The equation after completing the square is (z + 4)² = 80
The solutions to the given equation in the simplest radical form are z = -4 + 4√5 and z = -4 - 4√5
Completing the squareFrom the question, we are to solve the given quadratic equation by completing the square
The given equation is
z² +8z - 44 =20
First, add 44 to both sides of the equation
z² +8z - 44 + 44 = 20 + 44
z² +8z = 64
Now, divide the coefficient of z by 2, square the value and add to both sides
The coefficient of z is 8
Dividing
8/2 = 4
Squaring
4²
Now, add this to both sides
That is,
z² +8z +4² = 64 + 4²
(z + 4)² = 64 + 16
(z + 4)² = 80
The equation after completing the square is
(z + 4)² = 80
Continuation
(z + 4)² = 80
Take the square root of both sides
√(z + 4)² = ±√80
z + 4 = ±√80
z = -4 ± √80
z = -4 ± 4√5
z = -4 + 4√5 and z = -4 - 4√5
Hence,
The equation after completing the square is (z + 4)² = 80
The solutions to the given equation in the simplest radical form are z = -4 + 4√5 and z = -4 - 4√5
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is 25 a perfect cube?
Answer: no 25 is a perfect square
Step-by-step explanation:
80% of the frogs in a pond are spring peepers. If there are 200 frogs in the pond, how many spring peepers are there?
Answer:
160
Step-by-step explanation:
If 80% of the frogs in a pond are spring peppers, and there are 200 frogs in the pond, to find how many spring peppers are in the pond, find 80% of 200.
[tex]\begin{aligned} \sf \implies 80\% \textsf{ of }200 & = \sf 80\% \times 200\\\\& = \sf \dfrac{80}{100} \times 200\\\\& = \sf \dfrac{80}{100} \times \dfrac{200}{1}\\\\& = \sf \dfrac{80 \times 200}{100 \times 1}\\\\& = \sf \dfrac{16000}{100}\\\\& = \sf 160\end{aligned}[/tex]
Therefore, there are 160 spring peppers in the pond.
michael read 135 pages in 90 minutes. select all of the rates that have the same constant rate of change as michael's rate.
#1) 180 pages in 2 hours?
#2) 60 pages in 30 minutes?
#3) 108 pages in 2 1/2 hours?
#4) 150 pages in 1 hour?
#5) 225 pages in 150 minutes?
#6) 210 pages in 2 hour 2 minutes?
Answer:
#1) & #5) are the rates that have the same constant rate of change as Micheal's rate.
If the big, green rectangle represents 1 whole, then what part of the whole is the shaded, gold
rectangle?
14
2 3
4
5
State your answer as a fraction.
6
The fraction that represents the part of a whole, which is shaded gold is 3/7.
What is fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole.
Given is a big green rectangle divided into seven equal segments. From the image, it can be seen that 3 segments out of the seven are colored with gold. Therefore, we can write that -
Number of segments colored = n[c] = 3
Total segments = n[T] = 7
We know that a fraction defines a part of a whole. The green Rectangle is one whole, therefore it can be concluded that -
1 whole = 7 segments = n[T].
Number of segments colored = n[c] = 3.
Therefore, we can say that the fraction that represents the part of a whole, which is shaded gold is given by -
n[c] / n[T] = 3 / 7
Therefore, the fraction that represents the part of a whole, which is shaded gold is 3/7.
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[The given question is not complete. Please refer to the image attached for complete question]
Please help me!! Please and thank you!! This is my last question yall…
Answer:
u didn't add any question so how are we gonna help
Translate the sentence into an equation.
The sum of 8 times a number and 9 is 7.
Use the variable b for the unknown number.
Answer:
8b + 9 = 7
Step-by-step explanation:
Whats 1,250 - 250 x 2?
Answer:750
Step-by-step explanation:
multiply the numbers
1250-250x2
1250-500
subract the two numbers and you will get
750
Compare 71.815 and 701.815
Answer:
71.815<701.815
Step-by-step explanation:
2) Which of the following is the correct factorization of 7x² - 36x +5?.
a. (7x + 1)(x - 5)
b. (7x-1)(x + 5)
c. (7x - 1)(x - 5)
d. (7x +1)(x + 5)
Ca
C
E
D
2 509
Answer:
c
Step-by-step explanation:
7x²-36x+5= 7x²-x-35x+5
=x(7x-1)-5(7x-1)
=(7x-1)(x-5)
State the cardinality of the set.
The set of subsets of {2, 3, 5, 9, 11}
c
ℵ0
32
25
none of these
Answer:
32
Step-by-step explanation:
The given set has 5 elements, meaning it has 2⁵ = 32 subsets.
This means the cardinality of the desired set is 32.
Toby needs to save a minimum of $250. If Toby can save $57 a month, how many months will it take for him to save enough? Select the inequality that represents this situation
Answer:
[tex]250 \leqslant 57m[/tex]
[tex]57m \: \geqslant 250[/tex]
Step-by-step explanation:
Minimum is a word meaning greater than or equal to.
Hope this helps!
If you have anyother question feel free to ask!
[IMC 2014 Q23] A sector of a disc is removed by
making two straight cuts from the circumference
to the centre. The perimeter of the sector has the
same length as the circumference of the original
disc.
What fraction of the area of the disc is removed?
Answer:
Well the IMC 2014 is
IMC 2014 + hMc
please help me I have mistake
Answer:
See below
Step-by-step explanation:
Here is one possible mistake:
Let y= u = ( 2ax^2 +c)^2 expand
4 a^2 x^4 + 4 a x^2 c + c^2
dy/ dx then becomes
16 a^2 x^3 + 8 a x c <====== you have 8 a^2x^3 + 8axc
MAYBE ??
[tex]y = (2ax^2 + c)^2 (bx^2 - cx)^{-1}[/tex]
By the product rule,
[tex]\dfrac{dy}{dx} = \dfrac{d(2ax^2+c)^2}{dx} (bx^2-cx)^{-1} + (2ax^2+c)^2 \dfrac{d(bx^2-cx)^{-1}}{dx}[/tex]
For the first derivative on the right side, let [tex]u=2ax^2+c[/tex]. Then by the chain rule,
[tex]\dfrac{d(2ax^2+c)^2}{dx} = \dfrac{du^2}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = \dfrac{du^2}{du}\dfrac{du}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = 2u \dfrac{du}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = 2(2ax^2+c) \dfrac{d(2ax^2+c)}{dx}[/tex]
and by the power rule, this reduces to
[tex]\dfrac{d(2ax^2+c)^2}{dx} = 2 (2ax^2+c) (4ax) \\\\ ~~~~~~~~~~~~~~~~~~ = 8ax (2ax^2 + c)[/tex]
For the other derivative, let [tex]v = bx^2-cx[/tex]. Then
[tex]\dfrac{d(bx^2-cx)^{-1}}{dx} = \dfrac{dv^{-1}}{dx} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{dv^{-1}}{dv}\dfrac{dv}{dx} \\\\ ~~~~~~~~~~~~~~~~~~~~ = -v^{-2} \dfrac{dv}{dx} \\\\ ~~~~~~~~~~~~~~~~~~~~ = -(bx^2-cx)^{-2}\dfrac{d(bx^2-cx)}{dx}[/tex]
which reduces to
[tex]\dfrac{d(bx^2-cx)^{-1}}{dx} = -(bx^2 - cx)^{-2} (2bx - c)[/tex]
So one expression for the derivative we want is
[tex]\dfrac{dy}{dx} = 8ax (2ax^2 + c) (bx^2-cx)^{-1} - (2ax^2+c)^2 (bx^2 - cx)^{-2} (2bx - c)[/tex]
What is the next term in each of the sequences below?
a) 16, 25, 36,49,
b) 8,27, 64, 125,
Answer:
a). 16, 25, 36, 49, 64
b). ???
Step-by-step explanation:
16 + 9 = 25
25 + 11 = 36
36 + 13 = 49
49 + 15 = 64
I don't think b is possible
There are 5,000 nails in five boxes. The first and second boxes have 2,700 nails altogether. The second and third boxes have 2,000 nails altogether. The third and fourth boxes have 1,800 nails altogether. The fourth and fifth boxes have 1,700 nails altogether. How many nails are in each box?
There are 5,000 nails in five boxes. The first and second boxes have 2,700 nails altogether. The second and third boxes have 2,000 nails altogether. The third and fourth boxes have 1,800 nails altogether. The fourth and fifth boxes have 1,700 nails altogether. How many nails are in each box
Purchases of both small and large boxes total:
two little boxes.
six huge boxes
Two equations must be created with the given data in order to answer the unknowns:
150X + 400Y = 2700 (the price of the boxes and the total number of nails, where X is the small boxes and Y the large boxes)
Y = 3X
Equation one is then changed to equation 2, and variable X is eliminated:
150X + 400 (3X) = 2700
150X + 1200X = 2700 1350X = 2700 X = 2700/1350 X = 2
In order to determine the number of big boxes, equation 2's value of X is finally changed:
Y = 3X
Y = 3
Y = 6
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The product of a number x and 0.28 is 13.44 which equation matches this statement
Answer:
x · 0.28 = 13.44
Equation: X multiplied by 0.28 = 13.44.
How to solve: Divide 13.44 ÷ 0.28 = 48.
Multiply to check. 48 x 0.28 = 13.44.
Give me a crown.
The highest point in a country has an elevation of 14,291 feet. The lowest point in a country is at 508 fest below sea level. How much higher is the highest point then the lowest point?
The highest point is ____ ft. higher than the lowest point
( the answer is not 13,783 )
The highest point is 14799 ft. higher than the lowest point.
How to calculate the value?From the information, the highest point in a country has an elevation of 14,291 feet. The lowest point in a country is at 508 fest below sea level.
The difference between the points will be:
= 14291 - (-508)
= 14291 + 508
= 14799 feet
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Liam bought pizza and wings for $17.58. How much change should Liam receive if he gave the clerk three $10 bills
Answer:
$12.42
Step-by-step explanation:
$10 x 3 = $30.00
$30.00 - 17.58 = $12.42
Which of these rational numbers is a repeating decimal? Type all that apply.
Answer:
- 0.347
2.153
Step-by-step explanation:
Answer:
- 0.347 and 2.153
Hope this helps :)
Explanation below.
Step-by-step explanation:
The lines on top of the decimals tell that the decimal is repeating, and both - 0.347 and 2.153 have lines so they are repeating decimals.
A picture frame is 20 cm long and 30 cm wide. This includes a pink border that is 5
cm wide surrounding the picture itself, as shown below. What is the area of this pink
border in square centimeters?
20 cm
30 cm
The area of the rectangular pink border is of 400 cm².
What is the area of a rectangle?The area of a rectangle of dimensions l and w is given by the multiplication of the dimensions, as follows:
A = lw.
Hence, the total area is given by:
A = 30 x 20 = 600 cm².
The area of the white region is given by:
A = (30 - 2 x 5) x (20 - 2 x 5) = 20 x 100 = 200 cm².
Hence the area of the pink border is:
600 cm² - 200 cm² = 400 cm².
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Solve the following equations.
(x+5)/2 + (x-3)/3 = 3 1/6
.
3(x+5) + 2(x-3) = 6(3(1/6))
3x + 15 + 2x - 6 = 3 X 1
5x + 9 = 3
5x = - 7
x = - 7/5
Write the mixed number 9 3/5 as an improper fraction
===========================================
Explanation:
Use the formula
a & b/c = (a*c + b)/c
So,
9 & 3/5 = (9*5+3)/5 = (45+3)/5 = 48/5
If m∠NOL=54° then m∠FOG=__
30 POINTS...PLEASE HELP ME ASAP
Look for a pattern in the table of values.
X -3 -2 -1 0 1 2
Y 32 16 8 4 2 1
A. Which model (linear, exponential, or quadratic) best describes the data?
B. Write an equation for the function that models the data.
wait a second...............
Martha has 9 feet of red ribbon and 6 feet of green ribbon. How many yards of
ribbon does she have altogether?
Answer:5
Step-by-step explanation:9 ft of red ribbon plus the 6 ft of green ribbon would make 15 feet of ribbon
1ft=3yds
Which mean you would have 5 yards of ribbon.(15 divided by 3=5)
In ANOP, OP = 12, PN = 7, and NO = 10. Which statement about the angles of ANOP
must be true?
Om/N> m/P> m/0
m/0> m/P> m/N
O m/0> m/N > m/P
Om/P> m/0> m/N
Om/P> m/N > m/0
Om/N> m/0> m/P
Submit Answer
Step-by-step explanation:
.............................-
The equation 2x2−6x−9=0 has two solutions.
The solution to the given equation is 3±3√3/2
Solving quadratic equationGiven the quadratic equation below
2x^2−6x−9=0
Solve using the general formula to have:
a = 2
b = -6
c = -9
Substitute
x = -b±√b²-4ac/2a
x = -(-6)±√(-6)²-4(2)(-9)/2(2)
x = 6±√36+72/4
x = 6±√108/4
x = 6±6√3/4
x = 3±3√3/2
Hence the solution to the given equation is 3±3√3/2
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Simplifiy the expression 1/2 cubed - 6 divide √64
Answer:-0.625
Step-by-step explanation:
A student is running a 10-kilometer race. He runs 1 kilometer every 4 minutes. Select the function that describes his distance from the finish line after x minutes. f of x equals one fourth x plus 4 f of x equals negative one tenth x plus 4 f of x equals one tenth x plus 10 f of x equals negative one fourth x plus 10
Answer:
in 40 minutes the man runs 10 kilometer
Answer:
I think its
f(x) = 1/10x + 10
Find the least common denominator (LCD) of 1/2 and 11/12
Answer:
LCD = 12
Step-by-step explanation:
