Angles A and B are complementary. The measure of angle A
is yº. What is the measure of angle B?

Answer:

[tex]a+b+c=10[/tex]

Step-by-step explanation:

We are given that the graph of the equation:

[tex]y=ax^2+bx+c[/tex]

Passes through the three points (0, 5), (1, 10), and (2, 19).

And we want to find the value of (a + b + c).

First, since the graph passes through (0, 5), its y-intercept or c is 5. Hence:

[tex]y=ax^2+bx+5[/tex]

Next, since the graph passes through (1, 10), when x = 1, y = 10. Substitute:

[tex](10)=a(1)^2+b(1)+5[/tex]

Simplify:

[tex]5=a+b[/tex]

The point (2, 19) tells us that when x = 2, y = 19. Substitute:

[tex](19)=a(2)^2+b(2)+5[/tex]

Simplify:

[tex]14=4a+2b[/tex]

This yields a system of equations:

[tex]\begin{cases} 5 = a + b \\ 14 = 4a + 2b\end{cases}[/tex]

Solve the system. We can do so using elimination (or any other method you prefer). Multiply the first equation by negative two:

[tex]-10=-2a-2b[/tex]

Add the two equations together:

[tex](-10)+(14)=(-2a+4a)+(-2b+2b)[/tex]

Combine like terms:

[tex]4 = 2a[/tex]

Hence:

[tex]a=2[/tex]

Using the first equation:

[tex]5=(2)+b\Rightarrow b=3[/tex]

Therefore, our equation is:

[tex]y=2x^2+3x+5[/tex]

Thus, the value of (a + b + c) will be:

[tex]a+b+c = (2) + (3) + (5) = 10[/tex]

Answer:

So required ans is 5*11+10=65 6x-41=25

Step-by-step explanation:

You can do as,

5x+10+6x-41=90

11x-31=90

11x=31+90

11x=121

x=121/11

x=11

Answer:

10

Step-by-step explanation:

f ( 1 ) = 18

First term ( a ) = 18

f ( n + 1 ) = f ( n ) - 2

When, n = 1

f ( 1 + 1 ) = f ( 1 ) - 2

f ( 2 ) = 18 - 2

f ( 2 ) = 16

f ( 2 ) - f ( 1 )

= 16 - 18

= - 2

Common difference ( d ) = - 2

f ( 5 )

= a + 4d

= 18 + 4 ( - 2 )

= 18 - 8

= 10

Given:

Consider the equation is:

[tex]\log_81000=\log_210[/tex]

To prove:

[tex]\log_81000=\log_210[/tex] by using the properties of logarithms.

Solution:

We have,

[tex]\log_81000=\log_210[/tex]

Taking left hand side (LHS), we get

[tex]LHS=\log_81000[/tex]

[tex]LHS=\dfrac{\log 1000}{\log 8}[/tex]                  [tex]\left[\because \log_ab=\dfrac{\log_x a}{\log_x b}\right][/tex]

[tex]LHS=\dfrac{\log (10)^3}{\log 2^3}[/tex]

[tex]LHS=\dfrac{3\log 10}{3\log 2}[/tex]                   [tex][\because \log x^n=n\log x][/tex]

[tex]LHS=\dfrac{\log 10}{\log 2}[/tex]

[tex]LHS=\log_210[/tex]                    [tex]\left[\because \log_ab=\dfrac{\log_x a}{\log_x b}\right][/tex]

[tex]LHS=RHS[/tex]

Hence proved.

Answer:

A

Step-by-step explanation:

First, the list of congruence theorems are:

SSS

SAS

ASA

AAS

HL

SSA is not on the list, so we can cross that out

Next, ASA implies that two angles are congruent, but we only know that one pair of angles (the right angles) are congruent, so we can cross that out

After that, the angle is not connecting the congruent sides, so D is not an option

Finally, we know that the longest sides (AD / AC) are congruent to each other, one other pair of legs/sides are congruent, and the triangles are both right triangles. Therefore, we can apply HL here

Answer:

108

Step-by-step explanation:

Surface area = total area of net

The net is made up of 2 unique shapes

A square with a side length of 6

The area of a square can be calculated by squaring the side length

6^2 = 36

The area of the square = 36

The net is also made up of 4 triangles

The triangles have a base length of 6 and a height of 6

The area of a triangle can be calculated by using the formula A = (bh) / 2

Where b = base length and h = height

If the triangles have a base length of 6 then b = 6 and if they have a height of 6 then h = 6

So A = 6*6/2

6 * 6 = 32

32/2 = 18

We then multiply that by 4 to get the area of all four triangles

18 * 4 = 72

Finally we add the areas together

72 + 36 = 108

The surface area is 108

Explanation:

The adjacent angle to the right of the (6x+1) angle is 180-(6x+1). Simply subtract it from 180 to get its supplementary counterpart.

The three inner angles of any triangle must add to 180, so,

(inner angle 1) + (inner angle 2) + (inner angle 3) = 180

[ 180-(6x+1) ] + (79) + (2x+10) = 180

180 - 6x - 1 + 79 + 2x + 10 = 180

(-6x+2x) + (180-1+79+10) = 180

-4x+268 = 180

-4x = 180 - 268

-4x = -88

x = -88/(-4)

x = 22

Answer:

x = 22

Step-by-step explanation:

2x + 10 + 79 = 6x + 1

Think alternate interior angles

2x + 10 + 79  makes up one of the alternate interior angles

6x + 1 is the other.

Combine like terms.

Subtract 2x both sides.

Subtract 1 from both sides.

Divide by 4 both sides.  

Answer:

Step-by-step explanation:

With some research I found that the medians (QK, RJ, and SI) are broken into 2:1 ratios.

So what this means is that QD is twice as long as DK.

QD = 2DK

QD = 2 * 6.5

QD = 13

Answer:

421

Step-by-step explanation:

5894 divided by 14 in decimal = 421 • 5894 divided by 14 in fraction = 5894/14• 5894 divided by 14 in percentage= 42100%

YOUR WELCOME :)))

Answer:

i think 5 is the answer not sure check with other helpers or brainer

Step-by-step explanation:

Answer:

not sure but good luck

Step-by-step explanation:

:))))

Answer:

4c² + 11cd + 5d

Step-by-step explanation:

(–4c2 + 7cd + 8d) + (–3d + 8c2 + 4cd)

-4c² + 7cd + 8d - 3d + 8c² + 4cd (opening bracket)

8c²-4c²+7cd + 4cd + 8d - 3d

= 4c² + 11cd + 5d

Answer:

hjjjnnnhjjjjj

Step-by-step explanation:

answer is d

Answer:

It's all integers x such that -1<=x<=2.

Step-by-step explanation:

The domain is the x values for which the relation exists.

Lets read from left to right.

First point I see from left exists at x=-1, next one at x=0, then x=1, and finally at x=2.

So it's all integers x such that -1<=x<=2.

*<= means less than or equal to

Answer:

Question 10:

Answer: b.

[tex]{ \tt{f(x) = 5 {x}^{2} + 9x - 4}} \\ { \tt{g(x) = - {8x}^{2} - 3x - 4 }}[/tex]

(f + g)x, add f(x) and g(x):

[tex]{ \tt{(f + g)x = (5 - 8) {x}^{2} + (9 - 3)x - 4 - 4}} \\ { \tt{(f + g)x = - 3 {x}^{2} + 6x - 8}}[/tex]

Question 11:

Answer: a.

In relation with solution of question 10, same procedure:

[tex]{ \tt{(f - g)x = - 3 {x}^{3} + (1 - 2) {x}^{2} + ( - 3 - 4)x + 9 - ( - 9)}} \\ { \tt{(f - g)x = - 3 {x}^{3} - {x}^{2} - 7x + 18 }}[/tex]

Answer:

Population of town in 2020 = 4626 (Approx.)

Step-by-step explanation:

Given:

Population of town in 2000 = 12,910

Decrease rate = 5% = 0.05 yearly

Find:

Population of town in 2020

Computation:

Number of year = 20 years

Population of town in 2020 = Population of town in 2000[1-r]ⁿ

Population of town in 2020 = 12,910[1-0.05]²⁰

Population of town in 2020 = 12,910[0.95]²⁰

Population of town in 2020 = 12,910[0.3584]

Population of town in 2020 = 4625.944

Population of town in 2020 = 4626 (Approx.)

Answer:

The population is 4628.

Step-by-step explanation:

Population in 2000 = 12910

Rate of decrease = 5 %

Time, t = 2020 - 2000 = 20 years

Let the population is P.

Use the formula

[tex]P = Po\left ( 1-\frac{r}{100} \right )^t\\\\P = 12910\left ( 1-0.05 \right )^2\\\\P = 4628[/tex]

Answer:

y>1

Step-by-step explanation:

7×(15+7-4+(x+y×38))^3 when x = 4 and y = 9

7×(15+7-4+(4+9×38))^3

=> 7×(15+7-4+(4+342))^3

=> 7×(15+7-4+346)^3

=> 7×364^3

=> 7×48228544

=> 337599808

Answer:

it doesn't exist

Step-by-step explanation:

the expression 0×7/11​ is equivalent to 0. 1/0 isn't possible, so its reciprocal doesn't exist.

Answer:

Following are the responses to the given question:

Step-by-step explanation:

[tex]\to y=(\frac{1}{2})(x-4)(x+4)\\\\\to y=(\frac{1}{2}) (x^2-16)\\\\\to y=(\frac{1}{2})(x-0)^2-8\\\\vertex \to (0,-8)[/tex]

The general x-intercept parabola equation [tex]y=k(x-4)(x+4)[/tex]

Parabola crosses the dot (2,-12)

[tex]\to k(2-4)(2+4)=-12\\\\\to k(-2)(6)=-12\\\\\to -12k=-12\\\\\to k=\frac{-12}{-12}\\\\\to k=1[/tex]

The parabolic equation which crosses the position [tex](2,-12)[/tex] is[tex]y=(x-4)(x+4)[/tex]

[tex]\to y=(x-4)(x+4)\\\\\to y=x^2-16\\\\\to y=(x-0)^2-16\\\\vertex \to (0,-16)[/tex]

The distance among the vertices of the two parabolas:

[tex]= \sqrt{(0 - 0)^2+(-8-(-16))^2}\\\\ = \sqrt{0+(-8+16))^2}\\\\ =\sqrt{0+(8)^2}\\\\=\sqrt{(8)^2}\\\\= 8\\\\[/tex]

Answer:

A plane has an unlimited number of points.

Step-by-step explanation:

A plane has an unlimited number of points.

An exact solution represents a point's position on the coordinate plane (x, y).

Even though a point has no dimensionality, the second assertion is incorrect.

Because a linear has only one component, length, the third assertion is likewise incorrect.

a: A point has no length or width.

B: a point indicates a location in a coordinate plane.

E: a plane consists of an ifinite plans

F: a line consists of an infinite set of points.

Answer:

96 in²

36 in²

60 in²

6.51 in

Step-by-step explanation:

Given that :

Dimension of paper = 12 in by 8 in

Dimension of right triangles :

2 in by 9 in ; 3 in by 6 in

Area of sheet of paper = 12 in * 8 in = 96 in²

Area of triangle = 1/2 base * height

Therefore, area of remnant right triangle :

2 * 1/2 * 2 * 9 = 18 in²

2 * 1/2 * 3 * 6 = 18 in²

Combined area of triangle left = 18in + 18in = 36 in²

Area of parallelogram = Area of sheet - Area of triangles left

Area of parallelogram = 96in² - 36in² = 60 in²

Base, b of parallelogram = 9.22 in

Area of parallelogram = base * altitude,h

60in² = 9.22h

h = 60 / 9.22 = 6.51 in

Answer:

y=-2x+2

Step-by-step explanation:

substitute either the x or y value into the equations, if you substitute x=3 and get back y=-4, the equation is correct

Answer:

The volume is approximately 50 m^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h where r is the radius and h is the height

The radius is 1/2 of the diameter r = 8/2 = 4

V = pi ( 4)^2 (1)

V = 16 pi

Letting pi be approximated by 3.14

V = 3.14 * 16

V = 50.24

The volume is approximately 50 m^3

Answer:

answer A

Step-by-step explanation:

A=(-4,7)

C=(2,-5)

midpoint = U=((-4+2)/2, (7+(-5))/2)=(-1,1))

B=(3,0)

D=(-5,2)

midpoint = V=((3+(-5))/2,(0+2)/2)=( -1,1)

Diagonals have the same middle, the quadrilater is a parallogram.

Answer:

y=4sqrt 3 X=8sqr 3

Step-by-step explanation:

4/y=y/12 y^2=48 y= sqrt 48= sqrt 4 * sqrt 3 * sqrt 4 = y = 4sqrt 3 then X

(4sqrt3)^2+144=x^2

48+144=192

sqrt 192

8sqrt3