What is the value of x in the figure?
X
40⁰
OA. 40°
OB. 70°
OC. 80°
OD. 120°
OE. 150°
70⁰

The banner attached to the archway will be at (1, 5) and (5.25, 3.938).

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The archway of the main entrance of a university is modeled by the quadratic equation

y = -x² + 6x ....1

The university is hanging a banner at the main entrance at an angle defined by the equation

4y = 21 − x ....2

Then the banner attached to the archway will be

From equations 1 and 2, we have

              4(-x² + 6x) = 21 - x

              -4x² + 24x = 21 - x

        4x² - 25x + 21 = 0

  4x² - 21x - 4x + 21 = 0

x(4x - 21) - 1(4x - 21) = 0

          (4x - 21)(x - 1) = 0

                             x = 5.25, 1

Then the value of y will be

When x = 5.25, then we have

y = -(5.25)² + 6(5.25)

y = 3.938

When x = 1, then we have

y = -(1)² + 6(1)

y = 5

The banner attached to the archway will be at (1, 5) and (5.25, 3.938).

The graph is given below.

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x²+12x<-11

x²+12x+11<0

x²+12x+11=0

(x+11)(x+1)=0

x+11=0 x+1=0

x= -11 x= -1

Solution: ] -11 , -1 [

Answer:

  20

Step-by-step explanation:

The proceeds from the sale can be described by an equation involving the original number of computers.

__

Let n represent the number of computers the school originally had. Then n-5 is "all but 5" and is the number sold. Each is sold for ₹1200, and the value of the sale is ₹18000. This can be expressed by the equation ...

  (n -5)×1200 = 18000

__

This 2-step linear equation can be solved by dividing by the coefficient, and adding the opposite of the constant.

  n -5 = 18000/1200 = 15 . . . . . divide by 1200

  n = 15 +5 = 20 . . . . . . . . . . add the opposite of -5

The school originally had 20 computers.

Answer: [tex]\frac{ML}{MK}[/tex]

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so since OP corresponds to ML and NP corresponds to MK (since they are opposite the corresponding congruent angles), the answer is ML/MK.

An absolute value inequality to find the range of SAT mathematics test scores within one standard deviation of the mean is; |x – 515| ≤ 114

A) We are told that;

Mean score = 515

Standard deviation = 114

We are now given that people within one deviation of the mean have SAT math scores that are no more than 114 points higher or 114 points lower than the mean. Thus, the absolute value inequality is;

|x – 515| ≤ 114

B) The range of scores to within ±2 standard deviations of the mean is;

Range = 515 ± 2(114)

Range = 287 to 743

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The reason why Fiona cannot make a valid prediction based on the mean of the population is that the variation of Fiona’s samples is too large.

Mean is quite sensitive to outliers so it is best used when the variation between variables is not too much.

In Fiona's case, there variation is quite high with high variable of 95 compared to a low value of 45.

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Answer: just confirming/

Step-by-step explanation:

If Tyler sold his car for $9200, then the approximate percentage profit for this product is 33.3%.

Final price - initial price

Calculate the percentage $2300 is equivalent to by using the information you already have.

33.3% is the profit percentage.

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The missing probability from the line in the diagram attached is 0.5.

The number line is a graduated straight line system showing the value of each real number from (-∞, +∞).

The probability of a number line in the diagram below is halfway (middle) between the impossible event and a certain event.

Thus,

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Answer:

Important: 3

6

looks like a fraction, but it is actually an improper fraction.

There is an infinity number of equivalent fractions to 3

6

.

To find an equivalent fraction to 3

6

, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:

By dividing the original fraction by 3, we get:

3 ÷ 3

6 ÷ 3

= 1

2

By multiplying the original fraction by 2, we get:

3 × 2

6 × 2

= 6

12

Step-by-step explanation:

Answer:

H = 5

Step-by-step explanation:

rectangular prism:

V = L x W x H

400 cm3 = 16 x 5 x H

400 cm3 = 80 x H

400/80 = 5

h = 5 cm

95% sure this is correct! :)

Answer:

5 cm

Step-by-step explanation:

Formula used :

Volume of the rectangular prism = Length × Width × Height

=========================================================

Given :

⇒ Volume = 400 cm³

⇒ Length = 16 cm

⇒ Width = 5 cm

===========================================================

Solving :

⇒ 400 cm³ = 16 cm × 5 cm × Height

⇒ Height = 400 cm³ / 80 cm²

⇒ Height = 5 cm

Answer:

m=1/3

equation y=1/3x+10

Step-by-step explanation:

Find the rise and run.

1. -6--9=run=3

2. 8-7=rise=1

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the slope of the line that passes through (-6, 8) and (-9, 7).

[tex]\triangle~\fbox{\bf{KEY:}}[/tex] (formula for Slope)

[tex]\longmapsto\bf{\cfrac{y2-y1}{x2-x1}}[/tex]

y2 & y1 = the y-coordinates of the two points

x2 & x1 = the x-coordinates of the two points

[tex]\ddot\bigstar[/tex] Remember this...

[tex]\fbox{y2\;and\;y1\;are\;y-coordinates\;of\;the\;two\;points,\;and\;x2\;and\;x1\;are\;x-coordinates}}[/tex]

So we substitute the values and obtain:

[tex]\bf{\cfrac{7-8}{-9-(-6)}[/tex]

Simplifying:

[tex]\bf{\cfrac{-1}{-9+6}}[/tex]

Simplifying more:

[tex]\bf{\cfrac{-1}{-3}}[/tex]

Divide the top and bottom by -1:

[tex]\bf{\cfrac{1}{3}}[/tex]

There's the slope.

Hope it helps you out! :D

Ask in comments if any queries arise.

~Just a smiley person helping fellow students

1. Mean of the data: 8

2. Median: 8

3. IQR = 4

4. Members that use the facility 10 days a month is: 2.

See reasons below.

Mean = sum of all values ÷ number of data values (easily solved using a dot plot

Median = middle value (easily found using a box plot).

Interquartile range (IQR) = Q3 - Q1 (easily found using a box plot).

1. Mean of the data: use the dot plot.

Reasoning: (3 + 3 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 11 + 12 + 14)/15 = 8

2. Median of the data set: Using the box plot, it is the value indicated by the vertical line that divides the box.

Median = 8

3. IQR = Q3 - Q1 = 10 - 6

IQR = 4

4. Members that use the facility 10 days a month, using the dot plot is: 2. 10 has 2 dots.

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Answer: 8/10

Step-by-step explanation: so you have to multiply 5 times x u till you get 10 so you’ll multiply it 2 times and since you multiplied the left 5 times two you have to multiply the 4 by 2 also to keep everything equal so the final answer is 8/10

Answer:

x < 5.

Step-by-step explanation:

Creo que esto es correcto. :')

Answer:

15/56

Step-by-step explanation:

15 and 56 have a GCF of 1.

Answer:

1. I went to a store four days in a row and only bought chocolate bars each day. All chocolate bars were the same and cost the same. On the first day, I bought 2 chocolate bars for $2.38. On the second day I bought 1 chocolate bar for $1.19. On the third day, I bought 10 chocolate bars for $11.90. On the fourth day, I bough 4 chocolate bars for $4.76.

2. A sink is full. It contains 20 gallons of water. The stopper is removed and water starts draining out. One minute after the stopper is removed, the volume of water in the sink is 18 gallons.  Two minutes after the stopper is removed, the volume of water in the sink is 16 gallons.  Four minutes after the stopper is removed, the volume of water in the sink is 12 gallons.  Ten minutes after the stopper is removed, the sink is empty.  

Answer: 2

Step-by-step explanation:

DE * CE = AE * BE (Two Secants Segment Theorem)

▪︎ DE = 1 + x + 4

▪︎ CE = x + 4

▪︎ AE = 11 + x + 1

▪︎ BE = x + 1

=> (1 + x + 4)(x + 4) = (11 + x + 1)(x + 1)

=> (x + 5)(x+4) = (x + 12)(x + 1)

=> x^2 + 9x + 20 = x^2 + 13x + 12

=> 9x + 20 = 13x + 12

20 - 12 = 13x - 9x

8 = 4x

x = 2

The sides of the triangle are (d) 12√2, 12√2, 24

The given parameters are:

In a 45-45-90 degree angle triangle, we have:

Hypotenuse = Opposite√2 and Hypotenuse = Adjacent√2

This means that:

Opposite =Adjacent

So, we have:

24 = Adjacent√2

Divide both sides by √2

Adjacent = 24/√2

Evaluate

Adjacent = 12√2

This means that:

Opposite = 12√2

Hence, the sides of the triangle are (d) 12√2, 12√2, 24

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Since the exponents were added based on the product rule, hence the multiplication law of exponents is TRUE

Indices are written in term of exponents. Some of the laws of indices;

[tex]a^m\times a^n=a^{m+n}[/tex] (product law of indices)

For the quotient law of indices

[tex]\dfrac{a^m}{a^n} =a^{m-n}[/tex]

According to the given expression, we are to determine if it is true or false

Check:

[tex]b^n.b^m=b^{n+m[/tex]

Since the exponents were added based on the product rule, hence the multiplication law of exponents is TRUE

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The maximum displacement of the tuning fork is 0.4 mm

A tuning fork is a acoustic resonator , It is used to tune musical Instruments.

It is given in the question that the

displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d = 0.4 sine (1760 pi t).

the maximum displacement of the tuning fork = ?

The equation for a sine function is given by

f(t) = A sin(Bt + C) + D

here A is the maximum Displacement

When this equation is compared with the given equation

d = 0.4 sine (1760 pi t).

A = 0.4

The maximum displacement of the tuning fork is 0.4 mm

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Answer: B- x/4

Step-by-step explanation:

The period is the horizontal distance needed for the values to repeat themselves.

I assume by f¹, you actually mean f⁻¹ as in the inverse of f. I also assume you are asked to find f(x) (as in the inverse of f⁻¹) and f⁻¹(4).

Given that

[tex]f^{-1}(x+2) = \dfrac{x-1}{x+1}[/tex]

with x ≠ 1, we can find f⁻¹(x) by replacing x + 2 with x :

[tex]f^{-1}(x + 2) = \dfrac{x-1}{x+1} = \dfrac{(x+2) - 3}{(x + 2) - 1} \implies f^{-1}(x) = \dfrac{x-3}{x-1}[/tex]

Then when x = 4, we have

[tex]f^{-1}(4) = \dfrac{4-3}{4-1} = \dfrac13[/tex]

Of course, we also could have just substituted x = 2 into the definition of f⁻¹(x + 2) :

[tex]f^{-1}(4) = f^{-1}(2+2) = \dfrac{2-1}{2+1} = \dfrac13[/tex]

To find f(x), we fall back to the definition of an inverse function:

[tex]f^{-1}\left(f(x)\right) = x[/tex]

Then by definition of f⁻¹, we have

[tex]f^{-1}\left(f(x)\right) = \dfrac{f(x)-3}{f(x)-1} = x[/tex]

Solve for f :

[tex]f(x) - 3 = x (f(x) - 1)[/tex]

[tex]f(x) - 3 = x f(x) - x[/tex]

[tex]f(x) - x f(x) = 3 - x[/tex]

[tex](1 - x) f(x) = 3-x[/tex]

[tex]f(x) = \dfrac{3-x}{1-x} = \dfrac{x-1}{x-3}[/tex]

Answer:

f(x) + g(x) = 3x - 2 + 2x + 1

(f + g)(x) = 5x - 1

The following recurring decimal as a rational number are 1/2, 13/100 and 341 / 1000

A rational number is a number that is expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator such as;

3/4. where,

Therefore,

0.5

= 5/10

= 1/2

0.13

= 13/100

0.341

= 341 / 1000

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Answer:

x² - 22x + y² + 18y + 58 = 0

Step-by-step explanation:

Using the equation of a circle :

(x - h)² + (y - k)² = r²

Solving :

Substitute 11, -9, 12 in place of h, k and r respectively.

Check the picture below.  so, that'd be the triangle's sides hmmm so let's use Heron's Area formula for it.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{15}) ~\hfill a=\sqrt{[ 15- 10]^2 + [ 15- 5]^2} \\\\\\ ~\hfill \boxed{a=\sqrt{125}} \\\\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{9}) ~\hfill b=\sqrt{[ 30- 15]^2 + [ 9- 15]^2} \\\\\\ ~\hfill \boxed{b=\sqrt{261}}[/tex]

[tex](\stackrel{x_1}{30}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill c=\sqrt{[ 10- 30]^2 + [ 5- 9]^2} \\\\\\ ~\hfill \boxed{c=\sqrt{416}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{125}\\ b=\sqrt{261}\\ c=\sqrt{416}\\ s\approx 23.87 \end{cases} \\\\\\ A\approx\sqrt{23.87(23.87-\sqrt{125})(23.87-\sqrt{261})(23.87-\sqrt{416})}\implies \boxed{A\approx 90}[/tex]

Answer:

help me to find Xian pleaseee:( i miss him so much:(

sorry for answering Non sense po i hope u understand me ty po!

Answer:

229

Step-by-step explanation:

(my work for the problem is in the photo I attached)

(I also wrote this step-by-step in the photo because I can explain things better as I do them)

This will be a little bit confusing without me writing out the numbers, so mainly this is if you can't read my handwriting

  -3       + 8         =      5    ;  5       + 8    =     13

(1st term)                   (2nd term)            (3rd term)

Instead of adding 8 repeatedly (repeated addition), we can use multiplication.

To get the 3rd term in this sequence, we had to add 8 twice, which could also be done by multiplying 8 twice (8 x 2)

13 + 8 = 21

         (4th term)

to get the 4th term, we added 8 three times (or, 8 x 3)

So, if we are looking for the 30th term in a sequence, we will have to add 8, 29 times (8 x 29) to our original term.

8 x 29 = 232

-3 + 232 = 229

This means that the 30th term of the sequence will be 229.