The slope and one point on the line are given. Find the equation of the line (in slope-intercept form).(1/4, -4) ; m = -3 y=
Answers
Answer
y = -3x - 13/4
Step-by-step explanation
Equation of a line in slope-intercept form
[tex]y=mx+b[/tex]where m is the slope and (0, b) is the y-intercept.
Substituting into the general equation with m = -3 and the point (1/4, -4), that is, x = 1/4 and y = -4, and solving for b:
[tex]\begin{gathered} -4=(-3)\cdot\frac{1}{4}+b \\ -4=-\frac{3}{4}+b \\ -4+\frac{3}{4}=-\frac{3}{4}+b+\frac{3}{4} \\ -\frac{13}{4}=b \end{gathered}[/tex]Substituting into the general equation with m = -3 and b = -13/4, we get:
[tex]\begin{gathered} y=(-3)x+(-\frac{13}{4}) \\ y=-3x-\frac{13}{4} \end{gathered}[/tex]Related Questions
ABC is dilated by a factor of 5 produce A'B'C.What is A'C, the length of AC after the dilation? What is the measure of angle A?
Answers
We have that the scale factor is 5, then, the dilation is an enlargement.
Then, the new lengths are:
[tex]\begin{gathered} A^{\prime}C^{\prime}=5AC=5\cdot5=25 \\ A^{\prime}B^{\prime}=5AB=5\cdot4=20 \\ B^{\prime}C^{\prime}=5BC=5\cdot3=15 \end{gathered}[/tex]therefore, A'C' =25.
Finally, the dilations don't affect the angles, therefore, angle A remains with the measure of 37°
What is the difference between chemical and physical change
Answers
Answer:
Step-by-step explanation:
In a physical change the appearance or form of the matter changes but the kind of matter in the substance does not. However in a chemical change, the kind of matter changes and at least one new substance with new properties is formed.
Miguel has 225 base ball cards. He plans to keep 75 cards and give the rest to his friends.Can Miguel give an equal number of cards to 6 friends? Explain.
Answers
We know what Miguel has 225 baseball cards, and he plans on keeping 75, while giving them the rest of them to his friends. We want to know if he can give an equal number to 6 of his friends.
For this objective, we know what he will have to give to his friends an amount of:
[tex]undefined[/tex]Consider functions h and k. Every x value has a relationship in k of x. What is the value of (h o k)(1)? A. 28 B. 4 C. 1 D. 0
Answers
Recall that:
[tex](f\circ g)(x)=f(g(x)).[/tex]Therefore:
[tex](h\circ k)(1)=h(k(1)).[/tex]From the given diagram we get that:
[tex]k(1)=3.[/tex]Then:
[tex]h(k(1))=h(3).[/tex]Now, from the given table we get that:
[tex]h(3)=28.[/tex]Therefore:
[tex](h\circ k)(1)=28.[/tex]Answer: Option A
how do I use a right triangle to write the following expression as an algebraic expression?
Answers
So, we want to express the following:
[tex]\sec (\sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}}))[/tex]As an algebraic expression.
If:
[tex]\begin{gathered} \sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}})=\theta \\ \text{Then,} \\ \sin (\theta)=\frac{x}{\sqrt[]{x^2+81}} \end{gathered}[/tex]We could draw the following triangle:
Remember that the secant function relations the hypotenuse of the triangle and the adjacent side of the triangle. So first, we should find the adjacent side using the pythagorean theorem:
[tex]\begin{gathered} a^2=(\sqrt[]{x^2+81})^2-x^2 \\ a^2=x^2+81-x^2 \\ a^2=81\to a=9 \end{gathered}[/tex]Therefore, the adjacent side is 81. And, the value of:
[tex]\sec (\sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}}))[/tex]Is:
[tex]\sec (\sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}}))=\frac{\sqrt[]{x^2+81}}{9}[/tex]Acetaminophen and liver damage. It is believed that large doses of acetaminophen
(the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the
liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users
who have liver damage. For participating in this study, he will pay each subject $20 and provide
a free medical consultation if the patient has liver damage.
(a) If he wants to limit the margin of error of his 98% confidence interval to 2%, what is the
minimum amount of money he needs to set aside to pay his subjects?
(b) The amount you calculated in part (a) is substantially over his budget so he decides to use
fewer subjects. How will this affect the width of his confidence interval?
Answers
Using proportions we can conclude that the researcher should recruit a minimum of 1509 subjects.
What is proportion?A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls).So, a study is being planned to determine the percentage of acetaminophen users who suffer liver injury.
With,
Level of confidence: 98%E=0.03 is the error margin.Then,
The z-value for 98% confidence is known Zₙ = 2.33.Calculation of the sample size: n = p(1 - p)(Zₙ/E)²In order to obtain the most cautious estimate, we should pick p = 0.5 because the researcher has no preconceived notions about what the sample proportion should be:
n = 0.5(1-0.5)(2.33/0.03)²1508.0277778 = 1509Therefore, using proportions we can conclude that the researcher should recruit a minimum of 1509 subjects.
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The correct question is given below:
It is believed that large doses of acetaminophen (the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users who have liver damage. If she wants to limit the margin of error of her 98% confidence interval to be no more than 3%, what is the minimum number of subjects that she needs to recruit? [Note: The researcher has no expectations about what the sample proportion should be ahead of time, so she – and you – should use p = 0.5 to get the most conservative estimate.]
the vertex of the parabola below is at the point (3,2) and point (4,6) is on the parabola
Answers
By using the vertex and the given point, we conclude that the quadratic equation is:
y = 4*(x - 3)^2 + 2
How to find the equation of the parabola?A quadratic equation with a vertex (h, k) and a leading coefficient A can be written as:
y = A*(x - h)^2 + k
In this case, we know that the vertex is (3, 2), replacing that in the general equation we get:
y = A*(x - 3)^2 + 2
We also know that the curve passes through (4, 6), so when x = 4, the value of y must be 6, replacing that in the quadratic equation we can find the value of A.
6 = A*(4 - 3)^2 + 2
6 = A*(1)^2 + 2
6 - 2 = A*1
4 = A
So we conclude that the quadratic equation is:
y = 4*(x - 3)^2 + 2
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Find the derivativef(x) = 1 / (x - 2)
Answers
ANSWER
[tex]\frac{df}{dx}=-\frac{1}{(x-2)^2}[/tex]EXPLANATION
We want to find the derivative of the given function:
[tex]f(x)=\frac{1}{x-2}[/tex]First, we have to rewrite the function as follows:
[tex]f(x)=(x-2)^{-1}[/tex]Next, make the following substitution:
[tex]a=x-2[/tex]The function now becomes:
[tex]f(x)=a^{-1}[/tex]Apply the chain rule of differentiation:
[tex]\frac{df}{dx}=\frac{df}{da}\cdot\frac{da}{dx}[/tex]Therefore, we have that:
[tex]\frac{df}{da}=-1\cdot a^{-1-1}=-a^{-2}[/tex]and:
[tex]\frac{da}{dx}=1[/tex]Therefore, the differentiation of the function is:
[tex]\begin{gathered} \frac{df}{dx}=-a^{-2}\cdot1 \\ \Rightarrow\frac{df}{dx}=-(x-2)^{-2}\cdot1 \\ \frac{df}{dx}=-\frac{1}{(x-2)^2} \end{gathered}[/tex]Question HelpMultiple Representations A vehicle ses 7 gallons of gasoline to travel 147 miles. The vehicle uses gasoline at a steady rate. Use pencil and paper to draw a picture that models the situation Write a table of equivalent ratiosThen use the table to find the number of gallons of gasoline the vehicle uses to travel 63 milesComplete the tableGallons Miles1231411421
Answers
We know a vehicle uses 7 gallons of gasoline to travel 147 miles.
This gives us a ratio: 147/7 = 21
The vehicle travels 21 miles per gallon of gasoline
The situation can be modeled as a line with a constant slope of 21 miles/gallon
If we use the horizontal axis for the number of gallons and the vertical axis for the miles traveled, we can draw an approximate graph
Let's give the gallons (g) some values to fill up the table:
For g=1, miles = 21
For g=2, miles = 42
For g=3, miles = 63
For g=7, miles = 147
For g=14, miles = 294
For g=21, miles = 441
The graph is shown below
Given f(x) = 2x - 1 h(x) = x^2 + 1Find f[h(7)]
Answers
Answer:
[tex]f\lbrack h(7)\rbrack\text{ = 99}[/tex]Explanation:
Given the functions:
[tex]\begin{gathered} f(x)=2x-1 \\ h(x)=x^2+1 \end{gathered}[/tex]We want to find:
[tex]f\lbrack h(7)\rbrack[/tex]First of all, we need to find:
[tex]f\lbrack h(x)\rbrack[/tex]This is done by inserting the value of h(x) into f(x)
So, we have:
[tex]\begin{gathered} f\lbrack h(x)\rbrack=2(x^2+1)-1 \\ =2x^2+2-1 \\ =2x^2+1 \end{gathered}[/tex]Substituting 7 for x in f[h(x)], we have f[h(7)]
[tex]\begin{gathered} f\lbrack h(7)\rbrack=2(7^2)+1 \\ =2(49)+1 \\ =98+1 \\ =99 \end{gathered}[/tex]Which is what we are looking for.
Factor the Expression. If the expression cannot be factored, say so. 8.) x^2 - 4x - 12
Answers
To factor an expression of the form:
[tex]x^2+bx+c[/tex]we find two numbers B and C that fulfills the following properties:
[tex]\begin{gathered} B+C=b \\ BC=c \end{gathered}[/tex]In this case we have b=-4 and c=-12. We can choose B=-6 and C=2. Then we write the expression as:
[tex]x^2-4x-12=x^2-6x+2x-12[/tex]and we factor the common factors in the first two and last terms:
[tex]\begin{gathered} x^2-4x-12=x^2-6x+2x-12 \\ =x(x-6)+2(x-6) \\ =(x+2)(x-6) \end{gathered}[/tex]Therefore:
[tex]x^2-4x-12=(x+2)(x-6)[/tex]Identify the side lengths that form a right triangle.a. 12, 13, 16b. 15, 20, 21c. 9, 40, 42d. 10, 24, 26Identify the side lengths that form a right triangle.a. 3, 4, 8b. 30, 40, 45c. 5, 12, 13d. 6, 12, 133. do the side lengths of 8, 10, and 13 form a right triangle? 4. Determine if ▼ABC is a right triangle if AB=36, AC=48 and BC=60
Answers
Answer:
d. 10, 24, 26
Explanation:
To identify the side lengths that form a right triangle, we check if it satisfies the Pythagorean theorem.
By the theorem:
[tex]\begin{gathered} a^2=b^2+c^2 \\ a\text{ is the hypotenuse, the longest side.} \end{gathered}[/tex]a. 12, 13, 16
[tex]\begin{gathered} 16^2=12^2+13^2 \\ 256=144+169 \\ 256\neq313 \end{gathered}[/tex]These side lengths do not form a right triangle.
b. 15, 20, 21
[tex]\begin{gathered} 21^2=15^2+20^2 \\ 441=225+400 \\ 441\neq625 \end{gathered}[/tex]These side lengths do not form a right triangle.
c. 9,40,42
[tex]\begin{gathered} 42^2=9^2+40^2 \\ 1764=81+1600 \\ 1764\neq1681 \end{gathered}[/tex]These side lengths do not form a right triangle.
d. 10, 24, 26
[tex]\begin{gathered} 26^2=10^2+24^2 \\ 676=100+576 \\ 676=676 \end{gathered}[/tex]These side lengths form a right triangle since both sides of the equation are the same.
34 Sat purchased some art supplies and cord stock in order to make greeting cards. The graphbelow shows the relationship between the number of cards Sat makes and the total cost etthe materials used te make the cardsCost of Noking Greeting CardsTotal Cost(dollars)2 4 6 8 10Number of Cards MadeBased on the graph what will be the total cost of making 25 greeting cards?*2.50G$50.00N $52.50$15.00
Answers
step 1
Find the slope
we have the points
(3,4) and (7,6)
m=(6-4)/(7-3)
m=2/4
m=$0.5 per card
the equation of the line in slope intercept form is equal to
y=mx+b
we have
m=0.50
b=?
point (3,4)
substitute
4=0.5(3)+b
b=4-1.50
b=2.50
y=0.50x+2.5
so
For x=25 cards
substitute
y=0.50(25)+2.50
y=15.00
answer is the option JHow to solve 11 3/7 × 7/10 =
Answers
Given:
The objective is to solve the given equation.
The given equation can be solved by,
[tex]\begin{gathered} =11(\frac{3}{7})\cdot\frac{7}{10} \\ =\frac{11\cdot3}{10} \\ =\frac{33}{10} \\ =3.3 \end{gathered}[/tex]Hence, the value of the equation is 3.3
HELP PLS (question in image)
Answers
Answer:
[tex]106-19\sqrt{x} 10[/tex]
Step-by-step explanation:
How to draw A Area Model For 29×56
Answers
First, notice that:
[tex]29\text{ x }56=1624[/tex]now, we can write 29 as 20 + 9 and 56 as 50 + 6, so, we can draw the following rectangles:
Then, if we calculate the area of each of the rectangles, we get the following:
then, if we add all the areas together, we get:
[tex]1000+120+450+54=1120+504=1624[/tex]which is the same result as 29 x 56
Which of the following pairs of numbers do not have a geometric mean of 12? A 11 and 13 B 20 and 7.2 C 3 and 48 D 5 and 28.8
Answers
Answer
Option A contains two numbers that do not have a geometric mean of 12.
11 and 13 do not have a geometric mean of 12.
Explanation
The geometric mean of two numbers, a and b, is given as
Geometric mean = √(a × b)
So, we want to find which two numbers will have a geometric mean of 12
12 = √(a × b)
Taking the square of both sides, we see that
144 = (a × b)
So, whichever two numbers give a product of 144 is our answer.
Option A
11 × 13 = 143
Option B
20 × 7.2 = 144
Option C
3 × 48 = 144
Option D
5 × 28.8 = 144
Hope this Helps!!!
Identify the type of polar graph for the equation: r = 2+2cos θ aLimacon with inner loop bCardioid cDimpled limacon dConvex limacon eRose Curve fCircle gLemniscate
Answers
is choice a
iner loop Limacon
What’s negative 5 + 1 fourth equal
Answers
Answer:
-4 3/4
Step-by-step explanation:
-5 x 4/4 + 1/4
-19/4 = -4 3/4
What is lim (2x² - x + 3)/(3x² + 5) as x approaches + ∞?
Answers
Given:
lim (2x² - x + 3)/(3x² + 5)
We are to
I need help with graph inequalityx < 1 on number lines
Answers
Answer:
The graph for the inequality x < 1 is shown below
Explanation:
The graph is marked on the number line, from the point 1 to the left, 1 is not included in this set, so the point is not shaded
(blank)+(7x+24)=180
7x + (blank)+ = 180
7x =
x =
Answers
Answer:
first blank: 72°
2nd blank: 96
next line: 84
last: 12
Step-by-step explanation:
The two marked angles are called same-side interior angles or consecutive angles.
They add up to 180°
Thats how you know how to set up the equation.
72° + 7x + 24 = 180
Add the plain numbers (the 72 and 24)
7x + 96 = 180
subtract 96 from both sides.
7x = 84
Divide both sides by 7.
x = 12
Derrick's football team needs to raise at least $1,000 for new uniforms they have collected 480 so far which inequality represents the amount of money,m, the team still needs to raise A. m>$480 B. m<$480 C.m<$520 D.m>$520
Answers
The inequality representing the amount of money, m. Derrick's football team needs to raise is D. m>$520
What is inequality?In mathematics, Inequality is part of equations solved with the use of the some special type of equality signs. The signs used inequality calculations are
greater thanless thangreater than or equal toless than or equal toGiven that:
Derrick's football team needs to raise at least $1,000
The team collected 480
To solve the given problem we have the inequality in the form
at least $1,000 ≡ greater than or equal to 1000
m > $1000
having collected $480 so far. The amount collected is subtracted from the $1000
m > $1000 - $480
m > $520
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O GRAPHS AND FUNCTIONSDomain of a rational function: Excluded values
Answers
Recall that the domain of a rational function consists of all the real numbers x except those for which the denominator is 0.
The denominator of the given rational function is:
[tex]d(x)=x^2+11x-18.[/tex]Notice that:
[tex]\begin{gathered} x^2+11x+18=x^2+2x+9x+9*2 \\ =x(x+2)+9(x+2)=(x+9)(x+2). \end{gathered}[/tex]Therefore d(x)=0 at x=-9 and x=-2, then those values are not in the domain of g.
Answer:
[tex]x=-9,-2.[/tex]REI pays $330.30 for a 6-person tent and the markup is 35% of cost. Find the markup.
Answers
First convert 35% into decimal
35% → 0.35
To find 35% of $330.30, multiply it to its decimal
$330.30 ˣ 0.35 = $115.605
Rounding off to the nearest cent.
The markup of the tent is $115.61
1 3/8 × 3 2/3=answer must be in simplest fraction form
Answers
EXPLANATION
Given the fractions 1 3/8 and 3 2/3
First we need to turn both fractions into improper ones
[tex]1\frac{3}{8}=\frac{11}{8}[/tex][tex]3\frac{2}{3}=\frac{11}{3}[/tex]Now, multiplying both fractions:
[tex]\frac{11}{8}\cdot\frac{11}{3}=\frac{121}{24}[/tex]The answer is 121/24
the table shows the number of jeans sold at a store at different prices
Answers
To make a plot of the data you first must choose your axis. In this case we've chosen the X axis to be the average cost of the jeans and the Y axis to be the number of copies sold. To graph the data we match the information we're given in the table as shown in the drawing.
Hey could someone help me out with this thank you
Answers
Karen will run more than 28
Your psychology class has 45 students. You want to ask an SRS of four students from your class whether they prefer taking online or face-to-face courses. You label the students 01, 02, . . . , 45. You enter the table of random digits at this line:
78314 96529 67532 98144 28944 26687 49634 88274 20361
Your SRS contains the students labeled
A. 14, 32, 42, 44.
B. 31, 29, 44, 28.
C. 31, 29, 29, 44.
D. 31, 49, 29, 44.
E. 78, 31, 49, 65.
Answers
Answer:
Step-by-step explanation:
The answer is c! :)
Answer:
The answer is B. 31, 29, 44, 28.
Step-by-step explanation:
find the value of. abe, bec, and the minor arc ec
Answers
Answer
Angle ABE = 64°
Angle BEC = 48°
Minor arc EC = 134°
Explanation
The key to solving this is to take a look at this image below
According to the tangent-chord theorem, we know that
Tangent Chord angle ABE = (Intercepted arc BE)/2
Angle ABE = (128°/2)
Angle ABE = 64°
Tangent chord angle CED = (Intercepted arc EC)/2
68° = (Minor arc EC/2)
Multiply both sides by 2
136° = Minor arc EC
To find the Angle BEC, we need to first obtain the arc BC
The total angle around a circle is 360°
Arc BE + Arc BC + Arc EC = 360°
128° + Arc BC + 136° = 360°
Arc BC = 360° - 128° - 136°
Arc BC = 96°
Then to find the Angle BEC, the image attached below guides us
So, we can easily say that
Angle BEC = ½ (Arc BC)
Angle BEC = ½ (96°)
Angle BEC = 48°
Hope this Helps!!!