Answer:
(x + 2)² = 9
x = 1 or - 5
Step-by-step explanation:
x² + 4x - 5 = 0
Solving first using completing the square method
x² + 4x = 5
x² + 4x + (4/2)² = 5 + (4/2)²
x² + 4x + 2² = 5 + 2²
x² + 4x + 4 = 5 + 4
x² + 4x + 4 = 9
Factorise
x² + 2x + 2x + 4 = 9
x(x + 2) + 2(x + 2) = 9
(x + 2)(x + 2) = 9
(x + 2)² = 9
Square root both sides
√(x + 2)² = √9
x + 2 = ± 3
x + 2 = +3
x = 3 - 2
x = 1
x + 2 = -3
x = -3 - 2
x = -5
Hence, x = 1 or - 5
Given f(x) = 5x - 7 and g(x) = x² - 3, find f(f(2)).
Step-by-step explanation:
Given f(x) = 5x - 7 and g(x) = x² - 3, find f(f(2))
What is the area, in square centimeters, of the shape below? Express your answer as a fraction in simplest form.
ZgotDripxx
What's up?
Answer:
a movie about a asian kid and a old man who take a ballon house to the sky. Step-by-step explanation:
David can run at a consistent rate of 8.2 miles per hour. If he has 3 and a half hours to
run, how far will he run if he runs at that rate?
Answer:
David can run 28.7 miles in 3.5 hours.
Step-by-step explanation:
8.2mph × 3.5hours = 28.7miles
good luck, i hope this helps :)
Determine if events A and B are mutually exclusive.
P(A) = 1/4 P(B) = 3/5 P(A or B) = 7/10
A) Not mutually exclusive
B) Mutually exclusive
Answer:
A) Not mutually exclusive
Step-by-step explanation:
Given
[tex]P(A) = \frac{1}{4}[/tex]
[tex]P(B) = \frac{3}{5}[/tex]
[tex]P(A\ or\ B) = \frac{7}{10}[/tex]
Required
Determine if they are mutually exclusive or not
Mutually exclusive are defined by:
[tex]P(A\ or\ B) = P(A) + P(B)[/tex]
So, we have:
[tex]P(A\ or\ B) = \frac{1}{4} + \frac{3}{5}[/tex]
Take LCM
[tex]P(A\ or\ B) = \frac{5+12}{20}[/tex]
[tex]P(A\ or\ B) = \frac{17}{20}[/tex]
By comparing:
[tex]P(A\ or\ B) = \frac{17}{20}[/tex] ---- Calculated
[tex]P(A\ or\ B) = \frac{7}{10}[/tex] ---- Given
We can conclude that A and B are not mutually exclusive because:
[tex]\frac{17}{20} \ne \frac{7}{10}[/tex]
When your doing online and your bestie tells you to not text them because they don't want to get in trouble but then they be texting their online friends all the time and also posting stuff on Twitter.......
Answer:
Oh..Im so sorry that happened, Thats what you call fake friends
Step-by-step explanation:
The function ggg models the number of mosquitoes (in millions of mosquitoes) in a certain area as a function of rainfall (in centimeters) in that area. Which of these statements are true? Choose all answers that apply: Choose all answers that apply: (Choice A) A More rainfall relates to more mosquitoes as long as rainfall is less than 2\text{ cm}2 cm2, start text, space, c, m, end text. (Choice B) B More rainfall relates to more mosquitoes as long as rainfall is more than 2\text{ cm}2 cm2, start text, space, c, m, end text. (Choice C) C When there is no rainfall, there are about 111 million mosquitoes. (Choice D) D When there is no rainfall, there are about 222 million mosquitoes.
Answer:
(Choice A) A More rainfall relates to more mosquitoes, as long as rainfall is less than 2 cm²
Step-by-step explanation:
The given function for the number of mosquitoes, (by analysis of the options) is, g(x) = 4·x - x²
Where;
x = The amount of rainfall
g(x) = The number of mosquitoes in millions
The given function can be expressed as follows;
g(x) = 4·x - x² + 0
The maximum point is given by g'(x) = d(4·x - x²)/dx = 4 - 2·x = 0
At the maximum (turning point), we have;
4 - 2·x = 0
4 = 2·x
x = 4/2 = 2
The level of rainfall that gives the maximum number of mosquitoes is, x = 2 cm²
The number of mosquitoes increases from zero rainfall up to the maximum number of 4 million mosquitoes at 2 cm² rainfall and then decreases to zero as the rainfall increases further more than 2 cm², as shown in the attached graph of the function g(x) that models the number of mosquitoes created with MS Excel
Therefore, the true statement is (Choice A) more rainfall relates to more mosquitoes, as long as (the level of) rainfall is less than (the maximum) 2 cm².
what is 2/5 of 9?
my answer is 18/5 can you simplify improper fractions in this case with these problems or no?
Step-by-step explanation:
2/5 of 9
= 2/5 × 9 = 18/5
18/5 = 3 3/5
3.
In which situation below would you want to use the Explicit Formula instead of the Recursive Formula
a.Find the 4th term when the first term is 7 and the common difference is -2.
b.Find the 7th term when the first term is -1 and the common difference is 10.
c.Find the 7th term when the first term is -1 and the common difference is 10.
d.Find the 11th term when the first term is -3 and the common difference is 4.
Answer:
b
Step-by-step explanation:
An explicit formula for a sequence allows you to find the value of any term in the sequence. ... A recursive formula for a sequence allows you to find the value of the nth term in the sequence if you know the value of the (n-1)th term in the sequence.
The explicit formula will be best used in finding the 7th term when the first term is -1 and the common difference is 10, the correct option is B.
What is a Recursive formula?A recursive formula is used to determine the nth term when (n-1) th term is given in the series.
The Explicit formula is when any term of the sequence has to be determined on the basis of the first term and the common difference.
The recursive formula just requires one operation, while the explicit formula requires multiple operations,
The recursive formula is limited to determining the consecutive terms while the explicit formula can be used to determine any term of the sequence.
The explicit formula will be best used in finding the 7th term when the first term is -1 and the common difference is 10.
To know more about Recursive Formula
https://brainly.com/question/8972906
#SPJ5
Please answer this for me correctly. THANK YOU!!
Answer:
45
Hope this helps!
PLEASE HELP!!!
△AOC~△BOD. Identify the coordinates of D and the scale factor.
A.) D (0, −7 1/12); 2/5
B.) D (0, −1 1/5); 5/2
C.) D (0, −7 1/2); 5/2
D.) D (0, −1 1/5); 2/5
The coordinate of D is [tex](0, -1\frac{1}{5})[/tex] and the scale factor is 2/5.
The correct option is D.) D (0, −1 1/5); 2/5
To determine the coordinates of D, we will first determine the length of /OD/
Consider △AOC and △BOD. They are similar triangles.
From the diagram, we can determine the lengths of the sides of each triangle /OB/ = 2 units, /OA/ = 5 units, /OC/ = 3 units and /OD/ is unknown
Since △AOC is similar △BOD, then we can write that
[tex]\frac{/OB/}{/OA/} = \frac{/OD/}{/OC/}[/tex]
∴ [tex]\frac{2}{5} = \frac{/OD/}{3}[/tex]
[tex]/OD/ \times 5 = 2 \times 3[/tex]
[tex]/OD/ \times 5 = 6[/tex]
Then,
[tex]/OD/ = \frac{6}{5}[/tex]
∴ [tex]/OD/ = 1\frac{1}{5}[/tex]
Hence, the coordinate of D is [tex](0, -1\frac{1}{5})[/tex] since D is on the negative side of the y-axis.
For the scale factor,
Scale factor = [tex]\frac{/OB/}{/OA/}[/tex]
Scale factor = [tex]\frac{2}{5}\\[/tex]
Hence, the scale factor is 2/5
The correct option is D.) D (0, −1 1/5); 2/5
Learn more here: https://brainly.com/question/12180991
Answer:
D(0, −115); 25
8 km
b
17 km
What is the length of the missing leg?
b. 48
C. 36
5. (x+4), (x+12), (x-1) and (x+5) are in proportion. Find the value of x.
b. 12
a. 15
c. 16
d., 20
Answer:
c
Step-by-step explanation:
Expressing the proportion in fractional form , that is
[tex]\frac{x+4}{x+12}[/tex] = [tex]\frac{x-1}{x+5}[/tex] ( cross- multiply )
(x + 4)(x + 5) = (x + 12)(x - 1) ← expand both sides using FOIL
x² + 9x + 20 = x² + 11x - 12 ← subtract x² + 9x from both sides
20 = 2x - 12 ( add 12 to both sides )
32 = 2x ( divide both sides by 2 )
16 = x → c
Find EF in the parallelogram
Answer:
EF = 13
Step-by-step explanation:
Opposite sides of a parallelogram are of equal lengths (properties of a parallelogram)
Therefore,
EF = DG
x + 3 = 2x - 7 (substitution)
Collect like terms
x - 2x = -3 - 7
-x = -10
Divide both sides by -1
x = -10/-1
x = 10
✔️EF = x + 3
Plug in the value of x
EF = 10 + 3
EF = 13
i rlly need help. can someone pls explain this?
Answer:
D
Step-by-step explanation:
the y intercept is the part where the slope touches the y axis (up and down)
Orlando's sports-card collection features players from four teams, as shown in the table below
Answer:D
Step-by-step explanation:
Sorry Ik it’s to late lol
area addition and subtraction
Answer:
is that a question? what is this supposed to mean?
: A box contains 512 grams of cereal. One serving of cereal is 56 grams. How many servings of cereal does the box contain? A. 9 1/4 B. 9 1/8 C. 9 8/56 D. 9 8/512
Answer:
C. 9 8/56
Step-by-step explanation:
According to the scenario, computation of the given data are as follows,
Box contain = 512 grams
One serving = 56 gram
So, we can calculate the number of serving by using following formula,
Number of serving = Box contain ÷ One serving
By putting the value, we get
Number of serving = 512 ÷ 56
= 9.14 or 9 8/56
A restaurant has a patio that is 8 feet wide and 12 feet long. The restaurant owners want to double the area of
the patio by increasing the width and the length by the same distance x. Write and solve an equation. What
are the new dimensions of the patio?
Answer:
12 and 16
Step-by-step explanation: 8+4=12 and 12+4=16 and 16x12=192 and 96x2=192 and 12x8=96
Ak190 has the best answers
Answer:
bhi
Step-by-step explanation:
hf
Answer:
ok
Step-by-step explanation:
Choose only the statements that can be taken from the diagram. Select all that apply
Answer:
Hello! Your answer would be BELOW
Step-by-step explanation:
A)
D)
C)
Hope I helped! Ask me anything if you have more questions! Brainiest plz! Have a nice mourning! Hope you make an 100%! -Amelia♥
Subtract 6 2/5 - 1 1/4. Simplify the answer and write as a mixed number.
Answer:5 3/20
Step-by-step explanation:
6 8/20 0- 1 5/20= 5 3/20
I invest $1,000 at 5% interest that compounds annually. How much will I have in 5 years?
Answer:
$250....................
Please help me!! How do I do this?
Answer:
I think 12 * 12/ 60 = ?
12*12= 144
144/ 60= ?
Answer:
360°
Step-by-step explanation:
I think
1/2 base ×height
1/2×60×12
30×12
=360
The right triangle on the right is a scaled copy of the right triangle on the left.
Identify the scale factor. Express your answer as a whole number or fraction
in simplest form.
15/4
5
Pleaseeee help
Answer:
1.25
Step-by-step explanation:
15 ÷ 4 = 3.75
3.75 ÷ 3 = 1.25
5 ÷ 4 = 1.25
The triangle is scaled by 1.25
One of the legs of a right triangle measures 9 cm and its hypotenuse measures 13 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
9.4
Step-by-step explanation:
Hopefully this explains it well enough, I can go deeper if needed :)
Translate 2 units up and 7 units right.
Answer:
R: 5,3
P: 2, -1
Q: 4, -1
Step-by-step explanation:
Hope this helped
Answer:
See pictures.
Step-by-step explanation:
Move the triangle 2 up, then 7 to the right.
Cal has a collection of 186 toy farm animals which she no longer 2,5 She code
stee them between her 3 young cousins. How many toys do they receive each?
Answer:
62 (I guess, if I understand your text correctly)
Step-by-step explanation:
you mean she did not need her toy farm animals anymore and gives all of them evenly to her 3 younger cousins ?
then it is a very simple division : 186 / 3 = 62
do you not know how to divide ?
186 / 3
you take the number on the right and compare it to the first (most left) digit position on the left side and see, if the right side can divide this left position.
so, in our case, 1 / 3. Is that possible ? no. so, the result is 0, and we keep the leftover from the left side (still this "1").
now we attach the next digit (going from left to right) from the left side : 18
and we compare again - can we divide now this left side by the right side ? in our example 18 / 3. is that possible ? yes ! the result is 6. we attach this result to our previous result (0) and get 06 (or simply 6). and now there is nothing left in our intermediate division (18/3 creates no remainder, it is just straight 6).
so, our leftover on the left side is 0, and we attach the next digit (again, going from left to right) on the left side to the leftover : 06 (or simply 6).
and we compare again - can we divide now this left side by the right side ? in our example 6 / 3. is that possible ? yes ! the result is 2. we attach this result to our previous result (06) and get 062 (or simply 62). and now there is nothing left in our intermediate division (6/3 creates no remainder, it is just straight 2).
so, our leftover on the left side is 0, and we attach the next digit (again, going from left to right) on the left side to the leftover : oh, there are no more digits. we are finished !
and we have calculated just by hand or mind without any calculator that 186/3 = 62
14788962389598
where is the 5
Answer:
The third number from the end :3
Step-by-step explanation:
Hope this helps ^^
A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 16 % are pennies and 30 % are dimes. There are 2 more nickels than pennies. How much money does the bag contain?