Step-by-step explanation:
Given
x = -2
Now
y = 3x - 2
= 3 * (-2 )-2
= -6 - 2
= -8
Find the inner product of (4,9,-3), (-6, 7,5)and state whether the vectors are perpendicular.
Answer:
24, not Perpendicular
Step-by-step explanation:
4×-6 + 9×7 + -3×5
-24 + 63 - 15
24
Perpendicular when inner product is 0
The whale swims down 300 feet to feed. What is the whale’s elevation now?
The elevation of the whale is -300 feet.
What is an expression?Expression in maths is defined as the collection of 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.
Given that the whale swims down 300 feet to feed. The elevation of the whale will be:-
Elevation = -300 feet
Therefore, the elevation of the whale is -300 feet.
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Given the equation 5 + x - 12 = x - 7.
Part A. Solve the equation 5 + x - 12 = x - 7. In your final answer, be sure to state the solution and include all of your work.
Part B. Use the values x = -4, 0, 5 to prove your solution to the equation 5 + x - 12 = x - 7. In your final answer, include all of your calculations.
Answer:
part A= x=1
part B= -13=-11 and -7=-7 and -2=-2
Step-by-step explanation:
part A
5+x-12=x-7
-7+x=x-7
x=1
part B
5+(-4)-12=-4-7
-1-12=-4-7
-13=-4-7
-13=-11
5+x-12=x-7
5+(-12)=-7
-7=-7
5+x-12=x-7
5+5-12=5-7
10-12=-2
-2=-2
What is the factor pair for the multiplication sentence below?
11 x 9 = 99
A. 9,99
B. 11.99
c. 11,9
Factor and solve: -3p^2 - p - 2 = 0
Please show step by step and how to factor trinomials when the leading coefficient is a negative number.
Answer:
Step-by-step explanation:
-3p² - p - 2 = 0
a = -3; b = -1 c = -2
[-b ±√(b² - 4ac)]/2a = [1 ± √(1-4*-3*-2) ] /2*-3
=[1 ± √(1-48) ]/-6
= - [1 ±√-47]/6
= - [1 ±√47i]/6
(r/s)(3) find the value.
Which shows the following expression after the negative exponents have been eliminated?
A)StartFraction m Superscript 7 Baseline n cubed Over m n Superscript negative 1 Baseline EndFraction, m not-equals 0, n not-equals 0
B)StartFraction m Superscript 7 Baseline n cubed n Over m EndFraction
m Superscript 7 Baseline n cubed m n
C)StartFraction m Superscript 7 Baseline n cubed Over m (negative n) EndFraction
D)StartFraction m n Over m Superscript 7 baseline n EndFraction
Answer:
its A
Step-by-step explanation:
Hence, the correct answer is (C)[tex]\frac{m^7.n^7}{mn^{-1}}[/tex]
What is an expression?a mathematical phrase that can contain ordinary numbers, variables, and operators.
How to solve?Given the expression [tex]\frac{m^7.n^7}{mn^{-1}}[/tex]
on simplification, if can be found,
=[tex]m^{7-1}.n^{3-(-1)}\\m^6.n^4[/tex]
which is the required answer.
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Find the value of each numbered angle.
Answer:
See below.
Step-by-step explanation:
m < 1 = 180 - 125 = 55 degrees (adjacent angles),
m < 2 = 180 - 56 = 124 degrees (adjacent angles).
m < 3 = 124 - 55 = 69 degrees ( external angle of a triangle theorem).
When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?
The faster pipe will fill the pool in 6 hours and the slower pipe will fill the pool in 12 hours.
What is time and work for commercial mathematics?Work Done = Time Taken × Rate of Work. Rate of Work = 1 / Time Taken. Time Taken = 1 / Rate of Work. If a piece of work is done in x number of days, then the work done in one day = 1/x.
Given here, two pipes fill the pool in 4 hours if they work together and If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours.
Let volume of the pool be LCM(9,4)= 36 unit³ and their efficiencies be E₁ and E₂ respectively then we have E₁+E₂ = 36/4
=9 units
Also 18/ E₁ +18/E₂ = 9
putting E₁=9-E₂ we get
18₁/ 9-E₂ +18/E₂ = 9
E²₂ -9E₂ +18 =0
(E₂ +3) (E₂ -6) =0
Therefore E₂ =6 units as efficiency cannot be negative and consequently E₁ =3 units
Hence, if they are working alone they finish the work in 36/3 =12 hours and 36/6=6 hours respectively.
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The angle of depression between a bird and its prey is 70 degrees. If the bird is 18 ft off the ground, what is the distance between the bird and its prey? Round to the nearest foot
Answer:
19 ft
Step-by-step explanation:
We are given that
[tex]\theta=70^{\circ}[/tex]
Height of bird from the ground=h=18 ft
We have to find the distance between the bird and its prey.
We know that
[tex]sin\theta=\frac{perpendicular\;side}{hypotenuse}[/tex]
Using the formula
[tex]sin70=\frac{18}{hypotenuse}[/tex]
[tex]hypotenuse=\frac{18}{sin70}=19.1 ft\approx 19ft[/tex]
Hence, the distance between the bird and its prey=19 ft
The length of a rectangle is 1 meter less than its
width. The area of the rectangle is 42 square
meters. Find the dimensions of the rectangle.
If the length of the rectangle is x, then we know the width is x + 1.
The area of a rectangle is length · width, so we can substitute as x · (x + 1)
Now, we now x · (x + 1) = 42
Expand
x² + x = 42
Solve
x² + x - 42 = 0
(x + 7)(x - 6) = 0
So, x = 6
That means the length is 6 meters and the width is 7 meters.
The dimensions of the rectangle are:
Width, W = 7 meters
Length, L = 6 meters
Let's denote:
L = the length of the rectangle
W = the width of the rectangle
Given that the length of the rectangle is 1 meter less than its width, we can write the equation:
L = W - 1
We're also given that the area of the rectangle is 42 square meters. The formula for the area A of a rectangle is:
A = length × width
Substituting the given values, we have:
42 = (W - 1) × W
Now, let's solve this equation for W to find the width of the rectangle.
42 = [tex]W^2[/tex] - W
Rearranging terms, we get a quadratic equation:
[tex]W^2[/tex] - W - 42 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula. Factoring seems simpler in this case:
Product = 1 × -42 = -42
Sum = -1
Required numbers: 6 × -7
[tex]W^2[/tex] - W - 42 = 0
[tex]W^2[/tex] + 6W - 7W - 42 = 0
W (W + 6) - 7 (W + 6) = 0
(W - 7) (W + 6) = 0
Setting each factor equal to zero gives us two possible values for W:
W - 7 = 0 or W + 6 = 0
Solving each equation:
W - 7 = 0W = 7
W + 6 = 0W = -6
Since the width of the rectangle cannot be negative, we discard W = -6.
So, the width of the rectangle is W = 7 meters.
Now, to find the length L, we can use the equation L = W - 1:
L = 7 - 1
L = 6
The question is:
The length of a rectangle is 1 meter less than its width. The area of the rectangle is 42 square meters. Find the dimensions of the rectangle.
This is for algebra 2 and I got stuck on this anyone know this?
The probability of rolling an even number with a six-sided number cube
is about 1/2 . Choose the likelihood that best describes the probability
of this event.
Answer:
Equally likely
Step-by-step explanation:
Equally likely means that it’s a 50% percent chance on both sides meaning that equally likely Is the answer.
Answer:
likely
Step-by-step explanation:
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted:
Write an equation to determine the area, A, of the patio that will be painted.
A = (x + 18)(x + 35)
A = (x + 15)(x + 25) + 30
A = (x + 5)(x + 22)
A = (x + 25)(x + 15) − 30
Answer:
A = (x + 25)(x + 15) - 30
Step-by-step explanation:
This question is not complete without a figure; find the figure attached.
Marissa is painting a regular patio with dimensions as
Length = (x + 25) units
Width = (x + 15) units
Area of this rectangular patio = Length × Width
Area = (x + 25)(x + 15) unit²
She has to paint the patio except the bench that does not need to be painted.
Dimensions of the rectangular bench,
Length = 10 units
Width = 3 units
Area of the bench = 10×3 = 30 units²
Area of the patio to be painted = Area of patio - Area of bench
A = (x + 25)(x + 15) - 30
Which list is in order from least to greatest?
9.4 x 10 -8, 9.25 x 10 -6, 2.5 x 10 3, 7 x 10 3
2.5 x 10 3, 7 x 10 3, 9.25 x 10 -6, 9.4 x 10 -8
9.25 x 10 -6, 9.4 x 10 -8, 7 x 10 3, 2.5 x 10 3
9.4 x 10 -8, 9.25 x 10 -6, 7 x 10 3, 2.5 x 10 3
Answer:
Step-by-step explanation:
last list
Answer:
it's the one at the bottom
9x^2-25
How do you solve this?
Answer:(3x+5) (3x-5)
Step-by-step explanation: a2-b2 =(a+b) (a-b) where a= 3x and b=5
What is the m in 45m - 900 = 90m
Step-by-step explanation:
[tex]45m - 900 = 90m \: [/tex]
[tex]45m - 90m = 900[/tex]
[tex] - 45m = 900[/tex]
[tex]m = \frac{900}{ - 45} = - 20[/tex]
Answer:
m=-20
Step-by-step explanation:
45m -900=90m
-900=45m
-900/45=45m/45
m=-20
60
boys at a summer camp were asked to complete a survey about their favorite outdoor activity.
18
boys chose biking and
29
29
boys chose fishing.
The remaining boys did not complete the survey.
What expression gives the percent of survey participants who chose fishing?
Expression for percent of survey participants who chose fishing =
Explanation:
Total number of boys = 60
Number of boys who took part in survey = 18 + 29 =47
Number of boys who chose fishing = 29.
Percentage of an outcome = (Number of favorable outcome/ Total number of outcome) x 100
Percentage of boys who chose fishing = (29/47)x100
Expression for percent of survey participants who chose fishing =
Hope I helped! :)
Answer:
Expression for percent of survey participants who chose fishing =
Explanation:
Total number of boys = 60
Number of boys who took part in survey = 18 + 29 =47
Number of boys who chose fishing = 29.
Percentage of an outcome = (Number of favorable outcome/ Total number of outcome) x 100
Percentage of boys who chose fishing = (29/47)x100
Expression for percent of survey participants who chose fishing =
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Step-by-step explanation:
Mai's water bottle had 24 ounces in it. After she drank x ounces of water, there were 10 ounces left. Select all the equations that represent this situation.
Answer:
x+10=24
Step-by-step explanation:
the actual equation would give you 14
To represent the situation, you can use the equation x = 24 - 10 or the proportion x/24 = 10/24.
Explanation:To represent the situation, we can use the equation: x = 24 - 10, where x represents the amount of water Mai drank. This equation represents the fact that the initial amount of water in the bottle (24 ounces) minus the amount of water that Mai drank (x ounces) equals the remaining amount of water (10 ounces).
Alternatively, we can also use the proportion x/24 = 10/24 to represent the situation. This proportion shows that the ratio of the amount of water Mai drank to the initial amount of water in the bottle is equal to the ratio of the remaining amount of water to the initial amount of water.
Mark sold 445 tickets for the school play. Student tickets cost $3 and adult tickets
cost $5. Mark's total income for the event was $1871. How any adult tickets did he
sell?
Answer:
Mark sold 268 adult tickets.
Step-by-step explanation:
We are given the following in the question.
Let x be the number of students ticket sold and y be the number of adult tickets sold.
Total number of tickets sold = 445
Thus, we can write the equation:
[tex]x + y = 445[/tex]
Cost of student ticket = $3
Cost of an adult ticket = $5
Total income = $1871
Thus, we can write the equation:
[tex]3x + 5y = 1871[/tex]
Solving the two equations, we get,
[tex]3x + 5y - (3x+3y) = 1871 - 3(445) \\2y = 536\\\Rightarrow y = 268\\\Rightarrow x = 445 - 268 = 177[/tex]
Thus, Mark sold 268 adult tickets.
Answer:he sold 268 adult tickets at the school play
Step-by-step explanation:
What is the solution to the division problem 426 Divided By 5113 written as a mixed number
Answer:
[tex]12\frac{1}{426}[/tex]
Step-by-step explanation:
please check the attached files for more explanation
A divisor is a number that divides another number either completely or with a remainder and the divisor [tex]5113[/tex] is divided by [tex]426[/tex] is [tex]12[/tex].
What is divisor ?
The divisor is any number that divides another number. A factor, however, is a divisor that divides the number entirely and leaves no remainder. So, all factors of a number are its divisors. But not all divisors will be factors.
To know more about divisors.
The solution using the "Long Divison Method'
Now, start the divisor [tex]426[/tex] on the left side and the dividend [tex]5113[/tex] on the right side :
12
[tex]\sqrt[426]{5113} \\426\\----\\853\\852\\----\\1[/tex]
Hence, the result of the divisor [tex]5113[/tex] divided by [tex]426[/tex] is [tex]12[/tex].
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A mug can hold 17.09 ounces of coffee without overflowing. The radius of the mug is 4 cm. Given that 1 cm³ equals 0.034 ounce, what is the height of the mug to the nearest centimeter
Answer:
10 centimeters
Step-by-step explanation:
Kindly refer to the attached image for explanations
2) What is 8% of 24.52? Round your answer to the nearest hundredth.
What is 8% of 24.52= 1.9616
just round up
Answer:
What is 8% of 24.52= 1.9616
Step-by-step explanation:
round it
The temperature drops 10 degrees and then rises 10 degrees.
Write an addition expression that represents this situation.
Please answer ASAP
Answer:
10-10+10=10 degrees
What is the gradient of the line 12x=15-3y
Answer:
-4
Step-by-step explanation:
12x=15-3y
+3y
12x+3y=15
-12x
3y=-12x+15
/3
y=-4x+15
Gradient= -4 as in the equation y=mx+c
, m=the gradient therefore the gradient is -4
Answer:
-4
Step-by-step explanation:
12x=15-3y +3y
12x+3y=15 -12x
3y=-12x+15 /3
y=-4x+15
HELP ASAP !!!
Please explain why
An element with a mass of 120 grams decays by 27.5% per minute. To the nearest tenth of a minute, how long will it be until there are 2 grams of the element remaining?
Answer:
12.7
Step-by-step explanation:
its right
It will take approximately 9.9 minutes until there are 2 grams of the element remaining.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
We can use the exponential decay formula to solve the problem.
The formula for exponential decay is:
[tex]A = A_0e^{-kt}[/tex]
where:
A₀ = initial amount
A = amount remaining after time t
k = decay rate constant
t = time
We can find the decay rate constant k using the given percentage decay per minute.
If the element decays by 27.5% per minute, then the decay rate constant is:
k = ln(1 - 0.275) = -0.3185
where ln is the natural logarithm.
Let's substitute the given values into the formula and solve for t:
[tex]2 = 120 e^{-0.3185t}[/tex]
Divide both sides by 120:
[tex]0.0167 = e^{-0.3185t}[/tex]
Take the natural logarithm of both sides:
ln(0.0167) = -0.3185t
t = ln(0.0167) / (-0.3185)
t ≈ 9.9 minutes (to the nearest tenth of a minute)
Therefore,
It will take approximately 9.9 minutes until there are 2 grams of the element remaining.
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Can you explain it and help me out please
Answer:
c.
Step-by-step explanation:
2x² - 4x - 3 = 0
[tex]x= \frac{-b+/-\sqrt{b^{2}-4ac} }{2a} \\\\x= \frac{-(-4)+/-\sqrt{(-4)^{2}-4*2*(-3)} }{2*2} \\\\x= \frac{4+/-\sqrt{16+24} }{4} \\\\x= \frac{4+/-\sqrt{40} }{4} = \frac{4+/-2\sqrt{10} }{4}=\frac{2+/-\sqrt{10} }{2}[/tex]
Which equation could be used to find the length of the hypotenuse?
Answer:
aaaaaaaaaaaaaaaaa
Step-by-step explanation:
i dont if i made it clear but the answer is A
The volume of a cylinder can be found using the formula V = pi r squared h.
Which is the correct first step in finding the height of a cylinder with a volume of 192 pi cubic inches and a radius of 5 inches?
5 = pi (192) squared h
V = pi + (5) squared + 192 pi
V = pi (5) squared (192)
192 pi = pi (5) squared h
Answer:
The answer is D
192 pi = pi (5) squared h
Step-by-step explanation:
Answer:
The answer is D
Step-by-step explanation:
It points out to find the height and it already gives you the volume and radius so all you have to do is plug in those to #'s.
So the "V" is always going to go first then the equal sign the the pi sign then a number followed by squared.
Right after that you should have an "H" which is the height you have to use to multiply.