Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?a. 1/4(x + 30 + 60) = xb. 1/4(x) = x(30 + 60)c. 1/4x(30 + 60) = xd. 1/4(x) = (30 + 60)

For this case we have that the variable "f" represents the number of cups of flour that Tomas had initially.

If of that amount Luis used [tex]3 \frac {1} {3}[/tex] of cups of flour, then we have the following expression:

[tex]f-3 \frac {1} {3}[/tex]

If Luis has[tex]1 \frac {2} {3}[/tex] cups of flour left, then we have the following equation:

[tex]f-3 \frac {1} {3} = 1 \frac {2} {3}[/tex]

Finally, the equation that represents the given situation is:

[tex]f-3 \frac {1} {3} = 1 \frac {2} {3}[/tex]

Answer:

Option B

For this case we must find the value of the following expression:

[tex](+328.62) - (+ 98.6) =[/tex]

We apply distributive property to the term within the parenthesis taking into account tha:

[tex]- * + = -[/tex]

Rewriting we have:

[tex]+ 328.62-98.6 =[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]+328.62-98.6 = 230.02[/tex]

Answer:

230.02

Option B

Answer:

Step-by-step explanation:

mono-, bi-, tri- are prefixes meaning 1, 2, and 3, respectively. A 3-term polynomial is a trinomial; a 2-term polynomial is a binomial.

Check the picture below.

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{27.6}\\ b=\stackrel{opposite}{h}\\ \end{cases} \\\\\\ \sqrt{30^2-27.6^2}=h\implies \sqrt{138.24}=h\implies 11.76\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the triangle}}{\cfrac{1}{2}bh\implies \cfrac{1}{2}(27.6)(11.76)}\implies 162.288\implies \stackrel{\textit{rounded up}}{162.3}[/tex]

To find the area of the right triangle with a given hypotenuse and adjacent leg, use the Pythagorean theorem to calculate the other leg. Then, use the base and height (the two legs) in the area formula for a right triangle. The area of the triangle is approximately 148.7 cm².

To find the area of a right triangle, you need two perpendicular sides, known as the legs of the triangle. Since we are given the hypotenuse (30 cm) and one adjacent leg (27.6 cm) which is one of the legs, we need to find the other leg. Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

In mathematical terms, this is expressed as a² + b² = c². Therefore, the length of the other leg (b) can be found using the equation b² = c² - a², where c is the hypotenuse and a is the given adjacent leg.

Substituting the given values, we have b² = 30² - 27.6². Calculating this gives b ≈ 10.8 cm.

Now, the area of the triangle can be calculated using the formula for the area of a right triangle, which is (1/2) × base × height. In this case, the base and height are the two legs of the triangle. Substituting the lengths of the legs we have, Area ≈ (1/2) × 27.6 cm × 10.8 cm. The result is approximately 148.7 cm², which is the area of the triangle rounded to the nearest tenth.

Answer:49

Step-by-step explanation: 9+4=13 4x2=8 8+1=9

9 is the units digit

4 is the tens digit

Answer:  A) (-1, 0) to (1, 2)

Step-by-step explanation:

Complex numbers are written in the form of ai + b  ; where "a" represents the x-coordinate and "b" represents the y-coordinate --> (a, b)

-i        →    -1i + 0    →   (-1, 0)

2 + i   →     1i + 2    →   (1, 2)

Which graph connects those two coordinates? OPTION A

Final answer:

The arc length intercepted by a central angle of π radians in a circle of radius 18.4 inches is calculated as arc length = θ × radius, resulting in 18.4π inches.

Explanation:

To find the arc length intercepted by a central angle of θ radians in a circle with radius r, we use the formula:

arc length (s) = θ × r

Given that the central angle θ is π radians and the radius r is 18.4 inches, we can compute the arc length as follows:

arc length (s) = π × 18.4 inches

By multiplying, we get:

arc length (s) = 18.4π inches

Therefore, the arc length intercepted by a central angle of π radians in a circle with a radius of 18.4 inches is 18.4π inches.

Answer:

vertex s is -2,-2

Step-by-step explanation:

and with the rectangle is q to p is 4cm coz one box is 1 cm and r to q is 3cm so you multiply them and the answer is 12cm

Answer:

See below in bold.

Step-by-step explanation:

If we add the 2 equations  we eliminate x  and we get 2y =2.

So y = 1.

Substituting y = 1 in the second equation 1 = x - 3.

So x = 4.

A. One solution: (4, 1).

If we drew a graph we would have 2 lines which intersect at the point (4, 1).

Answer:

Step-by-step explanation:

If we add the 2 equations  we eliminate x  and we get 2y =2.So y =1.

Substituting y = 1 in the second equation 1 = x - 3.So x = 4.

A.

One solution: (4, 1).If we drew a graph we would have 2 lines which intersect at the point (4, 1).

Answer:

We have 8 liters of 54% alcohol.

We will add "x" liters of 66% alcohol to make "8 +x" liters of 65% alcohol.

54 * 8 + 66 x =   65 (8 + x)

432 + 66x = 520 + 65x

x = 88 liters

Step-by-step explanation:

Volume = (edge)^3

Volume = (3/4)^3

Volume = (27/64) inches^3

Done.

Answer:

B) C,D,B,A

Step-by-step explanation:

First subtract the difference of the two by the total:

440 - 54 = 386

Now divide that by 2:

386 / 2 = 193

193 is the number of Sociology books sold.

Now add 54 to 193 for the total Physics books:

193 + 54 = 247 Physics books were sold.

Answer:

  y = 2/(x +8)

Step-by-step explanation:

Solve the first equation for t and substitute that expression into the second equation.

  x = t -3

  x + 3 = t

Then for y, we have

  y = 2/(t +5)

  y = 2/((x +3) +5) . . . . substitute for t

  y = 2/(x +8) . . . . . . . . simplify

Answer:

(xy + x)and (xy + x)

(2x - 3) and (-3 + 2x)

(4y² + 25) and (25 + 4y²)

Step-by-step explanation:

* Lets explain the meaning of the perfect square trinomial

- If a binomial multiply by itself, then the answer will be a perfect

 square trinomial

- Example: if the binomial (ax + b) multiply by itself, then

 (ax ± b)(ax ± b) = (ax)(ax) ± (ax)(b) ± (b)(ax) + (b)(b)

 (ax + b)(ax + b) = (ax)² ± 2(axb) + (b)²

∵ (ax + b)(ax + b) = (ax + b)²

∴ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

* From the example above the perfect square trinomial has 3 terms

# 1st term is the square the first term in the binomial

# 2nd term is twice the product of the two terms of the binomial

# 3rd term is the square of the second term of the binomial

* Lets solve the problem

- The product of (-x + 9)and (-x - 9)

∵ -x + 9 ≠ -x - 9

∴ The product of (-x + 9) and (-x - 9) is not a perfect square trinomial

- The product of (xy + x)and (xy + x)

∵ xy + x = xy + x

∴ (xy + x)(xy + x) = (xy + x)²

∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

∴ The product of (xy + x) and (xy + x) is a perfect square trinomial

- The product of (2x - 3) and (-3 + 2x)

∵ (-3 + 2x) can be written as (2x - 3)

∴ 2x - 3 = -3 + 2x

∴ (2x - 3)(-3 + 2x) = (2x - 3)²

∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

∴ The product of (2x - 3)(-3 + 2x) is a perfect square trinomial

- The product of (16 - x²) and (x² - 16)

∵ 16 - x² can be written as -x² + 16

- If we take -1 common factor from -x² + 16

∴ -x² + 16 = -(x² - 16)

∴ (-x² + 16)(x² - 16) = -(x² - 16)(x² - 16) = -(x² - 16)²

∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

∵ -(x² - 16)² = -(x^4 - 32x² + 256) = -x^4 + 32x² - 256

∵ x^4 - 32x² + 256 is perfect square trinomial

∵ -x^4 + 32x² - 256 is not a perfect square trinomial

∴ The product of (16 - x²) and (x² - 16) is not a perfect square trinomial

- The product of (4y² + 25) and (25 + 4y²)

∵ 25 + 4y² can be written as 4y² + 25

∴ 4y² + 25 = 25 + 4y²

∴ (4y² + 25)(25 + 4y²) = (4y² + 25)²

∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

∴ The product of (4y² + 25) and (25 + 4y²) is a perfect square trinomial

Answer:

- 32,100 ft

Step-by-step explanation:

Initial Altitude = 32,000 ft above sea level = +32,000 feet

Final Altitude = 100 ft below sea level = -100 ft

Altitude change,

= final altitude - initial altitude

=  - 100 - (32,000)

=  - 32,100 ft

The expression  [tex]\rm m^{2.5}[/tex] in radical form is [tex]\rm \sqrt[2.5]{m}[/tex] .

If n is a positive integer greater than 1 and n is a real number, then

[tex]\rm \sqrt[n]{a}[/tex] = aⁿ

Here the index is represented by n, the radicand is represented by a , and the sign is called the radical.

Left side of the equation is called the radical form

Right side of the equation is called exponent form.

The given exponent form is

[tex]\rm m^{2.5}[/tex]

In radical form this will be written as

[tex]\rm \sqrt[2.5]{m}[/tex]

Therefore the expression [tex]\rm m^{2.5}[/tex] in radical form is [tex]\rm \sqrt[2.5]{m}[/tex] .

To know more about Radical form

https://brainly.com/question/12966955

#SPJ2

Answer:

23

Step-by-step explanation:

30 + 9 = 39.

39 - 14 = 25.

25 - 2

= 23

Answer:

23

Step-by-step explanation:

Answer:

Floor 7

Step-by-step explanation:

He entered the elevator on floor x.

Then he rode up 10 floors. Now he is on floor x + 10.

Then he rode down 2 floors. Now he is on floor x + 10 - 2 = x + 8.

Then he pressed the Floor 1 button and rode down 14 floors to Floor 1. Now he is on floor x + 8 - 14 = x - 6 which is the same as Floor 1.

Floor x - 6 is the same as Floor 1, so we get the equation:

x - 6 = 1

Add 6 to both sides:

x = 7

Since we let x be the floor number he entered the elevator in, he entered the elevator on Floor 7.

Answer:

He began on floor 7

Step-by-step explanation:

This is a question where you have to use the question from the end and work your way backwards if that makes sense.

He had to go down 14 floors to get to floor 1. So 14 + 1 = 15. He was on the 15th floor.

Next he went down 2 floors. Since this is reverse, add two floors to the answer. 15 + 2 = 17. He was on the 17th floor.

And finally, he goes up 10 floors. Doing this in reverse, take away 10 floors to the answer. 17 - 10 = 7

Now to make sure it is correct, start from 7 and follow the original order of the question.

7 + 10 = 17

17 - 2 = 15

15 - 14 = 1

Answer:

  C.  f^-1(x) = 1/5x

Step-by-step explanation:

You know that f^-1(f(x)) = x, so you can try the answers.

____

You can also solve for f^-1(x). It will be "y" when ...

  f(y) = x

  5y = x

  y = 1/5x . . . . . divide by 5

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

If those 2 polygons are similar, then their corresponding angles are the same.  The thing that makes them similar as opposed to congruent is that their side lengths exist in proportion to one another instead of being the same.

Answer:

[tex]w = 120\°[/tex]

Step-by-step explanation:

In this case we know that

ABCD and FECG are similar polygons.

 This means that their sides are proportional and their corresponding angles are equal.

So if the lines FG and AD are parallel and of proportional length then by definition the angle w is equal to 120 °

Thus

[tex]w = 120\°[/tex]

Answer:

π/3

Step-by-step explanation:

We have to find the principal value of [tex]\text{arc sin}(\frac{\sqrt{3}}{2} )[/tex]

arc sin means sin inverse. The sin inverse is a one to one function with its range between [tex]-\frac{\pi}{2} \textrm{ to } \frac{\pi}{2}[/tex]

The principal value of the arc sin will lie within the above given range.

value of sin (60) or sin([tex]\frac{\pi}{3}[/tex]) is [tex]\frac{\sqrt{3}}{2}[/tex].

[tex]\frac{\pi}{3}[/tex] lies between [tex]-\frac{\pi}{2}\textrm{ and } \frac{\pi}{2}[/tex]

So, from here we can say that the Principal Value of Arc sin(square root of 3/2) is π/3

The principal value of the function Arc sin(√3/2) is,

⇒ π / 3

We have to given that,

⇒ Arc sin (√ 3/ 2)

Since, Value of arc sin lies between - π/2 and π/2.

Hence, The principal value of the function Arc sin(√3/2) is,

⇒ Arc sin(√3/2)

⇒ Arc sin(sin π/3)

⇒ π / 3

Therefore, The principal value of the function Arc sin(√3/2) is,

⇒ π / 3

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ6

Answer:

  A. $12,993.71

Step-by-step explanation:

Each year, the car's value is multiplied by 1-0.15 = 0.85. After 10 years, the car's value will be ...

  $66,000×0.85^10 ≈ $12,993.71

Answer:

  see below

Step-by-step explanation:

Apart from the pictures being drawn with the axis at a funny angle relative to the edges of the solid, it should be pretty clear from the pictures that the figure has both plane and axis symmetry.

Every point on one side of the axis has a matching point on the other side at the same distance. Every point on one side of the plane of symmetry has a matching point on the other side at the same distance.

Answer:

10y

Step-by-step explanation:

9y + y = 10y

Answer:

[tex]10y[/tex]

Step-by-step explanation:

[tex]9y + y = y(9 + 1) = y(1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) = y \times 10 = 10y[/tex]

Answer:

C

Step-by-step explanation:

B isn't right. The 0 makes x^2 go away leaving a linear equation.

A is a linear function.

D is a cubic, so the answer is

C which has an x^2 function