Sarah and Bryan went shopping and spent a total of $47.50. Bryan spent $15.50 less than Sarah spent. How much did Bryan spend?

320/31 gallons of hot water and 300/31 gallons of cold water are needed.

Here we are required to fill a 20-gallon bathtub and the water should be precisely 100° F.

It is given that hot water has a temperature of 175° F and cold water has a temperature of 20° F.

Let the amount of hot water used be x gallons.

Let the amount of cold water used be y gallons.

Since the bathtub has a capacity of 20 gallons,

x + y = 20                                                                                  [1]

or, y = 20 - x                                                                             [2]

The temperature after the water is mixed will be a weighted average of the temperature and amt of water used.

Hence we get,

(175x + 20y) / (x + y) = 100

from equation [1] we get

175x + 20y = 2000                                                                   [3]

from equations [2] and [3] we get

155x - 400 = 2000

or, x = 1600/155 = 320/31                                                        [4]

Similarly,

y = 20 - 320/31

= 300/31

Hence 320/31 gallons of hot water and 300/31 gallons of cold water are needed.

To learn more about Simultaneous equations visit

https://brainly.com/question/27911202

#SPJ4

Answer:

B

Step-by-step explanation:

The equivalent trigonometric identity to cot²θ + 1 is cot²θsec²θ

Trigonometric identities are equations which contain the trigonometric ratios.

Since we have the trigonometric identity cot²θ + 1,we need to find its equivalent expression.

So, we proceed as follows

Since cot²θ + 1 = 1/tan²θ + 1     (since cot²θ = 1/tan²θ)

Now taking the L.C.M, we have that

1/tan²θ + 1 = (1 + tan²θ)/tan²θ

We know that the trigonometric identity 1 + tan²θ = sec²θ

So, substituting this into the equation, we have that

(1 + tan²θ)/tan²θ =  sec²θ/tan²θ

Since cot²θ = 1/tan²θ, substituting the values of the variables into the equation, we have that

sec²θ/tan²θ = cot²θsec²θ

So, cot²θ + 1 = cot²θsec²θ

Learn more about trigonometric identities here:

https://brainly.com/question/29722989

#SPJ1

Answer:

109.30

Step-by-step explanation:

To find the radius of a circle given the area of a sector and the measure of the central angle of the sector, we can use the formula:

radius = sector area / (central angle measure / 360)

In this case, the sector area is 165.6 cm2 and the central angle measure is 129*. Plugging these values into the formula gives us:

radius = 165.6 / (129 / 360)

= 165.6 / (129 / 360)

= 165.6 / (0.3583)

= 462.9 cm

Rounding this value to the nearest tenth gives us a radius of approximately 463 cm.

A polynomial in which the degrees of all the variables is 0 is called a zero degree polynomial .

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.

For example- 6 x 0 , − 9 a 0.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division .

Degree of polynomial

The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial .

Learn more about polynomial here : -

https://brainly.com/question/20121808

#SPJ4

Answer:

x = 11.2

Step-by-step explanation:

We know that the second triangle is just a smaller scale of the bigger triangle.

So, first, we take

28 divided by 25 = 1.12

Then we take

10 times 1.12 = 11.2

So, x = 11.2

Answer: B

Step-by-step explanation: These lines are parallel. If you count over then down from point to point, then the slope for both lines is negative since it is going down, the slop is -2/1

Answer:

[tex]\boxed {\boxed {\sf D. \ 30 \ feet}}[/tex]

Step-by-step explanation:

The area of a square is found by multiplying the base and the height, but since all the sides are equal, it is equal to multiplying a side by another side.

[tex]a=s*s[/tex]

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

We know the square garden has an area of 900 square feet. We can substitute this value in for a.

[tex]900 \ ft^2=s^2[/tex]

Since we are solving for the side, we have to isolate the variable s. It is being squared. The inverse of a square is the square root, so we take the square root of both sides.

[tex]\sqrt {900 \ ft^2}= \sqrt{s^2}[/tex]

[tex]\sqrt {900 \ ft^2}=s \\[/tex]

[tex]30 \ ft=s[/tex]

One side of the garden is equal to 30 feet and choice D is correct.

Step-by-step explanation:

Area of square garden=a^2

ATQ

➝a^2=900 sq.feet

➝a=√900

➝a=30feets

Answer:

  36.9°

Step-by-step explanation:

You want to know the pitch angle of a staircase with a riser height of 6 inches and a tread depth of 8 inches.

The tangent of an angle is the ratio of the side opposite to the side adjacent:

  Tan = Opposite/Adjacent

The tangent of the staircase angle to the floor will be the ratio of the riser height to the tread depth:

  tan(α) = (6 in)/(8 in) = 3/4

The angle is found using the inverse tangent function.

  α = arctan(3/4) ≈ 36.9°

__

Additional comment

You need to be a little bit careful here. Different authors define "tread depth" differently. For the purpose of this question, it must be defined as the horizontal distance between corresponding points on adjacent treads, as shown in the attached illustration.

Some authors define tread depth as the distance from the nosing to the riser. If that definition is used, the "run" of the step will be the tread depth less the nosing depth. The pitch angle will be the arctangent of the ratio of riser height to "run".

The tread depth of 8 inches is a little too narrow to be in compliance with some building codes. A more usual minimum is about 10 inches with a riser height of 7 1/2 inches.

Answer:

0.75 tangent 0.75

Step-by-step explanation:

The area of one base of the triangular prism is given as 16√3 square cm, and since the base is equilateral, the sides of the triangle are of equal length.

The formula to calculate the area of an equilateral triangle is (sqrt(3)/4) * s^2 where s is the length of a side of the triangle.

So, plugging in the given area of base, 16√3, we can find the length of a side of the equilateral triangle, s.

16√3 = (sqrt(3)/4) * s^2

s = (4*16√3)/sqrt(3) = 16√3 cm

Now we can use the height of the prism, which is given as 30 cm, to find the area of the rectangular surface.

Area of the rectangular surface = 2 * base area * height = 2 * 16√3 * 30 cm²

This simplifies to:

960√3 cm²

So the total area of the rectangular surface of the prism is 960√3 square cm.

Answer:

1:11

Step-by-step explanation:

We know

There are 25 tables that seat 4 people

First, we find the total number of tables by taking

25 + 30 = 55 tables

Then we find the ratio of tables that seat 4 people to the total number of tables by

5 / 55 = 1/11 = 1:11

So, the ratio is 1:11

Answer:

f. 4h (greater than or equal to) 18

Step-by-step explanation:

hope this helps :)

Answer:

-5/3 would be the greatest.

because 5/3= -1.66666666667

Answer:

23°

Step-by-step explanation:

Since ACB is a right angle, the two angles ACB and BCD add up to 90°

just subtract 67 from 90 and bam 23

Answer:

-12x^2+15x

Step-by-step explanation:

-3x(4x-5)

Distributive property:

-3x*4x-(-3x)*5

-3*4x^2+3*5x

Simplify:

-12x^2+15x

Answer: 11, 23, 166

Step-by-step explanation:

Hiya! From the drawings, I'm assuming all of the triangles are right-angled triangles. If they aren't though, tell me and I'll tell you how to solve them.

Anyways, assuming they are right angled-triangles, you can use Pythagoras' Theorem (aka a² + b² = c²)

c is the hypotenuse or the side opposite the right angle.

a and b are just the other two sides (doesn't really matter which is which)

Question 7:

c² = a² + b²

12² = a² + 5²

144 = a² + 25

144 - 25 = a²

119 = a²

a = 10.908712114635714411502154487373

(To the nearest whole number: 11)

Question 8:

c² = a² + b²

24² = 7² + b²

576 = 49 + b²

576 - 49 = b²

527 = b²

b = 22.956480566497992703585747092065

(To the nearest whole number: 23)

Question 9:

c² = a² + b²

c² = 90² + 140²

c² = 8,100 + 19,600

c² = 27,700

c = 166.43316977093238068928214785346

(To the nearest whole number: 166)

Hoped this helped! Tell me if there's something you don't understand. :)

The percent of the people surveyed who were completed satisfaction with the car will be 48%.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100. The percentage then refers to a component per hundred. The word percentage simply means per 100 and it is represented by %.

In this case, a survey was given to people who own a certain type of car. 24 out of 50 stated that they were satisfied with the car.

The percent of the people surveyed were completed satisfaction with the car will be:

= 24 / 50 × 100

= 48%

Learn more about percentages on

brainly.com/question/24304697

#SPJ1

Complete question

A survey was given to people who own a certain type of car. 24 out of 50 stated that they were satisfied with the car. what percent of the people surveyed were completed satisfaction with the car?

Answer:

y = -1/2x + 5/2

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = 2x + 3. Its slope is 2. A line perpendicular to this one will have a slope of -1/2.

Plug this value (-1/2) into your standard point-slope equation of y = mx + b.

y = -1/2x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (1, 2). Plug in the x and y values into the x and y of the standard equation.

2 = -1/2(1) + b

To find b, multiply the slope and the input of x (1)

2 = -1/2 + b

Now, add 1/2 to both sides to isolate b.

5/2 = b

Plug this into your standard equation.

y = -1/2x + 5/2

This equation is perpendicular to your given equation (y = 2x + 3) and contains point (1, 2)

Hope this helps!

Answer:

Step-by-step explanation:

Let angle A = w - 15 degree , angle B = -w + 1 degree and angle X = w + 34 degrees then:

We know that the exterior angle of a triangle is equal to the sum of two interior opposite angles.

therefore, w + 34 = w - 15 + (-w +1)

w + 34 = w - 15 - w + 1

w = -15 - 34 = - 49 degrees

since angle cannot be negative

therefore w = 49 degrees

Answer:

what is your question? you have not attached anything.

Step-by-step explanation:

Answer:

-5 = |5|

Step-by-step explanation:

Absolute value is the number of distance from zero. Therefore, it doesn't matter if the number is positive or negative in absolute value it is always positive.

Answer:

1

Step-by-step explanation:

Answer:

(-3,0) (0,6)

hope this helps

Answer:

8

Step-by-step explanation:

8*8*8 = 512

or

8³ = 512

or

just punch it in a calculator

Answer:

Step-by-step explanation:

Answer:

900

Step-by-step explanation:

4F + F =1125

5F = 1125

F=225

C=4F

C=4(225)=900

900 + 225=1125