT GEOMETRY AND I WILL MARK BRAINLIEST AND DO NOT ANSWER FOR FREE POINTS OR I WILL REPORT YOU
△ABC∼△DEF , △ABC has a height of 6 meters, and △DEF has a height of 10 meters.
What is the ratio of the area of △ABC to the area of △DEF ?
Enter your answer, in simplest form, in the boxes.
:
Answers
height of DEF = H = 10m
Since they are similar, their bases must be in the same proportion: base of ABC = b = 6/10B = 3/5B
Since a = 1/2 bh = 1/2 (3/5B)(6) = 9/5B
A = 1/2 BH = 1/2 (B)(10) = 5B
So ratio of a:A = 9/5B:5B = 9/5:25/5 = 9:25
Final answer:
The ratio of the areas of two similar triangles with heights of 6 and 10 meters is 9/25.
Explanation:
To find the ratio of the areas of two similar triangles, △ABC and △DEF, with heights 6 meters and 10 meters respectively, we use the knowledge that the areas of similar triangles are proportional to the squares of the corresponding linear dimensions, such as their heights. For these triangles, the ratio of their heights is 6/10 or 3/5. Thus, the ratio of their areas is (3/5)2 or 9/25.
What is the rate of change from x = π to x = 2π? (6 points) trig graph with points at 0, negative 4 and pi over 2, 0 and pi, 4 and 3 pi over 2, 0 and 2 pi, negative 4
PLEASE HELP!!!!!!
a. 8 over pi
b. pi over 8
c. negative 8 over pi
d. negative pi over 8
Answers
We are given points on trig graph as
[tex](0,-4)[/tex]
[tex](\frac{\pi}{2} ,0)[/tex]
[tex](\pi ,4)[/tex]
[tex](\frac{3\pi}{2} ,0)[/tex]
[tex](2\pi ,-4)[/tex]
now, we can find rate of change from x = π to x = 2π
so, we will select two points
[tex](\pi ,4)[/tex] and [tex](2\pi ,-4)[/tex]
we can also write as
[tex]a=\pi , f(a)=4[/tex]
[tex]b=2\pi , f(b)=-4[/tex]
now, we can use average rate of change formula
[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]
now, we can plug values
and we get
[tex]A=\frac{-4-4}{2\pi -\pi}[/tex]
[tex]A=\frac{-8}{\pi }[/tex]
so, option-C.............Answer
Grant is a member of a book club. He pays a $10 yearly membership fee and can purchase books through the club for $2.75 each. His total annual cost is a function of the number of books that he purchases in a year.
Let b represent the number of books he purchases in a year. Which function, C(b), represents his yearly cost?
C(b) = 10b + 2.75
C(b)= 2.75b + 10
C(b) = 12.75b
C(b) = 2.75b + 20
Answers
Each book = $2.75
Number of books = b
Total cost of the books = 2.75b
C(b) = 2.75b + 10 (Answer B)
Answer:
B)C(b)= 2.75b + 10
Step-by-step explanation:
If two angles of one triangle are congruent to two angles in another triangle, then what must be true of the third angles of the triangles?
Answers
Final answer:
If two angles of one triangle are congruent to two angles in another triangle, the third angles must also be congruent since the sum of angles in any triangle must equal 180 degrees. This principle is supported by geometric theorems about the properties of triangles and the requirements for their congruence and similarity.
Explanation:
If two angles of one triangle are congruent to two angles in another triangle, then the third angles in both triangles must also be congruent. This is because the sum of the angles in any triangle must equal 180 degrees or two right angles. Since two angles are congruent in both triangles, whatever is left from the 180 degrees after subtracting these two angles must be what is left for the third angle, making them congruent by necessity.
There are several related theorems in geometry that confirm this. Theorem 11, also known as the Side-Angle-Side (SAS) Postulate, states that if one side and the two adjacent angles of two triangles are congruent, then the triangles are congruent. While this theorem refers mainly to the congruency of triangles, it supports our understanding that if two angles are congruent, the third must be as well to satisfy the congruence of all three angles.
Furthermore, in the context of similar triangles, when two triangles have congruent angles, they are similar, meaning all their angles are congruent, and their sides are in proportion. However, if we only consider the angles, as in the original question, knowing that two angles are congruent across two triangles is enough to deduct that the third angles will be congruent, regardless of side lengths or overall similarity.
Juan must choose a number between 61 and 107 that is a multiple of 3, 5, and 9. Write all the numbers that he could choose. If there is more than one number, separate them with commas.
Answers
62,63,64,65,66,67,68,69,70,....100,101,102,103,104,105,106
multiple of 5 are
65,70,75,80,85,90,95,100,105
multiples of 3 and 5
75,90,105
multiples of 3,5,9
90
30 Points! Please Help!
At the end of May, Janet told Sam that she has read 10 books this year and reads 2 books each month. Sam wants to catch up to Janet. He tracks his book reading with a table on his door. Using his table below, what month will Sam have read the same amount of books as Janet?
Month Books
June 3
July 6
August 9
Answers
the answer to this question is march
Paige’s back yard has an area of 95.9 square meters of the length of the yard is 14 meters what is the width