Answer:
[tex]log_{7} \frac{7}{x^{2} }[/tex]
Step-by-step explanation:
We need to write [tex]1 - 2log_{7}x[/tex] as a single logarithm.
We know that
[tex]log_{7}7 = 1[/tex]
Therefore we have:
[tex]log_{7}7 - 2log_{7}x[/tex]
→ [tex]log_{7}7 - log_{7}x^{2}[/tex]
→ [tex]log_{7} \frac{7}{x^{2} }[/tex]
The solution is: [tex]log_{7} \frac{7}{x^{2} }[/tex]
what is the sum of the polynomials (-x^2+9)+(3x^2-11x+4)
The answer is:
[tex](-x^{2}+9)+(3x^2-11x+4)=2x^{2}-11x+13[/tex]
Why?To solve the problem, we must remember how to add/subtract like terms. The like terms are the terms that share the same variable and the same exponent.
For example:
[tex]2x+3x+x^{2}=x^{2}+(2x+3x)=x^{2}+5x[/tex]
We were able to add only the linear terms (terms that contains the variable x") because they were like terms: they share the same variable and the same exponent.
We need to perform the following operation between polynomials:
[tex](-x^{2}+9)+(3x^2-11x+4)[/tex]
So, calculating we have:
[tex](-x^{2}+9)+(3x^2-11x+4)=2x^{2}-11x+13[/tex]
Have a nice day!
CraftWork rents a storage space that measures 200 ft x 300 ft x 30 ft.
CraftWork pays $1500 for the storage space each month. What is the cost
per cubic foot?
O
A. $0.008
O B. $0.0002
O C. $0.0015
O D. 50.00083
Answer:
0.00083
Step-by-step explanation:
200*300*30=1800000
1500/1800000=0.00083
The cost per cubic foot of the storage space is approximately $0.00083 per cubic foot. Hence the correct option is D.
To find the cost per cubic foot of the storage space, we need to calculate the total cubic footage of the space and then divide the monthly cost by that number. The storage space measures 200 ft x 300 ft x 30 ft, so the total volume is:
Total Volume = length times width times height
= 200 ft x 300 ft x 30 ft
= 1,800,000 cubic feet
Now, we calculate the cost per cubic foot:
Cost Per Cubic Foot = Total Monthly Cost / Total Volume
= $1500 / 1,800,000 cubic feet
= $0.00083 per cubic foot (rounded to five decimal places).
A boy is flying a kite. The length of the string is 61 meters and the
horizontal distance between the boy and the kite is 60 meters. Assuming
there is no slack in the string, find the height of the kite from the ground.
Answer:
11 meters
Step-by-step explanation:
Using the Pythagorean Theorem
a^2 + b^2 = c^2
a^2 + 60^2 = 61^2
a^2 + 3600 = 3721 (subtract 3600 from both sides)
a^2 = 121 (square root both sides so a^2 becomes a)
a = 11
Answer:
11 meters.Step-by-step explanation:
This problem models a right rectangle, where the hypothenuse is the length of the string, and the legs are the height and the horizontal distance. So, to find the answer, we just have to use the pythagorean theorem
[tex]a^{2}=b^{2}+c^{2}[/tex]
Where
[tex]a=61;b=60;c=x[/tex]
Replacing and solving for [tex]x[/tex], which is the height
[tex]a^{2}=b^{2}+c^{2}\\61^{2}=60^{2}+x^{2} \\x^{2}=61^{2}-60^{2}\\x=\sqrt{3721-3600}=\sqrt{121}=11[/tex]
Therefore, assuming there is no slack in the string, the height of the kite from the ground is 11 meters.
i need help please can someone help
Answer:
x = 8Step-by-step explanation:
[tex]\sqrt{\dfrac{896z^{15}}{225z^6}}=\dfrac{xz^4}{15}\sqrt{14z}\\\\\sqrt{\dfrac{896z^{15}}{225z^6}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=\sqrt{\dfrac{(64)(14)z^{15-6}}{225}}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b},\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\=\dfrac{\sqrt{64}\cdot\sqrt{14}\cdot\sqrt{z^9}}{\sqrt{225}}=\dfrac{8\cdot\sqrt{14}\cdot\sqrt{z^{8+1}}}{15}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{z^8z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]
[tex]=\dfrac{8\sqrt{14}\cdot\sqrt{z^8}\cdot\sqrt{z}}{15}=\dfrac{8\sqrt{14}\cdot\sqrt{z^{4\cdot2}}\cdot\sqrt{z}}{15}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{(z^4)^2}\cdot\sqrt{z}}{15}\qquad\text{use}\ (\sqrt{a})^2=a\\\\=\dfrac{8\sqrt{14}\cdot z^4\cdot\sqrt{z}}{15}=\dfrac{8z^4\sqrt{14}\cdot\sqrt{z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{8z^4\sqrt{14z}}{15}[/tex]
[tex]\dfrac{8z^4\sqrt{14z}}{15}=\dfrac{xz^4\sqrt{14z}}{15}\iff x=8[/tex]
Andy was playing a memory game with his sister. He turned over a tile to reveal a picture of the sun at the coordinates (5, 4). He looked under a tile that was 3 units to the left and 2 units down but revealed a picture of a tree. His sister knew that the other sun was 1 unit to the left and 1 unit up from the tree. What are the coordinates of the second sun? (JUSTIFY)
Answer:
(1, 3).
Step-by-step explanation:
The tree tiles coordinates are x = 5-3 = 2 and the y coordinate = 4 - 2 = 2
- that is (2, 2).
So the coordinates of the second sun are (2-1, 2 + 1)
= (1. 3).
Find the value of y for the following system of equations. -x - y = 7 x - y = 9
Answer:
y = -8
Step-by-step explanation:
It is given that,
-x - y = 7 ---(1)
x - y = 9 ---(2)
To find the solution
Add eq (1) and eq(2) we get
-x - y = 7 ---(1)
x - y = 9 ---(2)
0 - 2y = 16
y = 16/(-2) = -8
Substitute the value of y in eq(1)
-x - y = 7 ---(1)
-x - -8 = 7
-x + 8 = 7
x = 8 - 7 = 1
Therefore x = 1 and y = -8
A number cube has 6 faces, numbered from 1 to 6. If the cube
is rolled six times, what is the probability that a face with a 6
comes up exactly once?
[tex]|\Omega|=6^6\\|A|=6\cdot 5^5\\\\P(A)=\dfrac{6\cdot5^5}{6^6}=\dfrac{5^5}{6^5}=\dfrac{3125}{7776}\approx40.2\%[/tex]
The probability that a face with a 6 comes up exactly once will be 0.40.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
A number cube has 6 faces, numbered from 1 to 6.
If the cube is rolled six times.
Then the probability that a face with a 6 comes up exactly once will be
The total number of the event will be
Total event = 6⁶
Total event = 46656
Favorable event = 6 x 5⁵
Favorable event = 18750
Then the probability will be
P = 18750 / 46656
P = 3125 / 7776
P = 0.40
More about the probability link is given below.
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what are natural number less than 5
Answer:
Natural numbers = {1,2,3,4,5…} Answer 1: A is the set of Natural numbers between 1 and 5 inclusive. Answer 2: A is the set of Natural numbers less than 6.
Step-by-step explanation:
Answer:
n = 1, 2, 3, 4
Step-by-step explanation:
Natural numbers are any integers (whole numbers) that are positive.
In this case, all natural number (n) is less than (<) 5
n < 5 is your equality, but in reality it looks like: 0 < n < 5
The numbers that can fit into your problem is n = 1 , 2, 3, 4
n = 1, 2, 3, 4 is your answer.
~
A_____ is invested by Managers in a diversity of stocks bonds and other securities
Answer:
Step-by-step explanation:
A Mutual Fund is invested by Managers in a diversity of stocks bonds and other securities.
A mutual fund is a type of investment in which investors pool their money together to buy a portfolio of stocks, bonds or other securities in order to take advantage of diversification and professional portfolio management at a reasonable cost. It is operated by money managers, who invest the fund capital on the investors behalf. Investing in mutual funds enables those investing a modest amount of money to benefit from the same advantages enjoyed by large institutional investors....
7. Select True or False for each statement.
A. The ordered pair (2, -5.2) is located in Quadrant IV.
B. Quadrant Il contains ordered pairs of the form
(positive number, negative number)
C. The point (-6, 0) is located on the y-axis
D. The origin is located in Quadrant |
E. To plot points in Quadrant III, move left and down
From the origin.
The answer addresses the true or false nature of five statements about the properties of coordinate pairs in a two-dimensional graph with respect to their quadrants, and the location of specific points on the coordinate plane.
The coordinates (x, y) indicate the position of a point on a two-dimensional graph in relation to the origin, which is at (0, 0). In a standard coordinate system, Quadrant I has both x and y as positive, Quadrant II has x as negative and y as positive, Quadrant III has both x and y as negative, and Quadrant IV has x as positive and y as negative.
A. False - The ordered pair (2, -5.2) is located in Quadrant IV, which is incorrect since Quadrant IV should have x as positive and y as negative, which is actually the case here, so the statement should be True.B. False - Quadrant II contains ordered pairs of the form (negative number, positive number), not positive x and negative y.C. True - The point (-6, 0) located on the x-axis, not the y-axis, since the y-coordinate is zero.D. False - The origin (0, 0) is not located in any quadrant as it is the point of intersection of all the quadrants.E. True - To plot points in Quadrant III, one indeed moves left (negative x direction) and down (negative y direction) from the origin.A triangle has two sides of lengths 7 and 9. What value could the length of the third side be?
Answer:
The length of the third side could be all real numbers greater than 2 units and less than 16 units
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
so
Applying the triangle inequality theorem
Let
x ------> the length of the third side
we have
First case
1) 7+9 > x
16 > x
Rewrite
x< 16 units
Second case
2) 7+x > 9
x > 9-7
x > 2 units
therefore
The solution for the third side is the interval
(2,16)
All real numbers greater than 2 units and less than 16 units
which of the following is the quotient of the rational expressions shown below 2x/4x+3 divided x-1/2x
Answer:
4x^2/4x^2-x-3
Step-by-step explanation:
boomchakalaka
The quotient is 4x²/4x²-x-3.
What's known as a quotient?
In mathematics, a quotient is a quantity produced with the aid of the department of numbers.
How do you discover a quotient?The quotient is the solution acquired whilst we divide one range by using every other. for example, if we divide the quantity 4 by means of 2, we get the end result as 2, that's the quotient.
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Which of the following is equivalent to the expression below?
√(-300)
A. -10i √(3)
B. -3i √(10)
C. 3i √(10)
D. 10i √(3)
Answer:
D. 10i √(3)
Step-by-step explanation:
√(-300)
We know sqrt (ab) = sqrt(a) sqrt(b)
sqrt(-300) = sqrt(-3) sqrt(100)
= sqrt(-1) sqrt(3) sqrt(100)
The sqrt(-1) =the imaginary number 1 and sqrt(100) =10
= i * sqrt(3) * 10
=10i sqrt(3)
Complete the solution of the equation. Find the value of y when x equals 1. 9x+7y=-12
Hey there! :)
Find the value of y when x=1 : 9x + 7y = -12
To find the value of y, simply plug in 1 for x in our given equation.
9(1) + 7y = -12
Simplify!
9 + 7y = -12
Subtract 9 from both sides so that we can isolate y.
7y = -12 - 9
Simplify.
7y = -21
Now, divide both sides by 7 to fully isolate y.
7y ÷ 7 = -21 ÷ 7
Simplify!
y = -3
~hope I helped!~
Elise picks 6 pounds of apples.She uses 1/2 pounds to make 1 container of apple sauce. How many containers of applesauce can Elise make with all apples?
Answer:
12
Step-by-step explanation:
Mass of apples = number of containers × mass in each container
6 lb = No of containers × ½ lb
No of containers = 6/½
To divide a whole number by a fraction, invert the fraction and change divide to multiply.
6/½ = 6 × 2/1
Multiply the numerator by the whole number.
6 × 2/1 = 12/1
Simplify the fraction.
12/1 = 12
Elise can make 12 containers of applesauce.
Look at the figure. Find TW
Answer: NUMBER 9 I'm on gradpoint too
Step-by-step explanation:
Find the next two terms in the sequence.
0, 1, 4, 9, ...
oo o
16, 25
13, 17
o
13, 18
o
16, 23
0,1,4,9
0+1= 1
1+3= 4
4+5= 9
Add the numbers by using an odd number each time.
9+7= 16
16+9= 25
Answer is 16, 25 ( first choice):
0, 1, 4, 9, 16, 25
Each week your science teacher gives a fifteen-point quiz. Your current scores are shown in the table. What is your mean quiz score?
The answer is 12 points
I have the table so I added the numbers to get 108, and there are 9 numbers, so yu do 108/9 equaling to 12
12. A fruit basket contains oranges and grapefruits. One-third of the orange
and one-fourth of the grapefruits were spoiled. You threw away 4 oranges
and 7 grapefruits. How many pieces of fruit were in the basket?
Answer:
There were 12 + 28 = 40 pieces of fruit in the basket.
Step-by-step explanation:
Suppose there were x oranges and y grapefruit.
Then we have
1 /3 x = 4
x = 4*3 = 12.
1/4 y = 7
y = 7*4 = 28.
If a rectangle's length is y−2 and the width is 3y+2 write an expression for the perimeter and an expression for the area.
Answer:
Area = [tex]3y^2 - 4y - 4[/tex] units square.
Perimeter = 8y units.
Step-by-step explanation:
Area of a rectangle = length * width.
Perimeter of a rectangle = 2*(length + width).
It is given that length = y−2 units and width = 3y+2 units. To find the area and the area of the rectangle in terms of y, simply put the length and the width in the above area and perimeter equations.
Area = length * width = (y-2)*(3y+2).
Expanding the expression gives:
Area = 3y^2 + 2y - 6y - 4 = (3y^2 -4y - 4) units square.
Similarly,
Perimeter = 2*(length + width) = 2*(y-2 + 3y+2) = 2*4y = 8y units.
Therefore, the expression for the area and the perimeter of the given rectangle is ([tex]3y^2 - 4y - 4[/tex]) units square and (8y) units respectively!!!
What is the rule for the reflection?
This image is being reflected over the y-axis. When reflecting over the y-axis the y-coordinate will stay the same, but the x-coordinate will have the opposite sign. Here is the rule for this reflection:
(-x, y)
Hope this helped!
~Just a girl in love with Shawn Mendes
Given the diagram below, which of the following ordered pairs represents the
vertex, A?
A. (b cos C,c sin C)
B. (a cos B, a sin B)
C. (a cos C, b sin C)
D. (b cos c, b sin c)
What is the distance between the points (2,-3) and (-6,4) on the coordinate plane?
d = sqrt (2-(-6))² + (-3-4)²)
d = sqrt ( 8² + 7² )
d = sqrt ( 64 + 49 )
d = sqrt (113)
Answer: The distance between the two points is roughly 10,63:
B)
The distance between the points (2,-3) and (-6,4) on the coordinate plane is 10.63 units. This can be obtained by using the distance formula.
What is the distance formula ?
The distance between two points (x₁,y₁) and (x₂,y₂) is
d = [tex]\sqrt{{(x_{2}-x_{1} )}^{2} + (y_{2}-y_{1} )^{2}[/tex]
In the given question, (x₁,y₁) is (2,-3) and (x₂,y₂) is (-6,4),
the distance d = [tex]\sqrt{{(x_{2}-x_{1} )}^{2} + (y_{2}-y_{1} )^{2}[/tex]
=[tex]\sqrt{{((-6)-2 )}^{2} + (4-(-3) )^{2}[/tex]
=[tex]\sqrt{{(-8)}^{2} + (7 )^{2}[/tex]
= [tex]\sqrt{{64 + 49[/tex]
=√113 =10.63 units
Hence the distance between the points (2,-3) and (-6,4) on the coordinate plane is 10.63 units. Thus option B is correct.
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There are 10 pennies, 14 nickels, and 6 dimes in a bag, and you remove three at random without replacing any. What is the probability that you will remove a penny, a nickel, and a dime in that order?
1. 1/29
2. 1/10
3. 1/30
4. 1/812
Answer:
1/30
Step-by-step explanation:
Graph the linear equations in three points: -x-2y=-10
Answer:
Step-by-step explanation:
Rewrite -x-2y= -10 as -2y= x - 10 and then as y = (-1/2)x + 5.
Then choose any 3 x values and find the corresponding y values using this formula. For example:
x y = (-1/2)x + 5 (x, y)
----- -------------------- ---------
0 5 (0, 5)
-4 (-1/2)(-4) + 5 = 7 (-4, 7)
6 (-1/2)(6) + 5 = 2 (6, 2)
Plot these three points and then draw a line through them.
Answer:
0,5 2,6 4,7
Step-by-step explanation:
You have to solve the equation by keeping y on its own. The equation is
y=-1/2x-5
Coordinates are:
0,5 2,6 4,7
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5) A banker learned that $842.40 is withheld from his monthly check for taxes and insurance. If
this represents 18% of his total pay, find the total pay.
On Monday, Florencia's hair was h centimeters long. She got a haircut on Tuesday, so her hair was only 75%, percent of the length it was on Monday.
Which of the following expressions could represent how many centimeters long Florencia's hair was after the haircut?
Choose 2 answers
Answer:
.75
Step-by-step explanation:
What is the domain of the function y=^3 sqrt x-1
Answer:
Domain is all real numbers also known as [tex](-\infty,\infty)[/tex] in interval notation.
[tex]f(x)=\sqrt[3]{x-1}[/tex]?
Step-by-step explanation:
If your function is [tex]f(x)=\sqrt[3]{x-1}[/tex] then the domain is all real numbers because you can cube root any real number.
If x is a real number, then x-1 is a real number.
So if you cube root (x-1) for any x then you still get a real number back.
Now if it was a square root, that is when we can run into some problems.
Answer: -infinity and positive infinity
Step-by-step explanation: It's either a on your test or two zero's that look twisted :)
What is the absolute value of 9? -3?
Show your work
Answer:
|9| = 9|-3| = 3Step-by-step explanation:
The absolute value of number a:
|a| = a for a ≥ 0
|a| = -a for a < 0
|9| = 9
|-3| = -(-3) = 3
To bake one cake, Drew uses 18 ounces of flour. He has 850 ounces of flour. Let y represent the ounces of flour left and x represent the number of cakes he has baked. When the situation is modeled on a graph, what are the slope and the y-intercept of the line representing this situation?
A.
slope = 850 and y-intercept = 18
B.
slope = 18 and y-intercept = 850
C.
slope = -18 and y-intercept = 850
D.
slope = 850 and y-intercept = -18
Answer:
Choice C:
slope = -18x
y-intercept = 850
Step-by-step explanation:
Drew uses 18 ounces of flour
-18x represents the amount of flour used
850 ounces of flour
or (0,850) is the y-intercept and represents the total number of flour
Answer
slope = -18x
y-intercept = 850
Answer:
C
Step-by-step explanation:
C