Answers
Answer:
a. a = 1, b = -5, c = -14
b. a = 1, b = -6, c = 9
c. a = -1, b = -1, c = -3
d. a = 1, b = 0, c = -1
e. a = 1, b = 0, c = -3
Step-by-step explanation:
a. x-ints at 7 and -2
this means that our quadratic equation must factor to:
[tex](x-7)(x+2) = 0[/tex]
FOIL:
[tex]x^2 + 2x - 7x - 14 = 0[/tex]
Simplify:
[tex]x^2 - 5x - 14 = 0[/tex]
a = 1, b = -5, c = -14
b. one x-int at 3
this means that the equation will factor to:
[tex](x-3)^2=0[/tex]
FOIL:
[tex]x^2 - 3x - 3x +9 = 0[/tex]
Simplify:
[tex]x^2 - 6x + 9 = 0[/tex]
a = 1, b = -6, c = 9
c. no x-int and negative y must be less than 0
This means that our vertex must be below the x-axis and our parabola must point down
There are many equations for this, but one could be:
[tex]-x^2-x-3=0[/tex]
a = -1, b = -1, c = -3
d. one positive x-int, one negative x-int
We can use any x-intercepts, so let's just use -1 and 1
The equation will factor to:
[tex](x+1)(x-1)=0[/tex]
This is a perfect square
FOIL:
[tex]x^2-1=0[/tex]
a = 1, b = 0, c = -1
e. x-int at [tex]\sqrt{3} , -\sqrt{3}[/tex]
our equation will factor to:
[tex](x+\sqrt{3} )(x-\sqrt{3)} =0[/tex]
This is also a perfect square
FOIL and you will get:
[tex]x^2 - 3 = 0[/tex]
a = 1, b = 0, c = -3
Related Questions
A pound of grapes costs $2.49. Lucas bought two pounds of grapes. He gave the clerk a $10.00 bill. How much change did Lucas get?
Answers
Answer:
$5.02
Step-by-step explanation:
$2.49 × 2 = $4.98
$10 - $4.98 = $5.02
hi! how do i do this? the answer is 2k
Answers
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
[tex] log_{4}x = k \\ \\ \longrightarrow \: log_{4}x = log_{2 {}^{2} }x \\ \\ \longrightarrow \: 2 log_{2}x \\ \\ now , \\ \\ log_{2}x = k \\ \\ \therefore \: 2( log_{2}x) = 2(k) \\ \\ \longrightarrow \: 2k[/tex]
hope helpful ~
URGENT!!!! What is the number of solutions in this system?
A None
B one
C Infinite
Answers
Answer:
C? Not 100% sure
Step-by-step explanation:
A committee must be formed with 4 teachers and 7 students. If there are 9 teachers to choose from, and 8 students, how many different ways could the committee be made?
Answers
as compromises. One example of an adaptive con
bear's "thumb.' Modern pandas have five digits th
and a sixth digit that functions like a thumb. This
bone. Ancestral pandas with bigger wrist bones hac
ing and eating their food. Over time, this adaptati
is this right? pls be fast
Answers
Answer:
first 2 I'm not sure about. for the first one I think its 0.5 if that's an option
help please !!!!!!!!!!
Answers
Answer:
it is -3
Step-by-step explanation:
go to x=-4 and see what the y value of the line is
Answer:
1
Step-by-step explanation:
Find the equation of the line. Start with the y-intercept, which is -1. Next find the slope by doing rise/run. To get from (0, -1) to (2, 0) you rise 1 and run 2, so the slope is 1/2.
The equation is y= 1/2x -1.
Plugin 4 for x and solve for y.
y = 1/2(4) -1
y = 2 - 1
y = 1
What is the solution to the equation below?
Answers
Answer:
X=4
Step-by-step explanation:
The solution is in the file
Explanation: Determine the defined range. Write the number in exponential form with the base of 2. Use log a y (a^x) = x/y to simplify the expression.
Add fractions. Divide by both sides by 3. Convert the logarithm into exponential form.
PLEASE HELP?! IM SO CONFUSED!!
Answers
Answer:
C.
Step-by-step explanation:
-3 7/8 rounds down to -4
4.63 rounds up to 5
-4 x 6 + 5
-24 + 5
-19
her answer (-19.14) also rounds to -19
So yes, it is reasonable and the correct response is C.
18 positive integers and 13 negative integers are multiplied.
Answers
Using multiplication rules, it is found that the result of the multiplication will be a negative number.
What are multiplication rules?When two numbers of the same signal are multiplied, the result is positive.Hence, when an even number of negative numbers are multiplied, the result is positive. If an odd number is multiplied, the result is negative.Hence, in this problem we have that:
The result of the multiplication of the 13 negative integers is negative.The result of the multiplication of the 18 positive integers is positive.The multiplication of both results is the multiplication of a negative by a positive, hence it is negative.More can be learned about multiplication rules at https://brainly.com/question/4158962
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plssssss helppppp i give 98 points
Answers
To write 28 + 24 as a product of two factors, we need to determine the HCF of the addends (28 and 24). This can be done by listing the factors of the addends. The greatest factor that is common in 28 and 24 is the HCF.
If the number is in bolded text, the number is a common factor.
Factors of 28: 1, 2, 4, 7, 14, 28Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24Since 4 > 2 > 1, the HCF is 4.
2) Writing 28 and 24 as a product of two factorsNow, let us put the provided expression between parentheses.
⇒ (28 + 24)Finally, factor four out of the expression, as it is the GCF of 28 and 24.
⇒ (28 + 24)⇒ [(4 × 7) + (4 × 6)]⇒ 4(7 + 6)Therefore, 28 + 24 as a product of two factors is 4(7 + 6).
Learn more about this topic: https://brainly.com/question/18636885
2xy - 3x2y2 + 2xy +5x2y2
Answers
How many students were surveyed?
Answers
Answer:
20
Step-by-step explanation:
count the dots
Answer:
20 students
Step-by-step explanation:
You just need to count the number of dots.
hope this helps
have a good day
Help Me, I only have 2 minutes
Answers
Answer:
[tex]6 \frac{2}{13} [/tex]
what is the negation of x is greater than
39
Answers
Step-by-step explanation:
that means the opposite ...
the opposite of
x > 39
is
x <= 39
Two buildings are 96 ft apart . The first building is 164ft tall. The second building is 92ft tall. If a string is stretched between the top of the two buildings so that it forms a straight line from the top of one to the top of the other, how long would the string be
Answers
Answer:
120ft
Step-by-step explanation:
- On her first three quizzes Jenna averaged 8 correct answers. On the next two quizzes she averaged 9 correct answers. What decimal number shows Jenna's average score on all five quizzes?
Answers
Answer:
8.4
Step-by-step explanation:
Add 8+8+8+9+9=42 then 42/5 equals 8.4
Hope this helps! ;-)
The difference between a number and seven is less than or equal to -3. Find the possible numbers. n ≤ 4 n ≥ 4 n ≤ -10 n ≥ -10
Answers
Answer:
n ≤ 4
Step-by-step explanation:
"The difference between a number and seven is less than or equal to -3" can be written as n-7 ≤ -3
n-7 ≤ -3
Add 7 to both sides
n ≤ 4
Answer is n ≤ 4
See picture attached for the math
help will mark Brainliest
Answers
Answer:
The third box model
Step-by-step explanation:
Since she earns 162 from babysitting and got a total of $810, it would eman that (x represents the amount of money she got from mowing lawns) 810-162=x
x=648 so the third box model is correct
# The size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles. If the greater of the opposite interior angles exceeds smaller by 30°, find the measure of the interior angles of the triangle.
please help me
Answers
Answer:
30° and 60°
Step-by-step explanation:
Let the interior angles be ∠x₁ (smaller) and ∠x₂ (larger), and the exterior angle ∠X.
Making the statements into equations :
Size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles ⇒ ∠X + ∠x₁ + ∠x₂ = 180° [Equation 1]
Greater of the opposite interior angles exceeds smaller by 30° :
⇒ ∠x₂ = ∠x₁ + 30° [Equation 2]
By exterior angle property :
⇒ ∠x₁ + ∠x₂ = ∠X [Equation 3]
Substituting Equation 3 in Equation 1 :
⇒ ∠x₁ + ∠x₂ + ∠x₁ + ∠x₂ = 180°
⇒ 2 (∠x₁ + ∠x₂) = 180°
⇒ ∠x₁ + ∠x₂ = 90°
⇒ ∠x₂ = 90° - ∠x₁ [Equation 4]
Substituting Equation 4 in Equation 2 :
⇒ 90° - ∠x₁ = ∠x₁ + 30°
⇒ 2∠x₁ = 60°
⇒ ∠x₁ = 30°
Substituting the value of ∠x₁ in Equation 2 :
⇒ ∠x₂ = 30° + 30°
⇒ ∠x₂ = 60°
The measures of the interior angles are 30° and 60°
Please Help with this...
Answers
Answer: 3
Step-by-step explanation:
Which is an example of an isosceles right triangle?
Answers
Answer:
D.
Step-by-step explanation:
An isosceles triangle is a triangle with 2 equal sides (2 sides with the same length)
According to the fundamental theorem of algebra, which polynomial function has exactly 6 roots? f (x) = 5 x superscript 4 baseline 10 x squared 2 f (x) = 5 x superscript 5 baseline 3 x superscript 4 baseline 12 x cubed 7 x squared minus 2 x 15 f (x) = 6 x superscript 5 baseline x cubed minus 4 x squared x minus 5 f (x) = 7 x superscript 6 baseline 3 x cubed 12
Answers
The polynomial function has exactly 6 roots is f(x) = 7x⁶ + 3x³ + 12. Then the correct option is D.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
According to the fundamental theorem of algebra.
The polynomial function has only exactly 6 roots.
The roots are the value of the variables in the polynomial at which the value of the polynomial is zero.
If the degree of the variable is n then the number of the roots will be n or less than n.
If the number of the roots are 6, then the degree of the variable will be 6 in the polynomial.
Then the polynomial function has exactly 6 roots is f(x) = 7x⁶ + 3x³ + 12.
More about the Algebra link is given below.
https://brainly.com/question/953809
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A rectangle has a width that measures 11 in. and a length that measures 5.5 in.
Determine the area of the rectangle.
Answers
A = (11)(5.5)
A = 60.5
The area of the rectangle is 60.5 inches squared.
Answer: 60.5 in
Step-by-step explanation:
Area of rectangle = length times width
Length = 5.5 in
Width = 11 in
11 x 5.5 = 60.5
The area of the rectangle is 60.5 in
Use the information in the table to find the indicated probability.
Number of Degree Recipients at a Local College
Degree Male Female
Associate's 224 387
Bachelor's 547 776
Advanced 245 322
Find P(the recipient is male).
Answers
Using it's concept, it is found that the desired probability is given as follows:
P(the recipient is male) = 0.4242 = 42.42%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there was a total of 224 + 387 + 547 + 776 + 245 + 322 = 2501 recipients, out of which 224 + 547 + 245 = 1016 are males, hence the probability is given by:
P(the recipient is male) = 1016/2501 = 0.4242 = 42.42%.
More can be learned about probabilities at https://brainly.com/question/14398287
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Daniel's goal is to walk 100 miles.• He walks 5 miles every day.• He has
walked for 7 days. Daniel still needs to walk k more miles for his goal.
Which equation could be used to find how many more miles, k, Daniel
will have to walk to meet his goal
Answers
Answer:
65 miles
Step-by-step explanation:
Given:
k = how many more miles Daniel has to walkGoal = 100 milesDaily miles = 5 milesNumber of days already walked = 7 daysEquation:
5 × 7 + k = 100
Solving:
⇒ 5 × 7 + k = 100
⇒ 35 + k = 100
⇒ k = 100 - 35
⇒ k = 65
1. Suppose that the time required to drive across town is uniformly distributed between 12 and 20 minutes. What is the simulated (average)
time to cross town using the following random numbers: 0.21 0.53 0.05 0.89 015 0.73 0.06 0.28 0.81 0.74 (rounded to 2 decimal place)
Answers
Using the mean concept, it is found that the simulated average time to cross town is of 0.445.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem, the 10 values of the simulation are given by:
0.21 0.53 0.05 0.89 0.15 0.73 0.06 0.28 0.81 0.74
Hence, the mean is given by:
M = (0.21 + 0.53 + 0.05 + 0.89 + 0.15 + 0.73 + 0.06 + 0.28 + 0.81 + 0.74)/10 = 0.445.
More can be learned about the mean concept at https://brainly.com/question/24628525
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A pane of antique glass has dimensions of 30cm x 56cm. If the glass sells for 25 cents per square cm, what is the cost of the pane?
Answers
Given :-
Dimensions of pane is 30cm×56cmCost of pane per square cm is 25 centsTo find :-
Cost of the paneSolution:-
Hey mate , to find the total cost of pane we have to find the area of pane and multiply it by 25 cents
Area of pane :- 30×56cm²
Area of pane :- 1680cm²
Cost of pane :- 1860×25 cents
Cost of pane :- 42000 cents or 420$
Which ratio represents the number of vowels to total letters in the word JACKSONVILLE?
Answers
Step-by-step explanation:
4:12 there are four vowels and 12 letters?
Yellow Bird launches from point (10,0). His flight path reaches a maximum height of 22 yards and lands at point (42, 0).
Answers
The Equation for the launch of the yellow bird is y = -0.1( x - 26 )² + 20
what will be the equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values
Given:
Starting position of the bird = ( 10 , 0 )
Final position of the bird = ( 42 , 0 )
Maximum Height of the bird = 20 yards
To find: Equation that represent this condition.
Clearly, Birds flight path is not a straight line. It has a curved path.
So, the path bird follow is a PARABOLA.
Standard Equation of the parabola in vertex form, y = a( x - h )² + k
where ( h , k ) is the vertex of the parabola.
In our Question , vertex is the point at the highest position.
Vertex will be 20 yard above the mid point of the starting and final position.
Using Mid-Point Formula,
Mid-Point of ( 10 , 0 ) & ( 42 , 0 ) =
Now, the vertex = ( 26 , 0 + 20 ) = ( 26 , 20 )
⇒ Equation, y = a( x - 26 )² + 20
Now, we find value of by substituting value of (10 , 0) in the equation,
⇒ 0 = a( 10 - 26 )² + 20
a( -16 )² = -20
a(256) = -20
a = -20/256
a = −0.078125
a ≈ -0.1
Therefore, The Equation is y = -0.1( x - 26 )² + 20
To know more about Equations follow
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Max is creating a playlist and can have at most 180 minutes of music. He currently has 45 minutes. How many more minutes of music could Max include in the playlist?
Answers
Answer:
max could still add 135 minutes of music into his playlist
Step-by-step explanation:
180 - 45 = 135
Answer:
So we know that Max's playlist can have at most 180 minutes of music meaning that our amount of music cannot exceed that number. We are also given that Max already has 45 minutes of music on there so we need to subtract that from 180 minutes to see how much we have left.
[tex]180\ minutes - 45\ minutes[/tex]
[tex]135\ minutes[/tex]
Max still has 135 minutes left on his playlist that he can fill up.
Hope this helps! Let me know if you have any questions
