Answer:
[tex]\large\boxed{C.\ \log_55+-5\log_5x}[/tex]
Step-by-step explanation:
[tex]\log_ab^c=c\log_ab\\\\\log_a(bc)=\log_ab+\log_ac\\=====================\\\\\log_55x^{-5}=\log_55+\log_5x^{-5}=\log_55+-5\log_5x[/tex]
The value of logarithm log5 [tex]5x^{-5[/tex] is [tex]-5 (log_5 (5) + log_5 (x) )[/tex].
Thus, option (c) is correct.
To expand the logarithm log5 [tex]5x^{-5[/tex], use the logarithmic property.
According to power rule,
logarithm of a number raised to a power can be expressed as the product of the exponent and the logarithm of the number.
Using the power rule, we can rewrite the expression as:
[tex]{\text} log_5 5x^{-5} =[/tex][tex]\;{\text} -5 log_5 (5x)[/tex]
and, [tex]log _c (ab) = log_c (a) + log_c(b)[/tex]
So, [tex]\;{\text} -5 log_5 (5x)[/tex] = [tex]-5 (log_5 (5) + log_5 (x) )[/tex]
Thus, the simplified value is [tex]\;{\text} -5 log_5 (5x)[/tex] = [tex]-5 (log_5 (5) + log_5 (x) )[/tex].
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How to solve this!! Please!
Answer:
k^2 -3k +9/2
(k-3/2)^2
Step-by-step explanation:
k^2 -3k
Take b/2 and then square it to find the term to complete the square
(-3/2) ^2 = 9/4
k^2 -3k +9/2
The expression factors to (k-b/2)^2
(k-3/2)^2
A parabola opening down the vertex is (3,0) and passes through (12,-12) what is that written in vertex form?
Answer:
[tex]\large\boxed{y=-\dfrac{4}{27}(x-3)^2}[/tex]
Step-by-step explanation:
The vertex form of na equation of a parabola:
[tex]y=a(x-h)^2+k[/tex]
We have the vertex (3, 0). Substitute:
[tex]y=a(x-3)^2+0=a(x-3)^2[/tex]
A parabola passes through (12, -12). Put the coordinates of the point to the equation and solve for a:
[tex]-12=a(12-3)^2[/tex]
[tex]-12=a(9)^2[/tex]
[tex]-12=81a[/tex] divide both sides by 81
[tex]-\dfrac{12}{81}=a\\\\a=-\dfrac{4}{27}[/tex]
Finally:
[tex]y=-\dfrac{4}{27}(x-3)^2[/tex]
What is the perimeter of the figure shown?
A)22ft
B)84ft
C)30ft
D)36ft
Answer:
D
Step-by-step explanation:
The perimeter of the figure is the total distance around the figure.
Add each side to find the total distance.
10 + 8 + 8 + 2+2 + 6 = 36
Triangle A'B'C' is a dilation of
triangle ABC. what is the scale
factor?
enter your answer in the box
what is the exact volume of the cylinder?
Answer:
54π in³
Step-by-step explanation:
The volume (V) of a cylinder is calculated using the formula
V = πr²h ( r is the radius and h the height )
here r = 3 and h = 6, thus
V = π × 3² × 6 = π × 9 × 6 = 54π in³ ← exact value
Rewrite the function by completing the square (vertex form)
f(x)=x^2+16x-46
Answer:
[tex]\large\boxed{f(x)=(x+8)^2-110}[/tex]
Step-by-step explanation:
[tex]\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\\text{We have the equation:}\\f(x)=x^2+16x-46=x^2+2(x)(8)-46=x^2+2(x)(8)+8^2-8^2-46\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\to x^2+2(x)(8)+8^2=(x+8)^2\\\\f(x)=(x+8)^2-64-46=(x+8)^2-110[/tex]
The function f(x)=x^2+16x-46 can be rewritten by completing the square to achieve the vertex form of the function: f(x)= (x+8)^2 - 110. After rewriting, we can determine the vertex of this parabola is located at (-8,-110).
Explanation:The problem asks you to rewrite the function f(x)=x^2+16x-46 by completing the square. This involves manipulating the quadratic formula to write it in the form f(x)=a(x-h)^2+k where (h,k) is the vertex of the parabola.
So, let's start by rearranging the original function:
f(x)=x^2+16x-46
The coefficient of x is 16; halving this, we get 8. Then we add and subtract (which means adding 0, so we don't change the equation) this within the square to complete the square:
f(x)= (x^2+16x+64) - 64 - 46
Then, the equation can be written as:
f(x)= (x+8)^2 - 110
This is the vertex form of the function. We can see that the vertex of the parabola is at (-8,-110).
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Russel's weight is 3/4th of Brooke's weight. Find the ratio of Russel's weight to Brooke's weight?
the ratio would be 3/4 : 1
Final answer:
The ratio of Russel's weight to Brooke's weight, given that Russel's weight is 3/4 of Brooke's, is 3:4.
Explanation:
The student is asking how to find the ratio of Russel's weight to Brooke's weight given that Russel's weight is 3/4 of Brooke's weight. To find this ratio, it's straightforward since the value 3/4 already represents the ratio of Russel's weight to Brooke's weight.
Therefore, the ratio of Russel's weight to Brooke's weight is 3:4. This simply means that for every 3 parts of weight that Russel has, Brooke has 4 parts of weight. Ratios are usually expressed in simplest form, and since 3/4 is already in its simplest form, we use it as it is.
Jenny is holding a fraction tile labeled 1/3. How many 1/3- fraction tiles are needed to equal the fraction tile labeled 1
Answer:
3
Step-by-step explanation:
Let
x -----> the number of 1/3 fraction tiles
we know that
The linear equation that represent this problem is equal to
[tex]\frac{1}{3}x=1[/tex]
Solve for x
Multiply by 3 both sides to remove the fraction
[tex]\frac{1}{3}x(3)=1(3)[/tex]
[tex]x=3[/tex]
Verify
[tex]\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=1[/tex] -----> is correct
Three times 1/3 is equal 1
Can someone please have a heart to help me this is for a grade
Hey there!
Let's start by solving for x.
Take the first equation, y = -3x - 7, and substitute in the second equation, y = x + 9, for y.
We now have:
x + 9 = -3x - 7
Add 3x to both sides.
4x + 9 = -7
Subtract 9 from both sides.
4x = -16
Divide each side by 4.
x = -4
Let's use the second equation, y = x + 9, to solve for x.
Put in the value we just solved for.
We now have:
y = -4 + 9
Simplify.
y = 5
Let's check our answer, starting with the first equation, y = -3x - 7.
Put in the values for x and y.
5 = -3(-4) - 7
5 = 12 - 7
5 = 5
Do the same with the second equation, y = x + 9.
5 = -4 + 9
5 = 5
The solution to the system of equations is (5, -4).
Hope this helps!
Answer:
(-4, 5)
Step-by-step explanation:
Since y = -3x - 7 in the first equation, substitute y of the second equation with -3x - 7:
-3x - 7 = x + 9
Subtract x from both sides. Add 7 to both sides.
-4x = 16
Divide both sides by -4.
x = -4
Now, substitute -4 for x in the second equation.
y = -4 + 9
y = 5
The solution is:
x = -4; y = 5
As an ordered pair, the solution is:
(-4, 5)
Television sizes are determined by the length of their diagonal measure. Michael just bought a new television. The height of the television is 40 inches and the length is 71.5 inches. Using the Pythagorean Theorem, what is the size of Michael’s new television? Round your answer to the nearest whole inch (whole number).
Part A: What parts of the right triangle have you been given? Are you looking for a leg or the hypotenuse? The legs have already been given. I’m looking for the hypotenuse.
Part B: Set-up your equation by substituting the correct numbers in to the formula.
71.5^2+40^2=c^2
Part C: Solve for the missing length. Remember to show ALL work for each step.
Part D: What is the size of the television rounded to the nearest whole inch (whole number)?
PART A AND B ARE DONE ALREADY
I WILL GIVE BRAINLIEST TO THE CORRECT ANSWER.
Answer:
Part A) The legs have already been given. I’m looking for the hypotenuse
Part B) [tex]c^{2}=40^{2} +71.5^{2}[/tex]
Part C) The missing length is [tex]81.93\ in[/tex]
Part D) [tex]82\ in[/tex]
Step-by-step explanation:
Part A) What parts of the right triangle have you been given? Are you looking for a leg or the hypotenuse?
we know that
Applying the Pythagoras Theorem
[tex]c^{2}=a^{2} +b^{2}[/tex]
where
c ----> is the hypotenuse of the right triangle
a and b -------> are the legs of the right triangle
In this problem we have
[tex]a=40\ in[/tex]
[tex]b=71.5\ in[/tex]
so
The legs have already been given. I’m looking for the hypotenuse
Part B) Set-up your equation by substituting the correct numbers in to the formula
we have
[tex]a=40\ in[/tex]
[tex]b=71.5\ in[/tex]
substitute in the Pythagoras Theorem and solve for c (hypotenuse)
[tex]c^{2}=40^{2} +71.5^{2}[/tex]
Part C) Solve for the missing length
we have
[tex]c^{2}=40^{2} +71.5^{2}[/tex]
solve for c
[tex]c^{2}=1,600 +5,112.25[/tex]
[tex]c^{2}=6,712.25[/tex]
[tex]c=\sqrt{6,712.25}\ in[/tex]
[tex]c=81.93\ in[/tex]
Part D) What is the size of the television rounded to the nearest whole inch (whole number)?
[tex]81.93=82\ in[/tex]
The Pythagorean Theorem is used to find the size of the TV, which is the hypotenuse in this scenario and equals to approximately 82 inches when rounded to the nearest whole inch.
Explanation:Since we've set up our equation as 71.5^2+40^2=c^2, we can now simply solve for c, which is our hypotenuse, and in this case, represents the size of the television.
To do so, calculate the square of both given sides and add them: (71.5)^2 + (40)^2 = 5112.25 + 1600 = 6712.25.
The next step is to take the square root of that sum to get the length of the hypotenuse/c: sqrt(6712.25) = ~81.94 inches
Part D: Now, to answer the final part of your question, if we round this result to the nearest whole inch, we get 82 inches as the size of the new television.
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3. What’s the answer to this question please
C
the answer should be C because the 45.75 represents the price of the fruit trees and if x was 88 that means there are 88 fruit trees
pls mark brainliest!!
Answer:
The correct option is C.
Step-by-step explanation:
Solve the system of equations and choose the correct answer from the list of options
2x + y = -4
X=-2-1/2y should be the answer
Can anyone please explain and solve this Simplify 4^2 • 4^8?
4²+4⁸=(2²)²+(2²)8
=2⁴+2⁸
=16+256
=272
it's from the properties of indices
What is the length of segment CD question mark
CD = two square root of 10 end square root
CD = 6
CD = 8
CD = 40
Answer:
CD = two square root of 10 end square root
Step-by-step explanation:
To find the length of a segment, use the distance formula. Substitute the order pairs for the endpoints of the segment. CD has the end points (-7, -4) and (-1, -2).
[tex]d = \sqrt{(y_2-y_1)^2 + (x_2-x_1)^2} \\\\d = \sqrt{(-4--2)^2 + (-7--1)^2} \\\\d = \sqrt{-2^2 + -6^2}\\\\d = \sqrt{4 + 36}\\\\d=\sqrt {40} = 2\sqrt{10}[/tex]
Which box-and-whisker plot represents the data set?
12, 10, 16, 19, 18, 14, 4, 18, 4
Answer:
Its would be number 2
Step-by-step explanation:
Population size: 9
Median: 14
Minimum: 4
Maximum: 19
First Quartile: 7
Third Quartile: 18
Interquatile Range: 11
Answer: Number 2
Step-by-step explanation:
just did the test its the second one in your image.
What percentage is 4 out of 18
4/18=.2222x100=22.22%
What is the solution to the system of equations graphed below?
V= X + 2
= -2x =
-2v -4 = -2x
just move the +2 to the other side then multiply by a common multiple.
Solutions to systems of equations are typically found at the point where the lines intersect on a graph. For linear equations, this is represented by the equation y = mx + b. Quadratic equations also have solutions known as roots, and ones based on physical data typically have real, positive roots.
Explanation:
Due to the incomplete equation and graph not provided, we can first discuss general methods for finding solutions to systems of equations. One common method is the intersection of two lines on a graph, which illustrates the system of equations. Here, the zeros on the two-dimensional (x-y) graph represent the solution to the equations:
In this scenario, the y-axis represents the variable V, and the x-axis represents the variable X. The primary task is to find the point where these two lines intersect on the graph - this is the solution to the system of equations. The equation of a line is typically a linear equation, represented as y = mx + b, where m is the slope and b is the intercept.
If the equations are quadratic, these also have solutions, known as roots. Quadratic equations constructed on physical data always have real roots, but often only those having positive values are of any significance.
Without the specifics of your graph, an exact solution cannot be provided.
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At Manny's taco shop, you can get an order of chips and two tacos for $9.25. The cost for two orders of chips and five tacos is $21.75. What is the cost of an order of chips?
Define your variables:
Write your system of Equations:
Solve The System:
Answer The Question Being Asked:
Topic: Applying Systems of Equations
Define your variables:
At Manny's taco shop, you can get an order of chips and two tacos for $9.25. The cost for two orders of chips and five tacos is $21.75.
x = Chipsy = TacosWrite your system of Equations:You can get an order of chips and two tacos for $9.25.
1 Chips + 2 Tacos = 9.25
x + 2y = 9.25The cost for two orders of chips and five tacos is $21.75.
2 Chips + 5 Tacos = 21.75
2x + 5y = 21.75Solve The System:First equate the coefficient - in this case x:
(x + 2y = 9.25) * 2 = 2x + 4y = 18.50
2x + 4y = 18.50
2x + 5y = 21.75
Minus the equations from each other to remove the coefficient you equated:
(2x + 5y) - (2x + 4y) = 21.75 - 18.50
(2x - 2x) + (5y - 4y) = 21.75 - 18.50
y = 3.25Answer The Question Being Asked:What is the cost of an order of chips?1 Taco = $3.25
y = 3.25
Substitute this into the equation.
x + 2y = 9.25
x + (2 * 3.25) = 9.25
x + 6.50 = 9.25
Rearrange to find x:
x = 9.25 - 6.50
x = 2.75
Chips = $2.75
$2.75Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2x and y = 4x−2 intersect are the solutions of the equation 2x = 4x−2. (4 points)
Part B: Make tables to find the solution to 2x = 4x−2. Take the integer values of x between −4 and 4. (4 points)
Part C: How can you solve the equation 2x = 4x−2 graphically? (2 points)
Answer:
See below.
Step-by-step explanation:
Part A: You can solve the equations for an x value which make both true. You do this by setting each equation equal and using inverse operations.
2x = 4x - 2
2x - 4x = 4x - 4x - 2
-2x = -2
x = 1
Part B: You can make a table by substituting the values -4 to 4 in each equation and simplifying.
x y = 2x y = 4x - 2
-4 -8 -18
-3 -6 -14
-2 -4 -10
-1 -2 -6
0 0 -2
1 2 2
2 4 6
3 6 10
4 8 14
Part C: You can graph each equation and where they intersect will be the solution. They intersect at (1, 2). This is where they have the exact same x and y value in the table as well.
Answer:
When X= 1 both graphs are in (1,2)
Step-by-step explanation:
In order to evaluate the first part, where the lines intersect is you just have to equalize in opposite sides of the equation both equations:
2x=4x-2
Then you have to clear the x
2x-4x=-2
-2x=-2
x=[tex]\frac{-2}{-2}[/tex]
x=1
So your coordinates are x=1, and the Y coordinate you just evaluate one of the equations:
y=4x-2
y=4(1)-2
y=4-2
y=2
So your coordinate for y=2.
Part B, table.
To evaluate this, you just make a table, giving values to x, and you evaluate the Y:
X----Y
-4 -8
-3 -6
-2 -4
-1 -2
0 0
1 1
2 4
3 6
4 8
Part C.
YOu just hava to put it into the graph by evaluating with the tables above.
EASYY 90 POINTSS, I WILL GIVE BRAINLEASSTTTT..1
3. The triangle will be dilated by a scale factor of 2.5.
(a) What is the length of each of the sides after the dilation?
(b) Draw the new image and label it .
Answer:
Part a) The length of each of the sides after the dilation is
[tex]A'B'=30\ units[/tex]
[tex]B'C'=25\ units[/tex]
[tex]A'C'=35\ units[/tex]
Part b) The graph in the attached figure
Step-by-step explanation:
Part a) What is the length of each of the sides after the dilation?
In this problem we have that the scale factor is 2.5
The scale factor is greater than 1
so
The dilation is an enlargement
To find the length of each of the sides after the dilation, multiply the original length by the scale factor
so
[tex]A'B'=AB*2.5=12*2.5=30\ units[/tex]
[tex]B'C'=BC*2.5=10*2.5=25\ units[/tex]
[tex]A'C'=AC*2.5=14*2.5=35\ units[/tex]
Part b) Draw the new image and label it
using a graphing tool
see the attached figure
Answer:
Do you still need help with this? If so just say if you do in the comments and I can probably help.
Step-by-step explanation:
which expression is equivalent to the expression (7×2)^7
Answer:
9^7
Step-by-step explanation:
7*2=9
Click on the value for p that makes this inequality true.
Answer:0 is the answer
Step-by-step explanation:
The answer would be 0 since 0 is greater than -12.
Plz help me it’s due tomorrow
Answer:
7
Step-by-step explanation:
Again just cross multiplication.
84 = 12m
Divide each side by 12.
m = 7.
(2a/a+3b) + 10 = b
Rearrange and make “a” as subject
Answer:
a = -2b - 10
Step-by-step explanation:
a + 3b + 10 = b
a + 10 = -2b
a = -2b - 10
which sentence can reperesent the inequality 3.5x>7?
A) The sum of 3.5 and a number is greater than 7
B) The sum of 3.5 and a number is greater than or equal to 7
C) The product of 3.5 and a number is greater than 7
D) The product of 3.5 and a number is greater than or equal to 7
Answer:
Option C
Step-by-step explanation:
Given in an inequality in variable x as
[tex]3.5x>7[/tex]
In Algebra 3.5x represents the product of 3.5 with x
So the given inequality is equivalent to
the product of 3.5 and a number x is greater than 7.
Hence option C is right
C) The product of 3.5 and a number is greater than 7
Answer:
The product of 3.5 and a number is greater than or equal to 7.
Step-by-step explanation:
Besides 9 and 1, what is one factor of 9?
Answer:
3
Step-by-step explanation:
Besides 9 and 1, 3 is one factor of 9
Factor of 9:
1 • 9
3 • 3
Answer: 3
I have a question. I'm doing a project and want to see how many people would like dogs or cats please comment your answer and if you give me a reason i will give you 5 stars its for 15 points!
Answer:
I like dogs because its much fun to play with them, instead of a cat and you can go on a walk with them.
Step-by-step explanation:
FOR 37 POINTS AND BRAINIEST IF U GET THIS RIGHT
What are the square roots of 36/100 ?
A - 6/10 and 6/10
B- ⅗ and ⅗
C- 9/25 and 9/25
D-18/50 and 18/50
Answer:
A
Step-by-step explanation:
6 x 6 = 36
10 x 10 = 100
Answer:
A
Step-by-step explanation:
6x6=36
10x10=100
I need
PART A:
PART B:
PART C:
PART D:
Answer:
See below.
Step-by-step explanation:
Solve the equation using each of the properties listed.
3n - 5 = -8(6 + 5n)
3n - 5 = -48 - 40n Distributive Property
3n + 40n - 5 = -48
43n - 5 = -48 Addition Property of Equality
43n = -48 + 5
43n = -43 Addition Property of Equality
n = -43/43
n = -1 Division property of Equality
Answer:
Guess that was the answwr
Step-by-step explanation:
least to greatest 1 8/35, 1.3, 5/4
Answer:1/3 < 1 8/35 < 5/4
Step-by-step explanation:
Showing Work
Rewriting as fractions if necessary:
43/35, 1/3, 5/4
The least common denominator (LCD) is: 420.
Rewriting as equivalent fractions with the LCD:
516/420, 140/420, 525/420
Ordering these fractions by the numerator in order from least to greatest:
140/420 < 516/420 < 525/420
Therefore, your input in order from least to greatest is:
1/3 < 1 8/35 < 5/4