Example
Solve the quadratic equation
x² - 6x +13=0

Answer:

31/40

Step-by-step explanation:

Given expression:

[tex]\dfrac{2}{5} + \dfrac{3}{8}[/tex]

Note: Both fractions must have same denominators if we want to perform addition, subtraction, multiplication, or division.

The only way to simplify this expression is to have a common denominator, which can be determined by the LCM of 5 and 8.

Multiply the denominators with such a number that is equivalent to 40.

Note: The number you are multiplying should also be multiplied to the numerator.

[tex]\rightarrow \dfrac{2 \times 8}{5 \times 8} + \dfrac{3 \times 5}{8 \times 5}[/tex]

[tex]\rightarrow \dfrac{16}{40} + \dfrac{15}{40}[/tex]

Finally, simplify the expression to determine the solution.

[tex]\rightarrow \dfrac{31}{40}[/tex]

Since 31 is a prime number, we can't simplify this fraction. Thus, the final answer is 31/40.

Ah yes, adding fractions! Adding fractions can be a bit of a pain.

So, we have  [tex]\frac{2}{5} + \frac{3}{8}[/tex].

To add fractions, the bottoms, or denominators, must be the same number. So we must multiply the fractions by certain numbers to make the denominators the same number. So let's go easy and make the denominator 40, because 8 goes into 40 and so does 5. So, to make 8 become 40, we'll multiply the whole fraction by 5. For 5, we'll multiply by 8.

[tex]5 * \frac{3}{8} = \frac{15}{40}[/tex]

[tex]8 * \frac{2}{5} = \frac{16}{40}[/tex]

Now we'll add the two fractions. When we add fractions we only add the tops, the numerators.

[tex]\frac{15}{40}+\frac{16}{40} = \frac{31}{40}[/tex]

Then we must reduce (or try to reduce). This fraction cannot be reduced, so the answer is simply  [tex]\frac{31}{40}[/tex].

I hope this helps you understand.

-Toremi

Answer:

the angle is equal to 60 degree

Answer:

6/2(1+2)

First lets simplify whats in the parentheses

6/2(3)

So thats 6/2 * 3

6/2 = 3

3*3 =

9

Answer:

9

Step-by-step explanation:

first, you do (1+2) which is 3 and then you do 6/2 which is 3 then 3x3 is 9

The new perimeter of the rectangle if the dimensions are quadrupled would be 72 inches.

The perimeter is always obtained by adding all the sides. This means the possible side lengths of the original rectangle are:

5 inches x 4 = 20 inches

4 iches x 4 = 16 inches

20 + 20 + 16 +16= =72 inches

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Answer:

1.

First, I would solve for ACB.

Calculations:

63° = y?

I would do that because I know that angle 'y' is vertical to 63°, which is given. (Also vertical angles are congruent, meaning that the measure the same degrees).

2.

Second, I would solve for BAC.

Calculations:

x + 63 + 85 = 180

x + 148 = 180

-148        -148

x = 32°

I would do that because I know that there are two given angles so I could easily solve for the leftover angle, 'z', using the a + b + c = 180° formula.

3.

Next, I would solve for CED.

Calculations:

x + 130 = 180

-130        -130

x = 50°

I would do that because I know finding this angle will help me find angle CDE.

4.

Finally, I would solve for CDE.

Calculations:

x + 63 + 50 = 180

x + 113 = 180

-113        -113

x = 67°

I would do that because I know there are now two given angles so I could easily solve for the leftover angle, x, using the a + b + c = 180° formula.

Answer:

162.50

Step-by-step explanation:

6500 *  5/12 * .06 =

Answer:

Step-by-step explanation:

Heroes in Greek Mythology were men or women of special strength, courage, or ability. They were often of divine ancestry and noted for superhuman courageous acts.

What makes a hero in Greek Mythology?

Answer: sqrt(58)

Step-by-step explanation:

[tex] \huge \mathfrak \red{HeY \: ThErE♡}[/tex]

No. of mangoes sid has = 15

No. of apples sera has = 6

Total no. of fruits Sidra will have = 15 + 6 = 21

[tex] \huge \mathfrak \red{HoPe \: It \: HeLpS♤}[/tex]

A logarithimic function is a function of the sort; loga(a^x) = x. The function that is described by g(x) is a logarithmic function.

A logarithimic function is a function of the sort; loga(a^x) = x. We now have to look at this table to ascertain of this condition is met.

Given this condition, we can see that each of the entries in the table satisfies this basic criterion of a logarithmic function hence, the function that is described by g(x) is a logarithmic function.

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Answer:

Exponential

Step-by-step explanation:

The function g(x) described by the given table of values is most likely an exponential function because x increases by a constant factor and the values of g(x) increase or decrease by a consistent factor. This behavior aligns with the characteristics of an exponential function, where the variable x appears in the exponent. I put polynomial as my answer on the test and got it incorrect and then realized the answer was exponential.

Y=mx+b form:

y<2/5x+2

y ≥ -1/2x+3

I forgot how to do the inequalities :)

Step-by-step explanation:

Answer:

x < 2

Step-by-step explanation:

|-7x+4| < 18
7x + 4 < 18
7x + 4 - 4 < 18 - 4
7x < 14
7x/7 < 14/7
x < 2

im not sure if this is right but this is what i got.

x=-1/8y²

Interchange x and y

Compare to Vertex form y=a(x-h)²+k

Now

.So

Focus (-2,0)

Answer:

(-2, 0)

Step-by-step explanation:

Standard form of a parabola with a horizontal axis of symmetry:

[tex](y-k)^2=4p(x-h)\quad \textsf{where}\:p\neq 0[/tex]

[tex]\textsf{Vertex}=(h, k)[/tex]

[tex]\textsf{Focus}=(h+p,k)[/tex]

Given equation:

[tex]x=-\dfrac18y^2[/tex]

Rewrite in standard form:

[tex]\implies (x-0)=-\dfrac18(y-0)^2[/tex]

[tex]\implies -8(x-0)=(y-0)^2[/tex]

[tex]\implies (y-0)^2=-8(x-0)[/tex]

Comparing with the general standard form:

Therefore:

[tex]\textsf{Vertex }(h,k)=(0,0)[/tex]

[tex]\textsf{Focus }(h+p,k)=(0-2,0)=(-2,0)[/tex]

Answer:

Step-by-step explanation:

1.)  H (greater than or equal to) 36in

2.) N (Less than or equal to) 1200

3.) A (greater than or equal to) 13

Answer: ok well the answer is 631 if it were rounded it would be 630

Now if u mean those 2 numbers they would be 259:260 and 372:370 there hope it helps bye!

Given :  4(8 + 3x)

To Find : Describe the two factors in this expression

How many terms are in each factor of this expression

coefficient of the variable term

Solution:

4(8 + 3x)  

two factors in this expression  are

4  and ( 8 + 3x)

terms in each factor of this expression

1 term in 4

2 terms in (8 + 3x)

coefficient of the variable term is 3   in factorized form

4(8 + 3x) =   32 + 12x

and coefficient of the variable term is 12   in expanded form

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Using factor theorem, factorize each of the following polynomial ...

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Factorise: 1. a3 – 4a2 + 12 – 3a 2. a3x – x4 + a2x2

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The probability of the event of getting exactly 5 heads in 8 tosses of a coin(assuming unbiased coin) is given by: Option C: 0.219 (approximately).

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

The expected value and variance of X are:

[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]

For this case, we've got:

Each coin flip is a bernoulli distribution as it has two possible outcomes (assuming any other outcome like coin landing standing straight etc ignored). Take success = getting head in a flip, and failure = not getting success= not getting head = getting tail as the outcome of the flip.

Now, each of those 8 flips are independent in terms of result of each other (assuming coin stays unbiased).

If we take:

X = number of heads out of those 8 flips = number of successes in those 8 bernoulli trials, then:

[tex]X \sim B(n = 8, p)[/tex]

where p is the probability of success = P(Getting head in an unbiased coin with head or tail as only possible outcomes) = 1/2 = 0.5 (as head can come in 1 way, and total outcomes is 2, all equally likely).

Thus, we get:

[tex]X \sim B(n = 8, p=0.5)[/tex]

Now, P(Exactly 5 heads in those 8 flips) = P(X = 5)

Using the probability function of the binomial distribution, we get:

[tex]P(X = 5) = \: ^8C_5(0.5)^5(0.5)^{8-5} = \dfrac{8\times 7\times 6\times 5\times 4}{5 \times 4 \times 3\times 2 \times 1} \times (0.5)^8 \approx 0.219[/tex]

Thus, the probability of the event of getting exactly 5 heads in 8 tosses of a coin(assuming unbiased coin) is given by: Option C: 0.219 (approximately).

Learn more about binomial distribution here:

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#SPJ1

Answer:

I pressed this by an accident

Answer:

I'm going to assume the # is meant $, if that is the case then the trader made 8% profit

Step-by-step explanation:

200 out of 2500 is basically 200/2500. 200 divided by 2500 is 0.08, and to find the percent of a number you have to multiply it by ten (or just move the decimal two places to the right) 0.08 multiplied by 10 would give you 8, so the answer is 8 percent. Hope this helps!

Answer:

[tex]50\; {\rm ft} \times 50\; {\rm ft}[/tex] would maximize the area for a rectangle with the given circumference of [tex]200\; {\rm ft}[/tex]. (Note, that a circle of the same circumference would have an even larger area.)

Step-by-step explanation:

Assume that the base of the house is a rectangle. Let the length of the two sides be [tex]x\; {\rm ft}[/tex] and [tex]y\; {\rm ft}[/tex], respectively. The goal is to find the [tex]x[/tex] and [tex]y[/tex] that:

[tex]\begin{aligned} \text{maximize} \quad & x\, y \\ \text{subject to} \quad & 2\, (x + y) = 200 \\ & x > 0 \\ & y > 0 \end{aligned}[/tex].

Using the equality constraint [tex]2\, (x + y) = 200[/tex] (or [tex]x + y = 100[/tex]), the variable [tex]y[/tex] could be replaced with [tex](100 - x)[/tex] to obtain an equivalent problem of only one variable:

[tex]\begin{aligned} \text{maximize} \quad & x\, (100 - x) \\ \text{subject to} \quad & x > 0 \\ & (100 - x) > 0 \end{aligned}[/tex].

Simplify to obtain:

[tex]\begin{aligned} \text{maximize} \quad & -x^{2} + 100\, x \\ \text{subject to} \quad & x > 0 \\ & x < 100 \end{aligned}[/tex].

The objective function of this problem is [tex]f(x) = -x^{2} + 100\, x[/tex]. Derivatives of this function include

Since [tex]f^{\prime\prime}(x)[/tex] is constantly less than [tex]0[/tex], [tex]f(x)[/tex] is concave and would be maximized when [tex]f^{\prime}(x) = 0[/tex].

Setting [tex]f^{\prime}(x) = -2\, x + 100[/tex] to [tex]0[/tex] and solving for [tex]x[/tex] gives:

[tex]-2\, x + 100 = 0[/tex].

[tex]x = 50[/tex].

Notice that [tex]x = 50[/tex] satisfies both constraints: [tex]x > 0[/tex] and [tex]x < 100[/tex]. Therefore, [tex]x = 50[/tex] is indeed the solution that maximizes the area [tex]f(x) = -x^{2} + 100\, x[/tex] while at the same time meeting the requirements.

With the length of one side being [tex]x = 50[/tex] ([tex]50\; {\rm ft}[/tex],) the length of the other side would be [tex]100 - x = 50[/tex] ([tex]50\; {\rm ft}\![/tex].) Hence, a rectangular house of dimensions [tex]50\; {\rm ft} \times 50\; {\rm ft}[/tex] would maximize the area under the given requirements.

Answer:

B

Step-by-step explanation:

EZ

Answer:

l+s≥300

2.5l+2.1s≤670

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf 9300\ m\²}[/tex]

Step-by-step explanation:

The figure is made up of:

Formula for area of rectangle:

Formula for Area of triangle:

Area of rectangle:

Length = 90 m

Width = 70 m

= Length × Width

= 90 × 70

= 6300 m²

Area of Triangle:

Base = 170 - 70 = 100 m

Height = 90 - 30 = 60 m

[tex]\displaystyle =\frac{1}{2} (Base)(Height)\\\\= \frac{1}{2} (100)(60)\\\\= (50)(60)\\\\= 3000 \ m^2[/tex]

Total Area of the figure:

= Area of the rectangle + Area of the triangle

= 6300 + 3000

= 9300 m²

[tex]\rule[225]{225}{2}[/tex]

Answer: $1,271.88

Step-by-step explanation:

        The total cost of the camera with sales tax included will be 100% plus our sales tax:

100% + 9.75% = 109.75%

        Dividing a percent (%) by 100 gives us a decimal:

109.75% / 100 = 1.975

        We can multiply this decimal by the listed price of the camera to find our answer

643.99 * 1.975 = $1,271.88

     The camera will cost $1,271.88 with sales tax.

The annual percentage rate (APR) for the Payans is the yearly interest rate that's generated by a sum charged to borrowers.

Your information is incomplete as the values aren't given. Therefore, an overview will be given. Here, the APR is the cost that one has to pay to borrow money and it's expressed as a percentage.

Also, the mortgage payment is made up of the principal and the interest payments. It's how one will pay back their home loan.

Learn more about APR on:

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Answer:

1237.18

Step-by-step explanation:

Answer: A) from year 1 to year 2

Step-by-step explanation: subtract 46-38=8, I also just took the K12 test and got it right.

Answer:

A) from year 1 to year 2

Step-by-step explanation:

Convert into vertex form y=a(x-h)²+k

After calculating

Vertex at

Max height=42.3m

Graph attached

Answer:

B and D.

Step-by-step explanation:

4(2n) + n

= 8n + n

= 9n.

[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]

[tex] \large\underline{ \boxed{ \sf{✟\:Important\: point's✟ }}}[/tex]

→ Your given expression:- 4(2n)+n

☆ Hence option b (9n) is right ans

[tex]\pink{\underline{ \underline{ \boxed{ \sf{✰\: Option.\:B✓ }}}}}[/tex]

Hope it helps !

Answer:

i believe your answer is 41,

Step-by-step explanation:

because to find perimeter, you simply have to add up all of the sides unlike area where you have to multiply, giving you 18+18+2+2=41 for your answer

Answer:

41

Step-by-step explanation:

add up all the sides total to 41

Answer: 10

Step-by-step explanation: