Mr. Lynch bought some oranges and pears.
After giving away 10 oranges, he had twice
as many pears as oranges left. If he had 24
pears in the end, what was the ratio of
oranges to pears in the beginning?

Answer:

both substitutions

Step-by-step explanation:

in 5. based on 3 BC is substituted by its equal counterpart AB.

and in 6. we use 1. to substitute AC by its associated absolute value.

Answer:

3(a +3)

Step-by-step explanation:

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

FOIL

a^2 +3a+3a+9 -a(a+3)

Distribute

a^2 +3a +3a +9 -a^2 -3a

Combine like terms

3a +9

FACTOR out a+3

(a+3)( a+3 -a)

(a+3) (3)

3(a+3)

Answer:

3(a+3)

Step-by-step explanation:

Expand the first set of brackets first

(a+3)^2

A^2 + 3a + 3a +9

=A^2 + 6a + 9

Expand the second set of brackets

-a(a+3)

=-a^2 - 3a

Add both sets together

3a + 9

Factorise:

3(a+3)

Answer: 7.25

Step-by-step explanation:

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]\boxed{x = -4}[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\3x - 5 = 5x + 3\\-----------\\\rightarrow 3x - 5 + 5 = 5x + 3 + 5\\\\\rightarrow 3x = 5x + 8\\\\\rightarrow 3x - 5x = 5x - 5x +8\\\\\rightarrow -2x = 8\\\\\rightarrow \frac{-2x=8}{-2}\\\\\rightarrow \boxed{x = -4}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

Step-by-step explanation:

7

Answer:

x=10

Step-by-step explanation:

16/24=(x-2)/12

or, 16/2=x-2

or, 8=x-2

or, x-2=8

or, x=10

Answered by GAUTHMATH

Answer:

x= plus or minus 1 plus imaginary root times square root of 5.

Step-by-step explanation:

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

Complete the Square.

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

[tex] {x}^{2} - 2x + 1 = - 5[/tex]

[tex](x - 1) {}^{2} = - 5[/tex]

[tex]x = + - 1 + i \sqrt{5} [/tex]

Answer:

T = 55 + 6w and $103

Step-by-step explanation:

We have already saved $55, so that is our constant. We gain $6 per week, so that will be our w value

T = 55 + 6w

Solving for T when w = 8 weeks

T = 55 + 6(8)

T= 55 + 48

T = $103

Answer:

100998 is the answer.

I hope this help u.

Answer:

100998

Step-by-step explanation:

₁ ₁ ₁ ₁ ₁

99999

+   999

100998

you can also think of it as

99999(+1) + 999(-1)

100000+998

100998

Answer:

(A)

x= 5y-3

(x+3)/5

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

i took the test lol

Answer:

B only

Step-by-step explanation:

well to solve this question we can consider factor theorem which states that if a Polynomial f(x) is divided by a monomial x-a then x-a is a factor of f(x) if and only if f(a)=0

and to figure "a " we can consider the following equation:

[tex] \displaystyle x - a = 0[/tex]

substitute the given value of a:

[tex] \displaystyle x - 2= 0[/tex]

therefore,

[tex] \displaystyle x = 2[/tex]

plugin the value of x to the function A(x):

[tex] \displaystyle A(2) = {2}^{3} + {2}^{2} + 4[/tex]

simplify which yields:

[tex] \displaystyle A(2) = 16[/tex]

since A(2)≠0 x-2 is not a factor of A(x)

similarly substitute the value of x to the function B(x) which yields:

[tex] \displaystyle B(2) = {2}^{3} - {2}^{} - 6[/tex]

simplify:

[tex] \displaystyle B(2) =0[/tex]

so, B(2)=0 Hence x-2 is a factor of x³-x-6

substitute the value of x to the function C(x)

[tex] \displaystyle C(2) = {2}^{4} + 3.{2}^{} - 10[/tex]

simplify:

[tex] \displaystyle C(2) =12[/tex]

as C(2)≠0 x-2 is not a factor of C(x)

likewise plugin the value of x to the function D(x):

[tex] \displaystyle D(2) = {2}^{4} - 2.{2}^{3} - 2[/tex]

simplify and that yields:

[tex] \displaystyle D(2) = - 2[/tex]

therefore,D(2)≠0 hence,x-2 isn't a factor of D(-2)

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

The factor

we have find the value of x .

Now,

we have to select all the polynomial which has x-2 As a factor.

According to the question,

[tex]A(x)=x^3+x^2+4\\\\A(2)=(2)^3+(2)^2+4\\\\=8+4+4\\\\16≠0[/tex]

[tex]B(x)=x^3-x-6\\\\=B(2)=(2)^2-2-6\\\\0=0[/tex]

[tex]C(x)=x^4+3x-10\\\\=C(2)=(2)^4+3(2)-10\\\\=16+6-10\\\\12≠0[/tex]

[tex]D(x)=x^4-2x^3-2\\\\D(2)=(2)^4-2(2)^3-2\\\\=16-16-2\\\\-2≠0[/tex]

The option B is correct.

Answer:

[tex]x=opposite\: side\: of \:22[/tex]

[tex]16=hypotenese[/tex]

[tex]sin22=opp/hyp[/tex]

[tex]sin22=\frac{x}{16}[/tex]

[tex]\Longrightarrow x=16\times sin22[/tex]

[tex]x=5.99[/tex]

[tex]x=6.0[/tex]

[tex]OAmalOHopeO[/tex]

Answer:

I think its B.

Step-by-step explanation:

sorry if i am wrong.

Answer:

the 3rd won for sure

Step-by-step explanation:

hope I helped

Answer:

C

Step-by-step explanation:

The coordinates are all in (x, y) form.

X is how left or right

y is how tall.

If you just look for the individual coordinates given, you will see that all of the Coordinates in C are on the graph.

I hope this helps!

Answer:

32

Step-by-step explanation:

Green : black

3             4

We have 24 green

3+8=24

so  multiply each side by 8

Green : black

3*8         4*8

24            32

There are 32 black grapes

Answer:

32

Step-by-step explanation:

By Question :-

Let :-

Therefore,

Answer:

75°

Step-by-step explanation:

First, we need to know that the interior angle sum of a triangle is always 180°.

Now, to find the missing angle aside from x, we need to complete the sum 180-155=25, seeing 155° lies on a straight line. Remembering the interior angle sum of a triangle is always 180°, it is thus clear that 25+80+x=180. If we complete this equation, x=75.

Hope this helps!

0 = (x-8)^2 -100

Add 100 to both sides

100 = (x-8)^2

Take the square root of both sides

10 = (x-8)

Remove the parentheses

10 = x-8

Add 8 to both sides

18 = x

Answer: x = 18

Step-by-step explanation:

Answer with explanation is in the attachment

Hope it is helpful to you

Answer:

Step-by-step explanation:

The standard deviation is the square root of the variance, and the variance is found by using the mean. So we will do that first. I will use the population variance as opposed to the sample variance since our set of numbers is small.

The mean: 8 + 12 + 15 + 17 + 18 = 70 and divide that by 5 to get

[tex]\bar{x}=14[/tex] and use this to find the variance in the formula:

[tex]s^2=\frac{\sum(x_i-\bar{x})^2}{n}[/tex] it is a bit difficult to enter that formula in correctly, but here's how it works mathematically:

[tex]s^2=\frac{(8-14)^2+(12-14)^2+(15-14)^2+(17-14)^2+(18-14)^2}{5}[/tex]

Squaring this ensures us that we don't end up with zero, which would be useless.

[tex]s^2=\frac{36+4+1+9+16}{5}[/tex] so

[tex]s^2=13.2[/tex] which means that the standard deviation is

s = 3.633

(If you do it with n-1 = 4 in the denominator of the variance, you get a standard deviation of 4.062)

Answer:

i think its 24

Step-by-step explanation:

2=2

Given:

The inequality is:

[tex]y<\sqrt{x+3}+1[/tex]

To find:

The domain and range of the given inequality.

Solution:

We have,

[tex]y<\sqrt{x+3}+1[/tex]

The related equation is:

[tex]y=\sqrt{x+3}+1[/tex]

This equation is defined if:

[tex]x+3\geq 0[/tex]

[tex]x\geq -3[/tex]

In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set. Thus, -3 is not included in the domain.

So, the domain of the given inequality is x>-3.

We know that,

[tex]\sqrt{x+3}\geq 0[/tex]

[tex]\sqrt{x+3}+1\geq 0+1[/tex]

[tex]y\geq 1[/tex]

The points on the boundary line are not included in the solution set. Thus, 1 is not included in the range.

So, the domain of the given inequality is y>1.

Therefore, the correct option is A.

Answer: B and C

Step-by-step explanation:

the triangle inequality theorem states that any 2 sides of a triangle must be greater than the measure of the third side. now with this rule, let's apply it to all options!

option a:

7 + 5 > 6 .. yes!

6+ 7 > 5 .. yes!

5 + 6 > 7 .. yes!

option b:

9 + 12 > 19 .. yes!

12 + 19 > 9 .. no!

19 + 9 > 12 .. no!

option c:

7 + 11 > 18 .. no!

11 + 18 > 7 .. no!

18 + 7 > 11 .. yes!

option d:

6 + 8 > 11 .. yes!

8 + 11 > 6 .. yes!

11 + 6 > 8 .. yes!

i did this topic years ago so please let me know if there are any mistakes! hope this helped, and good luck! ◝(ᵔᵕᵔ)◜

Answer:

x = 52

y = 19

Step-by-step explanation:

The degree measure of a straight line is (180) degrees. One can use this to find the measure of the angle that is adjacent to the angle with a measure of (142) degrees. Form an equation and solve for the unknown,

142 + (unknown angle) = 180

unknown angle = 38

The inscribed angle theorem states that twice the measure of an angle with its vertex of the circumference (outer edge) of a circle is equal to the measure of the surrounding arc. Therefore, one can state the following:

(2)(unknown angle) = (surrounding arc)

(2)(38) = (surrounding arc)

76 = surrounding arc

The central angles theorem states that the measure of an angle whose vertex is the center of the circle is equal to the measure of the surrounding arc. Therefore, one can state the following:

m<O = (surrounding arc)

m<O = 76

The radius is the distance from the center of the circle to the circumference of the circle. All radii in a circle are congrunet. Therefore the triangle with angle (x) and vertex (O) is an isosceles triangle, as two of its sides are radii, and are thus congruent. One property of an isosceles triangle is the base angles theorem. This theorem states that the angles opposite the congruent sides in an isosceles triangle are congruent. Moreover, the sum of angles in any triangle is (180) degrees. Therefore, one can make the following statement:

m<O + x + x = 180

76 + 2x = 180

x = 52

Finally, one can use the property that the sum of angles in any triangle is (180) degrees to make the following statement:

(x + 19) + (x + y) + (38) = 180

52 + 19 + 52 + y + 38 = 180

161 + y = 180

y = 19

x=52°

y=19°

Answer:

Solution given:

<OCA=19°[base angle of isosceles triangle]

Since ∆AOC is similar to ∆ BOC

y=19°[corresponding angle of a similar triangle are equal]

<OAB=<OBA=x[base angle of isosceles triangle]

again

<A+<B=180°[exterior angle of a triangle is equal to the sum of two opposite interior angle]

x+19+x+19=142°

2x=142°-38°

x=104/2

x=52°

Answer:

90%

Step-by-step explanation:

63/70 = 0.9 = 90%

Answer:

63 out of 70

63×10÷70=9

9%

Answer: it’s 111

Step-by-step explanation:

Answer:

Horizontal line

Step-by-step explanation:

uehdjd

Answer:

I believe its (-3,-2)...........

Answer:

50

Step-by-step explanation: