1. The width of a rectangle is x centimeters and its length is (x + 5) cm.
(x + 5)
Diagram not drawn to scale
(a) Write down an expression for the perimeter of the rectangle, giving your
answer in its simplest form.
The perimeter of the rectangle is 62 cm.
(b) Work out the length of the rectangle.

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:

(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)

Answer:

Chase and his brother will both have a score of 31 points by making 4 successful shots.

Step-by-step explanation:

Given that initially Chase has 19 points and his brother has 27 points.

In one successful flip, Chase get 3 points and in one successful flip, his little brother get 3 points

Assuming that both have the same score after n number successful flip of the coin.

So, points earned by Chase in n successful flip [tex]= 3\times n =3n[/tex]

and points earned by his little brother in n successful flip [tex]= 1\times n=n[/tex].

Total points of Chase [tex]= 19+3n\cdots(i)[/tex]

Total points of his little brother [tex]= 27 + n\cdots(ii)[/tex]

As the brothers have tied scores in the game, that means both have the same score, so from equations (i) and (ii), we have

[tex]19+3n = 27 + n \\\\\Rightarrow 3n-n = 27-19 \\\\\Rightarrow 2n=8 \\\\\Rightarrow n=8/2=4[/tex]

So, after n successful throw, both have the same score.

Hence, each brother made 4 additional successful shots.

Now, put n=4 inequation (i) or (ii) to get the total points, i.e

Total points of each brother [tex]= 19+ 3\times 4 = 31.[/tex]

Hence, each brother has 31 points.

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:

C. y= 7x

Step-by-step explanation:

Answer:

Step-by-step explanation:

9x-5 is a factor of [tex]81x^{2} -25[/tex]

Answer:

b67

Step-by-step explanation:

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:

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:

9 m¹⁰

Step-by-step explanation:

(3m⁵)²

= (3)²(m⁵)²

= 9 (m⁽⁵⁾⁽²⁾)

= 9 m¹⁰

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:

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: 40320 ways

Step-by-step explanation:

From the question, we are informed that we should the number of arrangements that are in the letters in the word: CHAPTERS.

First, we should note that there are 8 letters in the word CHAPTERS, therefore the number of ways that the word can be arranged is 8! which simply means:

8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 40320 ways

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:

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:

3

Step-by-step explanation:

13 ÷ 4 = 3.25

but you wont by .25 of a shirt so he can only buy 3 shirts

5/8 ÷ 1/4

5/8 • 4/1

5/2

Answer:

2.5 If I am right

Step-by-step explanation:

5/8 divided by 1/4= 2.5

I think  

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:

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:

its 6 because the lines show they are parellel so it has to be equal to 18 and 12 plus 6 is 18

Step-by-step explanation:

Answer:

X=2.5

Step-by-step explanation:

On Edge

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:

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:

[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:

c is circumference which is equal to 3.14 multiplied by d  

Step-by-step explanation:

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

#SPJ2

Answer:

See Attached

Step-by-step explanation:

See Attached for proof of RHS = LHS

Answer:

≈ 5 ft

Step-by-step explanation:

Using the tangent ratio in the right triangle.

let the height of the board be h , then

tan22.5° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{12}[/tex] ( multiply both sides by 12 )

12 × tan22.5° = h , then

h ≈ 5 ft ( to the nearest whole number )