4sinθ – 1 = - 3 for 0<θ< 360

Answer:

The original width was 94.71 cm

Step-by-step explanation:

Given:

new smaller area = 1.2m^2

Decrease in length of the rectangular sheet = 34.5cm

Therefore:

1. the final width of the sheet is given as

2X^2 = 1.2 m^2

X^2 - 0.6 m^2

X^2 = 10000 * 0.6 cm

X = 77.46 cm (this is the width)

2. The length of the sheet

= 2 * 77.46

= 154.92 cm.

3. Initial length of the sheet

= 154.92 + 34.5

= 189.42 cm.

4. Initial width of the sheet ( original ).

= 189.42 / 2

= 94.71 cm.

5. Initial area of the sheet

= 94.71 * 189.92

= 17939.9 cm^2

New area of the sheet

= 79.46 * 154.92

= 12000.1 cm^2

Difference between the initial and new area

= 17939.9 - 12000.1

= 5939.86 cm^2

Percentage of area decrease

= 5939.86 ' 17939.9

= 33.1%

Answer:

67 units^2

Step-by-step explanation:

The surface area of the prism is found by

SA = 2 ( lw+lh + wh)

     = 2 ( 5*1.5+ 4*1.5 + 5*4)

     = 2 ( 7.5+6+20)

     = 2 (33.5)

    = 67

Answer:

67units²

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

The y- intercept is the value of the x- coordinate where the line crosses the x- axis.

Given the line crosses the x- axis at (4, 0 ), then

the x- intercept is x = 4

Answer:

Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet. ... If you are using a ruler with a centimeter (cm) scale, then your units are going to be in cm, and if you ... We have to do the same thing to volume like we did with the surface area.

:)

Answer:

Rectangular prism

I chose a box of cereal.

Part 1)List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).

Length: 20 cm

Width: 8 cm

Height: 32 cm

Part 2).

 Describe the shape of the cross-section when the box is cut parallel to the base.

The shape of the cross-section would be a rectangle in dimensions.

20 cm x 8 cm

Part 3)

What is the surface area of the box? 

surface area=2*area of the base + perimeter of the base*height

area of the base=20*8=160 cm²

perimeter of the base=2*[20+8]-----> 56 cm

height=32 cm

surface area=2*160+56*32------> 2,112 cm²

the answer part 3) is

2,112 cm²

Part 4)

What is the surface area of the box if it is scaled up by a factor of 10?

we know that

surface area of the larger box =[scale factor]²*surface area original box

scale factor=10

surface area original box=2,112 cm²

so

surface area of the larger box=10²*2,112-----> 211,200 cm²

the answer part 4) is

211,200 cm²

Part 5) 

What is the volume of the box?

volume of the box = L*W*H 20*8*32-5,120 cm³

the answer Part 5) is

5,120 cm³

Part 6) 

What is the volume of the box if it is scaled down by a factor of 1/10?

we know that

the volume of the smaller box =[scale factor]³volume original box

scale factor=1/10

volume original box=5,120 cm³

so

volume of the smaller box =[1/10]³*5,120 5.12 cm³

the answer part 6) is

5.12 cm³

The length is 6 in., the width is 2 in., and the height is 16 in.

Answer:

Step-by-step explanation:

This problem can be solved by applying the permutation strategy since it has to do with the number of ways of selection

Given

Number of items= 3

Therefore 3!= 3*2*1= 6

Hence the number of ways they can distribute the shirt among themselves is 6 ways

Answer:

See below.

Step-by-step explanation:

We want to find the unknown angle and we know the sides opposite to it and the hypotenuse. Therefore, we can use sine.

Recall that sine is the ratio of the opposite to the hypotenuse:

[tex]\sin(\theta)=opp/hyp[/tex]

Plug in the numbers. The opposite is 20 and the hypotenuse is 55.

[tex]\sin(\theta)=20/55[/tex]

Solve for theta (use a calculator):

[tex]\sin(\theta)=20/55\\\theta=\arcsin(4/11)\\\theta\approx21.23\approx21\textdegree[/tex]

Answer:

B.

Step-by-step explanation:

The null hypothesis will say that the mean is equal to what it is supposed to be. In this case, each box is supposed to have 24.3 ounces of cereal.

So, your null hypothesis would be that the average is equal to 24.3, or H₀ = 24.3. B.

Hope this helps!

Answer:

a) 20 students

b) 20 students

Step-by-step explanation:

a) From the given frequency table, we have to check the number of students that scored above 73.5 and add them up.

Therefore, the number of students that have grades above 73.5 are:

14 + 4 + 2 = 20 students

b) 75 falls in between 74 - 76 and we do not have the individual frequencies of the grades (74, 75, 76).

However, we can use the data we have from the table to make an assumption.

The number of students that have grades below 75 will be:

13 + 5 + 2 = 20 students

Answer:

1. True

2. False.

3. True.

Step-by-step explanation:

1. The total area within any continuous probability distribution is equal to 1.00: it is true because the maximum probability (value) is one (1), therefore, the total (maximum) area is also one (1).

Hence, for continuous probability distribution: probability = area.

2. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: False because it has an infinite number of possible values, which can not be counted or uncountable.

Hence, it cannot be computed.

3. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: True because it has a finite number of possible values, which are countable or can be counted.

Hence, it can be computed.

Answer:

x = 5.7 units

Step-by-step explanation:

By applying Sine rule is the triangle XYZ,

[tex]\frac{\text{SinX}}{\text{WY}}=\frac{\text{SinY}}{\text{WX}}=\frac{\text{SinW}}{\text{XY}}[/tex]

[tex]\frac{\text{SinX}}{\text{x}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{SinW}}{\text{10}}[/tex]

[tex]\frac{\text{Sin33}}{\text{x}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{Sin107}}{\text{10}}[/tex]

[tex]\frac{\text{Sin33}}{\text{x}}=\frac{\text{Sin107}}{\text{10}}[/tex]

[tex]x=\frac{10\times(\text{Sin33})}{\text{(Sin107)}}[/tex]

x = 5.69

x ≈ 5.7 units

Answer:

14,7

Step-by-step explanation: if it is being divided by 2 it is 14 and 7

Answer:

(6x + 1)^2.

Step-by-step explanation:

1 + 12x + 36x^2

= 36x^2 + 12x + 1

= (6x + 1)(6x + 1)

= (6x + 1)^2.

Hope this helps!

Answer:

[tex](6x+1)^2[/tex]

Step-by-step explanation:

Answer:

mM = 113 and mN = 61

Step-by-step explanation:

In a Cyclic quadrilateral, the rule states that:

The sum opposite interior angles is equal to 180°

In the above diagram, we have cyclic quadrilateral KLMN

According to the rule stated above:

Angle K is Opposite to Angle M

So, Angle K + Angle M = 180°

Angle K = 67°

67° + Angle M = 180°

Angle M = 180° - 67°

Angle M = 113°

Angle L is Opposite to Angle N

so Angle L + Angle N = 180°

Angle L is given as = 119°

119° + Angle N = 180°

Angle N = 180° - 119°

Angle N = 61°

Therefore, Angle M = 113° and Angle N = 61°

Answer:

a

Step-by-step explanation:

The standard form of the equation of a circle is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (0, 0), thus

(x - 0)² + (y - 0)² = r², that is

x² + y² = r² → a

Answer:

x = 1, y = 6

Step-by-step explanation:

y = 6x

2x + 3y = 20

Plug y as 6x in the second equation and solve for x.

2x + 3(6x) = 20

2x + 18x = 20

20x = 20

[tex]\frac{20x}{20}= \frac{20}{20}[/tex]

x = 1

Plug x as 1 in the first equation and solve for y.

y = 6(1)

y = 6

Answer:

y=6 , x=1

Step-by-step explanation:

y=6x

2x+3y=20

Substitute 6x into y because y=6x.

2x+3(6x)=20

2x+18x=20

20x=20

x=1

Then subsitiute 1 into the first equation in x value

y=6(1)

y=6

Answer:

The measure of the angle of each of the intercepted arc is 180°

Step-by-step explanation:

An intercepted arc is an encased (between chords) portion of the circumference of the circle. The chords that form the intercepted arc meet at a point

An inscribed angle is the angle is an angle formed between two chords that meet at a point called the end point

For the inscribed square, the symmetry has it that the diagonal is the same as the diameter of the circle as the diagonals bisect each other having equal distances on either side to the circumference of the circle.

Given that the angles in the vertices of the square are 90° and the point of intersection of the two chords forming the vertex are at the ends of the diameter of the circle, which passes through the center of the circle, the angle 90° at the vertex is half the angle at the center which is the angle of the intercepted arc

∴ The measure of the angle of each of the intercepted arc = 2× 90 = 180°.

Each year, your account is multiplied by 1.05 (5% increase). Thus, after 5 years, your account would have been multiplied by that value 5 times.

[tex](1.05)^5=1.27628...[/tex]

Thus, the total percent increase would have been 27.6% (rounded to the nearest tenths).

Answer:

Step-by-step explanation:

After reflection about y-axis, A'B'C' must be translated down 6 units to create image DEF.

ABC and DEF are congruent due to the following common properties of reflections and translations.

1. does not change the nature of geometric elements, i.e. maps a line to a line,  a segment to a segment, etc.

2. preserve lenths of segments.

3. preserves angles

By the congruent theorem of SSS, the two triangles are congruent.

The sequence of transformations that proves the triangles congruent is explained in the solution below.

The geometric transformation is a bijection of a set that has a geometric structure by itself or another set. If a shape is transformed, its appearance is changed.

After reflection about y-axis, A'B'C' must be translated down 6 units to create image DEF.

ABC and DEF are congruent due to the following common properties of reflections and translations.

It does not change the nature of geometric elements, i.e. maps a line to a line, a segment to a segment, etc., preserve lengths of segments, and preserves angles.

By the congruent theorem of SSS, the two triangles are congruent.

Learn more about transformation, click;

https://brainly.com/question/11709244

#SPJ3

Answer:

[tex]\large \boxed{\sf \ \ y=-2 \ \ }[/tex]

Step-by-step explanation:

Hello,

To guess the end behaviours when x tends to [tex]\infty[/tex] you only take into account the highest terms of polynomial expressions.

So the expression will be equivalent to

[tex]\dfrac{-2x^2}{x^2}=-2[/tex]

In other words we can say

[tex]\displaystyle \lim_{x\rightarrow+\infty} \dfrac{-2x^2+3x+6}{x^2+1}=\lim_{x\rightarrow+\infty} \dfrac{-2x^2}{x^2}=-2\\\\\displaystyle \lim_{x\rightarrow-\infty} \dfrac{-2x^2+3x+6}{x^2+1}=\lim_{x\rightarrow-\infty} \dfrac{-2x^2}{x^2}=-2\\\\[/tex]

So, the correct answer is y = -2

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

answer = no it does not measure a rate

Answer:

NO

Step-by-step explanation:

Percent is just a number out of 100

Answer: x ≥  -5

Step-by-step explanation:

First, let's see how the function f(x) = IxI works:

if x ≥ 0, IxI = x

if x ≤ 0, IxI = -x

Notice that for 0, I0I = 0.

Ok, we want that:

|x+5| = x+5

Notice that this is equivalent to:

IxI = x

This means that  |x+5| = x+5 is only true when:

(x + 5) ≥ 0

from this we can find the possible values of x:

we can subtract 5 to both sides and get:

(x + 5) -5 ≥ 0 - 5

x ≥  -5

So the graph in the number line will be a black dot in x = -5, and all the right region shaded.

something like:

-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4__ ...

Answer:

y= [tex]\sqrt{x}[/tex]

Step-by-step explanation:

Answer:

Find the area of all the shapes

Length x width = area

10 x 3 = 30

6 x 3 = 18

6 x 3 = 18

6 x 10 = 60

3 x 10 = 30

6 x 10 = 60

Add them all up

30 + 18 + 18 + 60 + 30 + 60 = 216 cm^2

Hope this helps

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

● cos O = 2/3

We khow that:

● cos^2(O) + sin^2(O) =1

So : sin^2 (O)= 1-cos^2(O)

● sin^2(O) = 1 -(2/3)^2 = 1-4/9 = 9/9-4/9 = 5/9

● sin O = √(5)/3 or sin O = -√(5)/3

So we deduce that tan O will have two values since we don't khow the size of O.

■■■■■■■■■■■■■■■■■■■■■■■■■

●Tan (O) = sin(O)/cos(O)

● tan (O) = (√(5)/3)÷(2/3) or tan(O) = (-√(5)/3)÷(2/3)

● tan (O) = √(5)/2 or tan(O) = -√(5)/2

Answer:

A. 2

Step-by-step explanation:

Well let’s first graph the following,

[tex]x^2 + y = 8[/tex]

[tex]x=y[/tex]

So on the graph the system of equations only have 2 real solutions which are

(-3.272, -3.272) (2.372,2.372)

Answer:

hello your question lacks some information below is the complete question

Suppose you are designing a cardboard box that must have a volume of  27 cubic feet. The cost of the cardboard is ​$0.15 per square foot. What is the most economical design for the box​ (one that minimizes the​ cost), and how much will the material in each box​ cost?

Answer : Box design , $8.1 ( cost of material in each box)

Step-by-step explanation:

Volume of cardboard box = 27 cubic feet

cost of cardboard = $0.15 square feet

i) The most economical design for the box would be Designing a square box because the dimensions of the box would be [tex]\sqrt[3]{27}[/tex] = 3 ft

ii) The cost of the material for each box can be calculated as

= surfaces * surface area * cost per square foot

= 6 * 3^2 * $0.15

= $8.1

Answer: She had 60% of the money left

Step-by-step explanation:

240/600=0.4

0.4 = 40%

100%-40%=60%

Answer:

60%

Step-by-step explanation:

LETS MAKE IT INTO A FRACTION

FIRST LETS CALCULATE HOW MUCH SHE SPENT

=240/600

WE CAN SIMPLIFY BY DIVIDING THE EQUATION BY 10

=24/60

LETS DIVIDE BY 6

=4/10

DIVIDE BY 2

=2/5

NOW LETS CALCULATE HOW MUCH SHE HAS LEFT

THE EASIEST WAY IS TO SUBTRACT

5/5-2/5=3/5

3/5 IS ALSO EQUAL TO 60/100

SO KAREN HAS 60% OF HER MONEY LEFT

HOPE I HELPED

PLS MARK BRAINLIST

(DESPERATELY TRYING TO LEVEL UP)

        ✌

The Answer is A.)

A picture of my answer

Answer:

544 + 545 + 546 + 547

explanation: if the numbers are consecutive whole numbers then it would be near the ¼ of the given number