Given that e parallel f and g is a transversal, we know that angle 4 is-congruent-to angle 5 by the alternate interior angles theorem. we also know that angle 1 is-congruent-to angle 4 and angle 5 is-congruent-to angle 8 by the ________. therefore, angle 1 is-congruent-to angle 8 by the substitution property. corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem

The length of the missing length in the triangle is 53.6 units

The given triangle is a right triangle.

Right triangles are triangles that have a measure of angle that is 90 degrees.

The missing side is x, and the value of x is calculated using the following sine rule

We have

sin(angle) = opposite/hypotenuse

This gives

sin(66) = 49/x

Divide both sides by sin(66)

1 = 49/x sin(66)

Multiply both sides by x

x = 49/sin(66)

Divide the expression

x = 53.6

Hence, the length of the missing length is 53.6 units

Read more about right triangles at

https://brainly.com/question/2437195

#SPJ1

If the time taken by 14 inches wide is one hour then the blade of 12 inches wide will take 1 hour 17 minutes to mow a lawn.

What is width?

The width of something is the measurement of one side of a body. It is generally less than length of that body or shape.

How to calculate time?

We have been given time of 1 hour if blade is 14 inches wide and we have to calculate time taken by 12 inches wide blade:

It will be as 14/12* 1 hour

=14/12

=1.167

=1.17 hour

Hence the time taken by the blade of 12 inches wide will be 1 hour and 17 minutes.

Answer:

70 mins

Step-by-step explanation:

This is called inverse proportion.

1hr : 14in

x hr : 12in

Ask yourself, what do you do to 14 to get 12? To find this out, we do:

14 / 12 = 1.16666667

Since the blade is smaller, it will take longer. So, we times 1hr by 1.16666667 to get

1.16666667 hrs =

1.17 hours (rounded)

This is 70.2 mins, or 1hr 10 mins

Hope this helps!

A)  Rotate by 90° counterclockwise.

B) Reflection transformation about the line y = 5.

C) Parallel Lines are C₂D₂ and A₂B₂; EF and E₁F₁.

D) Perpendicular lines are;  D₁F₁ and  E₁F₁; DF and EF; DC and AB.

E) Line segments with slope of 0 are; AB, C₂D₂, A₂B₂, EF and E₁F₁

F) Line segments on the boat that have an undefined slope are; Lines A₁B₁, DF and DC.

G) Slope of Line ED = 1

A) The blue segment CD is seen on the graph as a perpendicular line with 2 units while the line segment C₂D₂ is seen as a horizontal line. Thus, to match CD with C₂D₂, we will rotate by 90° counterclockwise.

B) The transformations that would be used on the blue triangle to get it to match with the red triangle is a reflection transformation about the line y = 5.

C) The line segments that are parallel to each other are; C₂D₂ and A₂B₂; EF and E₁F₁.

D) The line segments that are perpendicular are;  D₁F₁ and  E₁F₁; DF and EF; DC and AB.

E) Horizontal lines that are parallel to the x-axis have zero slope. Thus, AB, C₂D₂, A₂B₂, EF and E₁F₁ all have zero slopes.

F) Undefined slope is the slope of a vertical line. Thus, Lines A₁B₁, DF and DC have undefined slopes.

G) Slope of ED = (5 - 4)/(-10 - (-11))

Slope of ED = 1/1

Slope = 1

Read more about Transformations at; brainly.com/question/4289712

#SPJ1

abc =32 ft³  is the maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot.

A rectangle with all equal sides, commonly known as a square.  Multiplying the length by the length is the. Using L as the length of each side, solve for L X L = L2,

The maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot This Lagrange multiplier optimization is standard. If the box has a base of a, a height of c, and an area constraint of ab+2ac+2bc−48=0  we wish to optimize V= abc.

L(a,b,c,λ)= abc−λ(ab+2ac+2bc−48)

The four partial derivatives are zero at an ideal position, so:

δLδa=bc−λ(b+2c)=0

δLδb=ac−λ(a+2c)=0

δLδc=ab−λ(2a+2b)=0

Plus the restriction. The first two enlighten:

λ=bcb+2c=aca+2c

Consequently,  b(a+2c)=a(b+2c)  implies to b=a. The third partial, where b=a, now informs us that   a2=4aλ  and so  λ=a/4  nd by using this information in the second partial, we obtain  4c=a+2c  which informs us that c=a/2 .

Now that we've inserted these b and c expressions into the constraint, we get [tex]3a^2=1[/tex]  which means that a=4 feet, b=4 feet, and c=2 feet.

The maximum volume is therefore, abc=32 ft³

Learn more about surface area here:

https://brainly.com/question/28016184

#SPJ4

If [tex]x[/tex] and [tex]y-1[/tex] have the same sign, then either

[tex]x>0,y>1 \implies 2|x| + 3|y-1| = 2x + 3(y-1)=6 \implies 2x + 3y = 9[/tex]

or

[tex]x<0,y<1 \implies 2|x| + 3|y-1| = -2x - 3(y-1) = 6 \implies 2x + 3y = -3[/tex]

If [tex]x[/tex] and [tex]y-1[/tex] have opposite sign, then

[tex]x>0,y<1 \implies 2|x| + 3|y-1| = 2x - 3(y-1) = 6 \implies 2x -3y = 3[/tex]

or

[tex]x<0,y>1 \implies 2|x| + 3|y-1| = -2x + 3(y-1) = 6 \implies 2x-3y = -9[/tex]

This is to say that the region has boundaries given by these two sets of parallel lines, so we can equivalently describe the region with the set

[tex]R = \left\{(x,y) \mid -3\le2x+3y\le9 \text{ and } -9\le2x-3y\le3\right\}[/tex]

The area of [tex]R[/tex] is given by the double integral

[tex]\displaystyle \iint_R dx\,dy[/tex]

To compute the area, change the variables to

[tex]\begin{cases}u = 2x + 3y \\ v = 2x - 3y\end{cases} \implies \begin{cases}x = \frac14(u+v) \\ y = \frac16(u-v)\end{cases}[/tex]

The Jacobian for this transformation is

[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix}1/4 & 1/4 \\ 1/6 & -1/6\end{bmatrix}[/tex]

with determinant [tex]\det(J) = -\frac1{12}[/tex]. Then the integral transforms to

[tex]\displaystyle \iint_R dx\,dy = \iint_R |J| \, du \, dv = \frac1{12} \int_{-3}^9 \int_{-9}^3 dv\, du[/tex]

which is 1/12 the area of a square with side length 12. Hence the integral evaluates to

[tex]\displaystyle \iint_R dx\,dy = \frac1{12}\times12^2 = \boxed{12}[/tex].

Answer:

C = 364.24

Step-by-step explanation:

Comment

The circumference and the radius are related to one another. The constant relating them is pi which is a fixed number of 3.14 The formula for the circumference is C = 2*pi * r

Givens

pi = 3.14

r = 58 cm

Circumference = ?

Formula

C = 2*pi * r

C = 2 * 3.14 * 58

C = 364.24

Answer:

Below.

Step-by-step explanation:

x^2 + 4x  = 18

x^2 + 4x + (2)^2 = 15 + 2^2

x^2 + 4x + 4 = 18 + 4

(x + 2)^2 = 22

x  + 2 = +/- √22

x = -2 + √22 and x =  -2 + √22

x = 2.7  and -6.7  to nearest tenth.

Answer:

Obtuse, scalene.

Step-by-step explanation:

In ΔSVU, one angle is 120° which is obtuse angle.

So, ΔSVU is a obtuse triangle.

All the sides  have different measurements. So, It is a Scalene triangle.

Question 2

1) [tex]\overline{PR} \perp\overline{QS}, \overline{PQ} \cong \overline{PS}[/tex] (given)

2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)

3) [tex]\angle PRQ, \angle PRS[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\triangle PRQ, \triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)

5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)

Question 3

1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}, \overline{DE} \perp \overline{AB}[/tex] (given)

2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)

3) [tex]\triangle ACD, \triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)

4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)

5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)

6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)

7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)

Answer:

1:3.

Step-by-step explanation:

Probability(getting > 3 on one roll) = 3/6 = 1/2.

So on 2 cubes rolled the probability   of getting > 3 is 1/2 * 1/2 = 1/4.

As a ratio this is 1:3.

Used formula

Answer:

6x+5

Step-by-step explanation:

the derivative of a sum is equal to the sum of derivatives:

(3x^2 + 5x + 2)' = (3x^2)' + (5x)' + (2)' = 6x + 5

Q.E.D.

The sample variance for distribution of the means is 9

The average of the squared differences from the Mean is called Variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value.

The Standard Deviation is a measure of how spread out numbers are.

Its symbol is σ (the Greek letter sigma)

Its formula is the square root of the Variance

Given: Standard Deviation = 3

           Sample size = 36

∴ By formula we get

3 = √(Variance)

∴ 9 = Variance

Thus the sample variance for distribution of the means is 9

Learn more about variances here :

https://brainly.com/question/13708253

#SPJ4

The surface area of the composite figure is 524 square meters

The given composite figure is made up of a triangular prism and a rectangular prism. The surface area of the figure is given as:

Surface area = 2(16*5+5*4+16*4) + (16*6) + 2(50)

Take the sum

Surface area = 2(80+20+64) + 96 + 100

Surface area = 2(164) +196

Surface area = 328 + 196

Surface area = 524 square meters

Hence the surface area of the composite figure is 524 square meters

Learn more on surface area here: https://brainly.com/question/1297098

#SPJ1

Answer:

[tex]x^{3} ( x + 1 ) + y^{3} (x+1)\\= (x+1)(x^{3} + y^{3})[/tex]

Answer:

Step-by-step explanation:

YOU PLUS ALL OF THEM

The area of the minor sector DFE is gotten as; D: 66.1 square cm

Formula for area of sector is;

A = (θ/360) * πr²

We are given;

minor angle; θ = 100°

radius; r = 8.7 cm

Thus;

A =  (100/360) * π(8.7²)

A = 66.1 square cm

Read more about Area of Sector at; https://brainly.com/question/22972014

#SPJ1

[tex]\sqrt{3-2\sqrt{2} }[/tex] = 0.06

(2x)ˣ = 25√5

[tex]\sqrt{3-2\sqrt{2} }[/tex]  = [tex]\sqrt{3}-\sqrt{2\sqrt{2} }[/tex] = 1.73205080757 - 1.67428223427 = 0.06

4ˣ . 4ˣ⁻¹ = 24

4ˣ . 4ˣ / 4 = 24

4ˣ(1 - 1 / 4) = 24

4ˣ(3 / 4) = 24

multiply both sides by 4 / 3

4ˣ = 32

2²ˣ = 2⁵

2x = 5

x = 5 / 2 = 2.5

Therefore,

(2x)ˣ = 25√5

learn more on expression here: https://brainly.com/question/13882554

#SPJ1

We would reach our office by 7:34 a.m.

The average speed is given as 30 miles per hour.

Let us convert this into miles per minute.

30 miles/1 hour = 30 miles/60 minutes

= 0.5 miles per minute

The distance between the house and the office is 12 miles.

Therefore, we can find what it would take to reach the office by dividing the distance by the average speed:

Time taken = distance/average speed

= 12 miles/0.5 miles per minute

= 24 minutes

The time is given to be 7:10 a.m. Therefore we would reach our office by 7:34 a.m.

Therefore, we would reach our office by 7:34 a.m.

Learn more about average speed here: https://brainly.com/question/6504879

#SPJ4

The end behavior of the Polynomial f(x) = -4x⁶ + 6x² - 52 is;

B. f(x) is an even function so both ends of the graph go in the same

direction

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

Now, we are given the polynomial;

f(x) = -4x⁶ + 6x² - 52

Let us first test if the polynomial is even;

f(1) = -4(1)⁶ + 6(1)² - 52

f(1) = -50

Similarly;

f(-1) = -4(-1)⁶ + 6(-1)² - 52

f(-1) = -50

Since f(1) = f(-1), we can say that both ends of the graph go in opposite

directions.

Lastly, the leading coefficient is negative because it is -4 and as such it means that the left end goes down.

Read more about Polynomial End Behavior at; https://brainly.com/question/20347699

#SPJ1

Excel uses VAR function for determining the residual variance.

The variation of any error is known as residual variance, also known as unexplained variance or error variance.

Depending on the type of analysis you're doing, the precise definition will vary. For instance, random fluctuations in regression analysis produce volatility around the "actual" regression line.There are two components to a regression line's total variance: variation that can be explained and variance that cannot. Simply put, the residual variance after deducting the variation resulting from the regression from the total variance of the dependent variable is the residual variance.

Learn more about residual variance here:

https://brainly.com/question/27464491

#SPJ4

The factored expression of the polynomial is (x - 3)(x + 4)

The polynomial expression is given as;

x^2 + x - 12

Expand the expression

x^2 + 4x - 3x - 12

Factorize the expression

x(x + 4) -3(x + 4)

Factor out x + 4

(x - 3)(x + 4)

Hence, the factored expression of the polynomial is (x - 3)(x + 4)

Read more about polynomials at

https://brainly.com/question/4142886

#SPJ1

The EXPERIMENTAL REGION is the range of values of the independent variables in the data used to estimate the regression model.

According to the statement

There is a region where the range of values of the independent variables in the data used to estimate the regression model.

AND

Those region is called EXPERIMENTAL REGION

So, Experimental region is called a those region in which the region within which we can make valid predictions and doesn't go outside of the bounds of the data we were provided.

So, The EXPERIMENTAL REGION is the range of values of the independent variables in the data used to estimate the regression model.

Learn more about DATA here https://brainly.com/question/26711803

#SPJ4

Answer:

(-4,0) and (4,0)

Step-by-step explanation:

The x-intercepts occur for values of x where f(x) = 0.

f(x) = 0 when the nominator ([tex]x^{2} - 16[/tex]) = 0.

[tex]x^{2} -16[/tex] is a difference of squares,
so you can factor it as (x + 4)(x – 4)

When x = –4 or x = 4, the nominator is 0, and f(x) = 0

Answer:

[tex]log_{2}[/tex] 20

Step-by-step explanation:

using the rule of logarithms

loga + logb = logab

then

[tex]log_{2}[/tex]4 + [tex]log_{2}[/tex]5

= [tex]log_{2}[/tex] (4 × 5)

= [tex]log_{2}[/tex]20

The interface validation that would help to confirm that you meet the minimum age is the range check.

This is the term that is used to refer to the check that is done in such a way that it shows the data that are in a particular range.

This would help to ensure that there is a specified upper and lower boundary for the values to fall into.

Read more on the range check here:

https://brainly.com/question/25962668

#SPJ1

which of the following interface validation checks is useful in verifying that the birth data you entered on your job application indicates that you meet the minimum age requirement to serve alcohol?

Consistency check

Format check

Completeness check

Range check

Answer:

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

The minimum sample size required to estimate the mean usage of water = 2225.07

What is Standard deviation?

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

We can find the minimum sample size required to estimate the mean usage of water as shown below:

Standard deviation [tex]\sigma =3.61[/tex]

Margin of error E=0.15

Critical value for 95% confidence interval = 1.96

Required minimum sample size: [tex]n=(\frac{Z_{\frac{\alpha}{2}}.\sigma }{E} )^2[/tex]

[tex]=(\frac{1.96\times 3.61}{0.15} )^2[/tex]

=2225.07

Hence, the minimum sample size required to estimate the mean usage of water = 2225.07

Learn more about Standard deviation here:

https://brainly.com/question/22920224

#SPJ4

The decision would be to fail to reject the null hypothesis and conclude that there is insufficient evidence.

The formula is fx/n

To get fx we have to sum all of the values of x = 2430161

The total number in the data set = 35

Mean = 2430161/35

= 69433.17

This test is a left tail test.

sd = 8500

H0: u = 70000

H1 : U < 70000

z0.05 = 1.645

The decision would be to reject if z < critical value

Z= (69433.17 - 70000)/(8500/√35)

= -0.395

P-value can be gotten from the z score = 0.348

Given that the p value is > 0.05, we would have to fail to reject the null. The conclusion would be that there is insufficient evidence to support claim.

Read more on test statistics here:

https://brainly.com/question/15980493

#SPJ1

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

5x:9 = 7:3

→ 5x/9 = 7/3

→ x = (7 × 9)/(3 × 5)

→ x = 21/5

Step 1. You need x isolated.
[tex]x < 13+7[/tex]

When you move a number from the left to right (and its addition or subtraction, the sign stays (< ≤ > and ≥ is signs).
x<20 or in words, x is less than 20, and cannot be 20.

Answer:

x < 20

Any number less than 20 is a solution

Step-by-step explanation:

x-7 < 13

The first step to solve this inequality is to add 7 to each side

x-7+7 < 13+7

x < 20

Any number less than 20 is a solution