A conjecture and the paragraph proof used to prove the conjecture are shown. Given: angle 2 is congruent to angle 3. Prove: angle 1 and angle 3 are supplementary. A horizontal line. Two rays extend from upper region of the line diagonally down to the left and right and intersect the line forming interior angles labeled as 2 and 3 and an exterior angle labeled as 1. Drag an expression or statement to each box to complete the proof. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. ∠1 and ​∠2​ form a linear pair, so ∠1 and ∠2 are supplementary by the Response area. Therefore, m∠1+ Response area = 180° by the definition of supplementary. It is given that ∠2≅ Response area, so m∠2=m∠3 by the Response area. By substitution, m∠1+m∠3=180°, so ∠1 and ∠3 are supplementary by the definition of supplementary. angle congruence postulatelinear pair postulatem∠2m∠3∠3∠2

Answer:

[tex]140in {}^{3} [/tex]

Step-by-step explanation:

Substituting values of B and h into the Formular.

[tex]v = \frac{bh}{3} \\ v = \frac{15 \times 28}{3} = 140in {}^{3} [/tex]

Answer:

98

Step-by-step explanation:

Solution 1, (quick)

When enlarging by a scale factor, the shape's area is multiplied by the scale factor squared.

3.5*7*2^2=98

This works because for a rectangle width x and length y, width 2x and length is 2y, area is 4xy compared to area xy originally.

Solution 2, (technical)

Scale factor of 2 means multiplying by 2

3.5^2=7

7*2=14

7*14=98

This can be proved by using identities of trigonometry.

Given that,  

sin x + sin²x = 1 ⇒ sin x = 1 - sin²x

⇒ sin x = cos²x   (∵sin²x + cos²x = 1)

We have to prove that,

cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x = 1

LHS = cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x

= sin⁶x + 3sin⁵x + 3sin⁴ + sin³x

= (sin²x)³ + 3(sin²x)²sin x + 3(sin²x) (sin x)² + (sin x)³

= (sin²x + sin x)³           (∵(a+b)³ = a³ + 3a²b + 3 ab² + b³)

= 1³ = 1 = RHS

LHS = RHS

Hence the equation is proved since both sides of the equation are equal.

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Answer:

e(x)=0 will be  your answer

Step-by-step explanation:

First of all it is important to know about the fair game.  A game is said to be fair if it has equal chances of winning for both the parties.

In Statistical terms, this can be said as expected value =0

If E(X) = 1 where X is from the player, then organizer of the game would have more chances of losing.

Similarly if E(X)>0where X is from the player, then organizer of the game would have more chances of losing.

Also if E(X)>1, where X is from the player, then organizer of the game would have more chances of losing.

Hence a fair game is one where

Answer: A. E(X) = 0

Step-by-step explanation:

Answer:

t=-6

Step-by-step explanation:

Answer:

(3, - 6 )

Step-by-step explanation:

x - 2y = 15 ( add 2y to both sides )

x = 2y + 15 → (1)

2x + 4y = - 18 → (2)

substitute x = 2y + 15 into (2)

2(2y + 15) + 4y = - 18 ← distribute parenthesis and simplify left side

4y + 30 + 4y = - 18

8y + 30 = - 18 ( subtract 30 from both sides )

8y = - 48 ( divide both sides by 8 )

y = - 6

substitute y = - 6 into (1)

x = 2(- 6) + 15 = - 12 + 15 = 3

solution is (3, - 6 )

Answer:

x is 3 y is -6 I really hope this helps

Using proportions, the cost of the 17-ounce sundae is of $5.95.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Considering the 12-ounce sundae bought for $4.2, the cost per ounce is given by the following proportion:

$4.2/12 = $0.35.

Hence the cost of a 17-ounce sundae is:

$0.35 x 17 = $5.95.

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The probability that the employee sold two hurricane policies or sold one hurricane policy is 15/17.

According to the statement

Number of employees who sold three hurricane policies is 2

Number of employees who sold two hurricane policies is 6

Number of employees who sold 1 hurricane policies is 9

SO,

The total number of employees is 2+6+9=17.

The number that sold two hurricane policies or sold one hurricane policy is 6+9=15,

so the Probability = Total number of policies sold / total number of employees

Probability = 15/17

So, The probability that the employee sold two hurricane policies or sold one hurricane policy is 15/17.

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Answer:

[tex](9*10^{9})( 6*10^{8})[/tex] or 9.6×10^8

Step-by-step explanation:

The answer is written above.

Hope this helps!

Answer:

9.6 * 10^8  km.

Step-by-step explanation:

960,000,000

= 9.6 * 10^8  km.

The value of the exponent = number of digits after the 9, which = 8.

The rational numbers are explained below.

The complete question can't he found. Therefore, an overview will be given. Rational numbers are the numbers that can be represented by the quotient p/q of two integers.

In this case, p and q are integers and p isn't equal to 0.

The examples include 1/5, 1/3, -2, 5, etc.

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Answer:

The lines are parallel, this is because they both have the same slope/gradient of 6.

Answer:

parallel lines

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x + 3 ← is in slope- intercept form

with slope m = 6

y = 6x - 4 ← is in slope- intercept form

with slope m = 6

• Parallel lines have equal slopes

then the 2 given lines are parallel

The midpoints of A(-3,-9) and B (-8,-2) is the coordinate points (-5.5, -3.5)

Coordinate points are written in the form (x, y). The midpoint of two points (x1, y1) and (x2, y2) is expressed as:

M(x, y) ={(x1+x2)/2, (y1+y2)/2}

Given the following coordinates A(-3,-9) and B (-8,-2)

M(x, y) = {(-3+(-8))/2, (-9-(-2))/2}

M(x, y) = {(-3-8)/2, (-9+2)/2}

M(x, y) = (-11/2, -7/2)

M(x, y) = (-5.5, -3.5)

Hence the midpoints of A(-3,-9) and B (-8,-2) is the coordinate points (-5.5, -3.5)

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The value of x from the equation x/4 ÷ 2/3 = 1/5 is 8/15

x/4 ÷ 2/3 = 1/5

x/4 × 3/2 = 1/5

(x × 3) / (4 × 2) = 1/5

3x / 8 = 1/5

3x × 5 = 8 × 1

15x = 8

x = 8/15

Therefore, value of x from the equation x/4 ÷ 2/3 = 1/5 is 8/15

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Answer:

x = 21.013155617496

Step-by-step explanation:

we have a right triangle then ,

[tex]\cos \left( 36\right) =\frac{17}{x}[/tex]

Then

[tex]x=\frac{17}{\cos \left( 36\right) } = 21.013155617496[/tex]

Then

x ≈ 21

Step-by-step explanation:

imagine this right-angled triangle is the sine and cosine scenario in a circle. just turn it in your mind or on the paper until it looks like this.

the point with the 36° angle is the center of this circle.

x is the radius of the circle, that is under 36° connecting the center of the circle with the arc of the circle.

17 is the cosine of the angle multiplied by the radius (as the standard cosine function is normed for the standard circle with radius 1).

and the other leg is the sine of the angle multiplied by the radius (this is FYI, we don't need that for the solution here).

so,

17 = cos(36) × x

x = 17/cos(36) = 21.01315562...

Answer:

14.7 (Because you asked for no units)

Step-by-step explanation:

The volume of this triangular prism is 1/2 BHL

0.5 * 3.5 * 2 * 4.2 = 14.7 ft^3

The graph that represents y= cos(2x - π) +5 is illustrated below.

It should be noted that a graph simply means a series of connections among variables given.

In this case the graph that represents y= cos(2x - π) +5 is illustrated below.

The graph is attached.

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The length of the radius of the sphere is 9.26 inches.

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is denoted by the letter r, and the specified point represents its center.

Volume of cube=343 cubic inches

Side of cube=[tex]\sqrt[3]{343}[/tex] = 7 inches

The radius of the sphere is equal to half the diagonal length of the cube since the cube is inscribed inside the sphere, whose diameter is the cube's diagonal length. Utilizing the distance formula, we can determine the cube's diagonal length.

[tex]d=\sqrt{7^{2}+7^{2}+7^{2} } \\=\sqrt{7*7^{2} } \\=7\sqrt{7}[/tex]

To determine the radius of the sphere, divide the value by two.

Radius of sphere=[tex]\frac{7\sqrt{7} }{2}[/tex] = 9.26 inches

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Answer:

π & 4-π

Step-by-step explanation:

The ratio of the lemon water is 10:1

From the information, we have that;

The ratio of water to strawberry juice  is 2 : 1

That of strawberry juice to lemon juice is 5: 1

The, we have that of water to lemon juice to be 10: 1 when compared

Hence,  the ratio of the lemon water is 10: 1

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Answer:

315

Step-by-step explanation:

Answer:

Step-by-step explanation:

this is independent  

20/50= 2/5= 40% of getting pink, probability of getting 2= 20%

13/50=0.26= 26% of getting blue, probability of getting 2= 13%

17/50=0.34=34% of getting purple, probability of getting 2 = 17%

70%

The distance between two points (4,-2) and (-6,4) exists [tex]2\sqrt{34}.[/tex]

Distance between two points exists the length of the line segment that joins the two given points. Distance between two points in coordinate geometry can be estimated by finding the length of the line segment merging the provided coordinates.

Let the points be (4,-2) and (-6,4).

The distance between two points [tex](x_{1} ,y_{1})[/tex] and [tex](x_{2} , y_{2} )[/tex] exists provided by the distance between the two points

[tex]= $\sqrt\\(x_{2} -x_{1} )^{2} +(y_{2} -y_{1})^{2}[/tex]

substituting the points in the equation, we get

[tex]$=\sqrt\\(-6-(4)^{2} +(4-(-2)^{2}[/tex]

simplifying the equation, we get

[tex]$=\sqrt{136}[/tex]

[tex]$=2\sqrt{34}[/tex]

The distance between two points (4,-2) and (-6,4) exists [tex]2\sqrt{34}.[/tex]

Therefore, the correct answer is option c. [tex]$2\sqrt{34}.[/tex]

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V(t)=2000(1.02)^t function that gives the total value in dollars of the investment t years from now given that Shota invests $2000 in a certificate of deposit that earns 2 percent interest each year. This can be obtained by using the formula of compound interest formula.

Equation of compound interest compounded yearly,

A = P(1 + R/100)^t

where,

A = amount

P = principal amount

R = rate

t = number of years

Given that P = $2000, R = 2%, number of years = t,

V(t) = 2000(1+2/100)^t

V(t) = 2000(1+0.02)^t

V(t) = 2000(1.02)^t

Hence V(t)=2000(1.02)^t function that gives the total value in dollars of the investment t years from now given that Shota invests $2000 in a certificate of deposit that earns 2 percent interest each year.

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The equation which the civil engineer can use to find the number of rows is 2x² - 12x = 112. Option D

Let the number of rows be x

Number of cars in each row = x - 6 = 56

Number of rows for parking lot = 2x

Then,

Number of cars for new parking lot = 2x ( x - 6 = 56)

Expand the expression,

2 ( x - 6 = 56)

2x² - 12x = 112

Thus, the equation which the civil engineer can use to find the number of rows is 2x² - 12x = 112. Option D

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Answer:

[tex]\sf Sin \ S = \dfrac{2}{9}[/tex]

Step-by-step explanation:

 [tex]\sf \boxed{\bf Sin \ S = \dfrac{opposite \ side \ of \ \angle S}{hypotenuse}}[/tex]

             [tex]\sf = \dfrac{RQ}{SQ}\\\\= \dfrac{2}{9}[/tex]

Answer: Yes

Step-by-step explanation:

Since ABCD is a rectangle, [tex]\angle AXY[/tex], [tex]\angle YBZ[/tex], [tex]\angle WCZ[/tex], and [tex]\angle WDX[/tex] are all right angles, and are thus all congruent because all right angles are congruent. Furthermore, because ABCD is a rectangle, we know that [tex]\overline{AB} \cong \overline{CD}[/tex] and [tex]\overline{AD} \cong \overline{BC}[/tex]. Because we are given that X, Y, Z, and W are midpoints, using the fact that halves of congruent segments are congruent, we can conclude that [tex]\overline{AY} \cong \overline{YB} \cong \overline{CW} \cong \overline{WD}[/tex] and that [tex]\overline{AX} \cong \overline{XD} \cong \overline{BZ} \cong \overline{ZC}[/tex]. As a result, we can conclude that [tex]\triangle AYX \cong \triangle DXW \cong \triangle CWZ \cong \triangle BYZ[/tex] by SAS, and thus by CPCTC, [tex]\overline{AY} \cong \overline{XW} \cong \overline{ZW} \cong \overline{YZ}[/tex]. Therefore, since the quadrilateral formed by the midpoints has four congruent sides, it must be a rhombus.

s= d/t

s= 135/5

s= 27 mph

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The probability of not drawing a black marble is 4/5

The probability of drawing a red marble is 3/10

Probability determines the odds of the occurrence of a random event. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability of not drawing a black marble = total marbles that are not black / total number of marbles

(5 + 3) / (5 + 3 + 2) = 8/10 = 4/5

The probability of drawing a red marble = total number of red marbles / total number of marbles

= 3/10

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Answer:

See image

Step-by-step explanation:

Plato

Answer: The triangles are not similar.

Step-by-step explanation:

Two figures are similar simply if they have the same shape, but not necessarily the same size. In a more mathematical sense, similar figures have the same angle measures and proportionate side lengths.

For reference, side lengths are proportionate when the ratios between corresponding/matching sides are the same.

Since we do not have any angles, we will try using the SSS Similarity Theorem, which states that if all three sides of both triangles are in proportion, then the triangles are similar. We will first list all the side lengths and match corresponding ones.

[tex]\triangle ABC \rightarrow 18,20,32\\ \triangle UVT \rightarrow 14,15,24[/tex]

Since we matched corresponding sides, we can now check whether they have the same ratio).

[tex]\frac{18}{14}=\frac{20}{15}=\frac{32}{24}[/tex]

[tex]\frac{9}{7}=\frac{4}{3}=\frac{4}{3}[/tex]

Not all of the side lengths have the same ratio, so these triangles aren't similar. you must multiply 14 by 9/7 to get to 18, but you need to multiply the other two sides by 4/3 to get to their