Answer:
2n+7
Step-by-step explanation:
Y=|3x-3|-9 use x-values to find solution -1,0,4
Answer:
Step-by-step explanation:
By definition,
|a + bi| =
Answer:
|z| = |a + ib| = [tex]\sqrt{a^{2} + b^{2}}[/tex].
Step-by-step explanation:
By the definition of complex numbers the modulus of any complex number z = x + iy is given by |z| = |x + iy| = [tex]\sqrt{x^{2} + y^{2}}[/tex].
Say for example, z = 3 + 4i is a complex number then
|z| = |3 - 4i| = [tex]\sqrt{3^{2} + 4^{2}} = 5[/tex]
In a complex plane modulus of a complex number z = x + iy means the distance of the point (x, iy) from the origin. (Answer)
in the equation 3/4(x+8)=9 ,what does x equal
Answer:
x=4
Step-by-step explanation:
The given equation, the value of x is :
Solving the equation
[tex]3/4(x+8)=9\\0.75(x+8)=9\\0.75x+6.00=9\\0.75x=3\\x=3/0.75\\x=4[/tex]
The value of x is 4 .
The time a projectile spends in the air can be modeled by the equation t² -t - 8 = 0, in which t represents the amount of time traveled, in seconds. Which of the following is equivalent to the equation t² - 2t - 8 = 0?
(t + 4)(t - 2) = 0
t -4)(t - 2) = 0
(t + 4)(t + 2) = 0
(t - 4) (t + 2) = 0
Answer:
(t - 4)(t + 2) = 0
Step-by-step explanation:
The general formula for a quadratic expression is
y = ax² + bx + c
Your expression is
y = t² - 2t - 8 = 0
By comparison, we see that
a = 1; b = -2; c = -8
1. Find two numbers that multiply to give ac and add to give b.
In this case, find two numbers that multiply to give -8 and add to give -2.
It helps to list the factors of -8.
They are ±1, ±2, ±4, and ±8
After a little trial and error, you should find the numbers -4 and +2.
-4 × 2 = -8, and -4 + 2 = -2)
2. Rewrite the middle term with those numbers
t² -4t + 2t - 8 = 0
3. Factor the first and last pairs of terms separately
t(t - 4) +2(t - 4) = 0
4. Separate the common factor
The common factor is t - 4.
(t - 4)(t + 2) = 0
Sgt. Merritt has bought a house now that his tour of duty is up. He wants to stain the wood floors of the living room, which measure 18x14. The stain costs $120 per square yard. How much will it cost to stain floor of the entire room?
It costs $ 30240 to stain floor of the entire room
Solution:
Given that,
Sgt. Merritt has bought a house now that his tour of duty is up
He wants to stain the wood floors of the living room, which measure 18 x 14
Therefore,
length = 18 yards
Width = 14 yards
Find the area:[tex]Area = length \times width\\\\Area = 18 \times 14\\\\Area = 252[/tex]
Thus area of wood floors is 252 square yards
How much will it cost to stain floor of the entire room?The stain costs $120 per square yard
[tex]Cost = 252 \times 120\\\\Cost = 30240[/tex]
Thus it costs $ 30240 to stain floor of the entire room
To stain Sgt. Merritt's living room floors, which measure 18x14 feet, first calculate the area in square feet, convert to square yards, and then multiply by the cost per square yard. The total cost will be $3,360.
To determine the cost to stain the wood floors in the living room, first we need to calculate the total area in square yards since the stain is sold by square yard. The room measures 18 feet by 14 feet.
Step 1: Calculate Square Footage
Multiply the length and width in feet to get the square footage:
18 feet × 14 feet = 252 square feet
Step 2: Convert Square Feet to Square Yards
There are 9 square feet in 1 square yard. Therefore, we divide the total square footage by 9 to convert to square yards:
252 square feet / 9 square feet per square yard = 28 square yards
Step 3: Calculate the Cost
The cost to stain one square yard is $120. So, we multiply the total square yards by $120 to get the total cost:
28 square yards × $120 per square yard = $3,360
Therefore, the cost to stain the entire living room floor will be $3,360.
The sum of two numbers is 30 and their difference is 12 find the 2 numbers
Answer:
The two numbers are 21 and 9
Step-by-step explanation
(15+6) minus (15-6) gives a difference of 12
21- 9 = 12
If y = -x² + 14x + 7 , then x = 10 is a counterexample for which conjecture?
A.
y is always positive.
B.
y is always negative.
C.
y is a function of x.
D.
The graph of y is a parabola.
Answer:
The correct answer is B
Step-by-step explanation:
If we plug in x=10 to the equation, we get y=47
Since y is positive, A is not an counterexample
Since y is a function of x, C is not an counterexample
Since the graph of y is a parabola, D is not an counterexample
Hope this helped and mark as brainliest!
Black bears lose 1/5 of the body weight during hibernation. A black bear weighs 265 poundBlack bears lose 1/5 of their body weight during hibernation. A blackK Bear weighs 260 pounds. How much weight did it lose while hibernating
Answer:
52lbs
Step-by-step explanation:
To find out how much weight the black bear lost during hibernation, subtract the weight after hibernation from the weight before hibernation: 265 - 260 = 5 pounds.
Explanation:To find out how much weight the black bear lost during hibernation, we can use the information that black bears lose 1/5 of their body weight during hibernation. We know that the black bear weighed 265 pounds before hibernation and weighs 260 pounds after hibernation. To calculate the weight loss, we subtract the weight after hibernation from the weight before hibernation: 265 - 260 = 5 pounds. Therefore, the black bear lost 5 pounds while hibernating.
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Let n represent the position of a term in the sequence below.
8, 11, 14, 17, 20, 23,
Which algebraic expression can be used to find the nth term of the sequence
The algebraic expression can be used to find the nth term of the sequence is:
[tex]a_n = 5+3n[/tex]
Where, [tex]n\geq 1[/tex] and n is a positive whole number
Solution:
Given sequence is:
8, 11, 14, 17, 20, 23
Let us find the common difference between terms
11 - 8 = 3
14 - 11 = 3
17 - 14 = 3
20 - 17 = 3
23 - 20 = 3
Thus the common difference between successive term and previous term is constant
Thus this is a arithmetic sequence
The formula for nth term term of arithmetic sequence is given as:
[tex]a_n = a_1+(n-1)d[/tex]
Where,
[tex]a_n[/tex] is the nth term of sequence
[tex]a_1[/tex] is the first term of sequence
d is the common difference between terms
Here in this sequence, 8, 11, 14, 17, 20, 23
[tex]a_1 = 8\\\\d = 3[/tex]
Therefore,
[tex]a_n = 8+(n-1)3\\\\a_n = 8+3n -3\\\\a_n = 5+3n[/tex]
Where, [tex]n\geq 1[/tex] and n is a positive whole number
Thus algebraic expression can be used to find the nth term of the sequence is found
Write an algebraic expression half the quantity of X plus Y?
Final answer:
The algebraic expression for half the quantity of X plus Y is (1/2) × (X + Y) or (X + Y) / 2.
Explanation:
To write an algebraic expression for half the quantity of X plus Y, you start by adding X and Y together. This can be represented as (X + Y). To find half of this quantity, you multiply the sum by 1/2 or divide by 2. Therefore, the algebraic expression that represents half the quantity of X plus Y is (1/2) × (X + Y) or (X + Y) / 2.
1|4)
4x + 3y = 4 4 (3.2) +
2X- $y = -28
20:0)
6x=
The solution to the system of equations is x = -2 and y = 4
How to solve the equation
To solve this system of equations using Cramer's rule, we need to first express the equations in standard form: Ax + By = C
According to the problem, we have the equations
4x + 3y - 4 = 0
6x = 8 - 5y.
This is the same as
4x + 3y = 4
6x + 5y = 8
The determinants required for Cramer's rule:
Coefficient matrix (D)
[tex]\[D = \begin{vmatrix} 4 & 3 \\ 6 & 5 \end{vmatrix} = (4 \times 5) - (3 \times 6) = 20 - 18 = 2\][/tex]
For Dₓ
[tex]\[D_x = \begin{vmatrix} 4 & 3 \\ 8 & 5 \end{vmatrix} = (4 \times 5) - (3 \times 8) = 20 - 24 = -4\][/tex]
For D y
[tex]\[D_y = \begin{vmatrix} 4 & 4 \\ 6 & 8 \end{vmatrix} = (4 \times 8) - (4 \times 6) = 32 - 24 = 8\][/tex]
Using Cramer's rule:
[tex]\[x = \frac{D_x}{D} = \frac{-4}{2} = -2\][/tex]
[tex]\[y = \frac{D_y}{D} = \frac{8}{2} = 4\][/tex]
complete question
Solve the following simultaneous equations using Cramer's rule.
4x + 3y - 4 = 0
6x = 8 - 5y
The perimeter of a rectangular garden is 110ft. The length is 5 ft greater than the width. Find the length and width.
P = perimeter
L = length
W = width
Formula for the perimeter of a rectangle = L + L + W + W or P = 2L + 2W
You know:
P = 110ft
L = W + 5 [length is 5ft greater than the width]
So plug this into the formula:
P = 2L + 2W Substitute/plug in (W + 5) for L
110 = 2(W + 5) + 2W Distribute/multiply 2 into (W + 5)
110 = (2)W + (2)5 + 2W
110 = 2W + 10 + 2W Combine like terms (2W + 2W)
110 = 4W + 10 Subtract 10 on both sides
110 - 10 = 4W + 10 - 10
100 = 4W Divide 4 on both sides to get "W" by itself
[tex]\frac{100}{4}=\frac{4W}{4}[/tex]
25 = W Now that you know the width, plug it into the equation for length
L = W + 5 Plug in 25 for W
L = 25 + 5
L = 30
L = 30 ft
W = 25 ft
PROOF
P = 2L + 2W
110 = 2(30) + 2(25)
110 = 60 + 50
110 = 110
Plz, I'm desperate for 5 answers. help me ASAP on the attachments I'll give everything I can, Brainly award, high ratings, thanks, everything, I need help! Please I need help!
Answer:
[tex]1.\ 8n+4\\\\2.\ 5x+13\\\\3.\ x+3\\\\4.\ x-6\\\\5.\ 4x+1[/tex]
Step-by-step explanation:
1.
[tex]Sum=2n+6+6n-2\\\\Sum=2n+6n+6-2\ \ \ \ \ \ \ \ (using\ commutative\ property\ of\ addition\ a+b=b+a)\\\\Sum=8n+4[/tex]
2.
[tex]Sum=3x+9+2x+4\\\\Sum=3x+2x+9+4\ \ \ \ \ \ \ \ (using\ commutative\ property\ of\ addition\ a+b=b+a)\\\\Sum=5x+13[/tex]
3.
[tex]Difference=(3x+5)-(2x+2)\\\\Difference=3x+5-2x-2\ \ \ \ \ \ \ [using\ distributive\ property\ -(a+b)=-a-b]\\\\Difference=3x-2x+5-2\ \ \ [commutative\ property]\\\\Difference=x+3[/tex]
4.
[tex]Difference=(4x+3)-(3x+9)\\\\Difference=4x+3-3x-9\ \ \ \ \ \ \ [using\ distributive\ property\ -(a+b)=-a-b]\\\\Difference=4x-3x+3-9\ \ \ [commutative\ property]\\\\Difference=x-6[/tex]
5.
[tex]Difference=(6x+2)-(2x+1)\\\\Difference=6x+2-2x-1\ \ \ \ \ \ \ [using\ distributive\ property\ -(a+b)=-a-b]\\\\Difference=6x-2x+2-1\ \ \ [commutative\ property]\\\\Difference=4x+1[/tex]
Suppose the two line segments in a coordinate plane one with a length of 120 units and other with a length of 240 units were both rotated 90 degrees about the origin and then translated 50 units up one of the resulting segments could have a length of...units.
In the image, the length of the segment will be 120 units.
Step-by-step explanation:
Whatever may be transformation, either rotation, reflection or translation, the length the line segment will not change.
Here one segment with 120 units and other segment with 240 units is rotated 90 degrees about the origin and then it is translated 50 units up, we will get the image of the segment with the same size.
In the image, the length of the segment will be 120 units.
Identify all the sets to which the number belongs. Choose from Rational Number, Irrational number, whole number, and integer. 1.256...
A. Rational number
B. Irrational number
C.Integer, and rational number
D. Whole number, Integer, and rational number
Answer:
The number 1.256 is A)rational number.
Step-by-step explanation:
A whole number is a non-negative number without any digits behind the decimal. An integer is a set of negative and non negative numbers that don't have any digits behind the decimal.A number that can be shown as a fraction of two whole numbers is a rational number.And the numbers that are not rational are irrational numbers.Here, 1.256 is a fraction of whole numbers 1256 and 1000 , so it is a rational no.[tex]\frac{1256}{1000} =1.256[/tex]
But since it has digits behind the decimal it is neither a whole number, or an integer.The number 1.256... is a rational number because it can be expressed as a ratio of two integers. It is not an integer, whole number, or irrational number.
Explanation:The number 1.256 repeated is a rational number because it can be expressed as the ratio of two integers, which fits the definition of a rational number as ratios of integers such as 2/1, 3/4, and so on.
Even though the decimal representation may appear to continue forever, if the pattern of digits repeats indefinitely, it is still rational.
This number is not an integer, whole number, or irrational number, so it does not belong to those sets. An integer is a whole number without any fractional or decimal part, positive or negative, including zero.
Therefore, the correct option that defines the sets to which the number 1.256... belongs is Option A: Rational number.
7 + (5 – 9)2 + 3(16 ÷ 8).
Answer:
5
Step-by-step explanation:
7 + (5 - 9)2 +3(16/8)
7 + (-4)2 +3(2)
7+(-8) +6
7 -8 +6
7 -2
5
The slide at the playground has a height of 6 feet.The base of the slide measured on the ground is 8 feet.what is the length of the slide
Answer: 10ft
Step-by-step explanation:
Using the Pythagorean theorem (a² + b² = c²) you would end up with an equation like this: 36 + 64 = 100. You would then square root 100 and the answer would be 10 ft
The tree diagram represents an experiment consisting of two trials.
P(A and C) = [?]
Yo sup??
P(A)=0.5
P(C|A)=0.4
Therefore
P(A and C)=0.5*0.4
=0.2
Hope this helps.
The required probability is P(A and C) is 0.2 which is represented in the tree diagram.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The given tree diagram represents an experiment consisting of two trials.
The tree diagram represents an experiment consisting of two trials. In this case, the probability of event A and event C occurring is represented by the intersection of branches A and C in the tree diagram.
This probability can be calculated by multiplying the probability of each individual event together.
As per the given question, we have
P(A) = 0.5
P(C|A) = 0.4
So, P(A and C) = 0.5 × 0.4 = 0.2
Thus, the required probability is P(A and C) is 0.2
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A garden supply store sells two types of lawn mowers. The smaller mower costs $249.99 and the larger mower costs $329.99. If 30 total mowers were sold and the total sales for a given year was $8379.70, find how many of each type were sold.
19 small mowers and 11 large mowers are sold
Solution:
Let "a" be the number of small mowers sold
Let "b" be the number of large mowers sold
Cost of each small mower = $ 249.99
Cost of each large mower = $ 329.99
30 total mowers were sold
Therefore,
a + b = 30
a = 30 - b ------------- eqn 1
The total sales for a given year was $8379.70
Thus we frame a equation as:
number of small mowers sold x Cost of each small mower + number of large mowers sold x Cost of each large mower = 8379.70
[tex]a \times 249.99 + b \times 329.99 = 8379.70[/tex]
249.99a + 329.99b = 8379.70 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
249.99(30 - b) + 329.99b = 8379.70
7499.7 - 249.99b + 329.99b = 8379.70
80b = 8379.70 - 7499.7
80b = 880
Divide both sides by 80
b = 11
Substitute b = 11 in eqn 1
a = 30 - 11
a = 19
Thus 19 small mowers and 11 large mowers are sold
April worked 1 1/8 times longer on her math project than Carl, he worked 5 3/4, how many more hours did April work? Please show how to get answer. Thank you
Answer:
[tex]\frac{23}{32}\ hours[/tex]
Step-by-step explanation:
step 1
Find out the number of hours worked by April on her math project
Multiply 1 1/8 by 5 3/4
so
[tex]1\frac{1}{8} (5\frac{3}{4})[/tex]
Convert mixed number to an improper fraction
[tex]1\frac{1}{8}=1+\frac{1}{8}=\frac{1*8+1}{8}=\frac{9}{8}[/tex]
[tex]5\frac{3}{4}=5+\frac{3}{4}=\frac{5*4+3}{4}=\frac{23}{4}[/tex]
substitute
[tex]\frac{9}{8} (\frac{23}{4})=\frac{207}{32}\ hours[/tex]
Convert to mixed number
[tex]\frac{207}{32}=\frac{192}{32} +\frac{15}{32} =6\frac{15}{32}\ hours[/tex]
step 2
How many more hours did April work?
Subtract the hours worked by Carl from the hours worked by April
[tex]\frac{207}{32}-\frac{23}{4}=\frac{207-8*23}{32}=\frac{23}{32}\ h[/tex]
what is the wavelength of an electromagnetic wave with a frequency of 135,000 Hz?
The wavelength of an electromagnetic wave with a frequency of 135,000 Hz is approximately 2,222 meters. This can be calculated using the equation λ = c / f, with c being the speed of light and f the frequency of the wave.
Explanation:The wavelength of an electromagnetic wave can be calculated from the frequency when we understand their relationship through the wave's speed. In the case of an electromagnetic wave, this speed is the speed of light (denoted by c), which is approximately 3.00 x 108 m/s. This relationship is expressed by the equation c = fλ, where f is the frequency and λ is the wavelength.
To calculate the wavelength (λ) from the frequency (f), we rearrange the equation to λ = c / f. Substituting 3.00 x 108 m/s for c and 135,000 Hz for f, gives λ = 3.00 x 108 m/s / 135,000 Hz. After performing the calculation, we find the wavelength to be approximately 2,222 meters.
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The wavelength of an electromagnetic wave with a frequency of 135,000 Hz is approximately 2,222 meters, based on the relationship provided by the equation c = fλ.
Explanation:The wavelength of an electromagnetic wave is directly related to its frequency by the equation c = fλ, where 'c' is the speed of light in vacuum, 'f' is the frequency and 'λ' is the wavelength. In this equation, the speed of light 'c' is typically 3.00 × 108 m/s. Therefore, if we want to figure out the wavelength of an electromagnetic wave with a frequency of 135,000 Hz, we can rearrange the equation to solve for the wavelength: λ = c/f. Substituting the given values, we have λ = (3.00 × 108 m/s)/(135,000 s-1), which simplifies to λ = 2,222 m.
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What is the probability of getting a number less than 7 on a standard six-sided die
Answer:
100%
Step-by-step explanation:
You cant get a number on a 6 sided die higher than 7.
What is 12 percent of 29
Answer:
3.48
Step-by-step explanation:
12%=0.12
0.12*29=3.48
Can you please explain how to do this
ANSWER ASAP!!!!!!!!!
x = 0,1
y = 0,-5
hope this helped ___~ ~___
0
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You have 3 quarters, 7 dimes, and 5 nickles in your pocket. A coin is chosen at random. What is the BEST answer for the probability of drawing a quarter?
A) impossible
B) unlikely
C) very likely
D) certain
Answer:
B) Unlikely
Step-by-step explanation:
Your chance drawing a quarter is a low 20%
Answer:
B:Unlikely
Step-by-step explanation:
Because you have 7 dimes and 5 nickels so those ones would be more likely to be picked than the quarter but it is still possible.
100 POINTS!!!!
Which number should each side of the equation 2/3x=10 be multiplied by to produce the equivalent equation of x = 1/5?
−2/3
1/3
3/2
3
Answer:
2/3x = 10.....multiply both sides by 3/2 giving u :
x = 10 * 3/2
x = 30/2 which equals 15
Step-by-step explanation:
So your answer is 3/2 or 32
3(4x-5)+4(2x+6) simplify
Answer:
20+9
Step-by-step explanation:
Answer: 20x+9 (I THINK that’s the answer but I’m not completely sure so...)
Step-by-step explanation: (12x-15) + (8x+24)
12x+8x= 20x
-15+24 (or 24-15)= 9
20x+9
solve for x: 3(9-8x-4x)+8(3x+4)=11
Answer:
x=4
Step-by-step explanation:
3(9-8x-4x)+8(3x+4)=11
Subtract 4 x from − 8 x
3 ( 9 − 12 x ) + 8 ( 3 x + 4 ) = 11
Distribute
27 − 36 x + 24 x + 32 = 11
Simplify
− 12 x + 59 = 11
Subtract 59 to both sides
− 12 x = − 48
Divide by -12
x=4
The area of a rectangular field is 7050m^2. If the width of the field is 75m, what is its length?
Answer:
Step-by-step explanation: Area =length × width
7050m^2 = X× 75m
7050 =75X
Divide both sides by 75
7050÷75 =75÷75
74m= X
Write a phrase $3 more than four times the cost of a pretzel as an algebraic expession
Answer:
[tex]4x+3[/tex]
Step-by-step explanation:
Let
x ----> the cost of a pretzel
we know that
The phrase" $3 more than four times the cost of a pretzel" is equal to multiply the cost of a pretzel x by 4 and adds the number 3
so
The algebraic expression is
[tex]4x+3[/tex]
Answer:
4p + $3
Step-by-step explanation:
more than= + (plus sign)
four times the cost of a pretzel= 4p
Remember 4 times cost of pretzel
times= multiplication sign
p=cost of pretzel
So: 4p + $3