Answer:
y = 2/7x + 7
Step-by-step explanation:
We start off by putting the original equation into slope-intercept form. Subtract 7x from both sides, then divide both sides by -2. Your new equation should be y = -7/2x - 8. It's important to know that when two lines are perpendicular, their slopes (m) are opposite reciprocals of each other. So -7/2 becomes 2/7. The first part of your final equation is y = 2/7x + b.
Next, we need to find the y intercept (b). You need to plug the x and y values from the given coordinate point (-7,5) into your final equation. You should end up with: 5 = 2/7(-7) + b. Then, solve for b.
5 = -14/7 + b
5 = -2 + b
7 = b
Finally, plug the b value into your final equation and you will have your answer.
How do you do these questions? With step by step instructions please
Answer: n = 3 n = 4
Upper Sum ≈ 3.41 Upper Sum ≈ 3.25
Lower Sum ≈ 2.15 Lower Sum ≈ 2.25
Step-by-step explanation:
You are trying to find the area under the curve. Area = height x width.
Height is the y-value at the given coordinate --> f(x)
Width is the distance between the x-values --> dx
n = 3
First, let's figure out dx: the distance from -1 to +1 is 2 units. We need to divide that into 3 sections because n = 3 --> dx = 2/3
So the points we will evaluate is when x = {-1, -1/3, 1/3, 1}
For the upper sum, we find the max y-value for each interval
For the lower sum, we find the min y-value for each interval
Next, let's find the height for each of the x-values:
f(x) = 1 + x²
f(-1) = 1 + (-1)² = 2
f(-1/3) = 1 + (-1/3)² = 1 + 1/9 --> 10/9
f(1/3) = 1 + (1/3)² = 1 + 1/9 --> 10/9
f(1) = 1 + (1)² = 2
Interval Max Min
{-1, -1/3} f(-1) = 2 f(-1/3) = 10/9
{-1/3, 1/3} f(-1/3) = 10/9 f(0) = 1 (vertex lies in this interval)
{1/3, 1} f(1) = 2 f(1/3) = 10/9
Now, let's find the Area: A = f(x) dx:
[tex]\text{Upper Sum:}\quad A=\dfrac{2}{3}\bigg(2+\dfrac{10}{9}+2\bigg)\\\\.\qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{46}{9}\bigg)\\\\.\qquad \qquad \qquad =\dfrac{92}{27}\\\\.\qquad \qquad \qquad =\large\boxed{3.41}[/tex]
[tex]\text{Lower Sum:}\qquad A=\dfrac{2}{3}\bigg(\dfrac{10}{9}+1+\dfrac{10}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{29}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{58}{27}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.15}[/tex]
*****************************************************************************************
n = 4
First, let's figure out dx: the distance from -1 to +1 is 2 units. We need to divide that into 4 sections because n = 4 --> dx = 2/4 = 1/2 (simplified)
So the points we will evaluate is when x = {-1, -1/2, 0, 1/2, 1}
For the upper sum, we find the max y-value for each interval
For the lower sum, we find the min y-value for each interval
Next, let's find the height for each of the x-values:
f(x) = 1 + x²
f(-1) = 1 + (-1)² = 2
f(-1/2) = 1 + (-1/2)² = 1 + 1/4 --> 5/4
f(0) = 1 + (0)² = 1
f(1/2) = 1 + (1/2)² = 1 + 1/4 --> 5/4
f(1) = 1 + (1)² = 2
Interval Max Min
{-1, -1/2} f(-1) = 2 f(-1/2) = 5/4
{-1/2, 0} f(-1/2) = 5/4 f(0) = 1
{0, 1/2} f(1/2) = 5/4 f(0) = 1
{1/2, 1} f(1) = 2 f(1/3) = 5/4
Now, let's find the Area: A = f(x) dx:
[tex]\text{Upper Sum:}\qquad A=\dfrac{1}{2}\bigg(2+\dfrac{5}{4}+\dfrac{5}{4}+2\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{26}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{13}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{3.25}[/tex]
[tex]\text{Lower Sum:}\qquad A=\dfrac{1}{2}\bigg(\dfrac{5}{4}+1+1+\dfrac{5}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{18}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{9}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.25}[/tex]
Your math teacher is only giving three tests this quarter. They count equally and your quarter grade will be the average of the tests. You scored a 79% on the first test and an 84% on the second test. If your quarter grade is below a 75% you will be grounded from your phone. What scores will get you into trouble on your report card?
3 tests at 75% each = 3 x 75 = 225 total points
First two tests = 79 + 84 = 163
Third test needs to be at least: 225 - 163 = 62%
So any score less than 62 would get you into trouble.
A factory worker can produce 28 toys in an eight hour day If there are 42 workers in total how many toys are produced every hour
Answer:
147 toys
Step-by-step explanation:
for 1 person, 28toys/8hours = 3.5toys/ 1hour
for 42 people, 42 * 3.5toys/ 1hour = 147 toys/hour
~Hope it Helps!~
Find g(-2) + h(4) if g(x)= 5-2x and h(x) = - x2 pls help
Answer:
-7
Step-by-step explanation:
g(x)= 5-2x and h(x) = - x^2
g(-2) + h(4)
First find g(-2)
g(-2) = 5 -2(-2) = 5 +4 = 9
Then find h(4) = - 4^2 = -16
g(-2) + h(4) = 9-16 = -7
Answer:
-7
Step-by-step explanation:
Substitute -2 into g(x) equation,
g(x) = 5 - 2x
g(-2) = [5 - 2(-2)] = 9
Substitute 4 into h(x) equation,
h(x) = -x^2
h(4) = [-(4)^2] = -16
Therefore,
g(-2) + h(4) = 9 + (-16) = -7
What is the measure of r
Answer:
The two marks on the right and left side of the triangle means that it's an isosles triangle which means that the base angles are equal and any triangle in the world the sum of its angles is 180° and you have an angle with 100° so you should subtract 100 from 180 that gives 80° and dived 80 by 2 that gives you 40°
I'm trying to find sin of (7pi/12) exactly using an angle of addition or subtraction formula could anyone help me
Answer:
(√2 + √6)/4.
Step-by-step explanation:
Use the addition formula
sin (A+ B) = sinAcosB + cosAsinB
sin (7pi/12) = sin( 3pi/12 + 4pi/12)
= sin(pi/4 + pi/3) = sin pi/4 cos pi/3 + cos pi/4 sin pi/3
= 1/√2 * 1/2 + 1/√2 * √3/2 (using the 45-45-90 and 30-60-90 triangles)
= 1 / 2√2 + √3/2√2
= √2/4 + √6/4
= (√2 + √6)/4
Amy, Ray, Kim, and Jamal are on a trivia team. They gain points for correct answers
and lose points for incorrect answers. During the contest, Amy gains 3 points, Ray loses
4 points, Kim loses 2 points, and Jamal gains 5 points. How many points does the team
have at the end of the contest?
Answer:
2 points
Step-by-step explanation:
0+3-4-2+5=2 points
The grades in period 3 Algebra 2 have an average of 82% and vary by 12 percentage points. Formulate an absolute value equation that could be used to solve for the maximum and minimum grade.
|x______ | = _______
x = __________ (smaller number here)
x = _______ (larger nember here)
Blank 1:
Blank 2:
Blank 3:
Blank 4:
Answer:
[tex]|x - 85| = 12[/tex]
[tex]x = 73 \ (smaller\ number )[/tex]
[tex]x = 97 \ (larger \ number )[/tex]
Step-by-step explanation:
From the question we are told that
The grade is [tex]k = 85\%[/tex]
The variation is [tex]v = 12 \%[/tex]
Generally the absolute value equation is mathematically represented as
[tex]|x - 85| = 12[/tex]
=> [tex]x -85 = \pm 12[/tex]
So
[tex]x = 85 + 12[/tex]
[tex]x = 97 \ (larger \ number )[/tex]
And
[tex]x = -12 + 85[/tex]
=> [tex]x = 73 \ (smaller\ number )[/tex]
Given the following formula, solve for I.
P =
2(1 + b)
Answer: [tex]l=\dfrac{P}{2}-b[/tex]
Step-by-step explanation:
P = 2(l + b)
Divide both sides by 2:
[tex]\dfrac{P}{2}=l+b[/tex]
Subtract b from both sides:
[tex]\dfrac{P}{2}-b=l[/tex]
Note: You can also multiply b by [tex]\frac{2}{2}[/tex] if you want the left side to be one fraction.
[tex]\dfrac{P}{2}-\bigg(\dfrac{2}{2}\bigg)b=l\\\\\\\dfrac{P-2b}{2}=l[/tex]
Point R is on line segment QS. Given RS = 13 and QS = 20, determine the length of QR
Answer:
Length of QR = 7
Step-by-step explanation:
20 - 13 = 7
When you woke up this morning, the temperature was -5.8°C. At noon, the temperature was 2.9°C. Which expression and statement describes the situation?
Answer:
-5.8<2.9
Step-by-step explanation:
(!20 POINTS PLEASE HELP!) The students in a class are randomly drawing cards numbered 1 through 28 from a hat to determine the order in which they will give their presentations. Find each probability. Solve each problem below 1. P(13) 2. P(less than 14) 3. P(not 2 or 17)
Since there is 28 cards, the chance of drawing 1 card will be [tex]\frac{1}{28}[/tex]
Therefore, [tex]P(13)=\frac{1}{28}[/tex].
There are 13 numbers less than 14 and greater than 0.
Therefore [tex]P(>14)=\frac{13}{28}[/tex]
There are 26 numbers that are not 2 or 17.
Therefore [tex]P(\neq 2,17)=\frac{26}{28}=\frac{13}{14}[/tex]
Hope this helps.
頑張って!
Probability of
Option (1). P(13) =[tex]\frac{1}{28}[/tex]
Option (2). P(less than 14) = [tex]\frac{13}{28}[/tex]
Option (3). P(not 2 or 17) =[tex]\frac{13}{14}[/tex]
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur
Given,
Total number of card = 28
Probability = Number of favorable outcome / Number of total outcome
Probability of picking 13 = [tex]\frac{1}{28}[/tex]
Probability of picking a card less then 14 = [tex]\frac{13}{28}[/tex]
Probability of not picking 2 or 17 = [tex]\frac{26}{28}=\frac{13}{14}[/tex]
Hence, the probability of
Option (1). P(13) =[tex]\frac{1}{28}[/tex]
Option (2). P(less than 14) = [tex]\frac{13}{28}[/tex]
Option (3). P(not 2 or 17) =[tex]\frac{13}{14}[/tex]
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Students in a large statistics class were randomly divided into two groups. The first group had a midterm exam that was printed on canary paper while the second group had the exam printed on pale green paper. The exam scores of the two groups were then then compared.This experiment was not blind because:_______a. Students were allowed to keep their eyes open while taking the exam.b. The exam was too long.c. The students knew whether or not music was playing while they were taking the exam.d. Some of the students did not study for the exam.e. Students were randomized into the two groups.
Answer:
e. Students were randomized into the two groups.
Step-by-step explanation:
A bag contains 6 RED beads, 3 BLUE beads, and 11 GREEN beads. If a single bead is picked at random, what is the probability that the bead is RED or GREEN?
Answer:
17/20
Step-by-step explanation:
Total no. of beads = 6 + 3 + 11 = 20
We need RED or GREEN bead .
So no. of beads needed = 6 + 11 = 17
So probability of getting GREEN or RED beads = 17/20
Glados
spent the day at the mall, First, she bought
three bikes for $10 each. Later, she found 22
dollar bills. Write the total change
an integer.
to Glado's
funds as an integer
Answer:
8
Step-by-step explanation:
do all sets have subsets?
Answer:
yes
Step-by-step explanation:
d) 256 chocolates are distributed among the students of class 5.
If the number of chocolates obtained by each students is the same
as the number of students in the class, find the number of students
in the class?
Answer:
16
Step-by-step explanation:
Let x be the number of chocolates obtained by each student
Since the number of chocolates obtained by each student = the number of students in the class, then, number of students in the class = x
256/x = x
Multiply both sides by x
256 = x × x ( x squared)
Multipy powers raised on both sides by 1/2
X = 16
use the values in the table to determine the slope.
Answer:
-3/2
Step-by-step explanation:
Take two points from the table and use the slope formula
m= (y2-y1)/(x2-x1)
= ( 19 - 13)/ ( -4 - 0)
= 6/-4
= -3/2
y varies inversely with x. If y = 5 when x = 60, find y when x = 150
pre cal
Answer:
y = 2 when x = 150
Step-by-step explanation:
Inverse variation is
xy = k
5*60 = k
300 = k
xy = 300
150y = 300
Divide by 150
150y/150 = 300/150
y = 2
T is the midpoint of SU, ST = 8x + 11 and TU = 12x-1, find the value of x.
Answer:
x = 3
Step-by-step explanation:
mid point means it bisects the segment into two equals halfs meaning
ST = TU
8x + 11 = 12x - 1
8x + 12 = 12x
12 = 4x
3 = x
Write the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 in this order and insert '+' or '-' between them to get the result 3? Please Help
Answer:
0 - 1 - 2 + 3 - 4 + 5 - 6 +7 - 8 + 9 = 3
Step-by-step explanation:
02.01)Which is the ratio of the number of months that begin with the letter J to the total number of months in a year? 12 to 3 3 to 9 9 to 12 3 to 12 HELP!!! FOR MY MATH TEST
Answer:
3 to 12
Step-by-step explanation:
3 months (January, June, July) and 12 monthes
Answer: the answer is 3 to 12
Step-by-step explanation: hope this will help
A plane is a _____ figure
Answer:
bold
Step-by-step explanation:
hshsjjsududidididiidododododokdodkdjdndndnjdudududuididjdjdjd
A plane is a two dimensional figure.
There was 1 liter of water in the water bottle. Tom drank 200 milliliters of water. How many liters of water are left?
Answer:
.8L
Explanation:
Logic
The liters of water left are 0.8 liters.
What is an Equation?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
The equations are useful in the determination of unknown parameters.
The quantity of water in a water bottle is 1 liter.
The amount of water Tom drank is 200 milliliters.
Let x be the amount of water left in the bottle.
The liter has to be converted into milliliters.
1 liters = 1000 milliliters
The equation formed is,
1000 - 200 = x
x = 1000 - 200
x = 800 milliliters.
The water left in the water bottle is 800 milliliters.
1000 milliliters = 1 liters
800 milliliters = 0.8 liters
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alex buys six equally priced candy bars for $9:00 what is the unit rate?
Answer:
$1.5 unit
Step-by-step explanation:
According to the given situation, the calculation of the unit rate is shown below:-
Candy bars = 6
Amount of candy bars = $9:00
Unit rate
[tex]= \frac{Amount\ of\ candy\ bars}{Number\ of\ candy\ bars}[/tex]
Now we will put the values into the above formula
[tex]= \frac{\$9:00}{6}[/tex]
Which gives result
= $1.5 unit
Therefore for computing the unit rate we simply divide the amount of candy bars by the number of candy bars.
what is -3.5+(-4.9)=?What is the answer please?
Answer:
The answer is -8.4
Emma and Clair are planning to sell lemonade on their street. They have two recipes to choose from. Emma’s recipe calls for the juice of 5 lemons and 2 cups of water. Clair’s recipe calls for the juice of 2 lemons and 1 cup of water. Why will the first recipe taste more “lemony”?
Answer:
Emma's recipe will be more lemony because
5/2=2.5
2/1=2
Step-by-step explanation:
Answer:
The ratio of lemon juice to water in Emma’s recipe is 5 to 2; the ratio in Clair’s recipe is 4 to 2. Emma’s recipe will taste more lemony because it has a greater ratio of lemon juice to water.
Step-by-step explanation:
Sample Answer
Can someone plz tell me if I’m right?
Answer:
Step-by-step explanation:
Since x is used a lot as a variable in algebra, I would use another symbol for multiplication. Though if your teacher requires you to use x as a multiplication symbol, then keep it as is. I use the asterisk symbol
Example: 2 times 3 = 2*3
------------------------------------------
For problem 2, you have the parenthesis in the wrong spots. Saying "the sum of four plus five" means we have 4+5 as you'd expect. Then you multiply that group with 2. So you'd really have (4+5)*2
How is this different from 4+5*2 back in problem 1? It comes down to how the order of operations handles things. To evaluate 4+5*2, we multiply first, then add. So we have 4+5*2 = 4+10 = 14
With the other expression, we add first because it is in the parenthesis block. Afterward we multiply the values to get (4+5)*2 = 9*2 = 18
Bolts are packed into bags at a factory. Each bag should have 25 bolts in it but a bad with 22 or 28 is acceptable. Formulate an absolute value equation that could be used to solve for the minimum and maximum number of bolts in a bag.
|x____ | = ______
x = _____(smaller number here)
x = ________(larger number here)
Blank 1:
Blank 2:
Blank 3:
Blank 4:
Answer:
Absolute value equation is; |x - 25| ≤ 3
Minimum number of bolts is 22 while Maximum number of bolts is 28
Step-by-step explanation:
We are told that;
Each bag should have 25 bolts in it but 22 or 28 is acceptable.
Since 22 or 28 is acceptable, it means the allowable error is ±3.
Thus, if x is the number of bolts in the bag, the absolute value equation would be;
|x - 25| ≤ 3
Minimum number of bolts is 22 while maximum is 28
CAN SOMONE PLEASE HELP ME ASAP PLEASEEE!!!
Answer:
The yellow polygon is the scaled version of the red one (scaled by 3×), so the variable w = 9
Answer:
9
Step-by-step explanation:
The similarity ratio is 4/x = z/9 = 2/6 = 3/w = y/15
2/6 = 3/w cross multiply expressions 2w = 18 and w = 9