II
Initial Knowledge
This morning, Leila's car had 19.79 gallons of fuel. Now, 2.8 gallons are left. How much fuel did Leila use?

Answer:

22.5º

Step-by-step explanation:

The angle of one shaded part and one unshaded part is 90º

We have shaded part ([tex]s[/tex]) and unshaded part ([tex]u[/tex])

[tex]90\º = u+s[/tex]

[tex]$u=\frac{s}{3} $[/tex]

[tex]$90\º = \frac{s}{3} +s$[/tex]

[tex]$90\º = \frac{s}{3} +\frac{3s}{3} $[/tex]

[tex]$90\º = \frac{4s}{3} $[/tex]

[tex]$270\º = 4s $[/tex]

[tex]s=67.5\º \implies u=22.5\º[/tex]

Answer: 22.5º

Step-by-step explanation:

Answer:

Option (A)

Step-by-step explanation:

In the figure attached,

A prism has been given with two triangular bases.

If we put this prism with one of the triangular face as the base of the prism, height of the prism will be 6 in.

Volume of a prism is calculated with the formula,

Volume = (Area of the triangular base) × Height

Area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height of the triangular base})[/tex]

                                             = [tex]\frac{1}{2}(3)(5)[/tex]

                                             = 7.5 in²

Volume of the prism = 7.5 × 6

                                  = 45 in³

Therefore, Option (A) will be the answer.

Answer:

Step-by-step explanation:

We first need to find h. Since h is the x coordinate of Q, and Q is on the line 3x + 4y = 6, we will plug in the x value of h and the y value of 3 and solve for h:

3h + 4(3) = 6 and

3h + 12 = 6 and

3h = -6 so

h = -2

The coordinates for Q are (-2, 3). Now we can use that to find the slope of the line QR:

[tex]m=\frac{8-3}{3-(-2)}=\frac{5}{5}=1[/tex]

So the slope of QR is 1. Now we will choose one of the coordinates on line QR as our x and y coordinates to write the equation for the line in point slope form then in standard form:

y - 8 = 1(x - 3) and

y - 8 = x - 3 and

y - x = 5 or

-x + y = 5. If your teacher does not want you to lead with a negative:

x - y = -5 would be your equation in standard form.

Answer:

-49152

Step-by-step explanation:

The pattern is:

multiply for 4

then:

-3, -12, -48, -192, -768, -3072, -12288, -49152

Answer:

5 1/20

Step-by-step explanation:

2 ⅘=2+4/5

2 ¼=2+1/4

So: 2 ⅘-(-2 ¼)=

2 ⅘ + 2 ¼=

2+4/5+2+1/4=

4+(4/5+1/4)=

4+21/20=

4+(20+1)/20=

4+(1+1/20)=

5 1/20

Answer:

30

Step-by-step explanation:

if x is 5, then 6x=______.

sub in the value of x for 5

when a variable and coefficient as next to eachother that means to multiply

so 6*5= 30

Answer:

[tex]\large \boxed{\mathrm{30}}[/tex]

Step-by-step explanation:

[tex]x=5[/tex]

[tex]\sf{Substitute \ x \ as \ 5 \ for \ 6x.}[/tex]

[tex]6(5)[/tex]

[tex]6 \times 5 = 30[/tex]

ABC is a equilateral triangle .

Proof :-

Let's assume both circles as C1 and C2 [ as shown in the figure ]

AC is the radius of circle C1.

BC is the radius of circle C2 .

AB and AC both are radius of circle C1 so both are equal ie AB = AC .

AB and BC both are radius of circle C 2 so both are equal ie AB = BC .

Hence we conclude that .

AB = BC = AC.

So the triangle is equilateral triangle.

Answer: 4.2 cups

Step-by-step explanation: 63 divided by 15=4.2

Answer:

5 1/2

Step-by-step explanation:

a) r=d/t

   11/4x2/1= 22/4= 5 1/2

b) 1/2 hour x 2 equals one hour, so 2 3/4 x 2 equals rate per hr.

11/4x2=22/4= 5 1/2

Answer:

1 mph

Step-by-step explanation:

All you have to do is follow the formula. Distance/time=mph

Answer:

1 1/7.

Step-by-step explanation:

-9 2/7 - (-10 3/7)

= -9 2/7  + 10 3/7

= - 9 + 10 - 2/7 + 3/7

= 1 + 1/7

= 1 1/7.

Answer:

Option B is the correct option

Step-by-step explanation:

[tex] \mathsf{ - 9 \frac{2}{7} - ( - 10 \frac{3}{7}) }[/tex]

First thing we have to do is that convert the mixed number into improper fraction .

[tex] \blue{ \mathsf{how \: to \: convert \: \: the \: improper \: fraction \: to \: mixed \: number}}[/tex]

Follow the steps:

Now, let's do it!

[tex] \mathsf{ - \frac{ 9 \times7 + 2 }{7} - ( - 10 \frac{3}{7} )}[/tex]

⇒[tex] \mathsf{ - \frac{65}{7} - ( - 10 \frac{3}{7} )}[/tex]

When there is a ( - ) in front of an expression in the

parentheses , change the sign of each term in the expression

⇒[tex] \mathsf{ - \frac{65}{7} + 10 \frac{3}{7} }[/tex]

Convert mixed number into improper fraction

⇒[tex] \mathsf{ - \frac{65}{7} + \frac{73}{7} }[/tex]

While performing the addition and subtraction of like fractions , you just have to add or subtract the numbers for respectively in which the denominator is retained same

⇒[tex] \mathsf{ \frac{ - 65 + 73}{7} }[/tex]

Calculate

⇒[tex] \mathsf{ \frac{8}{7} }[/tex]

Convert the improper fraction into mixed fraction.

( Since 8 is being divided by 7 , I am gonna use long division )

( See attached picture )

⇒[tex] \mathsf{1 \frac{1}{7} }[/tex]

Hope I helped!

Best regards!!

Answer:

102

Step-by-step explanation:

Answer:

  55°

Step-by-step explanation:

Perhaps you want the measure of angle B. (There is no "b" in the figure.)

That measure is half the measure of the intercepted arc:

  m∠B = 110°/2 = 55°

Angle B is 55°.

Answer

[tex] \boxed{10p}[/tex]

Step by step explanation

[tex] \mathsf{ - 4p + (- 6p)}[/tex]

When there is a ( + ) in front of an expression in parentheses, the expression remains the same

[tex] \mathsf{ - 4p - 6p}[/tex]

Collect like terms

[tex] \mathsf{ - 10p}[/tex]

Hope I helped!

Best regards!

Answer:

Hey there!

That would result in 0.00735.

Let me know if this helps :)

Hence, the significant figures are [tex]0.00735.[/tex]

What is the approximation?

An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding. A calculation can be approximated by rounding the values within it before performing the operations.

Here given that,

Approximate [tex]0.007349[/tex] to  significant figures​

So, the significant figures are [tex]0.00735.[/tex]

Hence, the significant figures are [tex]0.00735.[/tex]

To know more about the approximation

https://brainly.com/question/29580932

#SPJ2

Answer:

Scalene Right Triangle

Step-by-step explanation:

A possible type of triangle that has no equal sides and one right angle is a right triangle.

Right triangles have just one angle that is equal to 90°, and they can be either isosceles or scalene triangles.

Hope this helped!

Answer:

13

Step-by-step explanation:

3|2(2)-9|-2

First evaluate inside the absolute value

3|4-9|-2

3|-5|-2

Taking the absolute value of -5

3*5-2

Multiply

15 -2

13

Steps to solve:

3|2(2) - 9| - 2

3|4 - 9| - 2

3|-5| - 2

3(5) - 2

15 - 2

13

Best of Luck!

Answer:

19

Step-by-step explanation:

The pattern is that it +6 every number.

-5 + 6 = 1

1 + 6 = 7

7 + 6 = 13

So the next number is 13 + 6 = 19.

EDIT - I can't add sorry.

Answer:

Step-by-step explanation:

This is an arithmetic sequence.

-5, 1 , 7 , 13 ,.....

First term = a = -5

Common difference =  d = second term - first term

                                   = 1 - [-5] = 1 + 5

                                  = 6

Next term = previous term + d

                 = 13 + 6 = 19

nth term = a +(n-1)*d

              = -5 + (n-1)*6

              = -5 + 6n - 6  {add like terms}

              = -5 - 6 + 6n

             = -11 + 6n

Pattern: 6n -11

Answer with explanation:

If the change in the value of his favorite card is $-7, that simply indicates that he is having a loss of $-7 that can be understand as the value of his this years card must be smaller than the last year card.

Hence, the best describes the meaning of integer:

"he is having a loss of $-7"

Answer:

358 and remainder of 3

Step-by-step explanation:

1. Divide it like any other problem

So your remainder would be 3

Hope this helps

Answer:

see below

Step-by-step explanation:

The phrase "at least" indicates that you use the symbol ≥, so that's where they got the ≥ from. The amount of water needed for each bushel is 1/3 * f or 1/3f because you need 1/3 gallons of water per one bushel. We know that the amount of water needed is at least 1/3 gallons per bushel. Since the amount of water is w, "at least" is ≥ and 1/3 gallons per bushel is 1/3f, the inequality is w ≥ 1/3f. I hope this makes sense.

[tex]t=\sqrt{\dfrac{ab-s}{r+ak}}\\\\t^2=\dfrac{ab-s}{r+ak}\\\\rt^2+akt^2=ab-s\\\\akt^2-ab=-rt^2-s\\\\a(kt^2-b)=-(rt^2+s)\\\\a=-\dfrac{rt^2+s}{kt^2-b}\\\\a=-\dfrac{rt^2+s}{-(b-kt^2)}\\\\a=\dfrac{rt^2+s}{b-kt^2}[/tex]

Answer:

321/8 ft^2

Step-by-step explanation:

The whole area is 49/4 × 5 = 245/4 ft^2

The area of tiled floor is 13/2 × 13/4 = 169/8

245/4 - 169/8 we need to equalise the bottom of fraction to subtract so

2/2 × 245/4 = 490/8

490/8 - 169/8 = 321/8 ft^2

Answer:

Anita's shape

Step-by-step explanation:

A shape with less number of sides will have longer sides.

Since, Anita's shape has less number of sides as compared to others.

Therefore, Anita's shape will have longest sides.

Answer:

78

Step-by-step explanation:

A 45-45-90 triangle has sides like..

So the height of the parallelogram is 6.5

6.5 x 12 = 78

Answer:

78 in^2

Step-by-step explanation:

The area of a parallelogram is

A = bh

A = ( 12) * h

We can find the height  from using trig functions

tan 45 = h /6.5

6.5 tan 45 = h

A = ( 12) * 6.5 tan 45

   =12 ( 6.5) * 1

   =78

Answer:

LP = 45

Step-by-step explanation:

MQ/NP = LQ/LP

= 9/27

= 1/3

if LQ is 15 and is 1u, LP (3u) is 15 × 3 = 45

Answer:

[tex]\huge \boxed{45}[/tex]

Step-by-step explanation:

We can solve by using ratios since the triangles are congruent.

[tex]\displaystyle \sf \frac{MQ}{NP} =\frac{LQ}{LP}[/tex]

Let the length of LP be x.

[tex]\displaystyle \frac{9}{27} =\frac{15}{x}[/tex]

Cross multiply.

[tex]9x=15 \times 27[/tex]

[tex]9x=405[/tex]

Divide both sides by 9.

[tex]\displaystyle \frac{9x}{9} =\frac{405}{9}[/tex]

[tex]x=45[/tex]

Answer:

exact arc length = 21pi

approximate arc length (using calculator) = 65.9734457253857

approximate arc length (using 3.14 for pi) = 65.94

units are in feet

============================================

Work Shown:

L = (x/360)*2*pi*r

L = (315/360)*2*pi*12

L = 21pi = exact arc length in terms of pi

If you use your calculator's stored version of pi, then L is approximately

L = 21pi

L = 65.9734457253857

Or if you end up using pi = 3.14, then

L = 21*pi

L = 21*3.14

L = 65.94

Fairly close to the other approximation though a bit off because pi = 3.14 is just a rough approximation.

Answer:

The shaded area is 18 ft^2

Step-by-step explanation:

First find the area of the total trapezoid

A = bh

A = 1/2 ( b1+b2) *h

   = 1/2 ( 6+12) *6

   = 1/2 ( 18)*6

   =54

Now find the area of the triangle

A = 1/2 bh

   = 1/2 ( 12) * 6

   = 36

Subtract the triangle from the trapezoid

54-36

18

The shaded area is 18 ft^2

Answer:

D. 18 sq.ft

Step-by-step explanation:

Lets make it simple and short.

Area of a triangle is 1/2 b h

b = 6

h = 6

Area = 1/2 * 6 * 6

Area = 18 sq.ft

Answer:

y= 68°

x= 34°

Step-by-step explanation:

78° alternates C= 78°

34+78= 112°

180-112= 68°

y alternates 68° y= 68°

68+78= 146°

180-146= 34°

Answer:

PRODUCT OF FIRST THREE POSITIVE INTEGERS=6

PRODUCT OF FIRST FIVE NEGATIVE INTEGERS=(-120)

Step-by-step explanation:

PRODUCT OF FIRST THREE POSITIVE INTEGERS:

1×2×3 = 6

PRODUCT OF FIRST FIVE NEGATIVE INTEGERS:

(-1)×(-2)×(-3)×(-4)×(-5) = (-120)

Answer:

6 and -120

Step-by-step explanation:

The first 3 positive integers

= 1×2×3=6

The first 5 negative integers

= (-1 ) × (-2 ) × (-3 ) × (-4 ) × (-5 ) = -120

Answer:

about 2.72 cm.

Step-by-step explanation:

Since, all the bowls are identical, I just added the heights of bothe stacks together and I divided that sum by the number of bowls in each stack all added together.

16.82+21.2=38.02 cm in total height of both stacks.

8+6=14 bowls in all from both stacks

38.02 cm/14 bowls=2.71571428, or rounded, about 2.72 cm