Let [tex]x[/tex] be the amount of the 30% alloy and [tex]y[/tex] the amount of the 60% alloy the metalworker will use. However much is used, the final alloy will have a mass of
[tex]x+y=100[/tex]
kilograms. For each kg of the 30% alloy used, 0.3 kg is copper; similary, each kg of the 60% alloy contributes 0.6 kg, so that
[tex]0.3x+0.6y=0.54(x+y)=54[/tex]
Now,
[tex]x+y=100\implies y=100-x[/tex]
[tex]\implies0.3x+0.6(100-x)=54[/tex]
[tex]\implies60-0.3x=54[/tex]
[tex]\implies0.3x=6[/tex]
[tex]\implies x=20[/tex]
[tex]\implies y=100-20=80[/tex]
The scatter plot shows the study times and test scores for a number of students. How long did the person who scored 81 study?
Answer: Option A
50 minutes
Step-by-step explanation:
Observe in the diagram that the vertical axis represents the score obtained and the horizontal axis represents the study time.
To find out how many hours the person with a score of 81 studied, locate the point that is at a vertical distance of 81.
Now draw a vertical line from this point to the horizontal axis. Note that the vertical line traced intercepts the vertical axis at x= 50
Then the person who got a score of 81 studied 50 minutes
The answer is the option A
The distance between the two points pictured is d = Use the distance formula to find n. d = n =
Answer:
the answer is 61units
n=61
Step-by-step explanation:
How do I solve this?
A football punted upward has a trajectory given by the equation y = 48x − 16x2, where y represents the football's height x seconds after it has been kicked. What is the maximum height, in feet, attained by the ball?
Giving brainliest + 30 points
The maximum happens at x = -b/2a
x = -48/2(-16) = 3/2
Now replace x in the equation and solve for y:
y = 48(3/2) - 16(3/2)^2
y = -72 - 36
y = 36
The maximum height is 36 feet.
Which equation represents a line that passes through (4, ) and has a slope of ?
y – = (x – 4)
y – = (x – 4)
y – = 4(x – )
y – 4 = (x – )
Answer:
the 1st one
Step-by-step explanation:
could anyone help me? I will mark you as brain liest who ever helps me!
Answer:
1)163.28 (3.14*52)
2)13ft 6in (163.28/12)
3)129 times
4) 31 times
Step-by-step explanation:
1) multiply 52 times pie(3.14)
2)divide 163.28(your total) by 12
3) 1760 divided by 52
4) 1760 divided by 56.52
this is for the other 2 ones
A picture that measures 8 cm by 6 cm is to be surrounded by a mat. The mat is to
be surrounded by a mat. The mat is to be the same widt
all sides of the picture. The combined area of the mat and the picture is double the arca
What is the width of the mat to the nearest tenth? Include a diagram. (5)
Answer:
1.4 inches
Step-by-step explanation:
The picture is a rectangle 8 cm by 6 cm. The area of a rectangle is length * width. The area of the picture is 8 cm * 6 cm = 48 cm^2
After the mat is applied, the area doubles, so the new area will be 2 * 48 cm^2 = 96 cm^2.
Let the width of the mat be x. The mat has the same width all around the rectangular picture, so it adds x on each side of the length and x on each side of the width.
old length: 8
new length: 2x + 8
old width: 6
new width: 2x + 6
Area of the new rectangle with mat = new length * new width
area = (2x + 8)(2x + 6)
The new area is 96, so that give us an equation.
(2x + 8)(2x + 6) = 96
Use FOIL on the left side:
4x^2 + 12x + 16x + 48 = 96
Combine like terms, and subtract 96 from both sides:
4x^2 + 28x - 48 = 0
Divide both sides by 4:
x^2 + 7x - 12 = 0
To factor the trinomial, we need two numbers that add to 7 and multiply to -12. There are no such numbers, so we need to use the quadratic formula.
x = [-b +/- sqrt(b^2 - 4ac)]/(2a)
x = [-7 +/- sqrt(7^2 - 4(1)(-12)]/[2(1)]
x = [-7 +/- sqrt(49 + 48)]/2
x = [-7 +/- sqrt(97)]/2
x = 1.4 or x = -8.4
Since the mat cannot have a negative width, the negative solution is discarded.
Answer: The width of the mat is 1.4 inches.
What is the standard deviation of the following data set rounded to the nearest tenth?
30, 26, 28, 32, 28, 30
Answer:
Standard Deviation is: 2.09762 or rounded to nearest tenth is 2.1
Step-by-step explanation:
find the conplex conjugate of z1 of z1=i+4
Answer:
- i + 4
Step-by-step explanation:
Given a complex number a + bi then the complex conjugate is a - bi
Note the real part remains unchanged while the sign of the imaginary part is negated.
Hence conjugate of i + 4 = - i + 4
Find the value of X
Answer:
C. 66
Step-by-step explanation:
32 + x =98
The sum of interior angles of a triangle add up to the exterior opposite angle;
solving for x yields;
x = 98 - 32
x = 66 degrees
Answer:
x = 66°
Step-by-step explanation:
Since DAC is a straight line, the angles must add up to 180° and 98° is given so the missing angles is 180° - 98° = 82°
Angles in a triangle add up 180° and 32° and 82° are given →
x + 32° + 82° = 180°
x + 114° = 180°
x = 66°
Which is the solution of the quadratic equation (4y – 3)2 = 72?
Answer:
y = 9.75
Step-by-step explanation:
(4y - 3)2 = 72
Opening the brackets;
8y - 6 = 72
8y = 72 + 6 = 78
y = 78 ÷ 8 = 9.75
Answer:
[tex]y = \frac{3+6\sqrt{2}}{4}\text{ and } y = \frac{3-6\sqrt{2}}{4}[/tex]
Step-by-step explanation:
Given quadratic equation,
[tex](4y-3)^2=72[/tex]
[tex]\implies 4y - 3 = \pm \sqrt{72}[/tex] ( Taking root on both sides )
[tex]4y=3 \pm 6\sqrt{2}[/tex] ( Additive property of equality ),
[tex]y = \frac{3 \pm 6\sqrt{2}}{4}[/tex] ( Division property of equality )
[tex]\implies y = \frac{3+6\sqrt{2}}{4}\text{ or }y =\frac{3-6\sqrt{2}}{4}[/tex]
Hence, the solution of the given equation is,
[tex]\implies y = \frac{3+6\sqrt{2}}{4}\text{ and }y =\frac{3-6\sqrt{2}}{4}[/tex]
Andy and Jacob work as technicians in a laboratory where gemstones are tested and certified. Andy has already tested 30 gemstones and continues testing at a rate of 30 gemstones per hour. Jacob has already tested 40 gemstones and continues testing at a rate of 25 gemstones per hour. Which function can Andy and Jacob use to determine the total number of gemstones they have tested after x hours? How many gemstones will they have tested after 5 hours? A. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 10. Thus, they will have tested 285 gemstones in 5 hours. B. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 70x + 55. Thus, they will have tested 405 gemstones in 5 hours. C. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 70. Thus, they will have tested 345 gemstones in 5 hours. D. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 60x + 65. Thus, they will have tested 365 gemstones in 5 hours.
Answer:
Option C is correct.
Step-by-step explanation:
Andy tested gemstones already = 30
Jacob tested gemstones already = 40
Total gemstones tested by Andy and Jacob already = 30+40 = 70
Andy continue to test gemstones per hour = 30
Jacob continue to test gemstones per hour = 25
Total gemstones tested by Andy and Jacob per hour = 30 +25 = 55
The total number of gemstones tested by Andy and Jacob after x hours will be: 55x
So, the equation will be: f(x) = 55x + 70
After 5 hours i.e. x =5
f(5) = 55(5) + 70
f(5) = 275 + 70
f(5) = 345
Andy and Jacob will have tested 345 gemstones in 5 hours.
So, Option C is correct.
What is the area of the kite
Answer:
The area of the kite is 60 square feet
Step-by-step explanation:
The area of a kite is given as half multiplied by the product of the diagonals.
The longer diagonal measures 30 feet.
The shorter diagonal measures 4 feet.
The area of the kite is; [tex]\frac{1}{2}*30*4=60[/tex]
ANSWER
The area of the kite is 60 square feet
EXPLANATION
The area of a kite is half times the product of the diagonals.
The longer diagonal is 10+20=30 feet.
The shorter diagonal is 2+2 =4 feet.
The area of this kite
[tex] = \frac{1}{2} \times 30 \times 4[/tex]
This simplifies to,
[tex] = 60 {ft}^{2} [/tex]
Therefore the area of the kite is 60 square feet
what is the solution to this equation?
x/5=-20
Answer:
-100
Step-by-step explanation:
Answer:
-100
Step-by-step explanation:
You need to multiply
-20 x 5= -100
Hope this helped please mark me the brainliest answer? Have a good day :)
Michael earned 50.43 in 6.15 hours. how much did he earn in an hour?
Answer: $8.2
Step-by-step explanation:
Answer:
8.2 dollars an hour is the answer
Step-by-step explanation:
50.43 divided by 6.15 is 8.2
The graph of the function f(x)=6/x-3 is shown below. What is the vertical asymptote of the function
Answer:
The vertical asymptote is [tex]x=3[/tex]
Step-by-step explanation:
we know that
The vertical asymptote is the value of x that makes the denominator equal to zero:
In this problem we have
[tex]f(x)=\frac{6}{x-3}[/tex]
[tex]x-3=0[/tex]
Solve for x:
[tex]x-3+3=0+3[/tex]
[tex]x=3[/tex]
The vertical asymptote is [tex]x=3[/tex]
see the attached figure to better understand the problem
I NEED HELP PLEASE!!!!!
Answer is 1)
3V= pi•h•r^2 divide both sides by (pi•h) ; 3V/pi•h = r^2; sqrt (3V/pi•h) =r
The graphs below have the same shape. f(x) = x^2 what is the equation of the graph of g(x)?
Answer:
A. [tex]g(x)=(x-4)^2[/tex]
Step-by-step explanation:
The graph of [tex]f(x)=x^2[/tex] is transformed to obtain the graph of g(x).
We can see from the diagram that, f(x) is shifted 4 units to the right to obtain the graph of g(x).
Therefore [tex]g(x)=f(x-4)[/tex].
Hence the equation of g(x) is
[tex]g(x)=(x-4)^2[/tex]
The correct answer is A.
The equation of the graph of g(x) is g(x) = (x - 4)²
How to determine the equationFrom the graph shown, we can see that the f(x) = x² as shown is shifted 4 units to the right to obtain the graph of g(x).
Then, we have that this shift can be achieved by replacing x in the equation of f(x) with x - 4 to represent the horizontal shift.
We have the equation of the graph of g(x), to be;
g(x) = (x - 4)²
This equation represents a horizontal shift of the graph of f(x) by by 4 units to the right, as g(x) remains the same shape f(x) but is shifted horizontally to the right by 4 units.
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what is the value of 6(2b-4) when b=5
Answer:
36
Step-by-step explanation:
6(2b-4)
Let b = 5
6(2 (5)-4)
Work inside the parentheses out
6(10-4)
6(6)
36
Answer:
36
Step-by-step explanation:
Well, we can do this 2 ways: Distribute first, or do it last.
Distribute First:
12b-24=
12(5)-24=
60-24=
36
Distribute last:
6(2(5)-4)=
6(10-4)=
Now you can take this two ways.
Distribute:
60-24=36
OR
Parenthessess: (I dont know how to spell.)
6(6)=36
Anyone? i dont understand
Answer:
1725ft^2
Step-by-step explanation:
Hi!
First you have to find your two bases B1 and B2, which are 50 and 65.
Then you find the height, which is 30ft.
Finally, you plug those into the equation 1/2*h*(B1+B2) and solve.
1/2*30*(50+65)
1/2*30*(115)
15*115
1725ft^2 is your answer.
I hope this helps!
What type of number is [tex]\sqrt{13}[/tex]
Choose all answers that apply:
(Choice A)
A
Whole number
(Choice B)
B
Integer
(Choice C)
C
Rational
(Choice D)
D
Irrational
The number √{13} is an irrational number because it cannot be expressed as a ratio of two integers and is not a whole number or integer either.
The number √{13} is not a whole number, an integer, or a rational number because it cannot be expressed as a ratio of two integers. The square root of a positive number that is not a perfect square is always irrational. Therefore, the only correct choice for the type of number that represents √{13} is (Choice D) Irrational.
At a book fair, 1/4 of the people bought 1 book.3/5 of the remaining
people bought 2 books each and the rest of the people bought 3
books each. A total of 4469 books were sold. How many people
were at the book fair?
Answer:
2,180 people
Step-by-step explanation:
Let
x-----> number of people at the book fair
we know that
1) 1/4 of the people bought 1 book each
(1/4)x=(5/20)x
2) 3/5 of the remaining people bought 2 books each
The remaining people is (3/4)x
so
(3/5)(3/4)x=(9/20)x
3) the rest of the people bought 3 books each
The rest of the people is x-(5/20)x-(9/20)x=(6/20)x
The linear equation that represent this situation is
(1)*(5/20)x+(2)*(9/20)x+(3)*(6/20)x=4,469
(5/20)x+(18/20)x+(18/20)x=4,469
(41/20)x=4,469
x=4,469*20/41
x=2,180 people
An artist made a 54-inch-tall statue of a former president. If the president was 6 feet tall, what scale did the artist use?
1 foot = 12 inches.
The president is 6 x 12 = 72 inches tall.
54 inch model / 72 inches = 0.75 = 3/4
The model is 3/4 scale.
Find the specific solution of the differential equation dy/dx= 4y/x^2 with condition y(-4)=1
A. y=-1-4/x
B. y=-e^1/x
C.y=e^(-4/x)
D. None of these
This ODE is separable:
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4y}{x^2}\implies\dfrac{\mathrm dy}y=\dfrac4{x^2}\,\mathrm dx[/tex]
Integrating both sides gives
[tex]\ln|y|=-\dfrac4x+C[/tex]
Given the initial condition [tex]y(-4)=1[/tex] we find
[tex]\ln|1|=-\dfrac4{-4}+C\implies C=-1[/tex]
so that the particular solution is
[tex]\ln|y|=-\dfrac4x-1[/tex]
[tex]\implies y=e^{-(1+4/x)})[/tex]
so the answer is D.
Can someone please help me with this?
Answer:
The answer is A; 19
Step-by-step explanation:
4 × (3/4 - 2/4) + 3 × 6
= 4 × 1/4 + 3 × 6
= 1 + 3 × 6
= 1 + 18
= 19
Write a function describing the relationship of the given variables.
V
varies directly with the square of
t
and when
t
=
6
,
V
=
108
V
=
Answer:
The function describing the relationship of V and t is V = 3t²
Step-by-step explanation:
* Lets explain the meaning of direct variation
- The direct variation is a mathematical relationship between two
variables that can be expressed by an equation in which one
variable is equal to a constant times the other
- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the
constant of variation
* Now lets solve the problem
# V is varies directly with the square of t
- Change the statement above to a mathematical relation
∴ V ∝ t²
- Chang the relation to a function by using a constant k
∴ V = kt²
- To find the value of the constant of variation k substitute V and t
by the given values
∵ t = 6 when V = 108
∵ V = kt²
∴ 108 = k(6)² ⇒ simplify the power 2
∴ 108 = 36k ⇒ divide both sides by 36 to find the value of k
∴ 3 = k
- The value of the constant of variation is 3
∴ The function describing the relationship of V and t is V = 3t²
A lifeguard at a swimming pool gives one-hour swim lessons to children in the morning before the pool is open to the public. She earns four dollars per class and fifty cents per swimmer. The minimum wage in her state is $7.25. She hopes to earn more than that amount of money during each class. Write an inequality that models the situation and find the minimum number of students she must teach in each class so that her earnings for that hour exceeds the minimum wage in her state.
Answer:
brainliest ps :)
Step-by-step explanation:
her wage is $4.00 + s*0.5 so 7.25-4> s*.5== 3.25 > s*.5 == 6.5 > s
The inequality for the given information can be written as 6.5 > s.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
A lifeguard at a swimming pool gives one-hour swim lessons to children in the morning before the pool is open to the public. She earns four dollars per class and fifty cents per swimmer. The minimum wage in her state is $7.25.
The inequality can be written as:-
$4.00 + ( s x 0.5 )
7.25-4 > ( s x 0.5 )
3.25 > ( s x 0.5 )
6.5 > s
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the graphs of the linear functions f and g are shown. Enter the solution to the equation f(x)=g(x)
I’m pretty sure the answer is (-4, 4) because when the equations are equal, that is when the points intersect. That happens to be at point (-4,4)
Maggie spent $46.20 to by pencil sharpeners for her gift shop. If each pencil sharpener cost 60 cents how many pencil sharpeners did she buy
Answer:
Maggie bought 77 pencil sharpeners
$46.20 divided by .60 = 77
Step-by-step explanation:
46.20÷0.60= 77
Maggie can buy 77 pencil sharpeners is she would like
Please, please, pppllleeeeaassssee
Mark Brainlyest
Question 3 answer please
Answer:
34.48
Step-by-step explanation:
Use PEMDAS
12.98-(7.6÷19)+22
12.98-0.4+22
12.48+22
34.48
Answer:
34.480000000000000000000000
Step-by-step explanation:
Kate is painting a ceramic paperweight shaped like a rectangular prism, as shown here. (dimensions of .8 ft , 1.2 ft, 1.2 ft)She wants to find the surface area of the paperweight so she can determine how much paint she needs.
The area of one of the bases is _____
The area of each lateral rectangular face is _____
The surface area of the paperweight is _____
Answer:
The area of one of the bases is 0.96 ft²
The area of each lateral rectangular face is 4.8 ft²
The surface area of the paperweight is 6.72 ft²
Step-by-step explanation:
we know that
The surface area of the rectangular prism is equal to
SA=2B+LA
where
B is the area of one of the bases
LA is the lateral area of the prism
Find the area of one of the bases B
B=(0.8)(1.2)=0.96 ft²
Find the lateral area LA
The lateral area is the area of each lateral rectangular face
LA=2[(0.8)(1.2)]+2[(1.2)(1.2)]=4.8 ft²
Find the surface area
SA=2(0.96)+4.8=6.72 ft²
Answer: 1.44, 0.96, and then 6.72.
Step-by-step explanation:
the person who answered first is wrong.