Making t the subject of formula gives the following expression: t = (2 - 3q)/(q + 4).
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
How to make t the subject of formula?In this exercise, you're required to describe the steps that should be taken to make t the subject of formula. Therefore, the appropriate and required steps are listed as follows:
q = (2 - 4t)/(t + 3)
Cross-multiplying, we have:
q(t + 3) = (2 - 4t)
qt + 3q = 2 - 4t
Collecting like terms, we have:
qt + 4t = 2 - 3q
Factorizing t, we have:
t(q + 4) = 2 - 3q
Dividing by (q + 4), we have:
t = (2 - 3q)/(q + 4)
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A figure has vertices at X(3, -3), Y(1, -2), and Z(3, 0). After a transformation, the image of the figure has vertices at X'(-3,-3), Y'(-1, -2), and Z'(-3, 0). Draw the preimage and the image. Then identify the transformation.
Answer:
here to help!
Step-by-step explanation:
no; Sample answer: If the vertices of ABC are A(1, 2), B(3, 4), and. C(1, 4), then the vertices of the final image are A"(-3, −1), B"(-5, 1), and C"(-3, 1).
24 -7.2(-4x + 3) ≤-26.4
Answer:
x [tex]\leq[/tex]-1
Step-by-step explanation:
first distribute
24+28.8x-21.6[tex]\leq[/tex]-26.4
add like numbers
2.4+28.8x[tex]\leq[/tex]-26.4
move the constant to the right
28.8x[tex]\leq[/tex]-26.4-2.4
calculate
28.8x[tex]\leq[/tex]-28.8
divide both sides by 28.8
x[tex]\leq[/tex]-1
write 658. 129 and expanded form
Answer:
Six hundred fifty eight and one hundred twenty nine thousandths
Use the table to answer the table Input: 2, 3, 6.
Output: 6, 9, 18 what ratio is represented in the table?
A: 1:3
B: 1:4
C: 1:5
D: 1:13
Thanks to whoever answers this. :D
The required ratio of the input value to the output value is 1:3. option D is correct.
The table has been shown with input and output data we have to determine the ratio of the input value to the output values.
Here,
1) for input 2 there is output 6
Ratio = input / output = 2 / 6 = 1 : 3
2) for input 3 there is output 9
Ratio = input / output = 3 / 9 = 1 : 3
2) for input 6 there is output 18.
Ratio = input / output = 6 / 18 = 1:3
Thus, the required ratio of the input value to the output value is 1:3. option D is correct.
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I'm having problems with this can someone help asap pls
Answer:
C I think good luck brother bye bye
John is driving to his office to attend a meeting. In the first 10 minutes, he covers a distance of 1 mile every minute. Then he stops at a local restaurant for 15 minutes to have breakfast. After that, he covers a distance of 0.5 miles every minute in the next 10 minutes to reach his office.
Which graph models the piecewise function for the given situation?
Answer:
Letter D is the correct answer.
Step-by-step explanation:
In the graph, the first line is an increasing diagonal and it stops in 10, meaning that John travelled 10 miles in 10 minutes.
After that, there is a horizontal line that indicates how much time he spent at the restaurant.
Finally, the last diagonal shows the distance travelled (5 miles) and the time it took (10 minutes.)
had the same question a couple minutes ago
hope it helps you;)
Find X, pls show the steps on how to do this equation
Answer:
perpendicular angle are=90
so there for: (4x-2)+(3x+8)=90
4x-2+3x+8=90
7x+6=90
7x=90-6
7x=84
so there for:x=12
Write each expression in simplest form. 4√7-∛7
The simplified expression after solving the given equation is 8.4721 .
The given expression is,
[tex]4\sqrt{7} - \sqrt[3]{7}[/tex] equation 1
Name the given expression as equation 1.
To simplify the given expression first we need to solve step wise,
As we know [tex]\sqrt{7}[/tex] = 2.6457 , we can write,
4[tex]\sqrt{7}[/tex] = 4 × (2.6457) = 10.5830
[tex]\sqrt[3]{7}[/tex] = 1.9129
Now, we need to substitute the above solved values in equation 1 and after substituting them we can write as follows:
[tex]4\sqrt{7} - \sqrt[3]{7}[/tex] = 10.5830 - 1.9129
On further simplifying, we will get
[tex]4\sqrt{7} - \sqrt[3]{7}[/tex] = 8.4721
Thus we can write that the simplified expression after solving the given equation is 8.4721.
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Multiply. State any restrictions on the variables.
2 x⁴ / 10 y⁻² . 5 y³/ 4 x³
According to the question, the given expression is written as below:
The expression is : [tex](\frac{2x^{4} }{10y^{-2} } )(\frac{5y^{3} }{4x^{3} } )[/tex]
Using indices concept, the same variables get cancelled with each other. The divisible numbers get divided by their respective numbers.
And finally, the negative power becomes positive in numerator. Using these concepts the above expression can be re-written as:
Final expression: [tex]\frac{xy^{5} }{y4} =xy[/tex]
Hence, the evaluated expression is [tex]xy[/tex].
What is indices?
In mathematics, the indices are the power or the exponent which is either raised to numbers or variables.
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Hans will run 27 miles this week. so far, he has run 18 miles. what are the possible numbers of additional miles he will run? use t for the number of additional miles he will run.
Hans will run additional 9 miles to the 18 miles he has run to complete 27 miles in wants to run for the week.
If Hans is to run 27 miles this week and he has run 18 miles, the additional miles he has to run in the week is t. Meaning that t plus eighteen is equal to 27, which is expressed mathematically below
t + 18 = 27
To solve the equation above, use balancing method. To use balancing method, subtract 18 from both side of the equation.
t +18 -18 = 27-18
t + 0 = 27-8
t = 27 -18
t = 9
Therefore, Hans will run additional 9 miles to complete 27 miles for the week.
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for f (x) = 4x+1 and g(x) = x squared- 5 find (g divided by f) (x)
The value of the composite function (g/f)(x) is (x^2 - 5)/(4x + 1)
How to evaluate the composite function?The definition of the functions are given as
f(x) = 4x + 1
g(x) = x^2 - 5
The composite function is given as
(g/f)(x)
The composite function is calculated using
(g/f)(x) = g(x)/f(x)
Substitute the known values in the above equation
So, we have
(g/f)(x) = (x^2 - 5)/(4x + 1)
Hence, the value of the composite function (g/f)(x) is (x^2 - 5)/(4x + 1)
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Factor this expression completely.
6x^2- 13x - 28
Answer: (2x-7)(3x+4)
Step-by-step explanation:
There is a technique called the “Slide Method” that can make this easier to solve.
The first step is to slide the coefficient of the 1st term and multiply it to the last term; which becomes:
X^2-13x-28(6) or x^2-13x-168
Next, factor this equation normally. The two factors that go into this are -21 and 8, so we can set this up as: (x-21)(x+8)
After that, divide both sides by the 6 that you previously slid:
(X-21/6)(x+8/6)
Then, reduce the fractions:
(X-7/2)(x+4/3)
After this is the last step. Take the denominator of the fraction, and make it the coefficient of the x variable: (2x-7)(3x+4)
Checking our Work; we get: (6x^2+8x-21x-28)=(6x^2-13x-28)
So, we know that (2x-7)(3x+4) is correct.
Ivan bought a new television. He was able to pay $120 at the time he received the television,
He will pay $44 each month on the balance. The original cost of the television was $736. Ilow
many months will it take Ivan to pay off the television?
You are helping your friend with his math homework. He made an order of operations mistake. Which part did he do in the wrong order
Multiply 4.5x and 3x please!!
Answer:
13.5x
Step-by-step explanation:
Move all terms containing x to the left, all other terms to the right.
Cross multiply.
Answer: 13.5x
Step-by-step explanation: all that needs to happen is the numbers multiplied. after, put the x on the
In the given right-angled triangle ABC, ∠B = 90°. Find the value of x.
Given - Sides of a triangle
Find - Value of x
Solution - The value of x is 3.
The sides of the right angled triangle are calculated by the Pythagoras theorem. As per the theorem,
Hypotenuse² = Base² + Perpendicular²
In the given triangle, Hypotenuse is (x+2), Perpendicular is 5 and Base is (x-3).
(x+2)² = 5² + (x-3)²
x² + 4x + 4 = 25 + x² - 6x + 9
On solving, the equation will be -
6x + 4x = 25 + 9 - 4
Performing addition and subtraction to find the value of x
10x = 30
x = 30/10
Performing division to find the value of x
x = 3
So, the value of x is 3.
Write 7380 to the nearest thousand
Answer:
7000
Step-by-step explanation:
Your answer is 7000.
Name two attributes that squares and rhombuses always share. Name an attribute they only sometimes share.
&
Name one attribute that isosceles and equilateral triangles always share. Name one attribute they only sometimes share.
THANK YOU!!
Attributes shared by rhombuses and rectangles:
Both are quadrilaterals.
Both have their opposing sides equal and parallel.
If a rhombus and a rectangle have the same length and width,
The perimeter of the rhombus equals the sum of the diagonals of the rectangle.
The sum of the diagonals of the rhombus equals the semiperimeter of the rectangle.
The angles of the rhombus equal the angles formed by the diagonals of the rectangle.
The angles formed by the diagonals of the rhombus are all right angles, as are the angles of the rectangle.
The area of the rhombus is one half of the area of the rectangle.
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Simplify each expression.
lne/4
[tex]\frac{ln(e)}{4}=\frac{1}{4}[/tex], by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now, as we know that ln (e) = 1,
In the given expression, [tex]\frac{ln(e)}{4}[/tex], for ln(e) = 1,
The expression becomes: [tex]\frac{ln(e)}{4}=\frac{1}{4}[/tex]
Hence, [tex]\frac{ln(e)}{4}=\frac{1}{4}[/tex], by properties of logarithm.
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The minimum distance from Earth to the Sun is 91.4 million miles. The maximum distance is 94.5 million miles. represent these 2 distances on a number line.
The required number line representation is attached
To solve this question we need to know the concept of number line :
Number lines are a horizontal straight lines in which the integers are placed in equal intervals all this numbers in a sequence can be represented in a number line . this line extends infinitely in both sides.
the numbers on the number line increases as one move right and decreases on moving from right to left . A number line can be used to depict both positive and negative integers. Writing numbers on a number line facilitates number comparison. The numbers on the left of the number line are smaller than the numbers on the right.
A number line can also be used to carry out addition , subtraction , multiplication and division . We move right to add move left to subtract and skip count to multiply .
The required number line is attached in the picture below :
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5. Hong Wu's gross pay is $61,400. He takes a married exemption of $4,000. His state income tax rate is 3.5
percent. How much will he pay in state tax?
a. $1,995
b. $1,722
15.000
c. $2,009
d. $2,296
21 $2.000
Answer:
$2,009
Step-by-step explanation:
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Find the value of c + 4 when c = 2
The answer is 6 because you replace c with the 2 (because it says that c equals 2) and add it normally which you get 6
Evaluate p+(-q)-2p+(−q)−2p, plus, left parenthesis, minus, q, right parenthesis, minus, 2 where p = -3p=−3p, equals, minus, 3 and q = 5q=5q, equals, 5.
Kahn Academy
The value of the expression when p =-3 and q =5 is -4
What are algebraic expressions?
Algebraic expressions are defined as expressions made up of variables, terms, factors, constants and coefficients.
They are also made up of mathematical or arithmetic operations such as:
AdditionSubtractionMultiplicationDivisionBracket, etcGiven the expression;
p + (-q) -2p
Where:
p = -3q = 5Now, substitute the values of p as - 3 and q as -5 in the expression, we have:
(-3) + (-5) - 2(-3)
expand the bracket
-3 - 5 + 6
add the values first
-3 - 1
-4
Thus, the value of the expression when p =-3 and q =5 is -4
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Assume that 632 people purchased pies that day. Explain how you could determine exactly how many people bought each type of pie.
In order to determine exactly how many people bought each type of pie, one will have to multiply the percentage by 632.
How to illustrate the information?It should be noted that this is a pie chart and the information shows the percentage for each group.
In this case, to determine exactly how many people bought each type of pie, one will have to multiply the percentage by 632.
For example, berry will be:
= 15.4% × 632
= 97
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Solve each equation. Round to the nearest ten-thousandth. Check your answers.
8+10x=1008
8 + [tex]10^x[/tex] = 1008 => x = 3, by exponentiation.
What is exponentiation?Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as [tex]b^n[/tex].Its pronunciation is "b (raised) to the (power of) n."Given: 8 + [tex]10^x[/tex] = 1008
=> [tex]10^x[/tex] = 1000
=> [tex]10^x[/tex] = 10³
=> x = 3
Hence, 8 + [tex]10^x[/tex] = 1008 => x = 3, by exponentiation.
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Which expression is equivalent to log₅32 ?
(A) log 5+ log 32 (B) log 5- log 32 (C) (log 5)(log 32) (D) log 32/log 5
The given expression log₅32 is equivalent to the expression (D) log32/log5.
What do we mean by an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent rules. To help determine the order of operations and other aspects of logical syntax, mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.To find which expression is equivalent to log₅32:
Law of logarithms:
The law of logarithms states that: log(a) b = log(10)b/log(10)aGiven the log function, which is written as log₅32
a = 5b = 32Substitute as: log₅32 = log32/log5
Therefore, the given expression log₅32 is equivalent to the expression (D) log32/log5.
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3 (a) in prime factor form 1250 = 2 x 5 and 525 = 3 x 5² x 7. Find the HCF and LCM of 1250 and 525.
The LCM of 1250 and 525 is 26,250.
The HCF of 1250 and 525 is 5.
What is the LCM and HCF?
The factors of a number is the number that perfectly divides another number. For example, a factor of 30 is 3. A prime number is a number that is perfectly divisible by 1 and itself. An example of a prime number is 3. The highest common factor is the highest factor that is common to two or more numbers.
A multiple is the product of a number and another number. For example, the multiple of 3 is 15. This is because 3 multiplied by 5 is 15. The lowest common multiple is the smallest multiple that is common to two or more numbers.
Prime factors of 1250 = 2 x 5 x 5 x 5 x 5
Prime factors of 525 = 3 x 5 x 7
HCF = 5
LCM = 2 x 3 x 5 x 5 x 5 x 5 x 7 = 26,250
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Mr. Jackson has a circular garden with a diameter of 10 feet surrounded by edging. Using the same length of edging, he is going to create a square garden. What is the maximum side length of the square?
If Mr. Jackson has a circular garden with a diameter of 10 feet surrounded by edging and using the same length of edging, he is going to create a square garden, then the maximum side length of the square is equal to 7.85 feet.
First, we have to find the amount of edging Mr. Jackson has. This can be calculated by finding the circumference.
Circumference can be found by using diameter by the formula;
c = π (diameter)
c = π (10)
c = 3.416 feet
This is the amount of edging on the circular garden. As he has to use the same amount of edging on the square garden, the edging on the square garden is the parameter of the square garden. As the parameter of the square is four times the side length, therefore;
3.416 ÷ 4 = 7.85
Hence, the maximum side length of the square is equal to 7.85 feet.
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It costs Kobel $3.50 in tolls to drive to work and back each day, plus he uses 5 gallons of gas. It costs him a total of $23.50 to drive to work and back each day. How much per gallon is Kobe paying for his gas? How do you know?
The cost spent per gallon of the gas is a $4 and the total money spent on gas is a 20$.
According to the statement
We have to find that the cost of the gas he used.
So, For this purpose, we know that the
A cost function may be a mathematical formula wont to wont to chart how production expenses will change at different output levels.
From the given information:
It costs Kobel $3.50 in tolls to drive to figure and back day after day, plus he uses 5 gallons of gas. It costs him a complete of $23.50 to drive to figure and back daily.
Then
Total money he spent = Toll cost + amount of gas she used
$23.50 = $3.50 + 5 gallons
Then
Cost of the 5 gallons = 23.50 - 3.50
Cost of the 5 gallons = 20
Then
cost of the 1 gallon gas = 20/5
cost of the 1 gallon gas = $4.
So, The cost spent per gallon of the gas is a $4 and the total money spent on gas is a 20$.
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please help me quick
the answer is pyramid or cone