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Answer:

Length of rectangle = 16 cm

Width of rectangle = 4 cm

Step-by-step explanation:

Given:

Area of rectangle = 64 cm²

Find:

Length and width

Computation:

Assume;

Length of rectangle = a

So,

Width of rectangle = a -12

Area of rectangle = l x b

So,

a(a-12) = 64

a² - 12a - 64 = 0

a² - (16-4)a - 64 = 0

a² - 16a+ 4a - 64 = 0

a (a-16) + 4(a-16)= 0

(a-16)(a+4) = 0

a= 16 , a = -4

So,

Length of rectangle = 16 cm

Width of rectangle = a -12

Width of rectangle = 16 -12

Width of rectangle = 4 cm

Answer:

the slope would be rise over run

it is shown in the graph it rise 3units and run 2units therefore it's 3/2

Answer:

a) 0

Step-by-step explanation:

the equation of the slope (m) for a line from two points is given as (y2-y1)/(x2-x1)

we are given the points (3,-2) and (9,-2)

we can label the points:

x1=3

y1=-2

x2=9

y2=-2

now substitute into the equation:

m=(-2--2)/(9-3)

simplify

m=(-2+2)/6

m=0/6

m=0

the slope of the line is 0, which is option a

Hope this helps!

Given:

The equation is:

[tex](2x+1)(x-2)=0[/tex]

To find:

The values of a, b and b from the standard form.

Solution:

The standard form of a quadratic equation is:

[tex]ax^2+bx+c=0[/tex]            ....(i)

We have,

[tex](2x+1)(x-2)=0[/tex]

In can be rewritten as

[tex]2x(x)+(2x)(-2)+(1)(x)+(1)(-2)=0[/tex]

[tex]2x^2-4x+x-2=0[/tex]

[tex]2x^2-3x-2=0[/tex]             ...(ii)

On comparing (i) and (ii), we get

[tex]a=2,b=-3,c=-2[/tex]

Therefore, the correct option is C.

Given:

The height of 44 students (in centimeter) are presented in the given frequency distribution.

To find:

The median of the given data.

Solution:

The given intervals are inclusive first make the intervals exclusive by adding 0.5 in upper limit and by subtracting 0.5 from the lower limit.

The complete frequency distribution table is shown below:

Height              Frequency           L                            <cf

182 - 188                  1                  181.5 - 188.5            44

175 - 181                   3                 174.5 - 181.5             43

168 - 174                  6                 167.5 - 174.5            40

161 - 167                 15               160.5 - 167.5            34   Median class

154 - 160                 12                153.5 - 160.5           19

147 - 153                   4                146.5 - 153.5             7

140 - 146                   3                139.5 - 146.5             3

We have, [tex]n=44[/tex].

[tex]\dfrac{n}{2}=\dfrac{44}{2}[/tex]

[tex]\dfrac{n}{2}=22[/tex]

The 22th term is include in the class 160.5 - 167.5 because is cf is greater than 22 but the cf of o preceding class is less than 22. So, it is the median class is 160.5 - 167.5.

Formula for median:

[tex]Median=l+\dfrac{\dfrac{n}{2}-cf}{f}\times h[/tex]

Where, l is the lower limit of median class, cf is the cumulative frequency of preceding class, f is the frequency of median class and h is the size of the class.

Now, [tex]l=160.5,f=15,cf=19,h=7[/tex].

[tex]Median=160.5+\dfrac{22-19}{15}\times 7[/tex]

[tex]Median=160.5+\dfrac{3}{15}\times 7[/tex]

[tex]Median=160.5+1.4[/tex]

[tex]Median=161.9[/tex]

Therefore, the median of the given data table is 161.9.

Answer:

x = 50°

y = 50°

Step-by-step explanation:

x = y because it is an isosceles triangle

2x + 80 = 180°

2x = 100°

x = 50°

y = 50°

Answer:

360 tons

Step-by-step explanation:

Coke burned : cast iron = 15 : 16

The smelter produces 384 tons of cast iron a day

Let x = tons of coke burned

Coke burned : cast iron = x : 384

Equate both ratios

15 : 16 = x : 384

15/16 = x/384

Cross product

15 * 384 = 16 * x

5,760 = 16x

x = 5,760/16

x = 360

x = tons of coke burned = 360 tons

Answer:

-1/3

Step-by-step explanation:

-6+3=-3

2 and -7 is 9

Answer:

the correct answer is B

Step-by-step explanation:

go it right!!!

Answer The answer is c.

Step-by-step explanation:

cause i said it was

Answer:

s/2 is the equation

Step-by-step explanation:

Answer:

D.)

2/3 1/6 1/7

Step-by-step explanation:

Given the fractions :

A. 3/14 1/42 1/6 B. 2/84 1/16 1/42 C. 2/21 1/4 1/3 D. 2/3 1/6 1/7

We need ot Obtian the set of fractions whose L. C. M of denominator multiplied by the numerator gives an of 84 for all its values.

A.)

L. C. M of 14, 42 and 6 = 42

42 * 3 = 126 ( not true)

B.)

L. C. M of 84, 16, 42 = 336

Can't be true

C.)

L. C. M of 21, 4, 3 = 84

84 * 2 = 168 (not true)

D.)

L.C.M of 3, 6, 7 = 42

Answer:

d

Step-by-step explanation:

Answer:

it's the 3rd option (eeeexxxxttteeennndddeeerrr)

Answer:

the correct answer is c i hoped this helped

Answer:

x=27

Step-by-step explanation:

Answer:

The answer would be 27

Step-by-step explanation:

Times three by nine to get the value of x.

Answer:

3rd one

.

.

...................

Answer:

210

Step-by-step explanation:

Answer:

217

Step-by-step explanation:

5³ − (64/8) + 10²=125-8+100=217

Answer:

Step-by-step explanation:

So it 22

Answer: 0.007

Step-by-step explanation:

Step-by-step explanation:

I need the graph. I'll answer if you send me the graph that is uses

Answer:

$52

Step-by-step explanation:

first 2/3*156 and you get 104

Then you do 156 -104 and you will have your answer

Answer:

Max has $52 remaining

Step-by-step explanation:

[tex]\frac{2}{3}*\frac{156}{1} = \frac{312}{3} \\[/tex]

simplify [tex]\frac{312}{3}[/tex] by 3 to get [tex]\frac{104}{1}[/tex]

Answer:

J

Step-by-step explanation:

If you use a calculator, 3/4 x 60 = 45

It’s the number closet to 100-55

Answer:

(-12 , 2)

Step-by-step explanation:

GIVEN :-

TO FIND :-

FACTS TO KNOW BEFORE SOLVING :-

Section Formula :-

Let AB  be a line segment where co-ordinates of A = (x¹ , y¹) and co-ordinates of B = (x² , y²). Let P be the midpoint of AB . So , by using section formula , the co-ordinates of P =

[tex](x , y) = (\frac{x^2 + x^1}{2} ,\frac{y^2 + y^1}{2} )[/tex]

PROCEDURE :-

Let the co-ordinates of another endpoint be (x , y)

So ,

[tex](-8 , -4) = (\frac{-4 + x}{2} , \frac{-10 + y}{2} )[/tex]

First , lets solve for x.

[tex]=> \frac{x - 4}{2} = -8[/tex]

[tex]=> x - 4 = -8 \times 2 = -16[/tex]

[tex]=> x = -16 + 4 = -12[/tex]

Now , lets solve for y.

[tex]=> \frac{y - 10}{2} = -4[/tex]

[tex]=> y - 10 = -4 \times 2 = -8[/tex]

[tex]=> y = -8 + 10 = 2[/tex]

∴ The co-ordinates of another endpoint = (-12 , 2)

Answer:

9x + 72

Step-by-step explanation:

Answer:

9x + 8

Step-by-step explanation:

Hope this helps have a nice day :)

*You don't have to read this part*

Parentheses can be removed by multiplying the outside factor to each term inside the parentheses using distributive property.

Answer:

80

Step-by-step explanation:

Area of latera = 3 bh = 10X3 +10x2.5 +2.5x10 = 30+25+25 = 80

b/c the 2 lines are equal

Answer:

Step-by-step explanation:

Multiple the numbers one by one and the answers you’ll get u can choose to divide multiple plus or minus and u will get the answer

Answer:

Blue = 30

Green = 24

Red = 54

Orange = 12

Step-by-step explanation:

hahahshahhahahahahahauehfudbrog f ghg

Answer: 3:8

Step-by-step explanation:

Number of rainy days = 42

Number of sunny days = 112

To calculate the rainy day to sunny day ratio, we can first use the numbers given as fraction and divide to its lowest term. This will be:

= Number of rainy days / Number of sunny days

= 42 / 112

= 3/8

Therefore, the ratio of rainy days to sunny days will be 3:8

Answer:

The correct answer is;

The replacement cone holds 4·π cubic inches more than the volume of the original cone  

Step-by-step explanation:

The given measurements of the cones are;

The radius of the original cone, r₁ = 3 inches

The height of the original cone, h₁ = 4 inches

The radius of the replacement cone, r₂ = 4 inches

The height of the replacement cone, h₂ = 3 inches

The volume of a cone, V = (1/3)·π·r²·h

The volume of the original cone, V₁ = (1/3)·π·r₁²·h₁

∴ V₁ = (1/3) × π × (3 in.)² × 4 in. ≈ 37.7 in.³

The volume of the replacement cone, V₂ = (1/3)·π·r₂²·h₂

∴ V₂ = (1/3) × π × (4 in.)² × 3 in. ≈ 50.27 in.³

The ratio of the volume of the two cones is given as follows;

Volume ratio = V₁/V₂

∴ Volume ratio = (1/3) × π × (3 in.)² × 4 in. /((1/3) × π × (4 in.)² × 3 in.) = 3/4

The difference in volume, ΔV = V₂ - V₁ = (1/3) × π × ((4 in.)² × 3 in. - (3 in.)² × 4 in. = 4·π in.³

Therefore, the volume of the replacement cone is 4·π in.³ more than the volume of the original cone.