System A has 2 real solutions, System B has 0 real solutions and System C has 1 real solution.
Given a system of equations for A is x²+y²=17 and y=-(1÷2)x, a system of equations for B is y=x²-7x10 and y=-6x+5 and a system of equations for C is y=-2x²+9 and 8x-y=-17.
For system A,
The two systems of equations are
x²+y²=17 ......(1)
y=-1÷2x ......(2)
Substitute the value of equation (2) into equation (1) as
x²+(-x÷2)²=17
x²+(x²÷4)=17
Simplify the above equation by taking L.C.M. as
(4x²+x²)÷4=17
5x²=68
x²=68÷5
x=±3.688
Find the value of y by substituting the value of x in equation (2).
When x=3.688 then y is
y=-(1÷2)×3.688
y=-1.844
And When x=-3.688 then y is
y=-(1÷2)×(-3.688)
y=1.844
Thus, the points where the equations of system A intersect each other is (3.688,-1.844) and (-3.688,1.844)
So, the system of equations of A has 2 real solutions.
For system B,
The two systems of equations are
y=x²-7x+10 ......(3)
y=-6x+5 ......(4)
Substitute the value of equation (4) into equation (3) as
-6x+5=x²-7x+10
x²-7x+10+6x-5=0
x²-x+5=0
Simplify the above quadratic equation using the discriminant rule,
x=(-b±√(b²-4ac))÷(2a)
Here, a=1, b=-1 and c=5
Substitute the values in the discriminant rule as
x=(1±√(1-4\times 5\times 1))÷2
x=(1±√(-19))÷2
x=(1±√(19)i)÷2
Here, the value of x goes into the complex.
So, the system of equations of B has 0 real solutions.
For system C,
The two systems of equations are
y=-2x²+9 ......(5)
8x-y=-17 ......(6)
Substitute the value of equation (6) into equation (5) as
8x-(-2x²+9)=-17
8x+2x²-9+17=0
2x²+8x+8=0
Simplify the above quadratic equation using factorization method as
2x²+4x+4x+8=0
2x(x+2)+4(x+2)=0
(2x+4)(x+2)=0
x=-2,-2
Find the value of y by substituting the value of x in equation (5).
When x=-2 then y is
y=-2(-2)²+9
y=-8+9
y=1
Thus, the point where the equations of system C intersect each other is (-2,1)
So, the system of equations of C has 1 real solutions.
Hence, the system of equations for A is x²+y²=17 and y=-(1÷2)x having 2 real solution, a system of equations for B is y=x²-7x10 and y=-6x+5 having 0 real solution and a system of equations for C is y=-2x²+9 and 8x-y=-17 having 1 real solution.
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What is the vertex of the function f(x)=|x-9|+2
Answer:
vertex = (9, 2 )
Step-by-step explanation:
given the absolute value function
f(x) = a |x - h | + k
with vertex = (h, k )
then
f(x) = | x - 9 | + 2
has vertex = (9, 2 )
Evaluate the algebraic expression.
z^2+1+y when y=4, and z=3.
Answer:
your question is
z²+1+y where, y=4,z=3
3²+1+4
9+5
14
is your answer
1. Select all the true statements.
A. √-I is an imaginary number.
-1
B. There are no real numbers that satisfy the equation x = √√-1.
C. Because √-I is imaginary, no one does math with it.
D. The equation x² = -1 has real solutions.
E. √-T = -1 because -1 -1 = -1.
Answer:
A , B , D
Step-by-step explanation:
Which term describes the red curve in the figure below?
Solve the equation.
4.5=0.5n
If area of a circle is 49/64 pie cm square,then find the circumference of the circle?
Answer:
7/4 * pi
Step-by-step explanation:
Area of circle = pi * r^2
Find radius:
pi * 49/64 = pi * r^2
49/64 = r^2
7/8= r
Circumference of circle = 2pi * r
2 * pi * (7/8) = 7/4 * pi
Assuming that the answer is in terms of pi as the question is in terms of pi
Let a and b be real numbers where a . Which of the following functions could represent the graph below?
f(x) = x(x – a)3(x – b)3
f(x) = (x – a)2(x – b)4
f(x) = x(x – a)6(x – b)2
f(x) = (x – a)5(x – b)
It can be deduced that the option that represents the graph is B. f(x)=(x-a)²(x-b)⁴
How to solve the graph?From the graph, a and b be real numbers where a = b = 0. In this case, zero is not a root of the polynomial function
When the graph touches the x-axis at two point l, it implies that means that both the roots of the polynomial equation are of even degree.
Thus, the correct option B. i.e. f(x)=(x-a)²(x-b)⁴
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Find the range of f(x) = 3x + 2 for the domain = {1, 2, 3}.
Answer:
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.Interval Notation:..
(-∞,∞)
Set-Builder Notation:
{x|x∈ℝ}
The range is the set of all valid yy values. Use the graph to find the range…
Interval Notation:
(-∞,∞)
Set-Builder Notation:
{y|y∈R}
Determine the domain and range…
Domain: (−∞,∞),{x|x∈R}
Range: (−∞,∞),{y|y∈R}
Answer:
{ 5, 8, 11 }
Step-by-step explanation:
the range is the corresponding values of f(x) for the values of x in the domain.
substitute the x- values from the domain into f(x)
f(1) = 3(1) + 2 = 3 + 2 = 5
f(2) = 3(2) + 2 = 6 + 2 = 8
f(3) = 3(3) + 2 = 9 + 2 = 11
range is { 5, 8, 11 }
What are the minor arcs of O?
Answer:
3rd answer
Step-by-step explanation:
Pay attention to the arcs, minor arcs are less than 180 degrees
Some people took part in a game. The frequency shows information about their scores. Score Frequency 1 - 7 13 8 - 10 14 11 - 15 18 16 - 20 6 21 - 35 13 36 - 50 19 Estimate the mean. Give your answer rounded to 2 decimal places.
The mean is 20.7
What is Mean?Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Class Frequency{f} Midpoint of frequency{x} fx
1-7 13 4 72
8-10 14 9 126
11-15 18 13 234
16-20 6 18 108
21-35 13 28 364
36-50 19 43 817
Sum 83 1721
So,
Mean = 1721/83 = 20.7
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B is decreased by 40% and decreased again by 40%. What is the result?
10 pts for anyone who helps!
Answer:
result is 20%
Step-by-step explanation:
initially B was 100%
therefore 100% - 40%
=60% remaining
60% - 40%
= 20%
Answer:
The answer is 0.36b
Step-by-step explanation:
b-0.4xb=b-0.4b=0.6b
0.6b-0.4(0.6b)=0.6b-0.24=0.36b
The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
1 0 -1 -3
0 1 5
00 1
a.
X=-3
y--9
z-1
b. x-2
y=-9
N
I
T
C. X=-2
y--9
2-1
d. x-3
y=-9
2-1
The question is incomplete. Below you will find the missing content.
The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
The correct option will be Option C: x=5t-3
y=4t-5
z=t
where t is the real number.
A matrix is in row echelon form when the first non-zero number from the left i.e. leading coefficient is always to right of the first non-zero number in the row above and rows consisting of all zeros are at bottom of the matrix.
The row echelon form of the matrix is given in the question.
from row-echelon form of the matrix, we can write the equation as,
x-5z=-3
y-4z=-5
Let's assume z=t, where t is the real number
now we can find x and y by putting z=t in the equation
x-5t=-3
⇒x=-3+5t
y-4t=-5
y=-5+4t
Now we get the solution of x,y,z in terms of t
x=5t-3
y=4t-5
z=t
where t is the real number.
So the correct option will be Option C: x=5t-3
y=4t-5
z=t
where t is the real number.
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)In the figure below, lines m and n are parallel:
Two parallel lines are shown crossed by a transversal. The angles are labeled with number 1-8. The angles on line m where the line is crossed by the transversal are 1, 2, 4, and 3 in clockwise order from top left. The angles on line n where the line is crossed by the transversal are 5, 6, 8, and 7 in clockwise order from top left.
In the diagram shown, ∠6 measures 97 degrees. What is the measure of ∠5?
83 degrees
90 degrees
97 degrees
180 degrees
Based on the linear pair theorem, the measure of angle 5 is: A. 83 degrees.
What is the Linear Pair Theorem?The linear pair theorem states that if two angles are on a straight line, the sum of their measures equals 180 degrees.
∠5 and ∠6 are a linear pair. Therefore:
m∠5 = 180 - m∠6
m∠5 = 180 - 97
m∠5 = 83°
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Answer:83 degrees
Step-by-step explanation:topG
Calculate the middle number in the middle of 12.7 and 21.2.
The middle number is 16.95
What is Number system?The collection of numbers is called the number system. These numbers are of different types such as natural numbers, whole numbers, integers, rational numbers and irrational numbers.
Given:
Numbers are 12.7 and 21.2
Difference between number
= 21.2-12.7
=8.5
middle number
= 12.7+ 8.5/2
= 12.7+ 4.25
= 16.95
Hence, the middle number is 16.95.
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Write an equation in slope intercept form with the given information.
Goes through points (-2,-5) and (3,5)
Answer:
infinity 2 is the slope for these point .
Step-by-step explanation:
given points are
(-2,-5) and (3,5)
comparison to
(x1,y1) and (x2,y2)
here ,
[tex]slope = \frac{y2 - y1}{x2 - x1} [/tex]
slope= 5-(-5)/3-(-2)
slope =10/5
slope=2
glad to help you this may help you :)
At Total Viewing, the
wholesale price of a 52-inch television is
$1.950. What does it cost to buy the
television if the store's markup is 15%?
Answer:
It would be 2242.5
Step-by-step explanation:
1950X0.15=292.5
292.5+1950=2242.5
Determine the missing information in the paragraph proof.
Given: Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular. Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).
Prove: The slopes of perpendicular lines are negative reciprocals.
On a coordinate plane, 2 perpendicular lines are shown. Line P Q has points (a, b) and (c, d). Line P prime Q prime has points (negative b, a) and (negative d, c).
The slopes of lines PQ and P’Q’ can be determined using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction
The product of these slopes is ________. This product shows that the slopes are negative reciprocals. It is given that the lines are perpendicular and we have shown that the slopes of the lines are negative reciprocals.
(StartFraction d minus b Over c minus a EndFraction) (StartFraction c minus a Over negative d + b EndFraction) = negative 1
(StartFraction b minus a Over a + b EndFraction) (StartFraction c minus d Over negative d minus c EndFraction) = negative 1
(StartFraction d minus b Over c minus a EndFraction) (StartFraction c minus a Over negative d + b EndFraction) = 1
(StartFraction b minus a Over a + b EndFraction) (StartFraction c minus d Over negative d minus c EndFraction) = 1
Mark this and return
The slopes of perpendicular lines are negative reciprocals is proved.
What is Equation of a Straight Line ?An equation of a straight line is given by
y = mx +c
It is given that
Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular.
Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).
The slopes of lines PQ and P’Q’ can be determined using the formula
[tex]\rm m = \dfrac{ v _2 - v _1 }{ x _2 -x _1 }[/tex]
The product of these slopes is -1 .
This product shows that the slopes are negative reciprocals
Therefore , The slopes of perpendicular lines are negative reciprocals is proved,
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An electronics store researched the TV sales in the last 6 months. The probability a customer would purchase the Brand 1 model TV was 70% while the rest of the customers purchased the Brand 2 model. Furthermore, 20% of the Brand 1 customers purchased an extended warranty while 40% of Brand 2 customers purchased an extended warranty. A customer is randomly selected from among all those who bought a TV from the store. What is the probability that the selected customer purchased a Brand 1 model and an extended warranty
The probability that the selected customer purchased a Brand 1 model is 0.14.
Given that probability a customer would purchase the Brand 1 model TV was 70% while the rest of the customers purchased the Brand 2 model. and 20% of the Brand 1 customers purchased an extended warranty while 40% of Brand 2 customers purchased an extended warranty.
The probability that a customer would purchase Brand 1 model TV P(A)=0.70.
The probability that a customer purchases the extended warranty given that the customer purchased the Brand 1 model TV is
P(B|A)=0.20
P(A and B)÷P(A)=0.20
P(A and B)÷0.70=0.20
P(A and B)=0.14
Hence, the probability that the selected customer purchases a Brand 1 model and an extended warranty is 0.14.
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Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as
A data set having two values that have the highest and equal frequencies will have a bimodal distribution. Hence, option D is the right choice.
A symmetric distribution occurs when the mean, median, and mode all occur at the same location and the values of the variables occur at regular intervals.The few low scores in a negatively skewed distribution tend to push the mean to the left, thus the mean is typically lower than the median.The mode is consistently less than the mean and median in a positively skewed distribution.A continuous probability distribution having two distinct modes, that is, two separate values with the highest and equal frequencies is referred to as a bimodal distribution.Thus, a data set having two values that have the highest and equal frequencies will have a bimodal distribution. Hence, option D is the right choice.
The given question is incomplete. The complete question is:
"Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as:
A. Symmetric distribution
B. Negatively skewed distribution
C. Positively skewed distribution
D. Bimodal distribution."
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5y + 3= 14
pleaseeeee help
Answer:
5y + 3= 14
subtract 3 from each side
5y=11
divide each side by 5
5y/5=11/5
y=11/5 or 2.2 or 2 1/5
Hope This Helps!!!
Answer:
2.2
Step-by-step explanation:
Properties needed:
Subtraction Property of EqualityDivision Property of Equality
First we need to subtract 3 from both sides because of subtraction property of equality to make both sides equal.
5y + 3 = 14
-3 -3
5y = 11
Then we need to divide 5 from both sides (division property of equality) to get y.
[tex]\frac{5y}{5} = \frac{11}{5}[/tex]
And we get 2.2
Please mark brainliest!
I hope this helps!
Have a great day!
62 divided by 8,694
Answer:
50.007131355
Step-by-step explanation:
A calculator lol?
Expressions - Part 1
16÷(2+1/2)² ?
From the given expression, the equivalent expression would be 64/25.
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
Given;
16÷(2+1/2)²
16÷(5/2)²
16÷(25/4)
16 x (4/25)
= 64 / 25
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What is the size of the angle, below?
Answer:
The size of the angle is between 180 and 360*. I cannot say the exact angle but my guess is correct and the correct answer is in between the 2 numbers.
Step-by-step explanation:
Which of the following objects is considered to be one-dimensional because it ha length but no width or height?
A. Line segment
B. Point
C. Triangle
D.Cube
Which is true of dependent events?
a.) the probability of all dependent events can be calculated using the or formula
b.) you can use a two-way frequency table to calculate the conditional probability of events that are dependent.
c.) the outcome of one event has no effect on the outcome of a second event.
d.) you can find the and probability of dependent events using the formula
branliest to correct answer please no guessing
As per the attached picture Option fourth "the probability of all dependent events can be calculated using the OR formula P(A or B) = P(A) + P(B) - P(A and B)" is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
As we know the dependent events are dependent on what happened before.
Let A and B be dependent events:
Event B will be dependent on the Event A
P(A or B) = P(A) + P(B) - P(A and B)
Thus, option fourth "the probability of all dependent events can be calculated using the OR formula P(A or B) = P(A) + P(B) - P(A and B)" is correct.
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Carmela opened her piggy bank and found she had $15.30. If she had only nickels, dimes, quarters, and half-dollars and an equal number of coins of each kind, how many coins did she have in all
Answer:
68 coins
Step-by-step explanation:
We can use the given information to write two equations involving the numbers of coins. One will express the total number of coins; the other will express their value.
__
setupSince there are equal numbers of coins of each type, we can let n represent the number of each kind of coin. The total number coins will be ...
n +n +n +n + N . . . the sum of numbers of nickels, dimes, quarters, halves
The value of the coins is ...
0.05n +0.10n +0.25n +0.50n = 15.30
solutionThe second equation lets us find the value of n:
0.90n = 15.30
n = 17 . . . . . . . . divide by 0.90
Then the number of coins in all is ...
4n = N
4(17) = N = 68
Carmela had 68 coins in all.
Need help urgently please
Which integer is the smallest? A. -84 B. -4 OC. 34 OD. 24 Advanced Placement, AP AP Central", College Board", and SAT are trademarks registered by the Colleg ACT is a trademark registered by ACT, Inc., which is not affiliated with, and does not endorse, this website. Copyright 2010-2022 edtell, LLC. All rights reserved. Portions of this software are copyrighted by other partie. Which integer is the smallest ? A. -84 B. -4 OC . 34 OD . 24 Advanced Placement , AP AP Central " , College Board " , and SAT are trademarks registered by the Colleg ACT is a trademark registered by ACT , Inc. , which is not affiliated with , and does not endorse , this website . Copyright 2010-2022 edtell , LLC . All rights reserved . Portions of this software are copyrighted by other partie .
Answer: B -4
Step-by-step explanation: I think it is B because -4 is smaller than A,C and D.
The smallest integer among the options provided is option A, which is -84.
In the context of integers, smaller values are considered to be "less" than larger values.
In this case, we can compare the given integers to determine the smallest one.
Comparing the options:
A. -84
B. -4
C. 34
D. 24
Out of these options, -84 is the smallest integer because it has the lowest numerical value.
The negative sign indicates that it is a number less than zero, and the absolute value of 84 is greater than the absolute values of -4, 34, and 24.
Therefore, based on numerical value, -84 is the smallest integer among the options given.
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How do you find inverse functions?
will give brainliest to first helpful response
Answer:
swap x and y
Step-by-step explanation:
You can find an inverse function by replacing "x" and "y"
for example:
y = mx + b
becomes
x = my + b
if your equation is:
f(x) = 3(x²) - 3
{remember, f(x) means the same thing as y}
y = 3(x²) - 3
inverse:
x = 3(y²) - 3
this is it, hope this is helpful!!
Answer:
make every (x) a (y)
Determine the value of y, if x is 81.
Y=/x+6
The value of y for the given equation at x=81 is 87.
What is Equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Here, given equation;
y = x + 6
Put x = 81, we get
y = 81 + 6
y = 87
Thus, the value of y for the given equation at x=81 is 87.
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