Steven has 9 gold coins that are identical in appearance. However, one coin is counterfeit and weighs slightly less than the others. Using a balance scale, how can he find the counterfeit coin in just two weighings?

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft

Step-by-step explanation:

If ABC is a right triangle, where the right angle is B, then

∵ ABC is a right triangle

∵ m∠C = 90°

∴ c is the hypotenuse and a , b are its legs

∵ m∠A = 58.3°

- The sum of the two acute angles in the right triangle = 90°

∴ m∠A + m∠B = 90°

- Substitute the measure of angle A

∴ 58.3 + m∠B = 90

- Subtract 58.3 from both sides

∴ m∠B = 31.7°

∵ sin(A) = [tex]\frac{a}{c}[/tex]

∵ c = 24.8 feet

∴ sin(58.3) = [tex]\frac{a}{24.8}[/tex]

- By using cross multiplication

∴ a = (24.8) × sin(58.3)

∴ a = 21.1 ft

∵ sin(B) = [tex]\frac{b}{c}[/tex]

∵ c = 24.8 feet

∴ sin(31.7) = [tex]\frac{b}{24.8}[/tex]

- By using cross multiplication

∴ b = (24.8) × sin(31.7)

∴ b = 13.0 ft

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft

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Answer:

x = 4

Step-by-step explanation:

Solve the inequality

2x - 3 > 11 - 5x ( add 5x to both sides )

7x - 3 > 11 ( add 3 to both sides )

7x > 14 ( divide both sides by 7 )

x > 2

The only value of x greater than 2 is 4, thus

x = 4 is in the solution set

The value of x that is a solution set to the inequality is: D. 4.

Given the an inequality such as, 2x – 3 > 11 – 5x, solve to isolate x.

2x – 3 > 11 – 5x

2x + 5x > 11 + 3

7x > 14

Divide both sides by 7

x > 14/7

x > 2

All set of the solution must be greater than 2. 4 is the only value of x that is greater than 2, so the answer is: D. 4.

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Answer:

14 quarters and 28 nickels

Step-by-step explanation:

System of Equations where x = number of quarters and y = number of nickels

(1) equation with value of each coin

    0.25(x)+0.05(y) = 4.90

(2) total number of coins

    x + y = 42

Solve system of equations using either substitution or elimination

(elimination multiplying equation 2 by -0.5)

.25(x) + 0.05(y) = 4.90

-0.05(x) - 0.05(y) = 42 * (-0.05)

(3) Resulting equation

.20(x) = 2.8

x = 14

plug x into equation 2

14 + y = 42

y = 28

There are 14 quarters and 28 nickels in Mary's collection.

Answer:

-x^3+2x^2+4x-8

Step-by-step explanation:

(2-x)(x^2-4)

2x^2-8-x^3+4x

-x^3+2x^2+4x-8

The slope is already given in the question, so we only ned to solve for the y-intercept using  y = mx + b.

4 = 3(1) + b

4 = 3 + b

4 - 3 = 3 + b - 3

1 = b

Now, write the equation in slope-intercept form.

y = 3x + 1

_____

Best of Luck,

Wolfyy :)

To find the number of different arrangements of 3 books from 7, we use permutations, specifically P(7, 3) = 7! / (7-3)! = 210. Thus, there are 210 different arrangements possible.

The student's question involves determining the number of different arrangements of 3 books that can be made from a set of 7 books. In mathematics, this is known as a permutation problem, since the order in which the books are placed matters.

To calculate permutations, we use the formula P(n, k) = n! / (n-k)!, where n is the total number of items to choose from, in this case, 7 books, and k is the number of items to arrange, in this case, 3. Using the formula:

P(7, 3) = 7! / (7-3)! = 7! / 4! = (7 × 6 × 5 × 4!) / 4! = 210.

Therefore, there are 210 different arrangements possible when selecting and arranging 3 books out of 7.

Answer:

y=x^2-10x+27

Step-by-step explanation:

y=x^2

Shifted 5 to the right: y = (x-5)^2

Shifted 2 up: y = (x-5)^2+2

Simplify. You can use "(a-b)^2 = a^2-2ab+b^2" formula.

y = (x-5)^2+2 becomes y=x^2-10x+25+2 = y=x^2-10x+27

Answer:

Step-by-step explanation:

y=4x-2

The estimated increase in height each year for a boy, according to the model h = 3a + 28.6, is 3 inches.

The equation h = 3a + 28.6 is used to estimate the height h of a boy, in inches, in terms of the boy's age a, in years. The coefficient of a in this linear equation represents the rate of change of height with respect to age. Given that the coefficient is 3, this indicates that the estimated increase in height each year is 3 inches. Therefore, the answer to the question is A) 3.

Answer:

(0,5) and (10,0)

Step-by-step explanation:

The equation of the straight line is given by 2x + 4y = 20 .......... (1)

Now, point (0,5) satisfies the equation (1) as putting x = 0, we will get y = 5.

Now, point (0,10) does not satisfy the equation (1) as putiing x = 0, we get y = 5 ≠ 10

Again, point (1,2) does not satisfy the equation (1) as putiing x = 1, we get y = 4.5 ≠ 2

Now, point (1,4) does not satisfy the equation (1) as putiing x = 1, we get y = 4.5 ≠ 4

Again, point (5,0) does not satisfy the equation (1) as putiing y = 0, we get x = 10 ≠ 5

Finally, point (10,0) satisfies the equation (1) as putiing y = 0, we get x = 10 .

Therefore, only points (0,5) and (10,0) are on the graph of the line 2x + 4y = 20 (Answer)

Answer:

The points a. (0,5) and f. (10,0) will lie on the given line.

Step-by-step explanation:

The given equation of line is [tex]2x + 4y=20[/tex].

Now, it is required to check whether the given point lie on the line or not. To check it, put the points in the equation of line and if they satisfies, then the point will be on the line else not.

(a) The first point is (0,5). Put this point in the equation as,

[tex]2x + 4y=20\\2\times0+4\times 5=20\\20=20[/tex]

Thus, the point satisfies and it will lie on the line.

(b) The first point is (0,10). Put this point in the equation as,

[tex]2x + 4y=20\\2\times0+4\times 10=20\\40\neq20[/tex]

Thus, the point doesn't satisfy and hence, it will not lie on the line.

(c) The first point is (1,4). Put this point in the equation as,

[tex]2x + 4y=20\\2\times1+4\times 4=20\\18 \neq 20[/tex]

Thus, the point doesn't satisfy and hence, it will not lie on the line.

(d) The first point is (5,0). Put this point in the equation as,

[tex]2x + 4y=20\\2\times5+4\times 0=20\\10 \neq 20[/tex]

Thus, the point doesn't satisfy and hence, it will not lie on the line.

(f) The first point is (10,0). Put this point in the equation as,

[tex]2x + 4y=20\\2\times10+4\times 0=20\\20 =20[/tex]

Thus, the point satisfies and it will lie on the line.

Therefore, points (0,5) and (10,0) will lie on the given line.

Refer the graph of line and points.

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Answer:

$0.20 for 1 ounce of laundry soap

Step-by-step explanation:

7.90/40=0.1975

money can't be written like that so we have to round to the nearest hundredths

= $0.20

Answer:

[tex]x>-5.733[/tex]

Step-by-step explanation:

Given : Expression [tex]-1.5x-3.1<5.5[/tex]

To find : Solve the expression ?

Solution :

Step 1 - Write in inequality,

[tex]-1.5x-3.1<5.5[/tex]

Step 2 - Add 3.1 both side,

[tex]-1.5x-3.1+3.1<5.5+3.1[/tex]

[tex]-1.5x<8.6[/tex]

Step 3 - Divide by 1.5 both side,

[tex]-\frac{1.5x}{1.5}<\frac{8.6}{1.5}[/tex]

[tex]-x<5.733[/tex]

Step 4 - Multiply by -1 both side,

[tex]x>-5.733[/tex]

The number is -5.733 and symbol is greater (>).

Answer:

The total cost of the bond is none of the given choices.

Step-by-step explanation:

The selling price of a $1000 bond  =   $99.875

The brokerage fee = 5.5 %

Now, 5.5%  of $99.875 =  [tex]\frac{5.5}{100}  \times 99.875 = 5.493[/tex]

So, the brokerage fee = $5.493

Now, to find out the total cost of the bond:

Total Cost  = The selling Price + Brokerage Price

                  = $99.875 + $5.493

                  =  $105.368

or, the total price of the $1000 bond is $ 105.368.

Hence,  the total cost of the bond is none of the given choices.

2n + 1 will be an odd number.

If the number is divisible by 2 then the number will be an even number. Similarly, the number is not divisible by 2 then the number will be an odd number.

Given

2n+1 is a number where n is a positive integer.

The 2n + 1 is an odd number.

We know that if the integer is multiplied by 2 then it becomes the even number.

So the 2n is an even number.

We know that the sum of an even number and an odd number is an odd number. That is

Even + odd = odd

so 2n + 1 will be an odd number.

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The expression 2n + 1 represents an odd number for any positive integer n.

The expression 2n + 1 represents an odd number for any positive integer n. This can be shown through an algebraic proof.

Let's assume that n is any positive integer. When we multiply 2 by any integer, we always get an even number because an even number multiplied by 2 is always even. Adding 1 to an even number results in an odd number. Therefore, 2n is always an even number, and by adding 1 to it, we get an odd number (2n + 1).

For example, if we take n = 1, then 2n + 1 = 2(1) + 1 = 3, which is an odd number. Similarly, if we take n = 2, then 2n + 1 = 2(2) + 1 = 5, which is also an odd number.

Answer:

36 sqaured feet

Step-by-step explanation:

24 plus 12 i believe?

Answer:

its so easy : 36 square feet

Step-by-step explanation:

add 24+12=36

Answer:

The width of the rectangle is  [tex]\frac{1}{14}[/tex] miles

Step-by-step explanation:

Given as for rectangle

The area of rectangle = A = [tex]\frac{3}{4}[/tex] mile²

The Length of rectangle = L = [tex]\frac{21}{2}[/tex] mile

Let The width of rectangle = W miles

Now, From area of rectangle

I.e Area of Rectangle = Length × Width

Or , A = [tex]\frac{21}{2}[/tex] mile  × W mile

Or, [tex]\frac{3}{4}[/tex] mile² = [tex]\frac{21}{2}[/tex] mile  × W mile

or, W = [tex]\frac{\frac{3}{4}}{\frac{21}{2}}[/tex] mile

or, W = [tex]\frac{3\times 2}{4\times 21}[/tex]

∴  W = [tex]\frac{1}{14}[/tex] miles

Hence The width of the rectangle is  [tex]\frac{1}{14}[/tex] miles  Answer

Final answer:

The width of the rectangular piece of land is 0.3 miles.

Explanation:

To find the width of the rectangular piece of land, we need to divide the area of the land by its length.

Area = 3/4 square mile

Length = 2 1/2 miles = 5/2 miles

Width = Area / Length

Width = (3/4) / (5/2) = (3/4) * (2/5) = 6/20 = 0.3 miles

So, the width of the land is 0.3 miles.

Answer:

no

Step-by-step explanation:

it would not make a a circle

Answer:

No! :)

Step-by-step explanation:

It wouldn't create a circle, Hope this helps xx

Answer:

equation: -23 x -1

Step-by-step explanation:

two negatives equal positive

two positive equal positive

one positive and one negative equals negative

Answer:

24

Step-by-step explanation:

-3x^3*y^2=-3(-2)^3=(-3)(-8)*(-1)^2=24*1=24

Answer:

65 feet.

Step-by-step explanation:

80 feet roll of the fence is there.

It fits in the backyard the width must be 15 feet long.

So, there will be remaining (80 - 15 ) = 65 feet of fence.

If he wants to use the entire roll to fence the other side of the area then he can do it for more 65 feet length. (Answer)

Answer: The first one

Answer:

16 groups

Step-by-step explanation:

Add all the people up then divided it by 8 so now it will be 8 people in each group and there will be a total of 16 groups

30+32+29+28+9=128/8=16

The number of groups will be needed so everyone can see the exhibition is 16.

Given that, the fourth graders are going to the science museum.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here,

Total number of people

=30+32+29+28+9

= 128

Groups of 8 people can see a special exhibit on space travel.

Number of groups = Total number of people/Number of groups

= 128/8

= 16

Therefore, the number of groups will be needed so everyone can see the exhibition is 16.

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To model the money spent on a cell phone plan each month, the equation Cost = $15 + $0.10 × minutes can be used. A table and graph can be created by choosing different values for minutes and calculating the corresponding cost. The slope of the line represents the rate of change and the y-intercept represents the fixed cost.

Cost = $15 + $0.10 imes minutes

Minutes Cost

0 $15

10 $16

20 $17

Answer:

In 4 hours, Brad will travel 220 miles.

Step-by-step explanation:

Create the direct variation model-

y = kx

y- represents the total miles

x- represents hours

660 = k12

660/12 = k

k = 55

Model:

y = 55x

Replace x with 4:

y = 55(4)

y = 220

In 4 hours, Brad will travel 220 miles.

The answer is 220 miles.

[tex]\text{Hello there!}\\\\\text{We know that Brad traveled 660 miles in 12 hours. However, we need to}\\\text{find how many miles he traveled in 4 hours}\\\\\text{First, we need to find how many miles he can travel per hour}\\\\\text{Do this by dividing 660 by 12}\\\\660\div12=55\\\\\text{Now multiply 55 by 4 in order to see how many miles he traveled in 4 hours}\\\\55*4=220\\\\\boxed{\text{Answer: 220 miles}}[/tex]

Answer:

1. 35, 32, 29, 26 are in Arithmetic Sequence having common difference - 3.

5. -7, -9, -11, -13 are in Arithmetic Sequence having common difference - 2.

Step-by-step explanation:

1. 35, 32, 29, 26 are in Arithmetic Sequence having common difference - 3.

2. -1. 6, -36, 216 are not in Arithmetic Sequence.

3. -2, -4, -8, -16 are not in Arithmetic Sequence.

4. -1, 1, 4, 8 are not in Arithmetic Sequence.

5. -7, -9, -11, -13 are in Arithmetic Sequence having common difference - 2.

6. 1, -5, 25, -125 are not in Arithmetic Sequence. (Answer)

Answer:

Step-by-step explanation:

1/7+1/13=1/t

multiply both sides by 7*13*t

13t+7t=7*13

21t=91

t=91/19

it will take 4 hours and 8 minutes

Answer:

The Proof is given below.

Step-by-step explanation:

Given:

AD ≅ BD ≅ FD ≅ GD

To Prove:

AC ≅ GE

Proof:

In  Δ ADF and Δ  GDB

AD ≅ DG     ……….{Given}

∠ ADF ≅ ∠ BDG    …………..{Vertically Opposite angles are equal}

FD ≅ BD     ……….{Given}

Δ ADF ≅ Δ GDB ….{Side-Angle-Side test}

∴∠ FAD ≅  ∠ BGD .....{corresponding angles of Congruent Triangle ( c.p.c.t}

i.e ∠ CAD ≅  ∠ EGD.....{ F-C-A  and B-E-G straight line}.......( 1 )

Now ,

In  Δ CAD and Δ E GD

∠ CAD ≅  ∠ EGD    ……….{From ( 1 ) above}

AD ≅ GD     ……….{Given}

∠ ADC ≅ ∠ EDG    …………..{Vertically Opposite angles are equal}

Δ ADF ≅ Δ GDB ….{Angle-Side-Angle test}

∴ AC ≅   GE .....{corresponding sides of Congruent Triangle ( c.p.c.t}

[tex]\overline {AC} \cong \overline{GE}\ \textrm{......Proved}[/tex]

Answer:

Step-by-step explanation:

The formula of an area of a square:

[tex]A=s^2[/tex]

s - side

The formula of a perimeter of a square:

[tex]P=4s[/tex]

s - side

We have a perimeter

[tex]P=60\ in[/tex]

Substitute:

[tex]4s=60[/tex]             divide both sides by 4

[tex]\dfrac{4s}{4}=\dfrac{60}{4}\\\\s=15\ in[/tex]

Put it to the formula of an area of a square:

[tex]A=15^2=225\ in^2[/tex]

Answer: 225 in.²

Step-by-step explanation: First, we want to find the length of one side. Since we know that a square has 4 sides and the perimeter is 60 inches, we can set up the following equation to find the length of one side.

Let's use l as our variable to represent length.

4l = 60

To get l by itself, we need to divide by 4 on the left side of the equation. Since we divided by 4 on the left side, we must also divide by 4 on the right side. On the left side, the 4's cancel and we are left with l. On the right side, we have 60 over 4 which simplifies to 15.

This means that a side of the square is 15 inches.

Now, we are asking ourselves what is the area of a square with a side length of 15 inches.

To find the area of a square, remember that a square is a type of rectangle so we can use the following formula.

Area = length × width

However, since the length and width of a square are always equal, we use a special version of this formula to find the area of a square.

Instead of area = length × width, we say that the area of a square equals side × side or S².

Since the sides of the square each have a length of 15 inches, the area of the square is equal to (15 in.)² or (15 in) (15 in) which equals 225 in.²

Therefore, the area of the square is 225 in.².

Answer:

the slope is 0

Step-by-step explanation:

If 7 = -4, then the line will be horizontal on (-4) going on forever, never moving up or down. Therefore, there will be no slope.

Answer:

10 hours

Step-by-step explanation:

you need to drop 36 degrees, so 36/4 = 9 hours

1 pm + 9 hours = 10 pm

Answer:

Step-by-step explanation: