Rewrite 4 as a fraction.
4/4
4/1
1/4

[tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^2 \pm \stackrel{\stackrel{2\sqrt{x^2}\sqrt{c^2}}{\downarrow }}{6x} +c^2~\hspace{10em}6x=2\sqrt{x^2}\sqrt{c^2}\implies 6x=2xc \\\\\\ \cfrac{6x}{2x}=c\implies 3=c\implies 9=c^2~\hfill \boxed{(x\pm 3)^2}[/tex]

c=9 makes the given expression a perfect square trinomial.

The given expression is:

[tex]x^{2} +6x+c[/tex]

We can rewrite it as:

[tex]x^{2} +2*x*3 + c[/tex].....(1)

The expansion of [tex](a+b)^2[/tex] is [tex]a^{2} +2ab+b^{2}[/tex]

Comparing (1) with [tex]a^{2} +2ab+b^{2}[/tex]

We get

a=x

b=3

c=b²

So, c=3² =9.

So, c=9 makes the given expression a perfect square trinomial.

Hence,  c=9 makes the given expression a perfect square trinomial.

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Answer:

x = 62°

Step-by-step explanation:

Concepts:

Solving

Step 1: Combine like terms.

Step 2: Subtract 118 from both sides.

Step 3: Check if solution is correct.

Therefore, the answer is x = 62°.

Answer:

342

Step-by-step explanation:

9x38=342, so the answer is 342 crayons

Answer:

342 crayons

Step-by-step explanation:

Each child has 9 crayons. This means each one of the children has 9 crayons for himself or herself. So if there are 38 children,it means each one of the 38 children has 9 crayons.

The total number of crayons is therefore gotten by multiplyiong the number of crayons of each child(9) by the total number of children(38).

∴38×9=342.

Step-by-step explanation:

=[tex] =(3x + 2)(x + 1) \\ = 3x(x + 1) + 2(x + 1) \\ = {3x}^{2} + 3x + 2x + 2 \\ = {3x}^{2} + 5x + 2[/tex]

Answer:

Bro really?? Anyway it's

[tex]anyway \: its \: 3x { }^{2} + 3x + 2x + 2[/tex]

Answer:

D = 2mt

Step-by-step explanation:

D = (2m × 2t)/2

[tex] \sf \: d \: = \frac{2m \times t(2)}{2} [/tex]

[tex] \rightarrow \: \sf \: d = \frac{2m \times 2t}{2} [/tex]

[tex] \rightarrow \: \sf \: d = \frac{4mt}{2} [/tex]

[tex] \rightarrow \: \sf \: d = 2mt[/tex]

~Done~

------

Answer:

No, 20 ≠ -10

Step-by-step explanation:

20 = (-10) = (-20)+10

20≠-10=-20+10

20≠-10=-10

Answer:

  domain = {-8, -6, 8}

  range = {-4, -1, 0, 8}

Step-by-step explanation:

The domain is the set of first numbers of the ordered pairs. The range is the set of second numbers. We generally like to have the elements of a set arranged in order, with duplicates eliminated.

  domain = {-8, -6, 8}

  range = {-4, -1, 0, 8}

Answer:

93

Step-by-step explanation:

19x-2 =  18x+3

x=5

15(5) -2=93

18(5)+3=93

Answer:

80

Step-by-step explanation:

if he's read 70% then the 24 pages that are left are equal to 30 percent.

so the answer is 80. if you need extra steps don't hesitate to ask.

The equation will be:

[tex]m\angle 1=\dfrac{1}{2}(arc\ a-arc\ b)[/tex]

The arc of the circle is the curved line on the circle formed by the angle and the radius of the circle.

In the attached picture of the question, we can see that

The measure of the interior angle is the semi-sum of the arches that comprise it and its opposite.

So the equation will be

[tex]m\angle 1=\dfrac{1}{2}(arc\ a-arc\ b)[/tex]

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Answer: a

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that area of an equilateral traingle 50 square units.

Let the length of side of equilateral traingle be 'x' units. To calculate length of each side we will use the formula of area of equilateral traingle:

[tex] \: \: { \underline { \boxed{\pmb { \sf{ \purple {Area_{(equilateral \: traingle)} = \dfrac{\sqrt 3}{4} \times (Side)^2}} }}}} \\ [/tex]

By substituting the values in above formula:

[tex]~[/tex]

[tex] : \implies \sf \: \: 50 = \dfrac{ \sqrt{3} }{4} \times {(x)}^{2} \\ \\ \\ : \implies \sf \: \: {(x)}^{2} = \dfrac{50 \times 4}{ \sqrt{3} } \\ \\ \\ : \implies \sf \: \: {(x)}^{2} = \dfrac{200}{ \sqrt{3} } \\ \\ \\ : \implies \sf \: \: x = \sqrt{ \dfrac{200}{ \sqrt{3} } } \\ \\ \\ : \implies \: \: { \boxed{\pmb{ \frak{ x = 10.75 \: units }}}}\\ \\ \\ [/tex]

The graph of the pupil's score is an illustration of scatter plots

The student's expected score in paper 2 is 62

To predict the score of the pupil in the missed paper, we simply interpret the points on the line of best fit of the scatter plot

From the graph (see attachment), we have:

Paper 2 = 62 when Paper 1 = 50

This means that the student's expected score in paper 2 is 62

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Answer:

side length = 4

Step-by-step explanation:

Let x = the side length

Area is x•x, which is x^2.

Perimeter is x+x+x+x, which is 4x.

x^2 = 4x

x^2 - 4x = 0

Factor.

x(x-4) = 0

x = 0 or x = 4

Discard 0 as an answer as it is not useful.

x = 4.

Area = 4^2 = 16

Perimeter = 4(4)= 16

The side length is 4.

Answer:

Step-by-step explanation:

Compare the decimals using >, <, or =

Name two equivalent fractions for each fraction listed below.

If there are 16 cups in one gallon, how many cups are in 3 gallons?

16 cups = 1 gal.

? cups = 3 gals.

3 * 16 = 48 cups

How many cups are in 5 gallons?

5 * 16 = 80 cups

Compare and contrast squares are rectangles

Squares: have four sides and four equal sides

Rectangles: have four sides and have 2 parallel sides, meaning that they have 2 opposite sides that are equal.

Hope this helps!

Answer:

Ten apples cost 9 dollars

Step-by-step explanation:

C(10) = 9

The input is 10 and the output is 9

You bought 10 apples for 9 dollars

Answer:

The last one

Step-by-step explanation:

10 is a function of C which says that the cost of 10 = 9.

Answer:

C, Almost fifty percent

Step-by-step explanation: I just got it right.

The period of the given function is T = 2π

The period T of a function f(x) is such that:

f(x + T) = f(x).

In this case, our function is:

f(θ) = e^{iθ}

Remember that this can be written as:

f(θ) = cos(θ) + i*sin(θ)

So yes, this is in did a periodic function.

Then the period of the function f(θ) is the same as the period of the cosine and sine functions, which we know is T = 2π.

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The period of the considered function f(θ) = e^{iθ} is found to be P = 2π (assuming 'i' refers to 'iota' and 'e' refers to the base of the natural logarithm)

For any real value θ, we have:

[tex]e^{i\theta} = \cos(\theta) + i\sin(\theta)[/tex]

where 'e' is the base of the natural logarithm, and 'i' is iota, the imaginary unit.

Functions which repeats their values after a fixed interval, are called periodic function.

For a function [tex]y = f(x)[/tex], it is called periodic with period 'T' if we have:

[tex]y = f(x) = f(x + T) \: \forall x \in D(f)[/tex]

where D(F) is the domain of the function f.

Suppose that, the period of the function [tex]f(\theta) = e^{i \theta}[/tex] be P, then we get:
[tex]f(\theta + P) = f(\theta)\\\\e^{i(\theta)} = e^{i(\theta + P)}\\\\\cos(\theta) + i\sin(\theta) = \cos(\theta + P) + i\sin(\theta + P)[/tex]

When two complex numbers are equal, then their real parts are equal and their imaginary parts are equal.

That means,

[tex]\cos(\theta) + i\sin(\theta) = \cos(\theta + P) + i\sin(\theta + P)[/tex] implies that:

[tex]\cos(\theta) = \cos(\theta + P)\\\sin(\theta) = \sin(\theta + P)[/tex]

Also, we know that the period of sine and cosine function is [tex]2\pi[/tex]

Thus, we get:

[tex]P = 2\pi[/tex]

Thus, the period of the function [tex]f(\theta) = e^{i \theta}[/tex]  is P = 2π

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#SPJ4

Answer:

pq - 12r

step by step explanation:

The volume of the cone that was drawn by Mia is equal to 150.816 cubic inches.

Mathematically, the volume of a cone is given by this formula:

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Where:

Given the following data:

Radius of cone = 4 inches.

Height of cone = 9 inches.

Substituting the given parameters into the formula, we have;

Volume = 1/3 × 3.142 × 4² × 9

Volume = 3.142 × 16 × 3

Volume = 150.816 in³

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Answer:

60 days.

Step-by-step explanation:

Let the actual time be x, then:

x - 0.25x = 45

0.75x = 45

x = 45/0.75

= 60 days.

Answer:

Undefined Slope

Step-by-step explanation:

The points (2,6) and (2,7) are on the same vertical line of 2, which results in an undefined slope.

Answer:

m=undefined

Step-by-step explanation:

The formula to find the slope isn't very complicated. The formula is:

    y₂-y₁

m= --------

      x₂-x₁

You have the points (2,7) and (2,-6). In (2,7) 2 is your x and 7 is your y. Since (2,7) is your first coordinate set, we put 2 as our x₁ . We put 7 as our y₁ .

In (2,-6) 2 is your x and -6 is your y. Since (2,-6) is your second coordinate set, we put 2 as our x₂ . We put -6 as our y₂ .

Let's substitute all of these numbers in:

    -6-7       -13

m= -------  = -------

     2-2         0

So we have -13/0 .You would think that any number divided by                0 is 0, right?

                No. Any number divided by 0 is undefined.

Therefore, you slope, m, would be:

m=undefined .

Answer:

Step-by-step explanation:

A = 1/2 bh = 1/2 (12)(17) = 204 square inches

Using the Central Limit Theorem, it is found that the standard deviation is of 0.0971.

In this problem, for each sample, the standard error is given by:

[tex]s_I = \sqrt{\frac{0.25(0.75)}{50}} = 0.0612[/tex]

[tex]s_{II} = \sqrt{\frac{0.35(0.65)}{40}} = 0.0754[/tex]

Hence, for the distribution of differences, it is given by:

[tex]s = \sqrt{s_I^2 + s_{II}^2} = \sqrt{0.0612^2 + 0.0754^2} = 0.0971[/tex]

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Answer:

The 8th term is [tex]\frac{1}{729}[/tex].

Step-by-step explanation:

Let's begin with the formula for a geometric sequence. We know this is geometric because we are working with a common ratio, or the number we multiply to find each term.

[tex]a_n=a_0(r)^{n-1}[/tex]

In this formula, [tex]a_0[/tex] is the first term, [tex]r[/tex] is the common ratio, and [tex]n[/tex] is the desired term. We know the values of [tex]r[/tex], [tex]a_0[/tex], and [tex]n[/tex] from the given information:

[tex]a_0=3\\r=\frac{1}{3}\\n=8[/tex]

Substituting those values we get:

[tex]a_8=3(\frac{1}{3})^{8-1}[/tex]

[tex]a_8=3(\frac{1}{3})^7\\a_8=3(\frac{1}{2187})\\a_8=\frac{3}{2187}\\a_8=\frac{1}{729}[/tex]

A ratio shows the relation between two numbers. The amount of more material that is needed by Jake is 42.5 cm³.

A ratio shows us the number of times a number contains another number.

Given that the volume of the first prism is 14.5cm³, while the scale factor is 4. Since the scale factor is applicable to dimension, and volume is always the cube of three-dimension.

Therefore, the volume of the scaled prism will be the cube the of the volume of the first prism, which can be written as,

[tex]\rm \text{Volume of the Scaled prism}= (Scale\ factor)^3 \times \text{Volume of the first prism}[/tex]

Substitute the values,

[tex]\rm \text{Volume of the Scaled prism}= 4^3 \times 14.5 = 928\ cm^3[/tex]

Since, the volume of material with Jake is 900 cm³, while the material he has already used is 14.5 cm³, thus the volume of the material that is left with Jake is 885.5 cm³(900cm³-14.5cm³).

Now, since the material needed to make the scaled prism is 928 cm³, the amount of material that is with Jake is 885.5 cm³, therefore, the amount of the material that is needed by Jake to complete the scaled prism can be written as,

The Amount of more material Needed by Jake = Amount of material needed to make the scaled prism - Amount of material left with Jake

The Amount of more material Needed by Jake = 928 cm³ - 885.5 cm³

                                                                               = 42.5 cm³

Hence, the amount of more material that is needed by Jake is 42.5 cm³.

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The triangles PQR and PMN are similar triangles

The ratio MN/ QR is 2/3

The question is incomplete, as the figure of the triangles are not given.

So, I will give a general explanation

The given parameters are:

PM= 2MQ

PN = 2NR

Rewrite PM= 2MQ  as:

PM/MQ = 2/1

The equation becomes

PM/(PM + MQ) = 2/(2 + 1)

PM/(PM + MQ) = 2/3

Add PM and MQ

PM/PQ = 2/3

The above means that:

PM/PQ = MN/ QR = 2/3

Hence, the ratio MN/ QR is 2/3

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Answer: -20/21

Step-by-step explanation:

Using the Pythagorean identity, we can get that the sine of angle theta is [tex]\pm 20/29[/tex].

But since theta terminates in Quadrant II, the sine of angle theta is positive, meaning that it has a value of 20/29.

Now, since tan = sin/cos, tan theta = (20/29)/(-21/29) = -20/21

as far as I can read that, well, the company has a revenue income of 8250000 and their expenditure on purchases is 49% of that amount, how much is that?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{49\% of 8250000}}{\left( \cfrac{49}{100} \right)8250000}\implies 4042500[/tex]

so on saving 2.05% of purchasing expenses or namely 2.05% of 4042500

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{2.05\% of 4042500}}{\left( \cfrac{2.05}{100} \right)4042500}\implies 82871.25[/tex]

so sales must be increased by that much in order to match the 2.05% of 4042500.

The average is the arithmetic mean of all the observations of a set of numbers. The number of times Brandon rolls above the average is 7.

The average is the arithmetic mean of all the observations of a set of numbers. it is found by dividing the sum of all the observations of the set by the number of observations in the set.

[tex]\rm{Average=\dfrac{Sum\ of\ observations}{Number\ of\ observations}[/tex]

In order to know the number of times Brandon rolls the dice above the average, we first need to calculate the average of the twenty rolls.

The average of the 20 times dice rolls,

[tex]\rm Average = \dfrac{6+1+3+4+4+4+6+5+5+3+6+4+4+5+2+3+5+4+4+2}{20}[/tex]

[tex]\rm Average = \dfrac{80}{20} = 4[/tex]

Thus, the average of the 20 rolls of the dice is 4.

Now, the number of times the result of the dice roll is above 4(x>4) is 7.

Hence, the number of times Brandon rolls above the average is 7.

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Answer:

  1

Step-by-step explanation:

The square of the value in the empty space is the constant in the expanded expression. That is ...

  [ ]² = 1

The value in the space is ...

  [ ] = √1 = 1

The filled-in equation is ...

  (3x -1)² = 9x² -6x +1

_____

The expansion of the square of a binomial is ...

  (ax -b)² = a²x² -2abx +b²

Above, we used the constant term to find 'b', but we could also have used the linear term:

  -6x = -2(3)bx . . . . . a=3 in this problem

  1 = b . . . . . . . divide by -6x