How many times does the quadratic function below intersect the x-axis?
y = 2x2 +7x+6
Answers
Answer:
once
Step-by-step explanation:
since the equation is liner, with x simply to the first power, it will only cross the x axis once. x^2 would cross the x axis twice, x^3 would cross it three times, and so on
Given quadratic function [tex]y = 2x^{2} +7x+6[/tex] intersects the x-axis two times.
What is quadratic function?" Quadratic function is defined as the function which has variables with highest degree two."
According to the question,
Given quadratic function,
[tex]y = 2x^{2} +7x+6[/tex]
If quadratic function intersect x-axis value of [tex]y=0[/tex] we have,
[tex]2x^{2} +7x+6 =0\\\\\implies 2x^{2} + 4x+3x + 6=0\\ \\\implies 2x(x+2) + 3(x+2)=0\\\\\implies (2x+3) (x+2)=0\\\\\implies 2x+3 =0 \ or \ x+2=0\\\\\implies x = \frac{-3}{2} \ or \ x =-2\\\\\implies x = -1.5 \ or \ x =-2[/tex]
As shown in graph , quadratic function intersect x-axis at two points [tex](-2,0)[/tex] and [tex](-1.5,0)[/tex].
Hence, given quadratic function [tex]y = 2x^{2} +7x+6[/tex] intersects the x-axis two times.
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Related Questions
what is the quontet for 1060 divided by 48
Answers
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
Given the function h(x)=4(x−2)2 , what is the value of h(5) ? h(5) =
Answers
h(5)=4x3
h(5)=12
Answer:
h ( 5 ) = 36
Step-by-step explanation:
Given function :- h ( x ) = 4 ( x - 2 )²
Also, for h ( 5 ) ... we need to replace x with 5 from the given equation :-
h ( 5 ) = 4 ( 5 - 2 )²
h ( 5 ) = 4 ( 3 )²
h ( 5 ) = 4 ( 9 )
h ( 5 ) = 36
So, h ( 5 ) = 36
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]
Answers
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
How do you solve this problem? 3x(5+2)=
Answers
Answer:
21
Step-by-step explanation:
Add 5 and 2 together to get 7 and multiply it by 3
In seven minutes jack types 511 words how many words does he type per minute
Answers
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
What is the value of x? Identify the missing justifications
Answers
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
Solve -7m^2 + 2m + 7 if m = -3
Answers
Answer:
Step-by-step explanation:
if m = -3
-7(-3)²+2(-3)+7 = -63-6+7 = -62
Hey!
---------------------------
Solution:
= -7(-3)² + 2(-3) + 7
= -63 + -6 + 7
= -69 + 7
= -62
---------------------------
Answer:
-62
---------------------------
Hope This Helped! Good Luck!
which is bigger 64 cm or .64 m?
Answers
Answer:
They are the same size
Step-by-step explanation:
1 cm = .01 m
64 cm = .64 m
How do you solve 11-.5y=3+6x for y
Answers
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
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
Answers
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.
On Monday Henry with drill $49 from his bank account on Wednesday he would do $78 how much did he withdraw in total
Answers
What is the value of 9 in $2.29?
Answers
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!
A total that is divided into equal groups is called the
Answers
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!
Prove that the triangle with vertices with (3,5), (-2,6), and (1,3) is a right triangle.
Answers
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.
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
Answers
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
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 ?
Answers
Answer:
y=-2x+3
Step-by-step explanation:
Find the real zeros
x^4-40x^2+144=0
Answers
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
(15 − 8)9
-------------
[(5 + 2)3]2
The simplified expression is:
Answers
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:
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?
Answers
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.
Write the equation of a line that is perpendicular to y = 5 and that passes through the point (-7,-5).
Answers
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.
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
Answers
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:
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
Answers
Answer:
A. because 3.7 ×2 is 7.4. so the full answer would be 7.4 ×10^4
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
Answers
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
Need help division equation 54 ÷ 1099
Answers
Answer:
54/1099=0.04913557779= 0.05
Step-by-step explanation:
Simply put, all you do is divide the two numbers and round it to whatever it tells you to round it to. 5 and above, give it a shove. 4 and below, let it go.
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
Answers
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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solve for x 2(x+2)+2x=4(x+1)
Answers
1.) distributive property
2x+4+2x=4x+4
2.) combine like terms
4x+4=4x+4
3.) subtract 4x from both sides to get
4=4.
Because 4=4 is a true statement the answer is infinite solutions. Hope this helps!!!!
Ms. How bought a bag of rice for dinner. She used 3/5 kg of the rice and still had 2 1/4 kg left. How heavy was the bag of rice that Ms. How bought?
Answers
Answer:
Step-by-step explanation:
First let's look at this with just the whole numbers. Say someone used 2 kg and had 3 left. it should be pretty simple to see that you started with 5 kg. It's basically an algebra problem. if we say x is the starting amount then x-2 = 3. You could then solve for x=5. Now, let's dot he same for your actual numbers.
x - 3/5 = 2 1/4
x = 2 1/4 + 3/5
Now, to add fractions you need to get the same denominators. we are just really concerned with 1/4 + 3/5. Now, you need to knwo you can change fractions. so 1/4 = 2/8 = 3/12 = 4/16 and so on, You are basically multiplying the numerator and denominator by the same number. (1*2)/(4*2) = 2/8. Now, to make both denominators equal you can multiply one fraction by the other denominator.
1/4 + 3/5
(1*5)/(4*5) + (3*4)/(5*4)
5/20 + 12/20 = 17/20.
So now, back tot he main problem, we are adding 2 1/4 + 3/5 = 2 17/20. so the starting amount was 2 17/20 kg.
There is another way to add fractions but it is more involved and this always works so this is what I always use.
Ms. How bought a bag of rice that weighs 57/20 or 2 7/20 kg.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Ms. How bought a bag of rice for dinner.
Assuming she bought x kg of rice.
She used 3/5 kg of the rice and still had 2 1/4 kg left.
∴ x - 3/5 = 9/4.
x = 3/5 + 9/4.
x = (12 + 45)/20 kg.
x = 57/20 kg.
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Evaluate the expression 4-9/4×3/2
Answers
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.
[tex](6x+27) (12x-9)[/tex]
Answers
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]
Simplify these expressions.
a. 4x + 7x + (–x)
b. –5yz + yz + 2yz
Answers
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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