x = amount (kg) of 25% coper alloy
y = amount (also kg) of 70% copper alloy
Each kilogram of the 25% alloy contains 0.25 kg of copper, while each kilogram of the 70% alloy contains 0.7 kg of copper. When combined, the metalworker ends up with (x + y) kg of an alloy that should consist of 52% copper, so that it contains 0.52 (x + y) kg of copper.
The metalworker wants to make 50 kg of this new alloy, so that
x + y = 50
of which 52%, 0.52 (50 kg) = 26 kg, is copper, so
0.25x + 0.7y = 26
Solve for y in terms of x :
y = 50 - x
Substitute this into the other equation and solve for x :
0.25x + 0.7 (50 - x) = 26
0.25x + 35 - 0.7x = 26
9 = 0.45x
x = 20 → y = 30
Casandra earned 520$ this month by walking her neighbors dog . This is a 30% increase from amount she earned last month
Answer: last week she earned $364.
Step-by-step explanation:
A circle is centered at (5, −9) and has a radius of 12. Which of the following is the equation for this circle?
Answer:
[tex]\boxed {\boxed {\sf (x-5)^2+(y+9)^2=144}}[/tex]
Step-by-step explanation:
The standard form for the equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h,k) is the center of the circle and r is the radius.
For this circle, the center is (5, -9) and the radius is 12. Therefore:
[tex]h= 5 \\k= -9 \\r=12[/tex]
Substitute the values into the formula.
[tex](x-5)^2+(y-(-9))^2=(12)^2[/tex]
Distrubute the -1 into the -9.
-(-9)= -1*-9= 9[tex](x-5)^2+(y+9)^2=(12)^2[/tex]
Solve the exponent.
(12)²= 12*12=144[tex](x-5)^2+(y+9)^2=144[/tex]
The equation for the circle with a center (5,-9) and radius of 12 is (x-5)²+(y+9)²=144
Based on the calculations, the equation of this circle in standard form is equal to (x - 5)² +(y + 9)² = 144.
The equation of a circle.Mathematically, the standard form of an equation of a circle is given by;
(x - h)² +(y - k)² = r²
Where:
h and k represents the coordinates at the center.r is the radius of a circle.Given the following data:
Coordinates (h, k) = (5, -9).Radius = 12.Substituting the given parameters into the formula, we have;
(x - 5)² +(y - (-9))² = 12²
(x - 5)² +(y + 9)² = 144
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pls help u dont have to explain that much
Answer:
k = -7
Step-by-step explanation:
Given
x² - x - 42 = (x + k)(x + 6)
Required
Find k
x² - x - 42 = (x + k)(x + 6)
Expand the left hand side
x²-7x + 6x - 42 = (x + k)(x+ 6)
Factorize
x(x - 7) + 6(x- 7) = (x + k)(x+ 6)
Further factorize
(x - 7)(x + 6) = (x + k)(x + 6)
By comparison
x + k = x - 7
Subtract x from both sides
k = -7
PLEASE HELP IM GETTING TIMED 8. The graph shows the relationship between the depth of a diver and the time that has passed .
Which function best represents the relationship shown in the graph ?
A. y = 10x - 15
B. y = 2x - 15
С. y = - 10x - 15
D.y=-15x-10
Answer:
C
Step-by-step explanation:
Glad I could help!
Answer:
c
Step-by-step explanation:
rise/run
-20/2=-10 for the slope
Write the equation of the line in slope-intercept form (y = mx +b): 3y - 12x = 15
Answer:
y = 4x + 5
Step-by-step explanation:
3y - 12x = 15
Add 12x to both sides.
3y = 12x + 15
Divide by 3 to isolate y.
y = 4x + 5
Answer:
ACTUALLY IT'S, y=4x-5
Step-by-step explanation:
12x-3y=15 - Get y alone
-12x =12x
-3y=-12x+15
-3y=-12x+15 - Divide.
__________
-3 -3
y=12/3x-15/3 - Distribute division. Negative over a negative is positive. Positive over a negative is a negative.
y=4x-5 - Reduce fractions.
HELP HELP HELP
The function t relates the age of a plant fossil in years to the percentage c of carbon remaining in the fossil relative to when it was alive.
t(c)=-3970.9(ln c)
Use function t to complete the statements.
A fossil with 47% of its carbon remaining is approximately how old
1. 2998
2 11,910
3 7550
A fossil that is 7000 years old will have approximately
1. .2%
2. 57%
3 17%
Of its carbon remaining.
Select the correct answers
Answer:
2998 ; 17%
Step-by-step explanation:
Given the function:
t(c)=-3970.9(ln c)
c = % of carbon remaining ; t = time
1.) c = 47% = 47/100 = 0.47
t(0.47) = - 3970.9(In 0.47)
t = - 3970.9 * −0.755022
t = 2998.119
t = 2998
B.)
t = 7000
t(c)=-3970.9(ln c)
7000 = - 3970.9(In c)
7000 / - 3970.9 = In c
−1.762824 = In c
c = exp(−1.762824)
c = 0.1715596
c = 0.1715596 * 100%
c = 17.156% ; c = 17%
Answer: For plato family
The function t relates the age of a plant fossil, in years, to the percentage, c, of carbon-14 remaining in the fossil relative to when it was alive.
Use function t to complete the statements.
A fossil with 47% of its carbon-14 remaining is approximately
years old.
A fossil that is 7,000 years old will have approximately
17% of its carbon-14 remaining.
Step-by-step explanation:
The first box is 2,998
The second box is 17%
Find the missing angle.
Answer:
[tex]m\angle XYV=135^{\circ}[/tex]
Step-by-step explanation:
Notice that [tex]m\angle XYV=m\angle XYW+m\angle VYW[/tex].
The diagram already marks [tex]m\angle VYW=80^{\circ}[/tex], so we just need to find [tex]m\angle XYW[/tex].
[tex]\angle TYU[/tex] and [tex]\angle XYW[/tex] are vertical angles, which means they are equal in measure.
Therefore,
[tex]m\angle TYU=m\angle XYW=6x+7[/tex]
Since there are [tex]180^{\circ}[/tex] on each side of a line, we have the following equation:
[tex]m\angle XYW+m\angle VYW+m\angle UYV=180^{\circ},\\6x+7+13+4x+80=180,\\10x+20=100,\\10x=80,\\x=8[/tex].
Plugging in [tex]x=8[/tex], we have:
[tex]m\angle XYW=6(8)+7=55^{\circ}[/tex].
Therefore,
[tex]m\angle XYV=55^{\circ}+80^{\circ},\\m\angle XYV=\fbox{$135^{\circ}$}[/tex].
-44 x -44 × -44 × -44 =
Answer:
3748096
Step-by-step explanation:
Explain why the expressions 8x(6-4) and 8x6-4 dont not have the same value even though they look very similar? HELP!! PLEASE EXPLAIN IT IN 2 complete sentences. (ITS ALGEBRA)
Answer:
Because the first has () and the second doesn't so if u multiply the first one you will have to start with the () but if u answer the second u can start with anything
I will give brainiest to whoever answers correctly !!
Answer:
-6.08 or 6.08
Step-by-step explanation:
The Census Bureau says that the 10 most common surnames in the United States are, in order, Smith, Johnson, Williams, Brown, Jones, Miller, Davis, Garcia, Rodriguez, and Wilson. These names account for 9.6% of all U.S. residents. Suppose you look at the authors of the textbooks for your current courses and find that there are 8 authors in total. What is the probability that none of the 8 surnames of these authors were among the 10 most common
Answer:
0.4460 = 44.60% probability that none of the 8 surnames of these authors were among the 10 most common
Step-by-step explanation:
For each surname, there are only two possible outcomes. Either they are among the 10 most common, or they are not. Each author is independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
These names account for 9.6% of all U.S. residents.
This means that [tex]p = 0.096[/tex]
8 authors in total.
This means that [tex]n = 8[/tex]
What is the probability that none of the 8 surnames of these authors were among the 10 most common
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.096)^{0}.(0.904)^{8} = 0.4460[/tex]
0.4460 = 44.60% probability that none of the 8 surnames of these authors were among the 10 most common
1. Find the length a of the altitude drawn to the hypotenuse. [Triangle is not drawn to scale.]
a
4.
16
A. a = 64
B. a = 20
C. a = 2V5
D. a = 8
ninate Education Inc.
Answer:
C.
Step-by-step explanation:
Please help me ASAP I’ll Mark Brainly
Answer:72
Step-by-step explanation:
Answer:
3(4 + 3 + 17)
Step-by-step explanation:
The greatest common factor of the three numbers is 3. The equation would then become 3(4 + 3 + 17)
The diameter of the circle above is 20 cm. What is the circumference of the circle? (Use = 3.14.)
Step-by-step explanation:
diameter=20/2,radius=10
circumference of circle=2×pi×radius
circumference of circle=2×3.14×10
circumference of circle=62.8
Guy is self employed. In one year, Guy generates a gross income of $44,500. When calculating his taxes, Guy is allowed to deduct $2,500 in expenses from his gross income (the result is his 'operating income'). Guy must then pay 10% tax on all operating income up to $20,000 and then 20% on any operating income over $20,000. Calculate the amount of tax that Guy must pay. Give your answer in dollars to the nearest dollar. Do not include commas or the dollar symbol in your answer.
Answer:
20000÷20= the amount you need for the income price is 16000
Answer:
Step-by-step explanation:
Operating Income=$44,500−$2,500=$42,000.
So Guy will be taxed 10% on $20,000 and 20% on $(42,000−20,000)=$22,000, hence
Total Tax=10%×$20,000+20%×$(42,000−20,000)=$6,400.
The square ABCD has side length 20 cm,
E is the midpoint of BC,
20 cm
20 cm
Work out the length of AE,
Give your answer correct to one decimal place.
Answer:
AE=22.4
Step-by-step explanation:
BE is 1/2 of BC
BC is 20 cm All sides of a square are equal
BE = 1/2 BC Property of a midpoint.
BE = 10
Now just use Pythagorus
AB^2 + BE^2 = AE^2
AE^2 = 20^2 + 10^2 Perform the sqrs
AE^2 = 400 + 100 Add the terms
AE^2 = 500 Take the square root of both sides
√AE^2 = √500
AE = 22.36
AE ≈ 22.4
Please help it's due by 11 59 i will make as brainliest, thanks, and 5.0 for those who give actual and proper answers
Orange colors - Why are the locations of the police station and fire department congruent?
blue colors - Why are the locations of the restaurant and bank congruent?
Answer:
Step-by-step explanation:
Congruent are angles that are in identical angles. For example the orange colors are congruent because both of the angles are across each other, and because of them being crossed they are both the same degrees making the congruent, same with the blue but instead of being across eachother they are in the angle to the left of the parallel lines that are the same degrees as well.
prove that (n+5)^2-(n+3)^2 is a multiple of 4 for all positive integer values of n
Answer:
Proved
Step-by-step explanation:
Given
[tex](n+5)^2-(n+3)^2[/tex]
Required
Show that [tex](n+5)^2-(n+3)^2[/tex] is a multiple of 4
Expand each bracket
[tex](n+5)(n+5)-(n+3)(n+3)[/tex]
Open brackets
[tex]n^2 + 5x + 5x + 25 - (n^2 + 3x + 3x + 9)[/tex]
[tex]n^2 + 10x + 25 - (n^2 + 6x + 9)[/tex]
Open bracket
[tex]n^2 + 10x + 25 - n^2 - 6x - 9[/tex]
Collect Like Terms
[tex]- n^2 + n^2 - 6n + 10n + 25 - 9[/tex]
[tex]- 6n + 10n + 25 - 9[/tex]
[tex]4n + 25 - 9[/tex]
[tex]4n + 16[/tex]
Factorize
[tex]4(n + 4)[/tex]
Hence, the multiples of [tex](n+5)^2-(n+3)^2[/tex] are [tex]4[/tex] and [tex](n + 4)[/tex]
The artist realizes she has 49 ounces left . How many ounces of blue does she need to add
2 ounces of blue paint to every 7 ounces of yellow
Answer:
hwope this helps ＼(=^‥^)/’`
Step-by-step explanation:
Which table represents the statement "Di runs at a rate of 4 meters per second " ?
Answer:
The third one Edg
Step-by-step explanation: Brainlest plzzz
Hope this isn’t too difficult, my teacher said to show you're work... so I hope you don’t mind explaining how you found it.
Answer:
3/4 / 1/6
keep the first fraction the same
3/4
flip the second fraction
6/1
change the division to a multiplication it should then read
3/4 X 6/1
now multiply the fractions
3 X 6 = 18
4 X 1 = 4
18/4 this can then be turned into a mixed number.
there are four 4's in 18 with two left over. so it becomes
4 2/4 and simplified 4 1/2.
What is the value of q?
Pls help fast
Answer:
C
Step-by-step explanation:
maurice read 10 pages that is 50 percent of the paper lenght what i the paper lenght
Answer:
Would it not be 20?
Step-by-step explanation:
Answer:
The answer is 20
Step-by-step explanation:
If 10 pages is 50% of the paper length, to make it equal 100% you just multiply 10X2 or add 10+10 and that equals 20.
can anyone help me pls
Answer:
405 calories
Step-by-step explanation:
All we have to do is:
9 × 45
I hope this helps!
ABC and ACD are triangles.
a) Show that AC = 11.4 cm, correct to 3 significant figures.
А
17 cm
76°
429
D
13 cm
83
B В-
с
b) Calculate BC.
Answer:
a) 11.4
Step-by-step explanation:
cos42=0.74
d²=c²+a²-2caCosD
d²=17²+13²-2×17×13×Cos42
d²=17²+13²-328.47
d²=289+169-328.47
d²=458-328.37
d=√129.63
d=11.4
The length of AC is 11.4 cm and the length of BC is 30.9 cm after solving through trigonometric ratios.
What are trigonometric ratios?Trigonometric ratios deal with the sides and angles in a right angled triangle. sin, cos, tangent ,cosecant ,secant and cotangent are trigonometric ratios.
How to find the length of side of triangle?ABC and ACD are triangle,
The value of AC will be:
According to cosine formula:
[tex]AC^{2} =AD^{2} +AC^{2} -2AD*AC*Cos D.[/tex]
[tex]AC^{2} =17^{2} +13^{2} -2*17*13* cos 42[/tex]
[tex]AC^{2} =[/tex]289+169-328.47
[tex]AC^{2}[/tex]=129.52
AC=11.4 cm
The value of BC will be as under:
using the sine rule
BC/sin A=CA/sin B=AB/sinC
BC/sin76=11.4/sin 21=AB/sin83
from the first 2 in equal to form
BC/sin 76=11.4/sin 21
BC=30.9
Hence the length of AC=11.4 cm and BC=30.9 cm.
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i need help plz
State the coordinates of the point.
Answer:
(-5,8)
Step-by-step explanation:
Hope this helps ;)
Choose all the equations that have m =5 as the solution
A. m - 1 = 4
B. m + 4 = 20
C. m - 3 = 8
D. 22 + m = 25
E. 12 = m + 7
Answer:
A and E
Step-by-step explanation:
Plug 5 in for m in every equation, and see if the math works.
A.
[tex]m-1=4\\5-1=4\\\\[/tex]
A - works
B.
[tex]m+4=20\\5+4=9[/tex]
B - does not work
C.
[tex]m-3=8\\5-3=2[/tex]
C - does not work
D.
[tex]22+m=25\\22+5=27[/tex]
D - does not work
E.
[tex]12=m+7\\12=5+7[/tex]
E - works
Answer:
A and E just to make it quick hope this helps
Step-by-step explanation:
can someone plz help me with this , i cant find out who created this equation..
Answer:
Answering the part about who created the first equation:
There are a lot of different ways to solving cubic equations, but the first one is given by Gerolamo Cardano, who published it, and the equation was created by Scipione del Ferro, an Italian mathematician who was born in 1465. He did not make a lot of other contributions to mathematics, some of his other works were related to the rationalization of fractions with denominators containing sums of cube roots
This equation was called "Cardano's formula", and originally only worked for depressed cubic equations ( x^3 + p*x + q = 0)
But there are variations that can be used for more general cubic equations, of the form:
a*x^3 + b*x^2 + c*x + d = 0.
Which three types of transformations result in congruent shapes? Question 8 options: A) Reflection, rotation, translation B) Reflection, translation, dilation C) Reflection, dilation, rotation D) Rotation, dilation, translation
Answer: A
Step-by-step explanation:
Answer:
A. Reflection, rotation, translation
Step-by-step explanation:
Rotations, reflections, and translations are isometric. That means that these transformations do not change the size of the figure. If the size and shape of the figure is not changed, then the figures are congruent. Explore and discuss the examples of transformations below with your child. Examples of Transformations.Anna can buy 5 sweatshirts for a total of $75. How much would it could it cost if she were to buy 2 sweatshirts at the same price
Answer:
$75
Step-by-step explanation:
(45 / 3) x 5 = 75
To find the amount of money for each t-shirt, divide 45 by 3.
45 / 3 = 15
To find out the price of 5 t-shirts, multiple 15 by 5.
15 x 5 = $75
$75 is your answer :)