Which values are in the solution set of the compound inequality –8 < 3x 7 ≤ 10? Select three options. –15 –5 –3 0 1.

Answer:

Step-by-step explanation:

You can break the entire figure into two semi-circles, two triangles, and a rectangle.

The area of a semi-circle is 1/2 the area of a full circle. The area of a circle is πr^2. The area of the semi-circle is therefore:

[tex]\pi r^2/2=\pi (10^2)/2=50\pi[/tex]

The other semi-circle also contributes a value of 50π.

Moving on to the triangle, we must use Pythagorean's Theorem to find the value of the base:

[tex]a^2+b^2=c^2[/tex]

[tex]11^2+b^2=20^2[/tex]

[tex]121+b^2=400[/tex]

[tex]b^2=279[/tex]

[tex]b=\sqrt{279}[/tex]

The area of a triangle is:

[tex]Area=b*h/2[/tex]

[tex]A=(\sqrt{279} *11)/2[/tex]

The other triangle also contributes the same area.

Finally, the rectangle. To find the length of the rectangle, we must subtract the base of the triangle from 22. The length is:

[tex]l=22-\sqrt{279}[/tex]

The area of a rectangle is:

[tex]Area=l*w[/tex]

[tex]A=(22-\sqrt{279} )*(11)[/tex]

The total area of the figure is:

[tex]Area=2*(50\pi) +2*(\sqrt{279} *11/2)+11*(22-\sqrt{279} )[/tex]

[tex]Area=100\pi +11*\sqrt{279} +11*(22-\sqrt{279} )[/tex]

[tex]Area=100\pi +242[/tex]

[tex]Area=556.2[/tex]

Answer:

556.2 unit square

Step-by-step explanation:

Solution given:

Area of left semi circle= ½*πr²

where r is radiussince diameter is given 20.

so radius =diameter/2=20/2=10

substituting value

Area of left semi circle =½*π*10²=50π unit square

Since

Right semi circle's diameter is same as left semi circle

so

it's area will also be same.

Area of right semi circle= 50π unit square

Again

Area of middle rhombus= base* height

where base=22 and height is 11

substituting value

Area of middle rhombus=22*11 =242 square units

Now

Total Area=Area of left semi circle+Area of right semi circle+ Area of middle rhombus

Total Area= 50π+50π+242=556.159 unit square in nearest 10 is 556.2 unit square

Answer:

5.76

Step-by-step explanation:

i hope this was what u were looking for

We have: x is n% of y <=> y = x/n% (n < 100% or n = 100%)

So: 48 is 12% of y <=> y = 48/12% = 400

Answer: 400

Ok done. Thank to me :>

Answer:

Suppose, a triangle ABC, whose sides are a, b and c, respectively. Thus, the area of a triangle can be given by; Area= 30

Area = 1/2 x 15 x4 = 30 square yards

Step-by-step explanation:

Area of a triangle is 1/2 x base x height

Area = 1/2 x 15 x4 = 30 square yards

Answer:

(14, 23)

area = 400 square units

Step-by-step explanation:

Part (a)

To find the point where two equations meet (the point of intersection), equal the equations to each other, then solve for x.  Substitute the found value of x into one of the equations (it doesn't matter which) and then solve for y.  (x, y) is the point of intersection.

Equation 1:  y = 2x - 5

Equation 2:  y = 23

Equate the equations:

            y = y

⇒ 2x - 5 = 23

⇒       2x = 23 + 5

⇒       2x = 28

⇒          x = 28 ÷ 2

⇒          x = 14

Usually we'd substitute the found value of x into one of the equations and solve for y, however, as one of the equations is literally the y value, we don't need to do that.

So y = 23

Therefore, the point of intersection is (14, 23)

Part (b)

The vertices of the triangle will be the points where each pair of lines meet each other.  We have already determined that one pair of lines meets at point (14, 23).

y = 2x - 5 is a diagonal line, y = 23 is a horizontal line, and x = -6 is a vertical line.

So x = -6 and y = 23 meet at (-6, 23)

Now we just need to determine where y = 2x - 5  and  x = -6 meet.

Simply substitute x = -6 into y = 2x - 5:

⇒ y = 2(-6) - 5

⇒ y = -17

Therefore, the point of intersection is (-6, -17)

So we have three points of intersection which are the three vertices of the triangle:

(14, 23)  (-6, 23) (-6, -17)

As y = 23 is a horizontal line and x = -6 is a vertical line, their point of intersection (-6, 23) is a right angle.

Therefore the can determine that the height of the triangle is the difference between the y-coordinates of (-6, 23) and (-6, -17).

Similarly, the base (width) of the triangle is the difference between the x-coordinates of (-6, 23) and (14, 23).

Therefore, the height = 23 - -17 = 23 + 17 = 40

Therefore, the base = 14 - -6 = 14 + 6 = 20

Area of a triangle = 1/2 x base x height = 1/2 x 20 x 40 = 400 square units

see attached diagram

Answer:

12, 10, 8

Step-by-step explanation:

Substitute n = 1, n = 2 and n = 3 to find the 1st, 2nd and 3rd terms of the sequence:

[tex]a_n=12-2(n-1)[/tex]

[tex]\implies a_1=12-2(1-1)=12-2+2=12\\\\ \implies a_2=12-2(2-1)=12-4+2=10\\\\ \implies a_3=12-2(3-1)=12-6+2=8[/tex]

Answer:

19 square units

Step-by-step explanation:

Hello!

Step 1: Plot the points

We are first going to plot the points on the coordinate graph and connect the points to create a shape.

Refer to attachment titled "Step 1"

Step 2: Box the shape

Since this is an irregular shape, I'm going to make a box around the shape and subtract the area of the empty spaces to find the area of the original polygon.

Refer to attachment titled "Step 2"

Step 3: Area of Edges

We are going to find the area of the shapes A, B, and C and subtract them from the area of the big box to find the area of the polygon.

Area of a triangle = 1/2(base x height)

Area of A:

Area of B:

Area of C:

Step 4: Area of the polygon

Now, we can simply subtract the values of A, B, and C from the box to get the area of the polygon.

The area of the polygon is 19 un²

-Chetan K

Answer:

height: 36 cm

Step-by-step explanation:

volume of triangle prism = 0.5 * base * altitude * height

using the formula:

0.5 * 8 * 6 * height = 864

24 * height = 864

height = 864/24

height = 36 cm

Answer:

36 cm

Step-by-step explanation:

volume of a triangular prism = area of triangle x height of prism

area of triangle = 1/2 x base x height

Therefore, given the perpendicular sides of the triangle are 6 cm and 8 cm, the area of the triangle is:

⇒ area of triangle = 1/2 x 6 x 8 = 24 cm²

If the volume of the prism is 864 cm³:

⇒ 864 = 24 x height of prism

⇒ height = 864 ÷ 24 = 36 cm

Answer:

width = 10

length = 5

Step-by-step explanation:

It works

Answer:

A minimum

Step-by-step explanation:

This graph is a parabola which is a U-ish V-ish graph. Since there is no negative in front of the x^2 it opens UPWARDS, so it has a bottom. Thats a lowest point which is a minimum.

The matrix for the combined rotation transformation of 45° and dilation

of [tex]\sqrt{2}[/tex] gives the matrix for the transformation as follows;

[tex]Matrix \ for \ the \ rotation \ and \ dilation \ is;\left[\begin{array}{cc}1 &-1\\1&1\end{array}\right][/tex]

The angle by which the transformation rotates about the origin = 45°

The dilation following the rotation = A factor of √2

Required:

The matrix for the transformation

Solution:

The dilation matrix for a scale factor of [tex]\mathbf{\sqrt{2}}[/tex] is presented as follows;

[tex]\mathbf{\left[\begin{array}{cc}\sqrt{2} &0\\0&\sqrt{2} \end{array}\right]}[/tex]

[tex]The \ transformation \ for \ a \ rotation \ of \ 45^{\circ} \ is; \left[\begin{array}{cc}cos(45^{\circ})&-sin(45^{\circ})\\sin(45^{\circ})&cos(45^{\circ})\end{array}\right][/tex]

[tex]\left[\begin{array}{cc}cos(45^{\circ})&-sin(45^{\circ})\\&\\sin(45^{\circ})&cos(45^{\circ})\end{array}\right] = \mathbf{\left[\begin{array}{cc}\dfrac{\sqrt{2} }{2} &-\dfrac{\sqrt{2} }{2} \\&\\ \dfrac{\sqrt{2} }{2} &\dfrac{\sqrt{2} }{2} \end{array}\right]}[/tex]

Which gives;

[tex]\left[\begin{array}{cc}\dfrac{\sqrt{2} }{2} &-\dfrac{\sqrt{2} }{2} \\&\\ \dfrac{\sqrt{2} }{2} &\dfrac{\sqrt{2} }{2} \end{array}\right] \times \left[\begin{array}{cc}\sqrt{2} &0\\0&\sqrt{2} \end{array}\right] = \left[\begin{array}{cc}\dfrac{\sqrt{2} \times \sqrt{2} }{2} &-\dfrac{\sqrt{2} \times \sqrt{2} }{2} \\&\\ \dfrac{\sqrt{2} \times \sqrt{2} }{2} &\dfrac{\sqrt{2} \times \sqrt{2} }{2} \end{array}\right] = \left[\begin{array}{cc}1 &-1\\1&1\end{array}\right][/tex]

The required matrix for the transformation is therefore;

Learn more about other forms of transformation matrices here:

https://brainly.com/question/10212935

Check the picture below, notice, after 0 goes up then down back up at 4, and then it begins repeating after that, it begins to "periodically" be the same curve, that's the period.

Answer:

25. hope this helped you brother!

Answer: it will take 6 weeks for both of the to have the same amount of money

Step-by-step explanation: i hope this helps :d

synonym: a word of opposite meaning

contrast:  to show noticeable differences

Have an awesome day!

[tex]\huge\textbf{TheStarryNights :)}[/tex]

Answer:

16/7

Step-by-step explanation:

Answer:

-13.62

explanation:

use a method called keep change change, meaning you keep the -4.3, change the minus to a plus, and change the positive to a negative, and then add.

The probability that at most 8 of them take the bus to school is 0.925, written in percentage form this is 92.5%

We know that roughly 75% of the students take the bus, then, if we select a student at random.

The probability that at most 8 out of 9 students take the bus, is equal to one minus the probability of the 9 taking the bus, which is:

p = (0.75)^9 = 0.075

Then we have:

P = 1 - 0.075 = 0.925

The probability that at most 8 of them take the bus to school is 0.925, written in percentage form this is 92.5%

If you want to learn more about probability, you can read:

https://brainly.com/question/251701

Answer:

the real answer is 29.714

Kelly's answer is almost correct.

Answer:

The answer is 5.5

Step-by-step explanation:

6 x 6 = 36

2x2x2 = 8

36 + 8 =    44

2 + 6 = 8

44/8 = 5.5

Therefore, the answer to this problem is 5.5

I hope I helped! ^-^

answer:

when historians use the term ancient they mean “pre-historic” or “long ago” it symbolizes something old.

Answer: dividing the amount of posibilities the wheel has by the amount of spins you have

Step-by-step explanation:

hope this helps

Answer:

tripling the height (8.4 ft) will triple the volume of the barrel (from 857.39 to 2,572.17)

Step-by-step explanation:

By Tripling the height we can triple the volume of the barrel.

In geometry, a cylinder's volume is referred to as its capacity, which aids in determining how much material it can carry.

Given, A cylindrical barrel has a radius of 5.7 ft and a height of 8.4 ft.

From the general formula of volume of cylinder = πr²*h

The volume of the given cylinder = π * (5.7)² 8.4

The volume of the given cylinder = 856.95 ft³

As we can see that the volume of a cylinder is directly proportional to its height of the cylinder.

Therefore, The barrel's volume can be tripled by tripling the height.

learn more about the volume of the cylinder here:

https://brainly.com/question/16134180

#SPJ2

Answer:

16 years old

Step-by-step explanation:

let Gastas age be g

since Gasta is four years older

g=12+4

g=16 years old

Question hi what school do you do cuz i have the same question

Step-by-step explanation:

Answer: x = -3

Step-by-step explanation:

42=-7(x - 3)

-7(x - 3) = 42

-7(x - 3)/-7 = 42/-7

x - 3 = -6

x - 3 + 3 = -6 + 3

x = -3

[tex] \quad{\rule{300pt}{1.5pt}}\quad[/tex]

We are given that :

We know that :

[tex]\qquad\bull{\boxed {\mathfrak{Circumference = 2 \pi r }}}\bull[/tex]

Therefore,

[tex] \quad\dashrightarrow\quad \sf { 6.28 = 2 \pi r }[/tex]

[tex] \quad\dashrightarrow\quad \sf {r = \dfrac{6.28}{2\pi} }[/tex]

[tex] \quad\dashrightarrow\quad \sf {r = \dfrac{6.28\times 7}{22\times 2} }[/tex]

[tex] \quad\dashrightarrow\quad \sf {r =\cancel{\dfrac{43.64}{44}} }[/tex]

[tex] \quad\dashrightarrow\quad \sf {r = 0.9989 }[/tex]

As we know,

[tex] \quad\dashrightarrow\quad \sf { Diameter = 2\times radius}[/tex]

[tex] \quad\dashrightarrow\quad \sf { Diameter = 2\times 0.9989}[/tex]

[tex] \quad\dashrightarrow\quad \sf { Diameter = 1.98 }[/tex]

[tex] \quad\dashrightarrow\quad {\pmb{\sf {Diameter = 2 mm ( approx ) }}}[/tex]

[tex] \rule{300pt}{2pt}[/tex]

Answer:

Jane spent the most money, while Anne spent the least.

Step-by-step explanation

Anne spent less because Jane spent 0.888 in decimal form, whereas Anne spent 0.875 in decimal form.