lara makes salad dressing by mixing 8
spoonfuls of oil and some vinegar. The tape
diagram shows the ratio of oil to vinegar.

Answer:

108.8yd²

Step-by-step explanation:

Area of a Side Angle Side triangle : Area = 1/2 ( a × b ) × sin(c)

where a and b = the side lengths and c = the angle

Here the given side lengths are 23yds and 9.5yds and the angle given has a measure of 85° so a = 23, b = 9.5 and c = 85

Area = = 1/2 ( a × b ) × sin(c)

a = 23 , b = 9.5 and c = 85

Area = 1/2 ( 23 × 9.5 ) × sin(85)

==> multiply 23 and 9.5

Area = 1/2 ( 218.5 ) × sin(85)

==> multiply 1/2 and 218.5

Area = 109.25 × sin(85)

==> multiply sin(85) and 109.25

Area = 108.8yd²

Note: When the triangle is not a right triangle ( when there is no 90° angle ) we have to use a special formula in order to find the area. Here this is given a side an angle and a side, when given a side an angle and another side you can solve using the formula Area = 1/2 ( a × b ) × sin(c)

Answer:

acdfe

Step-by-step explanation

right

Answer:

The answer is B) 40 yards for $45.00

Step-by-step explanation:

Options:

A) 20 yards per $30.00

B) 40 yards per $45.00

C) 50 yards per $70.00

C) 65 yards per $85.00

Think if buying something at the lowest cost which gives more.

1 yard per $1.00, sounds like a good deal.

20 yards per $30.00 which mean $10.00 more.

40 yeards per $45.00 which mean $5.00 more.

50 yards per $70.00 which mean $20.00 more.

65 yeards per $85.00 which mean $25.00 more.

[tex]~~~~(3x-4)^2 = 22\\\\\implies 3x-4 = \pm\sqrt{22}\\\\\implies 3x = 4 \pm\sqrt{22}\\\\\implies x = \dfrac{4\pm \sqrt{22}}3 \\\\\text{Hence,}~~ x = \dfrac{4+ \sqrt{22}}3~~ \text{and}~~ x = \dfrac{4-\sqrt{22}}3[/tex]

Step-by-step explanation:

Using the formula:

Sin☆=Perpendicular ÷ Hypotenus

Sin☆ = 35 ÷ 48

Sin☆ = 0.7291666667

☆ = Sin^-1 (0.7291666667)

☆ =46.8165782066

where ☆= Degree.

Hence final answer is 46.816

I hope this is right.....

Answer:

5

Step-by-step explanation:

[tex]\frac{2}{3} +\frac{1}{6}= \frac{ }{6} \\[/tex]

Here LCM will be 6. (We made the denominator same)

so, now the equation will be :

[tex]\frac{2}{3}+\frac{1}{6} \\\\ =\frac{4}{6} + \frac{1}{6}[/tex]

= 5/6

So, the value in the red box is 5.

Hope it helps!

Answer:

y = 4(x+3)^2 - 3

Step-by-step explanation:

Vertex form  y = a(x+3)^2 -3    sub in   2,97   to calculate a

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

                        a = 4

Answer: 9cm

Step-by-step explanation:

Answer:

The answer should be: -2, 0, -8, -18

Answer:

355 miles

Step-by-step explanation:

Figure out how far the car travelled in 1 hour - 3 hours can be divided by 3 for 1 hour, so do the same for the miles - 213 / 3 = 71 miles.

So we know the car travelled 71 miles in 1 hour.

Now just multiply the miles by 5 to figure out the answer - 71 * 5 = 355 miles

:)

Answer:

30

Step-by-step explanation:

500 g = 1/2 kg => 2 weeks he loses 1 kg

105 - 90 = 15 kg

So he needs to take 30 weeks in total. ( 15 * 2)

Let weeks be x

So

Answer:

$30

Step-by-step explanation:

50÷5=10x3=30

Answer:

the difference of the numbers are 217 and 55.

Step-by-step explanation:

a+b=272

a/b=3…52

a=3b+52

4b+52=272

4b=220

b=55

a=272-55=217

multiples of 8 are all the numbers which are divisible by 8, for eg: 8,16,24,32,40,48...

P card has all multiples of 8

hope it helps...!!!

[tex]\text{Endpoints of diameter,}~~ A(4,6)~ \text{and}~ B(-3,-1)\\\\\text{Diameter,}~AB = \sqrt{(4+3)^2+(6+1)^2}\\\\~~~~~~~~~~~~~~~~~~~=\sqrt{7^2+7^2}\\\\~~~~~~~~~~~~~~~~~~~=7\sqrt2\\\\\text{So , radius}~ = \dfrac{AB}2 = \dfrac{7\sqrt 2}2 =4.9~\text{units.}\\\\\text{Hence the answer is B.}[/tex]

Answer:butt no ayes

Step-by-step explanation:10 is a yes is no

Answer:

a) growth

b) 3%

c) 6 years (since the beginning of the decade)

Step-by-step explanation:

Given:

The population P (in thousands) of Austin, Texas during a recent decade can be approximated by [tex]y=494.29(1.03)^t[/tex] when t is the number of years since the beginning of the decade.

General form of an exponential function: [tex]y=ab^x[/tex]

where:

If [tex]b > 1[/tex] then it is an increasing function

If [tex]0 < b < 1[/tex] then it is a decreasing function

a) The model represents exponential growth as 1.03 > 1

b) The annual percent increase of the population is 3%

1.03 - 1 = 0.03

0.03 x 100 = 3%

c) To estimate when was population about 590,000 set y = 590 and solve for t:

[tex]\implies 590=494.29(1.03)^t[/tex]

[tex]\implies \dfrac{590}{494.29}=(1.03)^t[/tex]

Take natural logs of both sides:

[tex]\implies \ln\left(\dfrac{590}{494.29}\right)=\ln (1.03)^t[/tex]

[tex]\implies \ln\left(\dfrac{590}{494.29}\right)=t\ln (1.03)[/tex]

[tex]\implies t=\dfrac{\ln\left(\dfrac{590}{494.29}\right)}{\ln (1.03)}[/tex]

[tex]\implies t=5.988069001...[/tex]

Therefore the population was about 590,000 6 years since the beginning of the decade.

Answer:

0.773 thousandths place

Answer:

0.772

Step-by-step explanation:

Thats what i got!

Hope this helps! :)

Answer:

1.97

Step-by-step explanation:

1 whole square is filled so that would equal 1

97 out of 100 squares in the second is filled so it would be = 0.97

combine them:

0.97+1=1.97

Answer: 48

Step-by-step explanation: sales rate =25%

75% $36

1% = 36/75

100% = 36/75 × 100/1

Answer:

1. 73.12, 2. 94.25, 3. 96, 4. 54, 5. 62.28, 6. 90.48

this is kinda rushed so you might want to check my answers

Step-by-step explanation:

1. find the area of the rectangle and semi circle seperately then add

4*12 = 48, (8/2)^2 *pi /2 = 8pi = 25.12

48+25.12 = 73.12

2. find the area of the triangle and semicircle then add

11*10/2 = 55, (10/2)^2 * pi / 2 = 39.25

55+39.25 = 94.25

3. split the shape into a trangle and a square

12*(2+6+2)/2 = 60, 6*6 = 36

36+60 = 96

4. split into 2 rectangles

10*3 = 30, 6*4 = 24

30+24=54

5. find area of rectangle and subtract area of semicircle

4*14 = 56, (4/2)^2 * pi /2 = 6.28

56+6.28 = 62.28

6. area of circle minus area of rectangle

(16/2)^2 * pi /2 = 100.48, 2*5 = 10,

100.48-10= 90.48

Answer:

Option D, [tex]2010\ cm^3[/tex]

Step-by-step explanation:

Step 1:  Determine the volume of a single cylinder

[tex]V=\pi r^2h[/tex]

[tex]V=\pi *(4\ cm)^2 * 10\ cm[/tex]

[tex]V = 3.14 * 16\ cm^2 * 10\ cm[/tex]

[tex]V = 502.4\ cm^3[/tex]

Step 2:  Determine the total volume

[tex]502.4\ cm^3 * 4[/tex]

[tex]2,009.6\ cm^3[/tex]

Answer: Option D, [tex]2010\ cm^3[/tex]

Answer:

The last one :)

Step-by-step explanation:

I hoped this helped have a good day! <3

Answer:

  13. x=11; MN=65°; NP=115°; NQP=245°

  15. x=9; AD=108°; BC=23°; DC=139°; DBC=221°

Step-by-step explanation:

The marked arcs are congruent, so we can equate the given expressions for their measures:

  10x -45 = 6x -1

  4x = 44 . . . . . . . . . add 45-6x

  x = 11 . . . . . . . . . . divide by 4

The arc measures are found by using the value of x in the corresponding expression. Arcs around a circle total 360°.

  arc MN = (10(11) -45)° = 65°

  arc NP = 180° -65° = 115°

  arc NQP = 360° -NP = 245°

__

The sum of arcs around a circle is 360°. We can use this fact to write an equation involving the given expressions. Clockwise from A, we have ...

  90 +(2x +5) +(17x -14) +12x = 360

  31x = 279 . . . . . . . subtract 81, collect terms

  x = 9 . . . . . . . . . divide by 31

The arc measures are found by using the value of x in the corresponding expression.

 arc AD = 12(9)° = 108°

  arc BC = (2(9) +5)° = 23°

  arc DC = (17(9) -14)° = 139°

  arc DBC = 360° -DC = 221°

Answer: A= 42 degrees

Step-by-step explanation:

A= 180-90-48=42 (degrees)

Answer:

A= 42 degrees

a = 27

c= 40.4

Step-by-step explanation:

48 - 90 = 42 (we know the remaining angle area is 90 because its a right triangle and a traingle is 180 degrees)

to find the answer of a we need to use tan(48) and when you convert that to radians you get 1.1106 ish tan is opposite over adjacent and we know the opposite is 30 but we dont know a so we put [tex]\frac{30}{a}[/tex] = 1.1106 and put a on both sides so you divide 30 by 1.1106 and dget 27.0124 and round to the nearest tenth to get 27

to find c you need to find the hypotanuse which is [tex]a^{2}[/tex]+[tex]b^{2} =c^{2}[/tex]

30 squared is 900 add that to 27 squared which is 729 and you get 1629

find the square root of 1629 to get 40.3608 and then round that to the nearest tentth to get 40.4

Answer:Slope=-240.000/2.000=-120.000

Step-by-step explanation:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    120*x+y-(1200)=0

STEP

1

:

Equation of a Straight Line

1.1     Solve   120x+y-1200  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

Answer:

$336

Step-by-step explanation:

Find the perimeter, 5x2 + 16x2 = 10 + 32 = 42

Fencing material = $8 per 1 meter

42 meters, so 42 * 8 = $336

Answer:

240m2 (square metre)

Step-by-step explanation:

Just too smart.

Answer:

The correct answer would be C) 30