Classify the triangle.

Answer:

Given:

[tex]\begin{aligned} \textsf{Perimeter} & =\textsf{shorter leg + longer leg + hypotenuse}\\ & = (x+5)+[3(x+5)-1]+[2(x+5)+13]\\ & = x+5+3x+15-1+2x+10+13\\ & = 6x+42\end{aligned}[/tex]

[tex]\begin{aligned} \textsf{Area} & =\dfrac12\textsf{(shorter leg)(longer leg)}\\ & =\dfrac12(x+5)[3(x+5)-1]}\\ & =\dfrac12(x+5)(3x+14)\\ & = \dfrac12(3x^2+29x+70)\\ & = \dfrac32x^2+\dfrac{29}{2}x+35 \end{aligned}[/tex]

[tex]\begin{aligned} \textsf{Area} & =2.5 \sf (Perimeter)\\ \implies \dfrac32x^2+\dfrac{29}{2}x+35 & =\dfrac52(6x+42)\\ 3x^2+29x+70 & =5(6x+42)\\ 3x^2+29x+70 & =30x+210\\ 3x^2 -x-140 & =0\\ 3x^2-21x+20x-140 & =0\\ 3x(x-7)+20(x-7) &=0\\ (x-7)(3x+20)& =0\end{aligned}[/tex]

Therefore:

[tex](x-7)=0 \implies x=7[/tex]

[tex](3x+20)=0 \implies x=-\dfrac{20}{3}[/tex]

[tex]x=-\dfrac{20}{3}[/tex] is not a viable solution as when inputting this into the formula for the shorter leg, it gives a negative value:

[tex]\textsf{Shorter leg}=-\dfrac{20}{3}+5=-\dfrac53[/tex]

As distance cannot be negative, this is not a viable solution.

When x = 7:

[tex]\textsf{Shorter leg}=7+5=12[/tex]

[tex]\textsf{Longer leg}=3(7+5)-1=35[/tex]

[tex]\textsf{Hypotenuse}=2(x+5)+13=37[/tex]

[tex]\textsf{Perimeter}=6(7)+42=84[/tex]

[tex]\textsf{Area} & =\dfrac32(7)^2+\dfrac{29}{2}(7)+35=210[/tex]

Therefore, there is one viable solution.  This solution in the form (x, A) is  (7, 210)

Answer...

Ok done. Thank to me >:3

Answer:

x = 9

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² + 6² = ([tex]\sqrt{117}[/tex] )²

x² + 36 = 117 ( subtract 36 from both sides )

x² = 81 ( take square root of both sides )

x = [tex]\sqrt{81}[/tex] = 9

Answer:

The value of a is 7.

Step-by-step explanation:

To calculate mean, add all of the numbers in the set and divide by the number of terms in said set. There are 7 numbers in this set, so the equation can be set up as follows.

(4 + 10 + 3 + 6 + a + 9 + 10)/7 = 7

Simplify the terms on the top.

(42 + a)/7 = 7

Multiply both sides by 7.

42 + a = 49

Subtract both sides by 42.

a = 7.

Proof:

(4 + 10 + 3 + 6 + a + 9 + 10)/7 = 7

Substitute variable.

(4 + 10 + 3 + 6 + 7 + 9 + 10)/7 = 7

Add in the parenthesis.

49/7 = 7

Divide.

7 = 7.

Answer:

D. 25.12 feet

Step-by-step explanation: C= r(pi)^2

Answer:

32.2 square feet

Answer:

x=4

Step-by-step explanation:

distributive property goes first.

you get 6x-9=15

add 9 on both sides so 9 cancells out on the left side.

you get 6x=24

divide by 6 and you get x=4

Angles ABC and CBD are complementary - they add up to 90°. This means

(4x + 52°) + (8x - 10°) = 90°

Solve for x :

12x + 42° = 90°

12x = 48°

x = 4°

It follows that angle CBD has measure

4 • 4° + 52° = 16° + 52° = 68°

Answer:

2.

Step-by-step explanation:

it's the reciprocal

so it's gonna reflect

Answer:

Use points (0,12) and (1,20) on graphing paper or a program to find final answer.

Step-by-step explanation:

In the problem, I was unable to understand the equation so I am presuming the equation actually means y=8x+12

Whenever you graph a Linear Function you always need two points. The first point is always easy to acquire.

You can plug in any value for x, which will be your x cordinate and the output (solution) of the equation will be you y cordinate.

I'm plugging in 0 for X first.

y=8x+12

y=8(0) +12

y=12

We have our first point as (0,12)

Now you can plug in any other number for X other then Zero.

I choose 1 this time for X.

y=8x+12

y=8(1)+12

y=8+12

y=20

We now have our second point (1,20). Two points will be enough to graph this graph, you can graph these two points and then draw a line if on paper or use an application and get the line that way.

Answer:

Use the rise/run strategy to draw the line. Start at the y-intercept (0, 12), and count 8 up and 1 to the right to the point (1, 20). Then, draw a line through the points. Test the point (3,36) in the equation y = 8x + 12 to verify that the line is correct.

Step-by-step explanation:

got it right

Step-by-step explanation:

11 cm, 6 cm, 17 cm

Answer::

11cm, 6cm, 17cm

step by step explanation:

the correct answer is 11cm 6cm and 17cm

because in a right angled triangle, the square of the hypothenus is equal to the square of the sum of the other two sides

hypothenus= 17cm other two sides=11cm and 6cm

The probability of the friend completing the new level in her first try is 22.5%

This is a concept that is used to talk about the likelihood or the chances of an event occuring.

For the digit 8, the frequency is 7

For the digit 9, the frequency is 11

The total number of frequencies is given as

10 + 9 + 6+ 7 + 8 + 12 + 4 + 6 + 7 + 11 = 80

7 + 11 = 18

Probability = 18/80

= 0.225 x 100

= 22.5%

Read more on probability here: https://brainly.com/question/251701

Answer:  [tex]C=31.4[/tex]

Step-by-step explanation: When you are finding the circumference of a circle you use the formula

[tex]C=2\pi r[/tex]

[tex]C=2*3.14 *5[/tex]

[tex]C=31.4[/tex]

Answer:

Step-by-step explanation:

I don't see any information on dimensions of the cans or box, so I'll assume the question wants a general solution.

Three steps will result in the volume of sand required to fill the remaining space in the box.

1.  Calculate the volume of a can using the equation for the volume of a cylinder:  Vol = πr²h

2.  Multiply the can volume by 12.  This will give the total volume of the 12 cans in the box.

3.  Calculate the volume of the box:  Volume = (Base)(Width)(Height)

[Make sure the units are the same as those used in calculating the can volume.  E.g., if the can is calculated with cm as the measue, the box dimensions must also be cm]

4.  Subtract the volume of the12 cans (from step 2) from the volume of the box.

The result from 4 will be the volume of sand required to fill the box containing 12 cans.  

I'm not clear why filling the box with sand is important, but perhaps it will absorb any soda released from cans broken when the heavy box is dropped by the person shocked that 12 cans of pop could be so heavy.

hi the awnser us defiantly going to be that I 56

Step-by-step explanation:

edge

Problem 25

Point P has the x coordinate x = -5, while point Z has the x coordinate x = 5. This is a distance of 10 units on the number line. Segment PZ is 10 units long which is the base of the triangle.

The height of the triangle is 8 units because it's the vertical distance from R to segment PZ. Notice we go from x = 4 to x = -4. The base and height are always perpendicular to one another.

Area = (base*height)/2

Area = (10*8)/2

Area = 80/2

Area = 40

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

Problem 26

I'm not sure about this one because the instructions mention a grid, but I don't see any grid lines here. I'm not sure if the grid lines are just really faint or if your teacher forgot to put them in.

Answer:

$53.33

Step-by-step explanation:

40/1 - .25

40/.75 = $53.33

The Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

We're given:

Plug these measurements into the Pythagorean theorem:

[tex]a^2+b^2=c^2\\9^2+12^2=c^2[/tex]

⇒ Combine like terms:

[tex]81+144=c^2\\c^2=225[/tex]

[tex]c^2=225[/tex]

Answer:

50.3

Set A to the value of pi times the radius squared.

[tex]4^2 = 4 * 4 = 16\\\\A = \pi *r^2(4^2) = 50.26548245...[/tex]

Answer:

195 cubic inches

Step-by-step explanation:

A fishing tackle box is 13 inches long, 6 inches wide, and inches high. What is the volume of the tackle box? SOLUTION: The volume of the tackle box is 195 cubic inches.

[tex]\text{Larger angle} =x\\\\\text{Smaller angle} =y\\ \\\text{According to the condition,}\\\\x=10y+15\\\\\text{The two angles are supplementary, so their sum is}~ 180^{\circ} \\\\x+y=180\\\\\implies 10y+15 +y = 180\\\\\implies 11y = 180-15\\\\\implies 11y=165\\\\\implies y = \dfrac{165}{11}\\\\\implies y = 15\\\\\text{So,} ~x =180-15 = 165\\\\\text{Hence the larger angle is}~ 165^{\circ}~ \text{and the smaller angle is }15^{\circ}[/tex]

Answer:

x is 36

Step-by-step explanation:

the way to find out is 1/4 multiplied by what gives you 9. 9 divided by 1/4 is 36. 36 1/4's gives you 9.

Answer: 2

Step-by-step explanation:first u subtract 1-9=8then u divide 4/8=2 tell me if wrong

Answer:

250

Step-by-step explanation:

Answer:

0.2

Step-by-step explanation:

the sum of 5 times 0.2 and 7 equals 8

Answer:

[tex]x=\frac{3}{2}[/tex]

Step-by-step explanation:

Step 1.  Put each term in [tex]3x-\frac{1}{2}[/tex] over the common denominator 2.

[tex]\frac{6x}{2}-\frac{1}{2}[/tex]

Therefore we have [tex](\frac{6x}{2}-\frac{1}{2})=4[/tex]

Step 2.

Combine [tex]\frac{6x}{2}-\frac{1}{2}[/tex] into a single fraction.

[tex]\frac{6x-1}{2}[/tex]  

Therefore we have [tex](\frac{1}{2}(6x-1))=4[/tex]  or [tex]\frac{6x-1}{2}=4[/tex]

Step 3.

Multiply both sides by a constant to simplify the equation.

Multiply both sides of [tex]\frac{6x-1}{2}=4[/tex]  by 2:

[tex]\frac{2*(6x-1)}{2}=4*2[/tex]

Step 4.

Cancel the common terms in the numerator and denominator of   [tex]\frac{2*(6x-1)}{2}[/tex]

Then we get [tex]\frac{2}{2}*(6x-1)[/tex]  which simplifies to [tex](6x-1)[/tex]

So all together we have [tex](6x-1)=2*4[/tex]

Step 5.

Multiply 2 and 4 together and remove the parenthesis.

[tex]6x-1=8[/tex]

Step 6.

Isolate terms with the variable x to the left hand side.

So add 1 to both sides:

[tex]6x+(1-1)=8+1[/tex]

Evaluate   [tex]1-1=0[/tex]  which cancels out

Step 7.

Add the like terms on the right side:

[tex]6x=9[/tex]

Step 8.

Divide both sides by a constant to simplify the equation.

Divide both sides of [tex]6x=9[/tex]  by 6.

[tex]\frac{6x}{6} =\frac{9}{6}[/tex]

Any non-zero number divided by itself is 1.

[tex]x=\frac{9}{6}[/tex]  which simplifies to [tex]x=\frac{3}{2}[/tex]

Answer:

Step-by-step explanation:

y=2x+3

y=-3x+3

**This is what's on the image.**

You need to aline the two together.

2x+3 = -3x+3

Add 3x both sides

3x+2x+3=3

5x+3=3

Now subtract 3 from both sides

5x=3-3

x= 0

This should be a vertical line from (0,0) to above since there is no slope you should have a straight line that is vertical.

Answer:

[tex]derivative \: of \: y = 6 {x}^{2} + 2x + 4[/tex]

Step-by-step explanation:

we know that

[tex] \frac{d}{dx} {x}^{n} = n {x}^{n - 1} [/tex]

Now the derivative of y=2x³+x²+4x

[tex] \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} + {x}^{2} + 4x)[/tex]

[tex] \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} ) + \frac{d}{dx}( {x}^{2} ) + \frac{d}{dx} (4x)[/tex]

[tex]\frac{dy}{dx} = 2(\frac{d}{dx} {x}^{3} ) + \frac{d}{dx} {x}^{2} + 4(\frac{d}{dx} x)[/tex]

here

[tex]\frac{d}{dx} {x}^{3} = 3 {x}^{2} [/tex]

[tex]\frac{d}{dx} {x}^{2} = 2x[/tex]

[tex]\frac{d}{dx} x = 1[/tex]

Now

[tex]\frac{dy}{dx} = 2(3 {x}^{2} ) + 2x + 4(1)[/tex]

[tex]\frac{dy}{dx} = 6 {x}^{2} + 2x + 4[/tex]

I hope it helped you

Answer:

1024 pages left

Step-by-step explanation:

19 pack  * 75 page/pack - 401 page =