Find the equation (in terms of x) of the line through the points ( − 1 , − 1 ) and( 4 , − 4 )
Answer:
[tex]y = -\frac{3}{5}x -\frac{8}{5}[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-1,-1)[/tex]
[tex](x_2,y_2) = (4,-4)[/tex]
Required
Determine the line equation
First, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-4 - (-1)}{4 - (-1)}[/tex]
[tex]m = \frac{-4 +1}{4 +1}[/tex]
[tex]m = \frac{-3}{5}[/tex]
[tex]m = -\frac{3}{5}[/tex]
The equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
This gives:
[tex]y - (-1) = -\frac{3}{5}(x - (-1))[/tex]
[tex]y + 1 = -\frac{3}{5}(x +1))[/tex]
Open bracket
[tex]y + 1 = -\frac{3}{5}x -\frac{3}{5}[/tex]
Make y the subject
[tex]y = -\frac{3}{5}x -\frac{3}{5}-1[/tex]
[tex]y = -\frac{3}{5}x +\frac{-3-5}{5}[/tex]
[tex]y = -\frac{3}{5}x +\frac{-8}{5}[/tex]
[tex]y = -\frac{3}{5}x -\frac{8}{5}[/tex]
. You got 46 out of 65 questions right on your exam. What's your grade?
Answer:
about like 8 /10
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Select five numbers that have 7, 13, and 3 as prime factors.
А
1,092
B
897
с
2,093
D
819
483
F
1,365
G
273
H
546
Answer:
ADFGH
Step-by-step explanation:
Good luck on your test!
The numbers having the prime factors 7, 13, and 3 are 1,092,819,1,365,273, and 546.
What is a prime factor?A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth. Now, we may also apply the so-called prime factorization, which actually involves using factor trees, for numbers.
The numbers having the prime factors 7, 13 and 3 are 1,092,819,1,365,273, and 546. Because all the numbers are completely divisible by the numbers 7, 13, and 3.
Therefore, the numbers having the prime factors 7, 13, and 3 are 1,092,819,1,365,273, and 546.
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How much should you invest at 5% annual interest rate to have the annual interest of $150?
Answer:
it is 7.5
Step-by-step explanation:
Answer:
It is 7.5
Step-by-step explanation:
Faucet A can fill up a water cooler in 8 minutes. Faucet B can fill the same water cooler in 12 minutes. How long will it take both faucets together to fill the water cooler?
!!!!!Explanation Needed!!!!!
Answer:
in average a it take both faucets together to fill the water cooler=(8+12)/2=10minutes
Simplify p^-8/7^-2q^-9
Answer:
[tex]\frac{7^2}{p^8 \cdot q^9}[/tex]
Step-by-step explanation:
[tex]\frac{p^{-8}}{7^{-2}} \cdot q^{-9} = \frac{\frac{1}{p^8}}{\frac{1}{7^2}} \cdot \frac{1}{q^9} = \frac{7^2}{p^8 \cdot q^9}[/tex] by the definition of negative exponents: [tex]a^{-b} = \frac{1}{a^b}[/tex] for all [tex]a,b[/tex] so long as [tex]a\ne 0[/tex].
The value of the exponential equation is A = 7²q⁹ / p⁸
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
A = p⁻⁸ / 7⁻² ( q ) ⁻⁹ be equation (1)
On simplifying the equation , we get
A = 7² ( q ) ⁹ / p⁸
Therefore , the value of A is 7²q⁹ / p⁸
Hence , the exponential equation is A = 7²q⁹ / p⁸
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Help me please
Determine the ratio for COS C in the picture below
Answer:
Step-by-step explanation:
Cos=opposite/hypotenuse
Cos C=32/40 or 4:5
Cos C=0.8
solve the equation (0°≤A≤360°)
a) √3sinA-cosA=√2
Step-by-step explanation:
√3sinA-cosA=√2
dividing both side by (√3²-1²=2 we get)
√3/2 sinA-1/2.cos A=√2/2
cos 30sinA-sin30cosA=√2/(√2×√2)
sinAcos30-cosAsin30=1/√2
sin(A-30)=sin45,sin(180-45)
therefore
A-30=45,135
A=45+30=75 or A=135+30=165
Help help help help help pls
1/9 ÷5/4 plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
0.8888888888
Step-by-step explanation:
that decimal just convert it to a fractoin
what is the value of 58 - 2 x 3 + 1
Answer:
53
Step-by-step explanation:
You apply the
{Select)
operation
[ Select ]
-for multiplication equations and
[ Select ]
for division equations
-to
[ Select ]
of the equation.
Answer:
ndhduejcijgisjcidjcjzjfjidjicjdici djcojzifcjdjcu
Step-by-step explanation:
no se weydgfds
Paul has a 40 ft. by 30 ft. pole barn on his farm that he wants to move. The southeast corner of the pole barn is currently located 50 ft. west and 25 ft. north of the stock tank where the cows get their water. Paul wants to move the pole barn so the southeast corner of the barn is located 80 feet east and 80 feet south of the stock tank
1. 1. Complete the transformation statement for moving Paul’s pole barn, (x,y) (x+ fill in the blank, y + fill in the blank)
2. Draw the new location of the pole barn on the graph below. Note that the stock tank is located at the origin
3. How far is it from the old location to the new location? (Hint: use the distance formula
Answer:
Step-by-step explanation:
(x,y) ↦ (x+130, y-105)
original position of SE corner: (-50,25)
new position of SE corner: (80,-80)
distance = [tex]\sqrt{(80-(-50))^{2}+(-80-25)^{2} }[/tex]≅167.1 ft
335.71 divided by 1000
PLEASE HELP!! WILL MARK BRAINLIEST!! DONT GUESS :)
Answer:
x=9
Step-by-step explanation:
180-108=72 so the equation using x has to equal 72
(15x-63)=72
+63
15x=135
divide by 15
x=9
A ladder is propped against the side of a building making a 30 degree
angle with the building
If the base of the ladder is 6 feet from the base of the building, how
high will the ladder be resting against the building, in feet? Round
your answer to the nearest whole number
43=0.34x+19.5
What is x
Step-by-step explanation:
43=0.34x+19.5
=> 0.34x+19.5 = 43
=> 0.34x = 43 - 19.5
= 23.5
[tex] = > x = \frac{23.5}{0.34} [/tex]
=> x = 69.117 (Ans)
After dinner, Mirna had a second serving of her chocolate bar, eating 3
more pieces. Which equation shows how much she has left of the
whole candy bar after this second serving ?
A.) 5/8 - 3/8 = 2/8
B.) 8/8 - 3/8 = 5/8
C.) 8/8 - 5/8 = 3/8
D.) 3/8 - 2/8 = 1/8
The answer is c because 8 - 5 is 3.
? points
Simplify completely :
5x - 20
9x - 36
Answer:
5/9
Step-by-step explanation:
What is the solution of the equation 13 + b = 37?
b=
Answer:
13 + 24 = 37 the answer is 24
Step-by-step explanation:
Answer: 24
Step-by-step explanation: 37-13= 24
x = 6y – 14
-X + 9y = 17
after substitution :
-6y + 14+ 9y = 17
= 14 + 3y = 17
by subtracting 14 :
3y = 3
by dividing over 3 :
y = 1
after substitution:
x = 6 * 1 - 14 = 6 - 14 = -8
x = -8
Reflect the figure across the x-axis then across the y-axis.
Answer:
A' is (-1,-1) B' becomes (-1,-4) C' becomes (-3,-1)
Step-by-step explanation:
To take a shortcut, reflecting a figure across both axes is the same as rotating a figure 180 degrees about the orgin using formula x,y goes to -x,-y but to explain it. Use formula (x,y) goes to (x,-y) to reflect it across x-axis then use formula (x,y) goes to (-x,y) to reflect it across y-axis. A' becomes -1,-1. B' becomes -1,-4 . C' becomes (-3,-1)
A screening test for a newly discovered disease is being evaluated for its performance as a screening test. In order to determine the effectiveness of the new test, it was administered to 270 workers. A total of 42 individuals who had been diagnosed with the disease tested positive for it. Results showed a negative test for an additional 25 people with the disease. A total of 51 people without the disease tested positive. What is the sensitivity, specificity, positive predictive value, negative predictive value, and accuracy of the test
Answer:
- Sensitivity = 62.7 %
- specificity = 74.9 %
- positive predictive value = 45.2 %
- negative predictive value = 85.9 %
- Accuracy of the test = 71.9 %
Step-by-step explanation:
Given the data in th question;
CONDITION POSITIVE CONDITION NEGATIVE TOTAL
TEST POSITIVE 42 51 93
TEST NEGATIVE 25 152 177
TOTAL 67 203 270
so; A=42, B=51, C=25 and D=152
Sensitivity = [A / ( A + C) ]×100= [42 /( 42 + 25)]×100 = [42 / 67] 100=
Sensitivity = 62.7 %
specificity = [D / ( D + B) ]×100= [152 /( 152 + 51)]×100 = [152 / 203] 100=
specificity = 74.9 %
positive predictive value = [A / ( A + B) ]×100 = [42 /( 42 + 51)]×100 =[42/93] 100
positive predictive value = 45.2 %
negative predictive value = [D / ( D + C) ]×100 = [152 /( 152 + 25)]×100 =[152/177] 100
negative predictive value = 85.9 %
Accuracy of the test = [A + D / ( A+B+C+D)] = [42 + 152 / ( 42+51+25+152)]
= [ 194 / 270 ]
Accuracy of the test = 71.9 %
Help? I’ll give brainliest
9514 1404 393
Answer:
10,466.7 in^3
Step-by-step explanation:
The volume of a cone is given by ...
V = (1/3)πr^2·h
where r is the radius and h is the height. Using your numbers, we have ...
V = (1/3)(3.14)(20 in)^2·(25 in) = 10,466.7 in^3
_____
A more accurate value of π will give a different result.
expand and simplify (x-3) (x+5)
Answer:
x^2 + 2x - 15
Step-by-step explanation:
(x-3)(x+5)
x^2 + 5x - 3x - 15
x^2 + 2x - 15
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\boxed{\mathsf{(x - 3) (x + 5)}}\\\\\large\text{DISTRIBUTE}\\\\\large\boxed{\mathsf{x(x) + 5(x) - 3(x) - 3(5)}}\\\\\large\boxed{\mathsf{x^2 + 2x - 15}}\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{x^2+ 2x - 15}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]What is the value of x in the equation 3×=1
Answer:
x=1/3
Step-by-step explanation:
Purple paint is made by mixing red paint and blue paint in the ratio 5:2
Yan has 30 litres of red paint and 9 litres of blue paint.
What is the maximum amount of purple paint he can make?
Which expression represents 3 times the sum of 7 and m ?
Answer:
3 (7+m)
Step-by-step explanation:
The correct expression is,
⇒ 3 (7 + m)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
''3 times the sum of 7 and m''
Now, We can formulate;
⇒ 3 × (7 + m)
⇒ 3 (7 + m)
Thus, The correct expression is,
⇒ 3 (7 + m)
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Meaning of part of a whole
Answer:
Step-by-step explanation:
a portion or division of a whole that is separate or distinct; piece, fragment, fraction, or section; constituent: the rear part of the house;to glue the two parts together.
Please thank me!
What operation should be done first to solve 6x + 5 = 35?
Answer:
Subtract 5
Step-by-step explanation:
Pemdas is done backwards in algebra