Step-by-step explanation:
2x²+3x=20
2x²+3x=20
(√2x)²+2(√2x)(3/2√2)+(3/2√2)²-(3/2√2)²=20
(√2x+3/2√2)²=20+9/8
(√2x+3/2√2)²= 169/8
(√2x+3/2√2)= ±13/2√2
√2x=10/2√2 or -16/2√2
x= 10/4 or -16/4
x= 5/2 or -4
wildflower mix contains several different types of seeds.
cornflower 40
primrose 3
black-eyed Susan 2
poppy 6
baby's breath 12
What is the probability that a randomly selected seed will be a poppy seed?
Which set of steps can be used to prove the sine sum identity, sin(x y) = sin(x)cos(y) cos(x)sin(y)?.
The trigonometry identity sin(x + y) = sinx cosy + cosx siny.
What is sin(x + y) identity in trigonometry?sin(x + y) is one of the identities in trigonometry for compound angles.
The angle (x + y) represents the compound angles.
sin(x + y) = sinx cosy + cosx siny
To prove
sin(x + y) = sinx cosy + cosx siny
Consider OX as a rotating line anti-clockwise. Let angle XOY = a
the making of an acute angle b the rotation in the same direction is
angleYOZ = b , angle XOZ = a + b
From triangle PTR,
∠TPR = 90 - ∠PRT , ∠ROX = a
From the right-angled triangle PQO
sin(a + b) = PQ/OP
= (PT + TQ) / OP
= PT/OP + TQ/OP
= PT/PR × PR/OP + RS/OR × OR/OP
= cos (∠TPR ) sinb + sina cosb
= sina cosb + cosa sinb
if we replace a=x and b=y
Therefore, sin(x + y) = sinx cosy + cosx siny.
Learn more about trigonometry identity;
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Ralph plotted the points (-4, 1) and (-4,-1) on a coordinate grid. What is the distance,
in units, between the points Ralph plotted?
a 1
B -2
C 2
D 0
A spinner contains four sections: red, blue, green, and yellow. Joaquin spins the spinner twice. The set of outcomes is given as S = {RB, RG, RY, RR, BR, BG, BY, BB, GR, GB, GY, GG, YR, YB, YG, YY}. If the random variable is "yellow (Y)," which of the following is the correct probability distribution? A 2-column table has 3 rows. The first column is labeled Yellow: x with entries 0, 1, 2. The second column is labeled Probability with entries 0. 5625, 0. 375, 0. 625. A 2-column table has 3 rows. The first column is labeled Yellow: x with entries 0, 1, 2. The second column is labeled Probability with entries 0. 75, 0. 25, 0. A 2-column table has 3 rows. The first column is labeled Yellow: x with entries 0, 1, 2. The second column is labeled Probability with entries 0. 5, 0. 375, 0. 125. A 2-column table has 3 rows. The first column is labeled Yellow: x with entries 0, 1, 2. The second column is labeled Probability with entries 0. 5, 0. 25, 0. 25.
The correct probability distribution of the random variable tracking "yellow (Y)" color is given by: Option A:
Yellow:x Probability
0 9/16 = 0.5625
1 6/16 = 0.375
2 1/16 = 0.0625
What is probability distribution?Probability distribution of a random variable is the collection of value and its probability pair for values of that considered random variable.
It might be a function, a table etc.
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
For this case, the experiment consists of a spinner with four color sections, and is spun twice.
The sample space is:
S = {RB, RG, RY, RR, BR, BG, BY, BB, GR, GB, GY, GG, YR, YB, YG, YY}
Let we take:
X = the number of times out of two spins the color yellow occurs in a pair of spin of the considered spinner.
Then, as there are only two spin going to happen, so the values X can take are:
X = 0 (no yellow color in both spin)X = 1 (one of the spin ended up yellow, and other doesn't)X = 2 (both the spins resulted in yellow color).Let we take:
A = event that in first spin of the considered spinner, color yellow occurs.B = event that in second spin of the considered spinner, color yellow occurs.Then, as there are four colors equally likely, so we get:
P(A) = 1/4 (yellow color can occur in 1 way in one spin, and total number of colors that can occur = 4).
Similarly, we get P(B) = 1/4
Also, as first and second spins are independent of each other's result, so both A and B are independent events.
Getting the probabilities for each value of X:
Case 1: X = 0[tex]P(X = 0) = P(A' \cap B') = P(A')P(B') = (1-P(A))(1-P(B)) \\P(X = 0) = \dfrac{3}{4} \times \dfrac{3}{4}\\\\P(X = 0) = \dfrac{9}{16}[/tex]
(where A' and B' are complement of A and B, and as (A and B) are independent, so as (A' and B') and (A' and B) and (A and B') )
Case 2: X = 1So either first spin had yellow color, or second, so we get:
[tex]P(X = 1) = P((A' \cap B) \cup (A \cap B'))\\ P(X=1) = P(A' \cap B) + P(A \cap B') - P((A' \cap B) \cap (A \cap B'))\\P(X=1) = P(A')P(B) + P(A)P(B') -0\\P(X=1) = \dfrac{3}{4} \times \dfrac{1}{4} + \dfrac{1}{4} \times \dfrac{3}{4} - 0\\\\P(X = 1) = \dfrac{6}{16}[/tex]
Case 3: X = 2Both event A and B occured this time, so we get:
[tex]P(X = 2) = P(A \cap B) = P(A)P(B) \\P(X = 0) = \dfrac{1}{4} \times \dfrac{1}{4}\\\\P(X = 0) = \dfrac{1}{16}[/tex]
Thus, the probability distribution of X is:
X=x P(X = x)
0 9/16 = 0.5625
1 6/16 = 0.375
2 1/16 = 0.0625
Learn more about probability here:
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Help plsss thankss
what do the coefficients of a quadratic function in standard form reveal about its graph?
Answer:
The coefficient of the quadratic term ,a,determines how wide or narrow the graphs are, and
weather the graph turns upward or downward
Step-by-step explanation:
this is your answer
Write another example that would use the same properties for each step
Answer:
I'm sorry but there isn't really any question to be answered
Please help i need quick answers
We see that 24 is split into 8q.
Therefore 8q equals 24 --> 8q = 24 --> q = 24/8 = 3.
So q = 3.
Hope it helped!
Please help and explain 15 points
Write an equation of a circle with the given center and radius center (3,4) and radius 6
A.) (x-3)^2 + (y-4)^2 = 36
B.) (x-3)^2 + (y-4)^2 = 6
C.) (x-3)^2 + (y-4)^2 =36
D.) (x+3)^2 + (y-4)^2 = 6
Answer:
a
Step-by-step explanation:
General equation of a circle : [tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h,k) is at center and r = radius
Here, we want to find the equation of a circle with a given center at (3,4) and a given radius of 6
This is very simple, all we have to do is assign variables and then plug in the values of the variables into the general equation of a circle
First lets assign variables.
(h,k) is center and the circle has a given center at (3,4)
so (h,k) = (3,4) thus, h = 3 and k = 4
r = radius and the circle has a given radius of 6 so r = 6
now we plug this into the general equation of a circle.
recall equation : (x-h)² + (y-k)² = r²
h = 3, k = 4 and r = 6
plug in values
(x-3)² + (y-4)² = 6²
simplify exponent
(x-3)² + (y-4)² = 36
and we are done!
The answer is A
Which expressions are aquivalent to j + j + 2k ?
Choose all answers that apply:
A 2jk
B 2(j+j+k0
C None of the above
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's see ~
[tex]\qquad \sf \dashrightarrow \:j + j + 2k[/tex]
[tex]\qquad \sf \dashrightarrow \:2j + 2k[/tex]
[tex]\qquad \sf \dashrightarrow \:2(j + k)[/tex]
・．━━━━━━━━━━†━━━━━━━━━━━━．・
PLEASE HELP ME!!!!!!!
Answer:
10 hours
Step-by-step explanation:
multiply b 2 then divided the miles and time and add to the total to get the time and miles you need
write 45920 in word form
Answer:
forty five thousand and nine hundreds twenty
Step-by-step explanation:
1. a) Solve the following quadratic-quadratic system of equations graphically.
y– 3x² +12x = 16
y + 4x²– 16x = -12
b.) GRAPH
c.) verify your solution (s) algebraically.
Answer:
see explanation
Step-by-step explanation:
look at the photo
HELP ASAP PLEASE NO LINKS
Jason researched the number of women and men enrolled in colleges in the United States.
. MO - 0.081 +6.18 represents the number of men enrolled, in millions
• WO) - 0.21 +4.93 represents the number of women enrolled, in millions
. t represents the number of years after 1975.
Which expression represents how many more women than men (in millions) were enrolled in colleges in the United States in 2001?
A) 0.39(2001) + 11.11
B 0.39(26) +11.11
(C
0.13(2001) - 1.25
D
0.13(26) - 1.25
Answer:
C
Step-by-step explanation:
0.081+6.18 =6.261
0.21+4.93 =5.14
6.261 - 5.14 = 0.13
If the sum of the 8th & 9th terms of an arithmetic progression is 72 and the 4th term is -6. Find the common difference.
Answer:
Correct Answer: Option D
Step-by-step explanation:
9 1/3
hope that helps
please help!!!!!!!11
Answer:
a = 6 , b = 5
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]
then
[tex]\sqrt{180}[/tex]
= [tex]\sqrt{36(5)}[/tex]
= [tex]\sqrt{36}[/tex] × [tex]\sqrt{5}[/tex]
= 6[tex]\sqrt{5}[/tex]
with a = 6 and b = 5
for every 1/2 cup portion of baby cereal you will need 4 oz of milk. how many ounces of milk will you need to prepare 20 portions
Answer:
80 oz
Step-by-step explanation:
20 portions times 4 oz is 80 oz
A teenager puts $50 into an investment account in January. If by December the balance in the account increases by 17%, what is the amount of money in the account in December?
A.$67.00
B.$58.50
C.$41.50
D.$33.00
Answer:
58.50
Step-by-step explanation:
C.$58.50
|| ▼ Answer ▼ ||
|| ✪ Solution ✪ ||
Step 1:
In this question, we are given the following:
A teenager puts $50 into an investment account in January.
If by December the balance in the account increases by 17%,
what is the amount of money in the account in December?
Step 2:
In this case, we are going to use:
[tex]Amount=Principal~(~1+\frac{Rate}{100})^{n}[/tex]
Here, Principal = $ [tex]50[/tex]
Rate = 17%
[tex]^{n}(Time)=~From~January~to~December=12=months=1~year[/tex]
Then, we have that:
[tex]Amount=50~(~1+\frac{17}{100})^{1}[/tex]
[tex]Amount=50~(~1+0.17~)^{1}[/tex]
[tex]Amount=50~(~1.17)[/tex]
[tex]Amount=[/tex] $ 58.50 (Option B)
CONCLUSION:
The amount of money in the account in December = $ 58. 50 ( OPTION B )
Hope this helps!
If you have any queries please ask.
plllsss hhhheelllppp mee pllllsss
Answer:
The theoretical probability states that it should be equal. That is should be 50/50 but the experimental results show that the coin favoured heads.
MATH MIDDLE SCHOOL ASAP due in 10 mins no explaining to do just answer thank you giving brainlist :)
Answer:
y-9=8
Step-by-step explanation:
Write the log equation as an exponential equation. You do not need to solve for x.
log 5 (5) = 3x
Answer:
[tex]5=5^{3x}[/tex]
Step-by-step explanation:
[tex]log_5(5)=3x\\\\5=5^{3x}[/tex]
Find the surface area of the prism.
13 m
5 m
11 m
12 m
The surface area is
(Type a whole number or a decimal.)
The function f(x) is defined below. What is the end behavior of f(x)?
f(x) = x^4– 47x² + x^3– 45x + 450
Answer:
Third option
Step-by-step explanation:
Since our leading coeffeicent has a leading even degree, and a positive number,
The end behavior will as
as x approaches oo, and -oo, f(x) approaches oo.
Frank grows evergreen trees. He grew 535 trees for
the holiday season. In November he sold 215 trees
and in December he sold 275.
a. Write an expression. Then solve.
b. Frank replanted the left over trees with the
addition of 650 more trees. How many trees will
he have for next season?
Answer:
Frank grows 535 trees during holiday season in November sold 215 then dec sold 275535 minus 490 which gives a total of 45 trees left then to find out how many trees he will have next season 650 plus 45 gives 6953647 divided by 6
Show work out
Answer:
607.83333333333......... hope it helps.........
Answer:
607.8
Step-by-step explanation:
just use your calculator 3647 divided by 6 and you get that answer
Two negative integers are 8 units apart on the number line and have a product of 308.
Which equation could be used to determine x, the smaller negative integer?
x2 + 8x – 308 = 0
x2 – 8x + 308 = 0
x2 + 8x + 308 = 0
x2 − 8x − 308 = 0
Answer:
X²-8x+308
Step-by-step explanation:
two negative integers -x and -x= +x²
8units apart=-8x
all equals 308
X²-8x=308
bring everything to the LHS
X²-8x-308=0
If a1= 7 and an = -4an-1 + n then find the value of a5
Answer:
a₅ = 1701
Step-by-step explanation:
[tex]a_1=7\\\\a_n=-4a_{n-1} + n\\\\a_2 = -4*a_1 + 2\\\\[/tex]
= -4*7 + 2
= -28 + 2
= -26
a₃ = -4a₂ + 3
= -4*(-26) + 3
= 104 + 3
= 107
a₄ = -4a₃ + 4
= -4*107 + 4
= -428 + 4
= -424
a₅ = -4a₄ + 5
= -4*(-424) + 5
= 1696 + 5
= 1701
What is the difference?
74 – 26 =
47
48
52
58
48 is the correct answer
Alice has a total of 12 dimes and nickels. She has 2 more nickles than dimes
The total number of nickles that Alice has got for this case is 14. The total amount of money from those nickle and dimes that Alice hold is $1.9
What are nickles, dimes, quarters and cents?A dollar is further divided into some majorly used parts as:
A cent = 100th part of a dollar = $1/100 = $0.01A nickle= 20th part of a dollar = $1/20 = $0.05A dime = 10th part of a dollar = $1/10 = $0.10A quarter = 4th part of a dollar = $1/4 = $0.25How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For this case, we're specified that:
Alice has a total of 12 dimes and nickels.She has 2 more nickles than dimesSuppose that she has got 'x' nickles.
Then, as it is given that she has 2 more nickles than dimes, therefore, we get:
number of nickles = 2 + number of dimes
x = 2 + 12 = 14
Thus, Alice has got 12 dimes and 14 nickles.
1 dime = $0.1 12 dime = [tex]12 \times 0.1 = \$1.2[/tex]Similarly, we have:
1 nickle = $0.0514 dime = [tex]14 \times 0.05 = \$0.7[/tex]Thus, the total amount of money she got is $1.2 + $0.7 = $1.9
Thus, the total number of nickles that Alice has got for this case is 14. The total amount of money from those nickle and dimes that Alice hold is $1.9
Learn more about forming equations here:
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1
* Write an expression that is equivalent to
1/2a - 4
Answer:
a - 8
Step-by-step explanation:
1/2 a - 4
if we scale both numbers by the same factor, we will be creating an equivalent expression.
So, let's say we multiply the equation by 2.
1/2 a (2) = 1 a = a
-4 (2) = -8
One equivalent expression would be
a - 8
[If you want to test this out, try plugging in any number for a. For example, if you plug in 10...
1/2 of 10 = 5, 5 - 4 = 1
1 times 10 = 10, 10 - 8 = 2
These answers are the same scaled as the original equation, the answer for the first expression is multiplied by 2 to get the second expression]
pls help i’ll reward brainliest
Answer:
A. y = 2x + 2
Step-by-step explanation:
For this function....
f(0) = 2
f(1) = 4
f(2) = 6
f(3) = 8
I hope this helps!