The system of equations best represents the number of apples a and the number of garonia bars g be a+b=60, 0.75x+0.15y=21.
Given that cost of 1 apple is $0.75, cost of 1 gargonia bars be $0.15 ,total things are 60 and total money paid be $21.
Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be a linear equation,quadratic equation, cubic equation.
Because we have been told that there are 60 total things and a represents the number of apples and g represents number of garonia represents the number of garonia bars.
a+b=60--------1
Money paid by consumers is cost per units*number of units
So,
0.75a+0.15b=21
Hence the system of equations best represent the number of apples and the number of garonua bars g are a+b=60, 0.75a+0.15b=21.
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Answer:
y is equal to 24
Step-by-step explanation:
If y is directly proportional to x when x is equal to 5 and y is 12, then when you multiply 5 by 2 which is 10, y will be proportional to that when you multiply 12 by 2 which is 24
Answer:
b: 25
Step-by-step explanation:
The previous answer wowwubbzy13 uploaded is absolutely correct!
I'll set up a proportion.
If y = 12, then x = 5
--> 12:5
We want to find the y when x is 10
--> y:10
12:5 = y:10
5y = 120
y = 25
So B: 25 is the correct answer!
A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material.
The width of the box is 3 ft that can be produced using the minimum amount of material.
What are the volume and surface area of a box?Consider a box with length 'l', width 'w' and height 'h',
Volume V = l × w × h
Surface area S = 2(lw + wh + hl)
Calculation:It is given that,
Volume of the box V = 36 cubic feet and l = 2w
Using the formulae,
V = 2w × w × h = 2w²h ...(1)
S = (2w² + 2wh + 4wh) = 2w² + 6wh ... (2) (here only single lw is considered since it is open top)
From equation (1),
36 = 2w²h
⇒ w²h = 18
⇒ h =18/w²
equation (2) becomes
S = 2w² + 6w(18/w²) = 2w² + 108/w ...(3)
So, for a minimum amount of material, the width of the box is,
On differentiating the surface area w.r.t 'w'
S' = 4w - 108/w²
For a minimum amount, substituting S' = 0 we get,
0 = 4w - 108/w²
⇒ 4w = 108/w²
⇒ 4w³ = 108
⇒ w³ = 27
∴ w = 3 feet
Therefore, the width of the given box is 3 feet.
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The piece of music that I am learning is 60 measures long. There are 13 beats in every measure, and every eighth note lasts for 1 beat. The last 17 measures of this piece are the finale. In every measure of the finale, there are 7 eighth notes played at middle C. If middle C never occurs in this piece outside of the finale, for what fraction of the whole piece do I play middle C
[tex]\frac{119}{780}[/tex] fraction of the whole piece you play middle C.
What is a fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction consists of a numerator above a line and a non-zero denominator below (or after) that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.To find for what fraction of the whole piece do you play middle C:
Since 7 out of every 13 beats in the finale are played at middle C, [tex]\frac{7}{13}[/tex] the finale is played at middle C.
The finale is 17 measures out of a 60-measure piece or [tex]\frac{17}{60}[/tex] of the whole piece.
[tex]\frac{7}{13}[/tex] of [tex]\frac{17}{60}[/tex] is [tex]\frac{7}{13}[/tex] x [tex]\frac{17}{60} = \frac{119}{780}[/tex]
Therefore, [tex]\frac{119}{780}[/tex] for a fraction of the whole piece you play middle C.
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[tex]Y-intercept = -4 Slope = 1/4[/tex]
Please help i need this
Answer:
Step-by-step explanation:
Answer:
Refer to the attached image!!
Hope it helps!
What is the area of this trapezoid?
Enter your answer in the box.
_cm²
Answer:
A = 336 cm²Step-by-step explanation:
Area Formula
A = (a + b) × h/2
A = (28 + 14) * 16/2
A = 42 * 8
A = 336 cm²
Find the interval in which the function is positive.
f(x)=x²-7x + 10
1. (-∞0, 2)
II. (2,5)
III. (5,00)
O I, II
O I, III
O II, III
O II only
Answer:
(b) I, III
Step-by-step explanation:
The correct answer can be chosen based on your knowledge of the shape of the graph of f(x).
General shapeThe leading coefficient of this quadratic function being positive tells you the graph will be a parabola that opens upward. The left branch of the parabola will extend to positive infinity, as will the right branch.
If there are x-intercepts, the x-values between those will be where the graph has crossed the x-axis and function values are negative.
Specific shapeThe answer choices suggest that x=2 and x=5 are x-intercepts of the function's graph. These can be checked, if you like, by evaluating f(2) and f(5).
f(2) = 2² -7·2 +10 = 4 -14 +10 = 0
f(5) = 5² -7·5 +10 = 25 -35 +10 = 0
This means the function will be positive for x < 2 and for x > 5. These intervals are described by I and III.
what is the height of figure 1?
Answer:
4
Step-by-step explanation:
The population of a bacteria culture are tripling. after 6 days, the population has quadrupled. what is the tripling time? find the answer to the nearest thousandth. b) how long did it take for the population to double in size?
The tripling time of population is 6 days and the population will be doubled in 3.5 days.
Given that the population of a bacteria is tripling in 6 days.
We have to find the tripling time of population and the time when the population will be doubled.
Suppose the population of bacteria in beginning be x.
The population of bacteria seems like arithmetic progression in which a =x, nth term =3x and n=6.
Aritmetic progression is a sequence which is having common difference.
nth term=a+(n-1)d
3x=x+(6-1)*d
3x-x=5d
2x=5d
d=2x/5
d=0.4x
So now we have to find the value of n where population will be 2x.
nth term=a+(n-1)d
put nth term=2x, a=x,d=0.4x
2x=x+(n-1)*0.4x
2x-x=(n-1)*0.4x
x/0.4x=n-1
2.5=n-1
n=2.5+1
n=3.5
Hence the population of bacteria willbe doubled after 3.5 days.
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Calculate the future value in five years of $8,000 received today if your investments pay future value a. 5 percent compounded annually $ b. 7 percent compounded annually c. 9 percent compounded annually d. 9 percent compounded semiannually e. 9 percent compounded quarterly.
The Future value is:
a) $10,210.25
b) $11,220.41
c) $12,308.99
d) $18,938.90
e) $44,835.28
What is future value?
The future value (FV) of any asset can be understood as an increase in its value at a fixed rate over a period of time. For a given principal sum P, rate of interest r, and time period t, the future value of an asset can be calculated as:
FV=P*(1+r) ^t
We can find future value as shown below:
P=$8,000
t=5 year
a) r=6%=0.06
FV=8000*(1+0.05) ^5
=8000*(1.0) ^5
=$10,210.25
b) r=7%=0.07
FV=8000*(1+0.07) ^5
=8000*(1.07) ^5
=$11,220.41
c) r=9%=0.09
FV=8000*(1+0.09) ^5
=$12,308.99
d) r=9% compounded semiannually
= 0.09
t=2*5=10
FV=8000*(1+0.09) ^10
=8000*(1.09) ^10
=$18,938.90
e) r=9 percent compounded quarterly
=0.09
t=5*4=20
FV=8000*(1+0.09) ^20
=8000*(1.09) ^20
=$44,835.28
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15. If 3x + 10 = 3y - 2(y + 4), what is the value of y in terms of x? (A) x + 18 (B) 3x+6 (C) 3x + 14 (D) 3x + 18
Answer:
3x + 18
Step-by-step explanation:
3x + 10 = 3y - 2(y + 4)
3x + 10 = 3y - 2y - 8
3x + 18 = y
Answer:
D, 3x + 18.
Step-by-step explanation:
3x + 10 = 3y - 2(y + 4)
3x + 10 = 3y - 2y - 8
3x + 10 = y - 8
y = 3x + 10 + 8
y = 3x + 18.
Use the pythagorean theorem to prove that this point lies on the unit circle. Find csc(0) where 0=-120.
By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.
How to prove this point lies on the unit circle?In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:
Reference angle = 180 - θ
Reference angle = 180 - 120
Reference angle = 60°.
For the coordinates, we have:
sin(-120) = -sin(60) = -1/2.
cos(-120) = -cos(60) = -√3/2.
By applying Pythagorean theorem, we have:
z² = x² + y²
z = √((-1/2)² + (-√3/2)²)
z = √(1/4 + 3/4)
z = √1
z = 1.
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Solve the inequality. 14 + 10y ≥ 3(y + 14)
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{14+10y\geq 3(y+14) } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{Simplify \ both \ sides \ of \ the \ inequality. }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{10y+14\geq 3y+14 } \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{Subtract \ 3y \ from \ both \ sides. }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{10y+14-3y\geq 3y+42-3y } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{7y+14\geq 41 } \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{ Subtract \ 14 \ from \ both \ sides. }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7y+14-14\geq 42-14 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{7y\geq 28 } \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{Divide \ both \ sides \ by \ 7. }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{7y}{7}\geq \frac{28}{7} } \end{gathered}$}\\\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{y\geq 4} \end{gathered}$} }[/tex]36a^(4)b^(10)-81a^(16)b^(20) factor the given expression using the difference of squares pls
The factorized expression using difference of squares is as follows,
9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)
Difference of Squares
Difference of squares is a factorization method where an expression can be factored as (a + b) (a - b) when considered as the difference of two perfect squares, a²-b². For instance, factoring x²-25 results in (x+5) (x-5). By enlarging the parentheses in (a + b) (a - b), the pattern (a + b) (a - b)=a²-b² is used as the foundation for this technique.
Factorization Using Difference of Squares
Given expression is,
36a⁴b¹⁰ - 81a¹⁶b²⁰
= (6a²b⁵)² - (9a⁸b¹⁰)²
Using square of differences, we have
a² - b² = (a + b) (a - b)
Here, a = 6a²b⁵ and b = 9a⁸b¹⁰
Thus, we get,
(6a²b⁵ + 9a⁸b¹⁰)(6a²b⁵ - 9a⁸b¹⁰)
Further Factorization
We can take out 3 common from both the bracket terms after applying difference of squares
3×3(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)
= 9(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)
Further, we can take out a²b⁵ as common from both the bracket terms
= 9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)
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Δ
X
Y
Z
and
Δ
A
B
C
are similar triangles. Given the dimensions shown in the diagram, what is the area of
Δ
A
B
C
? Express the answer in square units.
Answer:
3.528
Step-by-step explanation:
the scale factor from the large triangle to the smaller triangle is 1/2. All of the side lengths of the small triangle is 1/2 the side lengths of the large triangle.
A = 1/2 (bh) The area of a triangle. I need to know the base and the height of the little triangle to figure out the area. If I use AC as the base, the length is given to me. It is 4.2. I do not have the height of the base, but I know that it is half of the height of the large triangle and that number is given to me. It is 3.36, if I divide that by 2, I get 1.68. Now I know all that I need to find the area.
A = 1/2(4.2)(1.68)
3.528Units^2
Phone chargers in a store are priced $19, $18, $15, $17, $19, $12, $19, and $15.
What display would best show the measures of variation?
(ignore my answer. i didn't mean to click)
The display that would best show the measures of variation of the given prices is; B: Box and Whisker Plot
What is the importance of Box and Whisker Plot?We are given the prices of Phone chargers in a store as;
$19, $18, $15, $17, $19, $12, $19, and $15.
Now, since we want to determine the display that would best show the measures of variation, the best display would be a box and whisker plot. This is because Box and Whisker plots are a great chart to use when showing the distribution of data points across a selected measure. These box and whisker plots display ranges within variables measured.
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Find the lateral surface area of the
following prism:
5 cm
5 cm
apothem = 3.44 cm
cm
5 cm
10 cm
5 cm
LSA = [?] cm2
The laterals surface area of the given hexagonal prism is: 250 cm².
How to Find the Lateral Surface Area of Hexagonal Prism?Lateral surface area = 5ah, where:
a = edge length of the baseh = height of the prism.Given the following:
a = 5 cm
h = 10 cm
Lateral surface area of the hexagonal prism = 5ah = 5(5)(10)
Lateral surface area of the hexagonal prism = 250 cm²
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a) The cosine rule can be used to find the value of x in the triangle below.
What number completes the following calculation? x² = 12² +152 - 2 x 12 x 15 x cos(?)
b) What is the value of x? Give your answer to the nearest integer.
Answer:
see explanation
Step-by-step explanation:
(a)
(the side required )² = sum of squares of other 2 sides - ( 2 × product of other 2 sides and cos(angle opposite side required ) )
x² = 12² + 15² - (2 × 12 × 15 × cos71°)
(b)
x² = 144 + 225 - 360cos71°
= 369 - 360cos71° ( take square root of both sides )
x = [tex]\sqrt{369-360cos71}[/tex]
≈ 16 cm ( to the nearest integer )
Jared made a 15 minute phone call yesterday that cost $0.90. how long will jared be on the phone today if the call cost $1.32, assuming the rate of the cost remains constant
A linen napkin, in the shape of a square, has sides that are 10 inches long.
If the napkin is folded along the diagonal, whats the length of the diagonal?
round to the nearest tenth.
Answer: A=187.5,2
Step-by-step explanation:
Can someone help me please
Answer:
1/9, 3, 27
(A / the first option listed)
Step-by-step explanation:
Here, we are given an expression with an "x" in it, and we are to evaluate possible x values, which means we plug them in as the x in the expression
first,
x = -2
3ˣ → 3⁻²
when we raise something to a negative power, we simply find the positive version of that power, and put a 1 over it:
3² = 3 · 3 = 9
so, 3⁻² = [tex]\frac{1}{9}[/tex] (1/9)
next,
x = 1
3ˣ → 3¹
now, here we have something raised to the power of 1, which is always itself, so 3¹ = 3
(think of ^to the power of as how many times we multiply that number, so 3² = 3 · 3, 3¹ = 3)
and finally,
x = 3
3ˣ → 3³
here, we can multiply 3 by itself 3 times:
3 · 3 · 3 = 27
so, 3³ = 27
[important note: when we raise something to a power, we are not multiplying the base number by that number, but this is a common mistake. but the exponent is how many times we are multiplying that number, which is confusing at first}
So, our answers in order are:
1/9, 3, 27 (the first option listed)
hope this helps! let me know if I should clarify anything :)
Which of the following is the complete factorization of the polynomial below?
2x² +13x² +17x-12
a
jfjoydx9tdzrzfzixitxxytxixutx
What's a venn diagram, how to draw it and the steps too!
What is a Venn Diagram?
Explain : A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
How to draw a Venn Diagram?
Explain : To create an intersecting Venn diagram, draw three circles that overlap in the middle. You'll be able to show which attributes are unique to each circle, which overlap between two, and which are common characteristics of all three groups. Two circles overlapping is a classic venn diagram
What is a venn Diagram mostly used for?
Explain : A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.
Set notations: The concepts illustrated in Venn ...
Scaled Venn Diagram: Also called Area Propo...
Reuleaux Triangle: Shape formed from the int...
Intersection: The items that overlap in the sets. ...
Here's some question for Venn Diagrams!
A. What's the first step creating a Venn Diagram? https://www.math-only-math.com/practice-test-on-Venn-diagrams.html
B. What's the last step to create a Venn Diagram? https://www.purplemath.com/modules/venndiag4.htm
C. What does a Venn Diagram looks like?
( Try using those questions to partice more about Venn Diagrams! )
( Also, thank you for the points! )
What's the slope and y-intercept?
Answer:
Slope: 2; Y-Intercept: (0,3)
Step-by-step explanation:
As you can see from the graph, it rises 4 and runs 2. So, the slope is 2. It intersects the y axis at (0,3)
Answer:
Slope: 3/2
Y-intercept: 3
Step-by-step explanation:
The line passes the y-axis at 3, and to find the slope you use rise over run. Our rise (which is going up) is 3, and our run (which is going across) is 2 (and since it moves from left to right, it is positive). The slope would be 3/2.
I hope it helps! Have a great day!
bren~
Q1. suppose that lim(,)â(3,1)(,)=6. what can you say about the value of (3,1) ? what if is continuous?
Answer:39084620
Step-by-step explanation:
New questions in Mathematics
19 ft 4 ft l Find l. l = √ [?] ft
flying against the jet stream, a jet travels 3000 in 3 hours. Flying with the jet stream, the same jet travels 5360 miles in 4 hours. What is the rate…e of the jet in still air and what is the rate of the jet stream?
Please help! Express the area of the region bounded by the x-axis, y = 1/2x - 2, and y equals the cubed root of x, using definite integrals.
Solve the equation 7/4x-2=-5x+1
How to Convert 11010112 to base 10?
Answer the following. (a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation…. (b) A humpback whale can weigh up to ×1.1105 pounds. Write this number in standard notation.
Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)
Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)
The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = (k2 x,k2 y,k2 z)
Evaluate each expression if a=2,b=-3,C=-1, and d=4 5+d(3b-2d)
The equation y=ax^2 describes a parabola. If the value of a is positive, which way does the parabola open?
A.Up
B.Right
C.Left
D.Down
A. Up
Step-by-step explanation:Parabolas are graphs that make U-shapes and are formed from quadratic equations.
Vertical Parabolas
There are 2 different types of parabolas: vertical and horizontal.
Vertical parabolas have a vertical axis of symmetry. So, they open up or down.Horizontal parabolas have a horizontal axis of symmetry. So, they open left or right.If the x-value is squared, then the parabola is vertical. So, this graph must open up or down.
Positive A-Value
The a-value is the coefficient before the squared term. In a vertical parabola, the graph opens up if the a-value is positive. On the other hand, the graph opens down when the a-value is negative.
In this case, the graph is a vertical parabola that opens up. This means that the range will have a minimum value but no maximum.
Which polynomial is a quintic trinomial?
A. -x^4-5x^2
B. x^3+2x^2−8x+16
C. x² + 4
D. 3x^5+7x^2−9x^4
Answer:
D
Step-by-step explanation:
a quintic polynomial is a polynomial of degree 5
A is a polynomial of degree 4 (- [tex]x^{4}[/tex] term )
B is a polynomial of degree 3 (x³ term )
C is a polynomial of degree 2 ( x² term )
D is a polynomial of degree 5 ( 3[tex]x^{5}[/tex] term )
What is the maximum number of consecutive odd positive integers that can be added together before the sum exceeds $401$
The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
According to the statement
We have a given that the maximum sum of the positive integers is 400.
And we have to find the value of n which is a maximum number of integers by which the value of sum become 400.
So, to find the value of the n we use the
A.P. Series'Summation formula
According to this,
S = n (n+1)/2
Here the value of s is 401
Then
S = n (n+1)/2
401 = n (n+1)/2
401*2 = n (n+1)
802 =n (n+1)
n (n+1) = 802
n^2 + n -802 =0
By the use of the Discriminant formula the
value of n becomes n = -28 and n = 27.
The negative value of n is neglected.
Therefore the value of n is 27.
So, The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
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Which of the following systems of linear inequalities is represented by the
solution graphed below?
A. y 2 and ys x
B. x>2 and yz x
C. x22 and y> x
D. y 22 and y
The system is:
y < x
y ≥ 2
So we conclude that the correct option is D.
Which system of inequalities is represented in the graph?On the graph, we can see two lines. One with a positive slope that is dashed.
And a solid line that is constant of the form y = c.
We can see that the shaded region is above the constant line and below the line with a positive slope, so the system of inequalities is of the form:
y < line.y ≥ constant line (≥ is used because this line is solid).The only option that has this form is option d:
y < x
y ≥ 2
So we conclude that the correct option is D.
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Match each polynomial with its correct, most specific classification.
3x^2yz
2x^2+3xy-6y^2
3pq^2-3p
2xy+3x^2-2y^2-4x^2
The polynomials are classified as follows:
3x²yz: Monomial.2x² + 3xy - 6y²: Trinomial.3pq² - 3p: Binomial.2xy + 3x² - 2y² - 4x²: Polynomial.How are the polynomials classified?Depends on the number of terms, as follows:
3x²yz: Monomial, as it has one term.2x² + 3xy - 6y²: Trinomial, as it has three terms.3pq² - 3p: Binomial, as it has two terms.2xy + 3x² - 2y² - 4x²: Polynomial, as it has four terms.More can be learned about polynomials at https://brainly.com/question/24662212
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Solve 5x=125 using the one-to-one property of exponents.
A) X=In(125)
B) x = 1
C) x = 3
OD) x = 5
Answer:
C) x = 3
Step-by-step explanation:
Given equation:
[tex]5^x=125[/tex]
Rewrite 125 with base 5: 125 = 5³
[tex]\implies 5^x=5^3[/tex]
[tex]\textsf{Apply the one-to-one property of exponents}: \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]
[tex]\implies x=3[/tex]