Find the area of a triangle with the following measures:

B-12 inches

H-5 inches

Answer:

We have:

x = t^2 + 2*t

y = -t

where:

–4 ≤ t ≤ 1

Isolating t in the "y" equation, we get:

t = -y

Now we can use the limits of t, to find similar limits for y.

When t = -4

-4 = -y

4 = y

when t = 1

1 = -y

-1 = y

Then the limits for y are:

-1 < y < 4

Now, knowing that t = -y

we can replace that in the "x" equation:

x = t^2 + 2*t

x = (-y)^2 + 2*(-y)

x = y^2 - 2*y

Then the graph of the parametric equation is the one defined by:

x = y^2 - 2*y

in the range

-1 < y < 4

The graph of this can be seen below, where the two black dots are the points where the graph should start/end.

The graph that represents the parametric equations is a parabola with an axis of symmetry is parallel to the x-axis.

An approach to determine the possible graph consists in eliminating [tex]t[/tex] and simplify the resulting expression of the form [tex]f(x)[/tex]:

[tex]x = t^{2}+2\cdot t[/tex] (1)

[tex]y = -t[/tex] (2)

By (2):

[tex]t = -y[/tex]

(2) in (1):

[tex]x = (-y)^{2} + 2\cdot (-y)[/tex]

[tex]x = y^{2}-2\cdot y[/tex]

In a nutshell, the graph that represents the parametric equations is a parabola with an axis of symmetry is parallel to the x-axis.

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Answer:

The anwser is 2015, hope this helps out

Answer:

54

Step-by-step explanation:

55+71=126

180-126=54

Answer:

The third one.

Step-by-step explanation:

Answer: 1,058

Step-by-step explanation:

Answer:

Hello! answer: 80

Step-by-step explanation:

When doing the Pythagorean theorem you do...

a^2+b^2=c^2 which is just A multiplied byitself + B multiplied byitself that will equal the number that C multiplied by itself would equal then you just figure out what multiplied byitself equals that number and thats the answer so...

64 × 64 = 4096 48 × 48 = 2304

4096 + 2304 = 6400 80 × 80 = 6400 therefore c = 80 hope that helps!

Answer:

c = 80 inches

Step-by-step explanation:

The length of the hypotenuse can be found by using the following formula in which "c" is the length of the hypotenuse, and "a" and "b" are the legs of the right angles triangle.

[tex]c = \sqrt{a^{2} + b^{2} }[/tex]

[tex]c= \sqrt{64^{2} + 48^{2} } \\c= \sqrt{4096 + 2304} \\c = \sqrt{6400} \\c = 80 inches[/tex]

Answer:

30ml

Step-by-step explanation:

Answer:

the simplified expression of this is -23/2h + 3/2 or -11 1/2h + 1 1/2.

Step-by-step explanation:

7/2h - 3(5h - 1/2)

3(5h - 1/2)

First, we need to use the distributive property to distribute the expression which requires multiplication or division. We take 3 and multiply it by both values in the parentheses which gives us 15h - 1/2. However, since there is subtraction, we need to do the opposite of that which would be 15h +  1 1/2 or 15h + 3/2. Now we can't forget 7/2h at the beginning of the expression. Here is the remaining expression :

7/2h - 15h + 3/2 or 7/2h - 15h + 3/2

Now, we need to combine like terms which requires values to have the same variable. 7/2h and 15h have the same variable so combine like terms. We do subtraction.

7/2h - 15h

We subtract this and get a result of -23/2 or -11 1/2 but don't forget the variable.

-23/2h

1/2 doesn't have a variable so we no longer can combine like terms. Therefore, it would just be -23/2h + 3/2 or -23/h + 1 1/2.

Answer:

12 feet

Step-by-step explanation:

48 divided by 4 is 12 and 48 is the total area

Answer:

12 sq. ft.

Step-by-step explanation:

To find the area of a square (or rectangle) you multiply the length by the width.

To find the length of one side, when you have the area and one side, you divide the area by the side you have.

48 divided by 4 equals 12.

Hope this helps :)

Answer:

m<F = 53

Step-by-step explanation:

Exterior angles thm:

5x - 10 + 3x + 14 = 100

8x + 4 = 100

8x = 104

x = 13

m<F:

3x + 14

3(13) + 14

39 + 14

53

Answer:

linear equations, i assume

Step-by-step explanation:

Answer:

458 cm²

Step-by-step explanation:

5 × 5 × 2 + 5 × 18 × 4 = 50 + 360 = 410

2 × 2 × 4 × 3 = 48

410 + 48 = 458

Answer:

i don't know

Step-by-step explanation:

can you explain? thank you

Answer:

b. 395.59 m²

Step-by-step explanation:

It's honestly a lot to explain however I can explain if you want me too. Just let me know!

We can write the area of the given figure as 431.59 square meters.

Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫F(x, y) dx dy

Given is a figure as shown in the image.

It is asked to find the total area of the given figure.

We can write the area of the figure as -

Area = Area{triangle 1} + Area{rectangle} + A{triangle 2} + A{semi circle 1} + A{semi circle 2}

Area = {1/2 x 12 x 15} + {12 x 15 - √(18² - 12²)} + {1/2 x 12 x √(18² - 12²)} + {π(18² - 12²)/2} + {π(15² + 12²)/2}

Area = 431.59 square meters

So, it can be concluded that the area of the given figure as 431.59 square meters.

Therefore, we can write the area of the given figure as 431.59 square meters.

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Answer:

0.9821

Step-by-step explanation:

Probability that a randomly selected value will be less than 2.1 deviations from the mean ; this means the Zscore = 2.1

Hence, using :

P(Z < 2.1) = 0.9821 (standard normal table

= 0.9821

Given:

The system of inequalities:

[tex]x>3[/tex]

[tex]y<2x-5[/tex]

To find:

The point that represents a solution to the system by using the graph.

Solution:

We have,

[tex]x>3[/tex]

[tex]y<2x-5[/tex]

The related equations of these inequalities are:

[tex]x=3[/tex]

[tex]y=2x-5[/tex]

The line [tex]x=3[/tex] is a vertical line that intersect the x-axis at 3.

The table of values for [tex]y=2x-5[/tex] is:

x         y

0       -5

1        -3

Plot (0,-5) and (1,-3) on a coordinate plan and connect them by a straight line.

The boundary lines are dotted lines because the points on the lines are not included in the solution set.

Check the inequalities for (0,0).

First inequality: [tex]0>3[/tex]           ( False)

Second inequality: [tex]0<2(0)-5[/tex]

                               [tex]0<-5[/tex]     (False)

Both inequalities are false for (0,0). It means the shaded region of the lines is in the opposite direction of (0,0).

Plot the shaded region and the points (-3, -1), (1, 11), (4, -1), (5, 6) as shown in the below graph.

From the below graph, it is clear that the point (4,-1) is the only point lies in the common shaded region. So, (4,-1) represents a solution to the system.

Therefore, the correct option is C.

Answer:

Step-by-step explanation:

(44=6x-1+9x.-5)

We move all terms to the left:

(44-(6x-1+9x.-5))=0

We add all the numbers together, and all the variables

(44-(6x+9x.-6))=0

We calculate terms in parentheses: +(44-(6x+9x.-6)), so:

44-(6x+9x.-6)

determiningTheFunctionDomain

-(6x+9x.-6)+44

We get rid of parentheses

-6x-9x.+6+44

We add all the numbers together, and all the variables

-6x-9x.+50

Back to the equation:

+(-6x-9x.+50)

We get rid of parentheses

-6x-9x.+50=0

We move all terms containing x to the left, all other terms to the right

-6x-9x.=-50

Answer:

B) Angle 5 and angle 4

Step-by-step explanation:

Given

See attachment for sketch

See comment for options

Required

The alternate interior angles

Interior angles are such that they are located between the given parallel lines.

In the attached sketch, the interior angles are: 3, 4, 5 and 6

Alternate angles are at the opposite sides of the transversal

Hence:

4 and 5 are alternate interior

3 and 5 are also alternate interior

The requried simplified value of 4a is 16. Option C is correct.

Simplification is the process of reducing a mathematical expression to its simplest form by combining like terms, using the distributive property, and performing other algebraic operations.

If b=3, then substituting in the first equation, we get:

a + 3 = 7

Solving for a:

a = 4

Now, 4a = 4 x 4 = 16.

Therefore, the answer is C. 16.

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Answer:

C. y = -6

Step-by-step explanation:

3x – 6y = 9

–3x + 3y = 9

-3y = 18

y = -6

Answer:

The height of the second cylinder is 30mm

Step-by-step explanation:

Given

Cylinder 1:

[tex]R = 15mm[/tex]

[tex]H = 45mm[/tex]

Cylinder 2

[tex]r = 10mm[/tex]

See attachment

Required

Determine h, the height of the small one

To do this, we make use of the following equivalent ratios;

[tex]R : H = r : h[/tex]

This gives:

[tex]15 : 45 = 10 : h[/tex]

Express as fraction

[tex]\frac{15 }{ 45 }= \frac{10 }{ h}[/tex]

Simplify

[tex]\frac{1 }{ 3}= \frac{10 }{ h}[/tex]

Cross multiply

[tex]h *1 = 3 * 10[/tex]

[tex]h = 30[/tex]

Answer:

4x+6y

Step-by-step explanation:

distribute and add like terms

Answer:

[tex]4x + 6y[/tex]

Step-by-step explanation:

Collect like terms:

[tex]2(2x + 3y)[/tex]

Distribute 2 through the parentheses:

[tex]4x + 6y[/tex]

Therefore, the answer will be 4x + 6y.

Answer:

take 25 degree as reference angle

let hypotenuse be x

using cos rule

cos 25=adjacent/hypotenuse

0.90=4/x

0.90x=4

x=4/0.90

x=4.44

Step-by-step explanation:

Answer: 1008

Step-by-step explanation:

Given

5 small containers of capacity 16,72,12,24, and 56 litres is required to fill a big container.

The volume of big container is the LCM of the 5 given containers

[tex]LCM(16,72,12,24,56)=1008[/tex]

Therefore, the capacity of the bigger container is 1008 litres.