A certain number is increased by 30 and the result is divided by two. The number obtained is three times the original number. Find the number.
Plss show working​

Answer:

x = 5 and x = 11

Step-by-step explanation:

The segment through the center is a perpendicular bisector of the chord, thus

5x - 6 = 2x + 9 ( subtract 2x from both sides )

3x - 6 = 9 ( add 6 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

-------------------------------------------------------

Tangents to a circle from an external point are congruent, thus

4x - 1 = 3x + 10 ( subtract 3x from both sides )

x - 1 = 10 ( add 1 to both side

Answer:

x = 5 and x = 11

Step-by-step explanation:

The segment through the centre is a perpendicular bisector of the chord, thus

5x - 6 = 2x + 9 ( subtract 2x from both sides )

3x - 6 = 9 ( add 6 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

-------------------------------------------------------

Tangents to a circle from an external point are congruent, thus

4x - 1 = 3x + 10 ( subtract 3x from both sides )

x - 1 = 10 ( add 1 to both sides )

x = 11

Answer:

Step-by-step explanation:

let the number be x

x multiplied by x = [tex]x^{2}[/tex]

Adding 4 to the result

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

Hope this helps

plz mark as brainliest!!!!!

Answer:

"subset"

Step-by-step explanation:

The "set within a set" is called a "subset."

Answer:

The sum −3 is an indication that Sally is 3 feet below her initial position.

Step-by-step explanation:

Represent the distances going up (ascend) as positive and distances going down (descend) as negative so that the sum is:

224 + (-131) + 67+ (-163)

Add by using the commutative property:

224 + 67 + (-131) + (-163) = 291

The sum −3 is an indication that Sally is 3 feet below her initial position.

Answer:

x=44

Step-by-step explanation:

Pretty straightforward!

4-x/5 +x+2/3=6

3(4-x) + 5(x+2) = 90  (Multiply both sides of the equation by 15, a multiple of              both 5 and 3)

12-3x+5x+10=90 (Use Distributive property to multiply across parentheses)

-3x+5x=90-12+10 (Bring like terms together/Signs change when moved to the other side)

2x=88

x=44

Thank you for your time!

Answer: x=44

Step-by-step explanation: Pretty straightforward!

4-x/5 +x+2/3=6

3(4-x) + 5(x+2) = 90  (Multiply both sides of the equation by 15, a multiple of              both 5 and 3)

12-3x+5x+10=90 (Use Distributive property to multiply across parentheses)

-3x+5x=90-12+10 (Bring like terms together/Signs change when moved to the other side)

2x=88

x=44

Thank you for your time!

Answer: 169.2cm

Step-by-step explanation:

From the question, we are informed that three equal-sized cardboard boxes are stacked on top of each other and that each box is 56.4 cm in height.

To get the combined height of the 3 stacked boxes, we multiply 56.4cm by 3. This will be:

= 56.4cm × 3

= 169.2cm

Answer:

Read Exp:

Step-by-step explanation:

Area = 3.14 x r^2

I've Included a picture to tell you how to get the diameter as well as the circumference.

Answer:

formula is πr² ( pi x radius squared)

Step-by-step explanation:

the value of π is 3.142...

multiply this value with the squared radius of the circle and you'll get your answer.

For example:

we have a circle with diameter 5

so,  π x 5² = 3.142 x 25 = 78.5

Answer:

Please refer to the attached diagram for answer.

Step-by-step explanation:

Upper-left coordinates on a rectangle are (-1, 4)

Upper-right coordinates are (3, 4)

Perimeter of rectangle = 24 units

To find:

To draw the rectangle on the coordinate plane.

Solution:

Let the rectangle be ABCD.

So, sides AB  = CD and BC = DA

Let Point A has coordinates (-1, 4).

And upper right coordinates will be adjacent to A.

So, let Point B (3, 4).

Let us find the distance between A and B by distance formula:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where,

[tex]x_2 = 3\\x_1 = -1\\y_2 = 4\\y_1 = 4[/tex]

[tex]AB = \sqrt{(3-(-1))^2+(4-4)^2}\\\Rightarrow AB = \sqrt{(4)^2+(0)^2}\\\Rightarrow AB = 4[/tex]

AB = 4 = CD

Perimeter of rectangle = Sum of all four sides = 2 (AB+DA) = 24

[tex]2 \times 4 + 2DA = 24\\\Rightarrow 2DA=24-8\\\Rightarrow 2DA=16\\\Rightarrow DA =8\ units[/tex]

As it is a rectangle, its adjacent sides will be perpendicular to each other.

When we move from A to B only x coordinate is changing and it has changed by  4 (3- (-1) ) units. (Found by subtracting the x coordinates of the two points.)

Similarly, when we will move from D to A, only y coordinate will change by 8 units. (D is lower left coordinate so add 8 to y)

[tex]\Rightarrow y + 8 = 4 \Rightarrow y =-4[/tex]

[tex]x[/tex] coordinate will be same as that of A i.e. -1.

So, D will be (-1, -4)

Similarly, when we will move from C to B, only y coordinate will change by 8 units. (C is lower right coordinate so add 8 to y)

[tex]\Rightarrow y + 8 = 4 \Rightarrow y =-4[/tex]

[tex]x[/tex] coordinate will be same as that of B i.e. 3.

So, C will be (3, -4).

Now, let us draw

A(-1, 4)

B(3, 4)

C (3, -4)

D(-1, -4)

Please refer to the attached diagram for answer.

Answer:

A(-1, 4) B(3, 4)C (3, -4)D(-1, -4)

Step-by-step explanation: Brainliest plus-size

Answer:

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

km

k= -3

m= 6

km = -3*6

km = -18

Answer:

The answer is -18.

Step-by-step explanation:

k×m

-3×6

-18

Answer:

The answer is below

Step-by-step explanation:

Let the money charged to wrap a small gift be $x and the money charged to wrap a large gift be $y. The cost of wrapping 14 small gifts and 15 large gifts is $205, It can be represented by the equation:

14x + 15y = 205                 (1)

Also, the cost of wrapping 47 small gifts and 45 large gifts is $640. It can be represented by the equation:

47x + 45y = 640                 (2)

Solving equation 1 and equation 2 simultaneously. Multiply equation 1 by 3 and subtract from equation 2:

5x = 25

x = 25/5 = 5

x = 5

Put x = 5, in equation 1 and solve:

14(5) + 15y = 205

15y + 70 = 205

15y = 205 - 70

15y = 135

y = 135 / 15

y = 9

This means that the money charged to wrap the small gift is $5 and to wrap the large gifts is $9

Answer:

y = [tex]\frac{21}{4}[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{6}[/tex] y - [tex]\frac{1}{2}[/tex] = 3 - [tex]\frac{1}{2}[/tex] y

Multiply through by 6 to clear the fractions

y - 3 = 18 - 3y ( add 3y to both sides )

4y - 3 = 18 ( add 3 to both sides )

4y = 21 ( divide both sides by 4 )

y = [tex]\frac{21}{4}[/tex] = 5.25

Answer:

B; C; A; B

Step-by-step explanation:

So, let's go through each of the choices.

So we know that one of the angles is 60 degrees.

I) The triangle is scalene.

This might be true. Since there are 180 degrees in a triangle, and we know 60, that leaves 120 degrees. Anything two combinations of different values that add up to 120 will make the triangle scalene. However, if the two values are the same (e.g. 60;60), they it's not scalene. Thus, this might be true.

II) The other two angles add up to 120.

This must be true. The interior angles sum of a triangle is 180. Since we already know one is 60, then the other two must add up to be 180-60 or 120.

III) The other two angles are obtuse.

This cannot be true. We know that there is only 120 degrees left in the triangle. Obtuse angles are greater than 90 degrees.

Therefore, if we subtract the minimum: 120-90, we will get at most 30 left. This is not enough for another obtuse angle. The most we can have is one obtuse angle and two acute angles.

IV) The triangle is right-angled.

This might be true. Since there are 120 degrees left, the other two degrees may be 90 and 30, given us 30-60-90. This, however, doesn't have to be it. So, this statement may be true.

Answer:

Option a

4 is correct answer

hope it helped you:)

Answer:

1

Step-by-step explanation:

Answer: (22)(39) = 858.

Step-by-step explanation:

Product of a number simply means that one has to multiply the numbers that are given. For example, if a student is told to find the product of 2 and 5, it simply means that 2 × 5 = 10.

Regarding the above question, the product of 22 and 39 is represented by: (22)(39) = 858. It should be noted that 22 × 39 = 858

Answer:

-15.

Step-by-step explanation:

G(-5) = 2(-5) - 1

= -10 - 1

= -11

H(-11) = -11 - 4

= -15

Hope this helps!

Answer:

h(g(-5))= -15

Step-by-step explanation:

We are asked to find h(g(-5)).

First, we must find g(-5).

We know that g(x)=2x-1. Therefore, to find g(-5), we must plug -5 in for x.

g(x)= 2x-1

g(-5)= 2(-5) -1

Multiply 2 and -5.

g(-5)= -10 -1

Subtract 1 from -10.

g(-5)= -11

Now, we can substitute -11 in for g(-5).

h(g(-5)

g(-5)= -11

h(-11)

Now, we must find h(-11).

We know that h(x)= x-4. So, we can plug -11 in for x.

h(x)= x-4

h(-11)= -11-4

Subtract 4 from -11.

h(-11)= -15

h(g(-5)=  -15

Answer:

a(4+5a+2a+a) or

a(5a+2a+a+4)

Step-by-step explanation:

You could take out one A from each number since they all have an A in them. You could reorganize it and put it in numerical order. Hope this helped :)

Answer:

Step-by-step explanation:

c...................

Answer:

The 90% confidence​ interval is (-1.987, -1.320).

Step-by-step explanation:

The data provided is:

Sleep without        Sleep using

    the drug           the drug d=without-with

         2.5                       4.3                  -1.8

         2.7                       4.2                  -1.5

         3.8                       5.0                  -1.2

         3.8                       6.2                 -2.4

          1.8                       2.5                 -0.7

         4.7                        7.1                 -2.4

         4.8                        7.1                 -2.3

         2.7                        3.3                 -0.6

         1.8                        3.5                 -1.7

        2.2                        4.3                 -2.1

        3.6                        4.3                 -0.7

        5.3                        7.0                  -1.7

        5.2                        7.6                 -2.4

Compute the sample mean and sample standard deviation:

[tex]\bar d=\frac{1}{n}\sum d=\frac{1}{13}\times [(-1.8)+(-1.5)+(-1.2)+...+(-2.4)]=-1.654\\\\S_{d}=\sqrt{\frac{1}{n-1}\sum [d-\bar d]^{2}}=0.6753[/tex]

The degrees of freedom of the test is:

df = n - 1 = 13 - 1 = 12

Compute the critical value of t for 90% confidence​ level and 12 degrees of freedom as follows:

[tex]t_{\alpha/2, (n-1)}=t_{0.10/2, 12}=1.782[/tex]

Compute the 90% confidence​ interval as follows:

[tex]\bar d-t_{\alpha/2, (n-1)}\cdot\frac{S_{d}}{\sqrt{n}}<\mu_{d}<\bar d+t_{\alpha/2, (n-1)}\cdot\frac{S_{d}}{\sqrt{n}}[/tex]

[tex]-1.645-[1.782\cdot\frac{0.6753}{\sqrt{13}}]<\mu_{d}<-1.645+[1.782\cdot\frac{0.6753}{\sqrt{13}}]\\\\-1.645-0.334<\mu_{d}<-1.654+0.334\\\\-1.988<\mu_{d}<-1.320[/tex]

Thus, the 90% confidence​ interval is (-1.987, -1.320).

Answer: x=24

Step-by-step explanation:

The four angles form a linear pair and a linear pair is basically a line which means it forms 180°.

(x-5)+(3x-1)+(2x-6)+(2x)=180

Take off parentheses

x-5+3x-1+2x-6+2x=180

Move like terms together

x+3x+2x+2x-5-1-6=180

Combine like terms

8x-12=180

Add 12 on both sides

8x-12+12=180+12

8x=192

Divide 8 on both sides

8/8 x=192/8

x=24

Hope this helps!! :)

Please let me know if you have any question

Answer:

98.25

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Convert [tex]27^{\frac{4}{3} }[/tex]

[tex]27^{\frac{4}{3} }[/tex] = ∛(27⁴) = 81

Step 2: Convert [tex]32^{0.8}[/tex]

[tex]32^{0.8}[/tex] = 16

Step 3: Convert [tex]0.8^{-1}[/tex]

[tex]0.8^{-1}[/tex] = 1.25

Step 4: Combine

81 + 16 + 1.25

97 + 1.25

98.25

Answer:

[tex]E. \frac{5}{9} < \frac{4}{7} < \frac{2}{3}[/tex]

Step-by-step explanation:

Decimals are great for when you are dealing with money and want to round up, and fractions are used when baking (such as need 1/4 or a half cup of something)

Answer:

A

Step-by-step explanation:

The range is the y-values, so it’s all numbers less than or equal to 4.

The domain is the x-values, so it’s all real numbers.

Answer:

-x + 2y + 1 > 0

Step-by-step explanation:

Let's find the equation of the dashed line first. From the graph, we can see that it has a slope of 1/2 and a y-intercept of -1/2 so using slope-intercept form, the equation of the line is y = 1/2x - 1/2. Since the line is dashed and not solid, we know that we will use either < or > instead of ≤ or ≥, and because we can see that the shaded region is above the dashed line, we know that the linear equation is y > 1/2x - 1/2. However, we want the answer to be in the form ax + by + c > 0 where a, b, and c are integers so therefore:

y > 1/2x - 1/2

= 2y > x - 1

= -x + 2y + 1 > 0

A linear inequality is an expression which make comparison between linear expressions using inequalities. The linear inequality of the graph is: [tex]-x + 2y +1 > 0[/tex]

First, we calculate the slope of the dashed line using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Two points on the graph will be:

[tex](x_1,y_1) = (1,0)[/tex]

[tex](x_2,y_2) = (3,1)[/tex]

The slope (m) is:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{1-0}{3-1}[/tex]

[tex]m = \frac{1}{2}[/tex]

The equation of the line is calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

So, we have;

[tex]y = \frac12(x - 1) + 0[/tex]

[tex]y = \frac12(x - 1)[/tex]

Multiply through by 2

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

Now, we convert the equation to an inequality.

The line on the graph is a dashed line. This means that the inequality is either > or <. Also, the upper region of the graph that is shaded means that the inequality  is >.

So, the equation becomes

[tex]2y > x-1[/tex]

Rewrite as:

[tex]-x + 2y +1 > 0[/tex]

So, the linear inequality is: [tex]-x + 2y +1 > 0[/tex]

Learn more about linear inequality at:

https://brainly.com/question/19491153

Answer: -a+1

Step-by-step explanation:

 -4a+8+3a-9

=-4a+3a+8-9

=(-4a+3a)+(8-9)

=-a+1

Hope this helps!! :)

Answer: -a -1

Step-by-step explanation:

a) La utilidad marginal al precio de $ 5 es 1.091.

b) La utilidad marginal al precio de $ 10 es 0.662.

c) La utilidad marginal al precio de $ 15 es 0.402.

La utilidad marginal es la derivada de la función utilidad. Si [tex]r(p) = 2\cdot p\cdot e^{-0.1\cdot p}[/tex], entonces la función de utilidad marginal es la siguiente:

[tex]r'(p) = \frac{dr}{dp}[/tex]

[tex]r'(p) = 2\cdot e^{-0.1\cdot p}-0.2\cdot e^{-0.1\cdot p}[/tex] (1)

Ahora procedemos a evaluar (1) para cada valor citado en el enunciado:

a) $ 5

[tex]r'(5) = 2\cdot e^{-0.1\cdot 5}-0.2\cdot e^{-0.1\cdot 5}[/tex]

[tex]r'(5) = 1.091[/tex]

La utilidad marginal al precio de $ 5 es 1.091.

b) $ 10

[tex]r'(10) = 2\cdot e^{-0.1\cdot 10}-0.2\cdot e^{-0.1\cdot 10}[/tex]

[tex]r'(10) = 0.662[/tex]

La utilidad marginal al precio de $ 10 es 0.662.

c) $ 15

[tex]r'(15) = 2\cdot e^{-0.1\cdot 15}-0.2\cdot e^{-0.1\cdot 15}[/tex]

[tex]r'(15) = 0.402[/tex]

La utilidad marginal al precio de $ 15 es 0.402.

Invitamos cordialmente a ver esta pregunta sobre utilidad marginal: https://brainly.com/question/25517381

Answer:

Step-by-step explanation:

3[tex]x^{2}[/tex]+x-3= [tex]x^{2}[/tex] - 5x

combine like terms

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

x -5x = -4x

then combine 4[tex]x^{2}[/tex] and -4x