1. The hot-water tank in Rafael's house holds 17x + 11 gallons of hot water. Rafael used 4x + 1 gallons of hot water washing the dishes. Which of the following
binomials represents the number of gallons of hot water remaining in the tank?

Answer:

It is likely that Tom did not expand brackets fully or forgot to subtract and add from both sides.

Step-by-step explanation:

Step-by-step explanation:

[tex] - \frac{2}{3} + 1 \frac{5}{6} + ( - \frac{3}{2} )[/tex]

[tex] = 1 \frac{5}{6} - \frac{2}{3} - \frac{3}{2} [/tex]

[tex] = \frac{11}{6} - (\frac{2}{3} + \frac{3}{2} )[/tex]

[tex] = \frac{11}{6} - ( \frac{4 + 9}{6} )[/tex]

[tex] = \frac{11}{6} - \frac{13}{6} [/tex]

[tex] = \frac{11 - 13}{6} [/tex]

[tex] = \frac{ - 2}{6} [/tex]

After simplifying,

[tex] = \frac{ - 1}{3} (ans)[/tex]

Answer:

Reason 4 is wrong in Ethan's solution.

Step-by-step explanation:

Reason 4 is incorrect because at this step in the answer we already have one  variable which is unknown on the left side and then one constant which can be seen on the right. So, instead of multiplying the fractions the way Ethan is doing, all you need to do now is just simplify the expression instead of complicating the step.

Answer:

B,87

STEPS

78+89+83+80+84+95+100+86+84+91

10

870

10

Answer:

BCG

Step-by-step explanation:

This is because it is what you see when you look in the front of the shape.

HOPE THIS HELPED

Answer:

480

Step-by-step explanation:

Let x be the calories in 4 cups

Set it up

[tex]\frac{90}{\frac{3}{4}}=\frac{x}{4}[/tex]

Step 1: Switch sides

[tex]\frac{x}{4}=\frac{90}{\frac{3}{4}}[/tex]

Step 2: Apply fraction rule

[tex]\frac{x}{4}=\frac{90\cdot \:4}{3}[/tex]

Multiply

[tex]\frac{x}{4}=\frac{360}{3}[/tex]

Divide

[tex]\frac{x}{4}=120[/tex]

Step 3: Multiply both sides by 4

[tex]\frac{4x}{4}=120\cdot \:4\\\\=480[/tex]

There are 480 calories in 4 cups of the cereal.

Answer:

6

Step-by-step explanation: We observe that if 288 is multiplied by (2 x 3), then its prime factors will exist in triples. Thus, the required smallest number by which 288 be multiplied to make it a perfect cube i: (2 x 3)=6. 1,331 is a perfect cube.

Answer:

I don't know where can you find this question's answer.

Answer:

Angle Z = Angle V (as it is already said that ZY = VY and their ending points are Z and V respectively

Step-by-step explanation:

angle z = angle v​ can be proved by the SAS (Side angle side) Property

XZ = TV (Given)

Angle Z = Angle V (as it is already said that ZY = VY and their ending points are Z and V respectively

ZY = VY ( Given )

Answer:

x+ ( 1– a ) = 0

x= – 1 + a

I hope I helped you^_^

Answer:

Solution given:

-2b(-7)=11

open bracket

-2b*-7=11

+14b=11

divide both side by 14

14b/14=11/14

b=11/14

Answer:

[tex] - 2b ( - 7) = 11 \\ - 2b \times - 7 = 11 \\ 14b = 11 \\ b = \frac{11}{14} \\ thank \: you[/tex]

Answer:

Units of Length

10 millimeters (mm) = 1 centimeter (cm)

10 decimeters = 1 meter (m)

10 decimeters = 1000 millimeters

10 meters = 1 dekameter (dam)

Answer:

Step-by-step explanation:

It's D.

A theorem is true by some sort of mathematical logic.

It is not a definition. Not C

It is not in the end true because of inductive reasoning (a theorem may lend itself to inductive reasoning, but it must be proved.) Not A

It certainly not assumed to be true without proof. Not B

Answer:

4/9 and 30/9

Step-by-step explanation:

9, 18, 27, 36

3, 6, 9, 12,

4/9 already has 9 denominator

10/3 × 3/3= 30/9

so now both numbers have common denominators.

4/9 and 30/9

Answer:

x = 1/4

Step-by-step explanation:

-6x –(-9 – 4x) = -2(3x – 5)

-6x + 9 + 4x = -6x + 10

-2x + 9 = -6x + 10

-2x + 6x = 10 - 9

4x = 1

x = 1/4

Answer:

33

Step-by-step explanation:

608pages/16h = 33pages/h

Answer:

(14, 42)

Step-by-step explanation:

(-4, 2, 14, 34, 42) are all elements of b, and (-7. 14, 21, 42) are all elements of c. (14, 42) are the only elements that are in both sets

Answer:

9 3/4

Step-by-step explanation:

First you would want to multiply the whole number with their denominators and then add the numerator to that. 2*6+1 and 4*2+1  Then you keep the original denominator at the bottom of the fraction.

2*6+1/6  4*2+1/2 ---> 13/6 x 9/2

You would then simplify the crossing numbers 6 and 9. They both can be divided by three.

13/2 x 3/2 = 39/4

Now you would do long division where you divide 39 by 4

4 goes into 39 nine times subtracting 36 from 39.

You then end up with 1 which becomes you numerator, 4 is the new denominator and 9 is the whole number.

The answer of the given mixed numbers 2 1/6 x 4 1/2 is 9 3/4.

A mixed number is a whole number, and a proper fraction represented together. It generally represents a number between any two whole numbers.

You should first multiply the entire number by the denominators of the other numbers, and then add the numerator to that result. 2*6+1 and 4*2+1 The original denominator is then kept at the bottom of the fraction.

(2*6+1)/6 x ( 4*2+1)/2 —-> 13/6 x 9/2

Next, you would streamline the intersection of numbers 6 and 9. They are both divisible by three.

13/2 x 3/2 = 39/4

You would now perform a long division by dividing 39 by 4.
4 multiplies 39 by 9 and subtracts 36 from 39.

In the end 3 becomes the numerator, 4 becomes the new denominator, and 9 is the total.

Therefore, 2 1/6 x 4 1/2 = 9 3/4.

To know more about the mixed numbers, click on the link

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Answer:

3/6 or 1/2

Step-by-step explanation:

⇒ out of 6 blocks 3 are shaded so, it will be 3/6

⇒ out of 6 blocks 3 are shaded (3 is half of 6) so, it will be 1/2

Answer:

Answer: 3/6 or 1/2

Step-by-step explanation:

Basically there are six bars and we are to find the fractional part of the blue bars. The fractional part of the blue bars is 3/6 or 1/2.

if 6 litres cost £7.20

then 1/2 of it will cost 'x'(algebraic value)

we form equation

[tex] \frac{ 7.2}{6} \times \frac{1}{2}x[/tex]

which is equal to 0.6

Cost of 1/2 liter is £0.6.

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

According to the question

Cost of 6 liters ⇒ £7.20

Cost of 1/2 liter ⇒ X

According to the unitary method

6X = [tex]7.20\times\frac{1}{2}[/tex]

X  = [tex]\frac{7.20}{6}\times\frac{1}{2}[/tex]

X = [tex]\frac{3}{5}[/tex]

X = £0.6

Cost of 1/2 liter is £0.6

Find out more information about unitary method here

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Answer:

Here ia your answer

Hope it helps

Answer:

see explanation

Step-by-step explanation:

(a)

[tex]\frac{5}{a}[/tex] + [tex]\frac{3}{b}[/tex] + [tex]\frac{7}{c}[/tex] = 0 ( multiply through by abc to clear the fractions )

5bc + 3ac + 7ab = 0 ( subtract 5bc from both sides )

3ac + 7ab = - 5bc ( factor a out of each term on the left side )

a(3c + 7b) = - 5bc ← divide both sides by (3c + 7b)

a = - [tex]\frac{5bc}{3c+7b}[/tex]

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

(b)

p = [tex]\frac{\sqrt{4r(q^2-s)} }{q}[/tex] ( multiply both sides by q )

pq = [tex]\sqrt{4r(q^2-s)}[/tex] ← square both sides

(pq)² = 4r(q² - s) ← distribute

p²q² = 4rq² - 4rs ← subtract 4rq² from both sides

p²q² - 4rq² = - 4rs ( multiply through by - 1 )

4rq² - p²q² = 4rs ← factor out q² from each term on the left side

q²(4r - p²) = 4rs ← divide both sides by (4r - p²)

q² = [tex]\frac{4rs}{4r-p^2}[/tex] ( take the square root of both sides )

q = ± [tex]\sqrt{\frac{4rs}{4r-p^2} }[/tex]

1. ∠A and ∠B are complementary

2. ∠A + ∠B = 90° and ∠B + ∠C = 90°

3. ∠A = 90° - ∠B

4. ∠C = 90° - ∠B

5. ∠A ≅ ∠C

Answer:

the greatest common factor is 8

Answer:

-5

Step-by-step explanation:

According to formula:

m1 = m2

Since:

m2 = -5

∴ m1 = -5

Answer:

-5

Step-by-step explanation:

because -5 is parallel to AB

Answer:

[tex]{ \underline{ \sf{true}}}[/tex]

Answer:

The perimeter of a rectangle can be calculated by adding both lengths, and both widths

Step-by-step explanation:

Answer:

x/35=98/60

x=7/6

The value of x is 7/6

Answer:

[tex]\displaystyle \frac{28}{15}\; \text{radians}[/tex], which is approximately [tex]107^{\circ}[/tex].

Step-by-step explanation:

In a given circle, the angle of a sector is proportional to the length of the corresponding arc:

[tex]\displaystyle \frac{\text{angle of sector $1$}}{\text{angle of sector $2$}} = \frac{\text{length of arc of sector $1$}}{\text{length of arc of sector $2$}}[/tex].

For the circle in this question, [tex]r = 15\; \rm cm[/tex], and the circumference would be:

[tex]2\, \pi \, r = 30\, \pi\; \rm cm[/tex].

The full circle itself is like a sector with an angle of [tex]2\, \pi[/tex], with the arc length equal to the circumference of the circle.

[tex]\displaystyle \frac{\text{angle of sector}}{\text{angle of full circle}} = \frac{\text{length of arc of sector}}{\text{circumference of circle}}[/tex].

[tex]\displaystyle \frac{\text{angle of sector}}{2\,\pi\; \rm rad} = \frac{28\; \rm cm}{30\, \pi\; \rm cm}[/tex].

Rearrange the equation to find the angle of the sector:

[tex]\begin{aligned} & \text{angle of sector} \\ =\; & (2\,\pi\; \rm rad) \cdot \frac{28\; \rm cm}{30\, \pi\; \rm cm} \\ =\; & \frac{28}{15}\; \rm rad\end{aligned}[/tex].

In other words, the angle of this sector would be [tex]\displaystyle \frac{28}{15}\; \rm rad[/tex]. Multiply that measure in radians by [tex]\displaystyle \frac{360^{\circ}}{2\,\pi\; \rm rad}[/tex] to find the value of the angle measured in degrees:

[tex]\begin{aligned} & \frac{28}{15}\; \rm rad \times \frac{360^{\circ}}{2\,\pi\; \rm rad} \approx 107^{\circ}\end{aligned}[/tex].