Joe concluded that the expression 3x + 15 + 2x is equivalent to the expression 5(x + 3). Which of these best explains how Joe reached his conclusion?
o dividing each term in the first expression by 3
O combining like terms in the first expression and dividing each term by 3
O combining like terms in the first expression and dividing each term by 5
O subtracting 2. and applying the distributive property to the first expression

Answer:

c is circumference which is equal to 3.14 multiplied by d  

Step-by-step explanation:

Answer:

Option 3

Step-by-step explanation:

The two triangles are proved congruent to each other so CPCTC proves that the angles are also congruent.

Answer:

Step-by-step explanation:

So first I divided 240 by 2 to get the hourly rate, which is 120. Then i multiplied 120 times 36 and got 4,320 quarts in 36 hours. The daily rate is 2,880, I got that by multiplying 120 by 24 because there are 24 hours in a day.

Answer:

x=5.09 seconds (times at max)

Step-by-step explanation:

The time at which the height of the rocket is maximum is 5.09 seconds and the maximum height is 563.14 feet.

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

A rocket is launched from a tower.

The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation.

The quadratic equation is given below.

[tex]\rm y=-16x^2+163x+148[/tex]

Differentiate the equation with respect to x, then we have

[tex]\rm y' = \dfrac{dy}{dx}=\dfrac{d}{dx}(-16x^2+163x+148)\\\\y' =-32x + 163[/tex]

For y' = 0, then we have

32x = 163

   x = 5.09

Then the maximum value of the rocket will be

[tex]\rm y=-16(5.09)^2+163(5.09)+148\\\\y = - 414.53 + 829.67 + 148\\\\y = 563.14\ ft[/tex]

More about the quadratic equation link is given below.

https://brainly.com/question/2263981

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Answer:

x = 19 degrees

y = 84 degrees

Step-by-step explanation:

recall that for an isosceles triangle (which is pictured), the base angles have the same value.

In our case, we can see that the base angles are 48 deg and (3x-9) deg

if they are equal, we can equate them like this:

48 = 3x-9    (add 9 to each side)

48 + 9 = 3x

57 = 3x   (divide both sides by 3)

x = 57/3

x = 19 degrees  (answer)

also recall that the sum of the interior angles of a triangle add up to 180 deg, hence

48 deg + 48 deg + y deg = 180 deg

2(48) + y = 180

96 + y = 180

y = 180 - 96

y = 84 deg

Answer:

Step-by-step explanation:

1) (x+2)(x+2)=-x-2

[tex]x^{2}[/tex] +2x +2x +4+=-x-2

[tex]x^{2}[/tex]+4x+4+x+2

[tex]x^{2}[/tex]+5x+6

2) [tex]x^{2}[/tex] +4x +12 -16x +24=0

[tex]x^{2}[/tex] -12x+36=0

3) (x-4)(x+1)

x=4 and/or x=-1

4) (x-5)(x-6)

x=5 and/or x=6

5) (x-7)(x+2)

x=7 and/or x=-2

6) [tex]x^{2}[/tex]+3x-10=0

(x-5)(x+2)

x=5 and/or x=2

7) [tex]x^{2}[/tex]+x-20

(x-5)(x+4)

x=5 and/or x=-4

Answer:

7xy + 2x^2t

Step by step explanation:

You just group the like terms and simplify (pay attention to the signs)

5xy + 2xy = 7xy

-1x^2t + 3x^2t = 2x^2t

So the answer is : 7xy + 2x^2t

Answer:

b67

Step-by-step explanation:

Answer:

(15, 12)

Step-by-step explanation:

Let's generate two systems of equations that fit this scenario.

Number of trips to the airport = x

Number of trips from the airport = y

Total number of trips to and from the airport = 27

Thus:

[tex] x + y = 27 [/tex] => equation 1.

Total price for trips to the Airport = 14*x = 14x

Total price of trips from the airport = 7*y = 7y

Total collected for the day = $294

Thus:

[tex] 14x + 7y = 294 [/tex] => equation 2.

Multiply equation 1 by 7, and multiply equation 2 by 1 to make both equations equivalent.

7 × [tex] x + y = 27 [/tex]

1 × [tex] 14x + 7y = 294 [/tex]

Thus:

[tex] 7x + 7y = 189 [/tex] => equation 3

[tex] 14x + 7y = 294 [/tex] => equation 4

Subtract equation 4 from equation 3

-7x = -105

Divide both sides by -7

x = 15

Substitute x = 15 in equation 1

[tex] x + y = 27 [/tex]

[tex] 15 + y = 27 [/tex]

Subtract both sides by 15

[tex] y = 27 - 15 [/tex]

[tex] y = 12 [/tex]

The ordered pair would be (15, 12)

Natalie

Step-by-step explanation:

Esraa finishes in 12.2 secons making her first.

natalie finishes in 12.34 seconds making her second.

Ava finishes in 12.89 making her third.

and Savannah finishes in 12.988 seconds making her last.

Answer:

8,750 = 250 + 340x

I believe he is missing the cost of the house

Answer:

The coordinates of triangle A"B"C" will become

A( 5,-3  )  B( 9,6 )  C( -12 ,-4 )

Step-by-step explanation:

Original vertices of triangle ABC are ;

A ( -3, 5 ) B( 6, 9 )  C ( -4, -12 )

after reflection over x-axis

A( -3,-5 )   B( 6, -9 )  C( -4,12 )

when the triangle is rotated

x coordinates becomes -y  while y coordinates becomes x

The coordinates of triangle A"B"C" will become

A( 5,-3  )  B( 9,6 )  C( -12 ,-4 )

Answer:

y = 33h + 25

Step-by-step explanation:

Given that :

Equation for the amount charged for language art session :

20h + 25 ;

Slope intercept equation :

mx + c

c = intercept, m = hourly charge

Here, the one time fee = 25

For civics:

One time fee is the same;

Hence, c = 25

Amount charged for a 3 hours civic tutoring session = $124

y = mh + c

h = number of hours ; c = $25

Amount charged per hour (m) :

$(124 - 25)/ 3

= $99 /3

= $33

m = 33

Hence,

Total charge y ;

y = 33h + 25

Answer:

The 17th term number of the arithmetic sequence will be: -97

i.e.

Step-by-step explanation:

Given the arithmetic sequence

[tex]a_n=-6n+5[/tex]

Put [tex]n=17[/tex] in the arithemetic sequence to get the 17th term number

[tex]a_{17}=-6\left(17\right)+5[/tex]

[tex]a_{17}=-6\cdot \:17+5[/tex]

[tex]a_{17}=-102+5[/tex]

[tex]a_{17}=-97[/tex]

Therefore, the 17th term number of the arithmetic sequence will be: -97

i.e.

[tex]a_{17}=-97[/tex]

Answer:

Multiply them together.

Step-by-step explanation:

Multiply them together. If they multiply to a number greater than or equal to 10, then divide the product by 10 and add 1 to the exponent of the 10.

Answer:

$24.

Step-by-step explanation:

I multiplied 4 by 7 to get 28. Then I multiplied $28 by three weeks and got $84. Since $84 is more than I owe I subtracted $84 by $60 and got $24. I would give my friend $60 and keep $24. Hope this helps! Have a great day!

Answer:

6x³-x²-51x+40

Step-by-step explanation:

(2x − 5)(3x² + 7x− 8)

vv

6x³ +14x² -16x  -15x² -35x +40

add like terms:

6x³ -x² -51x +40

Answer:

9 m¹⁰

Step-by-step explanation:

(3m⁵)²

= (3)²(m⁵)²

= 9 (m⁽⁵⁾⁽²⁾)

= 9 m¹⁰

Answer:

m∠Y = m∠Z = 34

Step-by-step explanation:

m∠Y + m∠Z = 68

68 ÷ 2 = 34

Check:

180 - 68 = 112

112 + 34 + 34 = 180

Answer:

draw a line trough (2,3) and (0, 2)

Step-by-step explanation:

f(x)=(3/2)x+2

so 3/2 is your slope  and 2 is your y coordinate of y-intercept

pick any point to start for example (0, 0) and go slope=rise/run=3/2 and you will end-up at (2,3)

now you have a point (2,3) and a second the y-intercept (0,2)

draw a line trough those points

Answer:

9 cm

Step-by-step explanation:

Answer:

165 and 166

Step-by-step explanation:

You can divide 331 by 2 to get 165.5. You then round down for one answer, 165, and round up for the other, 166. This evens out the rounding, and to check your answer you can add 165 and 166, which is 331.

Answer:

C) 180

Step-by-step explanation:

I hope this helps

Good luck ;)

The difference between the intercepted arc is 180°

An angle is formed from the intersection of two or more lines. Angles less than 90 degrees are called acute angles, angles greater than 90° are called obtuse angles while angles with a measure of 90° are called right angles.

Circle theorem states that if a tangent and a sectant, two tangent or two sectant meets outside a circle, the measure of the angle formed is half the difference between the intercepted arcs.

A secant and a tangent meet at a 90° angle outside the circle. Hence:

90° = (1/2) * difference between the intercepted arc

Difference between the intercepted arc = 180°

The difference between the intercepted arc is 180°

Find out more on angle at: https://brainly.com/question/25770607

Answer:

2 feet

Step-by-step explanation:

12 feet in 6 minutes. 12/6=2

Answer:

C. y= 7x

Step-by-step explanation:

Answer:

less than or equal to 24

Step-by-step explanation:

this symbol ≤

Answer: B. 16 feet

Step-by-step explanation:

We know that the length is 20 feet longer that the width. If the length of the park is 36 feet, the width is 20 feet less.

36 - 20 = 16 feet

So, the width of the park is 16 feet.

hope this helps!

Answer:

[tex]\displaystyle x=\frac{-3+\sqrt{6}}{3}\text{ and } x=\frac{-3-\sqrt{6}}{3}[/tex]

Or, by approximating:

[tex]x\approx-0.1835\text{ or } x\approx -1.8165[/tex]

Step-by-step explanation:

Let’s convert this to standard form. We have:

[tex]-6x-1+5x^2=8x^2[/tex]

Subtract 5x² from both sides:

[tex]-6x-1=3x^2[/tex]

And add 6x and 1 to both sides:

[tex]0=3x^2+6x+1[/tex]

This is not factorable. So, we will need to use the quadratic formula.

The quadratic formula for a quadratic in standard form is given by:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]

In this case, a=3; b=6, and c=1.

Substitute appropriately:

[tex]\displaystyle x=\frac{-6\pm\sqrt{6^2-4(3)(1)}}{2(3)}[/tex]

Simplify:

[tex]\displaystyle x=\frac{-6\pm\sqrt{24}}{6}[/tex]

We can simplify the square root:

[tex]\sqrt{24}=\sqrt{4}\cdot\sqrt{6}=2\sqrt{6}[/tex]

Hence:

[tex]\displaystyle x=\frac{-6\pm2\sqrt{4}}{6}[/tex]

Simplify:

[tex]\displaystyle x=\frac{-3\pm\sqrt{6}}{3}[/tex]

Hence, we will have two solutions:

[tex]\displaystyle x=\frac{-3+\sqrt{6}}{3}\text{ and } x=\frac{-3-\sqrt{6}}{3}[/tex]

Approximating them, we can see that our solutions are approximately:

[tex]x\approx-0.1835\text{ or } x\approx -1.8165[/tex]

Answer:

"The given angle does not have a supplementary angle because supplementary angles add to the sum of 180°. The supplementary angle would then  need to be -3, and negative angles are not allowed based on the definition of supplementary angles."

Step-by-step explanation:

A supplementary angle completes an angle less than 180 degrees by filling in what's left. Ex. 170 and 10 are supplementary angles because they add up to a straight line, 180.

Since 183 is greater than 180, no angle (a negative angle isn't an angle) can complete it.