A triangle has one side length of 12 inches and another of 8 inches. Describe all possible lengths of the third side. Show and explain your reasoning.

Answer:scott

Step-by-step explanation:

I’m pretty sure Scott. Hope this helps!!!

Answer:

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

Step-by-step explanation:

[tex]\begin{array}{rcll}4 - 2(6x - 5) & = & -4 &\\- 2(6x - 5) & = & -8 &\text{Subtracted 4 from each side}\\6x - 5 & = & 4 &\text{Divided each side by -2}\\6x & = & 9 &\text{Added 5 to each side}\\x & = &\mathbf{\frac{3}{2}} &\text{Divided each side by 6}\end{array}[/tex]

Check:

[tex]\begin{array}{rlc}4 - 2(6\times\frac{3}{2} - 5)& = &-4\\4 - 2(9 - 5) & = & -4\\4 - 2\times4 & = & -4\\4 - 8 & = & -4\\-4 & = & -4\\\end{array}[/tex]

Answer:

[tex]\large\boxed{x=\dfrac{3}{2}}[/tex]

Step-by-step explanation:

[tex]4-2(6x-5)=-4\qquad\text{subtract 4 from both sides}\\\\-2(6x-5)=-8\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(-2)(6x)+(-2)(-5)=-8\\\\-12x+10=-8\qquad\text{subtract 10 from both sides}\\\\-12x=-18\qquad\text{divide both sides by (-12)}\\\\x=\dfrac{-18\!\!\!\!\!\diagup^3}{-12\!\!\!\!\!\diagup_2}\\\\x=\dfrac{3}{2}[/tex]

Answer:

c. x = -9.

Step-by-step explanation:

The excluded value is the value of x which gives a value of 0 to the denominator, so that value would be x =  -9.

Note: (x - 7) / 0 is undefined.

Finding rectangle surface areas(RSA) are: 2(14×7)+2(14×5)=336

R.S.A+side surface areas: 336+2(7×5)=406

Ans:406

To find the surface area of a prism using a net, you simply calculate the area of each individual shape in the net and then add those areas together. The sum of these areas is the prism's surface area.

To find the surface area of the prism using a net, you need to first understand what a net of a prism is. A net of a prism is essentially a 'flat' version of the shape. It's what you would get if you cut along the edges of the prism and flattened it out.

For a rectangular prism, for instance, the net would consist of 2 rectangles (the bases) and 3 or 4 rectangles (the sides), depending on whether the prism is a right prism or an oblique prism.

To find the surface area, calculate the area of each individual shape in the net and then add all those areas together. The sum of these areas is the surface area of the prism.

As an example, suppose we have a rectangular prism with length 4 cm, width 3 cm, and height 2 cm. The areas of the two bases are each 4*3=12 square cm. The areas of the four sides are two of 4*2=8 square cm and two of 3*2=6 square cm. So the total surface area is 2*12+2*8+2*6=48 square cm.

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Answer:

[tex]\log_{13}(169)=2[/tex]

Step-by-step explanation:

The given exponential form is:

[tex]169=13^2[/tex]

The base of the given expression on the right is 13 and the exponent is 2.

The number is 169.

In terms of logarithms, the base still remains the base and the exponent becomes the result of the logarithm of the number 169 to the given base 13.

[tex]\log_{13}(169)=2[/tex]

Answer:

Step-by-step explanation:The solution is x > 3

Answer:

the average rate of change is -1/6 per unit increase in x

Step-by-step explanation:

Looking at the table, we see that for each unit change in x, y decreases by 1/6.  Thus, the average rate of change is -1/6 per unit increase in x.

Answer with explanation:

Average rate of Change

             [tex]=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}\\\\=\frac{\frac{25}{3}-\frac{17}{2}}{4-3}\\\\=\frac{50-51}{6*1}\\\\=\frac{-1}{6}[/tex]

You can find average rate of change by taking any two distinct points on the curve.

Option B      

First you must combine like terms (x and x)

2y + 2 + (x + x)

2y + 2 + 2x

^^^All have the number two in common so we can take a two out like so...

2 (y + 1 + x)

or

2(x + y + 1)

There fore the answer is A!

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

A

Step-by-step explanation:

The only one you can eliminate on sight is C. You are going to get an x^3 somewhere along the line.

You can eliminate D on sight as well. The x^3 term is 12x^3 not 7x^3

Doesn't leave much does it?

(3x + 2)(4x^2 - 2x - 7)

3x: 12x^3 - 6x^2 - 21x

2 :              8x^2 - 4x   - 14

=======================     Add

     12x^3 + 2x^2 - 25x - 14

Answer: A

[tex](3x + 2)(4x^{2} - 2x - 7) \\ \: a. = 12 {x}^{3}+ 2x^{2} - 25x - 14[/tex]

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})~\hspace{10em} slope = m\implies \cfrac{5}{6} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{5}{6}[x-(-3)]\implies y-4=\cfrac{5}{6}(x+3) \\\\\\ y-4=\cfrac{5}{6}x+\cfrac{5}{2}\implies y=\cfrac{5}{6}x+\cfrac{5}{2}+4\implies y=\cfrac{5}{6}x+\stackrel{\textit{LCD of 2}}{\cfrac{(1)5+(2)4}{2}}[/tex]

[tex]\bf y=\cfrac{5}{6}x+\cfrac{13}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=x,\ leg=15.6cm:2=7.8cm,\ hypotenuse=8.8cm[/tex]

Substitute:

[tex]x^2+7.8^2=8.8^2[/tex]

[tex]x^2+60.84=77.44[/tex]          subtract 60.84 from both sides

[tex]x^2=16.6\to x=\sqrt{16.6}\\\\x\approx4.1\ cm[/tex]

Answer:

1 5/6

Step-by-step explanation:

Answer:

[tex]\large\boxed{\bold{No\ solution}}[/tex]

Step-by-step explanation:

[tex]C:\ y=6x+9\\\\D:\ y=6x+2\\\\\left\{\begin{array}{ccc}y=6x+9&(1)\\y=6x+2&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\6x+9=6x+2\qquad\text{subtract 6x from both sides}\\\\9=2\qquad\bold{FALSE}\\\\\text{Therefore the answer is:}\ \bold{no\ solution}[/tex]

Answer:

6

Step-by-step explanation:

Answer:

9/100

Step-by-step explanation:

There are 10 marbles in the bag

There are 3 pink marbles.

P (1st marble pink) = pink marbles/ total marbles

                              = 3/10

We put the marble back.

There are 10 marbles in the bag

There are 3 pink marbles.

P (2nd marble pink) = pink marbles/ total marbles

                                      = 3/10

Multiply the probabilities together

P (pink, then pink) = 3/10 * 3/10 = 9/100

Answer:

45-40

Step-by-step explanation:

The first interval is 15-19.

The width of this interval is: 19-15=4

The second interval is 30-34.

The width of this interval is: 34-30=4

The third interval is 40-45.

The width of this interval is: 45-40=5

The fourth interval is 45-49.

The width of this interval is: 49-45=4

Answer: $8.35

Step-by-step explanation:

Given: The amount as gross pay= $576.00

The rate of Medicare tax =1.45%  = 0.0145

Now, to calculate the medicare tax we need to multiply the rate of Medicare tax with the gross pay , we get

[tex]\text{Medicare tax=0.0145*Gross Pay}\\\\\Rightarrow\ \text{Medicare tax}=0.0145\times576.00\\\\\Rightarrow\ \text{Medicare tax}=\$8.352\approx\$8.35[/tex]

Answer:

30°

Step-by-step explanation:

Segment MP is the diameter of the circle, hence angle MOP has the measure of 180°.

Angles MON and NOP are supplementary angles (add up to 180°). Thus,

m∠MON+m∠NOP=180°

m∠MON=180°-m∠NOP

m∠MON=180°-150°=30°.

Angle MON is the central angle subtended on the arc MN. Thus, the measure of the arc MN is 30°.

Answer:

Step-by-step explanation:

It's important to know that the whole arc of a circle is 360°.

So, if MP is a diameter, that means it divides the circle in two equal parts of 180° each.

Now, one half of this arc is formed by MN and 150°, so we can formulate the expression

[tex]MN+150\° = 180\° \\MN= 30\°[/tex]

Therefore, the arc MN is 30°.

Answer:

x = 5

Step-by-step explanation:

You have a right triangle, so you can use the Pythagorean Theorem.

a^2 + b^2 = c^2

x^2 + 12^2 = 13^2

x^2 + 144 = 169

x^2 = 25

x = 5

Answer: x = 5

Answer:

just do 13 time 12

Step-by-step explanation:

Answer:

  Graph C; (2, 1)

Step-by-step explanation:

When equations are in standard form, finding the x- and y-intercepts is relatively easy. For ...

  ax +by = c

Using this idea on the first equation, we find its x-intercept to be -2. There is only one graph showing that has a line going through the point (-2, 0). That is Graph C. Checking the remaining intercepts for the two equations confirms that Graph C is the graph of this system of equations.

The two lines intersect at point (2, 1), so that is the solution to the system.

The correct graph is: Graph C

and the solution for this system is: (2,1)

The first equation is given by:

         [tex]x-4y=-2-------(1)[/tex]

and the second equation is given by:

   [tex]-2x-y=-5----------(2)[/tex]

from (1) we have:

[tex]x=-2+4y-------------(3)[/tex]

We put the value of x in equation (2) to get:

[tex]-2(-2+4y)-y=-5\\\\i.e.\\\\-2\times (-2)-2\times 4y-y=-5\\\\i.e.\\\\4-8y-y=-5\\\\i.e.\\\\4-9y=-5\\\\i.e.\\\\-9y=-5-4\\\\i.e.\\\\-9y=-9\\\\i.e.\\\\y=1[/tex]

Now on putting this value of y back to equation (3) we get:

[tex]x=-2+4\times 1\\\\x=-2+4\\\\x=2[/tex]

Hence, the solution to this system of equality is: (2,1)

Answer:

10

Step-by-step explanation:

Answer:

Slope = 0

Step-by-step explanation:

(y2 - y1) ÷ (x2 - x1) = (-3 - [-3]) ÷ (1 - [-9]) = 0 ÷ 10 = 0

a) The graph of the function is illustrated below.

b) The rocket's maximum height is 64 feet, it takes 2 seconds to reach this height.

c) The total time it was in the air is 4 seconds.

(A) Quadratic Function: To model the height of the rocket as it moves upward, we use a quadratic function in the form h(t) = at² + bt + c, where h(t) represents the height of the rocket at time t seconds. Since the rocket is moving vertically, we consider the acceleration due to gravity, which is -32 feet per second squared. The initial velocity of the rocket is 64 feet per second, so the coefficient of the linear term, b, is 64.

The equation for the height of the rocket is: h(t) = -16t² + 64t

(B) Graphing on the Coordinate Plane: To graph the quadratic function, we plot points on a coordinate plane. The vertex of the parabola represents the maximum height of the rocket, and the t-intercepts correspond to the times when the rocket hits the ground. The vertex of a quadratic function in the form h(t) = at² + bt + c is given by the coordinates (t_v, h(t_v)), where

t_v = -b / 2a.

In this case,

t_v = -64 / 2(-16) = 2 seconds.

(C) Finding Rocket's Maximum Height and Time in the Air: The vertex point we found earlier is (2, 64). This means that the rocket reaches its maximum height of 64 feet after 2 seconds of flight. To find the maximum height, we plug the value of t_v back into the equation:

h(t_v) = -16(2)² + 64(2) = -16(4) + 128 = 64 feet.

The rocket's maximum height is 64 feet, and it takes 2 seconds to reach this height. To find the total time the rocket is in the air, we look at the t-intercepts on the graph, which correspond to the times when the rocket hits the ground. From the equation h(t) = -16t² + 64t, we set h(t) to 0 and solve for t:

0 = -16t² + 64t t(0) = 0 (corresponding to the initial time of launch) t(4) = 4 seconds.

The rocket is in the air for 4 seconds.

To know more about function here

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Answer:

 The measure of G = 9.2°

Step-by-step explanation:

From the figure we can write,

The measure of <G is half the  the measure of arc AD

To find the value of x

We have  AD = (6x - 80)° and 2G = (x + 2)°

6x - 80 = (x + 2)

6x - 80 = x + 2

6x - x = 82

5x = 82

x = 82/5 = 16.4

To find the measure of <gG

m<G = (x + 2 )/2

 = (16.4 + 2)/2 = 18.4 = 9.2

Therefore the measure of <G =  9.2°

Answer:

A.

Rotational symmetry is when things look the same rotated.

Answer:

A

Step-by-step explanation:

It has buttons which are on the top but not on the other faces

Answer:

yes

Step-by-step explanation:

The formula to finding the hypotenuse of a right triangle is a^2+b^2=c^2. So since the longest side is the hypotenuse, the 82 in. is the hypotenuse. 18^2+80^2= 6724, then we square root it, square root of 6725 is 82.

Answer:

This is a right triangle

Step-by-step explanation:

We can check this using the Pythagorean theorem

a^2 +b^2 = c^2

where a and b are the legs and c is the hypotenuse

18^2  + 80^2 = 82^2

324+6400=6724

6724 = 6724

True, so this is a right triangle

The answer is:

The first and second options:

f(x) and g(x) intersect at exactly two points.

The x-intercepts of f(x) are common to g(x)

To find the correct option (or options) , we need to remember the following:

- When a function intercepts the y-axis, it means that the "x" coordinate will be equal to 0.

- When a function intercepts the x-axis, it means that the "y" coordinate will be equal to 0.

Now, to find the correct option, we also need to compare the graphed function (f(x))  to the given table (g(x)).

So, discarding each of the given options to find the correct option, we have:

- First option, f(x) and g(x)  intersect at exactly two points: True.

From the graph we can see that f(x) intercepts the x-axis at two points (-1,0) and (1,0), also, from the table we can see that g(x) intercepts the x-axis at the same two points (-1,0) and (1,0), it means that the functions intersect at exactly two points.

Hence,  we have that f(x) and g(x)  intersect at exactly two points.

- Second option, the x-intercepts of f(x) are common to g(x): True.

From the graph we can see that f(x) intercepts the x-axis at two points (-1,0) and (1,0), also, from the table we can see that g(x) intercepts the x-axis at the same two points (-1,0) and (1,0), so, both functions intercepts the x-axis at common points.

Hence,we have that the x-intercepts of f(x) are common to g(x)

- Third option, he minimum value of f(x) is less than the minimum value of g(x): False.

From the graph, we can see that the minimum value of f(x) is located at the point (0,-1), also, from the given table for g(x) we can see that there are values below the point (2,-3), meaning that the minimum value of f(x) is NOT less than the minimum value of g(x).

Hence, we have that the minimum value of f(x) is NOT less than the minimum value of g(x).

- Fourth option, f(x) and g(x) have the same y-intercept: False.

We can see that for the function f(x) the y-intercept is located at (0,-1) while from the given table, we can see the y-intercept for the function g(x) is located at (0,1)

Hence,  we have that f(x) and g(x) have differents y-intercepts.

Therefore, the correct answers are:

The first and second options:

f(x) and g(x) intersect at exactly two points.

The x-intercepts of f(x) are common to g(x)

Have a nice day!

Note: I have attached an image for better understanding.

The graph of f(x) overlaps with the graph of g(x). Then the correct option is A.

A statement, principle, or policy that creates the link between two variables is known as a function.

The table of values represents the function g(x) and the graph shows the function f(x).

The graph of f(x) overlaps with the graph of g(x).

Then the correct option is A.

More about the function link is given below.

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Answer:

90

Step-by-step explanation:

BP PERPENDICULAR 2 PC SO

BC=90

Answer: 90

Step-by-step explanation:

Given: A circle with center P and B and C are two points on circle such that

BP is perpendicular to PC, it gives [tex]\angle{BPC}=90^{\circ}[/tex]

We know that in a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc.

Therefore, the measure of  [tex]\overarc{BC}[/tex]= Central angle made by  [tex]\overarc{BC}[/tex].

⇒ the measure of  [tex]\overarc{BC}=90^{\circ}[/tex]

Answer: 29,500.

Step-by-step explanation: percentagecalculator.com

The answers are:

Second step:

First box, 4

Second box,

The width is:

[tex]x+4[/tex]

Fourth step:

Box, 16

The length cant be -16in,  the length is 12in, and the width is 16in.

To solve the problem, we are using the formula to calculate the area of a rectangle, however, since the dimensions of the rectangle are not constant numbers, we will work with the variable "x", also, we know that the area of the cookie sheet is equal to 192 square inches.

So, solving we have:

First step:

We have the expression:

[tex]x^{2} +x[/tex]

Which is equal to: [tex]192in^{2}[/tex]

So,

[tex]x^{2} +4x=492[/tex]

Second step:

We have that the common factor of the left side of the equation is "x", so, we can simplify the expression in the following way:

[tex]x(x+4)=492[/tex]

Now, using the formula to calculate the area of a rectangle, we have:

[tex]length*width=Area\\\\length*width=92in^{2}\\\\x(x+4)=192in^{2}[/tex]

Where,

The length of the rectangle is "x"

The width of the rectangle is "x+4"

Third step:

Rewriting the expression, we have:

[tex]x^{2} +4x-192=0[/tex]

We need to find the roots (zeroes) of the quadratic function, in order to find the width of the rectangle without using the variable "x".

So, finding the values of "x" (roots or zeroes of the expression), we have:

[tex]x^{2} +4x-192=0[/tex]

Fourth step:

We need to find two numbers which it product gives as result the number -192 (including its sign) and their algebraic sum gives as result "4", those numbers are, -12 and 16,

[tex]-12*(16)=-192\\-12+16=4[/tex]

Then, rewriting the equation, we have:

[tex](x+16)(x-12)=0[/tex]

So, we that the expression is equal to 0 for two values of "x", these values are:

[tex]x_1=-16\\x_2=12[/tex]

Now, since the length can't be -16in, its equal to 12in.

[tex]length=x=12in[/tex]

[tex]length=12[/tex]

Then, from the second equation, we have that:

[tex]width=x+4[/tex]

Substituting "x" we can find the value of the width, so:

[tex]width=x+4=\\\\width=12+4=16in[/tex]

Hence, we have:

[tex]length=12in\\width=16in[/tex]

Have a nice day!

OK so first you find the square root of 363 which is 19.05255888325765 then you find the square root of 27 which is 5.196252422706632 then times that by 3 you get 15.5884572681199 so then you have 19.05255888325765 subtract 15.5884572681199 which equals 3.46410161513775

Hope this helped!