The equation which shows the true solution to the given logarithmic equation is,
[tex]x=1[/tex]
What is power rule of logarithmic function?The power of the log rule says that the number written in the front of the logarithmic function can be raised to the power of the logarithmic function.
For example,
[tex]n\log_b(M)=\log_b(M)^n[/tex]
Given information-
The logarithmic equation given in the problem is,
[tex]3\log_2(2x)=3[/tex]
Using the power rule of the logarithmic function,
[tex]\log_2(2x)^3=3[/tex]
Using the exponent rule of the logarithmic function the above equation can be written as,
[tex](2x)^3=3[/tex]
Solve it further,
[tex]8x^3=3\\x^3=1\\x=1[/tex]
Hence, the equation which shows the true solution to the given logarithmic equation is,
[tex]x=1[/tex]
Learn more about the rules of logarithmic function here;
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Answer:
its B on edge
Step-by-step explanation:
please help IN 5-10 mins 15 points
Answer:
C, D and E
Step-by-step explanation:
volume of prism = W x L x H
where W = width, L = length and H = height
Volumes
Prism A: 5 x 6 x 4 = 120 cm³
Prism B: 4 x 8 x 3 = 96 cm³
Prism C: 3 x 7 x 5 = 105 cm³
True statements
C. Prism B has the least volume
D. The volume of prism A is 120 cubic centimeters
E. The volume of prism C is less than the volume of prism A
[tex]\text{volume}=4\times5\times6=120cm^3[/tex]
Prism B[tex]\text{volume}=3\times8\times4=96cm^3[/tex]
Prism C[tex]\text{volume}=5\times7\times3=105cm^3[/tex]
A. - incorrect
B. - incorrect
C. - correct
D. - correct
E. - correct
Answer: CDE
What is the center of a circle represented by the equation (x−5)2 (y 6)2=42? (−6,5) (−5,6) (5,−6) (6,−5).
The center of the circle is (5, -6). Option C shows the center of the circle.
What is a circle?
A circle can be defined as the set of all points in the plane that are a fixed distance from a fixed point on the plane.
Given that the equation of the circle is,
[tex](x-5)^2+(y+6)^2=42[/tex]
We know that the general form of the equation of the circle is,
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where h, k is the center of the circle and r is the radius of the circle.
Compare the given equation with the general form of the equation, we get,
[tex](x-h) = (x-5)[/tex] and [tex](y-k) = (y+6)[/tex] and [tex]r^2 = 42[/tex]
For x-axis,
[tex](x-h) =(x-5)[/tex]
[tex]h = 5[/tex]
For y-axis,
[tex](y-k) = (y+6)[/tex]
[tex]k = -6[/tex]
Hence we can conclude that the center of the circle is (5, -6). Option C shows the center of the circle.
To know more about the equation of the circle, follow the link given below.
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Answer: C
Step-by-step explanation:
right on edge
Please HELP ! It’s worth a lot of points and I don’t understand
• Admissions to a zoo cost $12 for adults and $8 for children. A group of 34 people attending the zoo paid a
total of $312 in admission fees.
(a) Write and solve a system of equations that model the problem. Show all your work
(b) How many adults went to the zoo?
(C) How many children went to the zoo?
Hi mate!
Please check my attached image for the answer with explanation.
Hope it helps...
I need help asap .....
Answer:
1/4^2 (A)
Step-by-step explanation:
hope this helped :D
The ratio tables at the right show the comparison of books to games at Bert's Store and at Gloria's Store. Complete the ratio tables. Which store has the greater ratio of books to games? Explain.
Books : 4|number goes here| number goes here| number goes here| number goes here|
Games: 6|number goes here| number goes here| number goes here| number goes here|
Birt's store has a greater ratio of books to games in comparison to Gloria's store.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given the table:
Bert’s store
Books: 4,8,12,16,20.
Game: 6,12,18,24,30
Gloria’s store
Books: 5,10,15,20,25.
Games: 8, 16, 24, 32,40,
Since the fourth data of the birt store has an equal base to the third data of Gloria's store.
Thus, we can compare the data from the upper tables
So, 16 > 15
thus,
we can say that Bert's store has a greater ratio.
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Complete question:
suppose Yolanda places $2,500 in an account that pays 8% interest compounded each year assume that no withdrawals are made from that account follow the instructions below do not do any rounding
Answer:2,127.33
Step-by-step explanation:
Nova's hair grew 2 1/2 inches in 12 weeks. How long will her hair be in 1 week?
Answer:
Hair can grow about 1/10th of an inch.
I need help with this
Answer:
-26
Step-by-step explanation:
Use the given formula to find the next terms.
c(1) = 6 . . . . . . given
c(2) = c(1) -16 = 6 -16 = -10
c(3) = c(2) -16 = -10 -16 = -26
The third term in the sequence is -26.
The 3rd term of an arithmetic sequence is -1 and the 7th term is -13. find the explicit formula for this sequence. What is a22?
Answer: Hopefully the math terms won't confuse anyone.
So in the series, a_3 = -1 and a_7 = -13. Since it's an arithmetic sequence, all the terms in the series can be represented as:
a_n = a_0 + n * k
where n is the nth number. K is a constant you add to reach the next term, and a_0 is the starting constant.
a_7 = a_0 + 7 * k
a_3 = a_0 + 3 * k
solving this system gives you that
k = - 3 and a_0 = 8
Hence:
a_22 = 8 + 22 * -3 = -58
Step-by-step explanation:
What is the greatest common factor of 30 and 27?
Answer:
3
Step-by-step explanation:
well my alexa said so and shes always right so dont worry lol
Answer: 3
Step-by-step explanation:
30: 1, 2, 3, 5, 6, 10, 15, 30
27: 1, 3, 9, 27
The GCF is 3
hope this helps!
The table below shows how much Joe earns, y, after working x hours.
Joe’s Earnings
Hours worked
Money earned
4
$30
10
$75
12
$90
22
$165
The relationship between money earned and hours worked is linear. Joe computes the slope between (4, 30) and (12, 90), then computes the slope between (4, 30) and (10, 75). How do the two slopes compare?
The slope between (4, 30) and (12, 90) is greater because the ordered pairs are farther apart on the x-axis.
The slope between (4, 30) and (12, 90) is greater because the ordered pairs are farther apart on the y-axis.
The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same.
The slope between (4, 30) and (12, 90) is less because 4 is a factor of 12 and 30 is a factor of 90.
At which store is the cost of apples the least?
A
B
C
D
Answer 10
Step-by-step explanation:
Answer:
A. The slope between (4, 30) and (12, 90) is greater because the ordered pairs are farther apart on the x-axis.
Step-by-step explanation:
no explanation just right
If x > 2, find lx-2l
Help pleaseee
Explanation:
If x > 2, then x-2 > 0 after subtracting 2 from both sides.
Since x-2 is always positive when x > 2, this means the absolute value bars around the x-2 aren't needed. The results of |x-2| and x-2 are perfectly identical.
For example, if we tried something like x = 5, then
x-2 = 5-2 = 3|x-2| = |5-2| = |3| = 3Both outcomes are 3. I'll let you try other x inputs.
So because |x-2| and x-2 are identical, this means |x-2| = x-2 for all x > 2.
In short, we just erase the absolute value bars.
Given f(x) = 3x^2 + kx-1, and the remainder when f(x) is divided by x + 4 is 27, then what is the value of k?
Answer:
k=10
do long or synthetic division. the quotient = 3x + 22 with remainder 81
with long division first divide x into 3x^2 to get 3x. Then
3x times (x-4) = 3x^2-12x
subtract that from 3x^2+kx to get (k-12)x bring down the -7 to get
(k-12)x -7
you want a remainder of 81, so you want -4 times a constant to = -88 (-7-(-88)=81
4 x 22 =88. 22 is the constant
22=12+k
k=10
Step-by-step explanation:
lmk if i helped!
Factor the polynomial 12c9 28c7. Find the GCF of 12c9 and 28c7. 4c7 Write each term as a product, where one factor is the GCF. 4c7(3c2) 4c7(7) Use the distributive property. What is the resulting expression? 4(3c9 7c7) 4c7(3c2 7) 4c7(3c9 7c7) 4c7(12c9 28c7).
Factors of a polynomial together constitute the polynomial by multiplication. The factored form of [tex]12c^9 + 28c^7[/tex] is [tex]= 4c^7(3c^2 + 7)[/tex]
What is distributive property of multiplication over addition?Suppose a, b and c are three numbers. Then we have:
[tex]a(b + c) = a\times b + a\times c[/tex]
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
Remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2 \times x = 2x[/tex]
The given polynomial is [tex]12c^9 + 28c^7[/tex]
To factor it, we can use the fact that 12 and 28 are both having 4 as common factor since:
[tex]12 = 4 \times 3 \\28 = 4 \times 7[/tex]
Thus, the given polynomial is factored as:
[tex]12c^9 + 28c^7 = 4 \times 3 \times c^7 \times c^2 + 4 \times 7 \times c^7 = 4c^7(3c^2 + 7)[/tex]
Thus,
The factored form of [tex]12c^9 + 28c^7[/tex] is [tex]= 4c^7(3c^2 + 7)[/tex]
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Answer:
Factors of a polynomial together constitute the polynomial by multiplication. The factored form of is
What is distributive property of multiplication over addition?
Suppose a, b and c are three numbers. Then we have:
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
Remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in
The given polynomial is
To factor it, we can use the fact that 12 and 28 are both having 4 as common factor since:
Thus, the given polynomial is factored as:
Thus,
The factored form of is
Learn more about factors of a polynomial here:
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Step-by-step explanation:
The LCM of two numbers is the product of the two numbers. Discuss
Answer:
Sometimes, not always.
Step-by-step explanation:
The LCM is the lowest common number between 2 numbers, sometimes it can represent the product of the 2 numbers, but sometimes it doesn't.
2 Examples:
2: 2, 4, 6, 8, 10.
3: 3, 6, 9, 12, 15.
6 is the least common multiple of 2 and 3 and it does represent the product between both numbers.
17: 17, 34, 51, 68, 85.
34: 34, 68, 102, 136, 170.
34 is the least common multiple of 17 and 34 and it does not represent the product between both numbers, the product is represented as 578.
We can prove that sometimes the LCM is the product between 2 numbers, and sometimes not.
The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is: Select one: A. 0.10 B. 0.667 C. 0.733 D. 0.25
Probabilities are used to determine the chances of events
The probability that an employee of the company is single or has a college degree is 0.733
How to determine the probabilityThe given parameters are:
n = 600 --- the number of employees
College graduate = 400
Single graduate = 100
Single and college graduate = 60
The number of people that are college graduate or single are:
n(Single or college graduate) = 400 + 100 - 60
Evaluate
n(Single or college graduate) = 440
The probability is then calculated as:
p = 440/600
Evaluate the quotient
p = 0.733
Hence, the probability that an employee of the company is single or has a college degree is 0.733
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There are 15 students in a class. 9 of them play basketball, and 11 of them play soccer. How many students in the class play both soccer and basketball
We will see that the number of students that play both sports is given by the inequality:
5 ≤ x ≤ 9
How to find the number of students that play both sports?
We do know that in the class, there are 15 students.
Such that:
9 of them play basketball.11 of them play soccer.If you add these numbers, you get:
9 + 11 = 20
This gives more than the number of students that we have, to get the minimum number of students that play both sports we subtract the number of students:
20 - 15 = 5
5 students play both sports, but this is the minimum number.
There is also the case where out of the 11 students that play soccer, there are 9 that play basketball (so 9 students play both sports) and 4 students don't play any sport.
So the number of students that play both sports is given by the inequality:
5 ≤ x ≤ 9
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.Solve for x. How many solutions are possible with this equation?
2/3 (3x + 6)-5
I need help
Answer:
17x1-4+183
Step-by-step explanation:
need help on this question.
Answer:
Choose A I know this cause I'm smart
Shade 9/50.
please help thank you
3 Bennett exercises by lifting weights. He can lift 200 pounds
3 times without resting between lifts. Which equation shows
a correct way to find the total number of ounces, n, he can lift
without resting?
Bennet can lift 600 pounds without resting.
EquationAn equation is an expression that shows the relationship between two or more numbers and variables.
Let n represent the total number of ounces he can lift without resting, hence:
n = 200 pounds * 3
n = 600 pounds
Bennet can lift 600 pounds without resting.
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What is the maximum area of a rectangle with a perimeter of 320 feet?
Answer:
For a rectangle of given perimeter, here 320 feet, the rectangle with the greatest are is the square. This square shall be 80 x 80. Maximum at (80, 6400)
Step-by-step explanation:
Which equation matches the line from the graph?
Answer:
y = 2x - 3
Step-by-step explanation:
use the graph to find another point, and then calculate the slope. you can also use the graph to find the y-intercept, and then use the slope you just found to put the equation in slope-intercept form.
hope this helps :)
Answer: y = 2x - 3
Step-by-step explanation:
Mark says he has 4/10 of a dollar. Matt says he has 40/100 of a dollar. Matt says he has more money than Mark. Is he correct? Why?
Group of answer choices
A.Matt is not correct because they have the same amount of money.
B.Matt is not correct because Mark has more money.
C.Matt is correct because 40 is greater than 4.
D.Mark is correct because 100 is greater than 10.
Answer:
A
Step-by-step explanation:
If you simplify 40/100, you should get 4/10, which is still the same amount that Mark has.
You simplify by finding the greatest common factor between 40 and 100. In this case, it is 10. So you divide 40 by 10 and 100 by 10 to simplify.
pls help me solve this pls
Answer:
no solution
Step-by-step explanation:
absolute value cant be negative
Given m||n, find the value of x.
Will give Brainliest!
Answer:
X = 8 because the two given angles are alternate interior, meaning they are equal. Knowing that, you set up the equation 6x-2=46 and solve algebraically for 8.
I HOPE THIS HELPS YOU, AND I HOPE ITS CORRECT, STAY SAFE :3
Nisha is looking out the window of her apartment building at a sculpture in a park across the street. The top of Nisha's window is 60 feet from the ground. The angle of depression from the top of Nisha's window to the bottom of the sculpture is 25°. How far away from the building is the sculpture? Round your answer to the nearest hundredth. 25. 36 feet 27. 98 feet 100. 22 feet 128. 67 feet.
Angle of depression is the angle from horizontal line to the line of sight. The distance from building of the sculpture is: Option d: 128. 67 feet.
What is angle of depression?You look straight parallel to ground. But when you have to watch something down, then you take your sight up by moving your head down. The angle from horizontal to the point where you stopped your head is called angle of depression.
For the given case, referring to the figure, we have:
Length of BC = |BC| = 60 ft.
Length of AB = |AB| = x ft (distance of sculpture from building horizontally).
∠CAB = 25°
Thus, using tangent ratio from point of view of ∠CAB, we get:
[tex]\tan(25^\circ) = \dfrac{|BC|}{|AB|} = \dfrac{60}{x}\\\\x = \dfrac{60}{tan(25^\circ)} \approx 128.67 \: \rm ft[/tex]
(value of tan25° was calculated from calculator available online)
Thus,
The distance from building of the sculpture is: Option d: 128. 67 feet.
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Answer: D:128.68
Step-by-step explanation:
i got it write on my test .
Match the following items. Determine the functions if θ is a first-quadrant angle, and sin = √10/5. So basically, find cosine, tangent, co-secant, secant, and cotangent please!!
Will give brainliest to the person who answers first as long as its a real answer.
Answer:
cosine=rootunder15/5
tangent=whole root under(2/3)
cosecant=5/rootunder10
secant=5/root under15
contangent=whole root under(3/2)
Step-by-step explanation:
Using the formulae of pythagoras and reciprocal for the given angles.
Can someone check this please!?
Answer:
Yes it is correct
Step-by-step explanation:
The length of the base of a triangle is twice its
perpendicular height. If its area is 36 cm2, find
its length and perpendicular height.
Answer: height = 6, length = 12
Step-by-step explanation:
Let the length of the height = x.
Then, the length of the base = 2x
The formula for the area of a triangle is base*height/2, which equals 36 in this case.
Therefore, x*2x/2 = 36
x^2 = 36
x = 6, 2x = 12
Thus, the height = 6 and then length = 12