The sum of two consecutive numbers is one less than three times the smaller integer. Find the two integers.

Step-by-step explanation:

[tex] - 6y + 11x = - 36 \\ - 4y + 7x = - 24 \\ 11x = 6y - 36 \\ x = \frac{6y - 36}{11} \\ - 4y + 7( \frac{6y - 36}{11} ) = - 24 \\ - 4y + \frac{42y}{11} - 22.91 = - 24 \\ - 4y + \frac{42y}{11} = - 1.09 \\ - 0.18182y = - 1.09 \\[/tex]

[tex] y = 5.99 = 6 \\ y = 6 \\ x = \frac{6(6) - 36}{11} \\ x = \frac{36- 36}{11} = 0[/tex]

Answer:

Step-by-step explanation:

Given angles are central angles and the measure of central angles are equal to the measure of the ark they see so the measure of arc BD is equal to angle <A and A is equal to 360 - 150 - 97 (since the sum of these angles equal to 360)

ark BD = 113 and the measure of arc DCB

150 + 97 = 113

Answer:

5^15

Step-by-step explanation:

5^10 * 5^5

We know that a^b * a^c = a^(b+c)

5^(10+5)

5^15

Answer:

5¹⁵

Step-by-step explanation:

5 ¹⁰ . 5⁵

5¹⁰+⁵

5 ¹⁵

'Option A' is the correct answer....

The solution is Option A.

The percentage of the data in the number line is 25 %

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

Let the number line be represented as A

Now , the percentage of the data between 25 and 30 on the number line be P

And , the equation will be

The data on the number line stretches from 30 to 50 with 4 equal parts

So , Since there are 4 equal parts , and each part equals 25 %

And , the percentage of data between 25 and 30 is a part

So ,

The percentage will be 25 %

Hence , the percentage of data is 25 %

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Answer:

y >= 5x - 3

Step-by-step explanation:

since the verbal description mentions "sum", we need to have at least two things to add together.

for this reason we cannot misinterpret the -3 as an element to be included in the "5 times" term, because otherwise we would not have a second thing to build a sum.

Step-by-step explanation:

a) 2z+3z+4z=180

9z=180

z=20

So,three angles are 40,60 and 80

b) (y+30)+(2y+80)+(y+10)=180

y+30+2y+80+y+10=180

4y+120=180

4y=60

y=15

Three angles are 45,110,25

Answer:

1 time 2 ratio per boy, and 3 to 2 ratio per girl

Step-by-step explanation:

Answer:

Step-by-step explanation:

You probably need to make your own version cause mine is super messy but here

Answer:

0.12 is the correct answer

Answer:

B) =

Step-by-step explanation:

When you calculate the equation on the left (32 + 4 = 36) then the one on the right (6 × 6 = 36), and they will be both be equal.

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Have a great summer :)

Answer:

D. 5 /12 + 1 /12 + 4/ 12 + 2 /12 + 5 /12

Step-by-step explanation:

Ive friends each knit one part of a scarf that is 1 5/ 12 yards long.

Hencfy, the fractions of the scarf each friend could have knit is calculated by comparing the options

A. 1 /12 + 2 /12 + 3 /12 + 8 /12 + 4 /12

Lowest Common Denominator = 12

Hence = 18/12 = 1 6/12 = 1 1/2

Option A is wrong

B. 1 /12 + 6/ 12 + 3 /12 + 2 /12 + 4 /12

Lowest Common Denominator = 12

Hence = 16/12 = 1 4/12 = 1 1/3

Option B is wrong

C. 2/12 + 3/ 12 + 3/ 12 + 2/ 12 + 5/ 12

Lowest Common Denominator = 12

Hence = 15/12 = 1 3/12 = 1 1/4

Option C is wrong

D. 5 /12 + 1 /12 + 4/ 12 + 2 /12 + 5 /12

Lowest Common Denominator = 12

Hence = 17/12 = 1 5/12

Option D is correct

Therefore, the fractions of the scarf each friend could have knit is Option D

Answer:

x=-7

y=6

Step-by-step explanation:

7x+10y=11

4x+3y=-10

-3(7x+10y=11

10(4x+3y=-10

-21x-30y=-33

40x+30y=-100

19x = -133 (divide 19 on both sides)

x= -7

Now put the x in one of the original questions.

7(-7)+10y=11

-49+10y=11 (Add 49 to both sides)

10y=60 (Divide 10 on both sides)

y=6

Answer:

Step-by-step explanation:

[tex] \frac{44}{4} [/tex]

= 44 ÷ 4

= 11 (Ans)

Answer:

solution

44÷4=11 ^_^

Thanks for points

Answer:

$252

Step-by-step explanation:

First you need to find how much is 20% is of 210

210*0.20=$42

Add 42 dollars to 210

210+42=$252

So the starting price per bag that he was selling was $252

Answer: 9 months

Step-by-step explanation:

Given

Weight of the person is 206 lb

If he looses 2 lb per month, his weight after x months becomes 188 lb

Net Reduction in weight is [tex]206-188=18\ lb[/tex]

for 18 lb , time period is

[tex]\Rightarrow x=\dfrac{18}{2}\\\\\Rightarrow x=9\ \text{months}[/tex]

Answer:

I'm probably just really bad at math and got this wrong, but I think the answer is 40 cm. Sorry if this doesn't help, like I said I think I'm just bad at math, which it doesn't really make sense as to why I'm answering a math problem, but anyways there's the (probably wrong) answer.

I really hope that helped :P

Answer:

11.2square feet

Step-by-step explanation:

Area of a sector = theta/360 * πr²

theta is the central angle = 80degrees

radius r = PC = 4ft

Substitute

Area of the sector = 80/360 * 3.14 * 4²

Area of the sector = 80/360 * 3.14 * 16

Area of the sector = 4,019.2/360

Area of the sector = 11.2ft²

Hence tthe area of the blue sector is 11.2square feet

Answer:

C

Step-by-step explanation:

I might be wrong. I hope it helps:)

Answer:

WX = 38

Step-by-step explanation:

To get this, we are gong to use the cosine rule

We have the general form as;

a^2 = b^2 + c^2 - 2bc Cos A

Let WX be a

a^2 = 17^2 + 26^2 -2(17)(26) cos 123

a^2 = 1446.46

a = √1446.46

a = 38.03

Answer:

The answer is (0,19) or (0,-5).

By distance formula,

after squaring on both sides we and solving we get,

so, y=19 or -5

Step-by-step explanation:

you get the idea, but i don't think this is the answer yet?

Answer:

x - 5(x - 2) - 1

Step-by-step explanation:

Answer:

x - 5(x - 2) - 1Step-by-step explanation:

Answer:

"The data is discrete, so the graph is a series of unconnected points."

1 quart = 0.9463 liters

8 quarts x 0.9463 = 7.5704 liters

Rounded to 3 places 7.540

Also depending on the exact conversion used it could would to 7.541 liters

Answer:

7 quarts = 7.5704

Step-by-step explanation:

We know that

1 quarts = 0.9463 litres

7 quarts = 8 × 0.9463 = 7.5704 litres

Answer:

SA= 882cm^2

Step-by-step explanation:

SA=2( width*length + hight*length + hight*width )

SA=2( 9*20+ 9*20+ 9*9)

SA= 2*441

SA=882cm^2

Answer:

Step-by-step explanation:

x+2y=10

6y=-3x+30

~~~~~~~~~~~~~~~~

x =10 -2y

substitution

6y=-3x+30

6y=-3(10 -2y)+30

6y = -30 + 6y + 30

6y = 6y

everything disappears.... that means the lines are "the same line"

"co-incident" ... "infinite solutions"

Note" if you ended up with something like 3=0 then the lines are parallel

Answer:

p(x) = -4*x^4  - 2*x^3 + 3*x^2 + 1*x - 2

Step-by-step explanation:

We want to find a polynomial p(x), such that if we add that polynomial to:

f(x) = 4*x^4 + 2*x^3 - 2*x^2 + x - 1

we get:

g(x) = x^2 + 2*x - 3

This is:

f(x) + p(x) = g(x)

Notice that f(x) is a polynomial of degree 4 and g(x) is a polinomial of degree 2, so p(x) must be also a polynomial of degree 4.

p(x) = a*x^4 + b*x^3 + c*x^2 + d*x + e

Then we get:

(4*x^4 + 2*x^3 - 2*x^2 + x - 1) + (a*x^4 + b*x^3 + c*x^2 + d*x + e) = x^2 + 2*x - 3

We can simplify the left side to:

(4 + a)*x^4 + (2 + b)*x^3 + (-2 + c)*x^2 + (1 + d)*x + (-1 + e) =  x^2 + 2*x - 3

Because in the right side we do not have terms with exponent 4 and 3, we must have that:

4 + a = 0

2 + b = 0

and for the other exponents of x we just match the exponent in the left side with the correspondent one in the right side:

(-2 + c) = 1

(1 + d) = 2

(-1 + e) = -3

Solving the 5 equations we get:

a = -4

b = -2

c = 1 + 2 = 3

d = 2 - 1 = 1

e = -3 + 1 = -2

Then the equation for p(x) is:

p(x) = -4*x^4  - 2*x^3 + 3*x^2 + 1*x - 2

Answer:

x = 3 + [tex]\sqrt{3}[/tex] , 3 - [tex]\sqrt{3}[/tex]

Step-by-step explanation:

(2x-3)(x-2) + (x9x-2) = (x)(2x-3)

(2x-3)(x-2)+x(x-2)=x(2x-3)

(2x-3)(x-2)=x(2x-3)-x(x-2)

2x^2 -4x = x(2x-3 - x -2)

2x^2 - 7x + 6 = x^2 - x

[tex]x^{2}[/tex] - 6x + 6 = 0

use quadratic equation to get to final answer

-b +- [tex]\frac{-b+\sqrt{b^{2} -4ac } }{2a} , \frac{-b-\sqrt{b^{2} -4ac } }{2a} where a = 1 b = -6 and c= 6[/tex]

Answer:

Step-by-step explanation:

yes

Answer:

Yes, the card is a right triangle.

Step-by-step explanation:

The card is a right triangle, specifically a 3-4-5 right triangle.

A 3-4-5 right triangle is any right triangle that has side lengths in the ratio of 3:4:5.

The 3-4-5 rule says that any triangle with a side length ratio of 3:4:5 is a right triangle.

So, the card is a right triangle.