Divide \frac{\left(10x^4+20x^3-31x^2+x+19\right)}{\left(x+3\right)}
(x+3)
(10x
4
+20x
3
−31x
2
+x+19)
​
. What is the Remainder?

Answer:

Yes.

RS ≅ PS

QS ≅ QS

Step-by-step explanation:

The Hypotenuse-Leg Congruence Theorem states that when the hypotenuse and one leg of a Right-angled triangle are congruent to that of another Right-angled triangle, the two Right-angled triangles are therefore congruent.

In the diagram given, the hypotenuse (RS) and a leg (QS), of ∆RQS is congruent to the hypotenuse (PS) and a leg (QS) of ∆PQS. Therefore, ∆PQS is congruent to ∆RQS by HL Congruence Theorem.

Yes, PQS congruent to RQS by HL is true statement according to the diagram.

Hence :

RS ≅ PS

QS ≅ QS

Step-by-step explanation:

Given information:

The hypotenuse RS and PS

And leg QS.

Hypotenuse-Leg (HL) theorem:

The H-L theorem states that If, the hypotenuse and one leg of a Right-angle triangle are congruent to that of another right angle triangle then the given two right angled triangle will be congruent.

As, we can see in the given diagram the hypotenuse (RS) and the leg (QS) of triangle ΔRQS is congruent to hypotenuse (PS) and leg (QS) of triangle ΔPQS.

Hence , we can say that the ΔPQS is congruent to ΔRQS by H-L Congruent theorem.

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Step-by-step explanation:

$4200 - $50

= $4150

4150 divided by 45 = 92.222.......

92.222 is approximately 93

So you can purchase 92/93 tickets in total

Since tickets are physical things, I dont think you can approximate it but that's my answer

The maximum amount of adult tickets they can purchase are 92.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given are tickets at an amusement park that are $25 for children and $45 for adults. The Jones family has 4200 cash and they have two children.

Assume that they could purchase [n] number of adult tickets.

Cash remaining for adult tickets = 4200 - 2(25)

The total number of adult tickets that can be buyed are calculated as follows -

45n = 4200 - 2(25)

45n = 4200 - 50

45n = 4150

n = 4150/45

n = 92 (exact value)

Therefore, the maximum amount of adult tickets they can purchase are 92.

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Answer: 6x^2+3x

Step-by-step explanation:

Answer:

r=-3

Step-by-step explanation:

the first step in this equation is to isolate 6r,to do this you got to add 12 to -30 which you get -18 which gives the equation 6r=-18 which now you got to divide both sides by 6 which you should get r=-3

Answer:

r=-3

Step-by-step explanation:

add 12 to -30 you get -18 divide -18 by 6 and you get -3

Answer:

Step-by-step explanation:

Meeee

Answer:

1.80

2.Overestimate.

Step-by-step explanation:

Answer:

Sorry I'm late

Step-by-step explanation:

Answer:

Part A: [tex].50x+120 = .70x+80[/tex]

Part B: [tex]200[/tex] miles

Step-by-step explanation:

So to start, we need to put this information into slope-intercept form. Slope intercept form is [tex]y=mx+b[/tex]  where [tex]m[/tex] represents the slope of a line and [tex]b[/tex] represents the y-intercept. In this question [tex]y[/tex] represents the total cost of the rental, [tex]x[/tex] represents the number of miles driven, [tex]m[/tex] represents the price per mile, and [tex]b[/tex] represents the base price of the rental. Now that we know the variables, we need to plug in the information we have.

Since we know that company A charges $125 a day and $0.50 per mile we would have [tex]y=.50x+120[/tex]

Since we know that company B charges $80 a day and $0.70 per mile we would have [tex]y=.70x+80[/tex]

Now that we have two equations we can move onto the next step. We're looking to know the number of miles ([tex]x[/tex]) that would make the total cost ([tex]y[/tex]) equal. To do this we can make the equations equal each other since we know that [tex]y[/tex] will be the same.

Written out, the equation will look like this: [tex].50x+120 = .70x+80[/tex]

Now, we are trying to find [tex]x[/tex] so we need to isolate the variable.

To start we need to put [tex]x[/tex] on the same side so we'll subtract [tex].70x[/tex] from both sides to get  [tex]-.20x+120=80[/tex]

Next, we'll subtract [tex]120[/tex] from both sides of the equation to get [tex]-.20x=-40[/tex]

Finally, we'll divide both sides by [tex]-.20[/tex] to get [tex]x=200[/tex]

This means that at [tex]200[/tex] miles, both companies will cost the same amount.

Answer:

p=2

Step-by-step explanation:

22-10=12

12/6p=2

See picture for math work and answer.

Answer:

I'd assume the last one but I don't know exactly what the graph is measuring

Answer:

Step-by-step explanation: it would be B= 3/20

hope this helps!!!!

Answer: B) m=3/20

Step-by-step explanation: X is increasing by 3 each time, while Y is increasing by 20. Therefore, it is 3/20.

Answer:

y = 1/2x + 2.5 and y = -1/5x + 8

Step-by-step explanation:

2x - 4y = 10 (subtract 2x on each side)

-4y = -2x + 10 ( divide by - 4 on both sides)

y = 1/2x + 2.5

x + 5y = 40 (subtract x on both sides)

5y = -x + 40 (divide by 5 on both sides)

y = -1/5x + 8

Hope this helped!!

Answer:

slope is 1

Step-by-step explanation:

Hope this helps

Answer:

(y= -3 and x = 9)

Step-by-step explanation:

For the y intercept, make x = 0 and solve. For the x intercept, make f(x) = 0 and solve.

Answer:

11

Step-by-step explanation:

0,4

is where it would land and you can

Answer: 73 feet

Step-by-step explanation:

1inch =5feet

L=3.5 inches W=2.5 inches

P= L1+L2+W1+W2

L=3.5(5) =17.5

W= 2.5(5) = 12.5

17.5+ 17.5 +12.5+ 12.5= 73 feet

Given that,

Shelley's pet food store sold one customer 5 peanut butter biscuits for $3. She sold another customer 7 beef treats for $4.20.

For peanut, the cost is ratio is

[tex]\dfrac{5}{3}[/tex]

For beef, the ratio is

[tex]\dfrac{7}{4.2}[/tex]

If we take cross product of these items,

[tex]\dfrac{5}{3}=\dfrac{7}{4.2}\\\\5\times 4.2=3\times 7\\\\21=21[/tex]

It implies, that the sale is in true proportion. From the cross product, we find that it is equal.

Answer:

21

Step-by-step explanation:

Answer:

Step-by-step explanation:

1+2/3m+2=2+1/6

We move all terms to the left:

1+2/3m+2-(2+1/6)=0

Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R

We add all the numbers together, and all the variables

2/3m+1+2-(1/6+2)=0

We add all the numbers together, and all the variables

2/3m+3-(1/6+2)=0

We get rid of parentheses

2/3m+3-2-1/6=0

We calculate fractions

There is no solution for this equation

Answer: m = 1/10

Step-by-step explanation:

1 2/3m + 2 = 2 1/6

Firstly, subtract 2 from both sides to get m alone:

1 2/3m = 1/6

Now, to get m alone, divide both sides by 1 2/3:

m = 1/10

Hope this helps!

Answer:

A

Step-by-step explanation:

2Red                                            6 Blue Balls

+4Yellow                                  

= 6 balls    

Answer:

The answer is 3.7

✨

Answer:

(- 9, - 6 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , thus

(9, - 6 ) → (- 9, - 6 )

Answer:

Step-by-step explanation:

The vertex form of an equation of the parabola:  

                                                       f(x) = a(x - h)² + k

the vertex is (7, -4)  ⇒   h = 7,  k = -4

so:

     f(x) = a(x - 7)² + (-4)

    f(x) = a(x - 7)² - 4

The parabola goes through the point (5, 8) ⇒   x=5,  f(x)=8

8 = a(5 - 7)²  - 4

8 = a(-2)²  - 4

+4           +4

12  = 4a

÷4       ÷4

a = 3

It means the equation of the parabola in vertex form:

                               f(x) = 3(x - 7)² - 4

Answer:

4(x+1)

Step-by-step explanation:

Factor 2x+3+2x+1

4x+4

=4(x+1)

Answer:

here's your answer

please mark me as brainliest

Answer:34.7

Step-by-step explanation:

h/ 13 = 2/0.75

h= 2 • 13 / 0.75

34.7 m (rounded)

Tree is 34.7m tall.

In similar triangle, shape is same but size is varing. So the ratio of corresponding sides are also equal.

So according to asked question,

Let height of the tree =h

The triangle formed by the tree and its shadow is similar with the triangle formd by the the trangle formed by the lamppost and its shadow.

So, according to the propoties of the similar triangle

a₁/a₂=b₁/b₂

h/x=2m/75cm

⇒h/13=2/(3/4)

⇒h/13=2*4/3=8/3

⇒h=8*13/3=34.666≅34.7m

Therefore tree is 34.7m tall.

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Answer:

They are called opposites.

Step-by-step explanation:

"Zero is called the origin, and it's neither negative nor positive. For every positive integer, there's a negative integer an equal distance from the origin. Two integers that lie the same distance from the origin in opposite directions are called opposites. For example, negative 5 is the opposite of positive 5."

-Google

Hope this helps :)

Answer:

C=24

Step-by-step explanations:

Answer:

-9+5=-4

Step-by-step explanation:

a negative times a negative is always a positive.

Answer:

-9 + 5

Step-by-step explanation:

If there is a negative sign in front of a negative number in parenthesis, then that makes the negative number a positive number which is -9 + 5

-3                   -24

-120               9

-21                  -9

8                   -48

Answer:

(-27) / 9 = -3                   4 * (-6 )= -24

12 * (-10) = -120              (-45) / (-5) = 9

7 * (-3) = -21                    72 / (-8) = -9

64 / 8 = 8                        (-8) * 6 = -48

Answer:   72

Step-by-step explanation:  i multiplied 18 and 4 and that gave me 72

hopefully im not wrong let me know if i am

Answer:

5 and half packet of seeds or 5.5 which is 6 packets

Step-by-step explanation:

12 / 4 = 3

he can plant 3 plants with 1 seed packet

which means he needs 5 packets and half

the answer is 6