The answer is A because completing the square gives a minimum of 2,-9 and factorising gives roots of 5 and -1 :)
Answer:
Minimum at (2,-9) and intercepts are (-1,5)
Step-by-step explanation:
f(x) = [tex]x^2 -4x-5[/tex]
completing square method adding and subtracting the square of half of coefficient of 4 ,we get
f(x) = [tex]x^2 -4x+4 -4 -5[/tex]
f(x) =[tex](x-2)^2 -9[/tex]
on comparing it with standard vertex form [tex](x-h)^{2} +k[/tex]
where k is suppose to be the minimum value
on comparing it we get k = -9
which is minimum value of f(x)
at x =2
and if we find the zeros of
[tex]x^2 -4x-5[/tex] ,we get
[tex]x^2 -5x+x -5[/tex]
[tex]x^2 -4x-5[/tex]
x(x-5)+1(x-5)
(x+1)(x-5)
on setting it equals zero ,we get
x+1 =0 and x=5
x =-1 and x=5
therefore option A is answer
Minimum at (2,-9) and intercepts are (-1,5)
solve the equation using the Quadratic Formula. Round your solutions to the nearest tenth if necessary.) please help I need explanation I'm stuck on this I need your help please
Answer:
Quadratic Formula x = [-b +- Sq root (b^2 - 4ac)] / 2a
In this example a= 2 b= -6 c= 5
x = [- - 6 +- Sq root ((-6^2) - 4 *2*5)] / 2*2
x = [6 +-sq root (36 -40)] / 4
x = 6 +- 2i / 4
x1 = 1.5 + .5i
x2 = 1.5 -.5i
Step-by-step explanation:
Answer:
x = 1.5 - .5i and 1.5 + .5i
Step-by-step explanation:
to start off - this is the quadractic fromula: x = -b ± √b²-4(a)(c) / 2(a)
a = 2x²
b = -6x
c = 5
now you just fill the numbers in to the formula!!
x = -(-6) ± √(-6)²-4(2)(5) / 2(2)
x = 6 ± √36 - 40 / 4
x = 6 ± √-4 /4
x = 6 ± 2i / 4
x = 6+ 2i/4 and 6 - 2i/4
x = 1.5 + .5i amd 1.5 - .5i
hope this helps!!
Find the total area 12 in 10 in 8 in 7 in 4 in 3 in
Answer:
80,640 IN 3
Step-by-step explanation:
Which is equivalent to 5 Square root of 1215^x
Final answer:
The expression 5 Square root of 1215^x can be simplified to 5^(1+x/2) × 3^(5x/2) by factoring 1215 and applying exponent rules.
Explanation:
To find what is equivalent to 5 Square root of 1215^x, we need to simplify the radical expression and apply exponent rules. The number 1215 can be factored into 3^5 × 5. Therefore, the square root of 1215 is the square root of each factor raised to the power of x. We know that the square root of a number can be expressed as the number raised to the power of 1/2. So 1215 raised to the power x can be expressed as (3^5 × 5)^x, and taking the square root gives us (3^5 × 5)^(x/2).
Applying exponent rules, like multiplying powers when the same base is raised to two different exponents (as per Eq. A.8 and what we know from Integer Powers), we can simplify the expression further. Our expression of 5 times the square root of 1215 raised to the power x becomes 5 × 3^(5x/2) × 5^(x/2).
We can then combine the coefficients (5 × 5^(x/2)) which simplifies to 5^(1+x/2). Our final expression of the original problem then becomes 5^(1+x/2) × 3^(5x/2), which is the simplified version of the original expression.
Multiply (2 4/5) (-5 2/3)
Final answer:
To multiply mixed numbers, convert them into improper fractions, multiply the numerators and denominators separately, and simplify the resulting fraction.
Explanation:
To multiply mixed numbers, we first convert them into improper fractions. Then, we multiply the numerators and denominators separately and simplify the resulting fraction if possible.
In this case, (2 4/5) can be written as 14/5 and (-5 2/3) can be written as -17/3. Therefore, (2 4/5) (-5 2/3) can be simplified to (-14/5) * (-17/3).
To multiply fractions, we multiply the numerators and denominators together. So, (-14/5) * (-17/3) = (14 * 17) / (5 * 3) = 238/15 = 15 13/15.
Find tan A for the triangle below.
a. 2.5 b. 0.4 c. 2.67 d. 0.375
It's A. 2.5
It's not B that person is wrong.
Which situation is best modeled by the inequality g ≤ 13?
A:You cannot play a game at age 13.
B:You must be no older than 13 to play a game.
C:You must be at least 13 to play a game.
D:You must be younger than 13 to play a game.
Answer:
You must be no older than 13 to play a game.
Step-by-step explanation:
≤ this sign means equal to or less than in this case it is 13
The situation that should be modeled by the inequality g ≤ 13 is option b.
Given information:
Inequality function g ≤ 13
Inequality function:We know that ≤ this sign represent that it is equal or lower than So here it should be no older than 13 for playing the game.
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A field is undergoing construction and needs land to be removed in the shape of a rectangular prism. The land to be removed has a length of 1.4 × 104 in, a width of 4.3 × 103 in, and a height of 1.6 × 103 in. Find the volume of the land in scientific notation and in standard form. Answers should not be rounded. The volume of the land written in scientific notation is a × 10b cubic inches, where a____ is and B is____ .
The volume of the land written in standard form is____ cubic inches.
Answer:
a = 9.632 and b is 10
9.632*10^10 in^3 scientific form
96,320,000,000 in^3 standard form
Step-by-step explanation:
To find volume of a rectangular prism
V = l*w*h
= 1.4 * 10^4 ( 4.3 * 10^3) (1.6* 10^3)
When multiply powers of 10, we multiply the numbers out front
1.4*4.3*1.6 =9.632
Then we add the powers of 10
10^(4+3+3)
10^10
The volume is 9.632*10^10 in^3
a = 9.632 and b is 10
In standard form we move the decimal 10 places to the right. If there are not enough numbers we add zeros
9.632*10^10 in^3
96,320,000,000 in^3
Find the diameter of a circle with an area of 95.03 square feet
Answer:
diameter ≈ 11 feet
Step-by-step explanation:
The area (A) of a circle is calculated using the formula
A = πr² ← r is the radius
To find r divide both sides of the equation by π
r² = [tex]\frac{A}{\pi }[/tex] = [tex]\frac{95.03}{\pi }[/tex]
Take the square root of both sides
r = [tex]\sqrt{\frac{95.03}{\pi } }[/tex] ≈ 5.5 feet
Diameter = 2r = 2 × 5.5 = 11 feet
A circle is a curve sketched out by a point moving in a plane. The diameter of the circle whose area is 950.3 square feet is 11 feet.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
As it is given that the area of the circle is 95.03 square feet. Therefore, if we apply the area of the circle, we will get,
[tex]\text{Area of the circle} = \pi r^2[/tex]
where r is the radius of the circle,
[tex]\rm 95.03 = \pi r^2\\\\r = \sqrt{\dfrac{95.03}{\pi}}\\\\r = 5.4999 \approx \rm 5.5\ feet[/tex]
The radius of the circle is half the diameter of the circle, therefore, the diameter of the circle,
[tex]\rm Radius = \dfrac{Diameter}{2}\\\\5.5 \times 2 = Diameter\\\\Diameter = 11\ feet[/tex]
Thus, the diameter of the circle whose area is 950.3 square feet is 11 feet.
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Which is greater three hours or 300 minutes
3 x 60 = 180
180 < 300
300 mins is greater.
If Catherine traveled 1,600 miles in 8 hours on her plane flight to her vacation destination, at what rate was the plane traveling
Answer:
c.200
Step-by-step explanation:
please help! 2 answer-choice math questions I give Brainliest, thanks, rattings, ect
its 50 POINTS
Question 2
What is the best approximation of the solution to the equations that these two lines represent?
(1, 1)
(1, 1.5)
(1.5, 1)
(0, 1)
Question 4
6x + 4y = 2
3x + 2y = 1
not enough information
coincident
inconsistent
consistent and independent
Answer:
2) (1,1.5)
4) Not enough information
Step-by-step explanation:
2) If you look along at the intersection point of the two lines it's (1,1.5).
4) Since only one equation is graphed, we can't tell anything.
if 3 1/2 is equivalent to 7/2 what is equivalent to 2 1/9
Answer:
[tex]\frac{19}{9}[/tex]
Step-by-step explanation:
To change the mixed number to an improper fraction.
Multiply the whole number by the denominator of the fraction and add the numerator. The denominator remains unchanged, that is
2 [tex]\frac{1}{9}[/tex]
=[tex]\frac{2(9)+1}{9}[/tex] = [tex]\frac{19}{9}[/tex]
A rental car agency charges $ 160.00 per week plus $ 0.25 per mile to rent a car. How many miles can you travel in one week for $ 370.00 question mark
Answer:
Report Me and sub To PewDiePie
Step-by-step explanation:
hey plz help me out i need all workings
a)x^2-4xy-12y^2 b)x^2+8x+12
Answer:
see explanation
Step-by-step explanation:
(a)
Consider the factors of the coefficient of the y² term ( - 12) which sum to give the coefficient of the xy- term (- 4)
The factors are - 6 and + 2
since - 6 × 2 = - 12 and - 6 + 2 = - 4, hence
x² - 4xy - 12y² = (x - 6y)(x + 2y)
----------------------------------------------------
(b)
Consider the factors of + 12 which sum to give + 8
The factors are + 2 and + 6, hence
x² + 8x + 12 = (x + 2)(x + 6)
I need to answer and explain number 27.
Answer:
y = 9x - 5
Step-by-step explanation:
Any line parallel to the given line y = 9x must also have the slope 9.
Substitute the known values (m = 9, h = 0, k = -5) into the point-slope equation of a straight line:
y - (-5) = 9(x - 0)
Then y + 5 = 9x, or
y = 9x - 5
Need help don’t understand
What is the sum of an infinite geometric series if a1 = 5 and r = 1⁄3?
A. 25⁄2
B. 30
C. 15⁄2
D. 15
Answer:
C
Step-by-step explanation:
The sum to infinity of a geometric series is
[tex]\frac{a_{1} }{1-r}[/tex] ( - 1 < r < 1 ) ← substitute values
S( ∞ ) = [tex]\frac{5}{1-\frac{1}{3} }[/tex] = [tex]\frac{5}{\frac{2}{3} }[/tex] = [tex]\frac{15}{2}[/tex]
The sum of the infinite geometric series is [tex]\frac{15}{2}[/tex]
What is infinite geometric series ?
The sum of all the terms of a geometric sequence is called infinite geometric series.
If a, ar, a[tex]r^{2}[/tex], ...., a[tex]r^{n-1}[/tex], .... is a geometric series, then a+ar+a[tex]r^{2}[/tex]+ ....+a[tex]r^{n-1}[/tex]+.... is the corresponding infinite geometric series.
where a is the 1st term & r is the common ratio between consecutive terms of the series.
Sum of infinite geometric series = [tex]\frac{a}{1-r}[/tex] ; |r|<1
What is the required sum of series ?Given, 1st term ([tex]a_{1}[/tex]) of the infinite geometric series = 5
Common ratio (r) = 1/3
∴ Sum of infinite geometric series = [tex]\frac{a_{1} }{1-r}[/tex]
= [tex]\frac{5}{1-\frac{1}{3} }[/tex]
= [tex]\frac{5}{\frac{2}{3} }[/tex]
= [tex]\frac{15}{2}[/tex]
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bruhhhh helppppppp meww
Answer:
B
Step-by-step explanation:
Given
V = [tex]\frac{Bh}{3}[/tex]
Substitute the given values for B and h into the formula
V = [tex]\frac{15(28)}{3}[/tex] = [tex]\frac{420}{3}[/tex] = 140 in³
Find RT of the triangle
Answer:
[tex]\large\boxed{RT=\sqrt{165}}[/tex]
Step-by-step explanation:
PT = NT. Therefore we have the equation:
[tex]4x-17=x+10[/tex] add 17 to both sides
[tex]4x=x+27[/tex] subtract 4x from both sides
[tex]3x=27[/tex] divide both sides by 3
[tex]x=9[/tex]
Therefore
[tex]NT=4(9)-17=36-17=19[/tex]
Use the Pythagorean theorem:
[tex]RT^2+RN^2=NT^2[/tex]
Substitute RN = 14 and NT = 19:
[tex]RT^2+14^2=19^2[/tex]
[tex]RT^2+196=361[/tex] subtract 196 from both sides
[tex]RT^2=165\to RT=\sqrt{165}[/tex]
Please help I’m stuck on this question!
Answer:
see explanation
Step-by-step explanation:
the fraction is boys over total in class, that is
fraction of boys = [tex]\frac{8}{24}[/tex] ( divide top/bottom by 8 )
fraction of boys = [tex]\frac{1}{3}[/tex] ← in simplest form
(b)
The number of girls in class = 24 - 8 = 16
fraction of girls = [tex]\frac{16}{24}[/tex] ( divide top/bottom by 8 )
fraction of girls = [tex]\frac{2}{3}[/tex] ← in simplest form
The number of boys is 1/3
The number of girls is 2/3
Step-by-step explanation:Total no of students = 24
No of boys in the class is 8
So in fraction form
Boys = 8 out of 24 which is 8/24 or simply 1/3
Now
For girls
no of girls will be Total students - boys students
Number of girls students = 24 - 8 = 16
In fraction form we can write 16/24 or simply 2/3
I am not sure how to this pleases help
The subject of this question is Mathematics.
Explanation:The subject of this question is Mathematics.As a tutor, I would need more information about the specific question or problem you are working on to provide a detailed answer. Mathematics encompasses a wide range of topics including algebra, geometry, statistics, and calculus, among others. If you can provide more details about the specific topic or concept you are struggling with, I can provide a step-by-step explanation to help you understand.
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add and simplify
(2x^2-11x)+(3x^2+10x-4)
the answers are either -
6x^2-11x-4
5x^4
5x^2-x-4
5x^2-4
Answer:
5x^2-x-4
Step-by-step explanation:
Combine the terms.
Help is appreciated! :D
Eva spent $11.61 downloading songs, each song cost $1.29. Four students wrote and solved equations to find s, the number of songs that she downloaded. Which student wrote and solved the equation correctly?
A. Seba’s work
1.29s=$11.61
S=10
B. Ari’s work
$1.29s=$11.61
S=9
C.Erick’s work
S/$1.29=11.61
S=14.98
D. Daniel’s work
S/$1.29=$11.61
S=9
Answer:
Option B.
Step-by-step explanation:
Let
s-----> the number of songs that Eva downloaded
we know that
The linear equation that represent the situation is
[tex]1.29s=11.61[/tex]
Solve for s
Divide by 1.29 both sides
[tex]s=11.61/1.29[/tex]
[tex]s=9\ songs[/tex]
therefore
Ari's work is correct
Answer:
answer b
Step-by-step explanation:
i took test
837.2 divided by 1:3 step my step
The value of the equation A = 837.2 / 1.3 is A = 644
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be p
The value of p = 837.2
Let the second number be q
The value of q = 1.3
Now , the equation A = p/q
Substituting the values in the equation , we get
A = 837.2 / 1.3
On simplifying the equation , we get
A = 644
Therefore , the value of A is 644
Hence , the equation is A = 644
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What is 16 cups converted to fluid ounces
Answer:
128 fluid ounces
Step-by-step explanation:
There are 8 fluid ounces in 1 cup.
There's 1 cup in 8 fluid ounces
16 cups x 8 = 128 fluid ounces
number 6 please
F.$16.10
H.$15.25
G.$15.50
J.$14.50
The Answer Is J.14.50
Answer: $14.50
Step-by-step explanation:
Multiply $5.95 by 2.
Multiply $0.65 by 4.
Add both of the answers to the multiplying problems
Your final answer... I hope I was able to help!
Can someone please help me????
The answer for the second question ( x < 3) is A
The answer for the first question is B
A store is having a sale where everything is discounted 30% find the discount and the sale price if a customer buys an item that normally sells for 365
Answer:
The discount is $109.50
The sale price is $255.50
Step-by-step explanation:
step 1
Find the discount
we know that
The discount is equal to the original price multiplied by the percentage rate of discount
we have
The original price is $365
The percentage of discount is equal to 30%
30%=30/100=0.30
so
the discount is equal to
0.30*($365)=$109.50
step 2
Find the sale price
The sale price is equal to the original price minus the discount
so
$365-$109.50=$255.50
What is the least common multiple of 2, 20, and 10?
Answer:
20
Step-by-step explanation:
The least common multiple is 20 :)