3 Quick algebra 1 Questions for 50 points!
For (lovetthannah9) or anyone who knows the answer! :)
Answers
Answer:
Step-by-step explanation:
6. The rate of change is essentially the slope. But in other words, it's how much the y changes as x increases by 1. If this rate of change is 0, that means the y-value is constant, while the x can be any real number. It can be generally given in the formula: y=b, which comes from simplifying the slope-intercept form: y=(0)x+b = b. You can also derive the same thing for a point-slope form: y-a = 0(x-b)=0 so y=a. In both cases, y is equal to some constant value. So graphing this makes a horizontal line.
7. To define a parallel line, you need the same slope, and a different y-intercept, which is under the assumption that the line has a slope that is definable. If the slope is definable, you'll have the equation: y=mx+b, where m is the same as the other line. Then you plug in the known values as x and y, to solve for b, which is the y-intercept. Now if the line is a vertical line, a parallel line can be defined as: x=a, where a doesn't equal the constant, the other vertical line is equal to. To make it pass through some point (c, d). Then you would simply set x=c, since the x is the only thing that matters, since the y-value is all real numbers, so it will eventually have the y-value d somewhere on the line.
8. To define a perpendicular line, you get the reciprocal of the slope and change the sign. So if the slope is: [tex]\frac{a}{b}[/tex] then it becomes [tex]-\frac{b}{a}[/tex] and vice versa depending on the sign. In this example, let's just say m=a/b, then the perpendicular slope would be -b/a. You can then plug this into the slope-intercept formula: [tex]y=-\frac{b}{a}+c[/tex] where c is the y-intercept. Then you plug in the known point as (x, y) and solve for c, the y-intercept. Now let's say for example that you have a vertical line: x=a. In this case you can see the slope as: [tex]\frac{1}{0}[/tex][tex]\frac{y_2-y_1}{a-a}[/tex]. Of course this isn't definable, but if you take the reciprocal you get something that is: [tex]-\frac{0}{y_2-y_1}[/tex] which will always evaluate to 0. This means you get a horizontal line, since the slope is 0. This means if you have a vertical line, any horizontal line should be perpendicular, which makes sense, since it should form a 90 degree angle when they intersect, because they're straight lines. To make sure that horizontal line passes through the point (b, c), you simply set the y equal to c. So y=c, will pass through (b, c), since the c is constant, and the x can equal anything so somewhere on the line it will intersect (b, c). But let's say we had a horizontal line, the reciprocal can be defined as: [tex]\frac{a-a}{x_2-x_1}[/tex] where a is the y constant. If you take the reciprocal, then you have a-a in the denominator, which gives you an undefined slope, because the perpendicular line to a horizontal line, is a vertical line. To ensure this perpendicular line passes through the point (b, c). You simply set x equal to b. so that x=b.
#6
y=mx+cif m is 0
y=c is the EquationHence line is parallel to x axis
#7
parallel lines have equal slopes
so we can use the point slope form of line to find the equation
y-y_1=m(x-x_1)#2
Same process like no 7 but
slope of perpendicular line is negative reciprocal of given line's slope
Related Questions
The graphs of f(x) and g(x) are shown below:
Graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 5, 0.
If f(x) = (x + 7)2, which of the following is g(x), based on the translation? (1 point)
g(x) = (x + 9)2
g(x) = (x + 5)2
g(x) = (x − 9)2
g(x) = (x − 5)2
Answers
Answer: [tex]g(x)=(x-5)^2[/tex]
Step-by-step explanation:
The graph of g is the graph of f translated 2 units to the right, so its equation is [tex]g(x)=(x-5)^2[/tex]
Just an easy question for 100 Points!
Check my other easy 100 point questions :)
Answers
#1
y=x+5
Shifted 5units left#2
y=3/8
Horizontally Streched by a factor 8/3 parallel to x axis#3
y=-x-2Reflection by y axis as x will be negative and shifting 2 units right
#4
y=6x+1
vertically streched by a factor 6 and shifting 1 units left#5
y=x-11
Shifting 11 units left#6
y=8x
Horizontally streched by 1/8 factor
Answer:
1. Translated 5 units left.
2. Vertical stretch by a factor of 3/8.
3. Reflection in the x-axis, then translated 2 units down.
4. Vertical stretch by a factor of 6, then translated 1 unit up.
5. Translated 11 units down.
6. Vertical stretch by a factor of 8.
7. Vertical stretch by a factor of 1/3, then reflection in the x-axis.
Step-by-step explanation:
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]
[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}.[/tex]
[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}.[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.[/tex]
Parent function:
[tex]y=x[/tex]
[tex]\textsf{1.} \quad y=x+5[/tex]
Translated 5 units left.
[tex]\textsf{2.} \quad y=\dfrac{3}{8}x[/tex]
Vertical stretch by a factor of 3/8.
[tex]\textsf{3.} \quad y=-x-2[/tex]
Reflection in the x-axis, then translated 2 units down.
[tex]\textsf{4.} \quad y=6x+1[/tex]
Vertical stretch by a factor of 6, then translated 1 unit up.
[tex]\textsf{5.} \quad y=x-11[/tex]
Translated 11 units down.
[tex]\textsf{6.} \quad y=8x[/tex]
Vertical stretch by a factor of 8.
[tex]\textsf{7.} \quad y=-\dfrac{1}{3}x[/tex]
Vertical stretch by a factor of 1/3, then a reflection in the x-axis.
1. Try It # 1 A company sells doughnuts. They incur a fixed cost of $25,000 for rent, insurance, and other expenses. It costs $0.25 to produce each doughnut.
b. Find and interpret the y-intercept.
Answers
Answer:
The y-intercept is 25000 . The intercept is the fixed cost of the doughnut selling company.
Step-by-step explanation:
In the question, it is given that the fixed cost is $25000 and the expense to produce each doughnut is $0.25.
It is required to find and identify the y intercept.
To do so, use the equation derived in previous part of the exercise to interpret the slope. Compare the equation with standard equation of the line.
Step 1 of 1
The total cost of the company is the sum of fixed cost and the expenses for the doughnut, C=0.25x+25000.
Compare the equation with general linear equation y=mx+c.
The y-intercept is 25000 .
The intercept is the fixed cost of the doughnut selling company.
Suppose that 15% of the population of a country are unemployed women, and a total of 25% are unemployed. What percent of the unemployed are women
Answers
The percentage of unemployed women from the total percentage of unemployed is 60%
PercentagePercentage of unemployed women = 15%Total percentage of unemployed = 25%Percentage of the unemployed women from the total unemployed = 15% / 25% × 100
= 0.60 × 100
= 60%
Therefore, the percentage of unemployed women from the total percentage of unemployed is 60%
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A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards are red on both sides. You pick a card uniformly at random from the box and look at a random side. Given that the side you see is red, what is the probability that the other side is red
Answers
The probability that both sides of the card is red is 0.33
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that both sides of the card is red = total number of cards in which both sides are red / total number of cards
2/6 = 1/3 = 0.33
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Parallel lines q and q are cut by transversal r forming 4 angles at each intersection. At the intersection of lines r and q, clockwise from top left, the angles are: 1, 2, 4, 3. At the intersection of lines r and s, clockwise from top left, the angles are: 5, 6, 8, 7.
Use the diagram to complete the statements.
Angles 1 and 5 are
because they are
angles.
Angles 4 and 6 are (blank)
because they are (blank)
angles.
Answers
The complete statements for the angles as in the task content are:
Angles 1 and 5 are congruent because they are corresponding angles.Angles 4 and 6 are congruent because they are alternate angles.Which statements about the angles are correct?It follows from the task content that the arrangement involves two parallel lines q and s which are cut by transversal line r.
On this note, according to the description in the task content, the angles formed at the intersections are related as follows;
Angles 1 and 5 are congruent because they are
corresponding angles.
Angles 4 and 6 are congruent because they are alternate angles.
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Total area=
Help please thanks you
Answers
Answer: 94
Step-by-step explanation:
The area of each of the top and bottom face is [tex](4)(6)-(2)(2)=20[/tex].
The area of each of the side faces is 12.
The area of each of the faces facing out is 6.
The area of each of the 3 'inner' faces is also 6.
Adding these together,
[tex]20(2)+12(2)+6(2)+6(3)=94[/tex]
The distance between earth and moon is 384000000 m. this distance can be expressed as ____m
Answers
This distance can be expressed as 3.84× [tex]10^{8}[/tex] m.
What is distance with example?
Distance is a scalar quantity. The distance of an object can be defined as the complete path travelled by an object.Given the distance between the earth and the moon is 384000km
Representing in exponential notation,
=384000×1000m [∵1km=1000m]
=384× [tex]10^{6}[/tex] m
=3.84× [tex]10^{8}[/tex] m
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The correct question is -
The distance between the Earth and the moon is approximately 384000 km. this distance can be expressed as ____m.
math!! please helpp!!!
What is the y intercept of the line below?
( i attached an image)
a) -3
b) 1/3
c) 4
d) (-1.5,0)
e) -1.5
f) (4,0)
g) 3
Answers
Answer:
C
Step-by-step explanation:
The exact point should be (0, 4) if you're looking for the Y intercept. I'm assuming that each square represents one unit. Hope I could help.
Answer:
c)4
Step-by-step explanation:
Hope it helps!!!
y= 4
x= 0
A 2-column table with 7 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries 15, 0, 3, 0, negative 3, 0, 15.
Predict which statements are true about the intervals of the continuous function. Check all that apply.
f(x) > 0 over the interval (−, 3).
f(x) ≤ 0 over the interval [0, 2].
f(x) < 0 over the interval (−1, 1).
f(x) > 0 over the interval (–2, 0).
f(x) ≥ 0 over the interval [2, ).
Answers
The true statements about the function are:
f(x) ≤ 0 over the interval [0, 2].f(x)>0 over the interval (-2,0)f(x) ≥ 0 over the interval [2,∞)How to determine the true statement?The complete question is in the image
From the table, the function values do not exceed 0 at the interval 0 to 2.
This means that f(x) ≤ 0 over the interval [0, 2].
Also from the table, the function values exceeds 0 at the intervals greater than -2 but less than 0
This means that f(x)>0 over the interval (-2,0)
Also from the table, the function values are at least 0 at the intervals greater than 2
This means that f(x) ≥ 0 over the interval [2,∞)
Hence, the true statements are (b), (d) and (e)
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Which value of a in the exponential function below would cause the function to shrink? f(x) = a(three-halves) superscript x
Answers
The value of a in the exponential function is 4/5.
Given the exponential function is f(x)=a(3/2)ˣ.
An function may be a mathematical relation of the subsequent form: f(x)=aˣ. where x may be a variable, and a could be a constant called the exponential of the function.
When multiplying the any function by a constant, we may expand or shrink the function in the y-direction.
y=a(b)ˣ
If a>1 then the function will enlarge.
If a<1 then the function will shrink.
When a=4/5
Then 4/5<1 means the function would shrink.
When a=5/4
Then 5/4>1 means the function would enlarge.
When a=3/2
Then 3/2>1 means the function would enlarge.
When a=7/4
Then 7/4>1 means the function would enlarge.
Hence, the given function f(x)=a(3/2)ˣ would shrink when a=4/5.
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Answer:
4/5
Step-by-step explanation:
got it right
If (4x-y,x-4y):(3,-3y) then find the value of x and y? please help me!
Answers
Answer:
x=1y=1Step-by-step explanation:
This looks like it is intended to represent two equations. They can be solved as a system in any of the usual ways.
The two equations seem to be ...
4x -y = 3x -4y = -3ySolutionAdding 4y to the second equation gives ...
x -4y +4y = -3y +4y
x = y . . . . . . . . simplify
Substituting for y in the first equation gives ...
4x -x = 3
3x = 3 . . . . simplify
x = 1 . . . . . divide by 3
y = 1 . . . . . same as x
The variables x and y both have a value of 1.
__
The attachment shows a graphical solution to these equations.
PLEASE HELP
place the figure in a coordinate plane and find the indicated length
an isosceles triangle with a base length of 60 units and a height of 50 units; find the length of one of the legs
Thanks
Answers
The length of one of the legs says line AC is 58.31.
How do we place a figure in a coordinate plane?A figure can be placed in a coordinate plane on the graph by determining the coordinate of the vertices.
For the given isosceles triangle with:
The base length of 60 units and A height of 50 units.The coordinate of the vertices are:
∠A = (0,0)∠B = (60, 0)∠C = (30, 50)The length of one leg is calculated as follows:
[tex]\mathbf{AC= \sqrt{(50-0)^2+(30-0)^2}}}[/tex]
AC = [tex]\mathbf{\sqrt{2500+900}}[/tex]
AC = [tex]\mathbf{\sqrt{3400}}[/tex]
AC = 58.31
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A post office always charges a flat one-time fee for any order. One time, Michael sent 35 letters and paid $26.00. The next time, he sent 18 letters and paid $14.10. How much does the post office charge to send one letter? What is the flat fee?
Answers
Answer:
$0.70 per letter, $1.50 flat fee
Step-by-step explanation:
Let x be the flat fee.
Let y be the cost of sending 1 letter.
Lets create 2 equations from those 2 instances.
First Instance: x + 35y = 26 - Equation 1
Second Instance: x + 18y = 14.1 - Equation 2
To find x and y , we can use elimination method in solving simultaneous equations.
Equation 1 - Equation 2
x - x + 35y - 18y = 26 - 14.1
17y = 11.9
y = [tex]\frac{11.9}{17} \\[/tex]
= $0.70
Now we substitute y into equation 1.
x + 35(0.70) = 26
x + 24.50 = 26
x = 26 - 24.50
= $1.50
From the above we know the post charges $0.70 per letter sent and charges $1.50 flat fee.
The grocery store charges a retail price of $6.99 for a 24-pack of juice boxes. If it is wholesale, the prices are presented on the graph below. What is the difference between the retail and wholesale unit
price
Answers
The difference between the retail and wholesale unit price is $ 0.99.
What is retail price?The retail price is the price that the item is sold for to the customer.
Here,
Coordinates extracted from the graph;
(4, 1) (12, 3)
Equation of straight line (Whole sale price)
(y - y₁) = m(x - x₁)
where, m = (y₂-y₁)/(x₂-x₁)
then, m = (3-1) / (12-4)
= 2/8
= 1/4
Now, (y - 1) = 1/4 (x - 4)
4y - 4 = x - 4
x = 4y
x - 4y = 0
Now, whole sale price for 24 boxes; x = 24
24 - 4y = 0
4y = 24
y = 24/4
y = 6
The wholesale price = $ 6
The retail price = $ 6.99
The difference between retail and wholesale = Retail - Wholesale
= 6.99 - 6
= $ 0.99
Thus, the difference between the retail and wholesale unit price is $ 0.99.
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The problem involves a conversion from feet to miles. How many feet are in one mile? Use the Internet or another resource if you need help.
Answers
The value of the 1 mile is equal to 5280 feet
We have given that,
The problem involves a conversion from feet to miles.
We have to determine how many feet are in one mile.
What is the conversion form?
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
1 mile is equal to 5280 feet
Therefore we get,
1mile=5280 feet.
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HELP ASAP PLEASE!!))
Find the area (in square units) of the circle with center O and radius 12 units long. Round your answer to the nearest whole number. (Enter only a number as your answer .)
Answers
To calculate the area of a circle, we use the formula : [tex]\pi r^{2}[/tex], where r is radius.
We replace the numebrs : 144[tex]\pi[/tex] = 452,389342.... = 452 (rounded)
So, the area of this circle is 452 (and whatever units)
Answer:
Area of circle = 452 units²
Step-by-step explanation:
We can use the following formula to calculate the area of a circle:
Area = π r²
where r = radius of circle (12 units)
Substituting into the formula:
Area = π × (12)²
= π × 144
= 452.39
= 452 units² (rounded to the nearest whole number)
You have a spinner that generates random numbers that are uniform between 0 and 1. You sum the spins until the sum is greater than one. What is the expected number of spins
Answers
These are the expected numbers of spins that is P(N=n)=n−1/n!
According to the statement
Let N is the number of spins AND
Let S is the sums of spins until the sum is greater than one.
we know that the For N=1, P(S) = 0.
The value of expected random variables are
E(X)=μ=∑xP(x).
Put all the integers values in it and integrate.
According to statement condition the expected number of variables become
P(N=n)=P(Sn−1<1≤Sn)
P(N=n)= P(Sn−1 < 1) - P(Sn <1)
P(N=n)=1/(n−1)!−1/n!
P(N=n)=n−1/n!
So, these are the expected numbers of spins that is P(N=n)=n−1/n!
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Un grupo de compañeros juegan canicas, cada uno de los 5 jugadores tiene 2 canicas y dicen que estas representan los factores de la descomposición del total de canicas. ¿Cuantas canicas tiene entre todos los jugadores en total?
Answers
Si cada jugador tiene un total de 2 canicas y hay 5 jugadores, se espera que el número total de canicas sea 10.
¿Cómo encontrar el número total de canicas?Multiplica el número de canicas por el de jugadores:
Número de canicas: 2Número de jugadores: 52 x 5 = 10 canicas.¿Cómo se puede descomponer este factor?Este factor se puede descomponer así:
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What is the only way to increase power of a significance test when lowering the probability of committing a Type I error
Answers
the probability of making a Type I error is equal to the significance level of power. To increase the probability of a Type I error, increase the significance level. Changing the sample size has no effect on the probability of a Type I error.
The electricity of a take a look at can be expanded in a number of methods, for example increasing the pattern length, reducing the standard errors, increasing the difference between the pattern statistic and the hypothesized parameter, or growing the alpha degree.
The chance of creating a kind I mistakes is α, that's the extent of importance you put for your hypothesis check. An α of 0.05 indicates which you are inclined to accept a five% chance which you are incorrect whilst you reject the null hypothesis. To lower this risk, you have to use a decrease cost for α
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Student Council is selling t-shirts and hats for $21 and $14, respectively. The club needs to raise at least $2730. They have received pre-sale orders of 80 t-shirts and 40 hats. Graph a system of linear inequalities that shows the number of t-shirts and hats they must sell in order to reach their goal. Use x for the number of t-shirts and y for the number of hats.
Choose the graph that shows all the possible combinations. List two possibilities.
Answers
The required inequality is 3x + 2y > 390 and two possibilities is given by (100,45) and (80,75).
Student Council is selling t-shirts and hats for $21 and $14, respectively. The club needs to raise at least $2730.
What is inequality?Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.
Let x for the number of t-shirts and y for the number of hats.
Now,
equation for to raise at least $2730.
21x + 14y > 2730
3x + 2y > 390
Two possibility can be caroled out from the graph i,e. (100,45) and (80,75).
Thus, the required inequality is 3x + 2y > 390 and two possibilities is given by (100,45) and (80,75).
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ASAP WILL GIVE BRAINLIEST
Which do you prefer: leaving 5–√ in radical form, or converting it to a decimal? Why? When would it be useful to use each?
Your response should be 3-5 sentences long and show that you’ve thought about the topic/question at hand. Please be aware we are looking for YOUR PERSONAL OPINION and there is not a single “correct answer.”
Answers
The preference is that ✓5 should be left in radical form as an irrational number.
What is radical form?It should be noted that a radical form is illustrated when n is a positive integer that is greater than 1.
Here, a rational number is a number that can be represented in the form of p/q where p and q are integers. In this case, ✓5 will nvwe give a perfect number in decimal form. Hence, it's better to leave it radical form.
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Point X is the incenter of ΔABC.
Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X. Lines are drawn from point X to the sides of the triangle to form right angles. Line segments X F, X G, and X E are formed.
If EX = 4z + 1, XF = 2z + 7, and mABC = 44°, find the following measures.
GX =
mABX = °
Answers
The length of GX is 13 and the value of ∠ABX is 22.
We know that the point at which the triangle's three interior angle bisectors converge is known as the incenter. It can be thought of as the intersection of the triangle's internal angle bisectors. Due to the junction point of the central axis being the center of the triangle's inscribed circle, this point will be equally spaced from each of the triangle's sides. The center of a triangle's inscribed circle, which is the biggest circle that can fit inside the triangle, is known as the incenter.
Given that EX = 4z + 1 and XF = 2z + 7.
Since X is the incentre of this triangle ΔABC, EX = XF = GX.
Now, 4z + 1 = 2z + 7
i.e. 4z - 2z = 7 - 1
i.e. 2z = 6
i.e. z = 6/2 = 3
Then GX = 2 * 3 + 7 = 6 + 7 = 13
Also given that ∠ABC = 44°.
Since X is the incentre of this triangle ΔABC, ∠ABX = ∠CBX
Let ∠ABX = ∠CBX = y
Now y + y = 44
i.e. 2y = 44
i.e y = 44/2 = 22
Then ∠ABX = 22°
Therefore, the length of GX is 13 and the value of ∠ABX is 22°.
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Use AABC to find the value of cos A
(Please use photo provided)
Answers
Answer:
40/41
Step-by-step explanation:
cos = adjacent/hypotenuse
adj = 40, hyp = 41
Which of the following statements are true? Select all that apply.
Answers
To solve a simultaneous equation on a graph, it is important to:
Draw the graph of the two equationsFind the two lines that intersect at a common pointThis common point would then be used to find the solution of the pair of simultaneous equations.What is a Graph?This refers to the diagram that is used to show the relationship between variables that are measured along a pair of axes.
Hence, we can see that your question is incomplete so I gave you a general overview to help you get a better understanding of the given concept.
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I need the answers for number 9 and 10
Answers
number 10 is no, they are not congruent because x=3, so segment xy=3(3)+5 which is 14 and segment yz=9(3)/2 which is 13.5
Construct the graph of the equation given. Categorize this graph a horizontal or vertical line. Label the intercept as well as the axis on the graph.
x = -2.5
Answers
x = -2.5 is a vertical line. The vertical graph of the equation is shown in the image attached below.
What is the Equation of a Vertical Line?The slope of a vertical line is undefined, therefore, the equation of a vertical line is expressed as x = a, where a is the x-intercept.
Given x = -2.5, the equation suggests it is a vertical line, where the line intercepts the x-axis at -2.5, which is the x-intercepts.
Thus, the graph for x = 2.5 is shown in the diagram below.
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Select the correct answer from each drop-down menu. The slope of the line in the graph is . The y-intercept is . The equation of the line is y = x .
Answers
The line with an equation of y = x have a slope of 1 and y intercept of 0.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard equation of a line is given as:
y = mx + b
Where m is the slope of the line and b is the y intercept.
The line with an equation of y = x have a slope of 1 and y intercept of 0.
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PLEASE HELPPP I REALLY NEED IT ASAP :C
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Answers
Answer:
D
Step-by-step explanation:
quadratic formula
Answer:
I hope this is helpful. I had done my calculations and got the answer. The last part in orange is the answer. Your going to have to simplify.
67 of the 645 parcels are damaged on the journey.
Calculate the percentage of parcels that are damaged.