Using proportions, it is found that 7.2q and q/6 are different terms, due to the different numeric coefficients.
How to convert a fraction to decimal?A fraction is converted to decimal by the division of the numerator by the denominator, that is, we apply the proportion of the numerator by the denominator.
For this problem, we have two terms, given as follows:
7.2q and q/6.
To verify if they are equal terms, we have to look at the numeric coefficients, hence:
The numeric coefficient of 7.2q is of 7.2.The numeric coefficient of q/6 is of 1/6 = 0.1667(result of the division of the numerator by the denominator).Hence 7.2q and q/6 are different terms, due to the different numeric coefficients.
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What are the solutions of each equation? Check your answers.
(c). ln 2 x+ln 3=2
According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.
Therefore, the given expression is [tex]ln2+ln3=2[/tex]
The values get multiplied in addition. Therefore, the above expression can be written as:
Expression = [tex]ln(6)=2[/tex]
Using logarithmic definition, we can write:
[tex]6 = e^{2}\\e = \sqrt{6},-\sqrt{6}[/tex]
The solution for the given expression is [tex]e = \sqrt{6},-\sqrt{6}[/tex]
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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What adds to be the bottom number but also multiplies to be the top? The top is 36 and the bottom is 12.
Answer:
The required number is 6. 6+6=12. 6×6=36.
Step-by-step explanation:
Kloe has 24 sunflowers, 16 roses, and 48 white carnations. She wants to make flower arrangements with the same number of each flower. How many flower arrangements can she make? How many of each type of flower is in a flower arrangement?
Kloe can make 4 flower arrangement
The number of flowers in each flower arrangement is 6 sun flowers, 4 roses and 12 white carnations.
The number of flower arrangements can be calculated as follows;
The first step is to calculate the HCF between the three numbers
24= 6 × 4
16= 4 × 4
48= 12 × 4
The HCF is 4
Hence the number of flower arrangement is 4 and the number of flowers in each flower arrangement is 6 sun flowers, 4 roses and 12 white carnations
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Jillian volunteered to work at the ticket booth for her school's Halloween carnival. The chart below gives the number of hours Gwen worked and the total amount of money she collected for the tickets she sold.
Tickets (t) Money (m)
10 $25.00
8 $20.00
6 $15.00
4 $10.00
Based on the table, write an equation for the relation between the number tickets Jillian sold and the amount of money she collected.
t= 2.50mt= 2.50m
t=m2.5t is equal to m over 2 point 5
tm = 25tm = 25
m=25tm is equal to 25 t
The equation for the relation between the number tickets Jillian sold and the amount of money she collected is m = 2.5t.
How to compute the equation?It should be noted that there's a constant relationship between the figures that are given.
This can be illustrated as:
= 25/10
= 2.5
Therefore, the equation for the relation between the number tickets Jillian sold and the amount of money she collected is m = 2.5t.
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help please im so lost. can somebody please explain!!!!?
Answer:
Step-by-step explanation:
Depreciation means value falling
10 is the scrap value which means the value that will remain after the product is properly used up.
depreciation for one year will be calculeted through
(original value - scrap value)/ no of years of use
(500 - 10)/3
= 163 is the annual rate of depreciation
If no scrap value is given, then you will simply divide the value by the no. of years of use
b. annual depreciation = 163
original value = 500
500 - 163(x) = worth of the poster after x years
worth remaining after a certain no. of years is also known as net book value.
Simplify each rational expression. State any restrictions on the variables.
x²+8 x+16 / x²-2 x-24
According to the question, the given rational expression is as follows:
Expression = [tex]\frac{x^{2} +8x+16}{x^{2} -2x-24}[/tex]
Simplify the numerator as well as denominator by doing factors which is shown below:
[tex]x^{2} +8x+16=x^{2} +4x+4x+16=(x+4)(x+4)[/tex]
Similarly, denominator factors are as follows:
[tex]x^{2} -2x-24=x^{2} -6x+4x-24=(x-6)(x+4)[/tex]
Now, substituting these values in the given expression, we get:
[tex]\frac{x^{2} +8x+16}{x^{2} -2x-24} = \frac{(x+4)(x+4)}{(x-6)(x+4)}=\frac{x+4}{x-6}[/tex]
Therefore, the final answer for the given expression is [tex]\frac{x+4}{x-6}[/tex].
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Fill in the blank to find an equivalent fraction to 8/9 = ?/9
Answer:
Due to the fact that the denomonator is the same your answer will be 8/9 but if there was a different denominator you would need to find the least common multiple. Dont forget anything you do to the bottom has to be done to the top
Step-by-step explanation:
Hope this helps!!
hii pls help, extra points for a sure and correct answer!!
Answer:
The answer is supposedly 0.25
Write each expression in simplest form. 2 √32 x²+3 √72 x²
Simplest form of expression is an expression written in its simplest of terms without changing the original value of the expression. There should be no like terms or parentheses.
In the given expression, there are two like terms and no parentheses. Hence, we solve for eliminating the like terms to find the simplest form of expression.
In order to eliminate the like terms, we need solve the square root terms to its simplest form.
√32=√2x2x2x2x2=4√2
√72=√2x2x2x3x3=6√2
Hence, the expression becomes,
2*4√2 x2+3*6√2 x2
Simplifying,
8√2 x2+18√2 x2
Adding the like terms,
(8+18)√2 x2
26√2 x2
Hence, the simplest form of expression 2 √32 x²+3 √72 x² is 26√2 x2.
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a person leaves home at 8:00 am and drives to a destination at a rate of 40 miles per hour. the person returns at a rate of 25 miles per hour and arrives at 2:30 pm. how far was the destination?
Answer:
100mi
Step-by-step explanation:
f(x) = 9x² +5; find f(10)
Answer:
f(10) = 905
Step-by-step explanation:
f(x) = 9x² +5; find f(10)
~Substitute x with 10
9(10)^2 + 5
~Solve exponent first
9(100) + 5
~Multiply
900 + 5
~Add
905
Best of Luck!
The answer is:
f(5) = 905Work/explanation:
To evaluate the given function, plug in 5 for x:
[tex]\bf{f(x)=9x^2+5}[/tex]
[tex]\bf{f(10)=9(10)^2+5}[/tex]
Remember, exponents first. So we square 10 first.
[tex]\bf{f(10)=9\cdot100+5}[/tex]
Multiply, then add:
[tex]\bf{f(10)=900+5}[/tex]
[tex]\bf{f(10)=905}[/tex]
Therefore, the answer is 905.Write the expanded form, the standard form, and the exponent form for each multiplication problem. Look for the patterns as you fill in the blanks.
Requirements:
1- You have to do every single problem shown inside the photo
2- Answers before 8:15AM
3- No fooling around or giving wrong answers.
Thank you :)
1. 10 * 10 * 10 = 1000 = 10^3
2. 10 * 10 * 10 * 10 = 10,000 = 10^4
3. 10 * 10 * 10 * 10 * 10 = 100,000 = 10^5
4. 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10,000,000 = 10^7
5. Summary
Multiplication Exp on first factor Exp on 2nd factor Exp on product
10^1 * 10^2 1 2 3
10^1 * 10^3 1 3 4
10^2 * 10^3 2 3 5
10^4 * 10^3 4 3 7
6. Multiplying two powers of ten, the product can be found by adding up the exponential values, the sum will be the exponent of the product and the base remain ten.
What are powers of ten?This refers to the exponential value of 10. Hence we can say that power as used in mathematics, is also called exponents.
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Look at the picture pleaseee
0. How many numbers of small boxes of dimensions 2cm x 2cm x 2cm are needed to fill a box of length 20cm, breadth 10cm and height 5cm. Find it.
Answer:
125 small boxes
Step-by-step explanation:
[tex]n = { \tt{ \frac{volume \: of \: big \: box}{volume \: of \: small \: boxes} }} \\ \\ { \tt{n = \frac{(20 \times 10 \times 5)}{(2 \times 2 \times 2)} }} \\ \\ { \tt{n = \frac{5 \times 5 \times 5}{1} }} \\ \\ { \tt{n = 5 {}^{3} }} \\ \\ { \tt{n = 125}}[/tex]
A square with side length ppp has an area of 169169169 square centimeters. The following equation shows the area of the square.
p^2 = 169p
2
=169p, squared, equals, 169
What is the side length of the square in centimeters?
Answer:
Side = 13 cm
Step-by-step explanation:
To find the side of the square:
Area = 169 square cm
[tex]\sf \boxed{\bf Side = \sqrt{area}}[/tex]
[tex]\sf = \sqrt{169}\\\\ = \sqrt{13*13}\\\\ =13 \ cm[/tex]
If f(x)=-x^2-1, and g(x)=x+5, then f(g(x)) =
Answer:
-8x^2+2x+5
Step-by-step explanation:
Distributive Property
Which of the following will result in a rational number? select all that apply. A, 1 sqare root of 4/ + 5/12 B. 1 square root of 9/7 + 7/15 C. square root of 2 - 5/7 D. square root of 2/7 ÷ 5/7
Answer:
A. & B.
Step-by-step explanation:
Square root of 4 is 2, and the square root of 9 is 3. These are rational, and adding fractions keeps them rational.
But the square root of 2 is irrational, and subtracting or dividing will not make them rational.
Hope this helps! :)
(b) Suppose a rocket, as designed, cannot provide enough velocity to achieve a stable orbit. Could alterations to the rocket make a stable orbit achievable? Explain.
The rocket moves really fast with high speed.
What is rocket ?A projectile that receives thrust from a rocket engine is known as a rocket (from the Italian rocchetto, which means "bobbin/spool"). All of the propellant carried by the rocket is used to create the exhaust from its engine.
In actuality, the absence of an atmosphere in space allows rockets to operate more effectively.
Due to their ability to reach Earth's escape velocity, multistage rockets can reach any maximum altitude. Rockets may produce significant accelerations and are powerful, light, and lightweight when compared to airbreathing engines.
In order for rockets to go forward and function in the vacuum of space, their action-reaction engines quickly discharge exhaust in the opposite direction.
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The highest temperature ever recorded in chicago was 105F and the lowest was -27F use absolute values to find the difference between the highest and the lowest temperatures
ΔT= 313.5k-240.3k = 73.2k.
Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).
One unit increase in the Kelvin scale is the same as a one-degree increase in the Celsius scale. The only difference between these two scales is zero points of the thermometer.
ΔT= highest T° in k - lowest T° in k
40.5°c+273= 313.5k
-32.7°c+273= 240.3k
therefore the difference will be 73.2k
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Tickets for an Amtrak train cost $17 for children and $36 for adults. Josie paid $2,297 for a total of 77 tickets. How many children tickets and how many adult tickets did Josie buy?
Adult tickets costs $63.8
Children tickets costs $13.2
How to calculate the amount of adult and children tickets ?Let x represent the adult tickets and y to represent the cost of children tickets
x + y= 77..........equation 1
36x + 17y= 2,297........equation 2
From equation 1
x= 77-y
Substitute 77-y for x in equation 2
36(77-y) + 17y = 2297
2772 - 36y= 2297
-36y= 2297-2772
-36y= -475
y= 475/36
y= 13.2
Substitute 13.2 for y in equation 1
x + 13.2 = 77
x= 77-13.2
x= 63.8
Hence adult tickets costs $63.8 and children tickets costs $13.2
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Write a variable expression to model real world situation.
A suit costs $65. Represent the cost of n suits.
Write each equation in exponential form.
log₂1/2=-1
The answer to this question is 1/2
Logarithmic scale: A measurement scale in which the position is marked using the logarithm of a value rather than the actual value.
A logarithmic equation includes a logarithm in the variable x.
An exponential equation is one in which the variable is represented by an exponent. A logarithmic equation is one in which the logarithm of a variable-containing expression is used.
For logarithmic equations, log b (x) = y is equivalent to b^y = x such that x > 0, b > 0 and b is not equal to 1.
In the given problem, b = 2, x = 1/2, and y = -1.
b =2
x = 1/2
y = -1
Substituting the values of b, x and y into the equation b^y = x;
2^(-1) = 1/2
therefore, the value of the given equation log₂1/2=1 is 1/2.
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If QS bisects
x=
m
m
m
The measure of PQT = 142.
We know what ray QS bisects angle PQT. If you draw out angle PQT and ray QS you can see that angle PQS is congruent to angle SQT. Because of the definition of angle bisector. This also means that angle SQT is half of PQT. Because of this we know that we can set the measure of PQT equal to 2 times the measure of SQT.
So we can set up and solve the following equation as such:
2(8x-25) = 9x +34
16x - 50 = 9x +34
7x -50 = 34
7x = 84
x = 12
Again I this doesn't seem to be your final answer. To find the answer the measures of each angle you're going to want to plug 12 in for x for one of the angles. So I'll do it for angle SQT.
8(12) - 25
96 -25
71
So the measure of angle SQT should be 71. Therefore since QS bisects PQR, the measure of angle PQS should also be 71. The measure of PQT should be double that which makes it 142.
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Find the greatest integer that is less than the value of the logarithm. Use your calculator to check your answers.
log 0.08
We need to know about logarithm to solve this problem. The greatest integer that is less than log 0.08 is -2.
Logarithm is the exponent which is raised to a base to get a certain number. There are a few rules of logarithm, log a + log b can be written as log ab, log a- log b can be written as log a/b, when the number for which the logarithm is calculated is raised to a power, then the power can be directly multiplied to the log itself. Logarithms when written as log has a base of 10 and the logarithm of a number same as its base is always 1, log of 1 is zero.
log 0.08= log 8/100= log 8- log 100 = [tex]log 2^{3} -log 10^{2}[/tex]
=3 log2 -2log10=3x0.30-2=0.9-2=-1.1
Therefore the greatest integer that is less than the value of log 0.08 is -2.
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What is the correct solution to the given equation?
Solve for 4X + 5 = 25
Answer:5
Step-by-step explanation:
4x + 5 = 5.. if its addition you take away the number if its subtraction you add the number.. take away 5 from 25.. 4 times 5 is 20
Evaluate each expression for the given value of the variable.
x³ + x²; x=2)
After evaluating the expression we get 12.
Given, x³ ₊ x²
Finding the value of an algebraic expression when a specified number is used to replace the variable is known as evaluating the expression. In order to evaluate an expression, we first replace the expression's variable with the given number, then we streamline the expression using the order of operations.
A procedure called evaluation involves analyzing a program critically. It entails gathering and studying data regarding a program's operations, features, and effects. Its objective is to assess a program, enhance its effectiveness, and/or provide information to help with programming decisions.
substitute the value of x =2
2³ ₊ 2²
= 8 ₊ 4
= 12
hence we get the answer as 12.
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Compare -√7 and 3.12345.... Justify your reasoning.
HELP PLEASE
If we compare numbers -√7 and 3.12345 we find that 3.12345 is always greater than -√7.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
It is given that there are two numbers which are -√7 and 3.12345.
Let's compare the,.
We know that an irrational number is a number which can't be expressed other than using roots.
Here -√7 is an irrational number and if we represent that in decimal form then it can be written as :
-√7 = - 2.6467
Now , as this number is negative decimal number it is less than the other number given which is 3.12345 because 3.12345 is a positive decimal number. And we know that value of a positive number is always greater than a negative number.
i.e.,
3.1245 > -√7
Therefore , if we compare numbers -√7 and 3.12345 we find that 3.12345 is always greater than -√7.
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Find the area of a triangle with the given base b and height h . b=6 in., h=15 in.
write an algebraic expression for the word phrase c divided by 7
Answer:c=7
Step-by-step explanation:
What is the actual number of kilometers that is represented by 4 centimeters on the map?
The actual distance that is represented by 4 centimeters on the map is 16 kilometers
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that the scale used on the map is:
1 cm = 4 km
Hence, for 4 cm represented on the map:
Actual distance = 4 cm * 4 km per 1 cm = 16 km
The actual distance that is represented by 4 centimeters on the map is 16 kilometers
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