Slope = m = 2
y = mx + b
y = 2x + b
Plug in (-2, 1) to find b
1 = 2(-2) + b
b = 5
y = 2x + 5
Estimate the difference of 25.92 - 5 4/10
Answer: 20 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
First of all, 5 [tex]\frac{4}{10}[/tex] = 5.4
Remember, 1/10 = 0.1, 2/10 = 0.2, and so on.
This means we can change the equation to 25.92 - 5.4, which gives us 20.52.
This is close to 20.50, which is equivalent to 20 [tex]\frac{5}{10}[/tex], which is equivalent to 20 [tex]\frac{1}{2}[/tex].
Solve the following linear equation and simplify your answer.
8z−6=−2(−4z+3)
Answer:
Step-by-step explanation:
8z-6=-2(-4+3)
8z-6=8z-6
on transposing,
8z-8z-6+6=0
A system contains two or more linear equations that can be solved or graphed together at once.
True
False
The statement "A system contains two or more linear equations that can be solved or graphed together at once" is true.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
A system contains two or more linear equations that can be solved or graphed together at once.
This statement is true.
For example,
The two linear equations can be:
ax + by = c ____(1)
dx + ey = F _____(2)
We can solve this equation using the substitution method or elimination method.
We can find the point of intersection.
And we can solve and graph together at once.
Thus,
The statement "A system contains two or more linear equations that can be solved or graphed together at once" is true.
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what - (-7/12) = a negitive number
Answer:
nu tg hi yum
Step-by-step explanation:
A jar contains 7 red marbles and 10 blue marbles. What is the probability of choosing a blue marble?
This answer should be written as a decimal. Answer to two decimal places.
The probability of choosing a blue marble is 0.59.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
The jar contains 7 red marbles and 10 blue marbles.
The probability of choosing a blue marble will be:
= Number of blue marbles / Total marbles
= 10/17
= 0.59
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Determine the range of f(x) = |x| − 4.
The range of the function f(x) = |x| - 4 is [-4, ∞).
What do you mean by domain and range of a function?
For any function y = f(x), Domain is the set of all possible values of y that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
We have -
f(x) = |x| - 4
According to question, we have -
f(x) = |x| - 4
We will draw the graph of the function -
f(x) = |x| + 4
Range is the set of value along the [y] - axis.
We can see that, the values of range of [y] variable is from -
[-4, ∞)
Therefore, the range of the function f(x) = |x| - 4 is [-4, ∞).
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6 Tara begins solving the system below. What do you think her next step will be?
6x + 8y = 7
- 2x+4y= -8 -2x = -4y - 8
x = 2y + 4
Answer: Substituting x = 2y + 4 into the equation 6x + 8y = 7.
Step-by-step explanation:
Since they solved for x, their next step will likely being solving by substitution, where you substitute for one variable to solve the other one.
There are a few different ways to solve systems of equations, so this might not be her next step.
write an equation in STANDARD FORM of the line that passes through (-6,-10) and has the slope m=1/6
The equation of the line passing through (-6,-10) and having slope m = 1/6 in Standard From is x - 6y = 54 .
In the question ,
it is given that ,
the required line passes through the point (-6,-10) ,
and has slope(m) = 1/6 ,
So , the equation of the line that passes through the given point and slope ,
is given by ,
(y - (-10)) = 1/6(x -(-6))
(y + 10) = 1/6(x + 6)
On cross multiplication ,
we get ,
6(y + 10) = x + 6
6y + 60 = x + 6
x - 6y = 60 - 6
x - 6y = 54
Therefore , The equation of the line passing through (-6,-10) and having slope m = 1/6 in Standard From is x - 6y = 54 .
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The sum of two numbers is eighty-three. If the larger number is divided by the smaller number, then both the quotient and the remainder are six. Find the numbers .
Answer:
The numbers are 72 and 11Step-by-step explanation:
Let the number be x and y.
Givenx + y = 83,x = 6y + 6Solve the system by substitution:
6y + 6 + y = 837y = 83 - 67y = 77y = 11Find x:
x + 11 = 83x = 83 - 11x = 72
Write an explicit equation for the following
sequence:
4/7,-4, 28, -196, 1372, ...
Answer:
a_n = (4/7)(-7)^(n - 1)
Step-by-step explanation:
a1 = 4/7 = 4/7 × 1 = (4/7)(-7)^0
a2 = -4 = 4/7 × (-7) = (4/7)(-7)^1
a3 = 28 = 4/7 × (-7)(-7) = (4/7) × (-7)^2
etc.
a_n = (4/7)(-7)^(n - 1)
Construct a 95% confidence interval for the number of toys that are from china in a random sample of 210 toys. It is estimated that 70% of all the world's toys come from china. Use the following Desmos Applet to help What would be the z-critical value? (two- decimal places) Answer 1 Choose... B) What is the standard error or standard deviation (Sigma value)? Answer 2 Choose... C) What is the margin of error? (Round to nearest whole number) Answer 3 Choose... D) What is the expected number of toys in random sample of 210 toys? Answer 4 Choose... E) What is the upper limit of confidence interval? Answer 5 Choose... F) What is the lower limit of confidence interval?
For the 95% confidence interval for the number of toys that are from China in a random sample of 210 toys, using the z-distribution, we have that:
a) The critical value would be of z = 1.96.
b) The standard error is of: 0.0316
c) The margin of error is of: 6%.
d) The expected number of toys in the sample is of: 147.
e) The lower limit of the interval is of: 64%.
f) The upper limit of the interval is of: 76%.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds obtained by the rule presented below as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The estimate and the sample size for this problem are given as follows:
[tex]\pi = 0.7, n = 210[/tex]
Hence the expected number of toys in random sample of 210 toys is of:
0.7 x 210 = 147.
The standard error is calculated as follows:
[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.7(0.3)}{210}} = 0.0316[/tex]
The margin of error is the multiplication of the critical value and of the standard error, hence:
M = 1.96 x 0.0316 = 0.06 = 6%.
The bounds of the interval are the estimate plus/minus the margin of error, hence they are given as follows:
Lower bound: 70% - 6% = 64%.Upper bound: 70% + 6% = 76%.More can be learned about the z-distribution at https://brainly.com/question/25890103
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The population of a pigeons in a city is
7000 and is growing exponentially at 19%
per year. Write a function to represent the
population of pigeons after t years, where
the quarterly rate of change can be found
from a constant in the function. Round all
coefficients in the function to four
decimal places. Also, determine the
percentage rate of change per quarter, to
the nearest hundredth of a percent.
Answer: p(t) = 100×1.0153^(12t)
1.53% per month
In general, the function will be written ...
p(t) = (initial value)×(growth factor)^t
where t is in units comparable to those applicable to the growth factor. The growth factor is found from ...
growth factor = 1 + growth rate
Here, the growth rate is given as 20% per year, so the growth factor per year is ...
1 +20% = 1.20
The initial value is given as 100, so we can write the exponential function as ...
p(t) = 100×1.20^t
__
The time period units for t are supposed to be years, but we want to find the growth rate for a month. We can do that by recognizing there are 12 months in a year. In the above equation, we can use (1/12)(12t) in place of t, then figure the growth factor (and growth rate) per month.
p(t) = 100×(1.20^(1/12))^( 12t)
p(t) = 100×1.0153^(12t) . . . . population exponential function
This shows the monthly growth factor is 1.0153, so the monthly rate of change (growth rate) is ...
1.0153 -1 = 0.0153 = 1.53% . . . . monthly rate of change
Step-by-step explanation:
Find the quotient of 3/5 3/7. Write your answer in the simplest form.
[tex]\cfrac{3}{5}\div\cfrac{3}{7}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5}\cdot \cfrac{7}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{7}{5}\implies 1\frac{2}{5}[/tex]
what is the slope of the line that passes thru (7,-6) and (6,-6)
The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.
Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.
Let the slope of the line joining A (7,-6) and B(6,-6) be m.
We know that the slope of a line is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of the line
= (6-7) / (-6+6)
= -1 / 0
= undefined
Since the slope is undefined we can say that the straight line is parallel to the y axis.
we know that tan 90° = ∞
So any line parallel to this line will have the same slope as the y axis.
Hence the slope of the given line is undefined or infinity.
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Question 3
Rearrange the formula 5√x + y = z to make x the subject
Answer:
x = [tex](\frac{z-y}{5}) ^{2}[/tex]
Step-by-step explanation:
5[tex]\sqrt{x}[/tex] + y = z ( subtract y from both sides )
5[tex]\sqrt{x}[/tex] = z - y ( divide both sides by 5 )
[tex]\sqrt{x}[/tex] = [tex]\frac{z-y}{5}[/tex] ( square both sides to clear the radical )
([tex]\sqrt{x}[/tex] )² = [tex](\frac{z-y}{5}) ^{2}[/tex]
x = [tex](\frac{z-y}{5}) ^{2}[/tex]
Find a polynomiat of degree n that has only the given zero(s). (There are many correct answers.)
x = -1, 3, 2, 4; n = 5
The polynomial function for the given zeros is x⁷+9x⁶+20x⁵-22x⁴-87x³+37x²+114x-72
Polynomial function:
An expressions that may contain variables of varying degrees, non-zero leading coefficients, positive exponents, and constants is known as polynomial function.
Given,
Here we have the value of zeros as x = -1, 3, 2, 4 and n = 5.
Now, we have to find the polynomial function from it.
Let us consider if a polynomial function f(x) has zeros x = -1, x = 3, x = 2, and x = 4, then it has factors
=> (x - 1)³ (x + 3)² (x +2) (x + 4)
Here there are four factor, in these polynomial so it can be Quintic Function.
Now, we have to expand this one to get the resulting polynomial,
=> x⁷+9x⁶+20x⁵-22x⁴-87x³+37x²+114x-72
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You are buying some television time and the station tells you that they reach 120,000 people. They quote you $2.50 CPM (cost per thouand). How much will you have to pay for the time?
The amount that you have to pay for the time is $300.
How to calculate the cost?From the information, the person is buying some television time and the station tells you that they reach 120,000 people and they quote you $2.50 CPM
The cost will be:
= Total people × Cost per thousand
= 120000/1000 × $2.50
= 120 × $2.50
= $300
The amount is $300.
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Divide f(x) by d(x). Your answer
should be in the following format:
f(x)
d(x)
f(x)
d(x)
Q(x) +
=
4x³8x²+2x1
2x + 1
[?]
R(x) = -²
R(x)
d(x)
The value of R(x) is - [1-7x]
What is division in algebra?
The four basic arithmetic operations of addition, subtraction, multiplication, and division are used to connect variables and constants in algebraic expressions. The procedure of multiplying and dividing algebraic expressions is the opposite of each other. You can divide algebraic expressions using the long division method, the division of a monomial by another monomial, or the division of a polynomial by another polynomial.
Dividend: The number or value that we divide is known as a dividend.
Divisor: The number that divides the dividend is known as a divisor
Quotient: The result obtained from the division process is known as a quotient
Remainder: The number left over after the division process is known as the remainder.
In the given question;
f(x) is dividend and
d(x) is divisor
Q(x) is the quotient
And we have to find the remainder i.e. R(x)
After dividing [tex]\frac{4x^3-8x^2+2x-1}{2x+1}[/tex] we get
Q(x) =[tex]2x^2-5x[/tex]
and R(x) = [tex]-[1-7x][/tex]
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Answer: 9/2
Step-by-step explanation:
please help me solve this question !
The solution of the function is x = 12
What are trigonometric ratios?Trigonometric ratios are the ratios of sides of a right-angle triangle. The most common trigonometric ratios are sine, cosine, and tangent.
Consider a right-angle triangle ABC, right-angled at C. In that case, side AB will be the hypotenuse. Also, if we chose AC as the base and BC as the perpendicular. Then, for ∠BAC, value of sinθ = Perpendicular/ hypotenuse = BC/AB
6cos(5x) = 3
divide both sides by 6, we have
cos(5x) = 3/6
cos(5x) = 0.5
taking the anti cosine of both sides
5x = Arc cos 0.5
5x = 60
x = 60/5
x = 12°
In conclusion, the value of x = 12°
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Brainliest if correct 5 points
Please HELP! Select ALL the transformations that DO NOT preserve distance but preserve angle measure
a. Reflection across the line x = y
b.Translation 4 units downward
c. Anticlockwise rotation of 180 about the origin
d. Dilation by a scale factor of 0.5 about the origin.
e. Dilation by a scale factor of 2 about the (1,2)
f. Translation of 2 units to the right then dilation by a scale factor of 1.5 about the g. point (1,2)
Answer:
D and E
Step-by-step explanation:
Dilations shrink or enlarge, but do not change angle measurements.
Please help! Thanks in advance
Answer:
D
Step-by-step explanation:
4/6 + 1/4 what's the answer pls
[tex]\boldsymbol{\sf{\dfrac{4}{6}+\dfrac{1}{4} }}[/tex]
We reduce the fraction 4/6 to its lowest expression by extracting and canceling 2.
[tex]\boldsymbol{\sf{\dfrac{4}{6}=\dfrac{4\div2}{6\div2}=\dfrac{2}{3} }}[/tex]
[tex]\boldsymbol{\sf{\dfrac{2}{3}+\dfrac{1}{4} }}[/tex]
Convert 2/3 and 1/4 to fractions with like denominators.
[tex]\boldsymbol{\sf{\dfrac{2\times4}{3\times4}+\dfrac{1\times3}{4\times3} \iff \ \dfrac{8}{12}+\dfrac{3}{12} }}[/tex]
Since 8/12 and 3/12 have the same numerator, we join numerators and add.
[tex]\boldsymbol{\sf{\dfrac{8+3}{12}= }}\boxed{\boldsymbol{\sf{\frac{11}{12} }}}[/tex]
What is the slope of the line that passes through the points (8, 2) and (10, 2)? Write
your answer in simplest form.
Answer:
0
Step-by-step explanation:
The y-coordinates are the same, so the line is horizontal. Therefore, the slope is zero.
math
The sum of two numbers is 36. Their difference is 4. Determine the two unknown numbers.
(NOTE: Show answer in the following format # and #. If not entered in this format, will be scor
incorrect.)
Enter answer:
Answer:
One number is 16 and the other number is 20
Step-by-step explanation:
Let x = one number
Let y = the other number
x + y = 36
x - y = 4 Or x = 4 + y
Substitue in 4 + y for x in the first equaion
4 + y + y = 36 Combine like terms
4 + 2y = 36 Subtract 4 from both sides
2y = 32 Divide both sides by 2
y = 16
Substitute 16 for y in either of the orginal equaions
x + y = 36
x + 16 = 36 Subtract 16 from both sides
x = 20
18x^5-3x^7+12x4 factor the following polynomial with the greatest common factor
Factoring the given polynomial expression with the greatest common factor gives 3x⁴(6x - x³ + 4)
Factoring a Polynomial expressionFrom the question, we are to factor the giving polynomial expression with the greatest common factor
The given polynomial expression is
18x^5-3x^7+12x4
This can be properly written as
18x⁵ - 3x⁷ + 12x⁴
First, we will determine the greatest common factor of the coefficients in the expression.
The coefficients in the expression are 18, 3, and 12.
The greatest common factor of 18, 3, and 12 is 3.
Now, we will determine the greatest common factor of x⁵, x⁷, and x⁴.
The greatest common factor of x⁵, x⁷, and x⁴ is x⁴.
Thus,
The greatest common factor of the polynomial expression is 3x⁴.
Now,
Factoring the polynomial with the greatest common factor
18x⁵ - 3x⁷ + 12x⁴
3x⁴(6x - x³ + 4)
Hence, the result of factoring the polynomial is 3x⁴(6x - x³ + 4)
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Now we will calculate the actual probability that all randomly chosen student has a schedule that excludes music theory. We have found that the probability is given as
P=4C38C3
Express your answer as a fraction in simplest form.
The simplified probability that all randomly chosen student has a schedule that excludes music theory is given as follows:
p = 1/14.
How to calculate a probability?The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
In the context of this problem, these numbers of outcomes are given as follows:
Desired outcomes: [tex]C_{4,3}[/tex]Total outcomes: [tex]C_{8,3}[/tex].The symbol [tex]C_{n,x}[/tex] represents the number of combinations of x elements that can be obtained from a set of n elements, and the combination formula is presented as follows:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Considering the formula presented above, the numeric values of the combinations are obtained as follows:
Desired outcomes: 4!/(3! x 1!) = 4.Total outcomes: 8!/(3! x 5!) = 56.Hence the simplified probability is of:
p = 4/56 = 1/14.
As the quotient of 56 and 4 is of 14.
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Write an equivalent expression for 11(9a + 3b)
The equivalent expression for 11(9a+3b) is 33(3a+b)
How should an equivalent be written?
The numerator and denominator must be multiplied or divided by the same number when writing equivalent fractions. This explains why these fractions have the same value when they are simplified.
How does math equivalent work?
We need to multiply the denominator of 7 by a number that will give us 21 in order to obtain equivalent fractions, which requires multiplying both the numerator and the denominator by the same number. We may find an equal fraction by multiplying the numerator and denominator by 3, so 3 times 7 gives us 21.
Given expression: 11(9a+3b)
Take 3 outside from the expression, we get,
= 33(3a+b), which is called the equivalent expression
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To solve we must expand the terms and then simplify and finally multiply.
¿What are equivalent expressions?The expressions are two algebraic expressions which are equivalent when they both take the same numerical value, for any value of the domain of each of the variables.
Solving the problem:11 (9a + 3b)11 × 9a + 11 × 3b99a + 11 × 3b99a + 33bSo the Result of the Expression is 99a + 33b
¡Hope this helped!
The telephone company offers two types of service. With plan A, you can make an unlimited number of local calls for $50 per month plus a $25 plan activation fee. With plan B you pay $25 monthly plus $50 activation fee
Y=mx+b form please
Forming the two telephone charge plans in a slope intercept equation form, like Y=mx + b, is as follows:
Plan A: Y = 50x + 25Plan B: Y = 25x + 50.What is the slope intercept equation?The slope intercept equation is an equation of a straight-line with its slope (constant unit rate) combining the x and y intercepts.
Generally, the formula y = mx + b depicts the slope intercept equation with the following values:
y = y coordinate
m = slope
x = x coordinate
b = y intercept
Plan A Plan B
Fixed cost (b) $25 $50
Variable cost (m) 50 25
x = monthly 12 12
y = the total cost for the period
Thus, Plan A will have a total cost of 50x + 25 and Plan B will have a total cost of 25x + 50.
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Linear Inequalities
y > 2/3 x + 1
Answer: cu
Step-by-step explanation: cmu