Answer:
One pound of jelly beans costs $3.75.
One pound of trail mix costs $1.75.
Step-by-step explanation:
Let [tex]x[/tex] be equal to one pound of jelly beans.
Let [tex]y[/tex] be equal to one pound of trail mix.
1) Form equations
We're given:
7 pounds of jelly beans + 9 pounds of trail mix = $42
⇒ [tex]7x+9y=42[/tex]
5 pounds of jelly beans + 3 pounds of trail mix = $24
⇒ [tex]5x+3y=24[/tex]
Now, we have our two equations:
[tex]\displaystyle\left \{ {{7x+9y=42} \atop {5x+3y=24}} \right.[/tex]
2) Solve for x using elimination
[tex]\displaystyle\left \{ {{7x+9y=42} \atop {5x+3y=24}} \right.[/tex]
Multiply the second equation by 3 to change 3y to 9y:
[tex]5x+3y=24\\3(5x+3y)=3(24)\\15x+9y=72[/tex]
Subtract the first equation from the second to eliminate y:
[tex]15x+9y=72\\- 7x+9y=42\\\rule{2.5cm}{0.4pt}\\8x=30[/tex]
Divide both sides by 8 to isolate x:
[tex]\displaystyle x=\frac{30}{8} \\\\x=3.75[/tex]
Therefore, one pound of jelly beans costs $3.75.
2) Solve for y using substitution
[tex]\displaystyle\left \{ {{7x+9y=42} \atop {5x+3y=24}} \right.[/tex]
Now, we know that x=3.75. Plug this value into one of the equations and solve for y:
[tex]5x+3y=24\\5(3.75)+3y=24\\18.75+3y=24\\3y=24-18.75\\3y=5.25\\\\\displaystyley=\frac{5.25}{3} \\\\y=1.75[/tex]
Therefore, one pound of trail mix costs $1.75.
I hope this helps!
Find the value of x
Answer:
[tex]sum \: of \: exterir \: anges \: for \: a \: polygon = 360 \\ 5x - 5 + x + 4x - 5 + 4x + 20 = 360 \\ x \: terms \: togather \\ 5x + x + 4x + 4x - 5 - 5 + 20 = 360 \\ 14x + 10 = 360 \\ 14x = 360 - 10 \\ 14x = 350 \\ x = \frac{350}{14} = 25 \\ x = 25 \\ thank \: you[/tex]
Answer:
SUM OF EXTERIOR ANGLES=360
Step-by-step explanation:
5x-5+4x-5+4x+20+x=360
14x+10=360
14x=350
x=350/14
x=25
Sin theta = 3/4, what are the values of cos theta and tan theta?
Answer:
[tex]\displaystyle \cos(\theta) = \frac{\sqrt{7}}{4}[/tex].
[tex]\displaystyle \tan(\theta) = \frac{3\sqrt{7}}{7}[/tex].
Step-by-step explanation:
By the Pythagorean identity, for any given angle [tex]\theta[/tex], [tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex].
Given that [tex]\displaystyle \sin(\theta) = 3/4[/tex], solve this equation for [tex]\cos(\theta)[/tex].
[tex](\sin(\theta))^{2} + (\cos(\theta))^{2} = 1[/tex].
[tex]\displaystyle \left(\frac{3}{4}\right)^{2} + (\cos(\theta))^{2} = 1[/tex].
[tex]\begin{aligned} \cos(\theta) &= \sqrt{1 - \frac{9}{16}} \\ &= \sqrt{\frac{7}{16}} \\ &= \frac{\sqrt{7}}{4} \end{aligned}[/tex].
The tangent of an angle is equal to the ratio between the sine and cosine of that angle. In this question:
[tex]\begin{aligned} \tan(\theta) &= \frac{\sin(\theta)}{\cos(\theta)} \\ &= \frac{3/4}{\sqrt{7}/4} \\ &= \frac{3}{\sqrt{7}} \\ &= \frac{3\sqrt{7}}{7}\end{aligned}[/tex].
$8,375.79 to the nearest thousand
Answer:
$8,000
Step-by-step explanation:
8,375.79 < 8,500 so it will round to 8,000
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If 1 pounds = 4 cups then 2 cups = ?
PLEASE HELP I AM STUCK
Answer:
1/2 pound
Step-by-step explanation:
Answer:
2 cups is equal to 0.5 pounds.
Step-by-step explanation:
4 divided by 2 is 2 and 1 pound divided by 2 is 0.5.
James is selling a bike on an internet auction website. he pays £1.45 insertion fee, £2.85 for an enhanced advert and a selling fee of £1.95 when the bike is sold. what are his total selling fees to the nearest pound (£)
Hello :D
£1.45 + £2.85 = £4.30
£4.30 + £1.95 = £6.25
£6.25 to the nearest pound = £6.00
Answer: Selling fees = £6 (rounded to the nearest pound)
Step-by-step explanation:
Given information
Insertion fee = £1.45
Enhanced advert = £2.85
Selling fee = £1.95
Given expression deducted from the given information
Total = insertion + enhanced advert + selling
Substitute values into the expression
Total = (1.45) + (2.85) + (1.95)
Simplify by addition
Total = 4.3 + (1.95)
Total = 6.25
[tex]\boxed{Total=6}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
what is the location of the circumcenter of triangle abc
Step-by-step explanation:
The circumcenter is the centre of the circumcircle. All the vertices of a triangle are equidistant from the circumcenter.In an acute-angled triangle, circumcenter lies inside the triangle. In an obtuse-angled triangle, it lies outside of the triangle.
if my answer helps you than mark me as brainliest
Find the inverse of g(x)=2x-3
Answer:
g^-1(x)=x/2+3/2
Step-by-step explanation:
Find the perimeter of this figure.
14 m
12 m
18 m
6 m
[? ] = meters
Answer:
The perimeter of it is going to be 50
Step-by-step explanation:
This is because when finding the perimeter you add up all the sides so
14 + 12 + 18 + 6 = 50
Answer:
50 m
Step-by-step explanation:
Perimeter
= Sum of the length of all sides
= 14 m + 12 m + 6 m + 18 m
= 50 m
Write 4 3/7 as a decimal.
Enter your answer as a decimal rounded to the nearest hundredth
Please help, and answer quickly please
Answer:
4.3
Step-by-step explanation:
17. Given f(x) = 3x - 1, find f(2)
Answer:
5
Step-by-step explanation:
you have to replace 2 were there's x in the function
f(2)=3(2)-1
=6-1
=5
I hope this helps
(PLEASE EXPLAIN HOW YOU GOT THE ANSWER) Which inequalities are true? Select the four correct answers.
0 less-than StartRoot 8 EndRoot
StartRoot 8 EndRoot less-than 3
StartRoot 8 EndRoot greater-than StartRoot 7 EndRoot
StartRoot 8 EndRoot less-than 2
StartRoot 8 EndRoot greater-than 8
1 less-than StartRoot 8 EndRoot
9514 1404 393
Answer:
T, T, F, F, T
Step-by-step explanation:
First of all, it is helpful to know ...
√8 ≈ 2.8284
√7 ≈ 2.6458
Now you can check the inequalities:
0 < √8 < 3 . . . . . . true√8 > √7 . . . . . . . . true√8 < 2 . . . . . false√8 > 8 . . . . . false1 < √8 . . . . . . . . . . true0, 1, 2, and √7 are left of √8 on a number line, so are all less than √8.
3 and 8 are right of √8 on a number line, so are greater than √8.
Answer:
T, T, F, F, T.
Step-by-step explanation:
Person above is correct!!
using 3 discs complete the puzzle. what is the smallest number of moves you can find
Simplify each expression -(20+d)
Answer:
-20 -d
Step-by-step explanation:
-(20+d)
Distribute he minus sign
-20 -d
Find all values of c such that 3^2c+1=28*3^c-9. If you find more than one value of c, then list your values in increasing order
[tex]3^{2c} + 1 = 28\times3^c - 9 \implies 3^{2c} - 28\times3^c = -10[/tex]
Complete the square on the left side:
[tex]3^{2c} - 28\times3^c = \left(3^{2c}-28\times3^c+14^2\right)-14^2 = \left(3^c-14\right)^2 - 196[/tex]
Then the equation becomes
[tex]\left(3^c-14\right)^2 - 196 = -10 \\\\ \left(3^c-14\right)^2 = 186 \\\\ 3^c - 14 = \pm\sqrt{186} \\\\ 3^c = 14\pm\sqrt{186}[/tex]
Both 14 + √186 and 14 - √186 are positive numbers, so we can take the logarithm (base 3) of both sides without issue:
[tex]\log_3\left(3^c) = c = \log_3\left(14\pm\sqrt{186}\right)[/tex]
Then in increasing order, the solutions are
c = log₃(14 - √186), c = log₃(14 + √186)
b. ¿Qué fracción representa el total de sillas ocupadas durante los tres días?
vean la imagen estoy en examen pliss ayudAAAAAAAAAAA
The fraction that represents the total number of seats occupied during the three days is 1.
The total number of seats in the auditorium is 200.
On day 1, 40% of the seats were occupied. So, 40/100 * 200 = 80 seats were occupied on day 1.
On day 2, 35% of the seats were occupied. So, 35/100 * 200 = 70 seats were occupied on day 2.
On day 3, 25% of the seats were occupied. So, 25/100 * 200 = 50 seats were occupied on day 3.
The total number of seats occupied during the three days is 80 + 70 + 50 = 200 seats.
The fraction that represents the total number of seats occupied during the three days is 200/200 = 1.
Here is the solution in mathematical form:
Let x be the fraction that represents the total number of seats occupied during the three days.
Then, x * 200 = 80 + 70 + 50
x = (80 + 70 + 50) / 200
x = 1
Therefore, the answer is 1.
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Round 475,805 to the nearest ten thousand.
475,805 rounded to the nearest ten thousand would be 476,000.
Which of the following collections of subsets of the plane, R2
, are partitions?
(a) {{(x; y) | x + y = c}| c R}
(b) The set of all circles in R2
(c) The set of all circles in R2
centered at the origin together with the set {(0; 0)}
(d) {{(x; y)} | (x; y) R
[tex]\{(x,y) | \ \ x+y = c, \ c \in \mathbb{R}\}[/tex]
Explanation:
The notation for choice A basically says "we have a line of the form x+y = c where c is a real number". Then points on the line in the form (x,y) will form a particular partition. A partition is where we break a set up into non-overlapping subsets and there are no gaps. Think of it like breaking up a house into multiple rooms. Each room is a subset of the house. There are no gaps or overlaps (ignore the regions in the walls).
Take note that if a point is on a line like x+y = 5, then it cannot be on any other line of the form x+y = c, where c is not equal to 5. Something like (x,y) = (2,3) is on x+y = 5 and not on any other line. If c is allowed to be any real number, then x+y = c will be able to partition the real numbers.
Put another way, we can pick any real number we want (aka the number c) and break it down into a sum of x and y values. Such a sum cannot yield any other c value. So going back to the house/room analogy, any particular (x,y) ordered pair will belong to one and only one room.
Let's look at an example of a non-answer. Choice B is not correct because it is perfectly possible to have circles intersect. Intersecting circles share at least one common point. Those common points are what break the idea of partitions. This idea also means choice C is false as well.
Choice D can be ruled out because the notation should be (x,y) in R2 and not simply R.
The collections of subsets of the plane, R2 is (a) {{x,y) : x + y = c} : c ∈ R}
What is a subset ?If X is a subset of Y then all the elements of A also contained in B.
According to the given statement we have o determine which of the following collections of subsets of the plane R2.
R2 defines a two dimension plane.
x+y = c where c is a real number.
Then points on the line in the form (x,y) will form a particular partition. A partition is where we break a set up into non-overlapping subsets and there are no gaps. Think of it like breaking up a house into multiple rooms. Each room is a subset of the house.
Take note that if a point is on a line like x+y = 7, then it cannot be on any other line of the form x+y = c, where c is not equal to 7. Something like (x,y) = (3,4) is on x+y = 7 and not on any other line.
B. Is not correct because it is perfectly possible to have circles intersect. Intersecting circles share at least one common point. Those common points are what break the idea of partitions.
C. is false as well
D. Is ruled out because the notation should be (x,y) in R2 and not simply R.
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You have 3 fair 6-sided dice. You repeatedly roll all 3 at once, until all 3 of them show thesame number. What is the probability that you have to tryat leasttwice
Answer:
35/36 or about 0.972
Step-by-step explanation:
The probability of rolling the same number
first die 6/6
second die 1/6
third die 1/6
1(1/6)(1/6) = 1/36
so there is a 35/36 chance that you will not get it done on the first roll and need to attempt at least one more time.
Please answer this question
Step-by-step explanation:
Using the properties of logarithms, the left side of the equation becomes
[tex]\log{3x^3} - \log{x^2} = \log{3x}[/tex]
while the right hand side becomes
[tex]\log{27} - \log{x} = \log{\frac{27}{x}}[/tex]
so we end up with
[tex]3x^2 =27 \Rightarrow x = 3[/tex]
Find the root(s) or zero(s) of the function.
Answer:
-1/2 , 3
Step-by-step explanation:
In order to find the roots of the function 2x² - 5x - 3
We have to solve the quadratic equation :
2x² - 5x - 3 = 0
Calculating the discriminant Δ :
Δ = b² - 4ac
= (-5)² - 4(2)(-3)
= 25 + 24
= 49
Then
√Δ = √49 = 7
Determining the Zeros :
[tex]x=\frac{-b+\sqrt{b^{2}-4ac} }{2a} = \frac{5+7} {2 \times (2)} =\frac{12}{4} =3[/tex]
or
[tex]x=\frac{-b-\sqrt{b^{2}-4ac} }{2a} = \frac{5-7} {2 \times (2)} =\frac{-2}{4} =\frac{-1}{2}[/tex]
Please help What's the volume of a cube with a side length of 9 cm? Question 19 options: 701 cm³ 729 cm³ 697 cm³ 752 cm³
<7 and <8 are complimentary angles. <5 = <8 and m<6 = 29. Find the measure of angle 7 and angle 5
Step-by-step explanation:
since < 5 = < 8, so,
< 7 = < 6 = 29°
and < 5 = 90° - 29° = 61°
which statement is true regarding the functions on the graph
A. f(6)= g(3)
B. f(3)=g(3)
C. f(3)=g(6)
D. f(6)=g(6)
I think it's C due to where they meet but I'm not sure
38) The length of a rectangle is 15.6 cm correct to 1 decimal place.
The width of a rectangle is 3.8 cm correct to 1 decimal place.
Calculate the lower bound for the perimeter of the rectangle.
Answer:
38.75
Step-by-step explanation:
perimeter = 2(15.6+3.8) =38.8
lower bound = the smallest value that would round up to the estimated value =38.75
Simplify (6+5x)+(7x+3)
Answer: 12x + 9
Step-by-step explanation:
Given
(6 + 5x) + (7x + 3)
Put like terms together
=5x + 7x + 6 + 3
Combine like terms
=[tex]\boxed {12x+9}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Which of the following number(s) rounds to 0.18?
Select all that apply.
A. 0.17714
B. 0.18582
C. 0.18321
D. 0.17217
Answer:
it's A or C
Step-by-step explanation:
because if it was be it would round to .19 but c and a round to .18
Kelly works two jobs. She usually works at a retail store for 5 hours during the day and is paid $7.18 per hour by the store. In the evening she works at a restaurant as a
manager for 7 hours and is paid $20.68 per hour. How much does she make on average per hour for the day?
Answer:
Think of two or three jobs with which you are familiar, perhaps a teacher, a retail worker, a nurse, or a police officer.
In each case, indicate why the employment contract is necessarily incomplete. What important parts of the person’s job—things that the employer would like to see the employee do or not do—cannot be covered in a contract, or if they are, cannot be enforced?
Step-by-step explanation:
Solve the following expression when
k= 12
(4k + 2) = 10
Answer:
5
Step-by-step explanation:
(4k + 2) ÷ 10
(4(12) + 2) ÷ 10
(48 + 2) ÷ 10
(50) ÷ 10
= 5
Hope this helps!! <3
The solution to the expression (4k + 2 ) ÷ 10 when k = 12 is 5
From the given expression, we are to solve for (4k + 2) ÷ 10
When
k = 12What we are going to do is that we will replace k with 12 wherever we see (k) in the expression given
∴
= (4k + 2 ) ÷ 10
= (4(12) + 2 ) ÷ 10
= (48 + 2) ÷ 10
= (50) ÷ 10
= 5
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Mark buys last year's best-selling novel, in hardcover, for $23.20. This is with a 20% discount from the original price. What was the original price of the novel?
Answer:
[tex]29[/tex]
Step-by-step explanation:
Let x be the original price.
( 1 - 20% ) x = 23.2
[tex] 0.8x = 23.2[/tex]
[tex] \frac{0.8x}{0.8} = \frac{23.2}{0.8} [/tex]
[tex] x = 29[/tex]
-3/5×(2/9×10/7)
what's the answer
Answer:
-4/21
Step-by-step explanation:
-3/5×20/63
-3×4/63
-4/21