The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, find the dimensions of the rectangle.
a
length = 18 cm; width = 5 cm
b
length = 5 cm; width = 18 cm
c
length = 13 cm; width = 5 cm
d
length = 13 cm; width = 8 cm

Answer:

110

Step-by-step explanation:

180-70=110

the full line is 180 so subtract the angle, 70.

Answer:

SAS

Step-by-step explanation: every triangle contains a total of 180 degrees if you substract 180 by 60+70(which is 130) you would get 50 degrees which is the exact degree missing in the first triangle, so after confirming that both triangles have an equal degrees on each side the answer would be SAS (which stands for Side-Angle-Side), SAS is the answer you would give to triangles that are congruent(equal)

Answer:

Number of ham sandwiches Tina made = 60

Step-by-step explanation:

Total number of sandwiches = 480

Fraction of total sandwiches which are Tuna = [tex]\frac{3}{8}[/tex]

Therefore, number of Tuna sandwiches = [tex]480\times \frac{3}{8}[/tex]

                                                                   = 180

Percentage of beef sandwiches = 35%

Therefore, beef sandwiches = [tex]480\times \frac{35}{100}[/tex]

                                                = 168

Ratio of ham sandwiches (h) and cheese sandwiches (c) = 5 : 6

[tex]\frac{h}{c}=\frac{5}{6}[/tex]

[tex]c=\frac{6}{5}h[/tex] ------(1)

Total number of Tuna sandwiches + Total number of beef sandwiches + Total number of ham sandwiches + Total number of cheese sandwiches = 480

180 + 168 + h + c = 480

h + c = 480 - 348

h + c = 132

Substitute the value of c from equation (1),

[tex]h+\frac{6}{5}h=132[/tex]

[tex]\frac{11}{5}h=132[/tex]

[tex]h=\frac{132\times 5}{11}[/tex]

[tex]h=60[/tex]

Therefore, number of ham sandwiches Tina made = 60

Answer:

0.2 = n

Step-by-step explanation:

Since we want to express 3:15 as n:1, we can say that they are equal ratios, so

3:15 = n:1. Next, ratios can be written as fractions, so 3/15 = n/1 .

3/15 = n/1

Since anything divided by 1 equals itself, we can write this as

3/15 = n

0.2 = n

Answer:

The length of the shortest side of the triangle is 10 units.

Step-by-step explanation:

Let a be the shortest side of the isosceles triangle and b be the two congruent sides.

The congruent sides b are each one unit longer than the shortest side. Hence:

[tex]b=a+1[/tex]

The perimeter of the isosceles triangle is given by:

[tex]\displaystyle P_{\Delta}=b+b+a=2b+a[/tex]

This is equivalent to the perimeter of a square whose side lengths are two units shorter than the shortest side of the triangle. Let the side length of the square be s. Hence:

[tex]s=a-2[/tex]

The perimeter of the square is:

[tex]\displaystyle P_{\text{square}}=4s=4(a-2)[/tex]

Since the two perimeters are equivalent:

[tex]2b+a=4(a-2)[/tex]

Substitute for b:

[tex]2(a+1)+a=4(a-2)[/tex]

Solve for a. Distribute:

[tex]2a+2+a=4a-8[/tex]

Simplify:

[tex]3a+2=4a-8[/tex]

Hence:

[tex]a=10[/tex]

The length of the shortest side of the triangle is 10 units.

Answer:

21.3 cm^2

Step-by-step explanation:

The altitude from vertex A to side BC has length

h = 8 sin 26.4°

h = 3.56

area = bh/2

area = 12 cm * 3.56 cm / 2

area = 21.3 cm^2

Answer:

21.312

Area= (a x b x sin c)/2

or you can use heron's formula (look that one up)

area = (8* 12* sin(26.4))/2 = 21.312

Step-by-step explanation:

Answer: £18693.96

Step-by-step explanation:

16470.45 + 16470.45(0.135)

= 16470.45(1 + 0.135)

= 16470.45(1.135)

≈ 18693.96

Step-by-step explanation:

S.A = 465

4πr²= 465

r². = 36.9

r. = 6.08

volume of a sphere = 4/3πr³

= 4/3π * 6.08³

= 941.8 cm³

The radius of the sphere will be 6.08 units. Then the volume of the sphere will be 942.87 cubic units.

A circular solid object or its surface whose points are all equally spaced from the center.

Let r be the radius of the sphere.

Then the volume of the sphere will be

V = 4/3 πr³ cubic units

The surface area of the sphere will be 465 square units.

The surface area of the sphere is given as,

SA = 4πr²

Then the radius of the sphere will be

4πr² = 465

   r² = 37

    r = 6.08 units

Then the volume of the sphere will be

V = 4/3 π (6.08)³

V = 4/3 π x 225.09

V = 300 π

V = 942.87 cubic units

Thus, the volume of the sphere will be 942.87 cubic units.

More about the volume of the sphere link is given below.

https://brainly.com/question/9994313

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Answer:

I only have the answer for B

Step-by-step explanation:

This is the answer: 1st blank: 7y

2nd blank: 9

3rd blank: 42xy

Answer:

The length and width that maximize the area are:

W = 2*√8

L = 2*√8

Step-by-step explanation:

We want to find the largest area of a rectangle inscribed in a semicircle of radius 4.

Remember that the area of a rectangle of length L  and width W, is:

A = L*W

You can see the image below to see how i will define the length and the width:

L = 2*x'

W = 2*y'

Where we have the relation:

4 = √(x'^2 + y'^2)

16 = x'^2 + y'^2

Now we can isolate one of the variables, for example, x'

16 - y'^2 = x^'2

√(16 - y'^2) = x'

Then we can write:

W = 2*y'

L = 2*√(16 - y'^2)

Then the area equation is:

A = 2*y'*2*√(16 - y'^2)

A = 4*y'*√(16 - y'^2)

If A > 1, like in our case, maximizing A is the same as maximizing A^2

Then if que square both sides:

A^2 = (4*y'*√(16 - y'^2))^2

      = 16*(y'^2)*(16 - y'^2)

      = 16*(y'^2)*16 - 16*y'^4

      = 256*(y'^2) - 16*y'^4

Now we can define:

u = y'^2

then the equation that we want to maximize is:

f(u) = 256*u - 16*u^2

to find the maximum, we need to evaluate in the zero of the derivative:

f'(u) = 256 - 2*16*u = 0

      u = -256/(-2*16) = 8

Then we have:

u = y'^2 = 8

solving for y'

y' = √8

And we know that:

x' = √(16 - y'^2) = √(16 - (√8)^2) = √8

And the dimensions was:

W = 2*y' = 2*√8

L = 2*y' = 2*√8

These are the dimensions that maximize the area.

Answer:

Step-by-step explanation:

Hello there

I'm also a student so I'm not 100% sure on this one, but I think I know.

Usually when you have functions you just replace the letters for their value:

f = 11x

g = x² - 6x + 3

h = -x + 4

Th exercise is asking for (g * h) (x)

Since there are parenthesis, here's what we have:

[(x² - 6x + 3)(-x + 4)](x)

Use the left side of the equation:

[(x² - 6x + 3)(-x + 4)](x)

And solve it:

-x³ + 6x² -3x + 4x² - 24x + 12

That's equal to

-x³ + 10x² -27x + 12

Multiply all that by that x on the left:

-x^4 + 10x³ -27x² + 12x

No idea if that's right so please tell me

Answer:

B or the second one

Step-by-step explanation:

There are the same numbers just positive and negative.

Hope it helps c:

Answer:

Hello there ,

The answer to this equation would be:

A=.50j+9

Step-by-step explanation:

this answer should be correct because he started with 9,

and he is selling each cup (j) for 0.50

Let me show you an example:

Ok lets say he sold 10 (j) cups:

you would replace the (j) with the 10

A=0.50(10)+6

A=5+6

A=11 and he would have $11

but that just an example so the real answer to your question is:

A=.50j+9

Hope this help. If correct please give brainliest.

Thank you,

Have a good day !!!!!

Let the Vertices of the  Δ  be  A , B ,  and  C

We will follow the Usual Notation for  Δ A B C ,  e.g., the side

opposite to the Vertex  A  will be denoted by  a , m ∠ A = A ,  etc.

In this notation, let us assume that,

a = 32 , b = 35 , & , C = 120 ° & we have to find  c

Using Cosine-Rule for  Δ A B C , we have,  

c²= a²+b² - 2 ab cos C = 32 ²+35² - 2 x 32 x 35 x cos 120° =

1024 + 1225 − 2240  cos ( 180 °− 60 °) = 2249 - 2240(-cos 60°)

2249+ 2240 (1/2)= 2249 + 1120=  3369

Answer: C= √3369 is about 58.04

Answer:  58.043087 (approximate)

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

Explanation:

Refer to the diagram below. We can use the law of cosines to solve for c

c^2 = a^2 + b^2 - 2*a*b*cos(C)

c^2 = 32^2 + 35^2 - 2*32*35*cos(120)

c^2 = 3369

c = sqrt(3369)

c = 58.043087 which is approximate

Round this value however you need to.

Answer:

1/2

Step-by-step explanation:

the answer will be

Hooe it helps!

Answer:

H

Step-by-step explanation:

lets say the first big square has side s, so the area will be s²

then the side of the small square is s/3, and the area is (s/3)²= s²/3² =s²/9

the area of the smaller square is 1/9 smaller than the area of the big square

Answer:

2/12

Step-by-step explanation:

The answer is 2/12 because there are two dice, each with 6 sides and the probability on each dice is one sixth

Answer:

zero

Step-by-step explanation:

5x+10 = 5x-8

5x-5x = -8-10

0 = -18

so zero

Answer:

20cm

Step-by-step explanation:

a square has 4 equally long sides.

when we know its perimeter, that means we know the sum of all 4 sides.

since all sides are equality long, we only need to divide the perimeter by 4 to get the length of an individual side.

80/4 = 20cm

Answer:

the equation would be (x+5)2+(y−4)2=r2

Step-by-step explanation:

The equation would be

(x+5)2+(y-4)2=r2

Answer:

0.07.

Step-by-step explanation:

Below. Lets say 1 is 100 dollars sale tax. If 1 is 100 7 would be 7.00

Answer:

d

Step-by-step explanation:

A linear pair sum to 180° , then

x - 13 + x + 7 = 180

2x - 6 = 180 ( add 6 to both sides )

2x = 186 ( divide both sides by 2 )

x = 93 → d

Answer:

1/4

Step-by-step explanation:

Given an event A and event B, the probability of both happening can be determined by multiplying the two individual probabilities.

We can start by finding the individual probabilities

The probability of rolling an odd number is 3/6 = 1/2, as there are 3 odd numbers (1,3,5) on a die and 6 possibilities total. Furthermore, there is a equal chance of rolling each number as it is a fair die

The probability of flipping a head is 1/2, as there are two equal possibilities (heads and tails), with one of them being heads

To find the probability of both happening, we can multiply them to get (1/2) * (1/2) = 1/4

Answer: r = 0.6h

your welcome :D

Answer:

The actual correct answer is r = 0.8h

Step-by-step explanation:

You divide 0.24 ÷ 0.30 and get 0.8

Do the same thing for all the rest of the numbers but,

you must put the numbers that are on the right FIRST then divide them by the numbers on the left, all of these are the same answer which means it's

r = 0.8h

Hope this helps!

Answer:

2.96

Step-by-step explanation:

Just multiply the payout by its probability

0*.12+1*.2+2*.38+5*.2+10*.1=2.96

If “the notation arcsin x represents the inverse function to sine” is true when the sine function is to the interval [ -pi/2, pi/2 ].

The sine function is one of the three primary functions in trigonometry, the others being cosine, and tan functions.

The confusion is compounded by the fact that we use the notation sin⁻¹(x) interchangeably with arcsin(x), and we call it the inverse sine.

Here is a counterexample disproving your given statement:

Let x = π.

The value π is in the domain of sin(x).

arcsin[sin(π)] = arcsin(0) = 0

arcsin[sin(π)] ≠ π

Therefore arcsin(x) is not the inverse of sin(x).

If you restrict the sine function to the interval [ -pi/2, pi/2 ]. Otherwise, arcsin will not be a function.

Hence, If “the notation arcsin x represents the inverse function to sine” is true when the sine function is to the interval [ -pi/2, pi/2 ].

Learn more about sin function here;

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