please solve for x and explain every step in detail!!! it’s urgent

Answer:

Let x be your first alloy

2/5x+7/10(30-x)=1/2(30)

4x+210-7x=150

3x=60

x=20

So, you need 20 lbs of the first alloy, and 10 parts of the second to make 30 lbs of half iron and half silver alloy

Answer:

20 pounds for first 10 for second.

Step-by-step explanation:

Answer:

You know that 5 g of sugar form 12%. Let x g be the amount of water needed. The total amount of syrup will be x+5 g. Then

5 g - 12%,

x+5 g - 100%.

mathematically you can write a proportion;

5/x+5=12/100

=>500=12(x+5)

,500=12x+60

,12x=400,

x=440/12

=110/3

36.66 grams of water is added  to make 12% sugar syrup using 5g sugar.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Let the amount of water is added be 'x'.

Amount of sugar = 5 g

We need to make 12% of sugar syrup.

x grams of water is added to 5 g of sugar, to 12% of sugar syrup.

5/5+x=12/100

Apply cross multiplication

5×100=12(5+x)

500=60+12x

Subtract 60 from both sides

440=12x

Divide both sides by 12

x=36.66

Hence, 36.66 grams of water is added  to make 12% sugar syrup using 5g sugar.

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Answer: She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

Step-by-step explanation:

Let P be the initial amount she invested in an account that pays 6% interest.

Then, amount invested in other account = 2P

Simple interest = Principal x rate x time

After one year, for the first account,

Interest = P(0.06)(1)  = 0.06P

For second account,

Interest = (2P)(0.07)(1)=0.14P

Total interest = [tex]0.06P+0.14P=1000[/tex]

[tex]\Rightarrow\ 0.20P=1000\\\\\Rightarrow\ P=\dfrac{1000}{0.20}\\\\\Rightarrow\ P=5000[/tex]

2P = 2(5000)=10000

Hence, She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

At the interest rate of 6%, amount invested is; $5000

At interest rate of 7%, amount invested is; $10000

Let P be the initial amount that Ms. Hagan invested in the 6% interest account that

Since she invested twice as much in the 7% interest account as in the 6% interest account, then;

Initial amount invested in the 7% interest account = 2P

Formula for Simple interest is;

I = Principal × rate × time

Interest after 1 year for the 6% interest account is,

I_1 = P × 0.06 × 1

I_1 = 0.06P

Interest after 1 year for the 7% interest account is,

I_2 = 2P × 0.07 × 1

I_2 = 0.14P

Total investment pays her $1000 after a year. Thus;

0.06P + 0.14P = 1000

0.2P = 1000

P = 1000/0.2

P = $5000

Then amount initially invested in the 7% interest account = 2P = $10000

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Answer:

8,000 m^3

Step-by-step explanation:

The computation of the volume of the modified cube in cubic meters is shown below:

Given that

Volume = 64 m^3

So each side would be

= ∛64

= 4

Now each side is scaled by 5 so each side would be

= 4 × 5m

= 20m

Now the volume of the modified cube is

= 20^3

= 8,000 m^3

Answer:

8,000

Step-by-step explanation:

When the sides of the cube are scaled by a factor of k, the volume increases by a factor of k3. Here, the new volume is 64 cubic meters × 53 = 8,000 cubic meters.

Answer:

x [tex]\geq[/tex] 5

Step-by-step explanation:

step 1: subtract 6 from both sides

step 2: divide both sides by 7

answer: x [tex]\geq[/tex] 5

interval notation: [5,∞)

Answer:

Your answer would be B. 3.2m and -m/5

Step-by-step explanation:

I did the test on edge and I got it right

Answer:

The person above is correct!

Step-by-step explanation:

Answer:

Step-by-step explanation:

if the triangles are similar then their sides are in proportion ( or you can think that they make equivalent fractions like 2/3 = 4/6 )

44/ (x+2) = 20/7 = 3x+1 /5 ( all of those are equivalent  fractions)

use that  [tex]\frac{a}{b} =\frac{c}{d}[/tex]  is the same as a*d = b*c

[tex]\frac{44}{x+2} =\frac{20}{7}[/tex]  is the same as 20(x+2) = 7*44

20x +40 = 308; subtract 40 from both sides

20x = 268; divide by 20 both sides

x= 13.4

Answer:

77.5 or 76

Step-by-step explanation:

You add all the sides together, since 7.75 is at the bottom, it'd also be at the top.

The amount of interest that's owed by Darius after 6 months will be $14

Principal = $500

Rate = 5.6%

Time = 6 months.

Based on the information given, the simple interest will be calculated as:

Simple Interest = PRT/100

Simple Interest = ($500 × 5.6 × 1/2) / 100

Simple Interest = $1400/100

Simple Interest = $14

Therefore, the amount of interest that's owed by Darius after 6 months will be $14

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Answer:

x = 3

Step-by-step explanation:

MN is exactly half of 6x + 2 (midpoint theorem)

2(2x + 4) = 6x + 2

4x + 8 = 6x + 2

-2x + 8 = 2

-2x = -6

x = 3

Answer:

AC

Step-by-step explanation:

The diameter of the circle is the length of a line that goes through the center and touches two points on the circle.

Therefore, AC is the correct answer because it is a straight line that goes through the center.

I hope this helped! :)

Answer:

AC is a diameter

Step-by-step explanation:

N/A

First, let's write what we know.

We can represent the number of students in the play from each class as L, G, and C. We know that L = 7, and if Gardener has 4 more students than Cho, then G = C + 4.

Then, taking the third line, we can write an inequality:

C < L < G

C < 7 < C + 4

C - 4 < 3 < C

3 < C < 7

If C is greater than 3 and less than 7 and is an integer, than means C is 4, 5, or 6.

Then, we need to find how many students are in the play.

C + L + G

C + 7 + C + 4

2C + 11

So we have our expression for the number of students in the play. Then, we need to find the total number of students. We know that 2C + 11 will be 30% of the total, so if T is the total, we can find T.

0.3T = 2C + 11

(Divide by 3/10 or multiply by 10/3 on both sides)

T = 20/3 C + 110/3

We know from before that C is 4, 5 or 6. We can plug these into our equation here to find which one produces a whole number.

T = 20/3 * 4 + 110/3

T = 190/3

T = 20/3 * 5 + 110/3

T = 210/3

T = 70

T = 20/3 * 6 + 110/3

T = 230/3

We can see here that only when C is 5 will the total be a whole number. That means Mrs. Cho has 5 students in the play. If Mrs. Gardner has 4 more than that, she has 9 students in the play in her class.  We now need to figure out the number of student in her class.

The total students are Cho's, Logan's, and Gardner's classes added together. We know that Logan's class is 23 students, so if we subtract that from the total, we can see that Cho's and Gardner's class have 47 students. If Mrs. Cho has 24 students in her class, we can subtract that from the 47, so we know that Mrs. Gardner has 23 students in her class.

9514 1404 393

Answer:

  A, C, E

Step-by-step explanation:

A. 0.6 • 25 = x . . . . . a direct translation of 60% of 25 (yes)

B. x • 1.6 = 25 . . . no (means 160% of x is 25)

C. 6/10=x/25 . . . . . . the ratio of x to 25 is 60% (yes)

D.60/100 = 25/x . . . no (means 25 is 60% of x)

E. x/25 = 60/100 . . . . . the ratio of x to 25 is 60% (yes)

F.6.0 • 25 = x . . . no (no means 600% of 25)

Answer:

A, C, E

Step-by-step explanation:

Answer:

y = (x – 6) / -3 = [2 – x/3]

Step-by-step explanation:

y = f(x) = -3x + 6

f⁻¹(x) → x = -3y + 6 → (x – 6) / -3 → x / -3 + -6/-3 → -x / 3 + 2 → 2 – x/3

Answer:

Step-by-step explanation:

Definition of constants: Contants are numbers that have no variables.

To find the constants of the expression 7r - 3 + 2s + 5, simply look for numbers without variables. We can see that the constants are -3 and 5, which matches Option B.

Hence, Option B is correct.

Answer:

two numbers are 37 and 20

Step-by-step explanation:

x+y=57

let x be the smaller number

y=x+17

x + x+17=57

2x=57-17

2x=40

x=20

y=x +17

y=20+17

y=37

Answer:

i7x+×52=/67, hope this helps!!!!

Answer:

Perpendicular

Answer:

answer is 10

Step-by-step explanation:

(4x+12)+(4x+12)+(5x+26)=180[sum of isosceles triangles]

8x+34+5x+26=180

X=10

Answer:

50

Step-by-step explanation:

35=70%*x

35=70/100*x

35=7/10*x

350=7*x

x=50

Answer:

8:3

Step-by-step explanation:

The GCF of each of them is 8. Divide both of them by it you'll get the ratio

in equivalence the answer is 8 3

Answer:

26 ounces per can

Step-by-step explanation:

28 is the unit rate of 56 ounces for every 2 cans

A division is a process of splitting a specific amount into equal parts.

A unit rate means a rate for one of something.

We need to find the unit rate  of 56 ounces for every 2 cans

To do this we need to divide Fifty six ounces with two.

56/2

Fifty six divided by two.

We get Twenty eight.

Hence 28 is the unit rate of 56 ounces for every 2 cans

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Answer:

y = -2x + 6

Step-by-step explanation:

This has sort of the same concept as your earlier question

Use the equation y = mx + b

To find the slope, take the second y value and subtract the first y value. Then take the second x value and subtract the first x value. Divide the answers. You'd get -2 in this case. -2 would be your slope (m).

The substitute any set of x and y values (either (1, 4) or (-2, 10)) and the slope into y = mx + b. You'd get 6 as your y-intercept (b).

Answer:

the answer would be 6...

Answer:

what do you mean?

Step-by-step explanation:

Answer:

60 divided by 8

Step-by-step explanation:

60 divided by 8

Answer:

volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx

Step-by-step explanation:

Given the data in the question and as illustrated in the image below;

R is in the region first quadrant with vertices; 0(0,0), A(a,0) and B(0,b)

from the image;

the equation of AB will be;

y-b / b-0 = x-0 / 0-a

(y-b)(0-a) = (b-0)(x-0)

0 - ay -0 + ba = bx - 0 - 0 + 0

-ay + ba = bx  

ay = -bx + ba

divide through by a

y = [tex]\frac{-b}{a}[/tex]x + ba/a

y = [tex]\frac{-b}{a}[/tex]x + b

so R is bounded by  y = [tex]\frac{-b}{a}[/tex]x + b and y =0, 0 ≤ x ≤ a

The volume of the solid revolving R about x axis is;

dv = Area × thickness

= π( Radius)² dx

= π ( [tex]\frac{-b}{a}[/tex]x + b )² dx

V = π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx

Therefore,  volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx

The volume of the solid generated when region R is revolved about the x-axis is [tex]\frac{b^{5} }{3a^{2} }[/tex].

Equation of the line AB

[tex]y-0 = \frac{b-0}{0-a} (x-a)[/tex]

[tex]y = \frac{-b}{a} (x-a)[/tex]

The volume generated when a curve f(x) is rotated about the x-axis in x∈(c,d) is given by:

[tex]V=\int\limits^d_c {y^2} \, dx[/tex]

So, the volume generated when line AB is rotated about the x-axis will be [tex]V=\int\limits^b_0 ({\frac{-b}{a} (x-a))^2} \, dx[/tex]

[tex]V=\frac{b^{5} }{3a^{2} }[/tex]

Therefore, the volume of the solid generated when region R is revolved about the x-axis is [tex]\frac{b^{5} }{3a^{2} }[/tex].

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9514 1404 393

Answer:

  1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42,

  55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310

Step-by-step explanation:

The trailing digit is 0, and the sum of digits is 6, so we know the number is divisible by 2, 3, 5. Dividing out those factors, we get a quotient of 77, which is 7×11. This means the prime factorization is ...

  2×3×5×7×11 = 2310

There are 5 prime factors, each with an exponent of 1, so the total number of divisors is 2^5 = 32. We will have found them all when all 32 are listed.

  1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42,

  55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310

Of course, the pairwise products working toward the center from the ends of the list are all 2310.