Rona mixes 2 pounds of meat with some chopped vegetables to make a mixture. She divides the mixture into 4 equal portions. Each portion weighs 3 pounds. Which equation and solution shows the total amount of chopped vegetables she used in the mixture?
One-fourth (2 + v) = 3; v = 10 pounds of chopped vegetables
One-fourth (2 + v) = 3; v = 4 pounds of chopped vegetables
4 (2 + v) = 3; v = 1 pound of chopped vegetables
4 (2 + v) = 3; v = 5 pounds of chopped vegetables

Answer:

A

Step-by-step explanation:

Hi!

An exponent is the same thing as just multiplying the expression by itself the number of times the exponent says. So we need to multiply 1/3 by itself three times.

1/3 * 1/3 * 1/3 = 1/27

Answer:

Step-by-step explanation:

In order to find the value of x we use sine

sin ∅ = opposite / hypotenuse

From the question

x is the hypotenuse

the opposite is 19

So we have

sin 20 = 19/x

x = 19/sin 20

x = 55.55

We have the final answer as

Hope this helps you

Answer:

x = 55.6

Step-by-step explanation:

Answer:

$11286.95 second year

$10335 first year

Step-by-step explanation:

9% of 9500 is 855, 9500 plus 855 = 10335. (first year)

9% of 10335 is 931.95, and 10335+931.95 is 11286.95. (second year)

The amount in the account at the end of 1 year  $10335 (first year)

The amount in the account at the end of 2 years $11286.95.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

here, we have,

$9500 is placed in an account that pays 9% interest compounded each year.

so, we get,

9% of 9500 is 855,

9500 plus 855 = 10335. (first year)

again,

9% of 10335 is 931.95,

and 10335+931.95 is 11286.95. (second year)

Hence, The amount in the account at the end of 1 year  $10335 (first year)

The amount in the account at the end of 2 years $11286.95.

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Answer:

The amount of money in Enid bank account can be written as a linear equation.

Ye = Xe + $4*m

where Ye is the money that Enid has in her account, m is the number of months that have passed since she opened it, and Xe is the initial deposit.

For Jim, the equation is similar:

Yj = Xj + $3*m

where Yj and Xj are similar as above.

Between May 15 and December 31 of the same year, we have 7 months (where i am counting December because the deposit is made in the first day of the month).

Then we have that:

Ye = $72 = Xe + $4*7 = Xe + $28

Xe = $72 - $28 = $44

So in May 15, Enid deposited $44.

For Jim we have:

Yj = $72 = Xj + $3*7 = Xj + $21

Xj = $72 - $21 = $51

So in May 15, Jim deposited $51.

Answer:

$5,000 per week

Step-by-step explanation:

Ruri is a 30 year old female.

there are about 4 weeks per month

there are about 52 weeks per year

52*5000 = 260,000

She would get 260,000 per year and lets see how much she would have at 40.

260,000*10

at 40 she would have 2,600,000

2,600,000*10

at 50 she would have 26,000,000

at 50 she already has earned more money that the $20 million.

She should go with the $5000 per week if she would like more money.

Answer:

The greatest common factor of the expression is 25x

Step-by-step explanation:

Here, we are interested in giving the greatest common factor of the expression.

We can do this by factorization till we have no common factors left.

the expression is;

100x^2 -250xy + 75x

we start with the common factor x;

x(100x -250y + 75)

The next thing to do here is to find the greatest common factor of 100,250 and 75.

The greatest common factor here is 25.

Thus, we have;

25x(4x -10y + 3)

There is no more factor to get from the terms in the bracket. This simply means that the terms in the bracket are no longer factorizable

So the greatest common factor we have is 25x

Answer:

[tex](-5)^{11}[/tex]

Step-by-step explanation:

We can use the exponent rules. If we have [tex]\frac{a^b}{a^c}[/tex], then it will simplify to [tex]a^{b-c}[/tex].

b is 5, c is -6, and a is -5 so:

[tex]-5^{5-(-6)}\\-5^{11}[/tex]

Hope this helped!

Step-by-step explanation:

when you are cooking you need to measure fractions of ingredients

Answer:

>

Step-by-step explanation:

Even though its 0 its still greater than any negative number.

Answer:

Step-by-step explanation:

Answer:

  1 1/8

Step-by-step explanation:

1/4 of the 4 1/2 gallons were Pepsi, so the amount is ...

  (1/4)(9/2) = (1·9)/(4·2) = 9/8 = 1 1/8

Yoxelt bought 1 1/8 gallons of Pepsi.

Answer:

Yes it will occur

Step-by-step explanation:

The lobby measures 45 feet by 45 feet

Area of the lobby = 45 * 45

=2025 ft^2

So, the lobby has 2025 tiles

subtract 1 black tile in the center

2025 tiles - 1 black tile =2024 tiles

The number of blue tiles and black tiles is 2024 tiles

He wants the outer edge to be the same color as the center tile so, divide by 2

2024/2 = 1012 tiles

The number of tiles in the outer edge is 1012 tiles and the number of tiles in the center is 1012 tiles

Answer:

Step-by-step explanation:

The formula we need for this is

4(4 + x) = 5(5 + 3) and

16 + 4x = 5(8) and

16 + 4x = 40 and

4x = 24 so

x = 6, choice C.

Answer:

4.61 m

Step-by-step explanation:

The angle of depression of the bottom of the shorter building from the top of the taller building = 48° equals the angle of elevation of the top of the taller building from the bottom of the shorter building

Using trig ratios

tan48° = H/d where H = height of taller building and d = their distance apart = 12 m

H = dtan48° = 12tan48° = 13.33 m

Also, the angle of elevation of the top of the shorter building from the bottom of the taller building is 36°

Using trig ratios

tan36° = h/d where h = height of shorter building

h =dtan36° = 12tan36° = 8.72 m

Now, the difference in height of the buildings is thus H - h = 13.33 m - 8.72 m = 4.61 m

Answer:

y- intercept = - 39

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 12x + 2 ← is in slope- intercept form

with slope m = 12

Parallel lines have equal slopes, thus

y = mx + c ← is the partial equation

To find c substitute (4, 9) into the partial equation

9 = 48 + c ⇒ c = 9 - 48 = - 39 ← y- intercept

Answer:

y-intercept = -39

Step-by-step explanation:

if two lines are parallel it means they have the same gradient so we compare the equation given to the default equation of a line

y=mx+c

y=12x+2

comparing we have the gradient m=12 now finding the equation of the line parallel to the given line we use

y-y1=m(x-x1)

y1=9 and x1=4

y-9=12(x-4)

y-9=12x-48

y=2x-48+9

y=2x-39

comparing to the default equation of a line y=mx+c where c is the y-intercept

therefore the y-intercept is -39

Answer:

p(x), q(x), and their product are all polynomials.

p(x) · q(x) = 6x² + 10x - 63

Step-by-step explanation:

First of all P(x) and q(x) are polynomials because polynomials refer to any sum, difference, or product of a collection of algebraic terms. The word polynomials is general. P(x) and q(x) are polynomials but more specifically they are binomials since they only have two terms. Their product is a polynomial as well, but more specifically its a trinomial because it has three terms.

process of multiplying

Using the distributive property (or foil method) when multiplying p(x) and q(x) you would first get the expression 6x² - 18x + 28x - 63. From here you would combine "like terms". This would give you your final answer of

6x² + 10x - 63. Sorry, I couldn't help you with the D question but I hope this helps ;)

Answer:

Here's what I get  

Step-by-step explanation:

a. Net of a cube

Fig. 1 is the net of a cube  

b. Does the formula work?

Tony's formula works if you ignore dimensions.

There are six squares in the net of a cube.

If each side has a unit length s, the total area of the cube is 6s.

c. Will the formula work for any rectangular prism?

No, because a rectangular prism has sides of three different lengths — l, w, and h — as in Fig. 2.

d. Area of a rectangular prism

A rectangular prism has six faces.

A top (T) and a bottom (b) — A = 2×l×w

A left (L) and a right (R)    —   A = 2×l×h

A front (F) and a back (B) —   A = 2×w×h

                                  Total area = 2lw + 2lh + 2wh

If l = 5 m, w = 6 m and h = 8 m,

[tex]\begin{array}{rl}A &=& \text{2$\times$ 5 m $\times$ 6 m + 2$\times$ 5 m $\times$ 8 m + 2 $\times$ 6 m $\times$ 8 m}\\&=& \text{60 m}^{2} + \text{80 m}^{2} + \text{96 m}^{2}\\&=& \textbf{236 m}^{2}\\\end{array}[/tex]

Answer:

Step-by-step explanation:

[tex]\sqrt{x-3} +5=x\\\sqrt{x-3} =x-5\\squaring ~both~sides\\x-3=x^2-10x+25\\x^2-10x-x+25+3=0\\x^2-11x+28=0\\x^2-7x-4x+28=0\\x(x-7)-4(x-7)=0\\(x-7)(x-4)=0\\x=7,4[/tex]

put x=7 in the given equation

[tex]\sqrt{7-3} +5=7\\\sqrt{4} +5=7\\2+5=7\\7=7[/tex]

which is true .

∴ x=7 is a solution of the given eq.

now put x=4 in the given eq.

[tex]\sqrt{4-3} +5=7\\1+5=7\\6=7\\[/tex]

which is not true.

∴x=4 is an extraneous solution.

Answer:

30.9 cm²

Step-by-step explanation:

To find the surface area of this figure, we find the area of the base and the 3 identical sides.

The base is split into two identical right triangles. Let's find the area of one and multiply by two.

Half of 3: 1.5

[tex]1.5\cdot2.6=3.9\\3.9\div2=1.95[/tex]

There are two right triangles:

[tex]1.95\cdot2=3.9[/tex]

The area of one of the sides will be the same thing, except the height is 6.

[tex]1.5\cdot6=9\\9\div2=4.5\\4.5\cdot2=9[/tex]

There are 3 sides identical to this one:

[tex]9\cdot3=27[/tex].

Add 27 and 3.9:

[tex]27+3.9=30.9[/tex]

Hope this helped!

Answer:

30.9 square centimeters

Step-by-step explanation:

3 * 1/2(3)(6) + 1/2(3)(2.6) = 30.9

Answer:

3/8 is your answer.

Step-by-step explanation:

Given:

8 kids bought a 3 cakes.

Required:

How many equal parts will need to divide it so that everyone can have it.

Solution:

3/8

Hope this helps ;) ❤❤❤

Answer: 4t - 3 < 12

Step-by-step explanation:

Answer:

What we need to do is simply multiply the values in both columns e.g 4 * 3/36 = 12/36

Please check explanation for complete answer

Step-by-step explanation:

Here, we are concerned about filling the empty columns of the table.

What we want to do here is simply straightforward. All we need to do is to

multiply the values of x by the values of P(x) in each of the individual rows.

Also recall, we do not need to reduce the fractions.

So we have;

2. 3 * 2/36 = 6/36

3. 4 * 3/36 = 12/36

4. 5 * 4/36 = 20/36

5. 6 * 5/36 = 30/36

6. 7 * 6/36 = 42/36

7. 8 * 5/36 = 40/36

8. 9 * 4/36 = 36/36

9. 10 * 3/36 = 30/36

10. 11 * 2/36 = 22/36

11. 12 * 1/36 = 12/36

Answer:

225.78 grams

Step-by-step explanation:

To solve this question, we would be using the formula

P(t) = Po × 2^t/n

Where P(t) = Remaining amount after r hours

Po = Initial amount

t = Time

In the question,

Where P(t) = Remaining amount after r hours = unknown

Po = Initial amount = 537

t = Time = 10 days

P(t) = 537 × 2^(10/)

P(t) = 225.78 grams

Therefore, the amount of iodine-131 left after 10 days = 225.78 grams

Answer:

C. x-2

Step-by-step explanation:

edge

Answer: the 3rd the answer c

x-2

Step-by-step explanation:

YES! quite easily.

I hope you can see the two pairs of corresponding angles between the parallel lines. they'll be equal

and then there's a pair of vertically opposite angle at centre.

that means all pairs of corresponding angles are equal, thus, triangles are similar by AAA

Answer:

[tex]\Large \boxed{\mathrm{D}}[/tex]

Step-by-step explanation:

The triangles can be proven by AA or Angle-Angle similarity.

[tex]\angle QUR \cong \angle TUS[/tex]

The vertical angles are congruent.

[tex]\angle R \cong \angle S[/tex]

The alternate interior angles are congruent.

Answer:

Option C and option E

Step-by-step explanation:

C.) 7,8,9,…

E.) 22

Natural numbers are also called counting numbers.

They begin from 1, 2, 3 to infinity.

Natural numbers are greater than zero (0)

They do not have decimal point in them.

They are positive integers, as such they do not have minus

Natural numbers can include commas when they are large like 3,000

Answer and Step-by-step explanation: The described right triangle is in the attachment.

As it is shown, AC is the hypotenuse and BC and AB are the sides, so use Pytagorean Theorem to find the unknown measure:

AC² = AB² + BC²

[tex]AB^{2} = AC^{2}-BC^{2}[/tex]

[tex]AB =\sqrt{AC^{2}-BC^{2}}[/tex]

[tex]AB =\sqrt{7^{2}-4.5^{2}}[/tex]

[tex]AB =\sqrt{28.75}[/tex]

AB = 5.4

Then, right triangle ABC measures:

AB = 5.4cm

BC = 4.5cm

AC = 7cm

Answer/Step-by-step Explanation:

Given, [tex]\frac{3}{4}*-4\frac{2}{9}[/tex]

Ivy solves this problem by writing each number as a fraction and then multiplies as shown below:

[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}* -\frac{38}{9} [/tex]

[tex] = \frac{3}{4}*-\frac{38}{9} = -\frac{3*38}{4*9} = -\frac{1*19}{2*3}[/tex]

[tex]= -\frac{19}{6}[/tex]

Fabian solves this problem by writing the mixed number as a sum and applies the distributive method of multiplication as shown below:

[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}(-4 + -\frac{2}{9}) [/tex]

[tex] = \frac{3}{4}*-4 + \frac{3}{4}*-\frac{2}{9} [/tex]

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

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

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

Answer:

The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.

Step-by-step explanation:

Let suppose that [tex]g(x) = \frac{1}{x^{2}}[/tex], then [tex]f(g(x))[/tex] is:

[tex]f(g(x)) = 7\cdot \left(\frac{1}{x^{2}} \right) + 10[/tex]

[tex]f(g(x)) = 7\cdot g(x) + 10[/tex]

Thus,

[tex]f(x) = 7\cdot x + 10[/tex]

The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.

Answer:

-15

Step-by-step explanation:

-7p+10p-16=6p+36-7

3p-16=6p+29

3p-6p=29+16

-3p=45

p=45/-3

p=-15

Answer:

Rate of Change/Slope = -20

Equation: y= -20x +100

Step-by-step explanation:

A. We know the rate of change is also known as the slope.  If we used the slope formula to find the slope we can find the Rate of Change.

[tex]\frac{y2 - y1}{x2 - x1} = \frac{100-80}{1-2} = \frac{20}{-1} = -20[/tex]

B. Since we know the slope and 1 point on the graph we can substitute them in for 'b'

(0,100)

(100)=-20(0) + b

b = 100

Since we know the slope and the b value we can write the equation:\

y = -20x +100

The rate of change refers to the slope of the line, that is the change in y-axis per unit change in the value on the x-axis. Hence, the rate of change is :

Slope = - 100 / 5 = - 20

General form of a slope - intercept relation :

The intercept, c can be calculated thus:

100 = - 20(0) + c

100 = 0 + c

c = 100

Hence, the slope - intercept equation will be y = - 20x + 100

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