Given the system of equations:
\(\begin{gathered} -4x-8y=8 \\ 3x-5y=16 \end{gathered}\)The solution of the system will be as follows:
\(\begin{gathered} -4x-8y=8\rightarrow\times3 \\ 3x-5y=16\rightarrow\times4 \\ ------------ \\ -12x-24y=24 \\ 12x-20y=64 \\ ------------ \\ (12x-12x)+(-24y-20y)=24+64 \\ \\ -44y=88 \\ \\ y=\frac{88}{-44}=-2 \end{gathered}\)Substitute with y into the first equation to find x:
\(\begin{gathered} -4x-2\cdot-8=8 \\ -4x+16=8 \\ -4x=8-16 \\ -4x=-8 \\ \\ x=\frac{-8}{-4}=2 \end{gathered}\)So, the solution of the system is:
\(\begin{gathered} x=2 \\ y=-2 \\ (x,y)=(2,-2) \end{gathered}\)Answer:
See below
Step-by-step explanation:
-4x -8y = 8
3x-5y = 16 <===== multiply this equation by 4/3 to get
4x - 20/3 y = 64/3 <=====add to first equation...this will eliminate 'x'
-8y - 20/3 y = 8 + 64/3 solve for y = -2
use this value of y in any of the equations to compute x
-4x - 8(-2) = 8
-4x = 8-16 shows x = 2
The annual property taxes on Jean's new home are 4. 23% of the value of the home. Her home cost \$238,500. What are the property taxes on her new home?
Jean would need to pay $10088.55 as property tax on her new home which cost $238500
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the value of Jeans property tax.
Jean's new home are 4. 23% of the value of the home. For a home of $238500:
x = 4.23% of $238500 = 0.0423 * $238500 = $10088.55
Jean would need to pay $10088.55 as property tax on her new home which cost $238500
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The elevations, in feet, of three citites are marked on the number line shown below. The point 0 on the number line represents sea level. Which statement is true?
Answer:
cityQ
Step-by-step explanation:
City Q is located at the sea level
The statement that should be true is
City P is above sea level and City Q is below sea level.
What is the number line?The word "number line" in mathematics refers to a straight line where a number should be positioned at similar intervals or segments along with its length.
Given:
The point 0 on the number line represents sea level.
As, It should be presented in a horizontal style and be infinitely in any direction.
As a result, option c should be the statement that is true. City Q is below sea level, but City P is above it.
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Which inequality is shown in the graph?
Over which interval is the graph of the parent absolute value function decreasing?
(–[infinity], [infinity])
(–[infinity], 0)
(–6, 0)
(0, [infinity])
The graph of the parent absolute value function is decreasing over the interval (-∞, 0). The function exhibits a decreasing behavior as x moves from negative infinity towards zero, where the absolute value decreases.
The parent absolute value function is defined as f(x) = |x|. To determine where the graph of this function is decreasing, we need to identify the intervals where the function's slope is negative.
Let's analyze the behavior of the parent absolute value function:
For x < 0, the function can be rewritten as f(x) = -x. In this interval, the function is a linear function with a negative slope of -1. As x decreases, f(x) also decreases, indicating a decreasing behavior.
For x > 0, the function remains f(x) = x. In this interval, the function is a linear function with a positive slope of 1. As x increases, f(x) also increases, indicating an increasing behavior.
At x = 0, the function is not differentiable since the slope changes abruptly from negative to positive. However, it is worth noting that the function does not strictly decrease or increase at x = 0.
Therefore, we can conclude that the graph of the parent absolute value function is decreasing over the interval (-∞, 0).
In this interval, as x moves from negative infinity towards zero, the function values decrease. The farther away x is from zero (in the negative direction), the larger the absolute value, resulting in a decrease in the function values.
On the other hand, the graph of the parent absolute value function is increasing over the interval (0, ∞), as explained earlier.
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approximate √200 to the nearest whole number.
TIA!
Answer:
it will be 14.14
Step-by-step explanation:
you have to find the square root
need help solving the equation, trying to figure whether I multiply or divide.
Answer:
m∠B = 43°
b = 26.1
c = 38.3
Step-by-step explanation:
By applying triangle sum in the given triangle,
47° + 90° + m∠B = 180°
137° + m∠B = 180°
m∠B = 43°
By applying sine ratio to the angle measuring 47°.
sin(47°) = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)
= \(\frac{28}{c}\)
c = \(\frac{28}{\text{sin}(47^{\circ})}\)
c = 38.28
c ≈ 38.3
By applying cosine rule,
cos(47°) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)
= \(\frac{b}{c}\)
= \(\frac{b}{38.3}\)
b = 38.3[cos(47°)]
b = 26.1
Write an equivalent equation to AB = AC using A^-1 such that, when it is simplified, the resulting equation will simplify to B = C. What property should be used to continue simplifying the above equation? A. (AB)^-1 = B^-1A^-1 B. (A^-1)^T = (A^T)^-1 C. A-^1A = 1 D. (A^-1)^-1 = A
The property that should be used to continue simplifying the above equation is A-^1A = 1. So, correct option is C.
We can start with the equation AB = AC and multiply both sides by A^-1 on the left:
A^-1(AB) = A^-1(AC)
Using the associative property of matrix multiplication, we can simplify the left-hand side:
(A^-1A)B = (A^-1A)C
Using the fact that A^-1A = I (the identity matrix), we get:
IB = IC
Simplifying further using the fact that I times any matrix is that matrix itself, we obtain:
B = C
Therefore, the equivalent equation to AB = AC using A^-1 that simplifies to B = C is A^-1(AB) = A^-1(AC), and the property used to continue simplifying the equation is A^-1A = I.
The correct option is (C) A^-1A = 1, which is equivalent to A^-1A = I, since the identity matrix is denoted as 1 in some contexts.
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What is the sum of all integers which are not divisible by 5 or 9 between 1 and 100?
The sum of all integers which are not divisible by 5 or 9 between 1 and 100 is 3541.
To determine what is the sum of all integers which are not divisible by 5 or 9 between 1 and 100, the following calculation must be performed:
1 + 2 + 3 + .... + 100 = 5050 (5050 - 9 - 18 - 27 - 36 - 45 - 54 - 63 - 72 - 81 - 90 - 99 - 5 - 10 - 15 - 20 - 25 - 30 - 35 - 40 - 50 - 55 - 60 - 65 - 70 - 75 - 80 - 85 - 95 - 100) = X 3541 = X
Therefore, the sum of all integers which are not divisible by 5 or 9 between 1 and 100 is 3541.
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i need help (-4z2-11u)-5z2
Two terms, \(-4z^2\) and \(-5z^2,\) both involving the variable z of degree 2, form an equation. We combine these similar concepts to make the expression more concise.
Adding or deleting terms raised to the same power(s) with the same variable(s) is known as combining like terms. Since both terms contain z2 in this example, we can add them.
We can combine like terms to simplify the expression\((-4z^2 - 11u) - 5z^2\).
It is possible to rewrite the expression\((-4z^2 - 11u) - 5z^2\) as:
\(-4z^2 - 5z^2 - 11u\)
The terms with the same variable (z) and constant term (-11u) can now be combined as follows:
\((-4 - 5)z^2 - 11u\)
Even more simply, we have:
\(-9z^2 - 11u\)
As a result, the expression\((-4z^2 - 11u) - 5z^2\) can be written as \(-9z^2 - 11u.\)
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Your question is incomplete, most probably the complete question is:
Simplify this equation:
\((-4z^2 - 11u) - 5z^2\)
Please help me with this question!!!!!
h = 11.9 cm
cos = adjacent/ hypotenuse
therefore:
cos(24) = h/ 13
rearrange:
h = 13cos(24)
put into calculator:
h = 11.8760...
rounded to one decimal point:
h = 11.9cm
of the 254 counties in texas, how many have child care programs that state they provide nighttime care for children?
By following these steps, you should be able to find the number of counties in Texas with childcare programs offering nighttime care for children.
To answer your question about how many of the 254 counties in Texas have child care programs that state they provide nighttime care for children, we would need to access current data on child care programs in Texas. Unfortunately, I do not have that specific data at the moment. However, I can guide you on how to find this information.
Begin by visiting the Texas Health and Human Services website (https://hhs.texas.gov) as they are responsible for overseeing child care licensing in the state. Look for information on licensed child care facilities that provide nighttime care.
Utilize websites such as Child Care Aware (https://www.childcareaware.org) or Child Care Finder (https://childcarefinder.com), where you can search for child care programs in Texas by county, and filter your search to include only programs offering nighttime care.
You may also want to check with local county websites or contact the County Clerk's office for information on child care programs within their jurisdiction, specifically those offering nighttime care.
Compile the data gathered from the above sources to determine how many of the 254 Texas counties have child care programs providing nighttime care for children.
By following these steps, you should be able to find the number of counties in Texas with child care programs offering nighttime care for children.
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Please help need it in the next 5 mins
Answer:
y = 4x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
here m = 4 , then
y = 4x + c ← is the partial equation
to find c substitute (2, 9 ) into the partial equation
9 = 8 + c ⇒ c = 9 - 8 = 1
y = 4x + 1 ← equation of line
which of the following is an example of systematic sampling? a) using a random number table, people are chosen and then only the people with even numbers are selected. b) in a population of 500, the first and last 100 for a total of 200 people are chosen. c) in a population of 1000 at a school, every 64th person is chosen. d) a government official uses a list of all the people that have returned tax forms and uses those people that h
The example of systematic sampling is option c) in a population of 1000 at a school, every 64th person is chosen.
In systematic sampling, the population is first divided into a sampling frame (for example, a list or a map) and then every kth individual is selected from the list. In this example, every 64th person is chosen from the list of 1000 individuals, which is an example of systematic sampling. In the example given, there is a list of 1000 individuals, and every 64th person is chosen from the list. This means that the sampling interval k is 64, and the first individual is selected randomly from the first 64 individuals in the list. From then on, every 64th individual is selected to be included in the sample. For instance, if the first individual selected is number 8, then the individuals selected for the sample would be 8+64=72, 8+264=136, 8+364=200, and so on.
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(02.01 LC) Solve:negative 1 over 2 x + 2 = −x + 7 (5 points)??.?.??????
Answer:
x=10
Step-by-step explanation:
let me know if correct
Answer:
x=10
Step-by-step explanation:
hayden wants to place 5 of his 8 trophies on the fireplace. how many ways can he arrange the trophies
Hayden can arrange his 5 trophies on the fireplace in 56 different ways.
The formula for combinations,
which is nCr = n!/r!(n-r)!, where n is the total number of items and r is the number of items being chosen. In this case, n=8 and r=5.
So, we can calculate the number of ways that Hayden can arrange his trophies as follows:
8C5 = 8!/5!(8-5)! = 8!/5!3! = (8x7x6)/(3x2x1) = 56
Therefore, there are 56 ways that Hayden can arrange his 5 trophies on the fireplace.
Hence, Hayden can arrange his 5 trophies on the fireplace in 56 different ways using the formula for combinations.
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A Warming Liquid - A liquid is taken out of a refrigerator and placed in a warmer room, where its temperature, in F, increases over time. It can be modeled using the equation Tm 74 390.87m. (a) What temperature did the liquid start at? Show the work that leads to your answer. (b) What is the temperature of the room?
Answer:
The temperature at the start is 35F
The temperature of the room is 74F
Step-by-step explanation:
Given
\(T(m) = 74 - 39(0.87)^m\)
Solving (a): The temperature at the start.
To do this, we set: \(m = 0\)
So, we have:
\(T(0) = 74 - 39(0.87)^0\)
\(T(0) = 74 - 39*1\)
\(T(0) = 74 - 39\)
\(T(0) = 35\)
Hence, the temperature at the start is 35F
Solving (b): The room temperature
We have:
\(T(m) = 74 - 39(0.87)^m\)
To get the temperature of the room, we simply remove the exponential function.
So, we have:
\(Initial = 74\)
Hence, the temperature of the room is 74F
The initial temperature of the liquid is 35 F and the room temperature is 74 F.
What is Melting Point?The melting point is the temperature at which the solid starts converting into liquid.
Given here,
\(T_m = 74- 39(0.87)^m\)
Leat the \(m = 0,\)
So,
\(T_0 = 74- 39(0.87)^0\\\\T_0 = 35 \rm \ F\)
Thus the initial temperature is 35 F.
Now remove the exponential to get the room temperature,
So,
\(T_{RT} = 74\)
Therefore, the initial temperature of the liquid is 35 F and the room temperature is 74 F.
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84 of %300. i somehow got 24 but the answer was something like 252, i dont really get how. can you help?
Answer:
252
Step-by-step explanation:
Of means multiply
84 % * 300
Change to decimal form
.84 * 300
252
Step-by-step explanation:
You need to set up a proportion. Percents always over percents, so our first fraction would be \(\frac{84}{100}\), which just means that out of 100%, we are given 84. We need to find a variable to solve for: x. We need to find the number that is 84% of 300, which means that 300 is 100%. Knowing this, it would be in the denominator, since both 100 and 300 are 100% of something. This would give us the fraction \(\frac{84}{100} = \frac{x}{300}\). I like to use the cross-multiply method, which just means you multiply by a diagonal and then divide by what's left. This would give us 300 x 84 = 25,200/100 = 252. Hope this helps!
NEED HELP NOW!!
True or False. If f(x)=3x^(2)-8x then f(2a)=12a^(2)-16a.
If (-3,-1) is in the function f(x), then which of the following points will be in the function f^-1(x)?
Which of the following equations would move the graph of f(x)=x^3 a distance of 4 units to the left?
If f(x) = 3x^(2) - 8x then f(2a) = 12a^(2) - 16a: True.
If (-3, -1) is in the function f(x), then a point that will be in the function f^-1(x) is (-1, -3).
An equation that would move the graph of f(x) = x^3 a distance of 4 units to the left is f(x) = (x + 4)^3.
What is a function?In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.
When x = 2a, we have the following output (y-value):
f(x) = 3x² - 8x
f(2a) = 3(2a)² - 8(2a)
f(2a) = 12a² - 16a
In Mathematics, a horizontal translation to the negative x-direction (left) is modeled by this mathematical expression g(x) = f(x + N).
Where:
N represents an integer.g(x) and f(x) represent a function.Therefore, we have:
g(x) = f(x + N)³
g(x) = (x + 4)³.
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Please answer fast!!!
Answer:
it's the 2and answer because
Step-by-step explanation:
1,15 is not the same ratio of 2,24
Answer:
No, because 1:15 is not the same ratio as 2:24.
Step-by-step explanation:
2/24 reduces to 1/12 not 1/15 so these ratios are not the same.
Boxes of tinned cat food are delivered to a shop. There are 28 boxes and in each box there are 16 tins how much is there all together ??
Answer:
448
Step-by-step explanation:
You just need to multiply 28 by 16
does a parallelogram have 2 pairs of parallel sides
Answer:
A parallelogram is a quadrilateral with 2 pairs of parallel sides
An airplane has a bearing of 30°. Find the velocity of the airplane in component form if it is traveling at 625 mph.Select one:a.<625sin60°, 625cos60°>b.<625cos30°, 625sin30°>c.<625cos60°, 625sin60°>d.<625sin30°, 625cos30°>
SOLUTION:
From the diagram, we can see that velocity in component form is;
\(\langle625cos30,625sin30\rangle\)In the definition of Imaginary Numbers i2 = 1, 1) How can we evaluate i10 ? I need the work step- by-step.
The final answer is -1.
The definition of Imaginary Numbers is actually i2 = -1. With this definition, we can evaluate i10 by using the rules of exponents and the fact that i2 = -1. Here are the steps to evaluate i10:
1. Rewrite i10 as (i2)5 using the rule of exponents that (ab)c = abc.
2. Substitute -1 for i2 using the definition of Imaginary Numbers.
3. Simplify (-1)5 to get -1.
So, i10 = (i2)5 = (-1)5 = -1. The final answer is -1.
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pls help :(
y= _x +_
Find the equation of the line
hi, I'm no bot just in case...
the grapgh of the line shows y intercept of -9 and rate of change by 4
SoThe equation of the lline will be: \(y=4x-9\)
Which angles are adjacent angles?
find a function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f.
A function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f is f(x) = 3x^4/4 + 729/4.
In the given question, we have to find a function f such that f'(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f.
The given function is f'(x) = 3x^3.
No integrating on both side,
f(x) = \(\int3x^3dx\) + C
f(x) = 3x^4/4 + C
As given, the line 81x + y = 0 is tangent to the graph of f.
So, slope at point of tangent; f'(x) = -81
So, 3x^3 = -81
Divide by 3 on both side, we get
x^3 = -27
Taking cube root on both side, we get
x = -3
So putting the value of x in 81x + y = 0, we get
y = 243
Thus, f(x) passes through (-3, 243).
So, 243 = 3/4(81) + C
Multiply by 4 on both side, we get
972 = 243 + 4C
Subtract 243 on both side, we get
4C = 729
Divide by 4 on both side, we get
C = 729/4
So, f(x) = 3x^4/4 + 729/4
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the number of books read by four students during each of the last 12 months is summarized in these boxplots. which student most likely read 9 or fewer books in the greatest number of months?
The distribution of the number of books read and identify the student who most likely read 9 or fewer books in the greatest number of months.
Based on the given information, it is not possible to determine which student most likely read 9 or fewer books in the greatest number of months without having the actual boxplots. Please provide the boxplots to give an accurate answer.
1. Boxplots are essential to analyze the data in this scenario.
2. The lower quartile (Q1), median (Q2), and upper quartile (Q3) in the boxplots can be used to determine the distribution of the number of books read.
3. Comparing the boxplots for each student can help determine the student who most likely read 9 or fewer books in the most months.
In order to answer the question accurately, please provide the boxplots for the four students. This will help in analyzing the distribution of the number of books read and identify the student who most likely read 9 or fewer books in the greatest number of months.
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Write an equation of the line in standard form?
The line has the same slope as 6x-y = 5 and the same y-intercept as the graph of 4y-9x = 8.
What is the equation in standard form?
The equation of the line in standard form that satisfies the provided conditions is 6x - y = -2.
To obtain the equation of a line in standard form that satisfies the provided conditions, we'll first convert the provided equations into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
1. We have the equation:
6x - y = 5
Subtract 6x from both sides:
-y = -6x + 5
Multiply through by -1 to isolate y:
y = 6x - 5
From this equation, we can see that the slope is 6.
2. We have the equation:
4y - 9x = 8
Add 9x to both sides:
4y = 9x + 8
Divide through by 4 to isolate y:
y = (9/4)x + 2
From this equation, we can see that the y-intercept is 2.
Now, we have the slope (m = 6) and the y-intercept (b = 2).
We can substitute these values into the standard form equation of a line, which is Ax + By = C, to obtain the equation in standard form.
Using the slope-intercept form equation (y = mx + b), we can rewrite it as -mx + y = b.
Rearranging, we get mx - y = -b.
Substituting the provided values:
6x - y = -(2)
Multiplying through by -1 to make the leading coefficient positive, we have:
-6x + y = 2
Now, rearranging the terms to obtain the standard form Ax + By = C, we get:
6x - y = -2
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Question 1 options:
f(x) = -2x-1
f(-2) =
Answer:
f(-2) = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = -2x - 1
f(-2) is x = -2
Step 2: Evaluate
Substitute: f(-2) = -2(-2) - 1Multiply: f(-2) = 4 - 1Subtract: f(-2) = 3Answer:
-5
Step-by-step explanation:
f(×)=2x-1
f(-2)=2×(-2)-1 (here,x= -2)
=-4-1
= -5
]find the midpoint m of ab a=[2,1] b=[-4,7
The coordinates of the midpoint M are (-1, 4).
To find the midpoint M of the line segment AB with endpoints A(2, 1) and B(-4, 7), we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint M(x, y) of two points A(x₁, y₁) and B(x₂, y₂) can be found by taking the average of their respective x-coordinates and y-coordinates:
x = (x₁ + x₂) / 2
y = (y₁ + y₂) / 2
Let's apply the formula to find the midpoint M of AB:
x = (2 + (-4)) / 2
= -2 / 2
= -1
y = (1 + 7) / 2
= 8 / 2
= 4
Therefore, the coordinates of the midpoint M are (-1, 4).
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\({\huge{\fbox{\tt{\green{Answer}}}}}\)
______________________________________
To find the midpoint of a line segment, we take the average of the x-coordinates and the average of the y-coordinates. So, for the line segment AB with endpoints A = (2, 1) and B = (-4, 7), the midpoint M is:
→ M = ((2 + (-4)) / 2, (1 + 7) / 2)
M = (-1, 4)
Therefore, the midpoint of the line segment AB is M = (-1, 4).
______________________________________