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3. x = 45

4. 73°

Step-by-step explanation:

3. The sum of the interior angles of a pentagon is 540° so

90° + 112° + 2x + (2x + 10) + 148° = 540°

Simplifying this, we get

4x + 360 = 540 => 4x = 180 or x = 45

4. The sum of the interior angles of a pentagon is 540° which means that the unknown interior angle is 107°. This angle is a supplementary angle to [tex]\angle{A}[/tex] so [tex]\angle{A}[/tex] is

180° - 107° = 73°.

Answer:

f(x) = -3x^2 + 10x + 3

Step-by-step explanation:

(0,3) (2,11)(3,6)

Using the form ax^2 + bx + c = y

From the first set we know that c = 3

Write an equation for the last two sets

x=2; y=11

a(2^2) + b(2) + 3 = 11

4a + 2b = 11 - 3

4a + 2b = 8

simplify divide by 2

2a + b = 4

and

x=3, y=6

9a + 3b + 3 = 6

9a + 3b = 6 - 3

9a + 3b = 3

simplify divide by 3

3a + b = 1

:

Use elimination to find a

3a + b = 1

2a + b = 4

--------------subtracting eliminate b

a = -3

Find b using the equation 2a + b = 4

2(-3) + b = 4

b = 4 + 6

b = 10

:

The equation: f(x) = -3x^2 + 10x + 3

Answer:

A.

Step-by-step explanation:

Step-by-step explanation:

First let solve the inequality

[tex]5 {x}^{2} + 2x - 3 < 0[/tex]

Factor by grouping

[tex]5 {x}^{2} + 5x - 3x - 3 < 0[/tex]

[tex]5x(x + 1) - 3(x + 1)[/tex]

So the factor are

[tex](5x - 3)(x + 1)[/tex]

So the factor are

[tex]x = \frac{3}{5} [/tex]

and

[tex]x = - 1[/tex]

Solutions to a quadratic can be represented by a absolute value equation because remeber quadratics

creates 2 roots and/or double roots.

The inequality

[tex] |x - b| < c[/tex]

works as

b is the midpoint between 2 roots. And c is the

[tex] |x + b| = c[/tex]

We know that the midpoint between both roots is-1/5.

so

[tex] |x - ( - \frac{1}{5} )| < c[/tex]

[tex] |x + \frac{1}{5} | < c[/tex]

Let use roots 3/5

[tex] | \frac{3}{5} + \frac{1}{5} | = \frac{4}{5} [/tex]

-1 works as well.

[tex] | - 1 + \frac{1}{5} | = | - \frac{4}{5} | = \frac{4}{5} [/tex]

So the absolute value equation is

[tex] |x + \frac{1}{5} | < \frac{4}{5} [/tex]

Answer:

2

Step-by-step explanation:

=3+5×5-25+3-4

=3+25-25+3-4

=28-22-4

=28-26

=2

Answer:

2

Step-by-step explanation:

3 + 5 * 5 - 50 / 2 + 3 - 4

3 + (5 * 5) - 50 / 2 + 3 - 4  => Multiplication what ever comes first

3 + 25     (-50 / 2) + 3 - 4  => Division left to right

(3 + 25)     - 25  +( 3 - 4)  => Addition what ever comes first

28  - 25 - 1 => Substraction  left to right

2

Leave comment if you're curious.

Depending on the length of the two sides of the triangle the length could be smaller than 1.

The answer that is not true is :

B. It is always greater than 1

Answer:

15% for both games

Step-by-step explanation:

30%÷2=15%

Answer:

(x-10)/4

Step-by-step explanation:

10 less than x means,

x - 10

and the divide by 4.

=> (x-10)/4

Answer:

x-10/4

10 less than x

x-10

divided by 4

/4

Answer:

-6

x - 6 is the equation, (unless there was a y, and it pasted wrong)

Step-by-step explanation:

You do additive property of equality by adding 1 to both sides.

-6x - 1 = 35

= -6x - 1 + 1 = 35 + 1

= -6x = 36

Division property of equality by dividing both sides by -6 or 6

= -6/-6x = 36/-6

= 1x = -6

x = -6

Answer:

Step-by-step explanation:

60  

600

Answer:

B

Step-by-step explanation:

The lateral area of the regular pyramid shown in the diagram is 540 unit². Hence, option B is the right choice.

The area of a figure is the two-dimensional space enclosed within the boundary of that figure.

In the question, we are asked to find the lateral area of the regular pyramid shown.

A regular pyramid is one with all lateral faces the same.

In the given diagram, the pyramid shown has a hexagonal base. So it has 6 equal lateral faces.

Each lateral face is a triangle, with the base as 12 units and height as 15 units.

Thus, the area of one lateral face = (1/2)*12*15 units² = 90 units².

Thus, the total lateral surface area = Lateral surface area of one lateral face*number of lateral faces = 90 units²*6 = 540 units².

Thus, the lateral area of the regular pyramid shown in the diagram is 540 unit². Hence, option B is the right choice.

Learn more about lateral surface area at

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You are falling by [tex]32[/tex],

[tex]128, 128 - 32, 128 - 32\cdot2,\dots[/tex]

In general your sequence is defined as,

[tex]a_n=128-32\cdot n[/tex] where [tex]0\leq n \lt\infty[/tex].

The question is at which [tex]n[/tex] does the value [tex]a_n=0[/tex].

If you divide [tex]128[/tex] with [tex]32[/tex] you get the number of steps needed to stuff [tex]128[/tex] with [tex]32[/tex], [tex]4[/tex].

If you plug in [tex]n=4[/tex], you get [tex]a_4=128-32\cdot4[/tex], since [tex]32\cdot4=128[/tex] you get [tex]a_4=0[/tex].

The zero turn of the arithmetic sequence is thus at [tex]n=4[/tex].

Hope this helps :)

Answer:

To find this answer, you would need to find how many miles 1 gallon of gas will take them. To find this, you would do 290÷8=36.25. So with this information, you will be able to find out how much gas it would take to travel 400 miles. You would do 400÷36.25=11.03. 11.03 would be how many gallons of gas is used to travel 400 miles. Hope this helps! :)

Step-by-step explanation:

Answer:

(2,3.5)

Step-by-step explanation:

B=(1,2)

A=(3,5)

Answer:

Step-by-step explanation:

Answer:

B) Both functions have a y-intercept of -2.

Step-by-step explanation:

Hi there!

A) Both functions are always increasing.

⇒ False

Let's first take a look at the given equation, [tex]y=3x-2[/tex]. This is a linear equation, and it is organized in slope-intercept form: [tex]y=mx+b[/tex]. m is the slope and b is the y-intercept. When m is positive, it is always increasing.

In [tex]y=3x-2[/tex], 3 is m, and because it's positive, this line is always increasing on a graph.

However, when we take a look at the given graph, this isn't the case. It is decreasing for values of x below 0 (on the left side of the y-axis).

B) Both functions have a y-intercept of -2.

⇒ True

In the given equation [tex]y=3x-2[/tex], this is true. -2 is the y-intercept.

On the given graph, we can see that the graph intercepts the y-axis at -2, so this is also true for the graph.

C) Both functions are symmetric about the y-axis.

⇒ False

The given graph is symmetric about the y-axis, but the line is not. Any line that would be symmetric about the y-axis would be in the form [tex]y=b[/tex], which isn't the case here with [tex]y=3x-2[/tex]. [tex]y=3x-2[/tex] has a slope.

D) Both functions are linear relationships.

⇒ False

Sure, [tex]y=3x-2[/tex] is a linear equation, making it a line, but not the given graph. The graph does not resemble a straight line, so it is not a linear relationship.

I hope this helps!

Answer:

Concept:

Here, we need to know the idea of the circle equation.

Circle equation: (x - h)² + (y - k)² = r²

(h, k) = center

r = radius

x = variable

y = variable

Solve:

Given expression

(x - 3)² + y² = 9

Find the point of the center

(h, k) = [tex]\boxed{(3,0)}[/tex]

Find the length of the radius

r² = 9

[tex]\boxed{r=3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

(2x3) x 4= 2 (3x4)

9514 1404 393

Answer:

  y = 10

Step-by-step explanation:

Put -3 where x is and solve for y.

  4(-3) +3y = 18

  -4 +y = 6 . . . . . . . divide by 3

  y = 10 . . . . . . . . . add 4

Answer:

It is 9214.2

Step-by-step explanation:

[tex](125 + 47 - 2.5) \div 140 + 37 \times 249[/tex]

first solve the bracket:

[tex] = (169.5) \div 140 + 37 \times 249[/tex]

form brackets of division and multiplication:

[tex] = (169.5 \div 140) + (37 \times 249)[/tex]

solve the brackets:

[tex] = 1.211 + 9213[/tex]

then add:

[tex] = 9214.211[/tex]

Answer:

example of Analog computer=

Operational amplifiers

Answer:

there are many types eg cosmic engine

Answers and Step-by-step explanation:

Question 8:

Since angle BCD is opposite angle DAB, this means that they are similar angles as the shape is a parallelogram, and so BCD is 115 degrees, or answer D

Question 3:

We can use process of elimination on this question - The first choice is all squares are rhombuses, which is true. The second question is all rectangles are squares, which is not true, therefore the answer is B

Question 4:

m angle 2 is equal to 106, as it is similar to question 8, and angle 3 is equal to 360 (the total degrees of the shape) - 106 - 106, then divided by 2 and divided by 2 again.

This will equal to angle 3 being 37 degrees, and the answer will be C

Question 5:

We can draw a rectangle from this graph. We can also tell that, in theory, the diagonals are the same, that rules out answer B, and also 5x-5 = x+11

We can then find out x.

+5 on both sides

5x = x+16

-x on both sides

4x = 16

x = 4.

Therefore, each of the sides will be 4+11 = 15, and the answer being C

Answer:

(3 ± √23 * i) /4

Step-by-step explanation:

To solve this, we can apply the Quadratic Equation.

In an equation of form ax²+bx+c = 0, we can solve for x by applying the Quadratic Equation, or x = (-b ± √(b²-4ac))/(2a)

Matching up values, a is what's multiplied by x², b is what's multiplied by x, and c is the constant, so a = 2, b = -3, and c = 4

Plugging these values into our equation, we get

x = (-b ± √(b²-4ac))/(2a)

x = (-(-3) ± √(3²-4(2)(4)))/(2(2))

= (3 ± √(9-32))/4

= (3 ± √(-23))/4

= (3 ± √23 * i) /4

Answer:

sum is 19,999,998 and difference is 0

please brainleist my answer

Answer:

Step-by-step explanation:

The greatest number of 7-digits number is 9,999,999

The least number of 7-digits number........is 1,000,000

Their sum......................................................... is 10,999,999

Their différence ............................................. is  8,999,999

Answer:

4

Step-by-step explanation:

because BC=CD as it is parallel that means all the sides are equal

The value of CD is 20/3.

The correct option is (A).

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

In ACB and ECD,

angle CAB= angle DEC

angle CBA= angle EDC

angle DCE = angle ACB

By, AA similarity criteria,

ΔACB~ΔECD

Now,

AC/CE= BC/CD

3/5=4/CD

CD= 20/3

Learn more about similarity property here:

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