The point slope equation of the line that passes through the points (-4,8) and (4,4) is x + 2y = 12 .
The point slope form of the line passing through the points (x₁,y₁) having slope as m is given by the formula .
y-y₁ = m(x-x₁)
In the question ,
it is given that
the required line passes through the points (-4,8) and (4,4) ,
So , the slope(m) is = (4-8)/(4-(-4)
= -4/8
= -1/2
the equation of the line passing through (4,4) and slope as -1/2 in the point slope form is
(y-4) = -1/2(x-4)
y - 4 = (-x + 4)/2
2y-8 = -x + 4
x + 2y = 12
Therefore , The point slope equation of the line that passes through the points (-4,8) and (4,4) is x + 2y = 12 .
The given question is incomplete , the complete question is
Write the point slope equation of the line that passes through the points (-4,8) and (4,4) .
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Answer:
y - 4 = -1/2 (x-4)
Step-by-step explanation:
thats the answer on khan
the temperature outside must be between 32 degrees Fahrenheit is 95 degrees Fahrenheit and inclusively for students for students to be allowed to play outside during recess at an elementary school.write the compound inequality to show the temperature that are within the given range
The compound inequality which correctly shows the temperatures that are within the given range is; 32°F ≤ T ≤ 95.
What is the compound inequality which shows the temperatures that are within the given range?It follows from the task content that the temperature outside is said to be between 32 degrees Fahrenheit and 95 degrees Fahrenheit and inclusively.
On this note, it follows from the statement above that the upper limit of the temperature is; 95°F while the lower limit is; 32°F.
Therefore, the required compound inequality is;
32°F ≤ T ≤ 95.
Ultimately, the required compound inequality which shows the temperature that are within the given range is; 32°F ≤ T ≤ 95.
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What is the equation of the graph?
The required equation of the graph is y = x - 1.
How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)
What is the y-intercept for a given line?
When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0.
What is the general equation of a line?
The equation for a standard line is y = mx + c, where m is the slope and c is the y-intercept.
Given, the line passes through the points (-1, 0) and (0, 1).
Also, the y-intercept for the line = c = -1
Now, using the formula established in the literature, we get:
slope = m = (y₂ - y₁)/(x₂ - x₁) = (1 - 0)/(0 - (-1)) = 1/1 = 1
y-intercept = c = -1
Therefore, equation of the standard line is y = mx + c, thus y = (1*x) + (-1)
Thus, the required equation of the graph is y = x - 1.
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we have a dataset of household income, with mean 80,000 and median 50,000 and standard deviation 40,000.we standardize this dataset by calculating the z-scores (the standard scores). a datapoint is mapped to number 2.5 in the standardized dataset. how much was the income of this household?
The income of the household having mean 80,000 and standard deviation 40,000 is 1,80,000
The mean of the Household income = 80,000
The median of the Household income = 50,000
Standard deviation of the household income = 40,000
Z- score of these household income = 2.5
Thus , the income of the household can be calculated by using the normal distribution formula
Z = (X - μ) /σ
where X is the income of the household
μ is the mean of the household income
σ is the standard deviation of the household income.
So, we can re-write this equation as
X = Zσ + μ
Now, let us substitute the known values in the above equation , we get
X = 2.5(40,000) + 80,000
X = 1,00,000 + 80,000
X = 1,80,000
Therefore, the income of the household is 1,80,000 .
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Measure of angle 1 = 110 degrees. You only need to type 110.
The unknown angles are as follows:
∠1 = 110°∠2 = 70°∠3 = 110°∠4 = 70°∠5 = 110°∠6 = 70°∠7 = 110°∠8 = 70°How to find angles?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, linear angles, alternate angles etc.
Therefore,
∠1 = 110 degrees(given)
∠2 = 180 - 110 (sum of angles on a straight line)
∠2 = 70°
∠3 = ∠1 (vertically opposite angles)
Vertically opposite angles are congruent.
Therefore,
∠3 = 110°
∠2 = ∠4 (vertically opposite angles)
∠4 = 70°
∠1 = ∠5 (corresponding angles)
Corresponding angles are congruent
∠5 = 110°
∠6 = ∠4(alternate angles)
Alternate angles are congruent.
∠6 = 70°
∠1 = ∠7 (alternate exterior angles)
∠7 = 110°
∠2 = ∠8(alternate exterior angles)
∠8 = 70°
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What point is located at (4, 1)?
Answer:
Step-by-step explanation:
I think it might be C
but I'm sorry if I'm wrong
on a bike trip across the united states rodney notes that he covers about 190 miles every 4 if he continues at this rate use a ratio table to determine about how man miles he could bike in 6 days
In 6 days 285 miles can be travelled.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
190 miles cover in 4 days.
let x miles travelled in 6 days
So, using proportion
190/4 = x/6
190 x 6 = 4x
4x= 1440
x= 285 miles.
Hence, in 6 days 285 miles can be travelled.
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HELP PLEASE!!!!!!!
A rectangle is 32ft by 8ft. Ross dilated the rectangle and the dimensions of the image were 80ft by 20ft. What was the scale factor used?
The scale factor of the dilation = 2.5
The original dimensions of the rectangle:
Length = 32 ft
Width = 8 ft
The dimensions of the rectangle after dilation:
Length = 80 ft
Width = 20 ft
Dilation is a transformation where the dimensions of the figure is enlarged by multiplying with a number. This number multiplied with all dimensions of the original figure is called its scale factor.
So the new dimension of the figure will be scale factor times the original dimensions of the figure.
Thus the scale factor can be defined as the ratio of larger dimension to the smaller dimension of a figure.
Hence the scale factor used here is the ratio of new length to the original length or the ratio of new width to the original width of the rectangle.
That is, scale factor = 80/32 = 20/8 = 2.5
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The quadratic 3x^2+4x-9 has two real roots. What is the sum of the squares of these roots? Express your answer as a common fraction in lowest terms.
If the quadratic [tex]3x^2[/tex]+4x-9 =0 has two real roots, then the sum of the square of the these roots is 7.77
The polynomial is [tex]3x^2[/tex]+4x-9 =0
Here,
a = 3
b = 4
c = -9
Here the quadratic equation
= [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
Substitute the values in the quadratic equation
= [tex]\frac{-4+/-\sqrt{4^2-4(3)(-9)} }{2(3)}[/tex]
The result will be
= [tex]\frac{-2+/-\sqrt{31} }{3}[/tex]
Therefore, the roots are
[tex]\frac{-2+\sqrt{31} }{3}[/tex] and [tex]\frac{-2-\sqrt{31} }{3}[/tex]
Square of the first root = [tex](\frac{-2+\sqrt{31} }{3} )^{2}[/tex]
= 1.414
Square of the second root = [tex](\frac{-2-\sqrt{31} }{3} )^2[/tex]
= 6.363
The sum of the square of the roots = 1.414+6.363
= 7.77
Hence, if the quadratic [tex]3x^2[/tex]+4x-9 =0 has two real roots, then the sum of the square of the these roots is 7.77
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Jai is 1.45 meters tall. At 11 a.m., he measures the length of a tree's shadow to be
39.55 meters. He stands 34.1 meters away from the tree, so that the tip of his shadow
meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
오ㅜ
39.55 m-
(Diagram is not to scale.)
1.45 m
34.1 m-
By using triangles laws, we know that the height of the tree is 8.42 meters.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.So, 1.45 m is Joshua's height.
Tree shadow length: L=31.65 mJoshua's distance from the tree is 26.2 meters.We must ascertain the tree's height.
BC = 26.2 mBD = 31.65mCD = BD-BCCD = 31.65-26.2=5.45 mEC = 1.45 mThe right triangles are all alike.
The ratio of the corresponding sides is equal when two triangles are comparable.
△ABD ≈ △ECDAB/EC = BD/CDNow, put values as follows:
AB/1.45 = 31.65/5.45AB = 31.65 × 1.45/5.45AB = 8.42mTherefore, by using triangles laws, we know that the height of the tree is 8.42 meters.
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The correct form of the question is given below:
Joshua is 1.45 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 31.65 meters. He stands 26.2 meters away from the tree so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Please I need help right now
A mathematical function is a mathematical relationship where each input value (x) has a unique output value (y), which means that it is a relationship where every individual value for the independent variable always results in a specific predictable value for the dependent variable.
What is meant by mathematical function?A mathematical function is a mathematical relationship where each input value (x) has a unique output value (y), which means that it is a relationship where every individual value for the independent variable always results in a specific predictable value for the dependent variable.
The exact same number of elements from Y are assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A mathematical phrase, rule, or law that establishes the relationship between two variables, one of which is independent and the other dependent (the dependent variable)
The complete question is:
What is a mathematical function? After studying the vending machine examples, write a definition that communicates precisely what it means for a mathematical relationship to be a function.
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Two exponential functions, f(x) and g(x), are graphed on the same coordinate plane. Graph of f of x equals 2 to the x power going through points 0 comma 1 and 1 comma 2 and graph of g of x equals 2 to the x power plus 4 going through points 0 comma 5 and 1 comma 6. What effect does adding 4 to the parent function have on the transformed function? a Adding 4 to the parent function shifts the function down four units. b Adding 4 to the parent function shifts the function up four units. c Adding 4 to the parent function shifts the function right four units. d Adding 4 to the parent function shifts the function left four units.
Answer:
b Adding 4 to the parent function shifts the function up four units.
Step-by-step explanation:
The original function is y(x) = 2^x
Adding four is y(x) = 2^x + 4
We've simply told y to take whatever value is generated for x and add four to it.
So the new value for the same x would have 4 added to y: (x,y+4),
Point (1,2) would shift to point (1,6).
Adding four to the parent function will shift the entire graph up by 4. See ate attached graph.
3.7416573868 to nearest tenth
Explanation:
The tenths decimal place is right after the decimal point
7 is in the tenths place
The digit just to the right of 7 is 4
Since the 4 is not 5 or larger, this means we erase everything after the 7 and go with 3.7
If we had something like 3.76, then the 7 bumps up to 8 to get 3.8
i'll give brainliest
Answer:
-40
Step-by-step explanation:
10/1*(-4) Set up equation
10/1 * -4 Open up parentheses
10/1 =10 Next, divide 10 by 1
10*-4 Now, multiply 10 and -4
-40 Answer
Answer:
-40
Step-by-step explanation:
Given expression
[tex]\dfrac{10}{1} \cdot (-4)[/tex]
When dividing and multiplying, follow the order of operations and work from left to right.
Divide the numbers
When dividing anything by 1, the quotient is the numerator:
[tex]\implies \dfrac{10}{1} \cdot (-4)=10 \cdot (-4)[/tex]
Multiply the numbers
When multiplying a positive number by a negative number, the product is always negative:
[tex]\implies 10 \cdot (-4)=-40[/tex]
Question 9
The preimage of M(-3,-5) under a translation is M'(6, -1).
Using the same translation, find the image of B', if B is (3,-2).
B'
By using the same translation applied to point M, the image of point B' is equal to (12, 2).
What is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure (object) in the same direction, as well as for the same distance.
Since the x-coordinate moved from a negative to a positive sign, we know that point M was translated to the right and then shifted down because it moved from a negative to a negative sign on the y-coordinate.
Next, we would determine the translation rule that was applied to point M:
(x, y) → (x + n, y - z)
-3 + n = 6
n = 6 + 3
n = 9.
-5 - z = -1
z = -5 + 1
z = -4
Now, we can determine the image of B':
(x, y) → (x + n, y - z)
Point B (3, -2) → Point B' (3 + 9, -2 - (-4)) = (12, 2).
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Help pls
Explain how to simplify ((a^3)^4)^-2 using the properties of exponents.
Answer: a^24
Hope this helps you!
graph this function f(x) = -7x - 64
The graph of the function f(x) = -7x - 64 will be a straight line.
A function may be defined as an expression in which for every input variable x there is only one output variable y. The input variable is called independent variable and output variable is called dependent variable. The function f(x) = -7x - 64 is in the form of linear equation in one variable as it is expressed in the form of f(x) = ax + b where a, b are coefficients and x are the independent variable. When we plot this function, we compare it from the slope intercept form of line that is y = mx + c where m is slope and c is y intercept. It will be a straight line having a negative slope which is equal to -7 and the y intercept will be equal to -64 as compared from slope intercept form. The graph of the function plotted is attached below. For x intercept we put f(x) = 0, so we get x intercept equal to -64/7. Coordinates of x intercept is (-64/7, 0) and that of y intercept is (0, -64).
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Look at this set of ordered pairs:
(7, -17)
(5,3)
(7,3)
Is this relation a function?
yes
no
The given relation is not a function.
What is function?
A function is a relationship between inputs where each input is related to exactly one output.
Given that, (7, -17) , (5. 3) , (7, 3)
Here 7 is connected with two elements i.e. -17 and 3 but the condition of a function is that one element must be related to only one element of another set.
Hence, the given relation is not a function.
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PLS HELP!!!
Zane deposited $3,000 in an account earning 11% interest compound annually. To the nearest cent, how much will he have in 4 years?
Answer:4554.21
Step-by-step explanation:
Write the word sentence as an inequality.
A number b multiplied by -5 is at most -30
The word sentence as an inequality phrase is -5[tex]\leq[/tex]30.
What is the inequality phrase?
An algebraic statement that uses the symbols less than (), less than or equal to (), larger than (>), or greater than or equal to () in place of the equal sign (=) is known as an inequality equation. How do you work out mathematical inequalities? Similar to how equations are solved, inequalities may be resolved by separating the variable and combining like terms.
Different types of inequalities
Equations that are linear
When the variables' highest exponent is power 1, inequality is said to be linear.
Triangle inequalities
A quadratic inequality is one in which the largest exponent is power 2, which is present in the inequality.
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What is the y-intercept of the equation 4x + 5y = 20?
(0, 4)
(0, 5)
(4, 0)
(5, 0)
Answer:
(0,5)
Step-by-step explanation:
Answer:
(0, 4 )
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4x + 5y = 20 ( subtract 4x from both sides )
5y = - 4x + 20 ( divide through by 5 )
y = - [tex]\frac{4}{5}[/tex] x + 4 ← in slope- intercept form
with y- intercept c = 4 or in coordinate form (0, 4 )
How many subsets does the set (1,2,3) have
Answer:
Answer down below!
Step-by-step explanation:
The set (1, 2, 3) would have 8 sets in total
A simple random sample of size n is obtained from a population that is skewed left with and. Does the population need to be normally distributed for the sampling distribution of to be approximately normally distributed? why? what is the sampling distribution of ?.
Normal distributions are frequently employed in the natural and social sciences to describe real-valued regressors with uncertain distributions, normal distributions are essential to statistics.
The central limit theorem is one reason they are significant.
This claim argues that, in some circumstances, the average of many samples (observations) of a random variable with finite variance and mean is itself a random variable, whose distribution tends to become normal with an increase in sample size. Because of this, distributions of physical quantities that are meant to be the culmination of multiple separate processes, such as error margins, frequently resemble normal distributions.Only the normal distribution has additional cumulants after the first two that are zero. It is also the continuous distribution with the highest level of entropy for a given mean and variance. Assuming that the mean and variance are finite, Geary has shown that the normal distribution is the only distribution in which the mean and variance calculated from a collection of independent drawings are independent of one another.The normal distribution is a form of elliptical distribution. The normal distribution is symmetric about its mean and non-zero over the whole real line. Consequently, it could not be an appropriate model for variables that are inherently positive or highly skewed, such as a person's weight or the value of a share.To learn more about normal distribution visit:
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Jeremy Charges his neighbors $15.00 to wash their car. Howmany cars must he wash next summer if his goal is to earn at least $2000?
Answer: 134 cars
Since Jeremy charges $15.00 per car and he plans to earn at least $2000, if we let 'x' be the number of cars, we will have:
[tex]15x=2000[/tex]Solving for x:
[tex]\begin{gathered} 15x=2000 \\ x=\frac{2000}{15} \\ x=133.33 \end{gathered}[/tex]Since cars can only be counted as whole numbers, Jeremy would need to wash 134 cars to earn at least $2000
Boris's art class is 8 hours long. How long is his class in minutes?
Answer:
480 minutes
Step-by-step explanation:
that's your answer
Answer:
480 minutes.
Step-by-step explanation:
8×60=480.
What common factor of 10 and 14 can you use to write in simpler form?
Answer:
1 and 2
and the greatest common divisor is 2
Johnathan is hosting a barbeque for 7 of his friends. He wants to buy twice as many sausages as burgers and the same number of buns as sausages and burgers combined.
Buns come in a packet of 6
Sausages come in a pack of 10
Burgers come in a pack of 8.
What is the smallest number of packets of buns that Johnathan could buy?
The smallest number of packets of buns that Jonathan could buy is 4.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
We have,
Buns come in a packet of 6
Sausages come in a pack of 10
Burgers come in a pack of 8.
Sausage = 2 x burgers ____(1)
Buns = Sausages + Burgers _____(2)
The smallest number of packets of buns can be calculated when only one packet of Burgers is bought.
So,
Burgers = 1 pack = 8
From (1) and (2),
Sausage = 2 x 8 = 16
Buns = 16 + 8 = 24
Buns = 24
This can be put in 4 packets.
Thus,
The smallest number of packets of buns that Jonathan could buy is 4.
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Two parallel lines are cut by a transversal. Suppose <1 and <2 are alternate interior angles and that m<1=4(x+2) and m<2=2x+24. What is the m<2?
The value of m∠2 will be equal to 40°.
Transversal may be defined as a line which cuts two different lines which lie on the same plane at two different points. Alternate interior angles may be defined as the angles which are formed when a transversal cut the two different lines. These angles lie on the interior of the parallel lines, but they are on the opposite side of the transversal. If two parallel lines are cut by a transversal, then their alternate interior angles are equal. Thus, m∠1 = m∠2
4(x + 2) = 2x + 24
4x + 8 = 2x + 24
2x = 16
=> x = 16/2
=> x = 8
Now, m∠2 = 2x + 24
m∠2 = 2×8 + 24
m∠2 = 40° which is the required answer.
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Evaluate compositions of function. Let f(x) = 3x + 2, g(x) = -x2, and h(x) = x-2/5. Find the indicated value. (SHOW WORK PLEASE))
The indicated numeric values for the composite functions are given as follows:
1. f(g(-3)) = -25.
2. g(f(2)) = -64.
3. h(f(-5)) = -3.
4. g(g(-3)) = -81.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is according to the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function. Hence, to calculate f(g(-3)), for example, we calculate g(-3), then we calculate the numeric value of function f(x) at x = g(-3).
For this problem, the functions are given as follows:
f(x) = 3x + 2.g(x) = -x².h(x) = (x - 2)/5.For item 1, the numeric values are found as follows:
g(-3) = -(-3)² = -9.f(g(-3)) = f(-9) = 3(-9) + 2 = -27 + 2 = -25.For item 2, the numeric values are found as follows:
f(2) = 3(2) + 2 = 6 + 2 = 8.g(f(2)) = g(8) = -(8)² = -64.For item 3, the numeric values are found as follows:
f(-5) = 3(-5) + 2 = -15 + 2 = -13.h(f(-5)) = h(-13) = (-13 - 2)/5 = -3.For item 4, the numeric values are found as follows:
g(-3) = -(-3)² = -9.g(g(-3)) = g(-9) = (-9)² = -81.More can be learned about composite functions at https://brainly.com/question/10687170
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Match the financial activities to their relevant management type within the wealth management phase. (Cash management or Credit and debt management)
keeping an emergency
fund
reducing credit use
spending plans
stop credit misuse
debt reduction
cash reserve
recording income and
spending
paying off credit cards
Each financial activities should be matched to their relevant management type within the wealth management phase as follows:
Cash management:
Keeping an emergency fund.Spending plans.Cash reserve.Recording income and spending.Credit and debt management:
Reducing credit use.Stop credit misuseDebt reduction.Paying of credit cards.What is wealth management?Wealth management can be defined as an investment advisory service that is designed and developed to provide advices and solutions to meet the needs of a wide array of affluent clients, especially by combining other financial services.
The phases of financial activities.Generally speaking, there are three (3) distinct phases of a person's financial activities and these include the following:
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Answer:
Cash management:
- keeping an emergency fund
- spending plans
- cash reserve
- recording income and spending
Credit and debt management:
- paying off credit cards
- stop credit misuse
- reducing credit use
- debt reduction
Step-by-step explanation:
correct on plato
Maria buys n pencils that cost p each, she pays with a $y note find in terms of n, p and y, the amount of change maria recieves. give your answer in cents
The amount of change Maria receives is 100y - np
What is Conversion rate ?
A conversion rate is the ratio between two currencies, most commonly used in foreign exchange markets, which designates how much of one currency is needed to exchange for the equivalent value of another currency.
Given,
The cost of each pencil is = p
Maria buys = n pencils
so, the cost of n pencils is = np
She pays for the n pencils is = $y
Now, in question given that we need to find answer in cents
so, We know 1$ = 100 cents
By that, $y = 100y
Maria received the change is = 100y - np
Therefore, the amount of change Maria receives is 100y - np
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