In Russel Elementary School there are 50 students. At the beginning of the year, each student planted three flowers in the school yard. During the year, eight flowers withered. Which of the following expressions represents the number of flowers that remained in the school yard? A. (3 × 50) – 8 B. (50 + 3) – 8 C. (50 × 8) – 3 D. (50 × 3) ÷ 8

Answer:

Vacuous proof is used.

Step-by-step explanation:

Given:

Proposition p(n) :

"if n is a positive integer greater than 1, then n² > n"

To prove:

Prove the proposition p (0)

Solution:

Using the proposition p(n) the proposition p(0) becomes:

p(0) = "if 0 is a positive integer greater than 1, then 0² > 0"

The proposition that "0 is a positive integer greater than 1" is false

Since the premises "if 0 is a positive integer greater than 1" is false this means the overall proposition/ statement is true.

Thus this is the vacuous proof which states that:

if a premise p ("0 is a positive integer greater than 1") is false then the implication or conditional statement p->q ("if n is a positive integer greater than 1, then n² > n") is trivially true.

So in vacuous proof, the implication i.e."if n is a positive integer greater than 1, then n2 > n." is only true when the antecedent i.e. "0 is a positive integer greater than 1" cannot be satisfied.

Answer:

(x + [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{41} }{2}[/tex] )(x + [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{41} }{2}[/tex] )

Step-by-step explanation:

solve the polynomial for x then express in product of factor form

Solve

x² + x - 10 = 0 ( add 10 to both sides )

x² + x = 10

Using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2([tex]\frac{1}{2}[/tex] )x + [tex]\frac{1}{4}[/tex] = 10 + [tex]\frac{1}{4}[/tex]

(x + [tex]\frac{1}{2}[/tex] )² = [tex]\frac{41}{4}[/tex] ( take the square root of both sides )

x + [tex]\frac{1}{2}[/tex] = ± [tex]\sqrt{\frac{41}{4} }[/tex] = ± [tex]\frac{\sqrt{41} }{2}[/tex] ( subtract [tex]\frac{1}{2}[/tex] from both sides )

x = - [tex]\frac{1}{2}[/tex] ± [tex]\frac{\sqrt{41} }{2}[/tex]

Thus corresponding factors are

(x - (- [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{41} }{2}[/tex] ) ) and (x - (- [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{41} }{2}[/tex] ), that is

(x + [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{41} }{2}[/tex] ) and ( x + [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{41} }{2}[/tex] )

Thus

x² + x - 10 = ( x + [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{41} }{2}[/tex] )(x + [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{41} }{2}[/tex] ) ← in factored form

Answer:

7.4

Step-by-step explanation:

NOT 8.1 !!

The length of arc RQ is 7.35 inch.

The distance between two places along a segment of a curve is known as the arc length.

Arc Length Formula (if θ is in degrees) s = 2 π r (θ/360°)

Given:

Angle = 65

radius = 6.48 inch

So, length of Arc

= 2πr( [tex]\theta[/tex]/ 360)

= 2 x 3.14 x 6.48 (65/360)

= 40.6944 x 0.1805

= 7.3453392

Hence, the length of arc is 7.35 inch.

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Explanation:

Everywhere you see an x, replace it with 5. Then simplify using PEMDAS

f(x) = x^2 - 3x

f(5) = 5^2 - 3(5) ... plug in x = 5

f(5) = 25 - 15

f(5) = 10

Answer:

Hey there!

Thus, the vehicle can cover 20 m per second and would have a speed of 20 meters per second.

Let me know if this helps :)

Answer:

Width of the new tv= 65.44 inches

Height of the new tv = 36.41 inches

If the newer television has an aspect ratio of 16:9, will the new tv fit in the old entertainment center?

Since the old entertainment set has a dimension of 70 inches by 35 inches

,new TV set, has dimension of 65.44 inches by 36.81 inches, the new TV may not be able to fit into the old entertainment set properly because it is 1.81 inches higher than the entertainment set.

Step-by-step explanation:

The newer TV set has an aspect ratio of 16: 9 and it is 75 inches

We are going to make use of Pythagoras theorem

= Width² + Height ² = Size of TV²

Width = 16x

Height = 9x

75² = (16x)² + (9x)²

5625 = 256x² + 81x²

5625 = 337x²

x² = 5625/337

x² = 16.691394659

x = √16.691394659

x = 4.0855103303

Approximately = 4.09

Hence, we can find the width and height of the new TV

Width = 16x

Width = 16 × 4.09

Width = 65.44 inches

Height = 9x

Height = 9 × 4.09

Height = 36.81 inches

Hence, the dimensions of the new TV set = 65.44 inches by 36.81 inches

If the newer television has an aspect ratio of 16:9, will the new tv fit in the old entertainment center?

Since the old entertainment set has a dimension of 70 inches by 35 inches

,new TV set, has dimension of 65.44 inches by 36.81 inches, the new TV may not be able to fit into the old entertainment set properly because it is 1.81 inches higher than the entertainment set.

Answer:

m = 2 (the slope is 2/1), b = 1 (the y-intercept is (0,1))

Step-by-step explanation:

First, plot a point on the y-intercept (0,1). Then go up twice and to the right once to find the next point (since the slope is 2/1). You can continue doing this to form a line. The graph is shown below

Answer:

m=2

b=1

Step-by-step explanation:

We are given the equation of a line. The equation is:

y=2x+1

This equation is in slope-intercept form, or

y=mx+b  

where m is the slope and b is the y-intercept. Essentially, the coefficient of x is the slope and number that is added or subtracted from that is the y-intercept.

When we analyze the equation given, we see that x is being multiplied by 2. Therefore, the slope must be 2.

We can also see that 1 is added to 2x. Therefore, the y-intercept must be 1.

The slope of the line is 2 and the y-intercept is 1.

m=2 and b=1

The graph of the line is shown below.

Answer:

Mrs Taylor should buy 45.5 yards of fabric ( 45.5364 actually but rounded to the nearest tenth)

Step-by-step explanation:

Here in this question, we are interested in calculating the total yards of fabric that Mrs Taylor should buy.

From the question, we are made to know that one uniform requires 26 inch of fabrics and she wants to make a total of 63 uniforms

The total inches of fabric needed is thus; 26 * 63 = 1,638 inches of Fabrics

But we want our answer in yards.

Mathematically;

1 inch = 0.0278 yard

1638 inches = x yard

x = 1638 * 0.0278 = 45.5364 yards which is approximately 45.5yards

Answer:

[tex] {x }^{2} - 100[/tex]

[tex] {x}^{2} - {10}^{2} [/tex]

[tex](x - 10)(x + 10)[/tex]

this is the answer

hope this is helpful for you.

Answer:

See below.

Step-by-step explanation:

4)

So we have the expression:

[tex](-6n^{-3})^2[/tex]

We can use the power of a product property, where:

[tex](ab)^n=a^n\cdot b^n[/tex]

So:

[tex]=(-6)^2\cdot(n^{-3})^2[/tex]

For the left, -6 squared is the same as -6 times -6. This equals positive 36.

For the right, we can use the power of a power property. The property says that:

[tex](a^n)^k=a^{nk}[/tex]

So:

[tex](n^{-3})^2=n^{(-3)(2)}\\=n^{-6}[/tex]

So, all together, we have:

[tex]=(-6)^2\cdot(n^{-3})^2\\=36n^{-6}[/tex]

6)

We have the expression:

[tex]-\frac{3x^0}{x^4}[/tex]

First, note that anything to the zeroth power (except for 0) is 1, thus, x^0 is also 1. Simplify:

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

And that's the simplest we can do :)

Notes for 6)

We can put the x^4 to the numerator. Recall that when you put an exponent to opposite side, you put a negative. In other words:

[tex]x^n=\frac{1}{x^{-n}}[/tex]

And vice versa:

[tex]\frac{1}{x^{-n}}=x^n[/tex]

So, we can write the above as:

[tex]=-\frac{3}{x^4}\\=-\frac{3}{x^{-(-4)}}\\=-3x^{-4}[/tex]

However, traditionally, we want only positive exponents, so this wouldn't be correct.

Answer:

Step-by-step explanation:

x^m×x^n=x^{m+n}

x^m÷x^n=x^{m-n}

[tex]\frac{1}{x^m} =x^{-m}\\x^{-n}=\frac{1}{x^n} \\(xyz)^m=x^m\times y^m \times z^m \\(x^m)^n=x^{mn}[/tex]

[tex]x^0=1[/tex]

Answer:

10i

Step-by-step explanation:

Step 1: Expand first 2

(1 + i)(2 + i)

2 + i + 2i + i²

2 + 3i + (-1)

1 + 3i

Step 2: Expand again

(1 + 3i)(3 + i)

3 + i + 9i + 3i²

3 + 10i + 3(-1)

3 + 10i - 3

10i

Answer:

p=2

Step-by-step explanation:

so how to find this u take the five and three and u subtract them both and whatever is left over that is your answer

Answer: -506.5 or -253.25

Step-by-step explanation:

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Hi my lil bunny!

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[tex]\frac{1}{2}-3\ \left(12\ +\ 1\right)^2[/tex]

[tex]= \frac{1}{2}-3 (13^2)[/tex]

[tex]= \frac{1}{2} - (3) (169)[/tex]

[tex]= \frac{1}{2} - 507[/tex]

[tex]= \frac{-1013}{2}[/tex]

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Have a great day/night!

❀*May*❀

Answer:

3x-12 is the simplififed answer

Step-by-step explanation:

the equation is almost already simplified. when you combine -8 and -4, which are like terms, you get 3x-12. because there are no more lie temrs in the equation, it can not be simplififed any further.

Answer:

3x-12

Step-by-step explanation:

3x-8-4                        -8-4=-12

 3x-12

Answer: Choice C)

(1/30)*(1/29)

Explanation:

Jack has a 1/30 chance of being picked since he is 1 person out of 30 total. After his name is picked, and not put back, there are 30-1 = 29 names left. The chances Jill is picked is 1/29. The two fractions are multiplied to get the overall probability both are picked.

Answer:

dx+9x+16d^2 dont know it it helps any but i tried

Step-by-step explanation:

Answer:

Step-by-step explanation:

To combine integers with different signs find their absolute values then subtract the smaller absolute value from the larger one. Give the sum the sign of the number with the largest absolute value.

Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{ - 3i + 1}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{(4 + 2i) + ( - 3 - 5i)}[/tex]

When there is a ( + ) in front of an expression in parentheses, there is no need to change the sign.

That means the expression remains the same.

Just remove the parentheses

[tex] \sf{4 + 2i - 3 - 5i}[/tex]

Collect like terms

⇒[tex] \sf{ - 3i + 4 - 3}[/tex]

Calculate the difference

⇒[tex] \sf{ - 3i + 1}[/tex]

Hope I helped!

Best regards!!

9514 1404 393

Answer:

  1 -3i

Step-by-step explanation:

For purposes of addition or subtraction, the i can be treated as though it were a variable. Terms can be collected in the usual way.

  4 +2i +(-3 -5i) = 4 +2i -3 -5i

  = (4 -3) +i(2 -5) = 1 -3i

Answer:

see below

Step-by-step explanation:

7.    1/3 ( n+2) = 5

Multiply each side by 3

n+2 = 5*3

n+2 = 15

Subtract 2 from each side

n+2-2 = 15-2

n = 13

8.x = bills

He started with 300 and paid 1/4 of the bills and ended up with -50

300 - 1/4 x = -50

Rearranging the order on the left

-1/4x + 300 = -50

Answer:

(A) [tex]-\frac{1}{4}x+300=-50[/tex]

Step-by-step explanation:

I "reversed" this problem to find the equation that works for it.

The balance was originally $300. If he's now at a balance of -50$ after paying off [tex]\frac{1}{4}[/tex] of his bills, then [tex]\frac{1}{4}[/tex] of his bills are $350, since [tex]300 - (-50) = 350[/tex].

If  [tex]\frac{1}{4}[/tex]  of his bills are $350, then his full bill is [tex]350\cdot4=1400[/tex]$.

So I tested each equation, where [tex]x=1400[/tex] to see if the equation worked out.

For a:

[tex]-\frac{1}{4}x + 300 = -50\\\\-\frac{1}{4}\cdot1400 + 300 = -50\\\\-350 + 300 = -50[/tex]

-350 + 300 is indeed -50, so I knew this equation works.

Hope this helped!

Answer:

[tex]0[/tex]

Step-by-step explanation:

[tex] \frac{1}{3}m - 1 - \frac{1}{2}n = \frac{1}{3}(21) - 1 - \frac{1}{2}(12) = 7 - 1 - 6 = 6 - 6 = 0[/tex]

Answer:

0

Step-by-step explanation:

1/3m - 1 - 1/2n
= 1/3(21) -1 1/2(12)
= 7 - 1 - 6
= 0

Answer:

V= 68.6 m/s

Step-by-step explanation:

height above the ground t seconds after it is dropped is 675-4.9t^2

For seven seconds

Height above ground= 675-4.9(7)²

height above ground= 675-240.1

Height above ground= 434.9 m

But it's dropped from a cliff and we need to find the distance traveled from the too of the cliff

Distance= 675-434.9.

Distance= 240.1

To determine it's speed

V²= U² +2gs

V= velocity we are looking for

U= initial velocity= 0

G= acceleration due to gravity= 9.8 m/s²

s= distance covered

V²= U² +2gs

V²= 0+2(9.8)(240.1)

V²= 4705.96

V= 68.6 m/s

Answer:

She forgot to flip the sign in the last step.

Step-by-step explanation:

In inequality, if you multiply or divide by a negative number, you would have to reverse the inequality sign.

Marice forgot to do this in the final step. She had to divide '-8' to get x completely on one side. All other steps are correct.

The correct answer is x ≥ -1.

Hope this helps.

Answer:

Velocity in still air is = 960 miles per hour  

Velocity of wind  = 230 miles per hour.

Step-by-step explanation:

The velocity when flying against the wind = 2920 / 4 = 730 miles per hour.

The velocity when flying with the wind = 7140 / 6 = 1190

Let the rate of jet in still Air = x

Let the rate of jet in wind = y

Therefore, velocity against wind = x-y and wind = x + y

x - y = 730

x + y = 1190

Add both equation, 2x = 1920

x = 960

Now find the value of “y” = 1190 – 960 = 230

Thus, velocity in still air is = 960 miles per hour  

Velocity of wind  = 230 miles per hour.

Answer:

Rate of jet in still air = 960 miles/ hr

Rate of the wind = 230 miles/ hr

Step-by-step explanation:

Let the speed of jet in still air = [tex]u[/tex] miles/hr

Let the speed of air = [tex]v[/tex] miles/hr

So, against the wind, the resultant speed = [tex](u-v)[/tex] miles/hr

And, with the wind, the resultant speed = [tex](u+v)[/tex] miles/hr

Distance traveled against the wind = 2920 miles

Time taken against the wind = 4 hrs

Formula for distance is:

[tex]\bold{Distance =Speed \times Time}[/tex]

[tex]2920 = (u-v)\times 4\\\Rightarrow u-v=\dfrac{2920}{4}\\\Rightarrow u-v=730\ miles/hr...... (1)[/tex]

Distance traveled with the wind = 7140 miles

Time taken against the wind = 6 hrs

[tex]\bold{Distance =Speed \times Time}[/tex]

[tex]7140 = (u+v)\times 6\\\Rightarrow u+v=\dfrac{7140}{6}\\\Rightarrow u+v= 1190 \ miles/hr...... (2)[/tex]

Adding (1) and (2):

[tex]2u = 1920\\\Rightarrow \bold{u = 960 miles/hr}[/tex]

Putting [tex]u[/tex] in (1):

[tex]960 -v = 730 \\\Rightarrow \bold{v=230\ miles/hr}[/tex]

Therefore, the answer is:

Rate of jet in still air = 960 miles/ hr

Rate of the wind = 230 miles/ hr

Answer:

-1/5+(√3)/20i   or   -0.2+0.05√3i

Step-by-step explanation:

  [tex]\dfrac{-8+\sqrt{-12}}{40}=-\dfrac{8}{40}+\dfrac{2\sqrt{3}i}{40}=\boxed{-\dfrac{1}{5}+\dfrac{1}{20}\sqrt{3}\,i=-0.2+0.05\sqrt{3}\,i}[/tex]

_____

Comment on answer form

Satisfying the input format requirements of a computer is always problematic. One never knows if fractions or decimals are preferred, whether radicals must be simplified, and so on. If no clues are offered by general instructions, other questions, or previous experience, then it might be useful to consult your instructor.

Let the number be "x" , then according to the question :

• 2x - 12 = -8

Further solving

→ 2x = -8 + 12

→ 2x = 4 .

→ x = 2

★ Solution :

Let number be n.

[tex]\rule{130}{1}[/tex]

☯ [tex]\underline{\boldsymbol{According\: to \:the\: Question\:now :}}[/tex]

[tex]:\implies\sf 2n - 12 = -8 \\\\\\:\implies\sf 2n = -8 + 12\\\\\\:\implies\sf 2n = 4\\\\\\:\implies\sf n = \dfrac{4}{2}\\\\\\:\implies\underline{\boxed{\sf n = 2}}\:\:\:\:\:\Bigg\lgroup\bf{Required\: number}\Bigg\rgroup[/tex]

[tex]\therefore\:\underline{\textsf{The required number is \textbf{2}}}.[/tex]

Answer:

x=3

Step-by-step explanation:

2/3x+15=17

first subtract 15 from both sides

2/3x=2

multiply by 3 to eliminate the fraction

2x=6

divide by 3

x=3

Answer:

x=3

Step-by-step explanation:

2/3x +15 = 17

2/3x = 17-15

2/3x = 2

x = 2  /  2/3

x = 2/1  *  3/2

x = 6/2

x = 3

Answer:

  30500 = 3.05·10^4

Step-by-step explanation:

Your calculator can do this for you. You may need to set the display to scientific notation, if that's the form of the answer you want.

__

This can be computed by converting both numbers to standard form:

  (5·10^2) +(3·10^4)

  = 500 +30000 = 30500 = 3.05·10^4

__

Addition of numbers in scientific notation in general requires that they have the same power of 10. It may be convenient to convert both numbers to the highest power of 10.

  5·10^2 + 3·10^4

  = 0.05·10^4 +3·10^4 . . . . now both have multipliers of 10^4

  = (0.05 +3)·10^4

  = 3.05·10^4

Answer:

11

Step-by-step explanation:

2 times 5 = 10 so 8+10 -7= 11

The required simplified value of the given expression at g = 7 is 11.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
y = 8 + 2g - 7

Now put g = 5,
y = 8 + 2(5) - 7
y = 8 + 10 - 7
y = 11

Thus, the required simplified value of the given expression at g = 7 is 11.

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