if two lines are perpendicular it is true that:
[tex]m1\cdot m2=-1[/tex]For the line:
[tex]\begin{gathered} y=3x+4 \\ m1=3 \end{gathered}[/tex]Let's check every line:
[tex]\begin{gathered} y=-\frac{1}{3}x \\ m2=-\frac{1}{3} \\ m1\cdot m2 \\ 3\cdot-\frac{1}{3}=-1=-1 \end{gathered}[/tex]So, A is a correct choice
[tex]\begin{gathered} 6x-2y=4 \\ y=3x-2 \\ m2=3 \\ m1\cdot m2 \\ 3\cdot3=9\ne-1 \end{gathered}[/tex]B is not a correct choice
[tex]\begin{gathered} 3y=-x+7 \\ y=-\frac{1}{3}x+\frac{7}{3} \\ m2=-\frac{1}{3} \\ m1\cdot m2 \\ 3\cdot-\frac{1}{3}=-1=-1 \end{gathered}[/tex]C is a correct choice
[tex]\begin{gathered} x+3y=4 \\ y=-\frac{1}{3}x+\frac{4}{3} \\ m2=-\frac{1}{3} \\ m1\cdot m2 \\ 3\cdot-\frac{1}{3}=-1=-1 \end{gathered}[/tex]D is a correct choice
[tex]\begin{gathered} y=3x-10 \\ m2=3 \\ m1\cdot m2 \\ 3\cdot3=9\ne-1 \end{gathered}[/tex]E is not a correct choice
What is f^-1(-7) plus f(-7)? I need help answering this question
Answer:
13
Step-by-step explanation:
You want the sum of f^-1(-7) and f(-7) given the function definition in the table.
Inverse functionThe inverse function f^-1(x) consists of ordered pairs that are the reverse of the ordered pairs (x, f(x)). That is ...
(x, f^-1(x)) ≡ (f(x), x)
Another way to describe f^-1(x) is "the value of z that gives f(z) = x". This means f^-1(-7) is the value of x that gives f(x) = -7. That x-value is 6:
f^-1(-7) = 6 . . . . . from the 4th column of the table
Function valueWe can read the function value directly from the table:
f(-7) = 7 . . . . . . the first column of the table
SumThen the sum of interest is ...
f^(-1)(-7) +f(-7) = (6) +(7)
f^(-1)(-7) +f(-7) = 13
__
Additional comment
The inverse function ordered pairs are ...
(x, f^-1(x)) = {(7, -7), (12, 11), (8, -13), (-7, 6), (13, 5)}
Write an equation of the line passing through the point A(6,-1) that is perpendicular to the line y=-2x+8
Answer:
[tex]y+1=\frac{1}{2}(x-6)[/tex]
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals, so the slope of the line to be found is 1/2.
Substituting into point-slope form, the equation is
[tex]y+1=\frac{1}{2}(x-6)[/tex]
Find the values of x and z
A rectangular dog pen is constructed using a barn wall as one side and 120m of fencing for the other three sides. a) give a sketch of the situation. b) express the area in terms of x. c) sketch the graph. d) find the value of x that gives the greatest area. e) find the dimensions of the pen. f) state the domain.
The solutions to the question are
The area of the pen in terms of x is A = x(120 - 2x)The x value that gives the highest area is 30The dimensions is 30 by 60The domain is 0 <= x <= 60a) How to determine the sketchThe given parameters are:
Sides = 3
Fourth side = barn wall
Perimeter = 120 m
Next, we sketch the dog pen using the above parameters (see attachment)
b) The area of the penHere, we have
P = 120m
Also, we have
P = 2x + y
This gives
2x + y = 120
Make y the subject
y = 120 - 2x
The area is calculated as
A = xy
So, we have
A = x(120 - 2x)
Hence, the area is A = x(120 - 2x)
The sketch of the graphSee attachment for the graph of A = x(120 - 2x)
The value of x that gives the greatest areaWe have
A = x(120 - 2x)
Expand
A = 120x - 2x^2
Differentiate
120 - 4x= 0
So, we have
4x = 120
This gives
x = 30
Hence, the value of x that gives maximum area is 30
The dimensions of the penRecall that
y = 120 - 2x
So, we have
y = 120 - 2 * 30
Evaluate
y = 60
Hence, the dimensions is 30 by 60
The domain of the functionFrom the graph, we have
x = 0 to 60
Hence, the domain of the function is 0 <= x <= 60
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Find the slope between the following points (8,-4) and (2, -4)
Let:
[tex]\begin{gathered} (x1,y1)=(8,-4) \\ (x2,y2)=(2,-4) \end{gathered}[/tex]We can find the slope m, using the following formula:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-4-(-4)}{2-8}=\frac{0}{-6}=0[/tex]Answer:
0
??????????????????/?
iven
adiius of circle = 3 ft
ind
rea and circumference of a circle
xplnanation
Circumference of a circle is given by
[tex]\begin{gathered} C=2\pi r \\ C=2\times3.14\times3 \\ C=18.84ft \end{gathered}[/tex]Area of circle =
[tex]\begin{gathered} A=\pi r^2 \\ A=3.14\times3\times3 \\ A=28.26ft^2 \end{gathered}[/tex]inal ANnswer
ircumference =
[tex]18.84ft[/tex]Area =
[tex]28.26ft^2[/tex]
How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?
Calculate identity exponents using the exponent of the quotient, degree of exponent, and the law of zero exponent equations and evaluate numerical equations with integer exponents.
The following is an equivalent numeric expression with an integer exponent that uses the quotient, the quotient, zero-degree rule, and the identity exponent, and evaluates the numeric expression.
[tex]2^{5} \\[/tex] × [tex]2^{6}[/tex] = [tex]2^{11}[/tex], using the product of powers.
2² × 2³ = (2×3)² = 6², using the power of a product.
[tex](2^{2})^{6}[/tex] = [tex]2^{12}[/tex], using the power of a power.
The seven laws of exponents are the power rule, the power ratio rule, the power rule, the power rule, the power quotient rule, the power zero rule, and the negative exponent rule. Arithmetic questions, as well as how to multiply, divide and add powers.
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Florence wants to invest money abroad. Florence is aware that France generally has a recession every 6 years and America generally has a recession every 8. in the year 2005, both France and America were in recession. Florence needs to work out the next time they will both be in recession. When will this be?
The most appropriate choice for LCM will be given by
After the year 2005, France and America will be in recession in the year 2029
What is LCM?
Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.
Here,
France has a recession every 6 years.
America has a recession every 8 years.
Florence works out when France and America will both be in recession.
It will be possible in the year which is a common multiple of 6 and 8
In the year 2005, both France and America were in recession
France and America will both be in recession again after (LCM of 6 and 8) years
Now,
6 = 2 x 3
8 = 2 x 2 x 2
LCM of 6 and 8 = 2 x 2 x 2 x3
= 24
France and America will both be in recession again after 24 years
After the year 2005, France and America will be in recession in the year (2005 + 24) = 2029
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Find 3/4 divided by 2/3 then draw a picture and write an explanation describing how to get the answer.
The outcome of the quotient between the two fractions 3/4 and 2/3 is 9/8
How to find the quotient between the two fractions?So let's define two fractions as:
a/b and c/d.
The quotient between the fractions a/b and c/d can be written as:
(a/b)÷(c/d).
Now, the quotient is equal to the product with the inverse, so we can rewrite this as:
(a/b)÷(c/d) = (a/b)*(d/c)
Now, in this case, we want to find 3/4 divided by 2/3, this will be:
(3/4)÷(2/3) = (3/4)*(3/2) = 9/8
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which graph represents the inequality 2.5 greater than the product of -0.5 and a number?
The graph of the inequaity expression is added as an attachment
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to plot the graph of the inequaity expression?The mathematical statement is given as
"2.5 greater than the product of -0.5 and a number"
Product means times
So, we have the following representation
"2.5 greater than the product of -0.5 and a number" ⇒ 2.5 greater than -0.5 * a number
Let the number be x
So, we have
"2.5 greater than the product of -0.5 and a number" ⇒ 2.5 greater than -0.5x
Greater than is represented by >
So, we have
"2.5 greater than the product of -0.5 and a number" ⇒ 2.5 > -0.5x
Next, we plot the graph of the inequality expression
See attachment for the graph of the inequality expression
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Exploring Sample Space
In the given sample spaces, which has the largest sample space?
M-{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A {10, 20, 30, 40, 50, 60, 70, 80, 90}
T{20, 25, 30, 35, 40, 45, 50, 55, 60}
H-{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22}
????
A bag of flour has a mass of 4.5 kilograms. How many grams are in 4.5 kilograms?
The first thing we have to know is that 1 kilogram is equal to 1000 grams
[tex]\begin{gathered} 1\operatorname{kg}\to1000gr \\ \frac{1000gr}{1\operatorname{kg}} \end{gathered}[/tex]if we have 5.4 kilograms
[tex]\begin{gathered} 4.5\operatorname{kg}\cdot\frac{1000gr}{1\operatorname{kg}}=(4.5)(1000gr) \\ \end{gathered}[/tex][tex]4.5kg=4500gr[/tex][x+(1/3)] + [x+(1/5)] = 1, where [x] is the whole part of x.
[tex](x + \frac{1}{3} ) + (x + \frac{1}{5} ) = 1 \\ x + x + \frac{1}{3} + \frac{1}{5} = 1 \\ 2x(15) + \frac{1}{3} (15) + \frac{1}{5} (15) = 1(15) \\ 30x + 5 + 3 = 15 \\ 30x = 15 - 5 - 3 \\ 30x = 7 \\ \frac{30x}{30} = \frac{7}{30} \\ x = \frac{7}{30} [/tex]
ATTACHED IS THE SOLUTION
What is the value of x?
6x-2(x+4)=12
Answer:
Step-by-step explanation:
6x-2x-8=12
4x-8=12 (add 6x and -2x)
4x=20 (8+12=20)
x=5 (4 divide by 20 =5)
A model of a rectangular stove top with four circular burners is shown. The side lengths of the stove top and the diameters of the burners are labeled.Which measurement is the best estimate of the area in square inches of the stove top that does not include the area of the burners?A)108 in.2B)492 in.2C)420 in.2D)528 in.2
Explanation
to find the area of the stove that does not include the area of the burnes ( yellow area), we can subtract the area of the 4 circles from the area of the full rectangle
so
Step 1
[tex]\begin{gathered} \text{Area}=\text{rectangle-}4\text{ circles} \\ Area=(length\cdot width)-4(\pi\text{ }\frac{diameter^2}{4}) \\ A\text{rea}=(length\cdot width)-(\pi\text{ }\cdot diameter^2) \end{gathered}[/tex]
then, Let
for circle:
diameter= 6 in
for rectangle
length= 24 in
width= 22 in
Step 2
replace,
[tex]undefined[/tex]12/4= x/5
can someone help me. i need a step-by-step answer!
Multiply both sides of the equation by 20, the lowest common denominator of 4,5.
5×12=4xMultiply 5 and 12 to get 60.
60=4xSwap the sides so that all the terms of the variables are on the left side.
4x=60Divide both sides by 4.
x = 60/4Divide 60 by 4 to get 15.
x=15which expression would be easier to simplify if you use the associative property to change the grouping A: [-14+(-26)]+67B: (2/5+3/5) +7/3C: (43 + 60) + 40D: (50+50)+63
The associative property let us associate different terms or factors in order to solve some expression.
We have to find the expression in which this property is more useful.
The only expression where the associative may be helpful is C, as we can associate this way:
(43 + 60) + 40 = 43 + (60 + 40) = 43 + 100 = 143
In the other expression there is no advantage in applying this property.
Answer: C
On a coordinate plane, point A is located (-2,2) and point B is located at (6,-1). Determine the coordinates of the point that is 7/8 of the distance from a to b
The coordinates of the point that at 7/8 from a to b are (5, -5/8)
How to determine the coordinate of the point on the line segment?On the segment, we have the following endpoints
A = (-2, 2)
B = (6, -1)
Also, we have the line ratio to be
Ratio, m : n = 7/8
Express the ratio as a ratio
So, we have
m : n = 7 : 8 - 7
Evaluate the difference
So, we have
m : n = 7 : 1
The coordinate of the point at the given distance is then calculated as
Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)
So, we have
Point = 1/(7 + 1) * (7 * 6 + 1 * -2, 7 * -1 + 1 * 2)
Evaluate the products
So, we have
Point = 1/8 * (42 -2, -7 + 2)
Evaluate the sum and the difference
So, we have
Point = 1/8 * (40, -5)
Evaluate the products
So, we have
Point = (5, -5/8)
Hence, the coordinates of the point that is 7/8 of the distance from a to b are (5, -5/8)
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Toby picks a 5-digit number. It is larger than 49,999 and it is a multiple of 5. How many different numbers could he have picked?
The total number of different numbers which Toby could have picked according to the task content as given is; 1,000.
How many different numbers could Toby have picked?It follows from the task content that the number of different numbers which Toby could have picked given the conditions is to be determined.
On this note, since the required number is to be greater than 49,999 and must be a 5-digit number, the numbers which he could pick would range from;
49,999 - 99,999.
Hence, there are 5000 numbers in between.
Additionally, since the number must be a multiple of 5, the total number of multiples of 5 from 5,000 consecutive numbers is;
= 5,000/5
= 1000 different numbers.
Therefore, Toby could pick any of 1000 different numbers.
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The area of the parallelogram is 24 square miles.find base and height
The base of the parallelogram is 3
The height of the parallelogram is 8
How to calculate the base and height of the parallelogram ?Let the base be represented as (x+2)
Let the height be represented as (x-2)
The area of the parallelogram is 24
The first step is to get two numbers that can be multiplied together to get 24
= 3 × 8
The two numbers are 3 and 8
Hence the base is 3 and the height is 8
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In August, a giant panda named Max was born at the Silver City Zoo. In September, Max weighed 3.04 pounds. Today, Max is weighed again and he is heavier than before. Now Max weighs 10.73 pounds.
The most appropriate choice for for linear equation will be given by -
Gain in weight of Max = 7.69 pounds
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Let the gain in weight be x pounds
Weight of Max in the month of September = 3.04 pounds
Weight of Max today = 10.73 pounds
By the problem,
3.04 + x = 10.73
x = 10.73 - 3.04
x = 7.69
Gain in weight of Max = 7.69 pounds
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There are 4 triangles and 8 squares. What is the simplest ratio of triangles to squares?
Answer:
1:2
Step-by-step explanation:
For every triangle there are two squares.
The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is 3.91. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is .24 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at confidence. Round up to the next whole number.
a. The desired margin of error is .11 The appropriate sample size is
.
b. The desired margin of error is .07 . The appropriate sample size is
.
c. The desired margin of error is .04. The appropriate sample size is
Answer:
3
Step-by-step explanation:
1 = 1
Constructing a Confidence Interval for a Population Proportion
If n = 130 and p= 0.69, construct a 99% confidence interval.
The Confidence Interval for a Population Proportion is 0.69 ± 1.13
(-0.44 to 1.82)
Confidence Interval:
Confidence Interval means a range of values that is determined through the use of observed data, calculated at a desired confidence level that may contain the true value of the parameter being studied.
Given,
n = 130 and
p= 0.69,
construct a 99% confidence interval.
Here we need to find the confidence interval.
According to the formula, the confidence interval is,
We know that,
Sample Size: 130
Sample Mean: 0.69
Confidence Level: 99%
99% Confidence Interval: 0.69 ± 1.13
(-0.44 to 1.82)
"With 99% confidence the population mean is between -0.44 and 1.82, based on 130 samples."
Margin of Error: 1.13
(to more digits: 1.13)
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Mark's football team has scored about 24 points each game. They played 12 games this season.
What is the best estimate for the total number of points they scored in the season?
Ο Α. 150
B. 250
OC. 20
OD. 360
Answer:
250
Step-by-step explanation:
someone please help me!!!!
Answer:
First Choice:
(1.4)(0.18)²
Step-by-step explanation:
Using the negative exponent rule
[tex]\left(\dfrac{a}{b}\right)^{-1} = \dfrac{b}{a}[/tex]
we get
[tex]\left(\dfrac{5}{7}\right)^{-1} = \dfrac{7}{5}[/tex]
[tex]\dfrac{7}{5} = 1.4\\\\[/tex]
Therefore
[tex]\left(\dfrac{5}{7}\right)^{-1}\left(0.18\right)^2\\\\= (1.4)(0.18)^2[/tex]
PLEASE HELP ME I NEED 4 ANSWERS !!!!!!!!!! a) Fill in the gaps to factorise the expression below.
3x² + 16x + 5 = (3x + −)(x + −)
b) Use your answer to part a) to solve 3x² + 16x + 5 = 0
The roots the the given quadratic equation, will be -1/3 and -5 so the factors will be (3x+1)(x+5). As the value of roots is known, so the value of quadratic equation will be zero (0) for both the roots.
As per the question statement, we are supposed to fill the gaps to factorize the quadratic equation given :
3x² + 16x + 5 = (3x + _)(x + _)
We need to solve the expression for finding out its factors.
y = 3x² + 16x + 5
y = 3x² + 15x + x + 5
y = 3x(x + 5) + 1(x + 5)
y = (3x + 1)(x + 5)
Therefore, the roots the the given quadratic equation, will be -1/3 and -5 so the factors will be (3x+1)(x+5). As the value of roots is known, so the value of quadratic equation will be zero (0) for both the roots.
Quadratic equation: Any equation where there is just one term that squares the unknown and none that raises it to a higher power.Roots: Roots of any quadratic equation / expression is the value of the variable at which the complete value of the expression becomes zero (0). Number of roots = highest degree.To learn more about Quadratic equation, click on the link given below:
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The freezing point of seawater is −2 °C. The freezing point of nitric acid is −42 °C.
A photo of frozen seawater is shown.
How much greater is the freezing point of seawater than the freezing point of nitric acid?
The difference between the freezing point of seawater and the freezing point of nitric acid is 40 °C.
As per the question, we can write
The freezing point of seawater = −2 °C.
The freezing point of nitric acid = −42 °C.
We were asked to calculate the difference between the freezing point of seawater and the freezing point of nitric acid. We can find the difference between the freezing point of seawater and the freezing point of nitric acid by following the steps mentioned below;
The difference between the freezing point of seawater and the freezing point of nitric acid = Freezing point of Seawater - Freezing point of nitric acid
The difference between the freezing point of seawater and the freezing point of nitric acid = -2 - (-42) = 40 °C.
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Question
Solve the formula C = πd for л.
Two or more expressions with an Equal sign is called as Equation.π= C/d for equation C = πd
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is C = πd
c equal to pi times of d
We need to solve it for π
To solve for π we have to separate π from d. To make this We have to divide both sides by d.
So C/d= π
Hence π= C/d for equation C = πd
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what is the answer of that
40° is the value of the angle ∠QPR.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.So, PQ ⊥ PS then, ∠QPS = 90°.
According to the given figure: ∠QPR + ∠RPS = ∠QPS
Then,
7x - 9 + 4x + 22 = 9011x + 13 = 9011x = 90 - 1311x = 77x = 7So, ∠QPR = 7x - 9°
Substitute x = 7 as:
7(7) - 9°49 - 9°40°Therefore, 40° is the value of the angle ∠QPR.
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