Answer:
The inequality is 3 + 2x ≥ 13
x ≥ 5
Step-by-step explanation:
on a number line, draw the line starting on 5 with a SHADED IN circle going infinitely to the right.
if a=1 b =2and c= -3 find the value of a2b2c-2
Hello !
you made a typo with the c^-2 because otherwise it does not make a round result
\(a^{2} *b^{2} *c^{2} \\\\= 1^{2} *2^{2}* (-3)^{2} \\\\= 1*4*9\\\\\boxed{= 36}\)
What are the steps in solving the equation 4(2x + 3) = 10x?
Answer:
Step-by-step explanation:
Distributive property, subtraction, division
4(2x + 3) = 10x
8x + 12 = 10x
12 = 2x
6 = x
Determine the center and radius of the following circle equation:
x? + y2 - 2x - 12y +36 = 0
Step-by-step explanation:
x²+ y² -12x - 18y +17 = 0 means : (x²-12x+36)-36+(y²-18y+81)-81-27 =0
(x-6)²+(y-9)² =12²....standard form when the center is (-6 , 9) and radius 12
Answer:
The center is at (1, 6) and the radius is 1.
Step-by-step explanation:
x^2 + y^2 - 2x - 12y +36 = 0
Convert to standard form:
x^2 - 2x + y^2 - 12y = -36
(x - 1)^2 - 1 + (y - 6)^2 - 36 = -36
(x - 1)^2 + (y - 6)^2 = -36 + 36 + 1
(x - 1)^2 + (y - 6)^2 = 1
The center is at (1, 6) and the radius is 1.
Who is life insurance best suited for?
A. Children
B. People with debt
C.Doctors
D. College students
Which linear function has the same y-intercept as the one that is represented by the graph?
On a coordinate plane, a line goes through points (3, 4) and (5, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 1, 1, 3. Column 2 is labeled y with entries negative 4, 2, 8, 14.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 2, 4. Column 2 is labeled y with entries negative 26, negative 18, negative 2, 6.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 3, 3, 5. Column 2 is labeled y with entries negative 15, negative 11, 1, 5.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative 4, 4, 6. Column 2 is lab
eled y with entries negative 26, negative 14, 34, 46.
The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).
First, let's find the slope of the line using the formula:
slope (m) = (change in y) / (change in x)
m = (0 - 4) / (5 - 3)
m = -4 / 2
m = -2
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Using the point (3, 4) as our reference point, we have:
y - 4 = -2(x - 3)
Expanding the equation:
y - 4 = -2x + 6
Simplifying:
y = -2x + 10
Now, let's check the given options to find the linear function with the same y-intercept:
Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)
The y-intercept is the same as the given line (10). So, this option is correct.
Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)
The y-intercept is not the same as the given line. So, this option is not correct.
Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
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Solve y = ax² + c for x.
O x
x= ± √ay-c
O
O
x = ±₁
X=
X=
у-с
a
y
y + c
a
In the quadratic equation y = a\(x^{2}\) + c ,the value of x = ± \(\sqrt \frac{y-c}{a}\)
A quadratic equation is any equation containing one term wherein the unknown is squared and no term wherein it's far raised to a higher power.
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, in which a and b are the coefficients, x is the variable, and c is the constant term.
To find the value of x
Assuming \(a\neq o\)
First, subtract c from both the sides to get:
\(y-c=ax^{2}\)
then, divide both sides by \(a\) and transpose to get:
\(x^{2} =\frac{y-c}{a}\)
So, \(x\) must be a square root of \(\frac{y-c}{a}\) and we can deduce:
\(x=\) ± \(\sqrt \frac{y-c}{a}\)
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For questions 3-4, use the graph of the polynomial function to find the factorization of the polynomial. Assume there is no constant term. 3
3. The factored polynomial is p(x) = (x - 1)(x - 5)
4. The factored polynomial is p(x) = (x + 3)²
What is a polynomial?A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.
3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.
This implies that its factors are (x - 1) and (x - 5)
So, the factored polynomial is p(x) = (x - 1)(x - 5)
4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots
This implies that its factors are (x - (-3)) = (x + 3) twice
So, the factored polynomial is p(x) = (x + 3)²
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Point Z (-3, 4) is translated using the (x, y) (x + 2, y-1). It is then reflected across the x-axis
Determine the point location of the image.
This is the new coordinate for Z (-1, 3)
What is graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
The point Z is (-3, 4) is translated using the rule
x,y → (x+2),(y-1)
Then simply plug-in the values of x and y which are x = -3 and y = 4
x,y → ((-3) +2), (4 -1) which is (-1, 3)
Hence, this is the new coordinate for Z (-1, 3)
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The heights of American men are normally distributed. If a random sample of American men is taken and the confidence interval is (65.3,73.7), what is the sample mean x¯? Give just a number for your answer. For example, if you found that the sample mean was 12, you would enter 12.
Answer:
69.5Step-by-step explanation:
Given the confidence interval of the heights of american heights given as (65.3,73.7);
Lower confidence interval L = 65.3 and Upper confidence interval U = 73.7
Sample mean will be the average of both confidence interval . This is expressed mathematically as \(\overline x = \frac{L+U}{2}\)
\(\overline x = \frac{65.3+73.7}{2}\\\overline x = \frac{139}{2}\\\overline x = 69.5\)
Hence, the sample mean is 69.5
find the domain and range of each f(x)^ * = 1 + x ^ 2
The function f(x)* = 1 + x^2 is defined for all real numbers x, so the domain is all real numbers, or (-∞, ∞).
How to explain the domainIn determining the function's output values, one must consider its collection of feasible results to extract the range. Reviewing f(x)* exhibits a minimum value of 1 due to x^2 being perpetually non-negative, while adding another factor merely preserves positivity.
Concurrently as x skyrockets, so too does the value of f(x)* given that approaching infinity generates infinitely larger powers than any constant coefficient subordinated by it. Consequently, the overall range of f(x)* becomes [1, ∞), enwrapping all feasible solutions equivalent or superior to 1.
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1. UV = 8 and WX = 5
TU=
WU=
TX=
TV=
All sides of a rhombus have equal measures, so TU = 8. Since a rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other, WU = 10. The diagonals of a rhombus are also perpendicular, meaning they form right angles. Using the Pythagorean theorem, you can find the length of TX. (TX)^2 + (WX)^2 = (WT)^2. Substituting in known values, (TX)^2 + 25 = 64. Solving gives you TX = the square root of 39. TV is double the length of TX, so TV = 2 times the square root of 39.
Simplify to create an equivalent expression.
4(-15 – 3p) - 4(-p+5)
Choose 1 answer:
(Α)
-8p - 80
B
- 13p - 80
-8p + 80
8p - 80
Answer:
A) I got this question right on my assignment
What the meaning of statement this?
The statement is asserting that the universal class (V) is defined as the collection of all sets, where every set is included. It signifies that V encompasses all possible sets within the given set theory framework.
The statement "The universal class set, or universe, is the class of all sets: V = {x: x = x}" is referring to the concept of the universal class or the universe in set theory.
In set theory, the universal class set, denoted as V, represents the collection or class that contains all sets. It includes every possible set that can be defined or exists within the context of the set theory being considered.
The notation "{x: x = x}" is used to define the elements of the universal class. Here, "x = x" represents a condition that is always true for any object or element, regardless of its nature. In other words, this condition holds for everything in the universe, as anything is equal to itself.
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The test scores for an exam are approximatoly normally distributed with a mean 73 points and a standard deviation of 6 points. Use this information to answer each of the following. Express your answer as a whole percent
John's z-score is 0.75.
John's score of 79 on the math test corresponds to a z-score of 0.75 and a percentile of 77.82%.
What is John's z-score and percentile?To get John's z-score, we will use the formula: z = (x - μ) / σ
Data
x = John's score (79)
μ = mean score (73)
σ = standard deviation (8)
z = (79 - 73) / 8
z = 6 / 8
z = 0.75.
To find John's percentile, we can use a standard normal distribution table or calculator.
The percentile represents the percentage of scores that fall below a given value. Using standard normal distribution table, we find that a z-score of 0.75 equals to percentile of 77.82%.
Full question:
The scores on a math test have a mean of 73 points and a standard deviation of 8 points. John scores a 79 on the test. Convert this score to a z-score and a percentile..
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Question is in the picture, please explain your answer with steps.
Solving a system of equations we can see that the washer costs $750, and the dryer costs $250.
How to find the costs?Let's define the variables:
x = cost of the washer.
y = cost of the dryer.
We know that the cost combined is $1000, then:
x + y = 1000
And the washer cost 3 times the cost of the dryer, then we will get:
x = 3y
So we have a system of equations, we can replace the second equation into the first one, so we will get:
3y + y = 1000
4y = 1000
y = 1000/4
y = 250
The cost of the washer is:
x = 3*250 = 750
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please help asap with work!!!! thank you
Answer:
answer is C
Step-by-step explanation:
midpoint = ((x¹ + x²)÷2 , (y² +y²)÷2)
example:
((-4+2)÷2 , (-15+-1)÷2)
= ((-2÷2) , (-16÷2))
=(-1 , -8)
Ryan wants to invest in a bank account that will double his money in the smallest
period of time. He has two options. Account A will compound his principal at 5% every
six months. Account B offers him a simple interest rive of 5% on his principal every
year.
Which account will double his principal first? Why?
Answer:
Account A
Step-by-step explanation:
Account A will double the money in:
72/2.5=28.8
28.8 x 6=172.8 months=`14.4 years
Account B will double the money in:
100/5=20 years
Is AB perpendicular to CD? Explain.
Answer:
IF the values are same....................
Answer:
IF the values are same....................
Step-by-step explanation:
IF the values are same....................
A bag contains eight white marbles, six red marbles and four blue marbles.
How many blue marbles must be added to the bag so that the probability
of choosing a blue marble is 1/2?
a. 6
b. 5
c. 10
d. 0
Answer:
c) 10
Step-by-step explanation:
you need to add the white and red marbles which would be 14.
then you subtract 14 by the amount of blue marbles.
How many unique ways are there to arrange the letters in the word PRIOR?
Answer:
60
Step-by-step explanation:
Answer:
it is 60
Step-by-step explanation:
(a) Show that if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^{T}\). Show with an example that the eigenvectors of A and \(A^{T}\) are not the same.
(b) Show that if λ is an eigenvalue of A, and A is invertible, then λ^-1 is an eigenvalue of A^-1.
If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.
What are eigenvalues and eigenvectors?The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.
The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.
Then, we have:
Av = λv
Taking transpose on both sides we have:
\(v^T A^T = \lambda v^T\)
The above equations thus relates transpose of vector and transpose of A to λ.
Now, consider a matrix:
\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)
Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.
The eigenvectors are:
\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)
Now, for transpose of A:
\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)
The eigen vectors are:
\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)
Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.
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help what is the answer for this
Which net represents the pyramid below?
The net which represents the pyramid is: B. A square with a triangle connected to each side with a dotted line.
What is a square pyramid?A square pyramid can be defined as a type of pyramid that has a square base, four (4) triangular sides, five (5) vertices, and eight (8) edges.
In this context, we can logically deduce that the net which represents the pyramid is a square with a triangle that is connected to each side with a dotted line as illustrated in the image attached below.
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Complete Question:
Which net represents the pyramid below? There are four squares attached left to right and a square above and below the last square. There are three rectangles connected vertically with dotted lines. There are triangles connected to the middle rectangle.
A. A hexagon with a triangle connected with a dotted line to each of the sides.
B. A square with a triangle connected to each side with a dotted line.
if f(x)=2^x and g(x)=x-4. The graph of (fog)(x) is shown below. What is the range of (fog)(x)?
Answer:
C) \(y > 0\)
Step-by-step explanation:
\(f(x)=2^x\\\\g(x)=x-4\\\\(f\circ g)(x)=f(g(x))=f(x-4)=2^{x-4}\)
This means that the parent function, \(f(x)=2^x\), will shift 4 units to the right along the x-axis, so this DOES NOT affect the range (nor the domain either). Thus, \(y > 0\) would be the range.
twice a number x increased by 10 is 52
Answer:
x = 21
Step-by-step explanation:
the equation is 2x + 10 = 52
2x = 42
x = 21
A rectangle has the length of (3x + 4) cm with a width of (2x - 2) cm. What is the perimeter of the rectangle?
Answer:
Step-by-step explanation:
Emma purchases a 20 ounce bottle of shampoo for 17$ What is the unit rate?
Answer:
1.176 ounces per dollar
Step-by-step explanation:
Question 2 of 3 Which expressions can be added to find the volume of the solid figure? Select all that apply. A solid shape is made up of 2 attached rectangular prisms. First rectangular prism has a length of 3 m, height of 1 m, and width of 4 m. Second rectangular has a length of 3 m, height of 7 m, and width of 4 m. The total length of the shape is 6 meters. A. 4 × 3 × 7 and 1 × 3 × 4 B. 4 × 6 × 7 and 1 × 3 × 3 C. 1 × 4 × 7 and 4 × 3 × 6 D. 4 × 6 × 1 and 6 × 4 × 3 E. 4 × 6 × 3 and 7 × 3 × 3
Answer:
a and d
Step-by-step explanation:
i had this same question and a and d were the correct answers
Answer this question please
Answer:
Step-by-step explanation:
we know this is a 2 dimensional shape so m*3 out, its m not ft so only answer is
24 m*2
Which ordered pair is a solution to the equation y=5x-25?
(12,50)
(5,10)
(2,25)
(10,25)
Answer:
c bye
Step-by-step explanation:
derrick is preparing to submit his taxes. over the year, he kept track of certain deductions he is able to claim (all rounded to the nearest dollar). these values are given below. 65,144,97,144,103,98,101,127,58,151 derrick figures that he will receive the following amounts: $25 for each deduction that is under $130 and $45 for each deduction that is $130 or more. use the ti-83 or 84 to draw a histogram for these values using 4 classes. using that histogram, determine how much total derick will receive from all of his deductions.
Derrick will receive total of $340 from all of his deductions
To create a histogram for these values using four classes, we must first determine the class width, which is determined as the data range divided by the number of classes. The data range is 151 - 58 = 93, which is the difference between the biggest and smallest numbers. The breadth of the class is 93/4 = 23.25. We'll round it up to 24 because we can't have a fractional class width.
Then, for each of the four classes, we'll start with the smallest number (58) and add the class width (24) again until we reach the maximum value (151). The lowest class boundaries for the four classes are as follows:
Class 1: 58
Class 2: 82
Class 3: 106
Class 4: 130
We'll determine the upper class limit for each lower class limit by adding the class width (24) - 1. The upper class restrictions are as follows:
Class 1: 81
Class 2: 105
Class 3: 129
Class 4: 153
Finally, we'll tally the amount of deductions made in each class and utilise that data to create the histogram. Each class has the following number of deductions:
Class 1: 1 (58)
Class 2: 3 (97, 98, 101)
Class 3: 3 (103, 127, 144)
Class 4: 3 (144, 151, 65)
We can compute the total amount Derrick will earn from all of his deductions now that we know the number of deductions in each class. He will earn $25 for each deduction of less than $130, and $45 for each deduction of $130 or more.
Derrick will receive the following total from all of his deductions:
$25 * 1 (for the single deduction of less than $130) + $45 * 7 (for the seven deductions of $130 or over) = $25 + $315 = $340
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