Given data:
The given equation of the line is x+3y=3.
The given equation can be written as,
[tex]\begin{gathered} x+3y=3 \\ 3y=3-x \\ y=\frac{1}{3}(-x+3) \\ =-\frac{1}{3}x+1 \end{gathered}[/tex]The standard equation of the line is,
[tex]y=mx+c[/tex]Here, m is the slope.
Compare the given equation with the standard equation of the line.
m=-1/3
Thus, the slope of the line is -1/3.
make a table of values then graph the following quadratic functions
We have the next quadratic function
[tex]f(x)=.5(x+2)^2[/tex]we need to find the values of the table
x=-3 f(x=-3)=.5(-3+2)^2=0.5
x=-2 f(x=-2)=.5(-2+2)^2=0
x=-1 f(x=-1)=.5(-1+2)^2=0.5
x=0 f(x=0)=.5(0+2)^2=2
x=1 f(x=)=.5(1+2)^2=4.5
x=2 f(x=2)=.5(2+2)^2=8
x=3 f(x=3)=.5(3+2)^2=12.5
then we will graph the points, and we will obtain the graph
Find the volume of the pyramid.A. 114 km³B. 80 km³C. 91 km³D. 240 km³
ANSWER
[tex](B)80\operatorname{km}[/tex]EXPLANATION
The volume of a pyramid is:
[tex]V=\frac{l\cdot w\cdot h}{3}[/tex]where l = length; w = width; h = height
Therefore, the volume of the given pyramid is:
[tex]\begin{gathered} V=\frac{6\cdot8\cdot5}{3} \\ V=80\operatorname{km}^3 \end{gathered}[/tex]The answer is option B.
Write an expression that is equivalent to 8 using each of the following numbers and symbols once in the expression. 2. + O 7 7 7 (exponent)
Explanation
to solve this we can check every option,so
Hello, how do you find the slope of the line that contained the points (6, -10) and (-18, 6)
Remember that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]In this problem we have
(6, -10) and (-18, 6)
so
(x1,y1)=(6,-10)
(x2,y2)=(-18,6)
substitute in the formula
[tex]\begin{gathered} m=\frac{6-(-10)}{-18-6} \\ m=\frac{6+10}{-24} \\ \\ m=\frac{16}{-24} \end{gathered}[/tex]simplify
[tex]m=-\frac{16}{24}=-\frac{4}{6}=-\frac{2}{3}[/tex]the slope is -2/3I need to know which rule explains why these teiangles are congruent
The theorem is AAS
Because
angle J and angle M measure the same
angle H measure the same is the same angle
and the segment
Determine the difference between the rate of change g(x) over the interval [9,49] and the rate of change of g(x) over the interval [25,81]. Round Your answer to the nearest hundredth.(b) Which is the following values represent the rate of change over the interval [121,225]1/13 1/11 2/13 2/11
Part A
g(9) = 6
g(49) = 14
The rate of change g(x) over the interval [9,49] is:
[tex]\frac{g(49)-g(9)}{49-9}=\frac{14-6}{40}=\frac{8}{40}=\frac{1}{5}[/tex]Likewise:
g(25)=10
g(81)=18
The rate of change of g(x) over the interval [25,81] is:
[tex]\frac{g(81)-g(25)_{}}{81-25}=\frac{18-10}{56}=\frac{8}{56}=\frac{1}{7}[/tex]The difference will be:
[tex]\begin{gathered} =\frac{1}{5}-\frac{1}{7} \\ =0.06\text{ (to the nearest hundredth)} \end{gathered}[/tex]Part B
g(121)=11 x 2=22
g(225)= 15 x 2 =30
Therefore, the rate of change over the interval [121,225]
[tex]=\frac{g(225)-g(121)}{225-121}=\frac{30-22}{104}=\frac{8}{104}=\frac{1}{13}[/tex]If a ratio is 4:5, how many parts are there intotal?
Given:
Ratio of terms 4:5
To know:
How many parts are there?
Explanation:
If x:y then parts included is x+y
Solution:
We have 4:5.
So, parts will be 4+5=9
.Hence, 9 is the answer.
What is the difference of 85.23 and 2.675 ? Enter your answer in the box.
Given the values 85.23 and 2.675 ?, we are to take the difference between the values and this is as shown;
85.23 = 85 + 0.23
2.675 = 2 + 0.675
85.23 - 2.675 = 85 + 0.23 - (2 + 0.675)
85.23 - 2.675 = 85 + 0.23 - 2 - 0.675
85.23 - 2.675 = 85-2 + 0.23 - 0.675
85.23 - 2.675 = 83 - 0.445
85.23 - 2.675 = 82.555
Hence the difference of 85.23 and 2.675 is 82.555
The graph of a function is shown on the coordinate plane below. Identify the slope of the function.
The line passes through the point (0,4) and (-4,5).
Determine the slope of function.
[tex]\begin{gathered} m=\frac{5-4}{-4-0} \\ =\frac{1}{-4} \\ =-\frac{1}{4} \end{gathered}[/tex]So slope of the function is -1/4.
Let X and Y be the following sets: X = {15, 9, 11} Y = {11,9,2} What is the set X NY?
We have that the intersection means the set of elements that are in X and Y in this case, so we have that
[tex]\begin{gathered} X\cap Y\text{ = }\lbrace15,\text{ 9, 11}\rbrace\cap\lbrace11,\text{ 9},\text{ 2}\rbrace \\ =\text{ }\lbrace9,\text{ 11}\} \end{gathered}[/tex]The answers is: A
What is the circumference of a circle with a radius of 2.09 in to the nearest hundredth:
circumference of a circle = 13.13 in
Explanation:
circumference of a circle = 2πr
r = radius = 2.09 in
let π = 3.14
circumference of a circle = 2 ×3.14 × 2.09
circumference of a circle = 13.1252 in
to the nearest hundredth:
circumference of a circle = 13.13 in
I found the derivative of the function using the quotient rule however I am lost from there
To answer this question we will use the quotient rule for derivatives:
[tex](\frac{h(x)}{g(x)})^{\prime}=\frac{h^{\prime}(x)g(x)-h(x)g^{\prime}(x)}{g(x)^2}\text{.}[/tex]We know that:
[tex]\begin{gathered} (\sqrt[]{x})^{\prime}=\frac{1}{2\sqrt[]{x}}, \\ (5x-6)^{\prime}=5. \end{gathered}[/tex]Then:
[tex]f^{\prime}(x)=\frac{\frac{1}{2\sqrt[]{x}}\cdot(5x-6)-\sqrt[]{x}\cdot5}{(5x-6)^2}\text{.}[/tex]Therefore, the slope of the tangent line to the graph of f(x) at (1,f(1)) is:
[tex]f^{\prime}(1)=\frac{\frac{1}{2\sqrt[]{1}}(5\cdot1-6)-\sqrt[]{1}\cdot5}{(5\cdot1-6)^2}\text{.}[/tex]Simplifying the above result we get:
[tex]\begin{gathered} f^{\prime}(1)=\frac{\frac{1}{2}(5-6)-5}{(5-6)^2} \\ =\frac{\frac{1}{2}(-1)-5}{(-1)^2}=\frac{-\frac{1}{2}-5}{1}=-\frac{11}{2}\text{.} \end{gathered}[/tex]Now, we will use the following slope-point formula for the equation of a line:
[tex]y-y_1=m(x-x_1)\text{.}[/tex]Therefore the slope of the tangent line to the graph of f(x) at (1,f(1)) is:
[tex]y-f(1)=-\frac{11}{2}(x-1)\text{.}[/tex]Now, we know that:
[tex]f(1)=\frac{\sqrt[]{1}}{5\cdot1-6}=\frac{1}{5-6}=\frac{1}{-1}=-1.[/tex]Therefore:
[tex]\begin{gathered} y-(-1)=-\frac{11}{2}(x-1), \\ y+1=-\frac{11}{2}x+\frac{11}{2}\text{.} \end{gathered}[/tex]Subtracting 1 from the above equation we get:
[tex]\begin{gathered} y+1-1=-\frac{11}{2}x+\frac{11}{2}-1, \\ y=-\frac{11}{2}x+\frac{9}{2}\text{.} \end{gathered}[/tex]Answer:
[tex]y=-\frac{11}{2}x+\frac{9}{2}\text{.}[/tex]in a poll, students were asked to choose which of six colors was their favorite. The circle graph shows how the students answered. if 19,000 students participated in the poll, how many chose purple?
Answer:
3,990 students.
Explanation:
From the circle graph, 21% of the students chose purple as their favorite.
If 19,000 students participated in the poll, then:
[tex]\text{The number that chose purple=}21\%\text{ of 19,000}[/tex]We simplify:
[tex]\begin{gathered} =\frac{21}{100}\times19,000 \\ =21\times190 \\ =3,990 \end{gathered}[/tex]3,990 students chose purple.
Solve the proportions 18/27=60/m
ANSWER
m = 90
EXPLANATION
To find m first we have to multiply both sides by m:
[tex]\begin{gathered} \frac{18}{27}m=\frac{60}{m}m \\ \frac{18}{27}m=60 \end{gathered}[/tex]Then multiply both sides by 27:
[tex]\begin{gathered} \frac{18m}{27}\cdot27=60\cdot27 \\ 18m=1620 \end{gathered}[/tex]And finally divide both sides by 18:
[tex]\begin{gathered} \frac{18m}{18}=\frac{1620}{18} \\ m=90 \end{gathered}[/tex]Question #3:The system of equations below form a line and a parabola. Select all possible solutions to this system from the answer choices below.x + y = 5x^2+ y = 11(-2,7)(7,2)(5,0)(3,2)(2,3)
x + y = 5 -----------------------------------------(1)
[tex]x^2+y=11-----------------(2)[/tex]From equation (1), we have
y = 5 - x ----------------------------------------(3)
Substituting equation (3) into equation (2), we have
[tex]\begin{gathered} x^2+(5-x)=11 \\ \Rightarrow x^2-x+5-11=0 \\ \Rightarrow x^2-x-6=0 \end{gathered}[/tex]Therefore
[tex]\begin{gathered} x^2+2x-3x-6^2=0 \\ x(x+2)-3(x+2)=0 \end{gathered}[/tex]Hence
[tex]\begin{gathered} (x-3)(x+2)=0 \\ \Rightarrow x=3\text{ or -2} \end{gathered}[/tex]When x = 3 and using y = 5 - x
y = 5 - 3 = 2
and when x = -2
y = 5 - (-2) = 5+2=7
Therefore the possible solutions are
(3, 2) and (-2, 7)
Hi I need help with this review question.Find the missing side length. Round your answer to the nearest tenth, if necessary. A. 7.1B. 8.4C. 11.6D. 12.2
To solve this, we can use the pythagorean theorem. if we have a right trinagle with legs C and c; and a hypotenuse H
Then:
[tex]H^2=C^2+c^2[/tex]
In this case,
• C = 10
,• c = 7
And we want to find H.
Using the theorem:
[tex]H^2=10^2+7^2[/tex]Then we can solve:
[tex]\begin{gathered} H=\sqrt{100+49} \\ H=\sqrt{149} \\ H\approx12.2 \end{gathered}[/tex]The answer is option D. 12.2
I need help on this problem! I only need help on 16 please
Angle WXZ = 23°
Explanation:Angle WXZ and angle YXZ are complementary angles.
Complementary angles sum up to 90 degrees
Angle WXZ = (2x + 1)°
Angle YXZ = (7x - 10)°
Angle WXZ + Angle YXZ = 90°
(2x + 1)° + (7x - 10)° = 90°
2x + 1 + 7x - 10 = 90
collect like terms:
2x + 7x + 1 - 10 = 90
9x - 9 = 90
add 9 to both sides:
9x - 9 + 9 = 90 + 9
9x = 99
divide both sides by 9:
9x/9 = 99/9
x = 11
Angle WXZ = (2x + 1)° = 2(11) + 1
Angle WXZ = 23°
How do you verify sin^2tan^2=tan^2-sin^2?
we will start with tan^2 theta - sin^2 theta
[tex]\tan ^2\text{ }\theta-sin^2\theta[/tex]
remember tan theta = sin theta / cos theta
[tex](\frac{\sin \theta}{\cos \theta})^2\text{ - }\sin ^2\theta[/tex][tex](\frac{\sin\theta}{\cos\theta})^2\text{ - }\sin ^2\theta\text{ }\ast\frac{\cos ^2\theta}{\cos ^2\theta}[/tex][tex]\frac{\sin ^2\theta(1-\cos ^2\theta)}{\cos ^2\theta}[/tex][tex]\tan ^2\theta\text{ (1 - }\cos ^2\theta\text{)}[/tex][tex]\tan ^2\theta\ast\sin ^2\theta[/tex]how do I find the measure of the side of a right triangle whose length is designated by the lower case c
The triangle ABC is a right triangle, you know one of the angles, ∠A=31º, the opposite side to the angle, BC=15m, and need to determine the measure of the hypothenuse AB=c
To determine the value of one side of a right triangle, when you know one angle and one side of it you have to use the trigonometric relationships:
[tex]\begin{gathered} \text{sin}\theta=\frac{\text{opposite}}{\text{hypothenuse}} \\ \cos \theta=\frac{\text{adjacent}}{\text{hypothenuse}} \\ \tan \theta=\frac{\text{opposite}}{\text{hypothenuse}} \end{gathered}[/tex]Where
θ indicates one angle of the triangle.
For the exercise, since we know the angle and the opposite side to it, we have to use the sine, because it relates the opposite side with the hypothenuse:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{\text{hypothenuse}} \\ \sin 31º=\frac{15m}{c} \end{gathered}[/tex]From this expression, we can calculate c as follows
[tex]\begin{gathered} c\cdot\sin 31º=15 \\ c=\frac{15}{\sin 31º} \\ c=29.12m \end{gathered}[/tex]The resistance R of a wire (in ohms) is given by
The resistance R of a wire (in ohms) is given by
[tex]R=\frac{KL}{d^2}[/tex]L is 1830 feet, d is 169 mils or inch and K is 10.7 ohms.
ExplanationThe resistance is given by
[tex]R=\frac{KL}{d^2}[/tex]Convert inch into feet,
1 inch =0.08333 feet.
169 inch=14.0833feetSubstitute the values,
[tex]\begin{gathered} R=\frac{10.7\times1830}{14.0833^2} \\ R=98.724 \end{gathered}[/tex]AnswerHence the resistance is determined as 98.724 ohms.
THE FIGURE SHOWDSS ANGLE ABD IS 90° SLIPT BY LINE BC . THE MEASURE OF ANGLE ABC IS X ° AND THE MEASUREMENT OF DBC (3X+10) . WHAT IS THE VALUE OF X . ENTER YOUR ANSWER IN THE BOX
From the picture,
∠ABC + ∠DBC = ∠ABD
Substituting with data,
x + (3x + 10) = 90
4x + 10 = 90
4x = 90 - 10
4x = 80
x = 80/4
x = 20
You and four friends plan a surprise party. Each of you contributes the same amount of money m for food. a. Write an algebraic expression for the total amount of money contributed for food. b. Evaluate your expression if each person contributed $5.25
a) The total amount contributed = 5m
b) The total amount contributed = $26.25
Explanations:a)The amount of money contributed by each of the firends = m
Since the party was planned by you and and four friends, the total number of people contributing the money is 5.
The total amount of money contributed = (Amount of money contributed by each friend) x (The number of friends)
The total number of money contributed = m x 5
The total amount contributed = 5m
b) If each person contributes $5.25
m = 5.25
The total amount contributed = 5 x 5.25
The total amount contributed = $26.25
Whixh coordinate best represents the location of point D on the coordinate
Answer : (-7, -6)
we are given different points on the graph
To locate the best coordinate that locate point D on the graph
Count 7 units to the right of x - axis and count 6 unit down to the y - axis
Hence, the coordinate is (-7, -6)
The answer is (-7, -6)
Find the inverse of the following relation.{(0, 3), (4, 2), (5, -6)}{(0,3), (2,5), (-6,2)}{(0,3), (4,2), (5,-6)}{(3,4), (0,5), (-6,4)}{(3,0), (2,4), (-6,5)}
Step 1
Given; Find the inverse of the following relation.
{(0, 3), (4, 2), (5, -6)}
{(0,3), (2,5), (-6,2)}
{(0,3), (4,2), (5,-6)}
{(3,4), (0,5), (-6,4)}
{(3,0), (2,4), (-6,5)}
Step 2
[tex]\begin{gathered} f(x)=\lbrace(0,3),(4,2),(5,-6)\rbrace \\ f^{-1}(x)=\lbrace(3,0),(2,4),(-6,5)\rbrace \end{gathered}[/tex]Answer;
{(3,0), (2,4), (-6,5)}
by himself, a person can mow his lawn in 80minutes. If his daughter helps, they can mow the lawn together in 60minutes. How long would it take his daughter to mow the lawn by herself.
The father mows the lawn in 80 min.
The father and the daughter mow the lawn in 60 min.
Let "x" represent the time it takes the daughter to mow the lawn by herself.
Express both times as rates:
The dad's mow rate is:
[tex]\frac{1\text{lawn}}{80\min }[/tex]Combined mow rate:
[tex]\begin{gathered} \frac{1\text{lawn}}{80\min}+\frac{1\text{lawn}}{x}=\frac{1\text{lawn}}{60\min } \\ \frac{1}{80}+\frac{1}{x}=\frac{1}{60} \end{gathered}[/tex]From this expression you can determine the value of x:
- Subtract 1/80 to both sides of the expression
[tex]\begin{gathered} \frac{1}{80}-\frac{1}{80}+\frac{1}{x}=\frac{1}{60}-\frac{1}{80} \\ \frac{1}{x}=\frac{1}{240} \end{gathered}[/tex]-Raise both sides by -1 to invert the fractions:
[tex]\begin{gathered} (\frac{1}{x})^{-1}=(\frac{1}{240})^{-1} \\ x=240 \end{gathered}[/tex]It will take her 240 minutes to mow the lawn by herself.
For a social studies project, Darius has to make a map of a neighborhood that could exist in his hometown. He wants to make a park in the shape of a right triangle. He has already planned 2 of the streets that make up 2 sides of his park. The hypotenuse of the park is 3rd Avenue, which goes through points (-3, 2) and (9, 7) on his map. One of the legs is Elm Street, which goes through (12, 5) and has a slope of -23. The other leg of the park will be Spring Parkway and will go through (-3, 2) and intersect Elm Street.A) What is the slope of Spring Parkway?B) What is the length, in units, of 3rd Avenue?C) The variable x represents the length of Spring Parkway in units. The measure of the angle formed by Spring Parkway and 3rd Avenue is approximately 33.69°. Write a trigonometric equation relating the measure of the angle formed by Spring Parkway and 3rd Avenue, the length of Spring Parkway (x), and the length of 3rd Avenue from part B.D) Solve for x, the length of Spring Parkway in units.
Answer
A) Slope = 1/5
B) Length = 13 units
(C) Equation: x = 13cos33.69°
(D) X = 10.82 units
Explanation
The given information in the question is represented in the figure below:
Step-by-step solution:
(A) The slope of Spring Parkway.
This can be calculated using the slope in two points formula
[tex]slope=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{12--3}=\frac{3}{12+3}=\frac{3}{15}=\frac{1}{5}[/tex]Slope = 1/5
(B) The length, in units, of 3rd Avenue.
The length, in units of 3rd Avenue, can be determined using distance between two points as follows
[tex]\begin{gathered} L=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ L=\sqrt{(9-(-3)^2+(7-2)^2} \\ \\ L=\sqrt{(9+3)^2+5^2} \\ \\ L=\sqrt{12^2+5^2} \\ \\ L=\sqrt{144+25} \\ \\ L=\sqrt{169} \\ \\ L=13\text{ }units \end{gathered}[/tex]Length = 13 units
(C) Since variable x represents the length of Spring Parkway in units and the measure of the angle formed by Spring Parkway and 3rd Avenue is approximately 33.69°, then the trigonometric equation relating the measure of the angle formed by Spring Parkway and 3rd Avenue, the length of Spring Parkway (x), and the length of 3rd Avenue from part B will be
[tex]\begin{gathered} cos\text{ }\theta=\frac{Adjacent}{Hypotenuse} \\ \\ \theta=33.69°,Adjacent=x,and\text{ }Hypotenuse=13\text{ }units \\ \\ \therefore cos\text{ }33.69°=\frac{x}{13} \\ \\ x=13cos\text{ }33.69° \end{gathered}[/tex]Equation: x = 13cos33.69°
(D) To solve for x, the length of Spring Parkway in units, use the trigonometric equation in part C above.
[tex]\begin{gathered} x=13cos33.69 \\ \\ x=13\times0.8321 \\ \\ x=10.82\text{ }units \end{gathered}[/tex]X = 10.82 units.
Given that the x-intercepts of a quadratic are 3 and 4, what could be a possible quadratic equation of this quadratic?
Given:
x intercepts of a quadratic equation are 3 and 4.
The objective is to find the quadratic equation.
The x intercepts can be written as,
[tex]\begin{gathered} x=3 \\ x-3=0 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} x=4 \\ x-4=0 \end{gathered}[/tex]Now, multiply both the term to get the quadratic equation.
[tex]\begin{gathered} (x-3)(x-4)=0 \\ x^2-3x-4x+12=0 \\ x^2-7x+12=0 \end{gathered}[/tex]Hence, the required quadratic equation is obtained.
2.1.9 Question Help An initial investment amount P, an annual interest rater, and a time t are given. Find the future value of the investment when interest is compounded (a) annually. (b) monthly, (c) daily, and (d) continuously. Then find (e) the doubling time T for the given interest rate. P = $2500, r=3.95%, t = 8 yr a) The future value of the investment when interest is compounded annually is $ (Type an integer or a decimal. Round to the nearest cent as needed.)
Answer:
(a) $3408.29
Explanation:
The future value of the investment can be calculated as:
[tex]A=P(1+r)^t[/tex]Where A is the future value, P is the initial investment, r is the interest rate and t is the period of time.
So, replacing P by 2500, r = 0.0395 and t by 8, we get:
[tex]\begin{gathered} A=2500(1+0.0395)^8 \\ A=2500(1.3633) \\ A=3408.29 \end{gathered}[/tex]Therefore, the future value of the investment is $3408.29
Given f(x) = x3 - 9x and g(x) = x², choosethe expression for (fºg)(x).Click on the correct answer.(X3 – 9x)2Xo_99²x5 813x2 - 9x
We have,
[tex]\begin{gathered} f(x)=x^3-9x \\ g(x)=x^2 \end{gathered}[/tex]To find (fºg)(x), we need to solve f(g(x)),
[tex](f\circ g)(x)=f(g(x))=(x^2)^3-9(x^2)=x^6-9x^2[/tex]product of (x+4) (x-3)
Here, we want to find the product of the two expressions
We have this as;
[tex](x+4)(x-3)=x(x-3)+4(x-3)=x^2-3x+4x-12=x^2+x-12[/tex]