Answer:
[tex]m=\frac{3}{2}[/tex]
Step-by-step explanation:
When two lines are perpendicular, their slopes will be opposite reciprocals:
[tex]-3[/tex] → [tex]\frac{1}{3}[/tex]
[tex]\frac{1}{4}[/tex] → [tex]-4[/tex]
Solve the first equation for y to rewrite in slope-intercept form:
[tex]y=mx+b\\\\3y+2x=7\\\\3y+2x-2x=7-2x\\\\3y=-2x+7\\\\\frac{3y}{3}=\frac{-2x}{3} +\frac{7}{3} \\\\y=-\frac{2}{3}x+\frac{7}{3}[/tex]
m is the slope, so the slope of this line is [tex]-\frac{2}{3}[/tex]. The opposite reciprocal is [tex]\frac{3}{2}[/tex], therefore, m is [tex]\frac{3}{2}[/tex]
i need help bad and fast
Answer: E) CD
Step-by-step explanation:
A segment with a slope of 0 on this graph represents a time where no distance is made, or a break. The only segment with a slope of 0(where distance does not increase) is segment CD.
Hope it helps <3
Answer:
CD
Step-by-step explanation:
CD is the answer because the graph becomes a flat line when a body is at rest
Pleasee help multiple choice whoever gets it correct gets brainlest
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{j = 6}}}}[/tex]Option D is the correct option
Step-by-step explanation:
[tex] \sf{(5 + 3)j = 48}[/tex]
Distribute j through the parentheses
⇒[tex] \sf{5j + 3j = 48}[/tex]
Collect like terms
⇒[tex] \sf{8j = 48}[/tex]
Divide both sides of the equation by 8
⇒[tex] \sf{ \frac{8j}{8} = \frac{48}{8} }[/tex]
Calculate
⇒[tex] \sf{j = 6}[/tex]
Hope I helped!
Best regards!!
For parts a through f., A denotes an mxn matrix. Determine whether each statement is true or false. Justify each answer. a. A null space is a vector space. Is this statement true or false?
A. True because the null space of an mx n matrix A is a subspace of Rm
B. False, a column space is a vector space, but a null space is not a vector space
C. False, a vector space is a null space, but a null space is not necessarily a vector space
D. True because the null space of an mxn matrix A is a subspace of Rn
Answer:
D. True because the null space of an m x n matrix A is a subspace of [tex]$R^n$[/tex]
Step-by-step explanation:
A null space is also the vector space.
We know that a null set satisfies the following properties of a vector space.
Now let [tex]$x,y \in Null (A), \alpha \in IR$[/tex] , then
[tex]A[\alpha x+y] = \alpha A(x)+ A(y) = \alpha . 0 + 0 = 0$[/tex]
Thus, [tex]$ \alpha x+y \in Null (A)$[/tex]
Hence, option (d) is true.
If tan Θ=3/4, then evaluate 3sin Θ +2cos Θ
Answer:
[tex]3\sin\theta+2\cos\theta=\dfrac{17}{5}[/tex]
Step-by-step explanation:
Given that,
The value of [tex]\tan\theta=\dfrac{3}{4}[/tex]
We know that, [tex]\tan\theta=\dfrac{\text{perpendicular}}{\text{base}}[/tex]
[tex]H^2=B^2+P^2[/tex]
H is hypotenuse
[tex]H^2=3^2+4^2\\\\H=5[/tex]
[tex]\sin\theta=\dfrac{P}{H}\\\\=\dfrac{3}{5}[/tex]
And, [tex]\cos\theta=\dfrac{B}{H}=\dfrac{4}{5}[/tex]
So,
[tex]3\sin\theta+2\cos\theta=3\times \dfrac{3}{5}+2\times \dfrac{4}{5}\\\\=\dfrac{9}{5}+\dfrac{8}{5}\\\\=\dfrac{17}{5}[/tex]
So, the value is 17/5.
f(x)=x2–5x+7, find f(3)
Answer:
1
Step-by-step explanation:
Hello!
To find f(3) we put 3 in for x
[tex]3^{2} -5(3)+7[/tex]
Follow PEMDAS
9 - 5(3) + 7
9 - 15 + 7
-6 + 7 = 1
The answer is 1
Hope this helps!
Answer:
f(3) = 1
Step-by-step explanation:
f(x) = x^2 – 5x + 7
f(3) = 3^2 - 5(3) + 7
f(3) = 9 - 15 + 7
f(3) = -6 + 7
f(3) = 1
Complete the following sentence. The coefficient of determination between the dependent variable, TEST SCORE, and the independent variable, HOURS SPENT STUDYING, equals 043. This means that:_________.
a. variation in the variable, HOURS SPENT STUDYING explains 43% of the variation in the variable. TEST SCORE
b. variation in the variable, TEST SCORE, explains 43% of the variation in the variable, HOURS SPENT STUDYING
c. the correlation between HOURS SPENT STUDYING and TEST SCORE equals 0.43
d. the correlation between HOURS SPENT STUDYING and TEST SCORE equals 0.57,
Answer: a. variation in the variable, HOURS SPENT STUDYING explains 43% of the variation in the variable. TEST SCORE
Step-by-step explanation:
The coefficient of determination is denoted by R square is the proportion of the variance in the dependent variable that is predictable from the independent variable.
Given: dependent variable = TEST SCORE
independent variable = HOURS SPENT STUDYING
coefficient of determination = 0.43
That means variation in the variable, HOURS SPENT STUDYING explains 43% of the variation in the variable. TEST SCORE.
Hence, the correct option is a.
Show that the curve x = 7 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and find their equations.
y = __________ (smaller slope)
y = __________ (larger slope)
The equations of the two tangents are; Larger slope; y = (5/7)x Smaller slope; y = (-5/7)x
What is the slope?Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
This is because the more the height of the line to thee amount we walk or run on the horizontal axis, the more the slope is. Thats why we took difference of horizontal axis in denominator and difference of vertical axis on numerator.
The curve x = 7 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and we need to find their equations.
We can write
cos(t) = x/7
so
y = 5(±√(1 -(x/7)^2)*x/7
Then
y' = (±5/7)*(√(1 -(x/7)^2) + x/(2√(1 -(x/7)^2)*(-2(x/7))
The limit as x → 0 is ±5/7
The equations of the two tangents are;
Larger slope; y = (5/7)x
Smaller slope; y = (-5/7)x
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24a + 72b - 40c what’s the answer can somebody help me I’m confused
Answer:
8⋅(3a+9b−5c)
Step-by-step explanation:
The equation in a simple form by using the greatest common factor is
8 ( 3a + 9b -5c ).
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The greatest common factor is the largest positive number which can be divided into given numbers evenly.
The expression will be simplified as below:-
E = 24a + 72b - 40c
Take the number 8 common from the expression.
E = 8 ( 3a + 9b -5c ).
Therefore, the equation in a simple form by using the greatest common factor is 8 ( 3a + 9b -5c ).
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Bank A charges $30 monthly fee for a check account bank B charges $15 a month How much would Keiko pay at each bank each month
Answer:
Keiko would pay $30 a month at bank A.
Keiko would pay $15 a month at bank B.
Both bank A and bank B combined would be $45 a month.
Step-by-step explanation:
PLEASE HELP MEEE
Simplify the expression to a polynomial in standard form
(x+3)(2x2+3x+7)
Answer:
2x^3 + 9x^2 + 16x + 21.
Step-by-step explanation:
We first multiply the expression in the second parentheses by x , then by +3:
(x + 3)(2x^2 + 3x + 7)
= x(2x^2 + 3x + 7) + 3(2x^2 + 3x + 7)
= 2x^3 + 3x^2 + 7x + 6x^2 + 9x + 21 Now we add like terms:
= 2x^3 + 9x^2 + 16x + 21.
Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
Twice the difference of a number and 8.
Answer:
2(x - 8)
Step-by-step explanation:
How do i write 2.200 (in decimals) into word form. Explain pls
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Two Thousand Two Hundred
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Answer:
Two and Two Tenths.
Step-by-step explanation:
The whole number if you were to just say it is two, so you have that part, but then for the decimals, the zeros don't really matter you can take them off and you have the same number ( but only if there is nothing after the zeros) so now you are left with 2.2 and the first decimal spot is the tenths so the wording for this would Two and Two Tenths.
4x+y=10
( ,-6)
find the x value
please hellllpppp !!
Answer:
x=4
Step-by-step explanation:
4x+y=10
y=-6
4x-6=10
4x=16
x=4
(4,-6)
Order these from least to greatest. -13/8, -2.1, -26/13, -9/4 I know how to do this I'm just to lazy too and I want to chat.
Answer:
-9/4, 2.1, -26/13, -13/8
Step-by-step explanation:
In a survey of 200 game lovers,it was found that 130 liked football, 90 liked cricket, and 20 didn't like both games.i) How many people were there who liked both football as well as cricket? ii)How many people like only cricket? A. 30,60 B. 40,50 C. 50,40
Step-by-step explanation:
Hey, there!!
Your required answer is:
i). = 40
ii). = 90
See explanation in picture..
Here, no(F) represents no. of people who just like football. and n (F intersection C) represents who like both games.
Hope it helps...
The deepest ocean depth is 35 , 840 feet, found in the Pacific Ocean's Mariana Trench. The tallest mountain is Mount Everest, with a height of 29 , 028 . What is the difference between the highest point on Earth and the lowest point on Earth?
Answer:
64868 feet
Step-by-step explanation:
The deepest point as a negative 35,840 feet mark
The tallest point has a positive 29,028 feet mark
The difference between them:
29,028 - (-35,840) = 64,868 feetAnswer is 64,868 feet
Find the z-scores (two of them) that separate the middle 48% of the distribution from the area in the tails of the standard normal distribution.
Answer:
The z-scores are [tex]Z_{\frac{\alpha }{2} } = 0643[/tex] and [tex]Z_{\frac{\alpha }{2} } = - 0643[/tex]
Step-by-step explanation:
From the question we are told that
The middle of the distribution area considered is 48%
Now the rest of the area under the standard normal distribution area is mathematically evaluated
[tex]\alpha = 100- 48[/tex]
[tex]\alpha = 52 \%[/tex]
[tex]\alpha = 0.52[/tex]
Now to obtain the area occupied by this proportion at the two tails we divide by 2 i.e
[tex]\frac{\alpha }{2} = \frac{0.52}{2} =0.26[/tex]
Now the z-score is obtained from the normal distribution table and the value is
[tex]Z_{\frac{\alpha }{2} } \pm 0.643[/tex]
The [tex]\pm[/tex] shows that we are considering the two-talil
c+2c+12=75 find the value of c
Answer:
c+2c+12=75
c = 21
Steps:
c+2c+12=75
Simplify both sides of the equation.
c+2c+12=75
(c+2c)+(12)=75(Combine Like Terms)
3c+12=75
3c+12=75
Subtract 12 from both sides.
3c+12−12=75−12
3c=63
Divide both sides by 3.
A sample of single persons in Towson, Texas, receiving Social Security payments revealed these monthly benefits: $426, $299, $290, $687, $480, $439, and $565. (a) What is the median monthly benefit? (b) Is the mean you computed in (a) a statistic or a parameter? Why?
Answer:
a) Median Monthly Benefit = $439
b) The mean computed above is a STATISTIC. This is because, the mean of their monthly benefits ($455.14) was calculated from a SAMPLE (which could have been known or random) of single persons in Towson Texas.
Step-by-step explanation:
In the above question, we are given:
: $426, $299, $290, $687, $480, $439, and $565.
a) Median Monthly benefits
First we arrange the monthly benefits from the lowest to the highest
$290, $299, $426, $439, $480, $565, $687
Median Monthly Benefit is the number found in the middle of the Monthly benefits.
We were given 7 monthly benefit
$290, $299, $426,) $439, ($480, $565, $687
The median monthly benefit = $439
(b) Is the mean you computed in (a) a statistic or a parameter? Why?
The Mean Monthly Benefit = Sum of terms/Number of terms
Number of terms = 7
($290 + $299 + $426 + $439 + $480 + $565 + $687)/ 7
= $3186/7
= $455.14285714286
Approximately ≈$455.14
In the question we are asked if the Mean calculated or computed above is a Statistic or a Parameter.
The mean computed above is a STATISTIC. This is because, the mean of their monthly benefits ($455.14) was calculated from a SAMPLE (which could have been known or random) of single persons in Towson Texas.
X+y+z=1
X-2y+3z=2
X+z-5=0
x+y+z=1
x=1/(y+z)
1/(y+z)-2y+3z=2
1-2y²-2yz+3yz+3z²=2(y+z)
(1-2y²+yz+3z²)/2=y+z
z=(1-2y²+yz+3z²)/2 -y/1
z=(1-2y²+yz+3z²-2y)/2
Hello. There is 2 questions in the links below if you could solve them that would be awesome!
The length of the longer leg of a right triangle is 19 cm more than five times the length of the shorter leg. The length of the hypotenuse is 20 cm more than five times the length of the shorter leg. Find the side lengths of the triangle
Answer:
13 cm, 84 cm, 85 cm
Step-by-step explanation:
Let the sides of triangle are be a, b, c
a = x, b = 5x + 19, c = 5x + 20As per Pythagorean theorem:
c² = a² + b²(5x+20)² = (5x +19)² + x²25x² + 200x + 400 = 25x² + 190x + 361 + x²x² - 10x - 39 = 0Solving the quadratic equation we get:
x= 13Then:
a= 13 cmb = 5*13 +19 = 84 cmc= 5*13 + 20 = 85 cmOn three science tests, Olivia has received scores of 89%, 98%, and 96%. What is the lowest score Olivia can get on her fourth and final science test to achieve an average score of 95%?
a
94%
b
97%
c
96%
d
95%
Answer:
97%
Step-by-step explanation:
Average = x1 + x2 + x3 + x4 + x5 ........ + xN
------------------------------------------
N
N = total numbers
=> (89 + 98 + 96 + x) / 4 = 95
=> (283 + x) /4 = 95
=> (283+ x) / 4 * 4 = 95 * 4
=> 283 + x = 380
=> 283 -283 + x = 380 - 283
=> x = 97
I divided the sum of all numbers by 4 we are adding 4 numbers.
So, she needs to get 97% in the last test in order to have an average score of 95%
A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and retinol. She feeds one group of laboratory rats a daily diet of precisely 41.59 units of niacin and 17,995 units of retinol. She uses two types of commercial pellet foods. Food A contains 0.22 unit of niacin and 100 units of retinol per gram. Food B contains 0.23 unit of niacin and 65 units of retinol per gram. How many grams of each food does she feed this group of rats each day
Answer:
Food A = 165 grams
Food B = 23 grams
Step-by-step explanation:
Daily precise diet fed to the group:
Niacin = 41.59 units
Retinol = 17,995 units
Two food types :
Food A :
Niacin = 0.22 units per gram
Retinol = 100 units per gram
Food B:
Niacin = 0.23 units per gram
Retinol = 65 units per gram
Let:
a = gram of food A fed per day
b = gram of food B fed per day
Hence in 'a' grams of food A:
0.22a of Niacin + 100a of Retinol
In 'b' grams of food B:
0.23b of Niacin + 65b of retinol
Recall :
Total Niacin = 41.59 ; total Retinol = 17995
Then,
0.22a + 0.23b = 41.59 - - - (1)
100a + 65b = 17995 - - - (2)
From (2) ; 100a + 65b = 17995
100a = 17995 - 65b
a = 179.95 - 0.65b - - - (3)
Substitute (3) into (1)
0.22(179.95 - 0.65b) + 0.23b = 41.59
39.589 - 0.143b + 0.23b = 41.59
0.087b = 2.001
b = 2.001 / 0.087
b = 23
Put b = 23 in (3)
a = 179.95 - 0.65(23)
a = 179.95 - 14.95
a = 165
Only a very small (<5) percentage of measurements can be more than 2 standard deviations from the mean of the normal distribution.
A. True
B. False
Answer:
A. True
Step-by-step explanation:
The empirical rule in statistics states that:
68% of the data will be within 1 standard deviation95% of the data will be within 2 standard deviations99.7% of the data will be within 3 standard deviationsSo yes, we can state that 5% or less of the data will be more than 2 standard deviations away from the mean. Of course, statistics is not 100% certain, so this rule is not 100% right all the time. Some exceptions might result, but generally speaking, the results should follow the empirical rule.
Answer:
The answer is true
Step-by-step explanation:
True
What percent of 175 is 7?
Answer:
12.25
7 percent of 175 = 12.25
(example attached below)
An account earned interest of 5% per year. The beginning balance was $250. The equation t=log1.05E250 represents the situation, where t is the time in years and E is the ending balance.
Answer:
t=3 years
Step-by-step explanation:
t=log1.05E250
t= time in years
E= ending balance.
Interest=5% per year
Ending balance=$289.41
Note: write Log 1.05 as written in the question
t= log1.05 E/250
=log1.05 (289.41 / 250)
=Log 1.05 (1.15764)
=Log (1.15764) / log (1.05)
= 0.0636 / 0.0212
=3
Therefore,
t=3 years
For a 7 1/2 hour day, Ed makes $90. How much does he make in 1 hour?
Answer:
he makes $12 an hour
Step-by-step explanation:
Ed makes $6 in one hour.
To find out how much Ed makes in one hour, we can divide the total amount he makes in a 7 1/2 hour day by the number of hours in a day.
First, let's convert 7 1/2 hours to a mixed fraction.
7 1/2 hours = 7 + 1/2 = 14/2 + 1/2 = 15/2 hours.
Now, we can calculate how much Ed makes per hour by dividing the total amount he makes ($90) by the number of hours (15/2):
Amount per hour = $90 ÷ (15/2) = $90 × (2/15) = $6.
Therefore, Ed makes $6 in one hour.
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can someone help me with this
if xy=4 then what is d²y/dx² × d²x/dy²
please read carefully there not the same so they don't equal one
Answer:
Actually, this is equal to 1.
Step-by-step explanation:
Hello, please consider the following.
First of all, we assume x and y different from 0.
[tex]xy=4\\\\y=\dfrac{4}{x}\\\\x=\dfrac{4}{x}\\\\\text{So}\\\\y'(x)=\dfrac{-4}{x^2}\\\\y''(x)=\dfrac{-4*(-2)}{x^3}=\dfrac{8}{x^3}\\\\x''(y)=\dfrac{8}{y^2}\\\\\text{So, we can conclude}[/tex]
[tex]\dfrac{d^2y}{dx^2}\cdot \dfrac{d^2x}{dy^2}=\dfrac{8}{x^3}\cdot\dfrac{8}{y^3}\\\\=\dfrac{64}{(xy)^3}\\\\\text{We replace xy by 4}\\\\=\dfrac{64}{4^3}\\\\=\dfrac{64}{64}\\\\=\large \boxed{\sf \bf \ 1 \ }[/tex]
Thank you
Write an equation parallel to the line y=3/2x-2 that goes through (5,1) in point slope form.
Answer: y=3/2x-13/2
Step-by-step explanation:
concept to know: two parallel lines have the same slope
y=3/2x+b
in order to find b or the y-intercept, we plug the point in
y=3/2x+b
1=3/2(5)+b
1=15/2+b
b=-13/2
----------------------------
y=3/2x-13/2
Hope this helps!! :)