Can someone help me with this math homework please!

Given:

The expression is:

[tex]b^2+20b[/tex]

To find:

The a monomial so that the trinomial may be represented by a square of a binomial.

Solution:

If an expression is [tex]x^2+bx[/tex], then be need to add square of half of coefficient of x, i.e., [tex]\left(\dfrac{b}{2}\right)^2[/tex] in the given expression to make in perfect square.

We have,

[tex]b^2+20b[/tex]

Here, coefficient of b is 20,so wee need to add square of half of coefficient of b, i.e., [tex]\left(\dfrac{20}{2}\right)^2[/tex].

[tex]\left(\dfrac{20}{2}\right)^2=10^2[/tex]

[tex]\left(\dfrac{20}{2}\right)^2=100[/tex]

Therefore, we need to add 100 to make [tex]b^2+20b[/tex] a perfect square binomial.

Answer:

y= -1/15x + 16/15

Step-by-step explanation:

When two lines are perpendicular to each other that means their slopes are the negative reciprocals of each other.

So that means if a line has has a slope of 6, a line perpendicular to that line will have a slope of -1/6.

(a reciprocal is when the fraction is flipped over)

In this case, the negative reciprocal of 15 would be -1/15. So the slope of the line that is perpendicular would be -1/15.

The equation we would have so far for that line would be: y=-1/15x+b

Now we have to find the 'b' or the y intercept, which we can get by plugging in the point that was given (1,1), which is on that line.

Which gives us 1=-1/15(1)+b.

1=-1/15+b

1+1/15=b

Then you solve for b and get b= 16/15.

The equation of the line that is perpendicular to the given line is y= -1/15x + 16/15.

The equation of the line that passes through the point (1, 1) and is perpendicular to y = 15x + 45 is

y = 15x - 14.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Let the equation of a line is y = mx + c.

The line is perpendicular to y = 15x + 45.

y = 15x + 45 is in the form of y = mx + c

This means,

Slope = 15

m = 15

The line passes through the point (1, 1) = (x, y).

This means,

y = mx + c

1 = 15 x 1 + c

1 = 15 + c

c = 1 - 15

c = -14

The equation of the line is y = 15x - 14.

Thus,

The equation of the line that passes through the point (1, 1) and is perpendicular to y = 15x + 45 is

y = 15x - 14.

Learn more about equation of a line here:

https://brainly.com/question/23087740

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Answer:

Entrance fee=15, fee per games played=2.50

Step-by-step explanation:

x=fee per games played, y=entrance fee

19x+y=62.50 equation 1

10x+y=40 equation 2

y=40-10x isolate y in equation 2

19x+40-10x=62.50 substitute y value from equation 2 into equation 1

9x=22.50

x=2.50

solve for y by substituting x value in either equation

10x+y=40

10(2.50)+y=40

25+y=40

y=15

Check answer:

19x+y=62.50

19(2.50)+15=62.50

47.50+15=62.50

62.50=62.50

Answer:

3m-8n

Step-by-step explanation:

Set up an equation:

(5m-3n)-(2m+5n) = ?

Solve:

   5m-3n

-  2m+5n

   3m-8n

Hope this helps!

Answer:

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

Step-by-step explanation:

Use distributive property to simplify both sides.

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

Use the Golden Rule of Algebra: (What we do to one side, we must do to the other).

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

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

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

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

Answer:

Step-by-step explanation:

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

distribute in the fractions

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

subtract [tex]\frac{1}{6}[/tex]  from both sides

-[tex]\frac{1}{6}[/tex]+[tex]\frac{1}{6}[/tex]-1x = -2x -[tex]\frac{1}{6}[/tex]-[tex]\frac{1}{6}[/tex]

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

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

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

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

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

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

see?  :/  

Answer:

hope it will be helpful to you

Step-by-step explanation:

anb shade and anbnc shade

Answer:

y = 3/2x +1

Step-by-step explanation:

The y int = is 1 by observation

To calculate the slope it is rise over run

3/2 as for every 3 up the line moves 2 across

Answer:

Condition A= 320 inches

Condition B= 190 Degrees F

Condition C= 2240 inches

Condition D= 350 inches

Condition E= 110 Degrees F 8 inches

Condition F= 180 Degrees F

Step-by-step explanation:

4 inches

8 inches

70 inches

60 D

40 D

90 D

4 inches

8 inches

70 D

5 inches

7 inches

12 inches

30 D

80 D

8 inches

40 D

80 D

60 D

Answer:

Condition A= 320 inches

Condition B= 190 Degrees F

Condition C= 2240 inches

Condition D= 350 inches

Condition E= 110 Degrees F 8 inches

Condition F= 180 Degrees F

Step-by-step explanation:

Answer:

[tex]10[/tex].

Step-by-step explanation:

See below for a proof of why all but the first digit of this [tex]N[/tex] must be "[tex]9[/tex]".

Taking that lemma as a fact, assume that there are [tex]x[/tex] digits in [tex]N[/tex] after the first digit, [tex]\text{A}[/tex]:

[tex]N = \overline{\text{A} \, \underbrace{9 \cdots 9}_{\text{$x$ digits}}}[/tex], where [tex]x[/tex] is a positive integer.

Sum of these digits:

[tex]\text{A} + 9\, x= 2021[/tex].

Since [tex]\text{A}[/tex] is a digit, it must be an integer between [tex]0[/tex] and [tex]9[/tex]. The only possible value that would ensure [tex]\text{A} + 9\, x= 2021[/tex] is [tex]\text{A} = 5[/tex] and [tex]x = 224[/tex].

Therefore:

[tex]N = \overline{5 \, \underbrace{9 \cdots 9}_{\text{$224$ digits}}}[/tex].

[tex]N + 1 = \overline{6 \, \underbrace{000 \cdots 000000}_{\text{$224$ digits}}}[/tex].

[tex]N + 2021 = 2020 + (N + 1) = \overline{6 \, \underbrace{000 \cdots 002020}_{\text{$224$ digits}}}[/tex].

Hence, the sum of the digits of [tex](N + 2021)[/tex] would be [tex]6 + 2 + 2 = 10[/tex].

Lemma: all digits of this [tex]N[/tex] other than the first digit must be "[tex]9[/tex]".

Proof:

The question assumes that [tex]N\![/tex] is the smallest positive integer whose sum of digits is [tex]2021[/tex]. Assume by contradiction that the claim is not true, such that at least one of the non-leading digits of [tex]N[/tex] is not "[tex]9[/tex]".

For example: [tex]N = \overline{(\text{A})\cdots (\text{P})(\text{B}) \cdots (\text{C})}[/tex], where [tex]\text{A}[/tex], [tex]\text{P}[/tex], [tex]\text{B}[/tex], and [tex]\text{C}[/tex] are digits. (It is easy to show that [tex]N[/tex] contains at least [tex]5[/tex] digits.) Assume that [tex]\text{B} \![/tex] is one of the non-leading non-"[tex]9[/tex]" digits.

Either of the following must be true:

If [tex]\text{P}[/tex], the digit in front of [tex]\text{B}[/tex], is a "[tex]0[/tex]", then let [tex]N^{\prime}[/tex] be [tex]N[/tex] with that "[tex]0\![/tex]" digit deleted: [tex]N^{\prime} :=\overline{(\text{A})\cdots (\text{B}) \cdots (\text{C})}[/tex].

The digits of [tex]N^{\prime}[/tex] would still add up to [tex]2021[/tex]:

[tex]\begin{aligned}& \text{A} + \cdots + \text{B} + \cdots + \text{C} \\ &= \text{A} + \cdots + 0 + \text{B} + \cdots + \text{C} \\ &= \text{A} + \cdots + \text{P} + \text{B} + \cdots + \text{C} \\ &= 2021\end{aligned}[/tex].

However, with one fewer digit, [tex]N^{\prime} < N[/tex]. This observation would contradict the assumption that [tex]N\![/tex] is the smallest positive integer whose digits add up to [tex]2021\![/tex].

On the other hand, if [tex]\text{P}[/tex], the digit in front of [tex]\text{B}[/tex], is not "[tex]0[/tex]", then [tex](\text{P} - 1)[/tex] would still be a digit.

Since [tex]\text{B}[/tex] is not the digit [tex]9[/tex], [tex](\text{B} + 1)[/tex] would also be a digit.

let [tex]N^{\prime}[/tex] be [tex]N[/tex] with digit [tex]\text{P}[/tex] replaced with [tex](\text{P} - 1)[/tex], and [tex]\text{B}[/tex] replaced with [tex](\text{B} + 1)[/tex]: [tex]N^{\prime} :=\overline{(\text{A})\cdots (\text{P}-1) \, (\text{B} + 1) \cdots (\text{C})}[/tex].

The digits of [tex]N^{\prime}[/tex] would still add up to [tex]2021[/tex]:

[tex]\begin{aligned}& \text{A} + \cdots + (\text{P} - 1) + (\text{B} + 1) + \cdots + \text{C} \\ &= \text{A} + \cdots + \text{P} + \text{B} + \cdots + \text{C} \\ &= 2021\end{aligned}[/tex].

However, with a smaller digit in place of [tex]\text{P}[/tex], [tex]N^{\prime} < N[/tex]. This observation would also contradict the assumption that [tex]N\![/tex] is the smallest positive integer whose digits add up to [tex]2021\![/tex].

Either way, there would be a contradiction. Hence, the claim is verified: all digits of this [tex]N[/tex] other than the first digit must be "[tex]9[/tex]".

Therefore, [tex]N[/tex] would be in the form: [tex]N = \overline{\text{A} \, \underbrace{9 \cdots 9}_{\text{many digits}}}[/tex], where [tex]\text{A}[/tex], the leading digit, could also be [tex]9[/tex].

Answer:

600g of Flour

Step-by-step explanation:

According to the question every 15 biscuits is 50g it need 50g of sugar and flour is 3 times the amount it needs for 15 biscuits so 50*3=150 now we know 15 biscuits need 150g of flour so 30 requires 300 and 300g +300g is equal to 600g of flour.

Answer:

600 g of flour.

Step-by-step explanation:

If Deon needs 50 g of sugar to make 15 biscuits, and she is going to make 60 biscuits, then she will need 200 g of sugar, since 60/15 is 4.

If the amount of flour she needs is equal to the amount of sugar multiplied by three, or 3x, if x is the amount of sugar, then she will need 200 x 3 g of flour.

Therefore, she will need 600 g of flour.

Answer:  no

Step-by-step explanationn.  .......................................................w:eorkeok,feoferkeorkoe

Answer:

The third one

Step-by-step explanation:

All show complementary angles ( angles that add up to 90 degrees ) except for the third one

First one: shows a square within the two angles which indicates that the angles form a right angle ( 90 degree angle ) meaning that they are complementary angles

Second: the angles add up to equal 90 ( 50 + 40 = 90 ) hence they are complementary angles

Third one: the angles form a straight line. Angles that form a straight line add up to equal 180 and are known as supplementary angles

Fourth: the angles shown add up to 90 ( 65 + 25 = 90) hence they are complementary angles

All are complementary but the third one

Answer:

in picture

Step-by-step explanation:

Brainliest please

Answer:

this is the best way for the question

Answer:

40%

Step-by-step explanation:

ok so first find the og price:

100% - 20% = 80%

so 80% = 200

let the 100% be x:

x * 0.8 = 200

x= 250

100% = 250

(difference/ og price) * 100% = the percentage decrease/ increase

(250-150/250)* 100% = 40%

OR

((the final price/ og price) * 100%) - 100%

((150/250)*100%) - 100% = 40%

There was a 40% decrease from the og price to the final price of 150.

Answer:

If you are talking about inequalities, t < r.

Step-by-step explanation:

Since s is bigger than t and r is bigger than s,

r should be bigger than t obviously.

Answer:

(0, 170) (5, 150) (60, -170)

Step-by-step explanation:

Plug each x value into the equation. The point is located on the line if the y values match.

Ex. -4 (170) + 170 = -510 this point is not on the line

-4 (0) + 170 = 170 this point is on the line because it is a "true" statement

Answer:

(0, 170) (5, 150) (60, -170)

Step-by-step explanation:

Step-by-step explanation:

This construction bisects the pqr angle.

This is done by placing a compass on the pqr angle and marking construction lines at the points c and a.

Then at where the construction lines at points c and a meet the lines qr and qp draw 2 more from that placement.

Then draw a line running through angle pqr and where the construction lines meet at point b.

Hope this helps and good luck!

This is because the nth term is found by adding the previous two terms

F(n) = nth term

F(n-1) = term just before the nth term

F(n-2) = term before the F(n-1) term

F(n) = F(n-1) + F(n-2)

We can re-index values of n to say this equivalent statement

F(n+2) = F(n+1) + F(n)

Based on either equation mentioned, adding F(51) and F(52) will get us F(53). In other words, the 51st and 52nd terms add to the 53rd term.

Answer:

1/12

Step-by-step explanation:

Chances of getting a 1 are 1/6 and chances of getting a prime number excluding 1 is 3/6. 3/6 x 1/6= 3/36 or 1/12 chance.

Answer:

a₂₀ = 77

Step-by-step explanation:

There is a common difference between consecutive terms , that is

5 - 1 = 9 - 5 = 13 - 9 = 4

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 1 and d = 4 , then

a₂₀ = 1 + (19 × 4) = 1 + 76 = 77

Answer:

8.5

Step-by-step explanation:

QR is 10

PQRS AREA is 45

10 times 4.5 is 45

meaning BC and PQ is 4.5

4.5 plus 4.5 is 9

26 minus 9 is 17

17 divided by two is 8.5

AB is 8.5

Answer:

Step-by-step explanation:

Picture this circumstance occurring within a circle. The center of the circle is where all the blades meet. That means that in terms of a circle's parts, these blades are the radii of the circle. And if they are all evenly spaced out, and there are 3 of them, the central angle in between each pair is 120 degrees (360/3). Once we know that, we can use the arc length formula for a circle which is

[tex]AL=\frac{\theta}{360}*2\pi r[/tex] and filling in:

[tex]AL=\frac{120}{360}*2(3.1415)(131)[/tex] so

AL = 274.4 feet

Answer:

x ≈ 28.8°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{3.9}{8.1}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{3.9}{8.1}[/tex] ) ≈ 28.8° ( to the nearest tenth )

Answer:

CF = 8.5

Step-by-step explanation:

Given 2 intersecting chords, then

The product of the parts of one chord is equal to the product of the parts of the other chord, that is

CF × DF = BF × EF , substitute values

CF × 14 = 7 × 17

14CF = 119 ( divide both sides by 14 )

CF = 8.5

Answer:

10

Step-by-step explanation:

Apply difference of squares.

[tex](x + y)(x - y) = {x}^{2} - {y}^{2} [/tex]

[tex](2 + 6i)(2 - 6i) = {2}^{2} - {6i}^{2} [/tex]

[tex] = 4 + 6[/tex]

[tex] = 10[/tex]

well, let's take a look at two independent events

A)  the potato is hot

B) it's raining

now, the potato could be hot whether is raining or not, A is totally independent of B, so what's the probability of "the potato being hot, GIVEN that it's raining" P(A | B)  is the same as if it wasn't raining, or P(A), the fact that B occurred, doesn't affect A at all, the potato is hot regardless, rain or not.  So P(A | B) = P(A).

Answer:

Pythagoras theorem states that c²=a²+b²

14²=12²+x²

14²-12²=x²

196-144=x²

52=x²

√52=√x²

7.2111025509279785=x

rounded up to the nearest hundredth=7.21