To solve this problem, we have to evaluate when f(x) = 4. Remember that y = f(x)
[tex]\begin{gathered} y=-3x+5\rightarrow f(x)=-3x+5 \\ 4=-3x+5 \end{gathered}[/tex]Then, we solve for x
[tex]\begin{gathered} 4-5=-3x \\ -3x=-1 \\ x=-\frac{1}{-3} \\ x=\frac{1}{3} \end{gathered}[/tex]Hence, th
Rita earns scores of 83, 87, 85, 88, and 90 on her five chapter tests for a certain class and a grade of 82 on the class project.
The overall average for the course is computed as follows: the average of the five chapter tests makes up 30% of the course
grade; the project accounts for 30% of the grade; and the final exam accounts for 40%. What scores can Rita earn on the final
exam to earn a "B" in the course if the cut-off for a "B" is an overall score greater than or equal to 80, but less than 90? Assume>that 100 is the highest score that can be earned on the final exam and that only whole-number scores are given.>To obtain a "B", Rita needs to score between>and>inclusive
Given:
Rita earns scores of 83, 87, 85, 88, and 90 on her five-chapter tests for a certain class.
And a grade of 82 on the class project.
First, we will find the average of the scores of the five tests
[tex]5-tests\text{ }average=\frac{83+87+85+88+90}{5}=\frac{433}{5}=86.6[/tex]The overall average for the course is computed as follows:
30% of the course grade ⇒ Rita get 86.6
30% of project grade ⇒ Rita get 82
40% of the final exam ⇒ let Rita get x
We will find the value of x provided that Rita will earn a "B" score
a "B" is an overall score greater than or equal to 80, but less than 90
So, we will find (x) as follows:
[tex]\frac{30*86.6+30*82+40*x}{100}\ge80[/tex]Solve the inequality to find (x):
[tex]\begin{gathered} 5058+40x\ge8000 \\ 40x\ge8000-5058 \\ 40x\ge2942 \\ x\ge\frac{2942}{40} \\ \\ x\ge73.55 \end{gathered}[/tex]And the upper limit will be as follows:
[tex]\frac{30\times86.6+30\times82+40x}{100}<90[/tex]Solve to find (x):
[tex]\begin{gathered} 5058+40x<9000 \\ 40x<9000-5058 \\ 40x<3942 \\ x<\frac{3942}{40} \\ \\ x<98.55 \end{gathered}[/tex]So, the answer will be:
To obtain a "B", Rita needs to score between 73.55 and 98.55
Given A(2,4) and B(5,-4) from problem #1. What is the slope of a line that is parallel to (AB) ⃡?What is the slope of a line that is perpendicular to (AB) ⃡?
Solution
Given that
[tex]\begin{gathered} A(2,4) \\ B(5,-4) \end{gathered}[/tex]To find the slope, m, of the line passing through the given points, the formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)\Rightarrow A(2,4) \\ (x_2,y_2)\Rightarrow B(5,-4) \end{gathered}[/tex]Substitute the coordinates into the formula to find the slope, m, of a line
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-4-4}{5-2}=\frac{-8}{3}=-\frac{8}{3} \\ m=-\frac{8}{3} \end{gathered}[/tex]The slope of the line AB passing through the given points is m = -8/3
A) If two lines are parallel, their slopes are equal.
Hence, the slope, m₁ of the line that is parellel to line AB is
[tex]m_1=-\frac{8}{3}[/tex]Thus, the slope of a line parallel to line AB is m₁ = -8/3
B) If two lines are perpendicular, the formula to find the slope m₂ of the line perpedicular to the slope of a given line
[tex]m_2=-\frac{1}{m_{}}[/tex]Where m = -8/3, the slope, m₂, of a line perpendicular to line AB will be
[tex]\begin{gathered} m_2=-\frac{1}{m_{}} \\ m_2=-\frac{1}{\frac{-8}{3}_{}}=\frac{3}{8} \\ m_2=\frac{3}{8} \end{gathered}[/tex]Thus, the slope of a line perpendicular to line AB is m₂ = 3/8
Assume f(x) = g(x). Which of the following pairsof functions may be used to represent theequation 3^x+^2 = 7x + 6?
We have that:
[tex]3^{x+2}^{}=7x+6[/tex]Let's name each side of it with f(x) and g(x):
Then, we have that:
[tex]\begin{gathered} f(x)=3^{x+2} \\ \text{and} \\ g\mleft(x\mright)=7x+6 \end{gathered}[/tex]Then, the answer is C
Answer: CSuppose you walk 2 miles in 35 minutes.Write a proportion to find how far you would walk in an hour if you were to continue at the same rate.이A.1235CaB.235C.235OD60235
To find the required proportion, you first write down the proportion between the distance you walk and time, just as follow:
proportion = 2/35
In this case numerator is distance and denominator is time in minutes.
Now, if you want to know hof war you would walk in 1 hour (60 mins) with the same rate, you can write:
for 1 hour:
x/60 =
x is the uknown distance, which have to stay in the numerator, and denominator is 60 because 1 hour = 60 mins.
But the two previous expression must be equal because you walk at the same rate both times. Hence, the searched equation is:
2/35 = x/60
Maria is using a meter stick to determine the height of a door. If the smallest unit on the meter stick iscentimeters, which measurement could Maria have used to most accurately record the height of thedoor?23 meters2 meters2.309 meters2.31 meters
The most accurate measure of the height in meters is in two decimal places
The most accurate measure for maria to use is 2.31meters
The Forth option is correct
6. What is the equation in standard form of the line that passes through the point 2 ? (10,-3) and has a slope of 5
The standard form of equation of line is :
[tex]y=m(x-x_1)+y_1[/tex]In the given question, we have coordinates : (10,-3) and slope m = 2/5
[tex]\begin{gathered} y=m(x-x_1)+y_1 \\ y=\frac{2}{5}(x-10)+(-3) \\ y=\frac{2}{5}x-\frac{2}{5}(-10)+(-3) \\ y=\frac{2}{5}x-2(-2)+(-3) \\ y=\frac{2}{5}x-4-3 \\ y=\frac{2}{5}x-7 \\ y+7=\frac{2}{5}x \\ 5y+35=2x \\ 2x\text{ -5y =35} \end{gathered}[/tex]The equation of line is 2x - 5y = 35
Anwer : C) 2x - 5y = 35
What is the equation of the line graphed below?A. y = -2xB. y = 2xC. y - xD. y = -x(1,2)
Answer:
B) y = 2x
Explanation:
We were given the following details:
The straight line passes through the origin; it passes through the point (0, 0)
The straight line passes through the point (1, 2)
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(1,2) \end{gathered}[/tex]The general equation of a straight line is given by:
[tex]\begin{gathered} y=mx+b \\ where: \\ m=slope \\ b=y-intercept \end{gathered}[/tex]We will obtain the equation of the straight line as shown below:
I. Obtain the slope of the straight line
[tex]\begin{gathered} \begin{equation*} slope,m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \end{equation*} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2-0}{1-0} \\ m=\frac{2}{1}=2 \\ m=2 \\ \\ \therefore slope,m=2 \end{gathered}[/tex]The slope of the straight line is 2
II. Obtain the y-intercept
Method 1:
The y-intercept refers to the point where the straight line crosses the y-axis.
In this case, the straight line crosses the y-axis at the origin (0, 0). This implies that:
[tex]\begin{gathered} b=0 \\ Remember:y=mx+b \\ \Rightarrow y=2x+0 \\ y=2x \end{gathered}[/tex]Method 2:
Using the point-slope equation:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-0=2(x-0) \\ y-0=2x-0 \\ y=2x \\ \\ \therefore y=2x \end{gathered}[/tex]Therefore, the answer is B (y = 2x)
35,876 rounded to nearest 100 and 1000
EXPLANATION:
To round a figure we must look specifically at what place value is the number immediately after the comma.
for example:
35,876 rounded round to the nearest thousand:
ANSWER:
As the figure that follows after the comma approaches 9, immediately add one unit to 5, transforming the number into an approximate value of 36,000
Now rounded to nearest 100:
35,900
to round to 100 we only look at the three-unit figures that correspond to the hundred, that is, the place value of the figure after the comma.
Matt drew the two rectangles shown in thediagram below.ABD16 in.ABD12 inсMatt dilated Rectangle ABCD to createRectangle A'B'CD'.What scale factor did Matt use todilate Rectangle ABCD?
Provide the correct reason for the statement in line 4.
We have to prove x = -16/3.
The steps are:
[tex]1)3(x+5)=-1\longrightarrow\text{Reason: Given}[/tex][tex]2)3x+15=-1\longrightarrow\text{Reason: Distributive property}[/tex][tex]3)3x=-16\longrightarrow\text{ Reason: substracting 15 from both sides}[/tex][tex]4)x=-\frac{16}{3}\longrightarrow\text{ Reason: divide both sides of the equation by 3}[/tex]Which of the following is true about a kite?a.All angles are rightb.The diagonals have the same lengthc.All four sides are equald.Adjacent sides are congruent
In a kite, there is always an angle that is not right, otherwise, it would have a rectangular shape.
The diagonals are not of the same length because that would mean it would have a rectangular shape as well.
The sides are not equal, because that would mean it would have a rhomboid shape, to which a square belongs to.
The top edges are congruent with each other, as well as the bottom ones. This is because you can turn one into the other by reflecting them using an isometry, so D is true.
What is the total percentage of college graduates who have found that their degree very helpful to develop specific skills and knowledge for the workplace?
From the graph given in the question, we can find out that
49% of the college graduates say that their college education was very useful for helping develop specific skills and knowledge for the workplace.
From the given question, the total percentage of college graduates who have found that their degree very helpful to develop specific skills and knowledge for the workplace is 49%
i need the answer i can’t figure it out and my teacher won’t help
Solution:
From the given question, we have
To solve for the ramp angle from the ground, we use trigonometric ratios.
Thus, we have
[tex]\sin\theta=\frac{opposite}{hypotenuse}[/tex]This gives
[tex]\begin{gathered} \sin\theta=\frac{11.5}{175} \\ \Rightarrow\sin\theta=0.06571 \\ take\text{ the sine inverse of both sides} \\ \sin^{-1}(\sin\theta)=\sin^{-1}(0.06571) \\ \theta=3.77^{\circ\:} \\ \therefore \\ \theta\approx3.8\degree(nearest\text{ tenth\rparen} \end{gathered}[/tex]Hence, to the nearest tenth, the ramp angle is
[tex]3.8\degree[/tex]Place the number 0 to 8 inclusive in the magic square so that the sum of the numbers in each row column and diagonal is the same number 12
To solve this type of problem we order the data from lowest to highest and compute the median, that number will be the one in the center of the magic square, also we group the numbers as follows:
first and last,
first+1 and last-1,
and so on.
The grouped numbers will be on opposite sides of the square with respect to the center.
In this case, the median is 4, and the grouped numbers are 0 and 8, 1 and 7, 2 and 6, 3 and 5.
Answer:
What is the output value for the following function, f(x) = 5x - 2 if the input value is 3?options:1751131
Solution:
Given the function below
[tex]f(x)=5x-2[/tex]Where
[tex]\begin{gathered} x\text{ is the input value} \\ f(x)\text{ is the output value} \end{gathered}[/tex]If the input value is 3, i.e. x = 3, the output value will be
[tex]\begin{gathered} f(x)=5x-2 \\ f(3)=5(3)-2=15-2=13 \\ f(3)=13 \end{gathered}[/tex]Hence, the output value is 13
[tex]3 = \frac{g}{ - 4} - 5[/tex]what does g equals ?
To solve the equation, first, add 5 to both sides
[tex]\begin{gathered} 3=\frac{g}{-4}-5 \\ 3+5=\frac{g}{-4}-5+5 \\ 8=\frac{g}{-4} \end{gathered}[/tex]Now, multiply by -4 from both sides of the equation
[tex]\begin{gathered} 8\cdot-4=\frac{g}{-4}\cdot-4 \\ -32=g \end{gathered}[/tex]Therefore, the value of g is -32.
One month Susan rented 5 movies and 6 video games for a total of $57. The next month she rented 3 movies and 2 video games for a total of $25. Find the rental cost for each movie and each video game?
The rental cost of each movie is $4.50
The rental cost of each video game is $5.75
Explanation:let the cost of one movie = m
let the cost of one video games = v
1st month:
Number of movies = 5
number of video games = 6
Total cost of both = $57
Total cost = cost of one movie(Number of movies ) + cost of one video (Number of video games)
57 = m(5) + v(6)
57 = 5m + 6v ...equation 1
2nd month:
Number of movies = 3
number of video games = 2
Total cost of both = $25
Total cost = cost of one movie(Number of movies ) + cost of one video (Number of video games)
25 = m(3) + v(2)
25 = 3m + 2v ...equation 2
57 = 5m + 6v ...equation 1
25 = 3m + 2v ...equation 2
Using elimination method:
To eliminate v, we would multiply equation 2 by 3:
3(25) = 3(3m) + 3(2v) ...equation 2
75 = 9m + 6v ...equation 2
57 = 5m + 6v ...equation 1
subtract equation 1 from 2:
75 - 57 = 9m - 5m + 6v - 6v
18 = 4m + 0
18 = 4m
m = 18/4
m = 4.5
Substitute for m in any of the equation:
Using eqauation1: 57 = 5m + 6v
57 = 5(4.5) + 6v
57 = 22.5 + 6v
57 - 22.5 = 6v
34.5 = 6v
v = 34.5/6
v = 5.75
The rental cost of each movie is $4.50
The rental cost of each video game is $5.75
hello can yoy help with this plane trigonometry question and in the question turn it into radians and thank you for your time for helping me
Answer:
The angle between 0 and 2 pie that is coterminal to the given angle is;
[tex]\frac{6}{7}\pi[/tex]Explanation:
We want to find the angle between 0 and 2 pie that is coterminal to;
[tex]\frac{34}{7}\pi[/tex]Angles that are coterminal with the given angle can be calculated using the formula;
[tex]x+n2\pi=\frac{34}{7}\pi[/tex]Where n=1,2,3...
and x is the coterminal angle.
At n = 1;
[tex]\begin{gathered} x+2\pi=\frac{34}{7}\pi \\ x=\frac{34}{7}\pi-2\pi \\ x=\frac{34}{7}\pi-\frac{14}{7}\pi \\ x=\frac{20}{7}\pi \end{gathered}[/tex]at n=2;
[tex]\begin{gathered} x+2(2\pi)=\frac{34}{7}\pi \\ x+4\pi=\frac{34}{7}\pi \\ x=\frac{34}{7}\pi-4\pi \\ x=\frac{34}{7}\pi-\frac{28}{7}\pi \\ x=\frac{6}{7}\pi \end{gathered}[/tex]At n=2;
The value of x is between 0 and 2pie;
So, the angle between 0 and 2 pie that is coterminal to the given angle is;
[tex]\frac{6}{7}\pi[/tex]What is 0.6222... as. a fraction, and how do I solve?
The given number is
[tex]0.6222\ldots[/tex]This number is a repeating decimal number, which is a rational number because it has a pattern that repeats infinitely. That pattern or period is 2.
To transform this decimal number into a fraction, we need to do it as follows
[tex]0.6\bar{2}=\frac{62-6}{90}[/tex]Notice that the difference is form by the complete number without a decimal point (62), and the digits before the repeating decimal (6). The denominator is formed by nines and zeros, in this case, we use one 9 because there's only one repeating digit, we use one 0 because there's only one digit between the decimal points and the repeating digit.
Now, we solve the fraction and simplify
[tex]0.6\bar{2}=\frac{62-6}{90}=\frac{56}{90}=\frac{28}{45}[/tex]Therefore, the fraction 28/45 is the one that represents the repeating decimal 0.6222...The U.S. Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxidelevels since 1959. At that time, there were 326 parts per million of carbon dioxide in theatmosphere. In 2005, the figure was 366 parts per million. Find the increase in carbon dioxide levelsand the percent of increase, to two decimal places.Increase carbon dioxide levels:parts per millionPercent increase:%
Answer:
12.27 % increase
Carbon dioxide increased by 40 ppm
Explanation:
We know that carbon diox
I need help with multi step equations if anybody that would be great
We have the following equation:
[tex]28=-k+16-2k-9[/tex]They ask us to solve this equation, in this case, we must solve for "k"
Now, we clear k
[tex]\begin{gathered} 28=-k+16-2k-9 \\ 28=-3k+7 \\ 3k=-28+7 \\ 3k=-21 \\ k=-\frac{21}{3} \\ k=-7 \end{gathered}[/tex]Compared with your solution, this is also correct, let's see the last step in which you are
[tex]\begin{gathered} -3k=21 \\ k=\frac{21}{-3} \\ k=-7 \end{gathered}[/tex]Your solution to this equation is correct in each step you did, you just need to move on to divide the (-3) to the other side
In conclusion, the answer si k = -7
help please and thankyou Graph the line y = 2x + 3
the line will be:
we can find the method of finding the intercepts and then link them with a unique line:
the x-intercept is when y=0 then 2x+3=0 then x=-3/2=-1.5
the y-intercept is when x=0 then y=3
then we can link the points (-1.5,0) and (0,3) and we have the graph of the given line.
if the point (-1,4)and (2,13)are on the graph of the quadratic function [tex]y = 7x {}^{2} + bx + c[/tex]what are the values of b and c
The Solution:
Given:
[tex]y=7x^2+bx+c[/tex]Given that the points: (-1,4) and (2,13) are on the graph of the given equation,
We are required to find the values of a and b.
Substitute (x= -1, y = 4) in the equation, we get:
[tex]\begin{gathered} 4=7(-1)^2+b(-1)+c \\ 4=7-b+c \\ -3=-b+c...eqn(1) \end{gathered}[/tex]Substitute (x= 2, y = 13) in the equation, we get:
[tex]\begin{gathered} 13=7(2)^2+b(2)+c \\ 13=28+2b+c \\ -15=2b+c...eqn(2) \end{gathered}[/tex]Solving eqn(1) and eqn(2) simultaneously by the elimination method:
Subtract eqn(1) from eqn(2):
[tex]\begin{gathered} -15--3=2b--b+c-c \\ -12=3b \end{gathered}[/tex]Divide both sides by 3.
[tex]b=\frac{-12}{3}=-4[/tex]Substitute -6 for b in eqn(1).
[tex]\begin{gathered} -3=-b+c \\ -3=-(-4)+c \\ \\ -3=4+c \\ -3-4=c \\ -7=c \\ c=-7 \end{gathered}[/tex]Therefore, the correct answers are:
b = -4
c = -7
A local road rises 33 feet for every 423 feet of pavement. What is the slope of the road? Simplify your answer.
If a local road rises 33 feet for every 423 feet of pavement, the slope of the road will be rate of change of pavement with respect to the road. This is expressed as;
slope of the road = 423/33
Slope of the road = 12.82
Hence the slope of the road is 12.82
Complete the explanation of whether the graph represents a proportional oa neno relationship 5 5 5 relationship The graph represents a (select) (select) proportional nonproportional
We are given the graph of a line, and we are asked to determine if it is a proportional or non-proportional relationship. Let's remember the general form of the equation of a line, that is:
[tex]y=mx+b[/tex]where "m" is the slope and "b" the y-intercept. The y-intercept is the value where the line touches the y-axis. According to the graph, the value of "b" is b = 1, therefore, the equation of the line would be:
[tex]y=mx+1[/tex]A proportional relationship is of the form:
[tex]y=kx[/tex]since the value of "b" is different from zero the relationship is non-proporsional.
The relationship is non-proportional
In AABC, AB5, BC8, and AC7. Name the largest angle of AABC
Given the dimensions of triangle ABC:
AB = 5
BC = 8
AC = 7
Let's determine the largest angle of triangle ABC.
We have a sketch of the triangle below:
In a triangle, the largest angle is the angle opposite the side with the largest side length.
From the given triangle ABC, the largest side is BC = 8.
The angle which is opposite BC is angle BAC.
Therefore, the largest angle of △ABC is ∠BAC
5/3×(-3/4) what's the answer
using the definition of multiplication between two fractions
[tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\cdot c}{b\cdot d}[/tex]we obtain,
[tex]\frac{5}{3}\times-\frac{3}{4}=-\frac{5\cdot3}{3\cdot4}=-\frac{5}{4}[/tex]Find the magnitude of u using the dot product. Write the result in radical form or decimal form, rounded to the nearest hundredth.u = (-2,-5)
|u| = √29
Explanations:Since we are only given one vector, we cannot compute its dot product. However, the magnitude of a vector (x, y) is expressed as:
[tex]|u|=\sqrt{x^2+y^2}[/tex]Given the vector u = (-2, -5), the magnitude of u is expressed as:
[tex]\begin{gathered} |u|=\sqrt{(-2)^2+(-5)^2} \\ |u|=\sqrt{4+25} \\ |u|=\sqrt{29} \end{gathered}[/tex]Hence the magnitude of the vector in radical form is √29
Find the mean, median, and mode for the data set. If there is no mode, write none. If there is more than one mode,write your solutions from least to greatest, separated by a comma.50,30,40,10,20,80,60,90,10,30,110, 70mean:median:mode:
Answer:
• Mean: 50
,• Median: 45
,• Mode: 10,30
Explanation:
Given the data set:
[tex]50,30,40,10,20,80,60,90,10,30,110,70[/tex]Before we begin, arrange the numbers from the least to the greatest.
[tex]10,10,20,30,30,40,50,60,70,80,90,110[/tex](a)Mean
To find the mean, add up the numbers and divide by the number of items (12 in this case).
[tex]\begin{gathered} Mean=\frac{10+10+20+30+30+40+50+60+70+80+90+110}{12} \\ =\frac{600}{12} \\ Mean=50 \end{gathered}[/tex]The mean of the dataset is 50.
(b)Median
The median is the number in the middle of the dataset when arranged in ascending order.
• There are two numbers in the middle: 40 and 50
,• Take the average to find the median.
[tex]Median=\frac{40+50}{2}=\frac{90}{2}=45[/tex]The median of the dataset is 45.
(c)Mode
The mode is/are the number(s) that appear the most number of times..
[tex]10,10,20,30,30,40,50,60,70,80,90,110[/tex]In the dataset:
• 10 appears twice
,• 30 appears twice
The modes of the dataset are 10 and 30.
A bottle holds 5/12 gallon of water. How many bottles can be filled with 2 1/4 gallons of water.1. 5 2/52. 3 3/43. 5/274. 45/48
The bottle holds 5/12 gallon of water
to fill bottles with 2 1/4 gallon of water
so, the number of bottles will be :
so, the answer is 5 2/5