Given that the jeweler has alloys that are 25% gold, 50% gold, and 82% gold.
As he wants to make 14 grams of an alloy by adding two different alloys that is precisely 75% gold, so one alloy must have a percentage of gold more than 75%.
One alloy is 82% gold and, the second can be chosen between 25% gold, 50% gold, so there are two cases.
Case 1: 82% gold + 50% gold
Let x grams of 82% gold and y grams of 50% gold added to make x+y=14 grams of 75% gold, so
75% of 14 = 82% of x + 50% of y
[tex]\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times y \\\\[/tex]
[tex]\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times (14-x)[/tex] [as x+y=14]
[tex]\Rightarrow 75 \times 14 = 82 \times x + 50 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 50 \times14-50\times x \\\\\Rightarrow 75 \times 14 = 32 \times x + 50 \times14 \\\\\Rightarrow 32 \times x =75 \times 14 - 50 \times14 \\\\[/tex]
[tex]\Rightarrow x =(25 \times 14)/32=10.9375[/tex] grams
and [tex]y = 14-x= 14-10.9375=3.0625[/tex] grams.
Hence, 10.9375 grams of 82% gold and 3.0625 grams of 50% gold added to make 14 grams of 75% gold.
Case 2: 82% gold + 25% gold
Let x grams of 82% gold and y grams of 25% gold added to make x+y=14 grams of 75% gold, so
75% of 14 = 82% of x + 25% of y
[tex]\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times y \\\\\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times (14-x) \\\\ \Rightarrow 75 \times 14 = 82 \times x + 25 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 25 \times14-25\times x \\\\\Rightarrow 75 \times 14 = 57 \times x + 25 \times14 \\\\\Rightarrow 57 \times x =75 \times 14 - 25 \times14 \\\\[/tex]
[tex]\Rightarrow x =(50 \times 14)/57=12.28[/tex] grams
and [tex]y = 14-x= 14-12.28=1.72[/tex] grams.
Hence, 12.28 grams of 82% gold and 1.72 grams of 50% gold added to make 14 grams of 75% gold.
A sequence has an initial value (I) of -17 and its fourth term (a4) is 35. What is its general equation? Its 14th term?
Also, A sequence has a CR of 4/5 and its eighth term (a8) is (393216/3125). What is its general equation? Its 3rd term?
Answer:
The sequence is an Arthemtic ProgressionAn=A1+(n-1)d
A1 is first term, An is nth term, n is number of term, and d is common difference
therefore
A4=35, A1= -17
A4=A1+(4-1)d
35= -17+3d
35+17=3d
52=3d
52/3=3d/3
14=d
common diffrence(d)=14
The general solution is given byAn= -17+(n-1)14
An= -17+14n-14
An= -31+14n
An= 14n-31
A14 term, means n=14
From An=A1+(n-1)d
A14= -17+(14-1)14
= -17+(13×14)
= -17+182
= 165.
Therfore, the 14th term is 165.
2. A sequence has a CR of 4/5 and its eighth term (a8) is (393216/3125). What is its general equation? Its 3rd term?
solution
common ratio(r)=4/5
eighth term(G8)=393216/3125
From Gn= G1r^(n-1)
G8 means n=8
G8=G1r^(n-1)
393216/3125=G1(4/5)^(8-1)
393216/3125=G1(4/5)^7
G1=(393216/3125)/(4/5)^7
G1=600
The first term is given by G1=600
ThereforeThe General equation is given by
The General equation is given by Gn= 600(4/5)^(n-1)
3rd term (G3)
G3= G1(4/5)^(3-1) where n=3,
=600(4/5)^2
=600(16/25)
=384
Therefore, the 3rd term is given by G3= 384.
I have made some Corrections i messed up somewhere.
HELP ASAP WILL GIVE BRANILEST Consider the inequality 7 + 4x > x − 2. Select all the values of x that are solutions.
THERE IS MORE THAN ONE ANSWER
Group of answer choices
x = 0
x = 3
x = 6
x = −3
x = −6
Answer:
x=3, x=6, x=-3, x=-6
Step-by-step explanation:
So, every single one except 0.
x > -3
x is greater than -3.
i.e -2, -1, 0, 1, 2, 3, 4, 5, . . . . .
From the given option we can select the correct answers.
We see that,
0, 3, and 6 are the correct answer.
The values of x that are solutions to the given inequality are 0, 3, and 6.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
7 + 4x > x - 2
Solve for x.
7 + 4x > x - 2
Subtract x on both sides.
7 + 4x - x > -2
7 + 3x > -2
Subtract 7 on both sides.
7 + 3x - 7 > -2 - 7
3x > -9
Divide both sides by 3.
x > -3
This means x is greater than -3.
i.e -2, -1, 0 , 1, 2, 3, 4, 5, . . . . .
From the given option we can select the correct answers.
We see that,
0, 3, and 6 are the correct answer.
Thus,
The values of x that are solutions to the given inequality are 0, 3, and 6.
Learn more about inequalities here:
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Can someone help me out please
Answer:
I am confused!
Step-by-step explanation:
Suppose that the marginal profit function for a certain product is P'(x)=300-0.15x^2, and the profit at a production level of 0 is P(0)=-1200. Find the profit function P(x)
9999999Answer:
Step-by-step explanation:
For the coins
Which answer is correct? Please hurry
Answer:
15
Step-by-step explanation:
40 of them are offense players, 5 are special teams which means that 15 are defensive
Answer: 2/3 of 60 = 40
1/12 of 60 = 5
40 + 5 = 45 obviously.
45 + 15 = 60.
Therefore the amount of defensive players would be 15.
Write the equation in slope-intercept form.
It's the second one.
Brainliest please!
Answer:
y=3x
Step-by-step explanation:
Comparing 3 fractions
3/8 4/5 1/2
I don't really need the answer I'd really appreciate an explanation of how to compare 3 fractions with different denominators though, thank you
Find the slope intercept form of the equation that passes through 6,1 and is PARALLEL to the line y=(2/3)x+20
Answer:
y= 2/3x - 3
Step-by-step explanation:
A baker sells bread for $4 a loaf and rolls for $1 each. The baker needs to sell $36 worth of baked goods by
the end of the day.
Enter a linear equation that describes the problem.
An equation for the value of the baked goods is
bread sold, and r is the number of rolls sold.
= $36, where b is the number of loaves of
Explanation:
Cost of 1 loaf of bread = $4
Cost of 1 roll = $1
The baker needs to sell both items and it should be worth $36.
To find the linear equation, Suppose, the baker sells "b" loaves of bread and "r" rolls.
Then the total cost of the sales has to be $36.
So, the linear equation will be:
4b + 1r = 36
Can you help me with #6??
(Algebra 1 sucks..)
Answer:
37
Step-by-step explanation:
Use the given functions to set up and simplify
simplify radical expression with variables. please helping super confused
Answer:
Work shown below!
Step-by-step explanation:
[tex]\sqrt{14*4xy^{10/2}z^{5/2} }=2y^{5}z^{2} \sqrt{14xz}[/tex]
Which algebraic expression represents the phrase “fourteen increased by a number”?
Answer: 14 + x
Step-by-step explanation:
The number 14 is given. The number being added to 14 is unknown. Thus, we can assign it a variable. I have chosen x. Add x (or any variable representing a number) to 14, for the expression 14 + x.
1.**
What is the slope of the line
y = 5x - 5/2
Answer:
5
Step-by-step explanation:
Slope is number by X
what's the midpoint of (0,9) and (10,5)
Answer:
[tex](5,7)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Step-by-step explanation:
Step 1: Define
Point (0, 9)
Point (10, 5)
Step 2: Find midpoint
Substitute: [tex](\frac{0+10}{2},\frac{9+5}{2})[/tex]Add: [tex](\frac{10}{2},\frac{14}{2})[/tex]Divide: [tex](5,7)[/tex]Step-by-step explanation:
Hey there!
Given points are: (0,9) and (10,5)
Then;
Using midpoint formula;
[tex](x,y) = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]
Put all values.
[tex](x,y) = ( \frac{0 + 10}{2} , \frac{9 + 5}{2} )[/tex]
Simplify it.
[tex](x,y) = (5,7)[/tex]
Therefore, the midpoint is (5,7)
Hope it helps...
Will give brainliest, urgent
Answer:
Refer to attachedStep-by-step explanation:
The answer is attached and provided below
Opposite angles = CongruentConsecutive angles = SupplementaryDiagonals = Bisects each otherOpposite sides = Parallel and congruentwhat is a good calculator that will give you the points to linear inequality systems?
Answer:
I would just recommend you using M A T H W A Y and paying for the measly little $9.99 for the step-by-step answers.
Step-by-step explanation:
Or desmos would work but I would highly recommend m a t h w a y
Multiple choice: Which of the following angles, when drawn in
standard position, would not be coterminal with an angle that
measures 270°?
(1)-90°
(3) 630°
(2) 990°
(4) 720°
Answer:
Step-by-step explanation:
4
The angle that should be drawn in standard position, would not be coterminal with an angle that measures 270° should be 720 degrees.
What is coterminal?Coterminal angles refer to the angles in standard position where angles should be along with the initial side on the positive x-axis that have a common terminal side.
Therefore, The angle that should be drawn in standard position, would not be coterminal with an angle that measures 270° should be 720 degrees.
Learn more about an angle here: https://brainly.com/question/17688754
if each board in a fence is 6 inches wide, how many boards will josee need to fence 4 sides of a playground that is 60ft wide by 125ft long?
A vertical parabola goes through (1,-2), (-3, 10), and (4, 31). Use matrices to
solve for D, E, and F, given the general form x² + y2 + Dc + Ey + F = 0 (since it
is a vertical parabola there is not a z term).
22.
2 +
Y +
0
Answer:
D = 1/2 , E = -1/2 , F = -5/2
Step-by-step explanation:
vertical parabola : ( 1,-2), ( -3, 10 ), (4, 31 )
General form ; [tex]x^2 + y^2 + Dx + Ey + F = 0[/tex]
( 1 ,-2 ) = x1, y1
( -3, 10 ) = x2, y2
( 4, 31 ) = x3, y3
hence :
[tex]y1 = ax_{1} ^2 + bx_{1} + c[/tex]
[tex]y2 = ax_{2} ^2 + bx_{2} + c[/tex]
[tex]y3 = ax_{3} ^2 + bx_{3} + c[/tex]
attached below is the detailed solution required
D = 1/2 , E = -1/2 , F = -5/2
I need help with this ASAP, I’ll give brainliest if correct
surface area of a net
Answer:
Step-by-step explanation:
This is really a sloppy diagram. You have to know if the base of the triangle is 5 or 10.
It is 5. So the area of 1 of the triangles is 1/2 * b * h
b = 5
h = 8.7
Area = 1/2 * 8.7 * 5 = 21.75
There are 4 such triangles. The total area = 4 * 21.75 = 87 sqr in
What do you call the number that you divide by?
Answer:
the number that you divide by is called the dividend and the number which the dividend is being divided by is the divisor.
Find the probability of rolling either a sum of 3 or 9 on a roll of two dice
Answer:
3eyhugfshdsasdfghgrew12345[pterfghrdfytfvbkyg12345678910
Step-by-step explanation:
ghgtgghjkjhffhjkuhytggbnm,
ap calc multiple choice question; attached below
please explain how, please!
Answer:
C. [tex]\frac{f(b)-f(1)}{b-1}=20[/tex]
General Formulas and Concepts:
Calculus
Mean Value Theorem (MVT) - If f is continuous on interval [a, b], then there is a c∈[a, b] such that [tex]f'(c)=\frac{f(b)-f(a)}{b-a}[/tex]MVT is also Average ValueStep-by-step explanation:
Step 1: Define
[tex]f(x)=e^{2x}[/tex]
f'(c) = 20
Interval [1, b]
Step 2: Check/Identify
Function [1, b] is continuous.
Derivative [1, b] is continuous.
∴ There exists a c∈[1, b] such that [tex]f'(c)=\frac{f(b)-f(a)}{b-a}[/tex]
Step 3: Mean Value Theorem
Substitute: [tex]20=\frac{ f(b)-f(1)}{b-1}[/tex]Rewrite: [tex]\frac{ f(b)-f(1)}{b-1}=20[/tex]And we have our final answer!
Identify the place of the 4 in the number: 45,348
Which on is correct?
Answer:
Congruent
Step-by-step explanation:
Type SSS, SAS, ASA, AAS, HL to justify why the two larger triangles are congruent.
AD = BC
The required triangle ADB and ABC, are congruent triangles by SAS postulate of congruency.
What is congruent geometry?In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
Here,
Consider triangle ADB and ABC,
AB = AB [common side between the two triangles]
∠A = ∠B [Both angles have an equal measure of 90°]
AD = BC [Given in the question]
So, both triangles are congruent triangles by the SAS postulate of congruency.
Learn more about congruent geometry here. https://brainly.com/question/12413243
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4 times a number is 12 less than the square of that number. Find the positive solution
Answer:
I think its 6
im not 100%sure
Step-by-step explanation:im in 7th grade tho
But can i get brainless
Answer:
6
Step-by-step explanation:
Have a good day :)
Lila rode her bike from 9:30 am to 11:10 am this morning. She rode 1.5 miles every 10 minutes. What is the total number of miles Lila rode this morning?
Answer:
15mi
Step-by-step explanation:
9:30am to 11:10am equals 100 minutes
100 minutes divided by 10 minutes per segment equals 10 segments
1.5 miles per segment multiplied by 10 segments equals 15 total miles
Approximate the value of 5 pie
Answer:
15.71Step-by-step explanation:
5*π = 15.7079633
15.7079633 rounded to the nearest hundredth is 15.71
give me brainliest please