Equation for the given pair of lines which are perpendicular to each other and intersect at the point (-3 , -7 ) are :
( y + 7 ) = m₁ ( x + 3) and ( y + 7 ) = (-1 / m₁ )( x + 3 )
As given in the question,
Pair of equations that are perpendicular to each other and intersect at point ( -3 , -7 ) are as follow:
let us consider slope of perpendicular lines are m₁ and m₂.
Product of the slope of perpendicular lines = -1
⇒ m₁ × m₂ = -1
⇒ m₂ = -1 / m₁
Pair of perpendicular intersect at point ( -3 , -7 ) .
Required equation of perpendicular lines is given by :
For line 1:
( y - (-7)) / ( x - (-3) ) = m₁
⇒ y + 7 = m₁ (x+3)
For line 2:
( y - (-7)) / ( x - (-3) ) = m₂
⇒ y + 7 = m₂( x+ 3)
⇒ y + 7 = -1 / m₁ ( x+ 3)
Therefore, equation for the given pair of lines which are perpendicular to each other and intersect at the point (-3 , -7 ) are :
( y + 7 ) = m₁ ( x + 3) and ( y + 7 ) = (-1 / m₁ )( x + 3 )
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The half-life of radium is 1690 years. If 30 grams are present now, how much will be present in 720 years?
Answer:
22.3 gm
Step-by-step explanation:
720 is this many half lives : 720 / 1690
so there will be this much left 30 gm ( 1/2)^(720/1690) = 22.3 gm
6. Solve the following inequalities for the variable and graph the solution.
3+4x>-5.
Answer:
3+4x>-5
4x>-5-3
4x>-8
x>-8/4
x> -2
Solve the equation: u^6 − 49 u^4 = 0 .
The given equation solved for u is u = 7 or u = -7
Solving an equationFrom the question, we are to solve the given equation.
The given equation is
u^6 − 49 u^4 = 0
First, we will write the equation properly
The given equation written properly is
u⁶ - 49u⁴ = 0
Now,
To solve the equation, we will determine the value(s) of the variable. The variable in the given equation is u.
Thus,
We will solve for u
u⁶ - 49u⁴ = 0
Add 49u⁴ to both sides of the equation
u⁶ = 49u⁴
Divide both sides by u⁴
u⁶/u⁴ = 49u⁴/u⁴
u² = 49
Then,
u²- 49 = 0
u² - 7² = 0
Factorize by applying the rule for difference of two squares
(u + 7)(u - 7) = 0
Then,
u + 7 = 0 OR u - 7 = 0
u = -7 OR u = 7
Hence, the value of u is -7 OR 7
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Explain if Todd’s Conclusion is logical.How did you decide? If it is not logical,what can you do to improve his reasoning?
Answer:
Todd's conclusion is logical. I know this because all people named Todd are logical beings who always come to logical conclusions. But seriously though, please comment down below more of your question so I can accurately answer it, thanks!
Step-by-step explanation:
If a = 2 and b = 3, what is the value of 2a³b2?
Answer:384
Step-by-step explanation:
first you multiply 2 times 2= 4 then 4 times 4 times 4= 64 then you multiply 3 times 2= 6 lastly you multiply 6 and 64. your welcome:)
Juan invested $110,000, 10 years ago at 8% compound quarterly. how much has he accumulated?
use the MS Excel FV function
Answer:
Below
Step-by-step explanation:
The equation ( you need to commit to memory) is:
FV = PV ( 1+i)^n FV = future value PV = present value(110 000)
i = decimal interest per PERIOD = .08 /4 = .02
n = # of periods = 40 (it is a quarterly period by 10 yrs)
FV = 110 000 ( 1 + .02)^40 = 242 884 .36 dollars
The table shows a set of points on a line.
y
6
5
4
3
What is the slope of the line?
X
-6
-3
0
3
The slope of the line is -3 and the equation of the line formed by the points is y + 3x = 6.
From the table we can see that the line passes through the points:
(-6,6) ,(5,-3) ,(4,0) and (3,3) .
Let us consider any two points on the line (4,0) and (3,3) .
We know that the slope of the line can be found by using the intercept formula
Hence slope = (3-0) / (3-4) = 3/ -1 = -3
Now the equation of the line is :
y - 3 = -3(x-3)
or, y - 3 = -3x +9
or, y + 3x = 6
The letter m is frequently used to represent the slope of an object that resembles a line in the plane that contains the x and y axes. The slope is defined as the difference in two independent locations along the line expressed in y coordinate less by the equivalent difference in x coordinate.
Therefore slope of the line is -3.
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Geometry Gina wilson pls help
For the given measures of angles of heptagon, the value of x is equal to 27° .
As given in the question,
Sum of all the interior angles of the heptagon is equal to 900.
Given measure of all the angles of the heptagon is given by :
135°+( 5x - 4 )° +( 7x - 64 )° + 120° +( 6x - 8 )° +( 4x + 15 )° + ( 3x + 31 )°= 900°
Arrange all the like terms of the given expression together we get,
⇒ ( 5x + 7x + 6x + 4x + 3x )° + ( 135 - 4 - 64 + 120 - 8 + 15 + 31 )° = 900°
⇒ 25x° + 225° = 900°
⇒ 25x° = 900° -225°
⇒ 25x° = 675°
⇒ x = 27°
Therefore, for the given measures of angles of heptagon, the value of x is equal to 27° .
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Brooklyn scored 27 points in the basketball game. That was 12 points more than her friend, Cienna, scored. How many points did they score altogether? * 2 points
Answer:
42 points
Step-by-step explanation:
If Brooke scored 27 points, 12 less than that would be what Cienna scored. To find this, you would do 27 - 12. This is equal to 15, so Cienna scored 15 points.
To find how much they scored together, you would add both their scores. Brooke scored 27 and Cienna scored 15, so 27 + 15 = 42. Therefore, they scored 42 points together.
100 points for this There was a blizzard. Snow was falling at the rate of 3
inches per hour. If the snow keeps acclimating how long will 5 feet of snow to accumulate ?
Since there are 60 inches in 5 feet (5*12), we know that it will take 20 hours for 5 feet of snow to accumulate (60/3).
Hope this helps!
(b) The graph of y=g(x) is shown. Draw the graph of y=g(1/2x)
The graph of the piece-wise function g(0.5x) is given by the second image at the end of the answer.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
In this problem, the function given by the first graph has two definitions, as follows:
To the left of x = 0.To the right of x = 0.The two functions are linear with intercept 0, hence the definitions are given as follows:
x < 0: y = 2x, as when x increases by 1, y increases by 2, hence slope of 2.x > 0: y = -0.5x, as when x increases by 2, y decreases by 1, hence slope of -0.5.After the transformation x -> 0.5x, the definitions are given as follows:
g(0.5x) = 2(0.5x) = x, x < 0.g(0.5x) = -0.5(0.5x) = -0.25x, x > 0.Missing InformationThe graph of g(x) is given by the first image at the end of the answer.
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h(t)= t+ 1/t^2+2t+2.
Find derivative.
The derivative of given function is H’(t) = 3 – 2/t3
A derivative is a two-party contract whose value/price is derived from an underlying asset. Futures, options, forwards, and swaps are the most prevalent types
Given that H(t)= t+ 1/t^2+2t+2
We must calculate the derivative
H(t)= t+ 1/t^2+2t+2
H(t) = 3t + 1/t^2 + 2
H’(t) = d/dt(3t + 1/t^2 + 2)
H’(t) = d/dt(3t) + d/dt (1/t^2) + d/dt ( 2)
H’(t) = 3xd/dt(t) + d/dt (1/t^2) + d/dt ( 2)
H’(t) = 3xd/dt(t) + d/dt (t-2) + d/dt ( 2)
H’(t) = 3 – 2t-3
H’(t) = 3 – 2/t3
Therefore the derivative of the given function is H’(t) = 3 – 2/t3
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Consider the following equation:
3|x+3|−12=0
Step 2 of 4: Using the definition of absolute values, convert the standard form of the given equation into two equations without absolute value signs.
The value of x in the following equation: 3|x+3|−12=0 is -7 and 1
The equation is 3|x+3|−12=0
The modulus function can be positive and negative
Considering it to be negative,
the equation is
3((-1)(x + 3) - 12
3(-x - 3) - 12
-3x - 9 - 12 = 0
3x + 21 = 0
3x = -21
x = -7
3(x + 3) - 12
3x + 9 - 12
3x - 3 = 0
3x = 3
x = 1
Therefore, the value of x in the following equation: 3|x+3|−12=0 is -7 and 1
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Which number line represents the graph of x = 2?
Answer:
The 3rd one
x = 2 means how far is the line from 0
PLEASE GIVE BRAINLIEST THANK YOU!!!
A line passes through the point (2, 7) and has a slope of 5. Write an equation in slope-intercept form for this line.
Answer: y = 5x - 3
Step-by-step explanation:
It is a line, so its formula is y = mx + b.
Slope(m) = 5Y-intercept(b) =[tex]y=5x+b\\7=5(2)+b\\7=10+b\\b=7-10=-3[/tex]
Therefore, the formula is y = 5x - 3.
Answer:
y=5x-3
Step-by-step explanation:
Choose a variable, write a inequality, and solve the inequality.
The sum of a number and -2 is no more than 6
Answer: 4
Step-by-step explanation: your going to divide -2 by 1 and you get 2 then add 4 and you get 6 pls give me brainliest :)
A candy company sells peanut brittle and almond bark. The information for both types of candy is shown.
graph labeled Peanut Brittle with x axis labeled weight in ounces and y axis labeled cost in dollars with a line from point 0 comma 0 going through 10 comma 10
Almond Bark
Weight (ounces) 2 6 14
Cost (dollars) 3 9 21
Determine how much more one candy costs per ounce than the other candy.
Peanut brittle costs $0.50 more per ounce than almond bark.
Almond bark costs $0.50 more per ounce than peanut brittle.
Peanut brittle costs $0.33 more per ounce than almond bark.
Almond bark costs $0.33 more per ounce than peanut brittle.
The difference between the cost of one candy per ounce and the other candy is that: Almond bark costs $0.50 more per ounce than peanut brittle.
How to determine the cost of candy?Mathematically, a direct proportion can be represented the following mathematical expression:
y = kx
Where:
x represents the weight in ounces of a candy.y represents the cost in dollars of a candy.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) for each candy as follows:
For Peanut Brittle, we have the following:
Constant of proportionality (k) = 10/10
Constant of proportionality (k) = 1.0
For Almond Bark, we have the following:
Constant of proportionality (k) = 3/2
Constant of proportionality (k) = 1.5
Next, we would determine the difference in cost:
Difference in cost = 1.5 - 1.0
Difference in cost = $0.50.
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solve for x;
2/7 x + 1/5 x=51
Answer:
x = 105
Step-by-step explanation:
To solve for x, we simply need to isolate it:
[tex]\frac{2}{7}x+\frac{1}{5}x=51\\ \frac{17}{35}x=51\\ x=105[/tex]
(-3,6), (0,3), (-1,2), and (2,-1) all lie on a line. Find the Slope of the Line. Make Sure You Do Number 11 On The Paper!
to get the slope of any straight line, we simply need two points off of it, let's use those two from the picture below
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{(-3)}}} \implies \cfrac{-4}{-1 +3} \implies \cfrac{ -4 }{ 2 } \implies - 2[/tex]
5) A woman drinks 8 bottles of water in 2 days. How many bottles of water would she drink in 4 days?
2. A local grocery store received 240 turkeys the week prior to Thanksgiving. On Sunday,
they sold 3/8 of them. How many turkeys were sold on Sunday? Solve the problem
using the Draw a Diagram strategy.
The number of turkeys that they sold on Sunday is 90 turkeys
Total number of turkeys = 240
On Sunday, they sold 3/8 of them
The fraction of turkeys they sold on Sunday = 3/8
To find the number of turkeys that they sold on Sunday we have to find the 3/8 fraction of 240
Then,
The number of turkeys that they sold on Sunday = Total number of turkeys × The fraction of turkeys they sold on Sunday
Substitute the values in the equation
The number of turkeys that they sold on Sunday = 240 × 3/8
= 240 × 0.375
= 90 turkeys
Hence, the number of turkeys that they sold on Sunday is 90 turkeys
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Given is a 30-60-90 Triangle. From the answer
choices below, select all that represent possible
side lengths.
○3√3; 3; 6
O 10√3; 15; 5√3
08:8√3:24
○ 5√2; 5√6; 10√/2
The represent possible side lengths of perimeter is 8;8√3;24.
What is perimeter?
perimeter is the distance of around the edge of a shape. Learn how to find of the perimeter by adding up to the side lenghth of various shapes.
The perimeter is the distance around the object.
Sol-as per the given question the angle value of the triangle is -
7 in
(x+4)in
(4x+1)in
Here,
X+4=4x+1
X=1
Perimeter:- 5+5+7 =
17 Inches.
Thus the perimeter of the triangle is 17 Inches.
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A deck of cards contains RED cards numbered 1,2,3,4,5 and BLUE cards numbered 1,2,3,4,5,6. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card. Drawing the Red 3 is an example of which of the following events? Select all correct answers.
The probability of drawing the Blue 4 is an example of .R′f.E′
Red cards = 1,2,3
Blue cards =1,2,3,4,5,6
Pr(R) = Drawing a red card = 3/9 = 1/3
Pr(B)= Drawing a blue card = 6/9 = 2/3
Pr(E) = Drawing an even card = 4/9
Pr(O) = Drawing an odd number card = 5/9
Probability of drawing the blue 4 ? = Pr(blue, 4) = 1/9
From the options
(A) R or O = Pr(R) + Pr(O) = 1/3 + 1/9 = 8/9 ........(Not equal to 1/9)
(B) B and O = Pr(B) × Pr(O) = 2/3 × 5/9 = 10/21......(Not equal to 1/9)
(C) R or E = Pr(R) + Pr(E) = 1/3 + 4/9 = 7/9.......(Not equal to 1/9)
(D) R and O = Pr(R) + Pr(O) = 1/3 × 5/9 = 5/27.......(Not equal to 1/9)
(E) R'. E' = 1-Pr(R)-1-Pr(E) =
1-1/3 =2/3- 1-4/9 =5/9
2/3-5/9 = 1/9......( equal to 1/9).
Hence, the probability of drawing the Blue 4 is an example of .R′f.E′
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Disclaimer: the question given by you is incomplete, the solution is done as per a similiar question which is
A deck of cards contains RED cards numbered 1,2,3 and BLUE cards numbered 1,2,3,4,5,6. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.Drawing the Blue 4 is an example of which of the following events? Select all correct answers.Select all that apply:a.R OR Ob.B AND Oc.R OR Ed.R AND Oe.R′f.E′
whats 28.2 × 4.42= in decimal form? lol
Answer:
124.644
Step-by-step explanation:
28.2*4.42=124.644.
Answer:
28.2 × 4.42= 124.644
and in non-decimal it's 124644 removing 3 decimal places
Step-by-step explanation:
Brainiest, please
thank you
Evaluate the following algebraic expression:
w + 8.5 when w = 6.3
O 3.2
O 14.8
O 2.2
O 4.8
Answer:
14.8 is the answer to the question
1. Write the radical below in the simplest radical form. Decimals are not allowed.
√175
2. Write the radical in simplest radical form. Decimals not allowed
√5/12
number 2 is a fraction btw
The simplest radical form of the radicals given are:
1. The simplest radical form of √175 is 5 √7.
2. The simplest radical form of √5 / 12 is √5 / 12.
First, let us understand the radical:
A radical can also be called a surd. A surd is an irrational number. We say that it is irrational because it can not be expressed as a terminating decimal.
1.
We are given:
√175
We need to write in the simplest radical form.
175 can be written as:
175 = 5 * 5 * 7
√175 = √ 5 * 5 * 7
√175 = √ 5 * 5 * √7
√175 = 5 √7
So, the simplest form of √175 is 5 √7.
2.
We are given:
√5 / 12
We need to write in the simplest radical form.
√5 / 12 is already in the simplest form.
So, the simplest form of √5 / 12 is √5 / 12.
Thus, the simplest radical form of the radicals given are:
1. The simplest radical form of √175 is 5 √7.
2. The simplest radical form of √5 / 12 is √5 / 12.
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Find the quotient and remainder
using synthetic division for
x³ + 4x² + 5x +9
x + 2
Answer:
quotient: x^2+2x+1
remainder: 7
Step-by-step explanation:
Step-by-step explanation:
x³+4x²+5x+9= (x+2)(x²+2x+1)+7
Quotient= (x²+2x+1)
Remainder=7
Evaluate the following algebraic expression:
64-9p when p = 7
O 14
O 63
O 36
01
Answer:
63 is the answer.
Step-by-step explanation:
9p=9xp, p=7, so 9x7=63. ;)
Michelle purchases a tablet that costs
$85. The sales-tax rate in her city is 7%.
What is the total cost of the tablet?
Answer:
$90.95
Step-by-step explanation:
85 + .07(85)
85 + 5.95
90.95
1/3 of the guests choose beef
5/12 choose chicken
69 are vegeterian
How many guests are at the wedding
The number of guests at the wedding is 276.
How to calculate the number of guests?Since 1/3 of the guests choose beef and 5/12 choose chicken, the fraction for vegetarian will be:
= 1 - (1/3 + 5/12)
= 1 - 3/4
= 1/4
Therefore, let the total number of guests be x.
This will be illustrated as:
1/4 × x = 69
0.25x = 69
Divide
x = 69 / 0.25
x = 276
Therefore, there are 276 guests.
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