What is the tenth term of an arithmetic sequence with second term 100 and common difference −12?

Answer:

A) (-8, -16)

B) (0, 48)

C) (-4, 0), (-12, 0)

Step-by-step explanation:

A) the vertex is the minimum y value.

extremes of a function we get by using the first derivation and solving it for y' = 0.

y = x² + 16x + 48

y' = 2x + 16 = 0

2x = -16

x = -8

so, the vertex is at x=-8.

the y value is (-8)² + 16(-8) + 48 = 64 - 128 + 48 = -16

B) is totally simple. it is f(0) or x=0. so, y is 48.

C) is the solution of the equation for y = 0.

the solution for such a quadratic equation is

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case here

a=1

b=16

c=48

x = (-16 ± sqrt(16² - 4×48)) / 2 = (-16 ± sqrt(256-192)) / 2 =

= (-16 ± sqrt(64)) / 2 = (-16 ± 8) / 2 = (-8 ± 4)

x1 = -8 + 4 = -4

x2 = -8 - 4 = -12

so the x- intercepts are (-4, 0), (-12, 0)

Answer:

$45.63

Step-by-step explanation:

[tex]50,145 cm^{3} * 2.6 g/cm^3 = 130,377 g\\130,377 g = 130.377 kg\\130.377 kg * $0.35/kg = $45.63\\[/tex]

or all together    

50,145 cm³  *  2.6 g/cm³ * 0.35/kg =  $45.63

Answer:

Step-by-step explanation:

let the  numbers be x and y.

x+y=16

x-y=6

add

2x=22

x=22/2=11

11+x=16

x=16-11=5

product xy=11×5=55

Answer:

I think this will help you

Answer:

10, 16

Step-by-step explanation:

List the factors of 160.

1 × 160 = 160

2 × 80 = 160

4 × 40 = 160

5 × 32 = 160

8 × 20 = 160

10 × 16 = 160

(there are more, but we don't need them)

Check to see which factors can be added together to make 26, half of 52.

10 and 16 make 26.

That's the answer!

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:

D) 20°

Step-by-step explanation:

Using the triangle sum theorem, you know that every triangle's interior angles add up to 180°. Therefore the bottom triangle's missing angle can be found by giving it the variable x.

57° + 30° + x = 180°

Simplify: 87° + x =180°

x=93°

By the vertical angles theorem, the vertical angle directly across this angle is congruent to this one. Meaning that the top triangle's angle are 67°, 93°, and unknown, which we can assign y. We can use the same method from above here.

67° + 93° + y = 180°

Simplify: 160° + y = 180°

y=20°

Answer:

(C). 26°

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

d = 0.5 * t    There are no conversions. You just substitute the value for t.

d = 0.5 * 27.9

d = 13.95 which is A

Answer:

The plane is going 325 kilometers per hour :)

Step-by-step explanation:

To find the average speed per hour, divide 1300 by 4.

1300/4 = 325

Answer:

B

Step-by-step explanation:

Hypotenuse=sqrt(Side^2+side^2)=sqrt(14^2+14^2)=14*sqrt(2)

Answer:  

B  

Step-by-step explanation:  

Hypotenuse=sqrt(Side^2+side^2)=sqrt(14^2+14^2)=14*sqrt(2)

Answer:

-39/15

Step-by-step explanation:

=-8/5-4/3+1/3

Taking LCM of 5,3 and 3.

=3(-8)-5(4)+5(1)/15

=-24-20+5/15

=-44+5/15

=-39/15

Note:if you need to ask any question please let me know.

Whats 5867 times 382?

answer;

5867×382

=2241194

Hope it helps you.........

Answer:

128500

Step-by-step explanation:

This is an arithmetic sequence with a common difference of 3500

The formula for an arithmetic sequence is

an = a1+d(n-1)  where a1 is the first term and d is the common difference

an = 48000+ 3500(n-1)

We want n = 24

a24 = 48000+3500(24-1)

       = 48000+3500(23)

       =48000+80500

       =128500

Answer:

The quadratic formula: (-b+-sqrtb^2-4ac)/2a

Plugging in the values of a=1, b=9, and c=10, the roots of the equation are: -7.7 and -1.3.

So, the first option is correct.

Let me know if this helps!

Answer:

C) 81 degrees

Step-by-step explanation:

all quadrilateral's sum of interiror angles is 360 degrees

right angles are 90 degrees

call measure of angle C =y

360=90+90+99+y

180=99+y

y= 81

Answer:

[tex]x=10[/tex]

Step-by-step explanation:

A secant is a line segment that intersects a circle in two places. One property of a secant is the product of the lengths ratio. This ratio can be described as the following, let ([tex]inside[/tex]) refer to the part of the secant that is inside the circle, and ([tex]outside[/tex]) refer to the part that is outside of it. ([tex]total[/tex]) will refer to the entirety of the secant or ([tex]inside+outside[/tex]). The numbers (1) and (2) will be used as subscripts to indicate that there are two different secants.

[tex](outside_1)(total_2)=(outside_2)(total_2)[/tex]

Substitute,

[tex](outside_1)(total_2)=(outside_2)(total_2)[/tex]

[tex](outside_1)(inside_1+outisde_1)=(outside_2)(inside_2+outside_2)[/tex]

[tex](6)(6+x+5)=(7)(7+x+1)[/tex]

Simplify,

[tex](6)(6+x+5)=(7)(7+x+1)[/tex]

[tex]6(x+11)=7(x+8)[/tex]

[tex]6x+66=7x+56[/tex]

Inverse operations,

[tex]6x+66=7x+56[/tex]

[tex]66=x+56[/tex]

[tex]10=x[/tex]

Answer:

1/9

Step-by-step explanation:

The vertex form is

y =a(x-h)^2 +k where (h,k) is the vertex

The vertex is (-2,-3)

y =a(x--2)^2 +-3

y =a(x+2)^2 -3

Substitute the point into the equation

-2 = a(-5+2)^2 -3

-2=a(-3)^2-3

Add 3 to each side

-2+3 = a(9)

1 = 9a

1/9 =a

y =1/9(x+2)^2 -3

The coefficient of the x^2 is 1/9

Answer:

[tex]\frac{1}{9}[/tex]

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (- 2, - 3) , then

y = a(x + 2)² - 3

To find a substitute (- 5, - 2 ) into the equation

- 2 = a(- 5 + 3)² - 3 ( add 3 to both sides )

1 = a(- 3)² = 9a ( divide both sides by 9 )

[tex]\frac{1}{9}[/tex] = a

y = [tex]\frac{1}{9}[/tex] (x + 2)² - 3

The coefficient of the x² term is therefore [tex]\frac{1}{9}[/tex]

Answer:

24 days LCM

prime factor :

4- 2, 2

8-2,2,2

12- 2,2,3

largest factors- 2,2,2,3

2*2*2*3 = 24

Step-by-step explanation:

Answer:

1a. 128

1b. 81

1c. 64

1d. 25

1e. 343

1f. 100000

1g. 64

1h. 0

1i. 13

1j. 1

2a. 243

2b. 64

2c. 36

2d. 625

2e. 1331

2f. 10000000

2g. 81

2h. 0

2i. 17

2j. 1

Answer:

solving for x

Step-by-step explanation:

4 or -6

Answer:

x = 4

Step-by-step explanation:

Those absolute value signs are a trick, well at least for this problem. Solve it how you usually would. However, if +2 was -2 or +/-2, then you would need to pay attention. Basically, those signs make the whole equation incased positive no matter what.

Answer:

lol Step-by-step explanation:

Answer:

When you multiply radical expressions you multiply the numbers under the radical symbols.3–√×7–√=21−−√

When you add radical expression you CANNOT add the numbers under the radical symbols.

3–√+7–√≠10−−√

Step-by-step explanation:

Answer:

Parallel: AC and DB, BA and CD

Perpendicular: AC and CD, DB and CD, DB and BA, BA and AC

Neither: None

Step-by-step explanation:

Step 1: Find Slopes

Let's first find the slopes of each side of the rectangle, as that will helps us determine which sides are parallel, perpendicular, or neither.

Recall that the formula for finding the slope between two points is [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex] where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the two points. To avoid confusion, I will be taking the first point I list as [tex](x_1,y_1)[/tex] and the second point as [tex](x_2,y_2)[/tex].

Slope of [tex]BA[/tex]:

[tex]\frac{-7-(-3)}{-1-(-4)}\\=\frac{-7+3}{-1+4} \\= -\frac{4}{3}[/tex]

Slope of [tex]AC[/tex]:

[tex]\frac{-4-(-7)}{3-(-1)} \\=\frac{-4+7}{3+1} \\=\frac{3}{4}[/tex]

Slope of [tex]CD[/tex]:

[tex]\frac{0-(-4)}{0-3} \\=\frac{4}{-3} \\=-\frac{4}{3}[/tex]

Slope of [tex]DB[/tex]:

[tex]\frac{-3-0}{-4-0} \\=\frac{-3}{-4} \\=\frac{3}{4}[/tex]

Step 2: Determine which sides are parallel, perpendicular, or neither

Now that we found the slopes of the sides, we can determine which sides are parallel, perpendicular, or neither.

Recall that parallel lines have the same slope. [tex]\bf AC[/tex] and [tex]\bf DB[/tex], along with [tex]\bf BA[/tex]and [tex]\bf CD[/tex], have the same slope, so they are parallel. No other pair of sides has the same slope, so these are our only parallel pairs.

For two lines to be perpendicular, the product of their slopes must be [tex]-1[/tex]. [tex]\bf AC[/tex] and [tex]\bf CD[/tex], [tex]\bf DB[/tex] and [tex]\bf CD[/tex], [tex]\bf DB[/tex] and [tex]\bf BA[/tex], and [tex]\bf BA[/tex] and [tex]\bf AC[/tex] [tex]\bf[/tex]meet that criteria, so they are perpendicular. No other pair of sides meets the criteria, so these are our only perpendicular pairs. Hope this helps!

Answer:

cos(θ) = -0.95

Step-by-step explanation:

Remember the relation:

sin(θ)^2 + cos(θ)^2 = 1

So if we have:

sin(θ) = 0.3

we can replace that in the above equation to get:

0.3^2 + cos(θ)^2 = 1

now we can solve this for cos(θ)

cos(θ)^2 = 1 - 0.3^2 = 0.91

cos(θ) = ±√0.91

cos(θ) = ± 0.95

Now, yo can see that there are two solutions, which one is the correct one?

Well, you can see that the endpoint of the segment that defines θ is on the second quadrant.

cos(x) is negative if the endpoint of the segment that defines the angle is on the second or third quadrant.

Then we can conclude that in this case, the correct solution is the negative one.

cos(θ) = -0.95

Answer:

DEF = 105

Step-by-step explanation:

The sum of the angles of a triangle is 180

28+47+DEF = 180

Combine like terms

DEF+75=180

Subtract 75 from each side

DEF +75-75 =180-75

DEF = 105

Answer: D

Step-by-step explanation: The answer is D because firstly we know that all right triangles add up to 180 degrees.

Using this knowledge we know 2 sides out of the 3. Therefore 47+28+x=180. Then we would add the first 2 numbers then minus 180 to get 105 as your last angle.

Answer:

The area of a regular polygon is A = (1/2)ap, where a is the apothem and p is the perimeter of the polygon.

The apothem is 8 inches and the perimeter is 6(7) = 42 since there are 7 sides of 6 inches.

Then the area is

A = (1/2)(8)(42) = 336/2 = 168 in2

I hope this helped!

Answer:

See picture below

Step-by-step explanation:

Let PK be the length and PS be the width of the rectangle.

Then LW =562

Assuming O is the center of the rectangle then ∠KST = ∠STO = 75/2

Hence tan ( 75/2 ) = PS/PK

Now solve the system of the equations

PS*PK=562

tan ( 75/2 ) = PS/ PK

Answer:

5ba^2 +ab^2 6a^2 + 2b

Step-by-step explanation:

ab(6a+b)-3a^2 (b-2)+2b(a^2 +1)

6ba^2 +ab^2 -3ba^2 +6a^2 + 2ba^2 +2b

6ba^2 -3ba^2 +2ba^2 +ab^2 +6a^2 +2b

5ba^2 +ab^2 6a^2 + 2b

Answer:

A) f(t) = 4(t − 1)^2 + 3; the minimum height of the roller coaster is 3 meters from the ground

Step-by-step explanation:

f(t) = 4t^2 − 8t + 7

Factor out 4 from the first two terms

f(t) = 4(t^2 − 2t) + 7

Complete the square

(-2/2)^2 =1  But there is a 4 out front so we add 4 and then subtract 4 to balance

f(t) = 4( t^2 -2t+1) -4 +7

f(t) = 4( t-1)^2 +3

The vertex is (1,3)

This is the minimum since a>0

The minimun is y =3 and occurs at t =1

Answer:

The above answer is correct.

Step-by-step explanation:

Answer:

Not Enough Information

Step-by-step explanation:

Unfortunately, you did not give us the "given information", so there is no way to prove the two parallel.