A mirror is in the shape of an isosceles right triangle and has a hypotenuse length of seven times the square root of two. What is the length of one of the legs?

square root of two.

3.5
seven times the square root of two.

7

The value of ∠X in triangle VWX ( ΔVWX) to the nearest degree is 2 degrees.

The angle X can be found using the cosine rule.

w² = x² + v² - 2xv cos W

w² = 110² + 700² - 2 × 110 × 700 cos 9°

w² = 12100 + 490000 - 154000 cos 9°

w² = 502100 - 154000 × 0.98768834059

w² = 502100 - 152104.004452

w = √349995.995548

w = 591.604593921

w = 591.60 inches

Using sine rule, let's find ∠X

Sine rule

110 / sin X = 591.60 / sin 9°

Therefore,

110 sin 9 = 591.60 sin X

sin X = 110 sin 9 / 591.60

sin X = 110 × 0.15643446504 / 591.60

sin X = 17.2077911544 / 591.60

X= sin⁻¹ 0.02908686807

∠X = 1.66678986656

∠X = 2 degrees

learn more on cosine law here : https://brainly.com/question/15268683

Answer:  called tthe term of an algebraic expression.

Examples of algebraic expressions and their terms:

(i)  x + 10

We observe that the number of terms used in the expression x + 10 is 2. The terms are x and 10.

(ii)  5m + 2n - 7

We observe that the number of terms used in the expression 5m + 2n – 7 is 3. The terms are 5m, 2n and 7.

(iii)  3a/b

We observe that the number of term used in the expression 3a/b is 1. The term is 3a/b.

(iv) 3xy + 7xz + 2yz - 6

We observe that the number of terms used in the expression 3xy + 7xz + 2yz - 6 is 4. The terms are 3xy, 7xz, 2yz and 6.

)  2abc + 1

We observe that the number of terms used in the expression 2abc + 1 is 2. The terms are 2abc and 1.

Therefore, the algebraic expressions are either simple or compound.

(i) Simple algebraic expressions consist of one term.

(ii) Compound algebraic expressions consist of two or more terms.

Answer:

60 days.

Step-by-step explanation:

This is  a proportion question. You compare two ratios. Unfortunately it is an inverse ratio.

12 = k/100                   Multiply both sides by 100

1200 = k

20 = k/x                       Multiply both sides by x

20x = k

20x = 1200                 Divide by 20

20x/20 = 1200/20

x = 60 days.  

An inverse proportion works by making a constant k. The  constant k makes the days shorter when the number of people increases. You should expect that. More people , less time.

Answer:

Adjacent, x = 60°

Step-by-step explanation:

Adjacent angles are pairs of angles next to each other. Vertical angles make an x shape, are across from each other, and have the same measure. These are adjacent angles.

This is a 90° angles, which is signified by the little red box. To solve for x, make an equation by adding the two angles together and set them equal to 90.

x - 30 + x = 90

2x - 30 = 90

2x - 30 + 30 = 90 + 30

2x = 120

2x/2 = 120/2

x = 60°

Here, the angles x° and (x - 30)° both are complementary angles, so they will add upto 90°, thus we can obtain a equation as ;

[tex]{:\implies \quad \sf x^{\circ}+(x-30)^{\circ}=90^{\circ}}[/tex]

[tex]{:\implies \quad \sf 2x^{\circ}-30^{\circ}=90^{\circ}}[/tex]

[tex]{:\implies \quad \sf 2x^{\circ}=120^{\circ}}[/tex]

[tex]{:\implies \quad \sf x^{\circ}=\dfrac{120^{\circ}}{2}=\bf \boxed{60^{\circ}}}[/tex]

Hence, the required value of x is 60

The area of waffle in the cone is the amount of space covered by the waffle

The cone has 5630 square millimeter of waffle

The surface area of a cone is calculated using:

A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))

For the complete 72 mm tall cone, we have:

Height (h) = 72 mm

Radius (r) = 42 mm/2 = 21 mm

So, the surface area is:

A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))

A = 3.142 * 21 * (21+[tex]\sqrt{[/tex](72^2 + 21^2))

Evaluate

A = 3.142 * 21 * (21+75)

A = 6334.272

When the cone is cut at the top, we have:

Height (h) = 24 mm

Radius (r) = 14 mm/2 = 7 mm

So, the surface area is:

A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))

A = 3.142 * 7 * (7+[tex]\sqrt{[/tex](24^2 + 7^2))

Evaluate

A = 3.142 * 7 * (7 + 25)

A = 703.808

Calculate the difference (d) between the areas

d = 6334.272 - 2.5*703.808

Evaluate

d = 5630.464

Approximate

d = 5630

Hence, the cone has 5630 square millimeter of waffle

Read more about surface area at:

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Answer:

[tex]\frac{21}{40}n[/tex] + [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The important part to understand about this problem is that you need to find a common denominator. You can ONLY add two fractions if they have the same denominator. A way to change the denominator of a fraction is to multiply the numerator and denominator of the fraction by the same number.

So, You want to make the 2/5n and 1/8n to have the same denominator so you can add them. An easy rule of thumb is multiply the one of the fraction by the other fraction's denominator, so in this problem:

[tex]\frac{2 * 8}{5*8} n[/tex] and [tex]\frac{1*5}{8*5}n[/tex]

this comes out as

16/40n and 5/40n

NOW, they have the same denominator and you can add the numerators together to make it one happy fraction

[tex]\frac{16}{40} + \frac{5}{40} = \frac{16+5}{40} = \frac{21}{40}[/tex]

Then, for the 3/6, you can simplify this fraction into:

1/2

This is because if you divide the top and bottom of the fraction by 3 like so:

[tex]\frac{3/3}{6/3}[/tex] (Always make sure you do the same for the top as you do to the bottom)

This comes out as

[tex]\frac{1}{2}[/tex]

Then for the full equation:

[tex]\frac{21}{40} n + \frac{1}{2}[/tex]

Answer:

A

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

100° is an exterior angle of Δ MLN , then

∠ LMN + 60° = 100° ( subtract 60° from both sides )

∠ LMN = 40°

Answer: 11/2

Reciprocal: 2/11

Step-by-step explanation: 11/2 is 5.5 (between 5 and 6) the reciprocal or 11/2 is 2/11

Answer:

it actually equals 5

Step-by-step explanation:

the reason it equals 5, is because there are 5 variables in there, so because of the addition sign, it becomes 1+1+1+1+1=5. you cannot prove me wrong.

Answer:

the correct answer is 4

Step-by-step explanation:

2 + 2 = 4

hope this helps

have an awesome day -TJ :)

Answer:

28 ft²

Step-by-step explanation:

area of the desk = (5×4) + (4×2) = 20 + 8 = 28 ft²

Answer:

28

Step-by-step explanation:

5 times 4 = 20

4 times 2= 8

20 plus 8=28

Answer:

6%

Step-by-step explanation:

To get sales tax, you multiply the percentage of sell tax to the total price. In this case, we were looking for the percent of sell tax so we needed to divide the total amount into the amount he payed in sells tax. You will get the decimal value so you will have to multiply it by 100 to get the percent.

Answer:

3 pounds of bananas

Step-by-step explanation:

1.84 ÷ 0.48 = 3.8333etc

since you can't buy 4 pounds with the money you have its 3 pounds of bananas

1 glass..........1/4 liter

n glass.......... 5 liters

n = 1 x 5 : 1/4

n = 5 x 4

so there are 20 glasses

Step-by-step explanation:

a) 2y = 3x + 4

b) given the perpendicular

3x + 5y = 1

5y = 1 - 3x

y = 1/5 - 3x/5

m¹ = -3/5

perpendicular

m¹m² = -1

-3m²/5 = -1

m² = 5/3

so (1,8)

x¹ = 1 y¹ = 8

m² = (y - y¹)/(x - x¹)

5/3 = (y - 8)/(x - 1)

5x - 5 = 3y - 24

3y - 5x + 5 - 24 = 0

3y = 19 + 5x

Answer:

x=74

Step-by-step explanation:

if angle ABE = 148. then, angle EBC = 32

and for angle ECB an BEC,

180-32 = 148

148/2 = 74

so, angle ECB and angle BEC  = 74

we know, angle BCE and angle CEF are equal because they are alternate angles

so, x = 74

Answer:

[tex]y = {4}^{x} [/tex]

is the answer

The rectangular point that represents (4, - pi/3) is the one in option b: (2, -2√3).

For a point (x, y), the polar coordinates are:

Then we must have:

R = 4 =  √(x^2 + y^2)

Notice that for all the given points we have the radius equal to 4, so the only part that we care is the angle one:

-pi/3 = Atan(y/x)

tan(-pi/3) = y/x = -1.73

So, y and x must have different signs, and because the angle is negative, we will say that the y-component must be negative.

So the correct option will be b: (2, -2√3)

y/x = -2*√3/2 = √3 = -1.73

If you want to learn more about polar coordinates, you can read:

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Answer: Quiz answer Unit 4 lesson 6

all answers are right

Step-by-step explanation:

1.) Given the polar coordinates (4,-pi3)which of the following rectangular coordinate pairs represents the same point?

Answer is B: (2,-2sqrt3)

2.) Given the rectangular coordinates (-5 5) which of the following polar coordinate pairs in, radians, represent the same points?

the correct option is D. (5√2,3π4)

3.)Rewrite in rectangular form: r=8 sin theta -2 cos theta.

Answer:

The equation in rectangular form is:

4.)Rewrite in polar form: x^2+y^2-6y-8=0

the  Answer is B. r^2=6r sin 0+8

5.)The graph of r=-9 cos theta has which of the following characteristics?

Answer:

"circle; diameter of 9; center at (-4.5,0)"

6.)Which conic section is represented by the polar equation r=1/4-6 cos theta?

Answer:

Option 2 - Hyperbola

7.)Identify the horizontal and vertical intercepts of the limaçon represented by the equation r=7+3 cos theta ?

Answer:

vertical intercepts: (7, pi/2) and (-7, pi/2)

horizontal intercepts: (10,0) and (-4,0)

8.) Classify the limaçon represented by the equation r=1/2-1/2 sin theta.

A. Cardioid

9.)Write the equation for the graph of the rose curve.

answer C: r=9 sin 4 theta

10.) Write the equation for the graph of the lemniscate.

answer D: r^2=-49 sin 2theta

(pls don't report for me not explain it took a lot of time typing this and im just trying to help people have less stress on their shoulders :p )

Answer:

The answer is -8

-4 l5 +(-3)l

-4 (2) = -8

Answer: Correct answer is  -8

Step-by-step explanation:

Substitute the given value of m into the expression:

-4|5 + (-3)|.

Then evaluate using the order of operations:

-4|5 + (-3)|

= -4|2|

= -4(2)

= -8

Edmentum Answer

Answer:

C

Step-by-step explanation:

because density equal all the rest

Answer:

Perhaps 2/5, if I understand your question.

Step-by-step explanation:

i don't understand the format of your question:

"3 6

Х

4 5

OL

Х

?"

Is this meant to be (3/6)*(4/5)  ??

If so:

(3/6)*(4/5) = (12/30)

(12/30) = 6/15

6/1`5 = 2/5

Answer:

1572864

Step-by-step explanation:

the nth term of a geoemtric series can be calculated using the following rule : [tex]a_n=a_1(r)^n^-^1[/tex]

where an = nth term, a1 = first term , r = common ratio and n = term position.

here, the first term is 6, the common ratio is 4 and the term position is 10 ( because we want to find the 10th term )

so a1 = 6 , r = 4 and n = 10

using these values we plug them into the rule

recall rule : [tex]a_n=a_1(r)^n^-^1[/tex]

==> plug in a1 = 6 , r = 4 and n - 10

[tex]a_1_0=6(4)^1^0^-^1[/tex]

==> subtract 10 and 1

[tex]a_1_0=6(4)^9[/tex]

==> simplify exponent

[tex]a_1_0=6(262144)[/tex]

==> simplify multiplication

[tex]a_1_0=1572864[/tex]

and we are done!

Note:

the common ration was found by dividing the first term by the next term

Answer:

11,682 the answer is that hope you get a A!

531

×22

+1062

+1062  

=11682

Therefore:

531 × 22 = 11,682

Answer:

fx is 4, gx is 3, hx is anything greater than, not equal to, 4.

Hope this helps!

Let's take 1 of x axis from plot (It has three values in y so much useful)

#A

#B

#C

#D

A and D are out of radar .Now we need to find most approx between B and C

Go to 2 now.(Same 3 values)

#B

#C

65 lies between 60 and 70 ,most approximately equal .

Option C is correct

Answer:

C [tex]y=10x+45[/tex]

Step-by-step explanation:

Line of best fit (trendline) : a line through a scatter plot of data points that best expresses the relationship between those points.

All the given options for the line of best fit are linear equations.

Therefore, we can add the line of best fit to the graph (see attached), remembering to have roughly the same number of points above and below the line.

Linear equation:  [tex]y=mx+b[/tex]

(where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept)

From inspection of the line of best fit, we can see that the y-intercept (where x = 0) is approximately 45.  So this suggests that option C is the solution.

We can also see that the line of best fit appears to be the same distance from points (3, 75) and (4, 85).  So we can use the slope formula with these points to give a rough estimate of the slope of the line of best fit:

[tex]\sf{slope=\dfrac{y_2-y_1}{x_2-x_1}}=\dfrac{85-75}{4-3}=10[/tex]

Therefore, this concurs that C is the solution and that the closet approximation to the line of best fit is [tex]y=10x+45[/tex]

The area of a rectangle is l*w. We have the length as 4.5 in and we can find the width by doing 3+2+4.5 = 9.5 in.

Then, we multiply them. 4.5*9.5 = 42.75 inches²

Answer:

56

Step-by-step explanation:

(84÷3) · 2 = x

28 · 2 = 56

Hope that helps!

45. 0 square units.

The area of the kite is 40.5 unit square.

The side of the kite inscribed in square is 9

We have to find the area of the kite

The area of a kite is,

[tex]A = (d_1d_2) / 2[/tex]

Where [tex]d_1[/tex] and [tex]d_2[/tex] are the diagonals of the kite.

The kite is inscribed in the square, and the sides of the square are 9 units, the diagonals of the kite are both 9 units.

Therefore we get,

[tex]d_1 = 9 units[/tex]

[tex]d_2 = 9 units[/tex]

[tex]A = (9units \times 9units) / 2[/tex]

[tex]A = 81units^2 / 2[/tex]

[tex]A = 40.5 units^2[/tex]

So the third option is correct .

Therefore ,The area of the kite is 40.5 unit square.

To learn more about the area of the kite visit:

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Imagine we drew a line from the centre (2,0) to the point (0,4).

Essentially the line we drew from the centre to that point on the circle is perpendicular to the tangent line slope-wise.

The slope of that line from the centre to the point is -2 based on the slope's equation or formula.

  slope = [tex]\frac{y2-y1}{x2-x1}=\frac{4-0}{0-2} =-2[/tex]

Therefore the tangent equation's slope is 1/2 since any perpendicular line's slope is the negative reciprocal of the original line's slope.

By using the point-slope form, we must have the point on the tangent plane (0,4) and the slope we found which is 1/2.

 [tex]y - 4 = \frac{1}{2}(x-0)\\ y= \frac{1}{2}x + 4[/tex]

Hope that helps!