Answer:
The coordinates of the vertex of the graph are (-2, -9).
Step-by-step explanation:
The quadratic function is described by the standard equation The graph of a quadratic function is called a parabola.
We have the quadratic function
We identify the coefficients a, b, and c. For this equation,
The axis of symmetry is , i.e., Thus, the statement in the question for the symmetry axis x = -2 is correct.
The vertex (or turning point) is where or
The parabola opens upward because a > 0, resulting in a vertex that is a minimum.
Finding the minimum value is as follows:
Therefore, the coordinates of the vertex of the graph are (h, k), i.e.,
Other components:
The y-intercept of the quadratic function f(x) = x² + 4x - 5 is (0, c), i.e., the point
The factorization of f (x) = x² + 4x - 5 becomes f(x) = (x + 5)(x - 1). Then we get the x-intercepts at
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Keywords: the axis of symmetry, for a function, f(x) = x² + 4x − 5, x = −2, which is the graph of f(x) = (x - 1)(x + 4), what, the coordinates of the vertex of the graph, the x-intercept, quadratic function, a standard equation, the y-intercept, parabola, upward, the minimum value
Answer:
the vertex of the graph is (-2, -9)
Step-by-step explanation:
The given function is:
[tex]f(x)=x^2+4x-5[/tex]
Given x = -2 is the axis of symmetry and because we know that the vertex of the graph lies on its axis of symmetry
=> coordinate of vertex is (-2, y)
When x= -2 we have
[tex]f(-2) =(-2)^2+4(-2)-5\\<=> y=4-8-5\\<=> y=-9[/tex]
So the vertex of the graph is (-2,-9)
which is bigger 64 cm or .64 m?
Answer:
They are the same size
Step-by-step explanation:
1 cm = .01 m
64 cm = .64 m
A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 150 lbs and each box of books weighs 50 lbs. The maximum capacity of the elevator is 1000 lbs. Part A Write an equation to represent this situation
Answer:
1000 = 160 + 50x
1000 - 160 = 840
840 = 50x
840/50 = 16.8
he can bring up 16.8 approx., but total boxes would be 16.
Step-by-step explanation:
The equation representing the situation is 150 + 50x <= 1000, where x represents the number of boxes of books the delivery person brings up to the office.
Explanation:To write an equation, we need to represent the information given in the situation. Let's assign a variable, x, to represent the number of boxes of books the delivery person brings up to the office. The weight of the delivery person is fixed at 150 lbs and the weight of each box is 50 lbs. So, the total weight carried by the elevator is 150 + 50x. The equation representing this situation is 150 + 50x ≤ 1000, since the maximum capacity of the elevator is 1000 lbs.
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HELP ME PLEASEEEEEEE
Step-by-step explanation:
You must first add 20 to all inqualies, leaving u with 0 is greater than or equal to 2x which is also greater than or equal to 40.
Divde everything by 2 to get rid of the 2 from the x
0 divided by 2 is 0, 2x divded by 2 is x, 40 divided by 2 is 20.
Thats the answers
solve for x 2(x+2)+2x=4(x+1)
[tex](6x+27) (12x-9)[/tex]
For this case we must apply distributive property term by term, to simplify the expression:
[tex](6x) (12x) + (6x) (- 9) + (27) (12x) + (27) (- 9) =[/tex]
We have to:
[tex]+ * - = -[/tex]
So:
[tex]72x ^ 2-54x + 324x-243[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]72x ^ 2 + 270x-243[/tex]
ANswer:
[tex]72x ^ 2 + 270x-243[/tex]
The graph represents a distribution of data.
What is the mean of the data?
35
40
45
50
55
60
65
Mark this and return
Sond
Mean: Average of the numbers in a set of data.
The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set. If we want to find the mean of the data set shown here, let's begin by adding the numbers.
35 + 40 + 45 + 50 + 55 + 60 + 65 = 350
Now, this will be divided by how many numbers are in the set which is 7.
350 ÷ 7 = 50.
Therefore, the mean of the set of data shown here is 29.2.
Answer: The mean of the data is Option 4. 50
Step-by-step explanation:
Larry claims that (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are equivalent because they have the same digits and the same operations.
a. Is Larry correct? Explain your thinking.
b. Which expression is greater? How much greater?
Answer:
[tex](14+12)\times (8+12) > (14\times 12)+(8\times 12)[/tex]
Step-by-step explanation:
First let us evaluate the value of both the expressions.
[tex](14+12)\times (8+12) = 26\times 20 = 520[/tex]
[tex](14\times 12)+(8\times 12) = 168 + 96 = 264[/tex]
a) Hence, Larry's claim that both the expressions are equivalent is wrong.
The evaluation of the expressions have been shown above. The second expression was obtained by swapping the addition and multiplication order and that created the difference.
b) Clearly,
520 > 264
Therefore,
[tex](14+12)\times (8+12) > (14\times 12)+(8\times 12)[/tex]
[tex](14+12)\times (8+12)[/tex] is greater by the expression [tex](14\times 12)+(8\times 12)[/tex] by a value of 520 - 264 = 256.
Final answer:
Larry is incorrect; the expressions (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are not equivalent. The first expression equals 520, and the second equals 264, with the first being greater by 256.
Explanation:
No, Larry is not correct. The expressions (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are not equivalent because they do not follow the same mathematical rules. The former is calculated using the distributive property of multiplication over addition, while the latter is simply a sum of two products.
To illustrate, let's compute both expressions:
For the first expression, (14 + 12) × (8 + 12), first, we add the numbers inside the parentheses: 26 × 20. Then, we multiply the results: 26 × 20 = 520.For the second expression, (14 × 12) + (8 × 12), we compute the products first: 168 + 96. Finally, we add those products together: 168 + 96 = 264.Comparing the results, 520 is evident greater than 264. The difference between them is 256.
The rules of mathematics are universally valid, and incorrect application of these rules can lead to different outcomes, as shown in Larry's claim.
17. Prison Education In a federal prison, inmates can
select to complete high school, take college courses, or
do neither. The following survey results were obtained
using ages of the inmates.
High School College
Age
Courses Courses Neither
Under 30
107
450
30 and over
32
367
If a prisoner is selected at random, find these probabilities:
a. The prisoner does not take classes.
b. The prisoner is under 30 and is taking either a high
school class or a college class.
c. The prisoner is over 30 and is taking either a high
school class or a college class.
27
To find the probabilities in this scenario, we will use the information provided in the survey results.
Explanation:To find the probabilities in this scenario, we will use the information provided in the survey results. Let's go through each question one by one:
a. The prisoner does not take classes: We can find this probability by adding the number of prisoners who do not take high school or college classes and dividing it by the total number of prisoners. In this case, the number of prisoners who do not take classes is 107 + 32 = 139. The total number of prisoners is 107 + 450 + 32 + 367 = 956. So, the probability is 139/956.
b. The prisoner is under 30 and is taking either a high school class or a college class: We can find this probability by adding the number of prisoners who are under 30 and taking high school or college classes and dividing it by the total number of prisoners. In this case, the number of prisoners who are under 30 and taking high school or college classes is 107 + 450 = 557. So, the probability is 557/956.
c. The prisoner is over 30 and is taking either a high school class or a college class: We can find this probability by adding the number of prisoners who are over 30 and taking high school or college classes and dividing it by the total number of prisoners. In this case, the number of prisoners who are over 30 and taking high school or college classes is 32 + 367 = 399. So, the probability is 399/956.
What is the value of x? Identify the missing justifications
Answer:
B. Angle Addition Postulate; Subtraction Property of Equality
Step-by-step explanation:
Given:
[tex]m\angle PQR=x+7\\ \\m\angle SQR=x+3\\ \\m\angle PQR+m\angle SQR=m\angle PQS=100^{\circ}[/tex]
Find: x
Solution:
1. [tex]m\angle PQR+m\angle SQR=m\angle PQS[/tex] - Angle Addition Postulate
2. [tex]x+7+x+3=100[/tex] - Substitution Property
3. [tex]2x+10=100[/tex] - Simplify
4. [tex]2x=90[/tex] - Subtraction Property of Equality
5. [tex]x=45[/tex] - Division Property of Equality
classify each of the power functions based on their end behavior (increasing or decreasing) as x = ∞
[tex] f(x) = - 2 {x}^{2} [/tex]
[tex]g(x) = (x + 2 {)}^{3} [/tex]
[tex]h(x) = - 1 +x\frac{1}{2} [/tex]
[tex]j(x) = \frac{1}{2} ( - {x})^{5}[/tex]
Answer: right side behavior:
f(x) is Decreasing
g(x) is Increasing
h(x) is Increasing
j(x) is Decreasing
Step-by-step explanation:
The rules for end behavior are based on 2 criteria: Sign of leading coefficient and Degree of polynomial
Sign of leading coefficient (term with greatest exponent):
If sign is positive, then right side is increasingIf sign is negative, then right side is decreasingDegree of polynomial (greatest exponent of polynomial:
If even, then end behavior is the same from the left and rightIf odd, then end behavior is opposite from the left and rightf(x) = -2x²
Sign is negative so right side is decreasing Degree is even so left side is the same as the right side (decreasing)as x → +∞, f(x) → +∞ Decreasing
as x → -∞, f(x) → -∞ Decreasing
g(x) = (x + 2)³
Sign is positive so right side is increasing Degree is odd so left side is opposite of the right side (decreasing)as x → +∞, f(x) → +∞ Increasing
as x → -∞, f(x) → -∞ Decreasing
[tex]h(x)=-1+x^{\frac{1}{2}}\implies h(x)=x^{\frac{1}{2}}-1[/tex]
Sign is positive so right side is increasing Degree is an even fraction so left side is opposite of the right side as it approaches the y-intercept (-1)as x → +∞, f(x) → +∞ Increasing
as x → -∞, f(x) → -1 Decreasing to -1
[tex]j(x)=\dfrac{1}{2}(-x)^5\implies j(x)=\dfrac{1}{2}(-1)^5(x)^5\implies j(x)=-\dfrac{1}{2}x^5[/tex]
Sign is negative so right side is decreasing Degree is odd so left side is opposite of the right side (increasing)as x → +∞, f(x) → +∞ Decreasing
as x → -∞, f(x) → -∞ Increasing
Write the equation of a line that is perpendicular to y = 5 and that passes through the point (-7,-5).
Answer:
x = -7
Step-by-step explanation:
The equation of the line in standard form is y=5.
This is a horizontal line, so the perpendicular line will be a vertical line of the form x=a.
Since we are given that the line should pass through the point (−7,−5) then the equation of the line is x=−7.
(15 − 8)9
-------------
[(5 + 2)3]2
The simplified expression is:
Answer:
The common denominator you can calculate as the least common multiple of the both denominators - LCM(9, 3) = 9. The fraction result cannot be further simplified by cancelling.
In words - seventeen ninths minus five thirds = two ninths.
Step-by-step explanation:
A student of one of the authors earned grades of 63, 91, 88, 84, and 79 on her five regular statistics tests. She earned a grade of 86 on the final exam and 90 on her
class projects. Her combined homework grade was 70. The five regular tests count for 60%
of the final grade, the final exam counts for 10%, the project counts for 15%, and homework
counts for 15%. What is her weighted mean grade? What letter grade did she earn (A, B, C, D,
or F)? Assume that a mean of 90 or above is an A, a mean of 80 to 89 is a B, and so on.
Answer:
Weighted mean grade: 81.2
Letter grade: B
Step-by-step explanation:
5 regular tests:
(63+91+88+84+79) / 5 * 60%
= 405 / 5 * 0.6
= 48.6
Final exam:
86 * 10% = 8.6
Project:
90 * 15% = 13.5
Homework:
70 * 15% = 10.5
So her weighted mean grade is
48.6 + 8.6 + 13.5 + 10.5 = 81.2
The student's weighted mean grade is 81.2, which corresponds to a letter grade of B.
Explanation:To calculate the student's weighted mean grade, we must apply the provided weights to each component. The five tests count for 60%, the final exam counts for 10%, the project counts for 15% and the homework counts for 15%.
First, find the mean of the five regular test scores: (63 + 91 + 88 + 84 + 79) / 5 = 81.
Then, calculate individual contributions by multiplying the scores by the corresponding weights:
Tests: 81 * 0.60 = 48.6Final exam: 86 * 0.10 = 8.6Project: 90 * 0.15 = 13.5Homework: 70 * 0.15 = 10.5Add these to find the student's weighted mean grade: 48.6 + 8.6 + 13.5 + 10.5 = 81.2. As her grade is above 80, her letter grade would be B.
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A total of 1000 people attended a benefit concert was held to raise money for a children foundation. Student
ticket cost $2 and an adult ticket cost $3. If the organizer raises a total of $5500, how many students attended
the concert?
Write expression and answer
Answer:
Problem can not be solved
Step-by-step explanation:
* Lets explain how to solve the problem
- A total of 1000 people attended a benefit concert was held to raise
money for a children foundation
∴ The number of students and adult is 1000
- Student ticket cost $2 and an adult ticket cost $3
∴ The cost of the student ticket is $2
∴ The cost of the adult ticket is $3
- The organizer raises a total of $5500
∴ The total money earns fro tickets is $5500
- Assume that the number of students who attended the concert
is x and the number of adults is y
- There are 1000 students and adults attended the concert
∴ x + y = 1000 ⇒ (1)
- The cost of student ticket is $2
∴ The money earned from students is 2 × x = 2x dollars
- The cost of adult ticket is $3
∴ The money earned from adults is 3 × y = 3y dollars
- The total money earned from students and adults is $5500
∴ 2x + 3y = 5500 ⇒ (2)
* Now lets solve the two equation by elimination method
- Multiply equation (1) by -3 to eliminate y
∴ (-3)x + (-3)y = (-3) × 1000
∴ -3x - 3y = -3000 ⇒ (3)
- Add equations (2) and (3)
∴ -x = 2500
- Multiply both sides by -1
∴ x = -2500
∵ x represents the number of the students and never the number
of student be negative , then the problem can not be solved
What is the value of 9 in $2.29?
Answer:
The Value of 9 would be hundredths since it is a decimal, and the value of the 2 that is in front of the 9 would be tenths. the 'th' is always used when numbers are behind the decimal, always remember that :)
Step-by-step explanation:
I hope this helped you!
Miss smith’s pay is directly proportional to the number of hours she work at the airport. Her pay for 22 hours is $297.How much should she earn in a 40 hour week
Answer:
$540
Step-by-step explanation:
You need first to calculate the hour rate that is payment divided to total number of hours done.
297/22 = 13.5
Now we know that she is earning $13.5/1 hour
We just need to multiply by 22 hours and we have 13.5*22 = $540
Answer:
Step-by-step explanation:
2,080
what are examples ofcomplentary angles
Answer:
Examples are:
Angle ABC is 65 degrees and Angle DEF is 25 degrees.
Angle MNO is 50 degrees and Angle XYZ is 40 degrees.
Step-by-step explanation:
Complementary angles are any two angles that when added together equal 90 degrees. Complementary angles do not have to be next to each other, but they must total 90 degrees.
Simplify these expressions.
a. 4x + 7x + (–x)
b. –5yz + yz + 2yz
Answer:A. 10x. B. -2yz
Step-by-step explanation:
A. 4x+7x=11x
11x+(-x) = 11x-1x=10x
B. -5yz+yz=-4yz
-4yz+2yz=-2yz
The simplified expresisons are 10x and -2yz.
What is an Expression?An expression is a mathematical statement which consists of variables, constants and mathematical operators.
The expression is
4x +7x + (-x)
To simplify means to reduce the expression into its simplest form, by performing the basic mathematical opertaion as given in the expression.
As the expressions only consist of one variable x,
The coefficients can be added.
(4+7-1) x
The like terms will be added, the sum obtained after Addition is,
10x
The expression is
–5yz + yz + 2yz
The expression has two variables, y and z.
The like terms will be added
( -5 +2+1) yz
The sum obtained after Addition is,
-2yz
Both the expressions are simplified.
Simplified expressions are easier to understand.
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{ (7+3) • 5-4} ÷2+2
Answer:
{ (7+3) • 5-4} ÷2+2
7 + 3 = 10
5 - 4 = 1
10 x 1 = 10
10 divided by 2 = 5
5 + 2 = 7
7 is your ansswer
Answer:
25
Step-by-step explanation:
For this, you would use PEMDAS.
PEMDAS stands for parenthesis, exponents, multiplication, division, addition and subtraction. That is the order that you would do those steps.
So first, you would do what is inside the parenthesis, 7+3 which is equal to 10.
So then, you would have { 10• 5-4} ÷2+2.
You next step would be to multiply 10 and 5. This would give you 50.
So your equation would be {50-4}÷2+2
The next step would be to subtract 4 from 50 which would give you 46. And the next step is to divide 46 by 2 which is 23. And the last step would be to add 2 to 23, which is 25.
So, your answer is 25.
A total that is divided into equal groups is called the
Greetings!
In division, the number being divided is considered the dividend, and the number dividing is called the divisor. The answer is the quotient.
A total that is divided into equal groups is called the dividend.
Hope this helps!
Two points on the graph of a linear function are (-4,5)and(-6,9). What is the slope intercept form of the equation of the line ?
Answer:
y=-2x+3
Step-by-step explanation:
How do you solve this problem? 3x(5+2)=
Answer:
21
Step-by-step explanation:
Add 5 and 2 together to get 7 and multiply it by 3
what is the quontet for 1060 divided by 48
When you divide 1060 by 48, your answer will be 22.08333... (repeated decimal) but when rounded, it will either be 22, 22.1, or 22.08 (just for rounding, you do not have to put this in.)
Hope this helped!
Nate
Answer:
22.0833333333 or 22.083 with the line above 3
Step-by-step explanation:
22.0833333333 or 22.083 with a line above the 3 because 1060 divided by 48 is 22.0833333333 repeating 3s
Evaluate the expression 4-9/4×3/2
Answer:
5/8
Step-by-step explanation:
4- 9/4 × 3/2 = 4 - (9 *3) / (4*2)
= 4 - 27/8
= 4*8/8 - 27/8
= 32/8 - 27/8
= ( 32-27) / 8
= 5/8
The correct value of the expression is 0.625.
To evaluate the expression 4 - 9/4 × 3/2, follow these steps:
Start with the multiplication and division from left to right:
Calculate 9 / 4, which equals 2.25.
Then multiply 2.25 by 3/2, which is 1.5. So, 2.25 × 1.5 = 3.375.
Subtract the result from 4: 4 - 3.375 = 0.625.
So, the evaluated value of the expression 4 - 9/4 × 3/2 is 0.625.
How do you solve 11-.5y=3+6x for y
Answer:
y= 1.6
Step-by-step explanation:
First you make x=0 and then since x=0 you plug it in the equation
11-5y=3+6(0)
11-5y=3
now you swing the 11 to the other side
-5y=3-11
-5y=-8
now you divide -8 by -5 to isolate the variable
y= 1.6
Find the real zeros
x^4-40x^2+144=0
Answer:
the first choice 2 ; -2 ; 6 :-6
Step-by-step explanation:
1) method : you can put this values 2 ; -2 ; 6 :-6 you are 0
2) method you can solve this equation
x^4-40x^2+144=0
let : x² = t and t ≥ 0
t² -40t +144 = 0
Δ = b²- 4ac a= 1 b = - 40 c = 144
Δ =(-40)²- 4(1)(144= 1600 -576 = 1024=32²
t1 = (40+32)/2 = 36 = 6²
t1 = (40-32)/2 = 4 = 2²
but : x² = t and t ≥ 0
1)case : x² = 6² x = 6 or x= -6
2() case : x² =2² x = 2 or x= -2
Find the product of (0.7) x 10^4 and 2.
1. 1.4 x 10^4
2. 1.4 x 10^3
3. 0.14 x 10^4
4. 14 x 10^4
Answer:
A. because 3.7 ×2 is 7.4. so the full answer would be 7.4 ×10^4
In seven minutes jack types 511 words how many words does he type per minute
The number of words Jack can type in a minute is 73 words.
In seven minutes, Jack types 511 words. To calculate how many words he types per minute, you divide the total number of words by the total time taken:
Words per minute = Total words / Total time
Words per minute = 511 words / 7 minutes
Words per minute = 73 words
On Monday Henry with drill $49 from his bank account on Wednesday he would do $78 how much did he withdraw in total
Prove that the triangle with vertices with (3,5), (-2,6), and (1,3) is a right triangle.
Answer:
The triangle with vertices with (3, 5), (-2, 6), and (1, 3) is a right triangle.
Solution:
Given that the vertices of triangle are (3, 5), (-2, 6) and (1, 3)
Let us consider A(3, 5) B(-2, 6) C(1, 3)
If the sum of square of distance between two vertices is equal to the square of distance between third vertices, then the triangle is a right angled triangle.
By above definition, we get
[tex]BC^{2} + CA^{2} = AB^{2}[/tex] ----- eqn 1
Where AB is the distance between vertices A and B
BC is the distance between vertices B and C
CA is the distance between vertices C and D
Distance between any two vertices of a triangle is given as
[tex]Distance = \sqrt{\left(x_{2} -x_{1}\right )^{2} + \left(y_{2} -y_{1}\right)^{2} }[/tex] ------- eqn 2
Step 1:
Let us find the distance between the vertices A(3,5) and B(-2,6)
By using equation 2, we get
[tex]x_{1} = 3, x_{2} = -2, y_{1} = 5 \text { and } y_{2} = 6[/tex]
Distance between vertices A and B =[tex]\sqrt{(-2-3)^{2}+(6-5)^{2}}[/tex]
= [tex]\sqrt{(-5)^{2} + (1)^{2}}[/tex]
= [tex]\sqrt{(-5)^{2} + (1)^{2}}[/tex]
= [tex]\sqrt{25+1}[/tex]
= [tex]\sqrt{26} units[/tex]
Step 2:
Let us find the distance between the vertices B(-2,6) and C(1,3)
By using equation 2, we get
[tex]x_{1} = -2, x_{2} = 1, y_{1} = 6 \text { and } y_{2} = 3[/tex]
Distance between vertices B and C = [tex]\sqrt{(1-(-2))^{2}+(3-6)^{2}}[/tex]
= [tex]\sqrt{(1-(-2))^{2} + (3-6)^{2}}[/tex]
= [tex]\sqrt{3^{2}+9}[/tex]
= [tex]\sqrt{9+9}[/tex]
= [tex]\sqrt{18} \text { units }[/tex]
Step 3:
Let us find the distance between the vertices C(1,3) and D(3,5)
By using equation 2, we get
[tex]x_{1} = 1, x_{2} = 3, y_{1} = 3 \text { and } y_{2} = 5[/tex]
Distance between the vertices C and A
= [tex]\sqrt{(3-1)^{2} + (5-3)^{2}}[/tex]
= [tex]\sqrt{2^{2} + 2^{2}}[/tex]
= [tex]\sqrt{4+4}[/tex]
= [tex]\sqrt{8} units[/tex]
Step 4:
By using equation 1,
[tex]BC^{2} + CA^{2} = AB^{2}[/tex]
[tex](\sqrt{18})^{2} + (\sqrt{8})^{2} = (\sqrt{26})^{2}[/tex]
18 + 8 = 26
26 = 26
Hence the condition is satisfied. So the given triangle with vertices with (3,5), (-2,6), and (1,3) is a right triangle.