In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle.


Write and solve an equation to determine the measure of angle x.

Answer:

110 is the answer

Step-by-step explanation:

Answer:

4[tex]x^{3}[/tex] - 16[tex]x^{2}[/tex] + 15x

Step-by-step explanation:

length = 5 - 2x

width = 3 - 2x

heighth = x

x(5 - 2x)(3 - 2x)

x(15 -16x + 4[tex]x^{2}[/tex])

4[tex]x^{3}[/tex] - 16[tex]x^{2}[/tex] + 15x

The largest volume of such a box is 4.345[tex]ft^{3}[/tex].

Given that,

A rectangular sheet of cardboard 3 feet by 5 feet will be made into an open box by cutting equal-sized squares from each corner and folding up the four edges.

The shaded region represents the area  that was cut from the corners of the box.

We have to determine,

The largest volume of such a box.

According to the question,

The height will be  x

The width will be  (3 − 2 x)

And the length will be ( 5− 2 x)

.

The formula for volume will be,

[tex]Volume = Length \times Height \times Width\\\\[/tex]

Substitute the values in the formula,

[tex]Volume = x(3-2x).(5-2x)\\\\Volume = (3x-6x^{2}).(5-2x)\\\\Volume = 3x(5-2x) - 6x^{2}(5-2x)\\\\Volume = 15x - 6x^{2} - 30x^{2} + 12x^{3}\\\\Volume = 12x^{3} -36x^{2} + 15x[/tex]

 Then,

To Find the derivative of the equation,

[tex]V = 12x^{3} -36x^{2} + 15x\\\\Differentiate\ with\ respect\ to\ x\ both\ sides,\\\\\dfrac{dv}{dx} = \dfrac{d(12x^{3} -36x^{2} + 15x)}{dx}\\\\V' = 36x^{2} - 72x+15[/tex]

The critical numbers by seeing where  V '  =  0,

[tex]= 36x^{2} -72x +15\\\\= 3 ( 12x^{2} - 24x +5 )\\[/tex]

By using the quadratic formula or your calculator to solve for  

x = 0.23, and 1.6

x = 1.6 is not in the domain since that would make one of our side lengths less than zero.  x  =  0.23

Plug x back into the equations to get the dimensions,

[tex]3-2x = 3- 2 \times -0.23 = 3+0.46 = 3.46\\5-2x = 5 - 2 \times -0.23 = 5+0.46 = 5.46[/tex]

Therefore, the dimension are  0.23 ft x 3.46 ft x  5.46 ft.

Hence, The largest volume of such a box is 4.345[tex]ft^{3}[/tex].

To know more about Dimension click the link given below.

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Answer:

21 hours

Step-by-step explanation:

After 2 hours the temperature has risen to 7°f

The time taken to rise to an additional 13°f can be calculated as follows

1 hour takes 3.5°f

13°f = 3.5×6

= 21 hours

Hence it would take 21 hours

Answer:

B

Step-by-step explanation:

Answer:

it's 0.625

Step-by-step explanation:

Answer:

1. m<a and m<h, m<e and m<d

2.m<a and m<c, m<b and m<d, m<e and m<g, m<f and m<h

3. m<a= 112

m<c=112

m<f=112

m<h=112

m<b=68

m<d=68

m<e=68

m<g=68

Answer: either I don't understand the question or its 72% and I'm fairly certain its 72%

Answer: y=36^(2)x*49

Step-by-step explanation: Graph.

Brainliest or a thank you if im right please :)) <3

Answer:

13 is c

14 is b

Step-by-step explanation:

Answer:

-1.5

Step-by-step explanation:

5x6=30

30-21=9

9/6=1.5

remember tht the answer is NEGATIVE,, thnk u hav a good nite

Hi!

[tex]1 \frac{2}{3} + 1 \frac{1}{2} = 1 \frac{4}{6} + 1 \frac{3}{6} = 2 \frac{7}{6} = 3 \frac{1}{6} [/tex]

Greetings!

Answer:

3.43%

Step-by-step explanation:

362-350=12

12:350*100 =

(12*100):350 =

1200:350 = 3.43

Answer:

38cm

Step-by-step explanation:

12.6 x 2= 25.2

6.4 x 2= 12.8

25.2 + 12.8= 38

Answer:

45 degrees

Step-by-step explanation:

The following shape is an octagon, having 8 sides and knowing that any regular polygon has an exterior angle value of 360 degrees, you can say 360/8 to find the measure of each exterior angle, leading to equal 45 degrees.

Hope it helped! (:

Answer:

9.42 cubic inches

Step-by-step explanation:

We are to find the volume of the cone.

The formula is given as:

1/3πr²h

From the question,

Diameter = 3 inches, Radius = D/2 = 3/2

r = 1.5 inches

h = 4 inches

Hence, the volume of the cone =

1/3 × π × 1.5² × 4

= 9.42 cubic inches

Therefore, the filter can hold 9.42 cubic inches of liquid without overflowing.

Answer:

(1,3)

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis, or when x is equal to 0).

We're given that this line contains the point (0,1). This tells us that the y-intercept (b) of the line is 1.  We're also given that this line has a slope (m) of 2. Plug these values into [tex]y=mx+b[/tex]:

[tex]y=2x+1[/tex]

Now, plug in all of the possible points to see which are solutions.

1) (1,3)

[tex]3=2(1)+1\\3=2+1\\3=3[/tex]

Because the left side of the equation is equal to the right, (1,3) also lies on this line.

2) (3,1)

[tex]1=2(3)+1\\1=6+1\\1=7[/tex]

Because the left side is not equal to the right, (3,1) does not lie on the line.

3) (2,2)

[tex]2=2(2)+1\\2=4+1\\2=5[/tex]

Because the left side is not equal to the right, (2,2) does not lie on the line.

4) (2,3)

[tex]3=2(2)+1\\3=4+1\\3=5[/tex]

Because the left side is not equal to the right, (2,3) does not lie on the line.

I hope this helps!

Answer:

3

Step-by-step explanation:

Considering she wore a black shirt 6 times in 20 days will give you the statistic of 3/10. If the question is about the next 10 days then she will wear 3 black shirts. (It's also 1/2 of the original question.)

Answer:

1:180

Step-by-step explanation:

We start by multiplying the 120 feet by 12 inches to get the height of the building in inches, which is 1440.

Then, we have a ratio of 8:1440, which simplifies to 1:180 when we divide 1440 by 8.

The required scale factor of the given model is 1/180.

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.

A building scale model is 8 inches tall. The original structure stands 120 feet tall.

Here 1 foot is equal to twelve inches which is given in the question.

As per the given situation, the required solution would be as :

Firstly we have to multiply 120 feet by 12 inches to obtain the building's height in inches, which is 1440.

The result is an 8/1440 ratio, which simplifies to 1/180 when 1440 is divided by 8.

Therefore, the required scale factor of the given model is 1/180.

Learn more about the Scale images here:

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Answer: x = 8.3334

Step-by-step explanation:

assuming im solving for x ??

(6x + 8) + (19x - 3) = 180

21x + 5 = 180

      - 5     - 5

21x = 175

/ 21   / 21

x = 8.3334

Answer:

Boys: 2/17

Girls: 4/17

Step-by-step explanation:

2 + 15 = 17 (to get the total number of boys in Sapphire's class)

4 + 13 = 17 (to get the total number of girls in the class)

The proportion is how many who are left handed over the total number of girls/boys. ^^

So, left-handed for boys = 2, which makes the proportion 2/17

And there are 4 left-handed girls, so the proportion is 4/17

Answer:

Jody has to pay $14.24 for total after splitting the tip amount with Karen.

Hope this helps!!!!!

Answer:

So  this is a negative slope remember this. We are going to use y = mx + b

m is the slope b is the y intercept. In this problem, the y intercept is 6.

The slope is -2;

Y = -2x + 6

Step-by-step explanation:

Answer:

$90.02

Step-by-step explanation:

Solve

Formula: Change money = paid money – bill. Paid money = change + bill.

Given: 2 buckets of baseballs that cost $19.49 each

A bat that cost $125.50, and 2 pairs of baseball socks that totaled $29.50

Tax on Alex's purchases equaled $16.

Paid with three $100 bills.

To find: How much change Alex received if he paid with three $100 bills

Total payment + Total Tax  -Total cost

19.49 + 125.50 + 29.50  = 174.49 (Don't add the $16 tax because that will be taken from the amount we pay)

∴, three 100 bills is 300

So, 300 - 174.49 = 109.51

109.51 - 16 = 90.51

90.51 - 0.49 = $90.02

Answer:

m<A=97

m<B=97

Step-by-step explanation:

m<A=m<B

Congruent angles and they are vertical angles. The other two are also the same because the angles given have the same degrees.

m<A is supplementary to 83 degrees

Supplementary angles are two angles that sum up to 180 degrees.

180-83=97

97 degrees is the answer for each missing angles.

Hello !

Answer:

[tex]\large\boxed{\sf Option\ 3 : 66cm}[/tex]

Step-by-step explanation:

The circumference of a circle is given by [tex]\sf C=2\times\pi\times r[/tex], where r is the radius.

Given :

Let's replace r with its value in the previous formula :

[tex]\sf C=2\times 3.14\times 10.5[/tex]

[tex]\sf C=65.94[/tex]

[tex]\boxed{\sf C\approx 66cm}[/tex]

Have a nice day

y=5x-3 I think so.....

Answer: n=-5/12

Step-by-step explanation: 1/3-3/4=-5/12

hoped this helped :))

Answer: n= 5/12

Step-by-step explanation: 13=+3413=n+3431​=n+43​13−34=+34−34

Hope this helps!

The shapes is the base of a cone is Circle.

A circle is often referred to as the locus of points drawn equidistant from the centre. The radius of a circle is the distance between its centre and its outer line. The diameter of a circle is the line that divides it into two equal sections and is equal to twice the radius.

A circle is a fundamental 2D form that is measured by its radius.

We have a Cone.

A Cone if compared as two dimensional then a cone have have Triangular shape.

and, the base of cone have a circular shape.

Thus, the shape of base of cone is Circle.

Learn more about Circle here:

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