Evaluate the following expression.
6!4!
Give your answer as an integer.

Using Vieta's Theorem the value of c = 72.

Suppose we have a quadratic equation, in the following format:

ax² + bx + c, were a, b, and c are constant.

The roots are p and q.

As, The Theorem states that:

p + q= -b/a

pq= c/a

We have given the polynomial  x²-17x+c=0

So, a= 1, b= -17

Since the difference of the solutions is 1, we have that:

p -q= 1

p = 1+ q

Now, using p + q= -b/a

1 + q + q= -(-17)/1

2q +1 = 17

2q= 16

q= 16/2

q= 8

and, p = 1+ q= 9

Again pq = c/a

8 x 9 = c/1

c= 72

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Answer:

t = 6.8 years

Step-by-step explanation:

The formula for compound interest is

\(A(t)=P(1+r/n)^n^t\), where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.

We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal).  We must solve for t and round to the nearest tenth:

\(5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t\)

Therefore , as a result Two of a triangle's sides and the included  SAS angle are said to be congruent if they match the corresponding sides and angles of another triangle.

The Side-Angle-Side rule is applied to check the congruence of a set of triangles. The SAS rule states that a triangle is congruent if its two sides and included angles match those of another triangle.

Here,

if the first triangle's two sides and one of its included angles are equal to the second triangle's sides and one of its included angles.

Consequently, the SAS declares two triangles to be congruent. Two triangles are said to be congruent if their matching two sides and their included angles are found in a single triangle, according to the SAS theorem of congruence.

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Answer: a square i think

Step-by-step explanation:

because you multiply the number by itself, you're squaring it.

Answer:

-----------------------------

If the two lines have same y-intercept then this is the point of intersection of the two lines.

Since the slopes are different, the y-intercept is the only point of intersection. So there is one solution.

Correct choice is D.

Question options :

A. There is sufficient evidence to reject the claim

u < 99.

B. There is sufficient evidence to support the claim

u < 99.

C. There is not sufficient evidence to reject the claim

u < 99.

D. There is not sufficient evidence to support the claim

u< 99.

Answer:

B. There is sufficient evidence to support the claim

u < 99.

Step-by-step explanation:

We construct the n*ll and alternative hypotheses to support our claim

The n*ll hypothesis :H0

The alternative hypothesis : Ha

N*ll hypothesis =H0: u=99

Alternative hypothesis =Ha: u<99

So if n*ll hypothesis (H0) u=99 is rejected, then we accept the alternative hypothesis that u<99

we can therefore have sufficient evidence to support our claim that u<99

Answer:(c)

Step-by-step explanation:

Given

The initial value of Adam's model is \(A_o=\$550\)

the value increases exponentially with the rate of \(r\%\)

Time period \(t=5\ years\)

Final amount \(A=\$736\)

Exponential growth is given by

\(\Rightarrow A=A_o(1+r)^t\)

Putting values

\(\Rightarrow 736=550(1+r)^5\\\\\Rightarrow (1+r)^5=1.338\)

\(\Rightarrow 1+r=1.05999\\\Rightarrow r=0.05999\ or\ 5.99\%\approx 6\%\)

Option (c) is correct

Answer:

x(y/2 + z)

Step-by-step explanation:

There are two triangles here.

The small triangle which is bound by dotted lines has base = y and height = x

The height of the larger triangle is 2x and its base is y + z

Area of larger triangle = 1/2 ·  2x · (y + z)
= x(y + z) = xy + xz

Area of smaller triangle = 1/2 · x · y = xy/2

Shaded region area = Area of larger triangle - area of smaller triangle

= xy + xz - xy/2

= xy/2 + xz

= x(y/2 + z)

Answer:

5x-4x+1=2

5x-4x=2-1

x=1ans

Answer:

D. 1

Step-by-step explanation:

Answer:

-100/500=-5

Step-by-step explanation:

you simply have to multiply them

-25×4=-100

50×10=500

you can further simplify it by dividing it

Answer:

\( - \frac{25}{50} \times \frac{4}{10} \\ \\ - \frac{25}{50} \times \frac{2}{5} \\ \\ - \frac{5}{50} \times \frac{2}{1} \\ \\ - \frac{1}{10} \times 2 \\ \\ - \frac{1}{5} \times 1 \\ \\ = - \frac{1}{5} \\ \\ = - 0.2\)

I hope I helped you^_^

Answer:

exactly normal

Answer:

a. The angles in the picture are: a, 2a, 2a, 3a, 3a, 4a, 4a, 5a.

Step-by-step explanation:

Higher rates of depression and anxiety are one negative mental health outcome associated with social media use

The paragraph discusses the role of social media in modern life and its impact on mental health. It notes that social media has become a ubiquitous part of life that allows people to connect with others from around the world, including friends, family, and strangers.

However, the paragraph goes on to mention that social media use has been linked to negative mental health outcomes such as depression, anxiety, and stress.

These negative outcomes may be due to the pressure individuals feel to present a perfect image of themselves online, leading to feelings of inadequacy and self-doubt.

Despite these negative outcomes, the paragraph notes that social media can also be valuable for promoting social support and connection, especially among marginalized communities.

Furthermore, it can be a source of education and awareness, allowing people to learn about important social and political issues and engage with them.

Hence,

Higher rates of depression and anxiety are one negative mental health outcome associated with social media use

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Answer:

y = 2/3x+3

Step-by-step explanation:

If you're talking about a discrete distribution, then

\(P(X=x)=\begin{cases}\frac1{61}&\text{for }x\in\{10,11,12,\ldots,70\}\\0&\text{otherwise}\end{cases}\)

(1/61 because there are 61 numbers in the range of integers from 10 to 70) so that

\(P(X<25)=\displaystyle\sum_{x=10}^{24}P(X=x)=\boxed{\dfrac{15}{61}}\)

If the distribution is continuous, we would have the same density function, but x can be any real number in the interval [10, 70]. So we have

\(P(X<25)=\displaystyle\int_{-\infty}^{25}P(X=x)\,\mathrm dx=\frac1{60}\int_{10}^{25}\mathrm dx=\dfrac{15}{60}=\boxed{\dfrac14}\)

Answer:

33%

Step-by-step explanation:

There are 8 total numbers, only 2 of which are even. Divide 2 by 6, and you get 0.33 repeating. Round the decimal back one place and you have 33%.

Answer:

x=15

Step-by-step explanation:

3*5=15

Answer:

x = 15

Step-by-step explanation:

x/3 = 5

3* x/3 = 3*5

x=15

In simplified form... multiply both sides by 3 to get x by itself and you should get, x = 15

The value of side length x in diagram a) is 4.3mm and side length x in diagram b) is 309.7 m.

The figures in the image are right triangles.

A)

angle D = 17 degree

Adjacent to angle D = 14 mm

Opposite to angle D = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( 17 ) = x/14

x = tan( 17 ) × 14

x = 4.3mm

B)

angle Z = 82 degree

Adjacent to angle Z = 43.1 m

Hypotenuse = x

Using trigonometric ratio,

cosine = adjacent / hypotenuse

cos( 82 ) = 43.1 / x

x = 43.1 / cos( 82 )

x = 309.7 m

Therefore, the measure of x is 309.7 meters.

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Answer:0.8p+1 and 1+0.8p

Step-by-step explanation:

0.5p+0.3p=0.8p

7-6=+1

0.8p+1

and

Swap both numbers

(0.5p+7)+(0.3p-6)=1+0.8p

Answer:

\(\(\(\red{\rule{500pt}{1000000pt}}\(\)\)

Answer:

\(f(x)=x^3-x^2+2x-1\)

Step-by-step explanation:

Since \(f''(x)=6x-2\), then \(f'(x)=3x^2-2x+C\), thus:

\(f'(x)=3x^2-2x+C\\\\f'(1)=3(1)^2-2(1)+C\\\\3=3-2+C\\\\3=1+C\\\\2=C\)

Therefore, since \(f'(x)=3x^2-2x+2\), then \(f(x)=x^3-x^2+2x+C\), thus:

\(f(x)=x^3-x^2+2x+C\\\\f(2)=2^3-2^2+2(2)+C\\\\7=8-4+4+C\\\\7=8+C\\\\-1=C\)

In conclusion, \(f(x)=x^3-x^2+2x-1\)

Number of packs of cups to be purchased = 5 packs and Number of cups remaining if 80% lemonade is sold = 85 cups.

The volume of cone is calculated using the formula (1/3)r2h, where "h" stands for the cone's height and "r" for the base radius. As a result, (1/3)r2 is the cone's volume in terms of the slant height "L." (L2 - r2).

Volume of a cone is given by the expression,

V = 1/3πr²h

Here,

r = radius of the cone

h = Height of the cone

Radius of the cone =  = 4 cm

Height of the cone = 11 cm

Amount of lemonade = 10 gallons

Volume of one cone = 1/3π(4)²× 11

 = 184.307 cm³

Covert the gallons into cubic cm,

  ∵ 1 gallon = 3785 cm³

  ∴ 10 gallons = 37850 cm³

  ∵1 cones are represented by a volume of 184.307 cm3.

∴ 1 cm³ will represent the volume = 1/184.307 cup

∴ 37850 cm³ will represent the volume = 37850/184.307 cups

                                                                  = 205.36 cups

                                                                   = 205 cups

Therefore, number of packs of cups to be bought = 205/50

                                                                                    = 5 packs

b). If 80% of the lemonade are sold, amount of lemonade sold = 10 × 80/100

= 8 gallons

Volume of 8 gallons lemonade in cm³ = 8 × 3785

                                                                    = 30280 cm³

Therefore, number of cups to be used = 30280/184.307 cups

= 164.29 cups

≈ 164 cups

Number of cups purchased = 250

And there are 250 cups left after subtracting 164.

                                                                = 86 cups

Therefore, number of cups remaining are 86 cups.

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Answer:

20?

Step-by-step explanation:

Hi there!  

»»————-　★　————-««

I believe your answer is:

\(2x + \frac{x}{2}=10\\\\\boxed{x=4}\)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(\boxed{\text{Setting up an Equation...}}\\\\\text{"The sum of twice a number..."}} \rightarrow 2x+\\\\\text{"And half the number..."}\rightarrow \frac{x}{2}\\\\\text{"is 10"}\rightarrow = 10\\\\\\2x +\frac{x}{2}=10\)

⸻⸻⸻⸻

\(\boxed{\text{Solving for 'x'...}}\\\\2x + \frac{x}{2}=10\\----------------------\\\rightarrow (2x + \frac{x}{2})2=10*2\\\\\rightarrow 4x + 2 = 20\\\\\rightarrow 5x = 20\\\\\rightarrow \frac{5x=20}{5}\\\\\boxed{x=4}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

The equation of line is D. y = 3x - 9

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The m is a common symbol for slope.

The equation of a straight line is given by y=mx+c where m is the slope, c is the intercept, and x and y are variables.

Formula to be used :

\(m=\frac{y_{1}-y_{2} }{x_{1} -x_{2} }\) where( y1,x1) and (y2 ,x2) are the coordinates of the points passing through the line.

Calculating Slope, \(m=\frac{3-(-3)}{4-2} =\frac{6}{2} =3\)

Now, writing the equation of line is

\(y -y_{1} =m(x-x_{1} )\\y -3 =3(x-4)\\y-3 =3x - 12\\y =3x -12+3\\y =3x -9\)

Thus, the slope-intercept form of the equation is y =3x -9.

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Answer:

$34,400

Step-by-step explanation:

35,500- 1,100= 34,400

A) $34,400 will the homeowner's insurance company pays for the damages

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

The homeowner's insurance company will pay for the damages after the deductible is subtracted from the claim amount.

In this case, the claim amount is $35,500 and the deductible is $1,100.

So, the insurance company will pay $35,500 - $1,100 = $34,400 for the damages.

Therefore, the answer is option A) $34,400.

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Data:

8% commisions on the first $8000

12% commisions on a sell over $8000

Total commisions: $1480

You have the next equation for the situation: x is the sells over the $8000

Total sells:

If the total commisions are $1480:

Answer:

slope = 2.25

Step-by-step explanation:

This equation is written in slope-intercept form, which has the general structure: y = mx + b.

In this form, "m" = slope and "b" = y-intercept.

Therefore, the slope is 2.25 since it is replacing the "m" variable.

Answer:

x = -3

y = -2

(-3, -2)

Step-by-step explanation:

x - 7y = 11

5x + 4y = -23

-----------------------

-5 (x - 7y = 11)

-5x + 35y = -55

--------------------------

-5x + 35y = -55

5x + 4y = -23

       39y = -78

     ÷39     ÷39

        y = -2

-----------------------------

x - 7y = 11

x -7(-2) = 11

x + 14 = 11

   -14    -14

x = -3

I hope this helps!