Buford should use 7.5 pounds of the 50% corn bag.
How do we solve a system of linear equations from word problems?A system of linear equation is an equation containing two different equations with variables and the coefficient.
From the given information, let:
The weight of the bag containing 50% corn be = xThe weight of the bag containing 90% corn be = ySp, we can a system of a linear equation that says:
x + y = 30
0.5x + 0.9y = 0.8(30)
Using elimination method
x + y = 30
-
x - 1.8y = -48
0 - 0.8y = -18
y = 18/0.8
y = 22.5
From x + y = 30
x = 30 - 22.5
x = 7.5
Therefore, we can conclude that he should use 7.5 pounds of the 50% corn bag.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.
The value of f(–10) = 82
The graph of the function is a parabola.
The graph of the function opens down.
The graph contains the point (20, –8).
The graph contains the point (0, 0).
Answer:
I will assume the equation is supposed to be f(x) = x^2 – 5x + 12 since it is said to be a quadratic equation.
Step-by-step explanation:
See attached graph.
The value of f(–10) = 82 False
f(-10) = (-10)^2 - 5*(-10) + 12
f(-10) = (100) +50 + 12
f(-10) = 162
The graph of the function is a parabola. True
The graph of the function opens down. False
The graph contains the point (20, –8). False
The graph contains the point (0, 0). False
Complete the equations
Answer:
[tex]\boxed{\bf f(x)=4\cdot \left(\cfrac{7}{4}\right)^x}[/tex]
Step-by-step explanation:
In exponential form, a* b^x,
Where, "a" is value of the function when x=0 and "b" is the constant ratio of f(x) for consecutive for integer values of x.
Y-intercept : (0, 4) so, a = 4.
The graph also passes through (1,7), because 0 and 1 are consecutive integer x-values.
[tex]\bf b=\cfrac{7}{4}[/tex]
So therefore, the equation for f(x) is :-
[tex]\bf f(x)=4\cdot \left(\cfrac{7}{4}\right)^x[/tex]
_______________________The function h(x) is a transformation of the square root parent function,
f(x)=√x. What function is h(x)?
-5
5
-5-
h(x)
f(x)
K
I
5
Answer: [tex]h(x)=\sqrt{x+4}[/tex]
Step-by-step explanation:
The graph of h(x) is the graph of f(x) shifted 4 units left.
#5 In *triangle* ABC, AB = 9 and BC = 15. What is the range the possible lengths for CA?
Why?
In a grop of 25 student 6 study art & biology 10 study biology but not art 3 study neither subject given that a randomly selected study art what is the probability the student study art & biology
½ 0r 50% is the probability that the student studies Art and biology.
What is Probability?Probability is a branch of mathematics that deals with the occurrence of a random event . i.e. Probability means possibility.
According to the question,
Total number of students in the group;
n = 25 students
No. of students that study both art and biology;
n(P u Q) = 6
No. of students that study biology but not art;
n(Q u P') = 10
No. of students that study none of the 3 subjects;
n(P' u Q') = 3
So,
No. of students that study only arts is;
n(P n Q') = 25 - 6 - 10 - 3 = 6
Since, n(P u Q) = 6
Therefore by using formula;
n(P) = n(P u Q) + n(P n Q')
n(P) = 6 + 6
n(P) = 12
Hence,
Probability of the students who studies Art and biology is;
P(P n Q) = [tex]\frac{6}{12}[/tex]
P(P n Q) = ½ i.e. 50%
The probability the student study art & biology ½ i.e. 50%.
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Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
Does the point (1, StartRoot 7 EndRoot) lie on the circle shown?
Explain.
Yes, the distance from (–2, 4) to (1, ) is 4 units.
Yes, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units.
No, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is not 4 units.
No, the distance from (–2, 4) to (1, StartRoot 7 EndRoot) is not 4 units.
Yes, the distance from (-2, 0) to (1, √7) is 4 units.
How to Interpret the Equation of a Circle?
We know that the general form of equation of the circle is given by;
(x - h)² + (y - k)² = r²
where;
(h, k) is the coordinate of the center
r is the radius
From the attached image, the radius is equal to the distance between the center and the point (-2,4). Thus, r = 4 and so we have;
(x + 2)² + (y - 0)² = 4²
(x + 2)² + y² = 16
If the distance between the center and the point is equal to the radius of the circle , then the point lies on the circle and the formula to calculate the distance between two points is;
d = √[(y₂ - y₁)² + (x₂ - x₁)²]
At A(-2, 0) and B(1, √7), we have;
d = √[(√7 - 0)² + (1 - (-2))²]
d = 4 units
Therefore we can conclude that the distance from (-2, 0) to (1, √7) is 4 units.
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Carol measured a straw and wrote down how long it was in inches. pete multiplied carol's straw length by and cut a straw to be that many inches long. joe multiplied carol's straw length by and cut a straw to be that many inches long. which straw belongs to whom?
Answer:
pete
Step-by-step explanation:
i think its pete???
Wesley and two of his friends are driving cross country nonstop and have agreed to take turns driving in 7 hour shifts. Each person will drive for one shift, and take two shifts off to rest. If Wesley’s first shift starts at 6:00 am, at what time will Wesley complete his third shift?
At 7:00 am Wesley complete his third shift if Wesley and two of his friends are driving cross country nonstop and have agreed to take turns driving in 7-hour shifts option (C) is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
Wesley and two of his friends are driving cross country nonstop and have agreed to take driving in 7-hour shifts.
Wesley’s first shift starts at 6:00 am
6:00 am = 6h 0m
= 6 + 7
= 13 h = 1:00 PM (Wesley's starts to rest)
Wesley will take a rest for 14 hours (7 + 7)
First shift = 7 + 14 = 21
Second shift = 7 + 14 = 21
Third shift = 7 = 7
= 21 + 21 + 7 = 49
= 49/24 = 2 days + 1 hour
6h + 1h = 7h = 7:00 am
Thus, at 7:00 am Wesley complete his third shift if Wesley and two of his friends are driving cross country nonstop and have agreed to take turns driving in 7-hour shifts option (C) is correct.
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The amount of money that kailyn earns varies directly with the number of hours she works. if she works for 15 hours and makes 146.25, how much will she make in 40 hours.
Answer:
$390
Step-by-step explanation:
The wage rate for Kailyn is ($146.25/15 hours) = $9.75/hour
40 hours would result in:
(40 hours)*($9.75/hour) = $390
Linda purchased a birthday gift from Bed Bath and Beyond for her mother. After applying the
coupon below Linda received a $12.25 discount off her purchase. What was the price of the
gift before and after the discount?
PLS HELP SOLVE !!!
Answer:
Before discount = $61.25
After discount = $49.00
Step-by-step explanation:
Given information:
Discount = $12.25Coupon = 20%The price of the gift before the discount is 100%.
If the $12.25 discount was 20% of the purchase price, then:
⇒ original price (before discount) = (12.25 / 20) × 100 = $61.25
To find the price after the discount, simply subtract the discount from the found original price:
⇒ $61.25 - $12.25 = $49.00
Conclusion
Before discount price = $61.25After discount price = $49.00Question 6 (Yes/No Worth 1 points)
(02.01 LC)
Is the following relation a function?
how to solve this???
[tex]\large\sf{\sqrt{\frac{1+sin\theta}{1-sin\theta}}+\sqrt{\frac{1-sin\theta}{1+sin\theta}}}[/tex]
[tex]\\[/tex]
[tex]\large \sf{=\frac{\left(\sqrt{1+sin\theta}\right)^{2}+\left(\sqrt{1-sin\theta}\right)^{2}}{\sqrt{(1-sin\theta)(1+sin\theta)}}}[/tex]
[tex]\\[/tex]
[tex]\large\sf{=\frac{1-sin\theta+1+sin\theta}{\sqrt{1^{2}-sin^{2}\theta}}}[/tex]
[tex]\\[/tex]
[tex]\large \sf{=\frac{2}{\sqrt{cos^{2}\theta}}}[/tex]
[tex]\\[/tex]
[tex]\large\sf{= \frac{2}{cos\theta}}[/tex]
[tex]\\[/tex]
[tex]\large\sf{= 2sec\theta}[/tex]
[tex]\\[/tex]
[tex]\large\sf{=RHS}[/tex]
Therefore,
[tex]\large\sf\red{\sqrt{\frac{1+sin\theta}{1-sin\theta}}+\sqrt{\frac{1-sin\theta}{1+sin\theta}}=2sec\theta}[/tex]
How would i work this out?
On a map of scale 1:20000 the area of a forest is 50cm^2.On another map the area of the forest is 8cm^2.Find the scale of the second map.
Answer:
The answer is 1: 50000... If you look down here↓:
Step-by-step explanation:
With a scale of 1:20000, a unit length on the map represents a length of 20000. So 1 cm^2 = 1 cm* 1 cm which represents 20000*20000 cm^2 will be = 4*10^8 cm^2.
50 cm^2 represents that 4*50*10^8 cm^2 = 200* 10^8 cm^2.
Now, on the other hand, the map has the same. 200* 10^8 is represented by 8 cm^2. So the scale is sqrt [ 200* 10^8 / 8 ] = sqrt [ 25* 10^8 ] = 5* 10^4 = 50000.
Therefore the scale on the second map is 1: 50000.
Identify the geometric mean of 9 and 9/4.
The geometric mean of 9 and 9/4 will be 9/2 or 4 1/2.
How to calculate the mean?It should be noted that in order to find the geometric mean of the numbers given, give to find the square root and then multiply.
This will be:
= ✓9 × ✓9/4
= 3 × 3/2
= 9/2 = 4 1/2
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_______________ is the value of the best alternative given up when a choice is made.
what is the square root of 10,000,000
Answer:
1000√10or 3162.2776601683795
Step-by-step explanation:
what is the square root of 10,000,000?
√10000000
= √2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5
= √26 x 2 x 56 x 5
= 1000√10
or 3162.2776601683795
Kyla has the number of cherries that Denise has. If Kyla has 46 cherries, how many cherries do they have altogether?
Answer:
92
Step-by-step explanation:
46 + 46 = 92
Mary has 20 flowers in 5 vases. How many flowers are there in every vase?
share 518 in ratio 2:5
please answer fast with the steps
Answer:
148:370
Step-by-step explanation:
2+5=7 parts
518÷7=74
1 part =74
2×74=148
5×74=370
Which equation represents this number sentence?
Three less than one-fifth of a number is 28.
3−15n=28
15n−3=28
(3−15)n=28
(15−3)n=28
The equation that represents this number sentence is 1/5n - 3 = 28
Translating word problemsLet the unknown number be "n". One-fifth of a number is expressed as 1/5n
Three less than one-fifth of a number is expressed as 1/5n - 3
Finally, if three less than one-fifth of a number is equal to 28, then the final expression will be 1/5n - 3 = 28
The equation that represents this number sentence is 1/5n - 3 = 28
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The price of a Year 7 mathematics textbook is $60. The store gives a discount of 20% on the textbook.
You have $50 to spend. Would you be able to buy the textbook? Explain.
Answer:
yes,you can buy the textbook
Step-by-step explanation:
determine discount
60 × 0.2(decimal form of 20%)
=12
apply discount
60-12
=48
50>48✓
Find the value of $x$ that satisfies $\frac{1}{3x-1} = \frac{2}{x+1}$. Can someone please explain this in detail?
The value of x = 3/5 or 0.6 will satisfy the equation given.
What is an Equation ?An equation is a mathematical statement which is formed when two expressions are equated by an equal sign.
It is given that
[tex]\rm \dfrac{1}{3x-1} = \dfrac{2}{x+1}\\[/tex]
It has to be solved and the value of x has to be determined
(x+1) = 2 (3x-1)
x +1 = 6x -2
5x = 3
x = 3/5
Therefore the value of x = 3/5 or 0.6 will satisfy the equation given.
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Solve for y, Look at the picture to help.
Using two triangle concepts, it is found that the solution for y is of y = 70º.
What are the two triangle concepts used in this problem?The sum of the internal angles of a triangle is of 180º.The sum of an angle with it's external angle is also of 180º.Hence:
x + y + 70 = 180.y + 3x - 10 = 180 -> y = 190 - 3x.Then:
x + y + 70 = 180
x + 190 - 3x + 70 = 180.
2x = 80.
x = 40.
Hence:
y = 190 - 3x = 190 - 3(40) = 70º.
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Riley has 51/4 cups of chocolate chips, she needs ¾cup of chocolate chips to make one batch of cookies. how many batches of chocolate-chip cookies can Riley make
Answer:
17 batches
Step-by-step explanation:
51/4 ÷ 3/4 = 51/4 x 4/3
=17
There is a basketball court. A basketball, who never misses takes a random shot at the basket. What is the probability that the ball will go into the basket
Answer:
100% probability or 1/1
Step-by-step explanation:
This is because since the basketball NEVER misses, there is no chance the the ball will not go inside the basket, leaving room for only the ball to GO inside the basket. Hope this helps!! :D
What percent of patients with type-B blood are male? Round your answer to the nearest tenth of a percent.
Answer:
54%
Step-by-step explanation:
To find the probability for a male patient to have B blood, find the number of male patients who do have B blood and divide it by the number of patients with type B.
The number of male and B blood is 99.
The number of patients with B blood is 183.
The probability is 99/183 = 0.54.
The percent is found by multiplying by 100.
0.54*100 = 54%
Select the correct answer.
One tactor of the polynomial 253 - 352 - 35 + 2 is (x - 2). Which expression represents the other factor, or factors, of the polynomial?
OA. (2:2 + 1)
OB. (252 - 5 + 1)
OC. (25 - 1 (s+1)
OD. (25 + 1) (5 - 1)
The expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)
A cubic equation in algebra is a one-variable equation of the form ax3+bx2+cx+d=0 where an is nonzero. The roots of the cubic function defined by the left side of this equation are the solutions to this equation.
Given expression 2x³-3x²-3x+2 whose one of factor is (x-2)
We have to find second factor of given equation
First we will be rational root theorem to given expression so will get following expression:
[tex]\left(x+1\right)\frac{2x^3-3x^2-3x+2}{x+1}[/tex]
So one factor is (x-1) and now simplifying [tex]\frac{2x^3-3x^2-3x+2}{x+1}[/tex] we get 2x² - 5x +2 and the factor of 2x² - 5x +2 will be (2x-1)(x-2)
Hence the expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)
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(This is an Edge question)
Question:
Which expression is equivalent to negative 3 minus 3 times a number minus 1 plus a number.
[tex] - 3 - 3x - 1 + x[/tex]
Answer Choices:
A.
[tex]2x - 4[/tex]
B.
[tex] - 2x + 4[/tex]
C.
[tex] - 2x - 4[/tex]
D.
[tex]4 - 2x[/tex]
I will verify the answer and give Brainlyest for fastest and most accurate answer and 15 pts.
Answer:
The answer is C. -2x -4
Step-by-step explanation:
Your given information.
-3 - 3x - 1 + x
Combine and simplify common numbers/variables.
(-3x + x) + (-3 - 1)
-2x - 4
HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
1. 6 km ≈ 3.73 mi
2. 2.5 L ≈ .66 gal
3. 90 lb ≈ 40.82 kg