Answer:
x < 6
Step-by-step explanation:
3x < 18 ( divide both sides by 3 )
x < 6
Find the coordinates of the intersection of the diagonals of ABCD
with vertices A(0, 2), B(8, 2), C(4, − 4), and D(−4, − 4).
The coordinates of the intersection of the diagonals are ( , )
If the coordinates of the intersection of the diagonals of ABCD
with vertices A(0, 2), B(8, 2), C(4, − 4), and D(−4, − 4). The coordinates of the intersection of the diagonals are (4/3, 0).
What is the coordinates?Using the two point form of the equation of a line to determine the The equation of the line that contains AC
y₋y₁ = (y₂-y₁)/(x₂-x₁) * (x₋x₁)
where:
(x₁, y₁) and (x₂, y₂)= two points on the line
y - 2 = (-4 - 2)/(4 - 0) * (x - 0)
Simplify
y - 2 = -3/2 * x
2y - 4 = -3x
3x + 2y = 4
Equation of the line that has BD
y - 2 = (-4 - 2)/(8 - (-4)) * (x - 8)
Simplify
y - 2 = -3/4 * x + 9/2
4y - 8 = -3x + 36
3x + 4y = 44
Now let find the point of intersection:
3x + 2y = 4
3x + 4y = 44
Multiplying the first equation by -2
-6x - 4y = -8
Eliminate x
0x + 0y = 36
So,
y = 0
3x + 2(0) = 4
3x = 4
x = 4/3
Therefore the coordinates is (4/3, 0).
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1. Allison is buying a home. It cost her $230,000. She has to put a down payment of 10% of the purchase price. How much is her down
payment?
$13,000
$23,000
$30,000
$2,000
dentify the radius and the center of a circle whose equation is (x – 5)² + y² = 81.
The radius of the circle is units.
The center of the circle is at (, ).
Answer:
Step-by-step explanation:
General formula
(x-h)^2 + (y-k)^2 = r^2
where (h,k) center of circle whose radius r
applying the formula to our Q
(x – 5)² + y² = 81
(x – 5)² + (y-0)² = 9^2
---> center of circle (5,0)
---> radius is 9
which equation is NOT true?
A -4+(-3) =-7
B -8(2) = -16
C 3-(-2)=5
D -12 ÷ (-3) = -4
What time is shown on the clock?
Answer:
3:55
Step-by-step explanation:
3:55
Write the factored form of the polynomial function with real coefficients, a lead coefficient of 1, and zeros of -4, -2, 4, and 2.
Step-by-step explanation:
Using the roots given in order given:
y= ( x+4)(x+2)(x-4)(x-2) would fit the bill.....
Suppose you want to purchase a $ 165000 house. If you put 20% down and finance the rest in a 20 year mortgage at an interest rate of 7.5%, what will your monthly payments be?
Monthly payment =
The monthly payments on the 20 yrs mortgage would be $946.69.
According to the question, the down payment on the house is 20% of $165000, which is:
0.2 * $165,000 = $33,000
The amount that is needed to be financed is:
$165,000 - $33,000 = $132,000
This rate of interest on the payment is 7.5% per year, which is equal to 0.075 as a decimal. We know that the mortgage is for 20 yrs or 240 months:
To calculate the monthly payment, we can use the formula:
monthly payment = [tex][P * r * (1 + r)^n] / [(1 + r)^n - 1][/tex]
where P is the principal amount i.e. the amount being borrowed, r is the monthly interest rate, whereas n is the number of payments.
we need to find the monthly interest rate, for which we can use divide the yearly interest by the number of months in a year, we get:
r = 0.075 / 12 = 0.00625
Now substituting the values into the formula above we get:
monthly payment = [tex][$132,000 * 0.00625 * (1 + 0.00625)^240] / [(1 + 0.00625)^240 - 1][/tex]
monthly payment = $946.69 which is rounded to the nearest cent.
Therefore, the monthly payments on the 20 yrs mortgage would be $946.69.
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A rectangle measures 2 3/4 inches by 2 3/4 inches. What is its area?
The area of the given rectangle is 121/16 square inches.
As know that the area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
To find the area of the rectangle, we need to multiply the length by the width. We have:
Length = 2 3/4 inches = 11/4 inches
Width = 2 3/4 inches = 11/4 inches
Area = Length x Width
Area = (11/4) inches x (11/4) inches
Area = 121/16 square inches
Therefore, the area of the rectangle is 121/16 square inches.
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Which expression will complete the proof?
O cos(k0-0) + i sin(k0 - 0)
O cos(k0 - 0) + / sin(k0 + 0)
O cos(k0 + 0) + i sin(k0 – 0)
O cos(k0 + 0) + i sin(k0 + 0)
The expression O cos(k0 + 0) + i sin(k0 + 0) is commonly used in proofs involving complex numbers and trigonometric functions, representing the complex exponential function [tex]e^(ik0)[/tex].
The expression that will complete the proof depends on the given context and what exactly needs to be proved. However, in general, the expression O cos(k0 + 0) + i sin(k0 + 0) is often used in proofs involving complex numbers and trigonometric functions.
This expression represents the complex exponential function [tex]e^(ik0)[/tex], where k0 is a constant. The cosine term represents the real part of the complex number, while the sine term represents the imaginary part.
The addition of 0 in the arguments of both cosine and sine indicates that the complex number is in polar form, with a magnitude of 1 ([tex]since cos^2 +[/tex] [tex]sin^2 = 1[/tex] for all angles).
Using this expression, we can perform various operations and manipulations to prove different results, such as De Moivre's theorem or Euler's formula.
Ultimately, the choice of expression will depend on the specific problem and what needs to be proved.
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which represents 10 times the value of the digit 8 in 308.19
Answer: 0
Step-by-step explanation:8th Place 100*10 1000th Place is 0
A. Determine if (x+2) is a factor of f(x) =x^3-3x^2-7x+6. Explain your reasoning.
Yes (x+2) is a factor of the function, because the remainder is zero.
No (x+2) is NOT a factor of the function, because the remainder is NOT zero.
B. Use division (long or synthetic) and/or factoring to write f(x) =x^3-3x^2-7x+6 in completely factored form, given that (x+2) is a factor of f(x).
select an answer
f(x)=
DNE
X=
Y=
C. Find all the zeros F(X)= x^3-3x^2-7x+6 . NO DECIMALS!
select an answer
y=
x=
DNE
F(X)=
A. Since the remainder is zero, (x+2) is indeed a factor of f(x).
B. So, f(x) is completely factored as (x+2)(x-1)(x-3).
C. The zeros of F(x) are: -2, 1, and 3.
To determine if (x+2) is a factor of f(x) = x³-3x²-7x+6 can use synthetic division or long division.
Using synthetic division:
-2 | 1 -3 -7 6
-2 10 -6
1 -5 3 0
Using the result from part A we can write:
f(x) = (x+2)(x²-5x+3)
The quadratic factor can be factored further using the quadratic formula or factoring by grouping:
f(x) = (x+2)(x-1)(x-3)
So, f(x) is completely factored as (x+2)(x-1)(x-3).
The zeros of f(x) are the values of x that make f(x) equal to zero.
From the factored form of f(x) we can see that the zeros are -2, 1 and 3. So:
The zeros of F(x) are: -2, 1, and 3.
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The local high school is hosting an ice cream social for new students. They
record the ice cream choices of the students throughout the event.
What is the probability that a female student chose strawberry ice cream?
Male
Female
Total
Vanilla Strawberry
6
4
8
9
14
13
Chocolate Total
13
23
21
44
4
17
The probability that a female student chose strawberry ice cream is 7/11 or approximately 0.6364 (rounded to four decimal places).
To calculate the probability that a female student chose strawberry ice cream, we need to consider the total number of female students who made an ice cream choice and the number of female students who chose strawberry ice cream.
From the given information, we have the following breakdown:
Male Female Total
Vanilla 6 4 10
Strawberry 9 14 23
Chocolate 13 4 17
Total 28 22 50
To find the probability, we divide the number of female students who chose strawberry ice cream by the total number of female students:
Probability = (Number of female students who chose strawberry ice cream) / (Total number of female students)
Therefore, the probability of a female student choosing strawberry ice cream is:
Probability = 14 / 22
Simplifying the fraction, we have:
Probability = 7 / 11
Therefore, the probability that a female student chose strawberry ice cream is 7/11 or approximately 0.6364 (rounded to four decimal places).
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Imagine a clock with the hour hand at 12 and the minute hand at 2. Does the angle formed by the two hands have a measure greater than, less than, or equal to 1/4 turn?
The angle formed by the two hands have a measure less than 1/4 turn
How to relate the measure of the angle to 1/4 turn?From the question, we have the following parameters that can be used in our computation:
A clock with the hour hand at 12 and the minute hand at 2
The turn represented by the above is represened as
Turn = (2 * 30)/360
When simplified, we have
Turn = 1/6
Next, we have
Angle at the turn = 1/4
1/6 is less than 1/4
This means that the angle formed by the two hands have a measure less than 1/4 turn
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While digging in his garden. Tyri pushes a shovel into the ground with a force of 630 newtons at an angle of 70° with the ground. Which diagram shows the resolution of the force Tyri exerts into its rectangular components?
The resolution of the given force applied to the shovel is: A vertical force of 592 NA horizontal force of 215.47 N
How to find the components of the force?The components of a force represent the combined vertical and horizontal forces that combine to make the resultant force. Components are two vectors that add up to the given vector which are perpendicular to each other.
Now, when we apply a force F to an object at an angle θ, it can be said that the resolution of the forces is:
In the horizontal direction: F_x = F * cos θIn the vertical direction: F_y = F * sin θTyri pushes a shovel into the ground with a force of 630 newtons at an angle of 70° with the ground.
Thus, the diagram that shows the resolution of the forces is:
A vertical line showing a force of 630 * sin 70 = 592 N
A horizontal line showing a force of 630 * cos 70 = 215.47 N
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The volume of a gas was measured as the temperature was increased from 173 K to
423 K in 50 K intervals. The gas volumes recorded, starting at 173 K, were 16, 21, 26, 30, 36, and 40 cm . Determine whether the data is best described by an increasing or decreasing function, and whether it is linear or exponential. Find a regression equation.
The data is best described by an increasing function. The regression equation is y =0.0965x - 0.61.
Here is a table of the data:
Temperature (K) Gas Volume (cm³)
173 16
223 21
273 26
323 30
373 36
423 40
The data is best described by an increasing function, and it is likely to be linear since the volume of the gas increases uniformly with the temperature.
Let x be the temperature and y be the volume of the gas.
The slope is given by (nΣxy - ΣxΣy) / (nΣx² - (Σx)²),
where n is the number of data points, Σxy is the sum of the products of x and y, Σx is the sum of x, Σy is the sum of y, and Σx² is the sum of the squares of x.
The y-intercept is given by (Σy - bΣx) / n, where b is the slope.
Using the data, we have n = 6, Σx = 17788, Σy = 169, Σxy = 4225, and Σx² = 43750.
Substituting these values into the formulas gives the slope b = 0.09657 and the y-intercept a = -0.61.
Therefore, the regression equation is y =0.0965x - 0.61.
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Please help me with this 12-14
The arc lengths and the angle measures are arc length = 0.67 meters, AC = 45 degrees and TV = 23 degrees
Calculating the arc lengths and the anglesArc length
Given that
Central angle = 6 degrees
Circumference = 40 meters
The arc length is calculated as
arc length = Central angle/360 * Circumference
So, we have
arc length = 6/360 * 40
Evaluate
arc length = 0.67 meters
The measurement of AC
Here, the arc AC subtends the angle 45 degrees at the center of the circle
This means that
AC = 45 degrees
The measurement of TV
Here, the arc TV subtends the angle 23 degrees at the center of the circle
This means that
TV = 23 degrees
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Kendall kept track of the number of hours that she spent in
pep band each week for several weeks. She spent 2, 4, 4, 5,
and 5 hours.
What is the mean number of hours that Kendall spent in pep band each
week?
OA. 5 hours
OB. 4 hours
OC. 20 hours
OD. 3 hours
The bedroom, garage, office, and bathroom of a house will be painted, each with a different color. There are 15 colors to choose from. This means that there are ________ color arrangements possible.
Answer: There are 32,760 color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options.
Step-by-step explanation: To determine the number of color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options, we need to calculate the number of permutations.
Since each room is assigned a different color, we can arrange the colors in a specific order. The number of ways to arrange 15 colors in 4 distinct positions is given by the permutation formula:
P(n, r) = n! / (n - r)!
where n is the total number of options (15 colors) and r is the number of positions (4 rooms).
Using the formula, the number of color arrangements possible is:
P(15, 4) = 15! / (15 - 4)!
= 15! / 11!
= (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1)
= 32,760
The bar graph above shows the number of T-shirts of different colors sold by a store one week. The following
week, the store had a sale, and sales of each color T-shirt sold increased by about 50 percent from the
previous week. Of the following, which is closest to the number of green T-shirts sold the week of the sale?
0 15
0 20
045
0 60
The number of green t-shirts sold are 45.
Given that a bar graph showing the sell of t-shirts of 4 different colour,
It is saying that the sell has increased by 50% next week, we need to find the number of green t-shirts to be sold in next week,
So, the number of green t-shirts sold in previous week = 30
So this week the sell should have been increased by 50%
Therefore, the number of green t-shirts sold this week = 150/100 × 30
= 1.5 × 30 = 45
Hence the number of green t-shirts sold are 45.
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Find the m angle DEG and angle DEF. H D 6x E 4x° G F
Based on the application of the complementary angles, the measures of the angles are: m<DEG = 54 degrees; mm<GEF = 36 degrees
What are Complementary Angles?When two angles make up a right angle, they are referred to as complementary angles because they add up to 90 degrees when summed.
6x and 4x make up a right angle, this means their sum will give us 90 degrees when we add them up. Therefore:
6x + 4x = 90
10x = 90
Divide both sides by 10
10x/10= 90/10
x = 9
measure of angle DEG = 6x = 6(9) = 54 degrees.
Measure of angle GEF = 4x = 4(9) = 36 degrees
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A dairy farm has a real estate tax rate of $57.26 per thousand dollars of assessed
value. If the farm is assessed at $665,500.00 what is the real estate tax?
If A and B are m × n matrices such that Ax = Bx for all x ∈ R n , then A = B. Please prove this.
From matrix property it can be showed that A=B.
Given,
If A,B and x are matrices with x≠0 and AX=BX
Now.
X must be non-singular matrix because
A[tex]XX^{-1}[/tex]=B[tex]XX^{-1}[/tex]
[tex]XX^{-1}[/tex] = I( identity matrix )
AI = BI
A = B
Hence Proved, A = B .
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Will Give Brainliest Please Help!
.
What is the x-coordinate of the solution to the following system of equations?
2x + y = -4
5x + 3y = -6
Ox=-6¹
Ox=6
Ox = -8
Ox=8.
Answer:
Option : A
Step-by-step explanation:
To find the x-coordinate of the solution to the system of equations, we need to solve the system by eliminating either x or y. Let's eliminate y by multiplying the first equation by 3 and the second equation by 1:
Equation 1: 2x + y = -4 (multiply by 3)
Equation 2: 5x + 3y = -6 (multiply by 1)
Multiplying equation 1 by 3 gives us:
6x + 3y = -12
Multiplying equation 2 by 1 gives us:
5x + 3y = -6
Now we can subtract equation 2 from equation 1 to eliminate y:
(6x + 3y) - (5x + 3y) = -12 - (-6)
6x + 3y - 5x - 3y = -12 + 6
x = -6
Therefore, the x-coordinate of the solution to the system of equations is x = -6.
The correct option is: Ox=-6.[tex][/tex]
The probability that a machine will produce
all bolts in a production run within
specification is 0.998. A sample of 8
machines is taken at random then the
probability that 7 or 8 machines is:
Select one:
O
a. 0.9999
b. 0.9841
c. 1
d. 0.8
The probability that 7 or 8 machines will produce all bolts within specification is approximately 0.9841.
Using the binomial distribution formula, we get:
P(X = 7) = (8 choose 7) * (0.002)⁷ * (0.998)¹ ≈ 0.0081
P(X = 8) = (8 choose 8) * (0.002)⁸ * (0.998)⁰ ≈ 0.000003
Therefore, P(X = 7) + P(X = 8) ≈ 0.0081 + 0.000003 ≈ 0.9841.
Probability is a branch of mathematics that deals with the study of the likelihood of occurrence of events or outcomes in situations where there is uncertainty or randomness. It is a measure of the degree of uncertainty of an event, typically expressed as a number between 0 and 1. Probability is used to make predictions and decisions in various fields, including science, engineering, economics, finance, and social sciences.
It is based on the analysis of past events or observations, and it enables us to estimate the likelihood of future events or outcomes. Probability theory provides a mathematical framework for modeling and analyzing random phenomena and helps us understand the laws of chance that govern various natural and artificial systems.
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If sinx= 5/13 and x is in quadrant 1, then Tanx/2=
OA. -5
O B. - 1/5
OC. 5
O D. 1/5
Answer: D: 1/5
Step-by-step explanation:
sinx = 5/13
this ratio is special; it is a 5-12-13 right triangle, (pythagorean triple).
there is also a formula to find tan(x/2); It is tan(x/2) = ±[tex]\sqrt{\frac{1-cosx}{1+cosx} }[/tex]
the + or - sign is decided by the quadrant the half angle is in;
since x is in quad one, it is somewhere between 0 and pi/2. To find the half angles position, simply divide it; x/2 is somewhere between 0/2 and pi/4.
so its also in the first quadrant. Since tangent is positive in the first quadrant, we will take the positive answer:
One more thing. we need the cosx in our formula. cosx will be 12/13, since this is a special right triangle as we said before.
tan(x/2) = [tex]\sqrt{\frac{1-12/13}{1+12/13} }[/tex]
tan(x/2) = [tex]\sqrt{\frac{1/13}{25/13} }[/tex]
tan(x/2)= [tex]\sqrt{1/25}[/tex]
tan(x/2) = 1/5
Option D is the answer :)
Please help I am struggling a lot thank you so much have a great day
Answer:
Step-by-step explanation:
To calculate the values of the given function, substitute the given values of x into the function f(x) = 7x^2 - 8x + 8:
f(-2) = 7(-2)^2 - 8(-2) + 8
= 7(4) + 16 + 8
= 28 + 16 + 8
= 52
f(-1) = 7(-1)^2 - 8(-1) + 8
= 7(1) + 8 + 8
= 7 + 8 + 8
= 23
f(0) = 7(0)^2 - 8(0) + 8
= 0 - 0 + 8
= 8
f(1) = 7(1)^2 - 8(1) + 8
= 7(1) - 8 + 8
= 7 - 8 + 8
= 7
f(2) = 7(2)^2 - 8(2) + 8
= 7(4) - 16 + 8
= 28 - 16 + 8
= 20
Therefore, the values of the function for the given inputs are:
f(-2) = 52
f(-1) = 23
f(0) = 8
f(1) = 7
f(2) = 20
what is the difference between a linear functuon and nonlinear function
Answer:
In mathematics, a function is a rule that assigns one unique output value for each input value. A linear function is a function that has a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will form a straight line.
For example, the function f(x) = 2x + 1 is a linear function because its graph is a straight line. As x increases by 1, the output of the function increases by 2.
On the other hand, a nonlinear function is a function that does not have a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will not form a straight line.
For example, the function f(x) = x^2 is a nonlinear function because its graph is a curve. As x increases, the output of the function increases at an increasing rate.
In general, nonlinear functions can take many different forms and can have complex behaviors, whereas linear functions have a simple, predictable behavior.
What is one value of x that could replace the missing value in the table
The value of x which could replace the missing value in the table so that y is not a function of x is; 7.
What is the missing value of x that could make y not a function?It follows from the task content that the value of x which could make y not a function of is required to be determined.
Recall that a function is a special kind of relation in which case each value of x is assigned one value of y.
On this note, if we assign 7 as the missing value of x, then y is not a function of x as u has now been assigned more than 1 output, y values.
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Benjamin is planning what to wear tomorrow evening.
• He has 3 shirts to choose from: red, white, and green.
• He has 2 pairs of pants to choose from: blue jeans and khaki pants.
• He has 3 pairs of shoes to choose from: sneakers, flip flops, and boots.
Benjamin randomly chooses one item from each group. What is the probability that he chooses
sneakers and the green shirt? Type in simplest form!!! Anything else will be considered correct, no exceptions
Answer:
1/9
Step-by-step explanation:
P =
[tex](no \: of \: favorable \: outcomes) \div (total \: numeber \: of \: outcomes \: )[/tex]
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