Answer: a) [tex]x=\dfrac{-9 \pm\sqrt{113} }{8}[/tex]
b) x₁ = - 14; x₂ = 6.
Step-by-step explanation:
a) 4x² + 9x - 2 = 0
[tex]x=\dfrac{-b \pm \sqrt{b^{2}-4ac } }{2a} \\\\a=4; \: \: b=9; \: \: c=-2\\x =\dfrac{-9 \pm \sqrt{9^{2}-4 \cdot 4 \cdot (-2) } }{2 \cdot 4} =\dfrac{-9 \pm\sqrt{113} }{8}[/tex]
b) x² + 8x - 84 = 0
[tex]x=\dfrac{-b \pm \sqrt{b^{2}-4ac } }{2a} \\\\a=1; \: \: b=8; \: \: c=-84\\\\x =\dfrac{-8 \pm \sqrt{8^{2}-4 \cdot 1 \cdot (-84) } }{2 \cdot 1} =\dfrac{-8 \pm\sqrt{400} }{2}=\dfrac{-8 \pm 20}{2} =-4 \pm 10\\\\x_{1} =-14\\x_{2} =6[/tex]
You rent an apartment that costs $1400 per month during the first year, but the rent
is set to go up $180 per year. What would be the monthly rent during the 5th year of
living in the apartment?
The rent in the 5th year is $2120.
What is Arithmetic?The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations. We can find the amount regularly increasing by using arithmetic.
As per the given data:
Cost of the apartment per month during the first year is given, also the increase in rent every year is given.
We have to find out the monthly rent during the 5th year of living in the apartment.
For finding out the monthly rent during the 5th year of living in the apartment:
Rent in first year + Increase in rent in each year × (5 - 1)
= 1400 + 180 × 4
= 1400 + 720
= $2120
The rent in the 5th year is $2120.
Hence, The rent in the 5th year is $2120.
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The coach mixes 15 scoops of powder with 2 gallons of water to make a sports drink for his team How many scoops of powder does the coach need to mix with 10 gallons of water
find the 19th term of the arithmetic sequence d=5 a1=2
Answer:
92
Step-by-step explanation:
nth term = a₁ + (n - 1)d
19th term = 2 + (19 - 1) * 5
= 2 + 18*5
= 2 + 90
= 92
can you help me please
The price of bananas can be determined by the equation P=0.25n, where P is the price and n is the number of bananas. What is the constant of proportionality (unit rate)?
Given:
The price of bananas can be determined by the equation P=0.25n, where P is the price and n is the number of bananas.
To find:
The constant of proportionality
Solution:
We have,
[tex]P=0.25n[/tex] ...(i)
where P is the price and n is the number of bananas.
Price P is directly proportional to the number of bananas. So,
[tex]P\propto n[/tex]
[tex]P=kn[/tex] ...(ii)
Where, k is the constant of proportionality.
On comparing (i) and (ii), we get
[tex]k=0.25[/tex]
Therefore, the constant of proportionality is 0.25.
Which of the following measurements, in centimeters (cm), could be the lengths of the sides of a triangle? Select all that apply
3 cm, 4 cm, 5 cm
4 cm, 10 cm, 14 cm
D5 cm, 11 cm, 15 cm
O 6 cm, 6 cm, 13 cm
7 cm, 4 cm, 12 cm
8 cm, 10 cm, 17 cm
I WILL GIVE BRAINLIST
Frank, Grey, Hala, and Inez will ride in the same car on the field trip. Three of the children will sit in the back seat of the car. What are the 4 possible combinations of three children? Use the abbreviations F, G, H, and I in your list. (Hint: The order of the children does not matter.)
Answer:
(FGH ; FGI ; GHI ; HIF)
Step-by-step explanation:
Frank, = F
Grey = G
Hala = H
Inez = I
3 children sitting in the back seat :
Using combination formula :
4C3
nCr = n! /(n-r)! r!
4C3 = 4! / 1! 3!
4C3 = 4 / 1 = 4
The 4 Possible combinations are :
(FGH ; FGI ; GHI ; HIF)
3. Find the value of a and b when
5+√6/5-√6 = a+b√6
The answer for A is,
[tex]a = 5 + \frac{ \sqrt{6} }{ \sqrt{5} } - \sqrt{6} - \sqrt{6b} [/tex]
And the answer for B is,
[tex]b = - 1 + \frac{5 + \frac{ \sqrt{6} }{ \sqrt{5} } - a }{ \sqrt{6} } [/tex]
hope it helps.
sorry of its wrong.
What is the Area of 28in circle rounded to the nearest hundred
Answer:
The circumference is similar to the perimeter in that it is the total length needed to draw the circle.
We note the circumference as c.
c = 2πr
or
c = πd
This depends on whether or not you know the radius (r) or the diameter (d)
Let’s calculate one manually, for example.
If r = 6 cm, then the circumference is c = 2π(6) = 12π cm, if writing in terms of π. If you prefer a numerical value, the answer rounded to the nearest tenth is 37.7 cm.
Suppose you only know the diameter? If the diameter is 8 cm, then the circumference is c = π(8) = 8π or 25.1 cm, rounded to the nearest tenth.
Step-by-step explanation:
Michelle compares 5.8 x 106and 2.32 x 107. What steps could she use to compare the two numbers?
Answer:
5.8 × 10^(6) is greater.
Step-by-step explanation:
The 2 numbers she wants to compare are;
5.8 × 10^(6) and 2.32 x 10^(7)
Now,for her to compare easily both numbers will need to have the same powers of 10.
To this effect, let's convert the power of ten of the second number to the power of 6.
We will divide by 10 to get it.
Thus; 2.32 x 10^(7) ÷ 10 = 0.232 × 10^(6)
Comparing 0.232 × 10^(6) to 5.8 × 10^(6), we can see that they have same power of 10 but the greater number that precedes the power of 10 is 5.8.
Thus, 5.8 × 10^(6) is greater.
Margo is practicing her free throws for basketball
tryouts. To make the team she has to make at least
80% of her free throws. How many free throws does
she have to make if she attempts 20 shots?
Answer:
16
Step-by-step explanation:
Well if you think about it, if she has a total of 10 attempts she has to make 8 of them to make it on the team. Now the total attempts is double so we double the number of throws she needs to make in order to make the team so to do this we would do 8*2 which is 16. She needs to make 16 throws to make it on the team.
What does
-$10 +$8 +$5 -$4
=
Answer:
It would equal 19 dollars
Step-by-step explanation:
Solve 3x - 5 = 16
Write your solution starting with x= .
Answer:
x = 7
Step-by-step explanation:
3x - 5 = 16
3x = 16 + 5
3x = 21
x = 21/3
x = 7
5
Which expressions are equivalent? Select all that apply.
A 3(x + 2) + 4x and 7x + 6
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B 2(x + 3) + 2x and 4x + 3
C -2 + 4(x + 3) and 4x + 10
D 3x + 5(x-1) and 8x-5
E
5x - 2(x + 4) and 3x + 8
F
4 - 5(x + 2) and 5x-6
Answer:
A
Step-by-step explanation:
3(x+2)+4x=3x+6+4x=7x+6
I need help answering b
The diagram should help
solve for 2/3(9 - 6) + 40
and 7/8 - (-1/10) + (-3/5)
Answer:
first one is 42
second one is 3/8
Step-by-step explanation:
Please helpppp will give brainliest
Answer: B it seems like
Answer:
A
Step-by-step explanation:
We can see that the y intercept is equal to 1
which means that we have the following equation
mx+1=y
We just need to solve for m at this point
We can use the ordered pair (-2,2) to help
We know that
-2m+1=2
Solve for m
-2m=1
m= -1/2
Put this together and we get
-1/2m+1=y which is A
Please Help Me I don’t understand
Answer:
The answer is 35 and here is why!
Step-by-step explanation:
It is because, m = 10
So, therefore 3.5m = 3.5*m = 3.5 * 10
Therefore, answer is 35.
Hope this helps.
The circumference of a circle is 8.85cm.
Find the length of the diameter.
Give your answer rounded to 2 DP
Answer:
The formula for finding the Circumference of a circle is: C = πd where d represents the diameter of the circle. The formula may also be written: C = 2πr where r is the radius of the circle. Example 1: The diameter of a circle is 16 cm.
Step-by-step explanation:
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brainliest
2.82
The angle of elevation from a boat to the top of a lighthouse is 50°.
If the boat is 150 feet from the base of the lighthouse, how tall is the lighthouse?
Round answer to the nearest foot.
9514 1404 393
Answer:
179 ft
Step-by-step explanation:
The applicable trig relation is ...
Tan = Opposite/Adjacent.
The height of the lighthouse is the opposite side of the right triangle. The adjacent side to the angle of elevation from the boat is the distance to the lighthouse base. Then ...
tan(50°) = height/(150 ft)
height = (150 ft)(tan(50°)) ≈ 178.76 ft
The height of the lighthouse is about 179 feet.
Hellllppp meee please due in 10 mins
Answer:
-3/2
Step-by-step explanation:
3/5 x 11 .................
Answer:
=6 3/5 or 33/5
Step-by-step explanation:
3/5 * 11
33/5
= 6 3/5
Step-by-step explanation:
[tex]{ \large{ \red{ ➠ \: \: \bf{ \frac{3}{5} \times 11}}}} \\ [/tex]
[tex]{ \large{ \blue{ ➠ \: \: \bf \frac{33}{5} }}}[/tex]
[tex]{ \large{ \green{ \therefore{ \boxed{ \bf6 \frac{3}{5} }} \: \: Ans}}}[/tex]
Lauren invests money in an account paying simple interest. She invests $50 and no money is added or removed from the investment. After one year, she has $50.50. What is the simple percent interest per year?
Based on the amount invested and the amount it grew to, the simple interest rate is 1%.
Lauren invested $50 and got $50.50 after a year.
What is the Simple Interest rate?This rate can be found by the formula:
= (Difference in investment in year 1) / Amount invested x 100%
Solving gives:
= (50.50 - 50) / 50 x 100%
= 1%
In conclusion, the rate is 1%.
Find out more about simple interest at https://brainly.com/question/2294792.
A 5-pint bottle of oil costs $9.20. What is the unit price for 1 pint of oil?
Answer:
$3.20, help this helps. lmk if it doesn't help
Answer:
$1.84
why do I have to write 20 characters
The ice cream vendor ‘s cold box holds 24 ice cream cups. The freezer has 8 cases of ice cream each with 48 cups. How many trips to the freezer will the vendor make if he sells all the ice cream? I have more for my brother.
Answer:
16
Step-by-step explanation:
24/8=3
48/3=16
Jordan's dog weights p pounds. Emmett's dog weighs 50% more than Jordan's dog.
Which expressions represent the weight, in pounds, of Emmett's dog?
the expression fir the weight of Emmett's dog is 1.25p
Step-by-step explanation:
The weight of Jordan's dog is p pounds.
And it has been given that Emmett's dog weighs 25% more than Jordan's dog.
Hence, 25% of weight of Jordan's dog is
25% of p
= 0.25p
Now, since, Emmett's dog weighs 25% more than Jordan's dog.
Hence, the weight of Emmett's dog is given by
Weight of Jordan's dog + 25% of weight of Jordan's dog
= p + 0.25p
=1.25 p
Therefore, the expression fir the weight of Emmett's dog is 1.25p
Draw the number line to represent.
Whole numbers which can divisible by 2 and 4 between 28 and 48.
Answer:
Mas não reconhecida como a face da sua vida
11 + 22x = 9 + 30x
(Please provide the steps to complete the equation)
Answer:
x = 4
PLS LOOK AT THE PIC I HAVE SENT YOU, HOPE THIS WILL HELP YOU!
Answer:
x = 1/4
Step-by-step explanation:
11 + 22x = 9 + 30x
subtract 22x from both sides
11 = 9 + 8x
subtract 9 from both sides
2 = 8x
divide both sides by 8
2/8 = x
simplify
1/4 = x
Plz help I don’t understand.
Determine whether the sequence is arithmetic. If yes, identify the common difference and give the next three terms.
( -3, -12, -48, -192, ...)
Answer:
I do my love a ti love
Step-by-step explanation:
coroneta
Answer:
The sequence is a Gp
Each term can be gotten from multiplying the common difference (4)
Next three terms
(-192×4)= - 768
(-768×4)= - 3172
(-3172×4)= - 12688
PLEASE HELP ME!!!!!!!!!
Answer:
1. Complementary
2 Supplementary
Hope this helped!
Answer:
Angles that add up to 90: Complementary
Angles that add up to 180 degrees: Supplementary
Step-by-step explanation: