Step-by-step explanation:
[tex](5x - 1)(x - 2) = 0 \\ 5x - 1 + x - 2 = 0 \\ 5x + x = 0 + 2 + 1 \\ 6x = 3 \\ 6x = 3 \\ 6 \: \: \: \: \: \: \: \: \: \: \: \: 6 \\ x = \frac{1}{2} [/tex]
HAND WRITTEN ANSWER ONLY!!
Draw and label each figure (exact measures are not expected) to the best of your
ability. Find the area, and make sure to label your answers properly.
a) A rectangle with a length of 4 cm and a width of 2.5 cm. (2 pts)
Based on the length and width of the rectangle given, the area of the rectangle is 10 cm²
What is the area of a rectangle?The area of a rectangle refers to the amount of a surface that the rectangle occupies.
This area can be found by the formula:
= Length x Width
Solving for the area of the rectangle therefore gives:
= 4 x 2.5
= 10 cm²
In conclusion, the area of the rectangle is 10 cm².
In conclusion, the area of the rectangle was 10 cm².
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Which is the logarithmic form of the exponential equation 2³=8 ?
(A) logB 2=3
(B) log₈ 3=2
(C) log₃ 8=2
(D) log₂ 8=3
The logarithmic form of the exponential equation 2³=8 is (D) log₂ 8=3 .
In mathematics, the inverse function of an exponent is a logarithm. This means that the logarithm of a fixed number, such as a, at base b, is used to represent the exponent to which the fixed number must be raised in order to create the number x.
The general properties of logarithm for a fixed base are:
logₐa=1logₐx+logₐy=logₐxylogₐx-logₐy=logₐ(x/y)logₐxⁿ=n logₐxlogₓy=(logₐy)/(logₐx)The given exponential equation is 2³=8.
To convert the above equation to logarithmic form we have to take logarithm to the base 2 on both sides of the equation.
Taking log₂ on both sides of the equation we get:
log₂(2³)=log₂(8)
Now we know from the properties of logarithms
logₐxⁿ=n logₐx
therefore:
3×log₂(2)=log₂8
Now logₐa=1, so
3×1=log₂8
or, log₂ 8 = 3
Therefore the required logarithmic equation is log₂ 8 = 3.
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can anyone help me out?
The value of x and y from the given angles 6x - 25, y and 4x + 15 will be x = 20 and y = 85 degrees.
What is vertically opposite angles?The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
The angles are given that 6x - 25, y and 4x + 15
WE can see that the angles 6x - 25 and 4x + 15 are vertically opposite angle, then
6x - 25 = 4x + 15
6x - 4x = 25 + 15
2x = 40
x = 20
Now by linear pair we get
y + 4x + 15 = 180
y + 4(20) + 15 = 180
y = 180 - 80 - 15
y = 100 - 15
y = 85
Therefore, the value of x and y from the given angles 6x - 25, y and 4x + 15 will be x = 20 and y = 85 degrees.
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PLSS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!
Mark is in charge of the fundraiser for his church. He is selling pre-sale tickets for $10 and at-the-door tickets for $15. The venue has the capacity to hold 300 people. The graph represents the number of raffle tickets he needs to sell to offset the upfront costs and raise $3,500:
How many at-the-door tickets must he sell to make his goal?
350
300
200
100
The number of at-the-door tickets that must be sold to reach the goal is 100.
How many at the door tickets must be sold to reach the goal?The system of linear equations that can be used to determine the required values are:
10p + 15d = $3500 equation 1
p + d = 300 equation 2
Where:
p = number of pre-sale tickets sold d = number of at-the-door tickets soldTo determine the value of d, take the following steps:
Multiply equation 2 by 10
10p + 10d = 3000 equation 3
Subtract equation 3 from equation 1
5d = 500
Divide both sides of the equation by 5
d = 500 / 5
d = 100
An alternate way to solve this question is to use the provided graph. Trace the point where the two curves meet to the y-axis. When traced the the y-axis the value gotten is 100.
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what is x-6>6 . solve for x
Answer:
x>12
Step-by-step explanation:
x-6>6
move constant (6) to right
x>6+6
x>12
alternate form
(12, infinity symbol)
hope this helps
Answer:
12
Step-by-step explanation:
An urn contains 5 tiles, each containing one of the numbers from 1 to 5. An experiment consists of selecting a tile, marking down its number, then replacing it and selecting a second tile and marking down its number. How many outcomes are in the sample space for this experiment?.
The number of outcomes in the sample space is 25
First time taking the tile out of urn and marking it down, the possibilities are 1,2,3,4,5
After replacement of the tile, once again there are 5 tiles in the urn.
Second time taking the tile and marking it down, the possibilities are 1,2,3,4,5
The sample space is set of all possibilities, which is
S = {(1,1),(1,2),(1,3),(1,4),(1,5),(2,1),(2,2),(2,3),(2,4),(2,5),(3,1),(3,2),(3,3),(3,4),(3,5),(4,1),(4,2),(4,3),(4,4),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5)}
S=25
The number of outcomes in the sample space is 25
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Expand each logarithm.
log₂√x
If the expression is [tex]log_{2}\sqrt{x}[/tex] then the expansion of the expression looks like ([tex]log_{2}x[/tex])/2
Given that the expression is [tex]log_{2}\sqrt{x}[/tex].
We are required to find the expanded form of the expression.
The power property says that if an exponent is being raised to another exponent, we can multiply the exponents. It says that
log[tex]a^{b}[/tex]=b log a.
The expression is [tex]log_{2}\sqrt{x}[/tex].
[tex]log_{2}\sqrt{x}[/tex]=[tex]log_{2}x^{1/2} }[/tex]
(We have to just put the power of x in front of the log to expand)
=([tex]log_{2}[/tex] x)/2
Hence if the expression is [tex]log_{2}\sqrt{x}[/tex], then the expansion of the expression looks like ([tex]log_{2}[/tex] x)/2.
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What is an equivalent form of 15(p + 4) − 12(2q + 4)?
15p − 24q + 12
15p − 24q + 8
60p − 72q
−9pq
Answer:
=15p+60-24q-48=15p-24q+12
it's the first one
The equivalent form of the given expression will be 15p - 24q +8. Hence, the first option is correct.
What is an Expression?In mathematics, expressions are assertions that must contain at least two words with variables or terms with numbers in them, or both, and connect them with an operator. It is possible for the mathematical operators to be addition, subtraction, multiplication, or division.
For instance, the equation (x+y) has the terms x and y with an addition operator in between. Numerical expressions, which just contain numbers, and algebraic expressions, which also include variables, are the two types of expressions used in mathematics.
The given expression in the question,
15(p + 4) - 12(2q + 4)
15p + 60 - 24q - 48
15p - 24q + 12.
Hence, it is proved that the equivalent form of the expression is 15p - 24q + 12.
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Between 10 P.M. and 7:36 A.M., the water level in a swimming pool decreased by 6/25 in. Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?
Answer:
The water level drop in temperature per hour is 40 °C per hour
Unit rate
Hours between 10 P.M. and 7:36 A.M = 9 hours 36 minutes
= 9.6 hours
The total decrease in temperature = 6/25
The unit rate of decrease in temperature per hour = Hours between 10 P.M. and 7:36 A.M ÷ Total drop in temperature
= 9.6 ÷ 6/25
= 9.6 × 25/6
= 240/6
= 40 °C per hour
Therefore, the water level drop in temperature per hour is 40 °C.
solve: |x + 11 | = x + 11
Answer: x>=-11
Step-by-step explanation:
|x + 11 | = x + 11
x+11=x+11 ==> x+11>0 since absolute value functions are greater than 0
x=x when x+11>0
x+11>0
x+11-11>0-11
x>-11
x+11=-(x+11)
x+11=0 ==> the only time a positive and negative number are equal is when the number itself is 0. Here, the number is 'x+11'.
x+11-11=0-11
x=-11
x=-11 and x>-11 ==> x>=-11
Find the number that makes the ratio equivalent to 1:5.
5:
Answer:
25
Step-by-step explanation:
[tex]\frac{1}{5}[/tex] = [tex]\frac{5}{x}[/tex] On the top, you need to multiply 1 by 5 to get 5, so multiply the bottom number 5 by 5 to get 25.
What is the value of the expression 2x² - 7x +3
when x = -4?
A. -1
B. -57
C. 63
D. 7
I did it with a calculator and got 63
a candidate was to subtract 15 from a certain number but mistakenly added 25 and his answer was 145 calculate the percentage error correct to 1 decimal places
The percentage error of the candidate is 38.1%.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, and the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.So, the percentage error:
Let x be the specified number.What he ought to have received is x-15.What he actually obtained is given as x+25, which equals 145.Now,
x+25 = 145x = 120He ought to have received x-15 = 120-15 = 105.
Percentage error = [(what he actually got - what he should have gotten)/what he should have gotten] × 100Percentage error = [(145 - 105)/105] × 100 = 38.1%Therefore, the percentage error of the candidate is 38.1%.
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how can I cheat on ixl other than the inspect element or a person to help me.
Answer:
Don't cheat, there is your answer.
Step-by-step explanation:
Scarlett is deciding between two parking garages. garage a charges an initial fee of $11 to park plus $5 per hour. garage b charges an initial fee of $8 to park plus $6 per hour. let a a represent the amount garage a would charge if scarlett parks for t t hours, and let b b represent the amount garage b would charge if scarlett parks for t t hours. write an equation for each situation, in terms of t , t, and determine the hours parked, t , t, that would make the cost of each garage the same.
The number of hours parked for the cost of each garage to be the same is 3 hours.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let t represent the number of hours parked at either garage A or garage B. Hence:
Total charges at garage A (A) = 5t + 11
A = 5t + 11
Total charges at garage B (B) = 6t + 8
B = 6t + 8
If both garages have the same cost:
5t + 11 = 6t + 8
t = 3
The number of hours parked for the cost of each garage to be the same is 3 hours.
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Two financial institutions offer different deals to new customers. The first bank offers an interest rate of 3% for the first year and 2% for the next two years. The second bank offers an interest rate of 2.49% for three years. You decide to invest the same amount of principal in each bank. To answer the following, assume you make no withdrawal or deposits during the three-year period.
a. Write a function that represents the total amount of money in the account in the first bank after three years.
Total amount of money in the account in the first bank after 3 years will be given by the function: P[tex]e^{0.07}[/tex].
The formula for calculating the amount (A) on a principal (P) invested at the rate of r%, compounded continuously after t years is-
A = P[tex]e^{rt}[/tex]
Here, we are given that there are 2 financial institutions-
1st financial institution:
interest rate = 3% for the first year
and interest rate for next two years = 2%
2nd Financial institution:
interest rate = 2.49% for three years
Let the principal amount deposited be P
We assume that the interest is compounded continuously.
Then for the 1st year-Amount = P[tex]e^{0.03}[/tex]
Since, there are no withdrawals or deposits,
The Amount of the 1st year will become the principal for the second year-Amount = (P[tex]e^{0.03}[/tex]) [tex]e^{0.02 * 2}[/tex]
= P × [tex]e^{0.03}[/tex] × [tex]e^{0.04}[/tex]
= P[tex]e^{(0.03 + 0.04)}[/tex]
= P[tex]e^{0.07}[/tex]
Thus, the total amount of money in the account in the first bank after 3 years will be- P[tex]e^{0.07}[/tex].
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Find the inverse of each function. Is the inverse a function?
y=3 x²-5
The inverse function returns the original value for which the output of a function was given
The inverse of this function is x = [tex]$\sqrt{\frac{y+5}{3} }[/tex]
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x.
If y varies inversely as x and x = 5 when y = 2, the constant of variation is k = xy = 5(2) = 10.
As a result, the equation for this inverse variation is xy = 10 or y = 10/x. Write an equation describing the inverse variation of y if it varies inversely as x and y = 6.
When x = 6, k = (6) = 8.
Let the function be y = 3x² - 5
y = 3x² - 5
Switch sides and add 5 to both sides
3x² = y + 5
Divide both sides by 3
x² = y + 5/3
Take the square root of both sides
x = ± [tex]$\sqrt{\frac{y+5}{3} }[/tex]
x = [tex]$\sqrt{\frac{y+5}{3} }[/tex]
Therefore, the value of x = [tex]$\sqrt{\frac{y+5}{3} }[/tex]
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Select the correct texts in the passage.
Julian factored the expression 2x4 + 2x³ x²-
At which step did Julian make his first mistake, and which statement describes the mistake?
Step 1
Step 2
Step 3
=
=
2x² + 2x³
x(2x²
= C
-
-
x²
x(2x³ + 2x² x − 1)
-
x (2x² (x + 1))
-
-
- X
-
-. His work is shown.
- 1(x − 1)
1) (x + 1)(x - 1)
Julian should have factored (2x²
Julian incorrectly factored -1 from the second group of terms.
Julian should have factored 2x from all terms instead of x.
Julian incorrectly factored 2x2 from the first group of terms.
1) as a difference of squares.
Julian factored the expression of [tex]2x^{4} +2x^{3} -x^{2} -x[/tex], then the
step 2 ( [tex]x(2x^{2} +1)) -1(x-1)[/tex]) statement is wrong statement.
Julian should have factored (2*2-1) as a difference of squares.
Julian incorrectly factored -1 from the second group of terms.
Julian should have factored 2x from all terms instead of x
Julian incorrectly factored 2*2 from the first group of terms
The expression is, [tex]2x^{4} +2x^{3} -x^{2} -x[/tex]
Factors greatest common factors out,
= [tex]x(2x^{3} +2x^{2} -x-1)[/tex]
Regroup terms into two proportional parts,
= [tex]x((2x^{3} +2x^{2} )+(-x-1))[/tex]
Factor the expression,
= [tex]x(2x^{2} (x+1)+(-x-1))[/tex]
= [tex]x(2x^{2} (x+1)-(x+1))[/tex]
= [tex]x(x+1)(2x^{2} -1)[/tex]
Hence, we can write,
= [tex]2x^{4} +2x^{3} -x^{2} -x[/tex]
= [tex]x(2x^{3}+2x^{2} -x-1)[/tex]
So step 1 is correct.
= [tex]x(2x^{2} (x+1)-(x+1))[/tex]
Then, step 2 is wrong.
Therefore, the expression of [tex]2x^{4} +2x^{3} -x^{2} -x[/tex], then the
step 2 ( [tex]x(2x^{2} +1)) -1(x-1)[/tex] )statement is wrong statement.
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Answer:
Julian should have factored (2x^2-1) as a difference of squares.
Step-by-step explanation:
CHOOSE THE CORRECT INEQUALITY !! HELP PLEASE :))
Carrie had 34 tiles. She said that she used all of her tiles to make an array with 5 rows. Could she be correct? Explain why or why not on the lines below.
pls help im confused! due soon!
The solution to the division operation is 3 with a remainder of 0.
Dividing PolynomialsFrom the question, we are to determine the quotient and the remainder from dividing the given polynomials
The given division operation is
(6x² + 6) ÷ (2x² + 2)
Using the long division method
3
2x² + 2 ) 6x² + 6
- 6x² + 6
0
The quotient of the division operation is 3 and the remainder is 0. The divisor is 2x² + 2
Hence, the solution is 3 + 0/(2x² + 2)
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Someone pls help! 3x ^2 and x = 10 pls help!
Answer:
300
Step-by-step explanation:
Because of PEMDAS (Order of Operations), you would do the exponent first.
So, 3(x)^2 and 3(100)
Then you get 300
Hope this helps!
Answer:
300
Step-by-step explanation:
3(10^2)
3(100)
300
what is:
| -8x + 14 | = -19
Answer:
No solutions.
Step-by-step explanation:
The absolute value cannot be less than 0
4[5+2(6-2*3)]-5(4(16/4-12/4)-4+2]
Answer:10
Step-by-step explanation:
Using the distributive Property method.
The mean height of the corn plants of variety A is 43.8 inches. Interpret the value of the mean in the situation.
Type your response in the space below.
The mean or the average height of all the corn plants is 43.8 inches.
There are various mean types in mathematics, especially in statistics.
Each mean is used to summarize a specific set of data, usually to clarify the overall magnitude and sign of the data set.The mean may be mistaken for the median, mode, or midpoint when using descriptive statistics because any of these could be referred to as a "average" (more formally, a measure of central tendency).The arithmetic mean of a set of observations is the sum of all the individual values; however, for skewed distributions, the mean could not be the same as the median or the mode.The average of the frequency distribution is given by the mean of the data set .
Hence the statement here indicates that the average height of all the plants combined is 43.8 inches
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The size of a computer monitor is given as the length of the screen's diagonal d in inches. The equation d=5/6√3A models the length of a diagonal of a monitor screen with area A in square inches.
b. Suppose you want to buy a new monitor with a screen that is twice the area of your old screen. Your old screen has a diagonal of 15 inches. What will be the diagonal of your new screen?
The diagonal of the new screen is approximately 21.21 inches.
The diagonal is a straight line that joins two opposite sides of a quadrilateral(polygon with 4 sides).
The length of the diagonal of the square is given as d=5/6√3A where A is the area of the square.
Now when diagonal d=15 cm then we substitute the value of d=15 to calculate area A of the square.
15=5/6√(3A)
or, 3A=15²×6²÷5² (squaring both sides)
or, A=108 square inches
The new monitor has an area of twice the old monitor.
Area of the new monitor =2×108 square inches=216 square inches.
Now we use the value of A=216 to calculate the value of diagonal d for the new monitor.
d=5/6√(3×216)
d=21.213.. inches
Therefore the diagonal of the new screen is approximately 21.21 inches.
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consider the following statement: more than 65% of the residents of los angeles earn less than the average wage for that city. could this statement be correct? if so, how? if not, why not?
Yes, there is a probability that there are some very high wages that strongly increases the average wage in Los Angeles like the wages of highly paid famous actors and actresses and some computer programmers in places like Silicon Valley.
This increases the gap between the highly paid and the low-income earners. As a result, finding the average gives a value that is below the average wage for that city.
The average annual wage in Los Angeles is Approximately $66,966 which narrows down to roughly $32.20 an hour. To calculate an average wage, we add all wages earned monthly, yearly or quarterly and divide by the number of workers registered.
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Horatio spends about 40 hours per week reading 2 different books in his spare
time. One book is more difficult, and one is lighter. He reads about 12 pages per
hour of the more difficult book and 25 pages per hour of the lighter book. If he
reads 610 pages per week, how many hours does Horatio spend on each book?
Answer:
you add 40+12+25+2+610 and you will get your answer
Answer:
Horatio spends 30 hours on the more difficult book and 10 hours on the lighter book
Step-by-step explanation:
Let X be the hours spent reading the more difficult book
Let Y be the hours spent reading the less difficult book
Total hours spent = X + Y = 40
Number of pages of difficult book in X hours at 12 pages per hour = 12X
Number of pages of easier book in Y hours at 25 pages per hour = 25Y
Total pages read = 12X + 25Y
So we have two equations in X and Y and we can solve them simultaneously. Equations are:
X + Y = 40 (1)
12X + 25Y = 610 (2)
We can eliminate one of the variable terms by making the coefficients of the other term equal and then subtracting
Multiply (1) by 12 to make X terms equal
12(X + Y) = 12 x 40
12X + 12Y = 480 (3)
Subtract (3) from (2)
(2) - (3)
==> 12X + 25Y - (12X + 12Y) = 610 - 480
==> 12X + 25Y - 12X - 12Y = 130
==> 25Y - 12Y = 130 (12X terms cancel)
==> 13Y = 130
==> Y = 130/13 (divide both sides by 13)
==> Y = 10
Using (1)
X + Y = 40
==> X + 10 = 40
==> X + 10 - 10 = 40 - 10
==> X = 30
So answer:
Horatio spends 30 hours on the more difficult book and 10 hours on the lighter book
At a gymnastics competition, each competitor performed one gymnastics routine. Each routine was at least 3 minutes long, but not longer than 7 minutes. Write a double inequality to represent the possible length, b, of a gymnastics routine at the competition in minutes.
We need to know about inequality to solve the given problem. The double inequality to represent the possible length of a gymnastics routine is given by 3≤b≤7.
Inequality is a realtion which makes comparison between numbers or other expressions. Double inequality means when two or more inequalities are joined together. Here in this question we know that each gymnastic routine is at least 3 minutes long. We assume that the length of a gymnastic routine is b, then we can say from the given information 3≤b. It is also said that no gymnastic routine is longer than 7 minutes, so maximum length of any gymnastic routine is 7 minutes, we can write it as, b≤7. Joining these two inequalities we get the double inequality which describes the possible length of a gymnastic routine.
3≤b≤7
Therefore using the concept of inequality we found the double inequality for possible length of gymnastic routine which is 3≤b≤7.
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10)
12
√144
Write the answer as a prime number base ?
Answer:
144
Step-by-step explanation:
12√144
12 × 12
=144
For a number to be classified as a prime number, it should have exactly two factors. Since 144 has more than two factors, i.e. 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, it is not a prime number.