Two brothers are saving money to buy tickets to a concert. Their combined savings is $55. One brother had $15 more than the other. How much has each saved?

Given the equation written by Fiona and Henry, If both linear equations have the same solutions, Henry's equation is x - 5/2y = 25/2.

Hence, option D is the correct answer.

This question is incomplete, the missing answer choices are;

A. x- 5/4y =25/4

B. x-5/2y=25/4

C. x-5/4y =25/4

D. x- 5/2y=25/2

Given the linear equation written by Fiona; y = 2/5x - 5.

From the answer choices provided, they are in the form of x - (m)y = b.

We will transform Fiona's equation into that form.

y = 2/5x - 5

Divide each term by the coefficient of x.

y(5/2) = (5/2)2/5x - (5/2)5

5/2y = x - 25/2

25/2 = x - 5/2y

x - 5/2y = 25/2

Given the equation written by Fiona and Henry, If both linear equations have the same solutions, Henry's equation is x - 5/2y = 25/2.

Hence, option D is the correct answer.

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Answer: x is -1/2,0 and y is 0,2

Step-by-step explanation:

Answer:

(4,0) , (0,2)

Step-by-step explanation:

Similar to the previous question.

x-intercept is where the line touches the x-axis , and y = 0.

when y = 0,

8x + 16(0) = 32

8x = 32

x = [tex]\frac{32}{8}[/tex]

x = 4

Therefore the coordinates of the x-intercept is (4,0)

y-intercept is where the line touches the y-axis, and x = 0.

when x = 0,

8(0) + 16y = 32

16y = 32

y = [tex]\frac{32}{16}[/tex]

y = 2

Therefore the coordinates of the y-intercept is (0,2)

Answer:

0.13 inches.

Step-by-step explanation:

1 inch = 2.54 cm

So 1 cm = 1/ 2.54 in

0.33 cm = 0.33/2.54 in

= 0.13 inches.

Using proportions, it is found that it will take Voyager 2 82,900 years from its location to travel to the second closest star.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, the Voyager 2 travels 15.4 km/s. In kilometers per year, considering that one hour has 3600 seconds, the measure is given by:

15.4 x 365 x 24 x 3600 = 485,654,400 km/year.

The distance to Proxima Centauri in km is given by:

d = |1.93 x 10^10 km - 4.24 x 9.5 x 10^12 km| = 4.02607 x 10^13 km.

Hence the time in years is given by:

t = d/v =  4.02607 x 10^13/485,654,400 = 82,900.

It will take Voyager 2 82,900 years from its location to travel to the second closest star.

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The radius of the table can be either 13 inches or 73 inches.

Let the radius of the table be r inches and the corner be the origin.

The coordinates of the center of the table exist (r, r).

The equation for the circumference of the table exists (x−r)²+(y−r)²=r².

The mark at the edge of the table exists 18 inches from one wall and 25 inches from the other wall. Therefore, the coordinates of this point exist (18, 25). It could also be (25, 18) but it does not make any difference to our estimations.

As the mark exists on the edge, it meets the requirements of the equation of the circumference of the table.

(18−r)² + (25−r)² = r²

324−36r+r²+625−50r+r² = r²

r²−86r+949 = 0

(r − 13)(r − 73) = 0

r = 13 inches and r = 73 inches

Therefore, the radius of the table can be either 13 inches or 73 inches.

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The answer is x = 4, y = -1 or (4, -1).

We are given :

Multiply the 1st equation with 3 and 2nd equation with 2.

3. 3(2x + 7y) = 3(1) ⇒ 6x + 21y = 3

4. 2(3x + 4y) = 2(8) ⇒ 6x + 8y = 16

Now, subtract : Equation 3 - Equation 4.

Substitute in the 1st equation.

Answer:

(4, - 1 )

Step-by-step explanation:

2x + 7y = 1 → (1)

3x + 4y = 8 → (2)

multiplying (1) by 3 and (2) by - 2 and adding will eliminate x

6x + 21y = 3 → (3)

- 6x - 8y = - 16 → (4)

add (3) and (4) term by term to eliminate x

0 + 13y = - 13

13y = - 13 ( divide both sides by 13 )

y = - 1

substitute y = - 1 into either of the 2 equations and solve for x

substituting into (1)

2x + 7(- 1) = 1

2x - 7 = 1 ( add 7 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

solution is (4, - 1 )

Using proportions, it is found that 1685% of an hour passes between 11:24 am and 415 am.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

One hour is composed by 60 minutes. Between 11:24 am and 4:15 am, there are 16 hours and 51 minutes, hence the number of minutes is given by:

M = 16 x 60 + 51 = 1011 minutes.

As a percentage of one hour = 60 minutes, we have that this measure is:

1011/60 x 100% = 1685%.

Hence 1685% of an hour passes between 11:24 am and 415 am.

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Answer:

x = 36

Step-by-step explanation:

The two lines are parallel and intersected by a transversal line.

The co-interior angles formed will sum up to 180°

Here angles 3x and 2x are the co-interior angles

So 3x + 2x = 180

5x = 180

x = 180/5 = 36

Answer:

Step-by-step explanation:

2x + 2x + 3x + 3x = 180°

10x = 180°

x = 180° : 10 =

x = 18°

-----------------------

check

2 × 18 + 2 × 18 + 3 × 18 + 3 × 18 = 180°

the answer is good

The surface area of the composite figure is: 300 cm².

Surface area of a triangular prism = (P)L + bh, where we have the following:

P = perimeter of the base

L = length of the triangular prism

h = height of the triangular base

b = base of the triangular base

Surface area = 2(wl + hl + hw), where:

h = height of prism

w = width of prism

l = length of prism.

The surface area of the composite figure = surface area of triangular prism + surface area of rectangular prism - 2(the area where both figures are joined at).

Surface area of the triangular prism = (5 + 12 + 13)4 + (5)(12)

Surface area of the triangular prism = 180 cm²

Surface area of rectangular prism = 2(wl + hl + hw) = 2·(4·12+3·12+3·4) = 192 cm²

The area where both figures are joined at = (l)(w) = (3)(12) = 36 cm².

The surface area of the composite figure = 180 + 192 - 2(36)

The surface area of the composite figure = 180 + 192 - 72

The surface area of the composite figure = 300 cm².

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39 number is the secret code as the unlock code for the safe.

According to the statement

we have given that  a some numbers as a code and we have to find the correct code after applying the given conditions.

So, For this purpose

The given number set is

5 17 29 22 11 26 27 35 39 41

So,

A. One condition : It is an odd number

so, the number set become

5 17 29 11 27 35 39 41

And

B. Second condition : It is greater than 20

so, the number set become

29 27 35 39 41

And

C. Third condition : It is smaller than 40

so, the number set become

29 27 35 39

And

D. Fourth condition : It is not a prime number

so, the number set become

27 35 39

And

E. Fifth condition : It has 13 as one of its factors

so, the number set become

39.

So, 39 number is the secret code as the unlock code for the safe.

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Answers:

16 cm²

24 cm²

40 cm²

Step-by-step explanation:

     The area of a rectangle can be found with A = L * W where A is the area, L is the length, and W is the width.

     [1] First shaded area

A = L * W

A = (4 cm) * (12 cm - 5 cm - 3 cm)

A = (4 cm) * (4 cm)

A = 16 cm²

     [2] Second shaded area

A = L * W

A = (2 cm) * (12 cm)

A = 24 cm²

     Lastly, we add them together.

16 cm² + 24 cm² = 40 cm²

Answer: 138.63 mm²

Step-by-step explanation:

    First, we will solve for the area of the rectangle.

A = L * W

A = 15 mm * 5 mm

A = 75 mm²

      Next, we will solve for the area of the semi-circles. Since there are two equivalent semi-circles, I will find the area of one circle with the same radius as these two.

      First, we need to find the radius.

15 mm - 3 mm - 3mm = 9mm, 9 mm / 2 = 4.5 mm

A = πr²

A = π(4.5)²

A ≈ 63.62 mm²

      Lastly, we will add them together.

75 mm² + 63.62 mm² = 138.63 mm²

The circulation of the field f = x i y j around the curve r(t) = [cos(t)] i [sin(t)] j is    2π ∫₀ (cos t sin t - sin t cos tj)dt = 0

Integration is described as blending matters or human beings collectively that have been formerly separated. An example of integration is while the schools have been desegregated and there have been now not separate public faculties for African individuals.

The method of finding integrals is referred to as integration. at the side of differentiation, integration is a fundamental, crucial operation of calculus, and serves as a device to solve troubles in mathematics and physics regarding the location of an arbitrary form, the length of a curve, and the extent of a solid, among others.

r (t) = cost i + sin t j = dr( sin ti + cos t)dt

F =  -xi -yj = -costi - sin tj

Flux = F .dr = [tex]\int\limit2n^0_b {-costi - sin tj} \, dx[/tex]j)-( sin ti + cos t)dt

           [tex]\int\limit2n^0_b {-costi - sin tj} \, dx[/tex] -( sin ti + cos t)dt

     2π ∫₀ (cos t sin t - sin t cos tj)dt = 0

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Answer:

60

Step-by-step explanation:

Answer: 60

Step-by-step explanation:

The percentage of Zachary's pay due to his deductions comprise exists 18.724%.

Zachary exists supposed to earn a paycheck of $20,160.00 but instead, he acquires a lesser amount of money due to deductions. The money he acquires after deductions exists at $16,385.31.

Money deducted = Original paycheck amount - deductions

= $20,160.00 - $16,385.31

= $3,774.69.

So Zachary obtains a deduction of $3,774.69.

To estimate the percent of deductions in terms of his pay we divide the deduction cost with the original paycheck amount and multiply it by 100 to transform it into a percentage.

Deduction % = ($3,774.69 / $20,160.00) [tex]*[/tex] 100

= 0.1872366 [tex]*[/tex] 100

= 18.72366%

We obtain the deduction percentage as 18.724%.

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In accordance with the Ferrari's method, all the roots of the quartic polynomial are complex numbers.

By fundamental theorem of algebra quartic polynomials have four roots. Based on characteristics of the quadratic formula, use for the solution of quadratic polynomials, there are three possible sets of roots:

There are several methods to solve quartic polynomials. In this case, we decide to use the Ferrari's method to determine all roots of the polynomial:

[tex]x_{1} = \frac{1 + i \sqrt{3}}{2}[/tex], [tex]x_{2} = \frac{1 - i\,\sqrt{3}}{2}[/tex], [tex]x_{3} = - \frac{5}{3} + i\,0.471[/tex], [tex]x_{4} = -\frac{5}{3} - i\,0.471[/tex]

All the roots of the quartic polynomial are complex numbers.

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Answer:

C

Step-by-step explanation:

for AB to be parallel to CD then the slopes of both segments must be equal

using the slope formula to find the slopes , then

A (x₁, y₁ ) and B (x₂, y₂ )

[tex]m_{AB}[/tex] = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

C (x₃, y₃ ) and D (x₄, y₄ )

[tex]m_{CD}[/tex] = [tex]\frac{y_{4}-y_{3} }{x_{4}-x_{3} }[/tex]

then

[tex]m_{CD}[/tex] = [tex]m_{AB}[/tex]

[tex]\frac{y_{4}-y_{3} }{x_{4}-x_{3} }[/tex] = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] → C

Answer: x < -2

Step-by-step explanation:

[tex]\frac{1}{2} x-7 < -8[/tex]

First add 7 to both sides

[tex]\frac{1}{2} x-7 +7 < -8+7[/tex]

[tex]\frac{1}{2} x < -1[/tex]

Now multiply by 2 to cancel out 1/2 and leave you with x

[tex]2*\frac{1}{2} x < -1(2)[/tex]

[tex]x < -2[/tex]

There are (A) 2.7 bacterias initially.

To find the number of bacteria:

Therefore, there are (A) 2.7 bacterias initially.

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The correct question is given below:
The growth of a strain of bacteria can be modeled by

the function graphed, where the x-values are the time

in seconds and the y-values are the number of

bacteria. How many bacteria are there initially?

(A) 2.7

(B) 2.8

(C) 4

Answer:

mine was b 2.7

Step-by-step explanation:

The amount of space (volume) that is in the larger spherical ball than the smaller = 1,084.8 in.³

To find the volume of a sphere, which is the amount of space the solid contains, the formula used is given as: 4/3 πr³, where r is the radius of the sphere, which is half the measure of the diameter. Volume of sphere (V) = 4/3 πr³.

Diameter of the smaller spherical ball = 5 inches

Radius of the smaller spherical ball = 5/2 = 2.5 inches

Volume of the smaller spherical ball = 4/3 πr³ = 4/3 × π × 2.5³

Volume of the smaller spherical ball ≈ 65.5 in.³

Diameter of the larger spherical ball = 13 inches

Radius of the larger spherical ball = 13/2 = 6.5 inches

Volume of the larger spherical ball = 4/3 πr³ = 4/3 × π × 6.5³

Volume of the larger spherical ball ≈ 1,150.3 in.³

The amount of space (volume) that is in the larger spherical ball than the smaller = 1,150.3  - 65.5

The amount of space (volume) that is in the larger spherical ball than the smaller = 1,084.8 in.³

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2 x 10² kcal are in the serving report your answer to 2 significant figures.

According to the question

A serving of fish contains 50 g of protein and 4. 0 g of fat.

i.e. content of protein = 50 g

Content of fat = 4 g

kcal are in the serving report your answer to 2 significant figures:

As the serving of fish contains 50g of protein that is 4.0kcal/g

Calories in 50 g protein = (Content of protein) × (caloric value in protein)

50g × (4.0kcal/g) = 200kcal

That means the kcal of the serving is 200kcal

In 2 significant figures: 2 x 10² kcal

Hence,

2 x 10² kcal are in the serving report your answer to 2 significant figures.

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Answer:

Step-by-step explanation:

i'd say with the given info it will be the same

The length of the ladder is 75ft.

The longest side, or hypotenuse, of a right-angled triangle is the side that faces away from the right angle. The Pythagorean theorem asserts that the hypotenuse's square length equals the sum of the squares of the lengths of the other two sides, and this can be used to determine the hypotenuse's length.

The ladder makes an angle of 28° with the ground and the top of the ladder reaches 35ft

Therefore, we have:

Sineα = opposite/hypotenuse

Where:

Opposite = 35

Hypotenuse = Length

α = 28°

substitute values and solve for the length, as following:

Sine(28) = 35/Length

Length = 35/Sine(28)

Length = 75ft

Therefore,

The length of the ladder is 75 ft.

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The value of the given expression is 9/10. The properties of real numbers, such as commutative and distributive are used for solving this expression.

The properties are:

The given expression is

(-3/7) × 6/5 + (3/2) - (6/5) × 1/14

applying commutative law (a + b = b + c)

⇒ (-3/7) × 6/5 - (6/5) × 1/14 + (3/2)

again applying commutative law (a × b = b × a)

⇒ (-3/7) × 6/5 - 1/14 × (6/5)+ (3/2)

applying distributive law (a × (b + c) = a × b + b × c) in reverse order

⇒ (-3/7 - 1/14) × (6/5)+ (3/2)

⇒ (-7/14) × (6/5)+ (3/2)

⇒ (-1/2) × (6/5)+ (3/2)

⇒ (-6/10) + (3/2)

⇒ (-6 + 15)/10

⇒ 9/10

Thus, the required value is 9/10 and the suitable properties are commutative and distributive.

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Answer:

84

Step-by-step explanation:

4 (-4)^2 - 5(-4)

4 × 16 - 5 × -4

64 + 20

84

Answer:2

Step-by-step explanation:

im just guessing

The answers are :

P (Drawing a number < 8) = 1

P (Spinning a 4) = 0

There are only 2 numbers in the bag, 4 and 7, both of which are less than 8. Hence, as it is a sure event, the probability of the event is 1.

There are only 3 numbers on the spinner, 1, 2, and 3. As 4 is not on the spinner, it is an impossible event, hence the probability of the event is 0.

a) 6x + 12 = 5x - 5y

6x-5x = -5y-12

x = -5y-12

b) 5a-10x = 9x+9

-10x-9x = 9-5a

-19x = 9-5a

x = 9-5a/-19

Answer: -2, -4, -1

Step-by-step explanation:

[tex]17-7x > 3(10x-4)+61\\\\17-7x > 30x-12+61\\\\17-7x > 30x+49\\\\-32 > 37x\\\\x < -\frac{32}{37}[/tex]

So, the values of x are -2, -4, -1.

The given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].

To complete the square to transform the expression:

Therefore, the given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].

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The correct question is shown below:

Complete the square to transform the expression x^2− 2x − 2 into the form a(x − h)^2+ k.

(A) (x − 1)2 + 3

(B) (x − 1)2 − 3

(C) (x − 2)2 − 3

(D) (x − 2)2 + 3

Answer:

Accurate AND Precise