Find the solutions to 8x2 + 56x = 0. Check all that apply.

A. X = 8

B. x = 0

C. X = -7

D. X = 7​

Answer:

5040

Step-by-step explanation:

The given series is :

24 + 48 + 72 + 96 +...+ 480

The first term, a= 24

Common difference, d = 24

The last term, [tex]a_n=480[/tex]

Let there are n terms in the AP.

So,

[tex]a_n=a+(n-1)d\\\\480=24+(n-1)24\\\\480=24+24n-24\\\\n=20[/tex]

There are 20 terms in the series. The sum of 20 terms is :

[tex]S_{20}=\dfrac{n}{2}(2a+(n-1)d))\\\\=\dfrac{20}{2}\times (2(24)+19(24))\\\\=5040[/tex]

So, the sum of the given arithmetic series is equal to 5040.

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:2}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]x + 11 + 8x = 29[/tex]

[tex]➺ \: x + 8x = 29 - 11[/tex]

[tex]➺ \: 9x = 18[/tex]

[tex]➺ \: x = \frac{18}{9} [/tex]

[tex]➺ \: x = 2[/tex]

Therefore, the value of [tex]x[/tex] is 2.

[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]

[tex]x + 11 + 8x = 29[/tex]

[tex]➺ \: 2 + 11 + 8(2) = 29[/tex]

[tex]➺ \: 2 + 11 + 16 = 29[/tex]

[tex]➺ \: 29 = 29[/tex]

➺ L. H. S. = R. H. S

Hence verified.

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35\:ヅ}}}}}[/tex]

☆Amy is 9 years older than her younger sister.

[tex]\\ \sf\longmapsto Age\:of\:Amy=1+9=10years[/tex]

Let after x years Amy will be 4times old as her sister.

ATQ

[tex]\\ \sf\longmapsto \dfrac{1+x}{9+x}=\dfrac{1}{4}[/tex]

[tex]\\ \sf\longmapsto 4(1+x)=1(9+x)[/tex]

[tex]\\ \sf\longmapsto 4+4x=9+x[/tex]

[tex]\\ \sf\longmapsto 4x-x=9-4[/tex]

[tex]\\ \sf\longmapsto 3x=5[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{5}{3}[/tex]

[tex]\\ \sf\longmapsto x=1.6[/tex]

[tex]\\ \sf\longmapsto x=2(approx)[/tex]

Answer: 1 pigeon is $320

1 love bird is $80

Step-by-step explanation:

Let the cost for 1 love bird be represented by x

Let the cost for 1 pigeon be represented by y.

Since John bought 8 birds and 6 pigeons for $2400. This will be:

8x + 6y = 2400 ...... i

If he had bought 1 more pigeon and 2 fewer birds, he would have paid $200 more. This will be:

6x + 7y = 2600 ...... ii

8x + 6y = 2400 ...... i

6x + 7y = 2600 ...... ii

Multiply equation i by 6

Multiply equation ii by 8

48x + 36y = 14400 ...... iii

48x + 56y = 20800 ...... iv

Subtract iii from iv

20y = 6400

y = 6400/20

y = 320

1 pigeon is $320

From equation i

8x + 6y = 2400

8x + 6(320) = 2400

8x + 1920 = 2400

8x = 2400 - 1920

8x = 480

x = 480/8

x = 60

1 love bird is $80

Answer:

x

Step-by-step explanation:

Answer:

a. 74°

Step-by-step explanation:

Angle BCD and angle ACB are supplementary because they form a straight line. This means they add up to 180. We can write an equation to model the situation:

m<BCD + m<ACB = 180

106 + m<ACB = 180

m<ACB = 74

Since we are given two sides of the triangle are congruent, the triangle is isosceles. The base angles of an isosceles triangle are congruent, so we can say:

m<ACB = m<A

This means m<A is equal to 74°

Answer:

A:He is trying to find the diameter

B: 3.14*14=43.96

C: 3.14*14^2=615.44

Hope This Helps!!!

Answer:

a) x^2 + y^2

b) 9-xy

Step-by-step explanation:

Here, we want to write the algebraic statements as expressions;

a) The sum of the squares of x and y

The square of x is x^2

The square of y is y^2

The sum of the squares is x^2 + y^2

ii) Product of x and y subtracted from 9

The product of x and y is x * y = xy

Subtracting these from 9, we have;

9-xy

Answer:

1

----------

x+1

Step-by-step explanation:

2x+12

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

2x^2 + 14x+12

Factor

2(x+6)

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

2(x^2+7x+6)

2(x+6)

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

2(x+6)(x+1)

Cancel like terms

1

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

(x+1)

Answer:

6.75

Step-by-step explanation:

that is the answer by the way

Answer:

the midpoint of it is 8,-6

Step-by-step explanation:

rhgsr egh

Answer:

Step-by-step explanation:

Answer:

1. plants

2. together

3. is

4. family

5. talking

6. weeds

7. experience

8. planter

9. on

10. fields

11. too

12. method

13. around

14. react.

Explanation:

The given passage talks about the impact of chemicals on the ecosystem. The speaker narrates how the ecology belongs to plants, animals, and humans, though man seemed intent to destroy it for himself.

The blanks in the given passage are filled with the appropriate words as follows-

Ecology is the study of how (1) plants, animals, and people live (2) together and help each other. But man sometimes forgets he (3) is a part of the (4) family of all living things. Here is an example. A planter is (5) talking about killing (6) weeds on his land. He remembers his first (7) experience with a weedicide. He was a (8) planter then, working (9) on a rubber plantation. He had a problem with weeds. The cost of weeding of the (10) fields by hand was getting (11) too high. So he used a new, cheap, and effective (12) method, good old Sodium Arsenate. He sprayed plenty of this (13) around to kill the weeds. The first thing to (14) react were the frogs.

Answer:

X=3

Y=1

Step-by-step explanation:

Vertex A forms dilation F

Answer:

35m^2

Step-by-step explanation:

4×2.5=10 10×2=20

3×2.5=7.5 7.5×2=15

20+15=35

Hope this helps! :)

Step-by-step explanation:

Given that,

The length of a carton, h = 9 cm

Width, b = 13 cm

height, h = 24 cm

I drink one-third of the fruit juice, then two third will be left. So, the volume is :

[tex]V=\dfrac{2}{3}\times lbh\\\\V=\dfrac{2}{3}\times 9\times 24\times 13\\\\V=1872\ cm^3[/tex]

Since, 1 L = 1000 cm³

1872 cm³ = 1.8 L

or

= 1800 mL

Hence, this is the required solution.

Answer:

third one....domain starts  negative (-7/3)

and range starts at -5

Step-by-step explanation:

Answer:

4.1 hours each day

Step-by-step explanation:

20.5 ÷ 5

= 4.1

Therefore 4.1 hours was spent on studying each day.

Answer:

a = 78.5 cm²

Step-by-step explanation:

a = πr²

a = 3.14 * 5²

a = 3.14 * 25

a = 78.5 cm²

Answer:

(12,0)

Step-by-step explanation:

So whenever you are asked for an "intercept" it is the point where a line crosses the axis. The x intercept is where the line crosses at the x axis (horizontal line on the graph) and the y intercept is where the y axis crosses (vertical axis).

So this question is really asking where is the point when y = 0

The x values in the chart are 5 apart-- 22 +5 = 27, 27+ 5 = 32

The y values are 18 apart --> 36 + 18 = 54, 54+ 18 = 72

Make a little chart where y = 0 (this is where the x crosses) and you can see

there is a point at (17, 18) and then (12, 0) and that point is the x intercept.

Answer:

(12, 0)

Step-by-step explanation:

the x-intercept is the point, where y=0.

so, the second coordinate is therefore 0, no matter what.

now, at what x is that ?

let's find the line function.

a line is

y = a×x + b

let's use the first point (22, 36)

36 = a×22 + b

a = (36 - b)/22

let's use the second point (27, 54)

54 = a×27 + b

now we use the first expression describing a in terms of b and insert that into the second expression.

54 = 27×(36 - b)/22 + b

54×22 = 27×(36 - b) + 22b = 972 - 27b + 22b

1188 = 972 - 5b

216 = -5b

b = -43.2

=>

a = (36 - -43.2)/22 = (36 + 43.2)/22 =79.2/22 = 3.6

our line is

y = 3.6x - 43.2

so, now back to the question, at what x is y=0 ?

0 = 3.6x - 43.2

3.6x = 43.2

x = 12

Answer:

8. B

9. B

Step-by-step explanation:

add all sides to get perimeter

multiply sections of the area to get area (length times width)

Answer:

4cm

Step-by-step explanation:

first find the length of the side of one square

the length of the rectangle will be twice the width

let y represent the width

area of a rectangle=length x width

2cm²=2yxy

2cm²=2y²

2cm²/2=2y²/2

1cm²=y²

1√cm²=√y²

1cm=y

perimeter of a square=4xside

4x1cm

4cm

Given:

The expression is:

[tex]6\div 8[/tex]

To find:

The value of the given expression by using the long division method.

Solution:

We have,

[tex]6\div 8[/tex]

Here, dividend is 6 and divisor is 8.

Since 6<8, therefore we will use the decimal in dividend and quotient as shown below:

[tex]\underline{\quad 8\quad}|\overline{\quad 6.00\quad }|\underline{\quad 0.75\quad }[/tex]

         [tex]\underline{\quad 56\quad }[/tex]

               [tex]40[/tex]                  (After subtraction)

           [tex]\underline{\quad 40\quad }[/tex]

             [tex]\underline{\quad 0\quad }[/tex]               (After subtraction)

Therefore, the value of the given expression is 0.75.

Well, If the area of ABC is 20cm², Then the area of ABS would be 10cm² and the area of ACS would also be 10cm². You basically are just cutting the ABC in half. I hope this helps!

Answer:

a) 400

b)160,000

Step-by-step explanation:

times 20 by 20 hence 20² for a. you get 400, for b, just do 400² which gets you 160,000.

If its wrong im so sorry

Answer:

4/33

Step-by-step explanation:

do the normal steps to conversion

Answer:

D. (10, 2)

Step-by-step explanation:

A' = [ 2(3)-(-4) ; 2]

=> (6+4 ; 2)

=> (10, 2)

Answer:

D

Step-by-step explanation:

Answer:

150°

Step-by-step explanation:

2x+x+90=180

3x=90

x=30

z= 180-x = 180-30 = 150°

Answer:

Step-by-step explanation:

Middle point of AB

x(m) = (6+1)/2 = 7/2

y(m) = (7+4)/2 = 11/2

slope of the line that contains AB

(4-7)/(6-1) = -3/5

eqaution of the perpendicular bisector

y-11/2 = 5/3(x-7/2)

y = 5/3x -35/6 + 11/2

y = 5/3x + (-35 + 33)/6

y = 5/3x -1/3

Middle point of AC

x(m) = (1+5)/2 = 3

y(m) = (7+5)/2 = 6

Slope of the line that contains AC

(5-7)/(5-1) = -1/2

equation of the perpendicular bisector

y-6 = 2(x-3)

y = 2x -6 + 6

y = 2x

Point of intersection

y= 5/3x -1/3

y = 2x

2x = 5/3x - 1/3

6x = 5x - 1

x = -1

y = -2

P(-1,-2)

Answer:

(1,7)

Step-by-step explanation:

Given:

A(1,7)

B(6,4)

C(5,5)

Solution:

Mid point of AB = M((1+6)/2,(7+4)/2) = M(3.5,5.5)

Slope of AB = (4-7)/(6-1) = -3/5

Perpendicular bisector of AB:

L1: y -  11/2 = -(3/5)(x-7/2) ............(1)

Mid point of AC, m= N((1+5)/2,(7+5)/2) = N(3,6)

Slope of AC, n = (5-7)/(5-1) = -2/4 = -1/2

perpendicular bisector of AC:

L2: y-6 = -(1/2)(x-3) ..........."(2)

To find the point of intersection,

(1)-(2)

-5.5 - (-6) = -(3/5)x +12/5 + x/2 - 3/2

1/2 = -x/10 + 6/10

x/10 = 1/10

x = 1

substitute x in (1)

y = 3/2+11/2 =7

Therefore Point of intersection is (1,7)

Answer:

3x+34+23y, You can not add in this equation as there are no like numbers.

Step-by-step explanation:

Answer:

isnt it 60xy

Step-by-step explanation: