why does an angle that is supplementary to an acute angle have to be obtuse

Answer: 15.5 is a rational number.

Step-by-step explanation:  We are given to check whether the number 15.5 is a rational or irrational.

We know that

a real number is said to be

(i) rational, if the digits after the decimal are either repeating or terminating.

(ii) irrational, if the digits after the decimal are non-repeating and non-repeating.

The given number is 15.5.

Here, the digits after the decimal are terminating.

So, the given number is a rational number.

Thus, 15.5 is a rational number.

We need to simplify the expression:

[tex]12x^{-6}y^{10} \times (3x^{7}y)[/tex]

Now, we know that we can resolve the exponents of the variables with the like terms only and we can multiply the coefficients independently:

Now,  

[tex]12x^{-6}y^{10} \times 3x^{7}y=(12 \times 3)\times (x^{-6}\times x^{7})\times (y^{10}\times y)[/tex]

On simplifying the above expression we get:

[tex]36\times x^{(-6+7)}\times y^{(10+1)}[/tex]

[tex]=36 \times x^{1}\times y^{11}[/tex]

[tex]=36 \times x \times y^{11}[/tex]

[tex]=36xy^{11}[/tex]

So the simplified form of the expression [tex]12x^{-6}y^{10} \times 3x^{7}y=36xy^{11}[/tex].

Answer:

d. 11.4

Step-by-step explanation:

point r is half the line qs. qr is 5.7 so to get the whole line multiply it by two to get 11.4

Christine has $20, Manuel has $60 and Henry has $29

let x be the amount Christine has then

Manuel has 3x and Henry x + 9

summing the amounts gives the equation

x + 3x + x + 9 = 109

5x + 9 = 109 ( subtract 9 from both sides )

5x = 100 ( divide both sides by 5 )

x = 20

thus Christine has $29, Manuel has (3 × 20 ) =$60 and

Henry has 20 + 9 = $29

check : 20 + 60 + 29 = 109

-3 is the answer when you do this equation. Or it could be 300 depending.

Answer:

-3

Step-by-step explanation:

B

the equation of a line in standard form is

Ax + By = C

where A is a positive integer and B, C are integers

3x + 5y = - 15 is in standard form → B

Answer:

Equation of line in Standard form is

[tex]ax \pm by \pm c=0,[/tex]

Among the two options given,

A. -2 x = 13

Here, coefficient of x= -2

Coefficient of y=0

But we can say that this is a point in one dimensional form.

So, it is not equation of line in standard form.

B. 3 x +5 y= -15

3 x + 5 y +15=0

Comparing with, a x + b y + c=0

a=3, b=5, c=15

Neither the coefficient of x ,nor the coefficient of y is equal to 0.

So, Option B: 3 x + 5 y = -15 →3 x+ 5 y+15=0

is equation of line in standard form.

the probability is a ratio of number of relevant outcomes and total number of possible cases.

In this scenario, the relevant outcomes are

4, 5, 10    (and their count is 3)

and the total number of possible outcomes:

12

so the probability is

3/12 = 1/4

the answer is 3/12 cause when you divied 12 by 4 you will get 3 and we know that there is 12 faces on the cube so that gives you the ratio 3/12.

See this explanation:

for the given point x=3 and y=-4.

It means, z=3-4i. Answer; C.

Answer:

Option (c)

Step-by-step explanation:

A complex number is a combination of a real number and an imaginary number.

Real number be represented on X axis and imaginary number be represented on Y axis.

Here real part of the complex number is 3 and the imaginary part is -4.

So, the complex number is 3 - 4i.

In order to show the correct time again, the clock has to be exactly 12 hours, or 12*60=720 minutes, behind. With 2 minutes per 3 hours, the clock will have to run for 3 * 720/2 = 1080 hours. 1080 hours = 45 days. The shortest interval the clock need to show the correct time is 45 days.

Answer:

1152 hours - 42 days =)

Step-by-step explanation:

Answer:

20a. 143 deg

20b. 37 deg

20c. corresponding angles, congruent

20 d. same-side interior angles, supplementary

Step-by-step explanation:

20a.

m<7 = 34

m<5 + m<7 = 180       (linear pair)

m<5 = 180 - 37 = 143

m<4 = m<5 = 143      (alt int angles)

20b.

m<2 = m<7 = 37     (alt ext angles)

20c. corresponding angles, congruent

20d. same-side interior angles, supplementary

(a)

∠7 = 37° = ∠6 ( vertical angles )

∠4 = 180° - 37° = 143° ( 4 and 6 are supplementary interior angles )

(b)

∠2 = 37° (2 and 4 form a straight angle )

(c)

∠4 and ∠8 are corresponding congruent angles

(d)

∠3 and ∠5 are supplementary interior angles

Answer:

Step-by-step explanation:

(−5y+1) - (3y+2) = −9

(-5y-3y) + (1-2) = -9

-8y - 1 = -9

-8y = -8

y = 1

the difference between the 2 expressions is

- 5y + 1 - (3y + 2 ) = - 9

- 5y + 1 - 3y - 2 = - 9

- 8y - 1 = - 9 ( add 1 to both sides )

- 8y = - 8 ( divide both sides by - 8 )

y = 1

Answer:

d

Step-by-step explanation:

We have to add the polynomials [tex](4x^2-4x-3)[/tex] and [tex](3x^2-3x-5)[/tex]

To add the polynomials we need to add the like terms, by like terms we understand that the terms with the same exponent of the variables.

So in this case,

[tex](4x^2-4x-3)+(3x^2-3x-5)[/tex]

We will add the coefficients of [tex]x^2, x[/tex], and constants separately, we get:

[tex](4+3)x^2+(-4-3)x+(-3-5)=7x^2+(-7)x+(-8)=7x^2-7x-8[/tex]

Similarly, for the polynomials [tex](4x^2-4x-3)-(3x^2-3x-5)[/tex]

We will subtract the coefficients of like terms, we get:

[tex](4-3)x^2-(4-3)x-(3-5)=x^2-x+2[/tex]

r =√ ( A / 4π )

given A = 4πr² ( isolate r² by dividing both sides by 4π )

A / 4π = r² ( take the square root of both sides )

r =√( A / 4π )

Answer:

The expression of r in terms of A is:

[tex]r=\sqrt{\dfrac{A}{4\pi}}[/tex]

Step-by-step explanation:

We are given the surface area, A, of a sphere in terms of its radius, r, as:

A(r) = 4πr²

[tex]A=4\pi\ r^2[/tex]

⇒ [tex]r^2=\dfrac{A}{4\pi}[/tex]

⇒ [tex]r=\sqrt{\dfrac{A}{4\pi}}[/tex]

Hence, the expression of r in terms of A is:

[tex]r=\sqrt{\dfrac{A}{4\pi}}[/tex]

To solve the equation, multiply both sides by 2 and simplify. The value of Qburgers is 5.

The question involves solving an equation for the variable Qburgers.

The value of Qburgers is 5.

∠B = 52°

Since the triangles are similar then

∠C = ∠S = 56°

∠B = 180° - (72 + 56)° = 52°

The answer is B) 25

Option: B is the correct answer.

B) 25

Joel is getting a dog, a cat, and a hamster.

He goes to the pet store and can choose from 8 dogs, 12 cats, and 5 hamsters.

i.e. the total number of combinations that are possible could be calculated with the help of Combination as:

[tex]8_C_1+12_C_1+5_C_1[/tex]

We know that:

[tex]n_C_r=\dfrac{n!}{(n-r)!r!}[/tex]

Hence, the value of [tex]8_C_1\times 12_C_1\times 5_C_1[/tex] is:

[tex]=\dfrac{8!}{(8-1)!1!}+\dfrac{12!}{(12-1)!1!}+\dfrac{5!}{(5-1)!1!}\\\\\\=\dfrac{8!}{7!}+\dfrac{12!}{11!}+\dfrac{5!}{4!}\\\\=8+12+5\\\\=25[/tex]

Hence, the number of combinations is:

25

Answer: y = 1/7(x) or y = x/7

Step-by-step explanation:

Hey there! Thank you for submitting your question to Brainly!

In order to vertically compress the equation y = x by 1/7, we would simply need to multiply x by 1/7. Therefore, this gives us the equation y=1/7(x) or y=x/7.

Hope this helps!! :)

A vertical compression by a factor of 1/7 to the equation y=x results in the new equation y=1/7x where each y-value of the original function is 1/7 of its original height.

A vertical compression by a factor of 1/7 to the equation y=x results in the new equation y=1/7x. In vertical compression, each y-value of the original function is multiplied by the factor of compression, in this case, 1/7. Thus y=x becomes y=1/7x. This means for any x value in the original function, the corresponding y value in the new function is 1/7 of its original height. For example, where x was 1, y was also 1 for the original equation. In the new equation, when x is 1, y is now 1/7.

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To answer the question, you need to determine the amount Mr. Traeger has left to spend, then find the maximum number of outfits that will cost less than that remaining amount.

Spent so far:

... 273.98 + 3×7.23 +42.36 = 338.03

Remaining available funds:

... 500.00 -338.03 = 161.97

The cycling outfits are about $80 (slightly less), and this amount is about $160 (slightly more), which is 2 × $80.

Mr. Traeger can buy two (2) cycling outfits with the remaining money.

_____

The remaining money is 161.97/78.12 = 2.0733 times the cost of a cycling outfit. We're sure he has no interest in purchasing a fraction of an outfit, so he can afford to buy 2 outfits.

B

the spread of the graph of a parabola is determined by the multiplier k

the standard comparison is against k = 1

• If k > 1 then the graph narrows towards the y-axis

• If 0 < k < 1 then graph widens towards the x- axis

[tex](x+y)^2 =x^2+2xy+y^2\not=x^2+y^2[/tex]

calculating each of the products

noting that i² = (√- 1 )² = - 1

(1 + 2i)(8i) ( distribute by 8i )

= 8i + 16i² = - 16 + 8i ← complex number

(1 + 2i)(2 - 5i) ( expand using FOIL )

= 2 - 5i + 4i - 10i²

= 2 - i + 10 = 12 - i ← complex number

(1 + 2i)(1 - 2i) ( expand using FOIL )

= 1 - 2i + 2i - 4i²

= 1 + 4 = 5 ← real number

(1 + 2i)(4i) ( distribute by 4i )

= 4i +8i² = - 8 + 4i ← complex number

(1 + 2i)(1 - 2i) is the only product which results in a real number

False.  That is a cubic equation.

-6 + 4x < x +3       : Distributive property

-6 + 3x < 3           : Subtraction property of inequality

3x < 9                  : Addition property of inequality

x  <3                    : Division property of inequality

Answer:

[tex]-2(3-2x)<x+3[/tex] Given,

[tex]-6+4x<x+3[/tex]: Distributive property,

[tex]-6+3x<3[/tex]: Subtraction property of order,

[tex]3x<9[/tex]: Addition property of order,

[tex]x<3[/tex]: Division property of order.

Step-by-step explanation:

We have been given an inequality. We are asked to match each step for solving the equation with reason.  

[tex]-2(3-2x)<x+3[/tex]

Using distributive property, we will get:

[tex]-2\cdot3-(-2)\cdot2x<x+3[/tex]

[tex]-6+4x<x+3[/tex]

Subtract x from both sides:

[tex]-6+4x-x<x-x+3[/tex]

[tex]-6+3x<3[/tex]

Add 6 on both sides:

[tex]-6+6+3x<3+6[/tex]

[tex]3x<9[/tex]

Divide both sides by 3:

[tex]\frac{3x}{3}<\frac{9}{3}[/tex]

[tex]x<3[/tex]

The digit _ that will make 2.4_1 be more than 2.463 must be 7, 8, or 9.

If the first number in your sequence is 2.48 (not 2.84), then the unknown digit must be 7.

2.48 > 2.471 > 2.463

The coefficient of x is not zero, so there is exactly one solution.

_____

6x +8 -2x(5) = 2(7) . . . . evaluate parentheses contents

6x +8 -10x = 14 . . . . . . . eliminate parentheses

-4x +8 = 14 . . . . . . . . . . collect x terms

-4x = 6 . . . . . . . . . . . . . . subtract 8

x = -6/4 = -3/2 . . . . . . . . divide by the coefficient of x

Answer:

The total price depends on the number of crates.

Step-by-step explanation:

Without seeing the graph, we can't provide a definitive answer. Generally, in such situations, total price would likely depend on the quantity of goods (pumpkins or crates) purchased (Options D and B).

To answer this question, we'd need to closely examine the given graph. However, generally, in a graph showcasing a transaction, the total price depends on the quantity of goods, such as pumpkins or crates, purchased. Hence without explicit information from the graph at hand, option D. 'The total price depends on the number of pumpkins', and option B. 'The total price depends on the number of crates' could potentially be accurate. But we cannot determine definitively without further information.

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The amount of money that Layla has saved, s, is going to be what the equation equals. She earns $150 each month, so that would be 150m (slope intercept form equation s=em+b). B is the y-intercept, or the amount that Layla already has saved, which is positive $650.

Your equation is:

s=150m+650

I hope this helps :)

To find out how much an angelfish has grown in feet, divide the number of inches by 12, since there are 12 inches in a foot. As an example, if an angelfish has grown 6 inches, it would be 6 inches / 12, equaling 0.5 feet.

To convert a measurement from inches to feet, we use the fact that one foot is equal to 12 inches. For example, if an angelfish has grown 6 inches, we divide the number of inches by 12 to find the growth in feet:

The angelfish has grown 0.5 feet.

Similarly, let’s convert 374 inches to feet as another example of going from a smaller unit to a larger unit: