what is the range of h?

Answer:

16 millimeters

Step-by-step explanation:

Now:

Volume of a Prism=Base Area X Prism Length

Since we have a triangular base:

Volume of the Prism=(0.5 X Base X Height) X Prism Length

Substituting the given values, we obtain:

416=(0.5 X 13 X Height) X 4

416=26 X Height

Divide both sides by 26

Height of its triangular face=16 millimeters

Answer:

h = 16 mm

Step-by-step explanation:

Th volume of the prism is:

[tex] V = A*l [/tex] (1)

Where:

V. is the volume of the triangular prism = 416 mm³

A. is the area of the prism = ?

l: is the large of the prism = 4 mm

The area of the triangular face of the prism is:

[tex] A = \frac{1}{2}bh [/tex]  (2)

Where:

b: is the base of the triangular face = 13 mm

h: is the height of the triangular face = ?

From equation (1) we have:

[tex] V = A*l [/tex]

[tex] A = \frac{V}{l} = \frac{416 mm^{3}}{4 mm} = 104 mm^{2} [/tex]

Now, using equation (2) we can find the height of the triangular face:

[tex] A = \frac{1}{2}bh [/tex]

[tex] h = \frac{2A}{b} = \frac{2*104 mm^{2}}{13 mm} = 16 mm [/tex]

Therefore, the height of the triangular face is 16 mm.

I hope it helps you!

Answer:

1

Step-by-step explanation:

3x+2=2x+13÷3

9x+6=2x+13

9x-2x=13-6

7x=7

x=1

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of x after solving the equation is 1.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 4 is an equation

3x + 5 = 3 is an equation

We have,

3x + 2 = (2x + 13) / 3

Multiply both sides by 3.

3 x (3x + 2) = 2x + 13

Remove the parentheses.

(3 x 3x) + 3 x 2 = 2x + 13

9x + 6 = 2x + 13

Subtract 2x on both sides.

9x + 6 - 2x = 13

7x + 6 = 13

Subtract 6 on both sides.`

7x + 6 - 6 = 13 - 6

7x = 7

Divide 7 on both sides.

x = 1

Thus,

The value of x after solving the equation is 1.

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Answer:

Step-by-step explanation:

By the Isosceles Triangle Theorem, if 2 sides of a triangle are congruent to each other, than the angles opposite those sides are also congruent. We see by the markings on the triangle that WX and WY are congruent. That means that angle Y (which is across from WX) and angle X (which is across from WY) are the same measure. We can set them equal to each other  because of this:

6y - 2 = 4x + 20

But we have a problem because we have 2 unknowns.

Let's try this out: the Triangle Angle-Sum Theorem says that all the angles of a triangle have to add together to equal 180. That means that

52 + 6y - 2 + 4x + 20 = 180.

But we STILL have a problem with those 2 unknowns. BUT...

If angle X and angle Y are the same, then we don't need both 6y - 2 AND 4x + 20.  We only need 1 of those multiplied by 2 because they're the same measure. Changing things up a bit to reflect that:

52 + 2(4x + 20) = 180 and

52 + 8x + 40 = 180 and

8x = 88 so

x = 11.

That means that

4(11) + 20 = 64 which is the measure of both angles X and Y.

Let's check:

64 + 64 + 52 better equal 180. And it does, so we're good.

The value of x is found this way:

4x + 20 = 64 and

4x = 44 so

x = 11 which we already knew. Now for y:

6y - 2 = 64 and

6y = 66 and

y = 11 also.

Answer:

2(x+4y)

Step-by-step explanation:

The greatest common factor would be 2. So 2/2 is 1 and then 8/2 is 4. Now if we plug back the variables, you should get 1x and 4y. To put it in distributive property, just put the greatest common factor outside and the variables inside. inside. That's your answer! Hope this helped and have a great dayyyyy!!!!

Answer:

B. (-7,-3)

Step-by-step explanation:

Given the circle: [tex](x + 7)^2 + (y - 10)^2 = 13^2[/tex]

The point (x,y) which lie on the circle are the coordinate which satisfies the given equation of the circle.

We now consider the given options.

Option A (5,12)

When x=5, y=12

[tex](5 + 7)^2 + (12 - 10)^2 =12^2+2^2=148\neq 169= 13^2[/tex]

Option B (-7,-3)

When x=-7, y=-3

[tex](-7 + 7)^2 + (-3 - 10)^2 =0^2+(-13)^2= 169=13^2[/tex]

Option C (-6,-10)

When x=-6, y=-10

[tex](-6 + 7)^2 + (-10 - 10)^2 =1^2+(-20)^2=401\neq 169= 13^2[/tex]

Option D (6,23)

When x=6, y=23

[tex](6 + 7)^2 + (23 - 10)^2 =13^2+13^2=338\neq 169= 13^2[/tex]

We can see that only (-7,-3) satisfies the equation of the circle. Thus it is the point which lies on the circle.

The correct option is B.

Answer:

11

Step-by-step explanation:

Since the y coordinates are the same, the distance is the values between the x coordinates

6 - -5

6+5

11

The right answer is 11 units.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Answer:

Amount of string let out by Jim will be 156.9 m.

Step-by-step explanation:

Distance between Jim and Patty = 200 m

Angle of elevation of the kite from Jim = 85°

Angle of elevation of the kite from Patty = 40°

Angle between the lines joining Jim and kite and Patty and the kite = 180° - (85 + 40)° = 55°

By applying Sine rule in the triangle formed by the kite, Jim and Patty,

[tex]\frac{\text{sin}55}{200}=\frac{\text{sin}40}{x}[/tex]

x = [tex]\frac{200\times \text{sin}40}{\text{sin55}}[/tex]

x = 156.94

  ≈ 156.9 m

Therefore, amount of string let out by Jim will be 156.9 m.

Answer:

(-8,7)

Step-by-step explanation:

5x+9y=23

-2x+y=23

 Step 1. When looking at the equation you need to find out what method you must use and a good way to find out if you use subtraction is to look for a variable of 1

just like -2x+y=23 has the variable 1y

 Step 2. solve for y in the second equation

-2x+y=23

+2x       +2x

y=2x+23

Step 3. rewrite your equation

5x+9y=23

y=2x+23

 Step 4. replace your y variable with the expression you just made

5x+9(2x+23)=23

Step 5. Distribute the 9 and solve

5x+18x+207=23

23x+207=23

23x=-184

x=-8

Step 6. enter your x value into the equation you solved in step one

y=2(-8)+23

y=-16+23

y=7

Step 7. determine if consistent or inconsistent

Because you have a x and y you have an consistent

...you can also graph it

Answer:

Step-by-step explanation:

First one is 7, since there is a minus sign by k, shifting the line 0.5x seven units down

the second one is too confusing due to spacing to find the answer

Answer:

the person that answer is correct

Step-by-step explanation:

Answer:

B:4

Step-by-step explanation:

i took the test

Answer    :Isaac wants the equation below to have no solution when the missing number is placed in the box.

Box (x + 2) + 2 x = 2 (x + 6) + 4 x

Which number should he place in the box?

2

4 this one

6

8

Step-by-step explanation:

Answer:

q=7

Step-by-step explanation:

3(q +4/3)+2=23

3q+4+2=23

3q+2=23

3q=23-2

q=21/3=7

Answer:

- 2/3

Step-by-step explanation:

on khan academy

Answer:

The interest rate= 12.05%

Step-by-step explanation:

The interest rate= 12.05%. I added the steps down below to help you understand.

Steps:

1: I=$160.67

2: p= $2000

3: t= 8 months = 8/12 = 2/3 years.  I=prt

4: 160.67 = 2000.r. 2/3 Substitute

5: 160.67 = 4000/3r  Multiply

6: 3/4000 .160.67= 3/4000 . 4000/3r Multiply both sides by 3/4000

The interest rate= 12.05%

Answer: 12.05%

Hope this helps.

Answer:

12%

Step-by-step explanation:

Your equation would be 160=2000xRx2/3 (8 months=2/3

First, multiply 2000x2/3 which equals 1333.33

So now we have 160=1333.33r

Second, divide 160 by 1333.33 which equals 0.1200003

Lastly, move the decimal two spots over to get your percent which is 12%

Hope this helped :)

Answer: A proper subset is one that contains few elements of the original set whereas an improper subset, contains every element of the original set along with the null set.

Answer:

Cost of procedure is $45

Step-by-step explanation:

In this question, we are concerned with finding the cost of the procedure, given the tip amount and the percentage of which it is of the procedure cost.

From the question, we are told that the cost of the procedure is b

Mathematically, 12% of b = tip

Thus,

12/100 * b = 5.4

12b = 5.4 * 100

12b = 540

b = 540/12

b = $45

Answer:

-7 ≤ x

Step-by-step explanation:

4x – 12 ≤ 16 + 8x

Subtract 4x from each side

4x-4x – 12 ≤ 16 + 8x-4x

– 12 ≤ 16 + 4x

Subtract 16 from each side

-16 – 12 ≤ 16 -16+ 4x

-28  ≤  4x

-28  ≤ 4x

Divide each side by 4

-28/4 ≤ 4x/4

-7 ≤ x

Answer:

The last graph or

Graph C

Step-by-step explanation:

Answer: See the explanation to understand.

Step-by-step explanation:

Well first off you have to understand the area concept. The area is shown on the grid clearly fir the square, 4cm (2x2). Now it might be a little tricky for the triangle but don’t worry, take it slowly, count the areas of the base of the triangle, the correct answer for that is 2cm so the base of the triangle is 2cm. Now go to highest point of the triangle and count down all the way to the base. The number you should get is 4. So now we know that the base is 2cm and the height is 4cm. Using the triangle Area formula which is base times height divided by two: bh/2 , substituting the values we have 2x4 is 8. 8 divided by two is 4cm. Now we know that the areas are the same by checking using the formula.

Hope this makes sense!

Answer:

Not sure what your choices are on the drop-down, but these expressions are equivalent to each other and include all solutions (all real numbers).

Edit:

1--Equivalent

2--29

3--Equivalent

Answer:

100

Step-by-step explanation:

perfect square  (a - b)^2 = a^2 - 2ab + b^2

In this case

20x = 2 * x * 10

and

10^2 = 100

so

(x - 10)^2 = x^2 - 20x + 100

Therefore, the missing constant term is 100

.

Answer: 1) 2, 3, 4, 9, 32, 279, 8896, 2481705, 22077238784

              2) 2,490,924

              3) Neither

Step-by-step explanation:

[tex]S_n=S_{n-2}\cdot (S_{n-1}-1)\quad \\\\S_1=2\quad given\\S_2=3\quad given\\S_3=S_1(S_2-1)\quad =2(3-1)\quad =4\\S_4=S_2(S_3-1)\quad =3(4-1)\quad =9\\S_5=S_3(S_4-1)\quad =4(9-1)\quad =32\\S_6=S_4(S_5-1)\quad =9(32-1)\quad =279\\S_7=S_5(S_6-1)\quad =32(279-1)\quad =8,896\\S_8=S_6(S_7-1)\quad =279(8896-1)\quad =2,481,705\\S_9=S_7(S_8-1)\quad =8896(2481705-1)\quad =22,077,238,784[/tex]

[tex]\sum^8_{k=1}S_k\\\\=S_1+S_2+S_3+S_4+S_5+S_6+S_7+S_8\\\\= 2,490,924\\[/tex]

Neither

Not arithmetic because the difference between each of the terms is not the same.            

                        S₂ - S₁          S₃ - S₂           S₄ - S₃      

                      3 - 2 = 1       4 - 3 = 1          9 - 4 = 5

Not geometric because the ratios between each of the terms is not the same.                

                       [tex]\dfrac{S_2}{S_1}=\dfrac{S_3}{S_2}\qquad \rightarrow \dfrac{3}{2}=\dfrac{4}{3}\qquad \rightarrow \text{cross multiply to get}: 9\neq 8[/tex]

Answer:

1: 2.65= x: 600

x= (1 * 600)/ 2.65= 226.41

Answer:

I'm glad you asked!

Step-by-step explanation:

Factor [tex]25x2+30x+9[/tex]

[tex]25x2+30x+9[/tex]

[tex]=(5x+3)(5x+3)[/tex]

Answer:

[tex]=(5x+3)(5x+3)[/tex]

Answer: C. (5x+3)(5x+3)

Step-by-step explanation:

This is assuming this is a quadratic with 25x2 actually being 25x^2

We can start by simplifying the 25 to be 5^2

As well as the 9 to be 3^2

The expression now looks like: [tex]5^{2}x^{2} + 30x + 3^2[/tex]

Now we can apply an exponent rule to the 5^2 x^2

The rule states: [tex]a^{m}b^{m} = (ab)^m[/tex]

So this means: [tex]5^{2}x^{2} = (5x)^2[/tex]

We can now rewrite 30x as 2 * 5x * 3

The expression now looks like: [tex](5x)^{2} + 2 * 5x * 3 + 3^{2}[/tex]

Now this expression matches with the perfect square formula which states:

[tex](a+b)^{2} = a^{2} +2* a * b + b^{2}[/tex]

Our a value is 5x and our b value is 3.

So: [tex](a+b)^{2} = (5x+3)^{2}[/tex]

The answer is (5x+3)(5x+3)

Answer:

x=10

Step-by-step explanation:

9*10=90+7=97

hope it helps

Answer:

x = 10

Step-by-step explanation:

[tex]9x +7 = 97\\Collect-like-terms\\9x = 97-7\\9x = 90\\Divide-both-sides-of-the-equation-by-9\\\frac{9x}{9} =\frac{90}{9} \\x = 10[/tex]

Answer:

A

Step-by-step explanation:

since the radius is 12, the most the circle expands out towards is 15 for x and 15 for y. (-6,-5) easily fits inside it.

Answer:

y= -1/2x +9

Step-by-step explanation:

The line equation of best fit is y = (-1/2)x+9 if the two points on the line are (2,8) and (8,5) option (C) is correct.

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

We have two points (2, 8) and (8, 5)

To find the line of best fit using these two points:

[tex]\rm (y-y_1)=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
[tex]\rm (y-8)=\frac{5-8}{8-2} (x-2)[/tex]

[tex]\rm (y-8)=-\frac{3}{6} (x-2)\\\\\rm (y-8)=-\frac{1}{2} (x-2)[/tex]

[tex]\rm y = - \frac{1}{2} x +9[/tex]

Thus, the line equation of best fit is y = (-1/2)x+9 if the two points on the line are (2,8) and (8,5) option (C) is correct.

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Answer:

A. 260°

Step-by-step explanation:

The measure of the arc in the circle given is 260°

A circle is the set of all points in the plane that are a fixed distance (the radius) from a fixed point (the centre). Any interval joining a point on the circle to the centre is called a radius. By the definition of a circle, any two radii have the same length.

Given is a circle, with an inscribed angle of 50°, we need to find the arc ABC,

So, according to the inscribed angle theorem,

∠ BAC = 1/2 arc BC

So, arc BC = 2 x ∠ BAC

arc BC = 2 x 50

∠ BAC = 100°

Now,

arc ABC = 360° - arc BC

Since, we know that the whole circle, measures 360°

So,

arc ABC = 360° - 100°

arc ABC = 260°

Hence, the measure of the arc in the circle given is 260°

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Answer:

3 hours

12 (the amount of cm it takes to overflow) divided by 4 (the amount of rainwater that falls in an hour) = 3