Mathematics High School

One-half the square of b

Answers

Answer 1
A machine produces 240 bolts in 25 minutes. At the same rate how many bolts would be produced in 45 minutes
Answer 2

Answer:

[tex]\frac{b^2}{2}[/tex]

Step-by-step explanation:

We are supposed to write an algebraic expression for given word phrase.

The square of b would be 'b' raised to second power: [tex]b^2[/tex].

Half the square of b would be [tex]b^2[/tex] divide by 2: [tex]\frac{b^2}{2}[/tex].

Therefore, our required expression would be [tex]\frac{b^2}{2}[/tex].

Related Questions

The net below is for a number cube. What are the three sums of the numbers on opposite surfaces of the cube?

Answers

I think the way you do it is you just add the numbers that are opposite of each other. A way you can figure it out is by imagining the net folding into a cube. The numbers that are opposite each other are 5 and 6, 2 and 4, and 1 and 3. 5+6=11, 4+2=6, and 1+3=4. 11, 6, and 4 are your answers.

Half of the product of two consecutive numbers is 105. Which equation can be used to solve for n, the smaller of the two numbers?


Answers

Let the smaller number be n:
Therefore 1/2 * n(n+1) = 105
n^2 + n = 210
n^2 + n - 210 =0
Use your preferred method to solve the quadratic, I'll factorise this since this is easy to factorise.
Two numbers':
product gives -210
summation gives 1
Therefore (n+15)(n-14)=0
So the smaller number n is either -15 or 14.

Answer with Step-by-step explanation:

We are given that:

Half of the product of two consecutive numbers is 105.

Let smaller number be n

Then, larger number will be n+1

[tex]\dfrac{1}{2}n(n+1)=105[/tex]

Multiplying by 2 on both sides, we get

n(n+1)=210

n²+n=210

n²+n-210=0

On splitting the middle term

n²+15n-14n-210=0

n(n+15)-14(n+15)=0

(n-14)(n+15)=0

either n-14=0 or n+15=0

either n=14 or n= -15

When n=14, n+1=15

when n= -15, n+1= -14

Hence, equation used to solve for n was:

[tex]\dfrac{1}{2}n(n+1)=105[/tex]

Now that you have x² - 8x + 16 = 9 + 16, apply the square root property to the equation.

Answers

This is what I found and your cute
Answer
Hi,

a) x² +8x + 16 = 7

(x + 4)² = 7

Take the square root of both sides, remembering the ± sign on the right.

√(x + 4)² = ±√7

x + 4 = ±√7

x = -4 ± √7 <==ANSWER


b) x² -6x +9 = 8

(x - 3)² = 8

√(x - 3)² = ±√8

x - 3 = ±2√2

x = 3 ± 2√2 <==ANSWER

Answer: ( x - 4 )² = 25

The solutions to the quadratic equation

x2 – 8x – 9 = 0. are

-1 and 9

Which transformation will be equivalent to rotating a figure 180° counterclockwise?

A) reflecting over the line y = x.
B) reflecting over the line y = -x.
C) reflecting over the x-axis and the y-axis.
D) translating left 3 units and down 5 units.

Answers

If we have given coordinates of the image are in form (h,k).

The resulting coordinates of image rotation of 180° around the origin would be (-h,-k).

We have rule (h,k) ---> (-h,-k).

We can see that x-coordinate is being multiplied by -1 and then y-coordinate is also being multiplied by -1.

Above rule could be break into two parts.

(h,k) ---> (-h,k) ---->  (-h,-k).

We can see in first step, (h,k) ---> (-h,k) is being reflecting over the x-axis and

in second step (-h,k) ---->  (-h,-k) is being reflecting over the y-axis.

Therefore, correct option is C) reflecting over the x-axis and the y-axis.

The transformation which is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise is reflecting over the [tex]x[/tex]-axis and [tex]y[/tex]-axis. Therefore, the [tex]\fbox{\begin\\\ \bf option (C)\\\end{minispace}}[/tex] is correct.

Further explanation:

Consider a coordinate in the form [tex](a,b)[/tex] where [tex]a[/tex] and [tex]b[/tex] are real numbers.

If [tex]a[/tex] and [tex]b[/tex] are positive then the point [tex](a,b)[/tex] lies in the first quadrant.

If we rotate the coordinate [tex](a,b)[/tex] [tex]180^{\circ}[/tex] counterclockwise then the coordinates become [tex](-a,-b)[/tex].

The coordinate [tex](-a,-b)[/tex] lies in the third quadrant.

If we reflect the coordinate [tex](a,b)[/tex] about the [tex]x[/tex]-axis then the coordinates become [tex](a,-b)[/tex].

The coordinate [tex](a,-b)[/tex] lies in the fourth quadrant.

If we reflect the coordinate [tex](a,-b)[/tex] about the [tex]y[/tex]-axis then the coordinates become [tex](-a,-b)[/tex].

The coordinate [tex](-a,-b)[/tex] lies in the third quadrant.

This implies that rotating a figure [tex]180^{\circ}[/tex] counterclockwise is equivalent to transformation of reflecting over [tex]x[/tex]-axis and reflecting over [tex]y[/tex]-axis.

Option (A)

In option (A) it is given that reflection about the line [tex]y=x[/tex] is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.

If we reflect the coordinate [tex](a,b)[/tex] about the line [tex]y=x[/tex] then the coordinates become [tex](b,a)[/tex].

This is not same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.

Therefore, the option (A) is incorrect.

Option (B)

In option (B) it is given that reflection about [tex]y=-x[/tex] is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.

If we reflect the coordinate [tex](a,b)[/tex] about the line [tex]y=-x[/tex] then the coordinates become [tex](-b,-a)[/tex].

This is not same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.

Therefore, the option (B) is incorrect.

Option (C)

In option (C) it is given that reflection about [tex]x[/tex]-axis and [tex]y[/tex]-axis is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.

If we reflect the coordinate [tex](a,b)[/tex] about [tex]x[/tex]-axis and [tex]y[/tex]-axis then the coordinates become [tex](-a,-b)[/tex].

This is same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.

Therefore, the option (C) is correct.

Option (D)

In option (D) it is given that shifting a point [tex]3[/tex] units left and [tex]5[/tex] units down is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.

If we shift the point [tex](a,b)[/tex], [tex]3[/tex] units left and [tex]5[/tex] units down the coordinate is [tex](a+3,b-5)[/tex].

This is not same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.

Therefore, the option (D) is incorrect.

Therefore, the [tex]\fbox{\begin\\\ \bf option (C)\\\end{minispace}}[/tex] is correct.

Learn more

1. Learn more about the rotation of the triangle   about the origin https://brainly.com/question/7437053.

2. Learn more about when a triangle is rotated  about the origin https://brainly.com/question/2992432.

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Geometry

Keywords: Transformation, rotation, reflection, clockwise, geometry, counterclockwise,  -axis,  - axis, coordinates, graph, origin, line, degrees, translation, symmetry.

You lose 3 pounds per week on your new diet. What integer represents the change in your weight after 3 weeks

Answers

Hello,

If you lose 3 pounds per week, after 3 weeks you lose (3)(3) = 9 pounds.

The change in your weight is represented by the integer 9 (pounds).

Hope this helps!

In your first week- 3 pounds is lost

#3 weeks later= 3 x 3
                       = 9 

Thus 3 weeks later 9 pounds is lost

t - 5w = 3j solve for t (literal equations)

Answers

T-5w=3j
T=5w+3j
Yes this is the answer
T - 5w = 3j
T = 3j  +  5w

hope it  helps

How do I solve this

Answers

Hello,

[tex]x^2-2x-27=-5x+1\\ x^2-2x+5x-27-1=0\\ x^2+3x-28=0\\ x^2+7x-4x-28=0\\ x(x+7)-4(x+7)=0\\ (x+7)(x-4)=0\\ x=-7\ or\ x=4\\ [/tex]
The answer is X1=-7, x2=4.

The following list shows the items and prices for a restaurant order. Calculate the total amount if there is a 7% tax and the customer leaves a 20% gratuity. 1 appetizer: $7.39 2 entrees: $16.99 each 1 dessert: $5.29 2 drinks: $2.30 each a. $65.82 b. $65.10 c. $54.85 d. $40.60

Answers

The answer is B. $65.10
7% of $51.26 is $3.59, which adds up to $54.85
20% of $51.26 is $10.25, which, with the tax included here, adds up to $65.10. Hope this helped.
the answer is b $65.10 . took the  test got it right

Which of the following shows the numbers ordered from least to greatest?

A)0.004, 0.07, 0.6, 0.32
B)0.004, 0.6 0.07, 0.32
C)0.004, 0.07, 0.32, 0.6
D)0.004, 0.32, 0.07, 0.6

Answers

I'm gonna say C cause 0.004 is less than 0.07 and 0.32 is less than 0.6 cause 0.6 = 0.60....so ya the answer is C

Calculate the area of the figure below using the following information:

Area of triangle ABC = 23.85 square units

Area of triangle ACD = 29.4 square units

Area of triangle AED = 26.25 square units


The area of the Figure ABCDE is ______ square units.

Answers

The area of ​​the figure ABCDE  is equal to the sum of the areas of the triangles ABC, ACD and AED

Area = 23.85 + 29.4 + 26.25 = 79.5 square units 

Answer:

Area of pentagon ABCDE =  23.85  + 29.4 + 26.25 = 79.5 unit²    

Step-by-step explanation:

Area of pentagon ABCDE is sum of area of triangles ABC, ACD and ADE

Area of pentagon ABCDE = Area of ΔABC +Area of ΔACD + Area of ΔADE

Area of ΔABC = 23.85 unit²

Area of ΔACD = 29.4 unit²

Area of ΔAED = 26.25 unit²

Area of pentagon ABCDE = Area of ΔABC +Area of ΔACD + Area of ΔADE

Area of pentagon ABCDE =  23.85  + 29.4 + 26.25 = 79.5 unit²          

help me ............

Answers

3 1/2 x 2 = 7

4 2/3 x 2 = 9 1/3

7 + 9 1/3 = 16 1/3 yards

The distance formula is d=r/t. how long will it take (in hours) to travel 100 miles at a rate of 22mph? Show all work.

Answers

divide the distance ( 100 miles) by the speed ( 22 mph) to get the time

100/22 = 4.545454 hours (Round to 4.5 hours ?)

 if you need hours and minutes multiply 0.545454 by 60 to get the minutes

4 hours 32.7 ( round to 33) 4 hours and 33 minutes


A minor league baseball team plays 117 games in a season. if the team won 13 more than 3 times as many as they lost. how many wins and losses

Answers

W + L = 117
W = 3L + 13

3L + 13 + L = 117
4L + 13 = 117
4L = 117 - 13
4L = 104
L = 104/4
L = 26 <=== 26 losses

W = 3L + 13
W = 3(26) + 13
W = 78 + 13
W = 91 <=== 91 wins

The midpoint of a segment is (6,−4) and one endpoint is (13,−2). find the coordinates of the other endpoint.

Answers

I hope this helps you can use the formula to find the middle point just replace the unknown x and y into the equation

A limousine service determines that its per-mile cost is $.36 and that it incurs $48 in miscellaneous expenses for each reservation.The service charges $3.56 per mile. What number of miles represents the break-even point?

Answers

2)

the limousine charges 3.56 per mile driven, so, their income from the sales, or revenue is say... if they drive "m" miles, then is 3.56*m or 3.56m.

now, their costs, how much does it cost to have the limousine up and rolling and a chaffeur and other, well, it boils down to $48 for each reservation, and it costs 36 cents or $0.36 per mile driven, so, if they drive  for "m" miles, then the cost for that will be 0.36*m or 0.36m.  So the total cost is 48 + 0.36m

when is the break-even point?

the break-even point is when... well, you break-even, when the income or sales is the same as the costs, so, you're not really losing any money, you're getting as much as you're spending, but you're not making any surplus or profit either.  That happens when the Revenue = Costs.

[tex]\bf \stackrel{revenue}{3.56m}=\stackrel{costs}{48+0.36m}\implies 3.56m-0.36m=48\implies 3.2m=48 \\\\\\ m=\cfrac{48}{3.2}\implies m=\stackrel{miles}{15}[/tex]

3)

the costs for the grower for planting and caring for a tree is 18.53, so if he plants say "t" trees, then the costs will be 18.53*t or 18.53t.

there's a fixed costs, overhead, for managing the farm, workers, cashiers, forklifts and so on, of $600.

so the total costs is then, 18.53t + 600.

now, he plans to charge for each tree 65 bucks, so if sells "t" trees, the Revenue is 65*t or 65t.

again, what's the break-even point? well Revenue = Costs

[tex]\bf \stackrel{revenue}{65t}=\stackrel{costs}{18.53t+600}\implies 65t-18.53t=600\implies 46.47t=600 \\\\\\ t=\cfrac{600}{46.47}\implies t\approx \stackrel{trees}{12.91}[/tex]

so, the break-even point is at 12.91 trees, or 12 trees and 0.91 of another, I guess you'll just have to chop off a few branches to make it 0.91, but anyhow, if we go up to say 13 trees, the break-even point is passed and he's on the black ink, he's making profit.

so, he'll start making profit after the 12th tree sold.

4)

is the same thing more or less.

costs is $7000 in overhead, plus 24.5 for one scooter, if he makes "s" scooters, then the costs are 24.5s, so total costs is 7000 + 24.5s.

revenue is the price times quantity, if the quantity is "s" and the price is 36.75, then the revenue is 36.75s.

when he doesn't lose money?  well, is the same break-even point, not making profit, but not losing money either.

[tex]\bf \stackrel{revenue}{36.75s}=\stackrel{costs}{7000+24.5s}\implies 36.75s-24.5s=7000 \\\\\\ 12.25s=7000\implies s=\cfrac{7000}{12.25}\implies s\approx \stackrel{scooters}{571.43}[/tex]

so, the break-even point is at 571.43 scooters, so using whole numbers wil just be 571 scooters then, well, you can't have 0.43 unless you're going to saw off the scooter, in which case you won't sell it anyway.

number 4 I have absolutely no idea how to do. I generally understand finding distance on the coordinate plane but this has really confused me. Please help.

Answers

For Part A, in creating the square, you did it correctly.

Now for Part B, you can create a right triangle by adding a point at -4, -3, and we'll call it, say, T.

Then you can use the Pythagorean's Theorem to find the length of one side of the square.

The Pythagorean's Theorem is [tex] a^{2} + b^{2} = c^{2} [/tex]

A would be the distance between P and T, and B would be the distance between Q and T. So then, a would be 7, and B would be 2. 

To fill it in, it would be [tex]7^{2} + 2^{2} = c^{2} [/tex]

or 49 + 4 = [tex] c^{2} [/tex]

or 53 = [tex]c^{2} [/tex]

or [tex] \sqrt{53} [/tex] = x

Which is equal to about 7.28

Now multiply that by 4 to get the perimeter, or 29.12

So the perimeter would be about 29.12


The Pythagorean formula is c^2 = a + b.
true
false

Answers

false.

 the Pythagorean formula is c^2 = a^2 + b^2

What are the solutions to the equations |x-10|-4=2x

Answers

x is going to equal two in this equation.

Tonya is twice Kevin's age. In three years, Tonya will be 17. And in another three years, Uncle Rob will be three times Tonya’s age.
How old is Kevin and Uncle Bob

Answers

Kevin is 7 1/2 and Uncle Rob is 54

17-3 = 14 ( Tonya's age now)

14/2 = 7 ( Kevin's age)

14*3 = 42 ( Uncle Bob's age)

The area of a rectangle is 72 cm². The length of the rectangle is 6 cm longer than the width.

What is the width of the rectangle?



2 cm

6 cm

8 cm

10 cm

Answers

Area =72 sq. cm

length = x+6

Width = x

l×b = Area
(x+6)x =72
x2 +6x=72
x2+6x-72=0
x2+12x-6x-72=0
x (x+12) -6 (x+12)=0
(x+12) ( x-6) =0
x=-12, x=6

since width can't be negative , the answer is x=6.

therefore, the width is 6cm

Answer:

6cm

step-by-step explanation

just dived each number bye 72 to find 12 witch we would get 6cm

What Do You Call It When Police Interrogate a Cow's Husband? *the answer isn't " Question-a-bull** && the answer is 12 letters long

Answers

The key in this problem is to find the answer in each number and then cross out the box containing that solution. Here are the following answers with their corresponding letters that need to be crossed out.

1 . 12 LK


2. 9 AM


3. -8 ST


4. -15 SH


5. 33 IN


6. -36 OO


7. 44 OP


8. 14 CO


9. 27FT ME


10. 23 ED


11. $580 WS


12. 11 DEGREES CELSIUS TO


13. 29 IT


14. -35m JA


After crossing out those letters, the answer for what do you call a when a policeman interrogate a cow's husband is QUESTIONABLE.

0. 135 written as a fraction

Answers

0.135 is the same as 135/1000 so change it to that

Find the GCF of 135 and 1000 and that would be 5.

Divide both the numerator and denominator by the GCF

Simplify

Answer: 27/200.

Explains how to write 0.135 as a fraction.

0.135 written as a fraction is 135/1000.

Vivian solved an equation. she showed all her steps and got the correct answer. what kind of reasoning did vivian use to solve the equation? convenient inductive predictive deductive

Answers

The type of reasoning that Vivian used into solving the equation is the deductive. This type of reasoning is able to describe on how the equation is done and this could be seen in the given scenario above as she was able to show the steps in obtaining the correct answer.

Find the mode of this data set: 3, 3, 4, 8, 5, 8, 1, 6, 7.

Answers

The modes are: 3 and 8

Find the equation of the tangent line to the curve 4x3+2y2−11=4xy−x at the point (−1,2).

Answers

hello : let : y = f(x)     so : y' = f'(x)
calculate : f'(x)  and : f'(-1)  given f(-1) = 2

by derivate : 4x3+2y2−11=4xy−x
12x² +4yy' = 4y +4xy' - 1
4yy' - 4xy' = - 12x² +4y -1 
y' ( 4y - 4x) = 4y -12x² -1 ...(*)
if x = -1   y = 2 subsct in : (*)
y' (4(2)-4(-1)) = 4(2)-12(-1)² - 1
2y' = - 9 
y' = - 9/2 = f'(- 1)  ( the slope of the tangent )
of the tangent line to the curve at the point (−1,2) is : 
y - 2 = (-9/2)(x +1)

If m<1 = 7x + 6 and m<2 = 8x - 6, find the value of x so that p is perpendicular to q

Answers

Answer:

x = 12

Step-by-step explanation:

Given: [tex]\angle 1=7x+6[/tex]

[tex]\angle 2=8x-6[/tex]

∠1 and ∠2 form by two intersection line p and q.

p is perpendicular to q.

Therefore, ∠1 = ∠2 = 90°

So, 7x + 6 = 90°

7x = 84

x = 12

8x - 6 = 90°

8x = 96

x = 12

7x + 6 = 8x - 6

x = 6 + 6

x = 12

So, we get x=12 from all three equations.

hence, The value of x is 12

he editors found that 0.0016 of the words in the book were misspelled. if there were 250,000 words in the book how many words were spelled properly

Answers

Since 0.0016 of the words were misspelled (and it's not in a percent), we can multiply 250,000 by 0.0016 to get 400
the answer is 400 
(⌐■_■)

What is x in 7x+2x-5=0

Answers

7x+2x-5=0

7x+2x=9x, so, now we have this:

9x-5=0, we, because is equal with 0, the terms are equal between them.

9x=5 

x=5/9

Triangle MRN is created when an equilateral triangle is folded in half. What is the value of y?

A. 2√3 units
B. 4 units
C. 4√3 units
D. 8 units

Answers

we know that

If Triangle MRN is created when an equilateral triangle is folded in half

then

[tex]RM=\frac{1}{2}*MN[/tex]

[tex]MN=6+2=8\ units[/tex]

so

[tex]RM=\frac{1}{2}*8=4\ units[/tex]

Applying the Pythagorean Theorem in triangle MRN

[tex]MN^{2}=NR^{2}+RM^{2}[/tex]

we have

[tex]MN=8\ units[/tex]

[tex]RM=x=4\ units[/tex]

[tex]NR=y[/tex]

substitute

[tex]8^{2}=y^{2}+4^{2}[/tex]

solve for y

[tex]y^{2}=8^{2}-4^{2}[/tex]

[tex]y^{2}=48[/tex]

[tex]y=\sqrt{48}=4\sqrt{3}\ units[/tex]

therefore

the answer is the option C

[tex]4\sqrt{3}\ units[/tex]

Answer:

The correct option is C.

Step-by-step explanation:

It is given that triangle MRN is created when an equilateral triangle is folded in half.

It means original equilateral is triangle MNO and NR is a perpendicular bisector. The side length of the triangle is

[tex]MO=NO=MN=MS+SN=2+6=8[/tex]

Since NR is a perpendicular bisector, therefore

[tex]RM=\frac{MO}{2}=\frac{8}{2}=4[/tex]

Using Pythagoras property in triangle MNR,

[tex]MR^2+NR^2=MN^2[/tex]

[tex]4^2+y^2=8^2[/tex]

[tex]y^2=64-16[/tex]

[tex]y=\sqrt{48}[/tex]

[tex]y=4\sqrt{3}[/tex]

Therefore option C is correct.

Solve the quadratic equation by taking square roots. Allow for imaginary solutions. Enter your answer in simplest form. Equation: 5x (squared) - 5 = -17

Answers

5x^2 - 5 = -17

First add 5 to both sides:

5x^2 = -12

Now, divide by 5

x^2 = -12/5

Take the square root of both sides

x = sqrt -12/5

Because there can't be a square root of a negative number, your answer is:

x = sqrt -12/5 * i

Hope this helps!
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