Find the values of x in the following figures.
Please help​

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

Read more about right triangles at:

https://brainly.com/question/2437195

#SPJ1

The area of the rectangle, as shown in the image given is calculated as: 48 square units.

The area of a rectangle = length × width.

Find the length and width of the rectangle:

Area of rectangle ABCD = 8 × 6 = 48 square units.

Learn more about area of a rectangle on:

https://brainly.com/question/25292087

#SPJ1

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:

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

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

The area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively, option (a) is correct.

It is defined as the four-sided polygon in geometry having four edges and four corners. Two pairs of congruent sides, and it has one pair of opposite congruent angles.

We know the area of the kite = pq/2

Where p and q are the length of the diagonals

p = 10+10 = 20 ft

q = 7+11 = 18 ft

Area = (20×18)/2

Area = 180 square feet

Thus, the area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively option (a) is correct.

Learn more about the quadrilateral here:

brainly.com/question/6321910

#SPJ1

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

Learn more on multiplication law of exponents here: https://brainly.com/question/847241

#SPJ1

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:

15/56

Step-by-step explanation:

15 and 56 have a GCF of 1.

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,

Learn more about missing probability here:

https://brainly.com/question/17165819

#SPJ1

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:

13

Step-by-step explanation:

The way to find the distance between two points on the coordinate plane is to use the distance formula, which is basically a way of applying the Pythagorean Theorem.

The distance formula is [tex]\sqrt{(x_{1}- x_{2} )^2 + (y_{1}- y_{2})^2}[/tex]. Let's say the coordinate (3, -8) is (x1, y1) and the coordinate (8, 4) is (x2, y2). We can plug these values into the formula:

[tex]\sqrt{(3- 8 )^2 + (-8 - 4)^2}\\\sqrt{(-5)^{2} + (-12)^{2}} \\\sqrt{25+144} \\\sqrt{169} \\13[/tex]

So, the distance between the two points is 13.

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.

More about the parabola link is given below.

https://brainly.com/question/8495504

#SPJ1

Answer:

65, 65, 115

Step-by-step explanation:

Attached image

Answer:

The period is 2π

Explanation:

The period is 2 times pi because 2 is the standalone-term multiplied by pi to get the period.

Answer:

-12 and 2

Step-by-step explanation:

-12 × 2 is -24

and

-12 + 2 is -10

Answer:

y=-15x+100

Step-by-step explanation:

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

Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357 or 3.57 %.

What is Probability ?

Probability is the measure of likelihood of an event.

For a Normal Distribution ,

the z-score formula is given by

[tex]\rm Z = \dfrac{X - \mu }{\sigma}[/tex]

Here [tex]\rm \mu\\[/tex] is the mean and [tex]\rm \sigma\\[/tex] is the standard deviation .

It is the measure of the deviation of the data from its central tendency.

Each z-score has a probability value.

It is given in the question that

Mean of 2.16% =  [tex]\rm \mu\\[/tex] = 2.16

Standard deviation of 1.36% means that  [tex]\rm \sigma\\[/tex] = 1.36

For Sample of 31 the value of standard deviation is [tex]\rm s = \dfrac{\sigma}{\sqrt{n}}[/tex]

s = 1.36/√31

s = 0.2442

Substituting the values

Z = (2.6 -2.16)/0.2442

Z =1.8

the p value from the graph of z and p , 0.9643

To determine value of probability  more than X is 1 - 0.9643= 0.0357

the

Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357.

To know more about Probability

https://brainly.com/question/11234923

#SPJ1

Answer:

Step-by-step explanation:

Answer:

x < 5.

Step-by-step explanation:

Creo que esto es correcto. :')

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]

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.

Learn more about the mean, median, and interquartile range on:

https://brainly.com/question/9821103

#SPJ1

The maximum height of the  pumpkin is 3 feet

We have given that,

A catapult hurls a pumpkin from a height of 32 feet at an initial velocity of 96 feet per second.

The function h(t)=-16t^2+96t+32 represents the heights of the pumpkin h(t) in terms of time t.

We have to determine the maximum height.

At the point of maxima f'(x)=0

first, find the maxima

Therefore differentiate the given function with respect to t we get,

[tex]h'(t)=-32t+96[/tex]

h'(t)=0

Then we get,

[tex]0=-32t+96\\-32t=-96\\t=\frac{-96}{-32} \\t=3[/tex]

Therefore the maximum height of the pumpkin is 3 feet.

To learn more about the maxima visit:

https://brainly.com/question/13995084

#SPJ1

Answer:

Step-by-step explanation:

Length=18

Width/Breadth =10

Height=2

The formula for a diagonal face of a cuboid is=√(l²+ b²)

Face diagonal=√(18²+10²)

= 20.59 to 2.d.p

The formula for the body diagonal of a cuboid is=√(l² + b² + h²)

Body diagonal=√(18² + 10² + 2²)

=20.69 to 2.d.p

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

Learn more about rational number:

https://brainly.com/question/12088221

#SPJ1

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

The value of (26 - 7) and (5 - 24) when they're multiplied will be -399.

From the information given, we are told to multiply (26 - 7) and (5 - 24). This goes thus:

= (26 - 7) × (5 - 24)

= 21 × -19

= -399

In this case, value of (26 - 7) and (5 - 24) when they're multiplied will be -399.

Learn more about multiplication on:

brainly.com/question/10873737

#SPJ1

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]