Given that,
An equation : [tex]y=x^2+9x+20[/tex]
To find,
The zeros of the above function.
Solution,
To find zero, put y = 0
[tex]x^2+9x+20=0\\\\x^2+5x+4x+20=0\\\\x(x+5)+4(x+5)=0\\\\(x+4)=0\ \text{and}(x+5)=0\\\\x=-4\ \text{and}\ x=-5[/tex]
So, the zeros of the above quadratic equation is -4 and -5.
a piggy bank has $6.95 and contains only nickles and dimes. If there are a total of 91 coins, how many nickles are there
Answer:
There are 43 nickels in the piggy bank.
Step-by-step explanation:
Given that:
Number of coins = 91
Worth of coins = $6.95 = 6.95*100 = 695 cents
Let,
x be the number of nickles
y be the number of dimes
According to given statement;
x+y=91 Eqn 1
5x+10y=695 Eqn 2
Multiplying Eqn 1 by 5
5x+5y = 455 Eqn 3
Subtracting Eqn 3 from Eqn 2
(5x+10y)-(5x+5y)=695-455
5x+10y-5x-5y=240
5y = 240
[tex]\frac{5y}{5}=\frac{240}{5}[/tex]
y = 48
Putting y=48 in Eqn 1
x+48=91
x=91-48
x= 43
Hence,
There are 43 nickels in the piggy bank.
Which ordered pair, when graphed, would not show a function?
(miles per gallon, gallons in tank)
(length of shadows/time of day)
(temperature in F, temperature in C)
O (number of employees, number of hours worked)
Answer: its the last answer I got it right
A mix of 32 quarters and dimes totals $6.35. Find the system of equations that would help you answer the question and then find how many quarters (x) and dimes (y) you would have?
Answer:
21 quarters and 11 dimes = 32 coins
Step-by-step explanation:
x + y = 32
0.25x + 0.10y = 6.35 [take the first equation and make it equal to x]
x = 32 - y [now take this equation and plug it in the above]
0.25 (32-y) + 0.10y = 6.35
8 - 0.25y + 0.10y = 6.35
8 - 0.15y = 6.35 [subtract 8 from both sides]
-0.15y = -1.65 [divide by -0.15 to isolate y]
y = 11 so there are 11 dimes
plug it into the first equation: x + 11 = 32; x = 21 so there are 21 quarters
Advance Algebra Logarithm Task
Assume your friend, Natalie, has $10,000 to invest. Complete the following chart to show how
much she would earn if her money was invested in each of the specified accounts for 10 years.
Frequency of Annual interest Formula with values Amount after 10
compounding
substituted in
years
Quarterly 3.65%
Monthly
3.65%
Continuously
3.6%
rate
Which account would you suggest for Natalie? Continuously
9514 1404 393
Answer:
3.65% monthly
Step-by-step explanation:
The same amount is invested for the same period in all accounts, so we only need to determine the effective annual rate in order to compare the accounts.
For compounding annual rate r n times per year, the effective annual rate is ...
(1 +r/n)^n -1
For the same rate r, larger values of n cause effective rate to be higher. As a consequence, we know that 3.65% compounded quarterly will not have as great a yield as 3.65% compounded monthly. The effective rate for the monthly compounding is ...
(1 +0.0365/12)^12 -1 = 3.712%
The effective rate for continuous compounding is ...
e^r -1
For a continuously compounded rate of 3.6%, the effective annual rate is ...
e^0.036 -1 = 3.666%
This tells us the best yield is in the account bearing 3.65% compounded monthly.
_____
If i is the effective annual rate of interest as computed by the methods above, then the 10-year account balance will be ...
10000×(1 +i)^10
This is the formula used in the spreadsheet to calculate the balances shown.
Please help, will read you with Brainliest. Please check ALL that apply.
Answer:correct answers are:
A.m<JPX=90°
B.XY & JK form right angles
E. JP=KP
F.XY⊥JK
Step-by-step explanation:
hope this helps
In ΔEFG, is it possible for segment GE to measure 4 units?
A. No, because 3 + 5 > 4, 5 + 4 > 3, and 4 + 3 > 5
B. Yes, because 3 + 5 4, 5 + 4 > 3, and 4 + 3 > 5
Answer:
Substitution
Step-by-step explanation:
We essentially have x = 180 and a+b+c = x.
So we are just substituting x for a+b+c
HELP ONLY ANSWER IF YOU ARE TODALLY SURE I WILL GIVE BRAINLEST TO WHOEVER IS RIGHT WORTH 18 POINTS DON'T JUST ANSWER BUT READ IT THEN ASWESR
Which equation can be used to calculate the area of the shaded triangle in the figure below?
A rectangle is shown with a width of 6 ft and a length of 16 ft. There is a diagonal line through the rectangle, and the bottom half is shaded in grey.
1. 2(16 × 6) = 192 square feet
2. 2(16 + 6) = 44 square feet
3. 1 over 2.(16 × 6) = 48 square feet
4. 1 over 2.(6 + 16) = 11 square feet
In Miami, Florida, there is an 80% probability of extreme high winds on a specific day. How was this probability most likely determined
Answer:
80%
Step-by-step explanation:
Since this is an 80% chance we can say that on these days with same conditions, the probability of extreme high winds is 80% of the time in Miami.
answer quickly please Which number is the BASE?
2 = 8
Answer:
The base of the number is 8
a group of hikers is progressing steadily along up uphill trail. the graph shows their elevation
Whenever Jean sees the white streaks left in the sky by an airplane, she excitedly tells her kids it's Buzz Lightyear. One day, her son asked her how fast Buzz could fly. Jean, knowing that Buzz is really an airplane, told him about 500 miles per hour. How many feet per second can Buzz travel? Show your work, friends.
Answer:
The Buzz can travel 733.33 feet per second.
Step-by-step explanation:
An hour has 60 minutes, each of which has 60 seconds. So one hour has 60*60 = 3600 seconds.
The airplane can fly 500 miles per hour. Each mile has 5280 feet. So the plane can fly 500*5280 = 2640000 feet in one hour.
Per second, we have:
[tex]\frac{2640000}{3600} = 733.33[/tex]
The Buzz can travel 733.33 feet per second.
can u pls help me with this question
Answer:
0.12$ , I'm probably wrong lolol
write an equation in point slope form for the line through the given point with the given slope (-4, -3); m=8
Answer:
An equation in point-slope form for the line will be:
[tex]y - (-3) = 8 (x - (-4))[/tex]
Please check the attached line graph also.
Step-by-step explanation:
Given
The point (-4, -3)
The slope m = 8
To determine
Write an equation in point slope form for the line.
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
m is the slope of the line(x₁, y₁) is the pointIn our case,
(x₁, y₁) = (-4, -3)The slope m = 8substituting the values m = 8 and the point (-4, -3)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - (-3) = 8 (x - (-4))[/tex]
Therefore, an equation in point-slope form for the line will be:
[tex]y - (-3) = 8 (x - (-4))[/tex]
Please check the attached line graph also.
what percent is a is b? pls help i need it right away
Answer:
what ???????????????????? repost this question
Valeria's Cupcakes recently sold 3 pumpkin cupcakes and 9 other cupcakes. Considering this data, how many of the next 8 cupcakes sold would you expect to be pumpkin cupcakes?
Answer: 24 Pumpkin cupcakes.
Step-by-step explanation:
We know that:
They recently sold 6 Pumpkin cupcakes and 8 other cupcakes.
Then we can model this with the ratio 6:8
This means that for each 6 Pumpkin cupcakes sold, they also sell 8 of another type of cupcakes.
With this information, if they sell 56
How many solutions does y=−2x−4
y=3x+3 have
Answer:
There is one solution
Answer:
It has one (-1.4,-1.2)
Step-by-step explanation:
I graphed both lines on desmos graphing calculator and they only crossed at one point.
What is the answer to this ? PLEASE HELP I HAVE 3 minutes
Answer:
(2, 4)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 2x
x = -y + 6
Step 2: Solve for y
Substitution
Substitute in x: y = 2(-y + 6)Distribute 2: y = -2y + 12Isolate y terms: 3y = 12Isolate y: y = 4Step 3: Solve for x
Define equation: x = -y + 6Substitute in y: x = -4 + 6Add: x = 2Match the expression to the correct property that is shown.
Question 3 options:
Identity Property of Addition 1.
9+2+(4+3)=9+(2+4)+3
2.
y(xz)=(yx)z
3.
4+3+2=2+4+3
4.
5x ∙ 0=0
5.
-12 + 0 = -12
6.
−110×1=−110
7.
m∙4∙3=4∙m∙3
8.
4(3x+1)=12x+4
Associative Property of Addition
Commutative Property of Addition
Commutative Property of Multiplication
Identity Property of Multiplication
Multiplicative Property of Zero
Associative Property of Multiplication
Distributive Property
Answer:
Step-by-step explanation:
This is a help site, so I'll explain each property and see if you can match them yourself.
Associative property of addition, you can add 3 or more different numbers any which way, the sum will be the same.
Commutative Property of Addition - same as the associative property but with 2 numbers.
Identity Property of Multiplication - Any number multiplied by one is itself
Multiplicative Property of Zero: x * 0 = 0
Associative Property of Multiplication - Same as that of addition, yet with multiplication.
Distributive Property: Factoring Out.
EX: (12 x 15) = 3(4 x 5)
The scholastic assessment test is standardized to be normally distributed with a mean μ=500 and a standard deviation σ=100. What percentage of SAT scores falls
a. between 500 and 600
b. between 400 and 600
c. between 500 and 700
d. between 300 and 700
e. above 600
f. below 300
Answer:
68.27%.
Step-by-step explanation:
Here we have [tex]\mu=500,\sigma=100[/tex]
Let X shows the SAT score. z-score for X=400 is
[tex]z=\frac{X-\mu}{\sigma}=\frac{400-500}{100}= -1[/tex]
z-score for X=600 is
[tex]z=\frac{X-\mu}{\sigma}=\frac{600-500}{100}=1[/tex]
So the proportion of SAT scores falls between 400 and 600 is
[tex]P(400<X<600)=P(-1<z<1)=0.6827[/tex]
hence, required percentage is 68.27%.
one can use the same method to find the% for all other cases as
well.
1. (04.01 LC)
Which unit rate is equivalent to 14 miles per gallon? (1 point)
2 gallons/32 miles
32 miles/2 gallons
3 gallons/42 miles
42 miles/3 gallons
Answer:
42 miles/3 gallons
Step-by-step explanation: Multiplying 14 by 3 and 1 by 3 will give you 42/3, which keeps the unit ratio.
Answer:
42 miles/3 gallons
Step-by-step explanation:
be quick! i will mark the correct one brainliest :)
Two boats leave the same place at the same time. The first boat heads due north at 10 kilometers per hour. The second boat heads due west at 16 kilometers per hour. After 2.5 hours, how fast is the distance between the boats increasing
Answer:
18.87 km/hr
Step-by-step explanation:
First boat is heading North with a speed of 10 km/hr.
Second boat is heading West with a speed of 16 km/hr.
Time for which they move = 2.5 hours
To find:
The speed at which the distance is increasing between the two boats.
Solution:
Let the situation be represented by the attached diagram.
Their initial position is represented by point O from where they move towards point A and point B respectively.
[tex]Distance = Speed \times Time[/tex]
[tex]Distance\ OA = 10 \times 2.5 = 25\ km[/tex]
[tex]Distance\ OB = 16 \times 2.5 = 40\ km[/tex]
We can use Pythagorean Theorem to find the distance AB.
AB is the hypotenuse of the right angled [tex]\triangle AOB[/tex].
According to Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^2 = 25^2 + 40^2\\\Rightarrow AB^2 = 2225^2\\\Rightarrow AB^2 \approx 47.17\ km[/tex]
The speed at which distance is increasing between the two boats is given as:
[tex]\dfrac{47.17}{2.5} \approx 18.87\ km/hr[/tex]
If $600 was placed in a savings account with an interest rate of 0.5%,
find the total amount in the account after 8 years and 3 months (8.25
years)?
I got it wrong so oof
Ms.Heinen's desk is 3 feet by 2 feet. What is the area of her desk?
Answer: The area would be 6 feet
Step-by-step explanation:
To find the area, we multiply the length and width
There are 54 bookshelves in the library
and 3,240 books total.
How many books does
each shelf hold?
Answer:
60
Step-by-step explanation:
Assuming that all 54 shelves hold the same number of books its just a matter of dividing them (or sharing them equally) on each shelf.
3240 / 54 = 60
Each shelf holds 60 books.
plz answer my question
Are the equations y – 5 = 2(x – 1)and y - 3 = 2(x + 3) the same equation? Explain
Answer:
No.
Step-by-step explanation:
y - 5 = 2(x - 1)
y = 2x + 3
y - 3 = 2(x + 3)
y = 2x + 9
The concept of hope is nothing more than giving up. A word that holds no true meaning.
Answer:
lol fr
Step-by-step explanation:
Answer:
Big pp
Step-by-step explanation:
What is a point-slope equation of the line with slope -12 that goes through the point (5, 3)?
A. y- 3 = -12(x - 5)
B. y + 3 = 12(x + 5)
C. y + 3 =-12(x + 5)
D.y-3 = 12(x - 5)
Answer:
A. y- 3 = -12(x - 5)
Step-by-step explanation:
Megan picked 15 blueberries on Monday, 35 on Tuesday, and 55 on Wednesday. Based on the pattern, how many blueberries will she pick on Thursday?