what is the midpoint of line segment EF

We know:

The product of two negative numbers is positive.

Therefore

(-12)(12)(-6.3)(-0.2)(-15.9) = (-12)(-6.3) (-0.2)(-15.9)(12) > 0  ANSWER

(12)(-6.3)(-0.2)(-15.9) < 0

(-12)(12)(-6.3)(-0.2)(-15.9)(0) = 0

(12)(12)(6.3)(0.2)(-15.9) < 0

Angles B and C are alternate interior angles where transversal BC cuts parallel lines AB and CD. Thus angles B and C are equal. Angle B is 65°.

Angle AEC is the exterior angle opposite interior angles A and B, which means its value is the sum of angles A and B.

∠AEC = ∠A +∠B = 47° +65°

∠AEC = 112°

Answer:

1. (0, -2/3), (2, 0)

2. y = x-6

Step-by-step explanation:

1. Since the equation is in slope-intercept form, you know the y-intercept is -2/3. The x-coordinate there is 0, so the ordered pair is (0, -2/3).

Substituting y=0 into the equation gives the value of the x-intercept.

... 0 = 1/3x -2/3

... 0 = x - 2 . . . . . multiply by 3

... 2 = x . . . . . . . . add 2

The x-intercept is (2, 0).

2. The given line has slope -1, so the perpendicular line has a slope that is the negative reciprocal of that: -1/-1 = 1. Then the point-slope equation of the line can be written ...

... y = 1(x -8) +2

... y = x - 6 . . . . simplify

(1)

to find the intercepts

• let x = 0, in the equation for y-intercept

• let y = 0, in the equation for x-intercept

x = 0 : y = - [tex]\frac{2}{3}[/tex] → (0, - [tex]\frac{2}{3}[/tex]) ← y-intercept

y = 0 : [tex]\frac{1}{3}[/tex] x - [tex]\frac{2}{3}[/tex] = 0 ( multiply by 3 )

x - 2 = 0 → x = 2 → (2, 0 ) ← x- intercept

(2)

the equation of a line in slope-intercept form is

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

y = - x is in this form with slope m = - 1

the slope of a perpendicular line = - [tex]\frac{1}{m}[/tex] = 1

the partial equation of the perpendicular line is

y = x + c

to find c substitute (8, 2 ) into the partial equation

2 = 8 + c → c = 2 - 8 = - 6

y = x - 6 ← equation of perpendicular line

A

note that r = 3.75% = 0.0375

A(9) = 10500 × [tex]e^{0.0375(9)}[/tex] = 10500 × [tex]e^{0.3375}[/tex] = 14, 715.12

We are given formula for continuous change function A(t) = Pe^rt.

We need to find the value of $10,500 investment amount grows 3.75% each year after 9 years.

Plugging values of P=10500

r= 3.75% = 0.0375 and

t=9 in given formula.

We get

[tex]A(9) = 10500e^{0.0375\times 9}[/tex]

Let us simplify it now.

[tex]e^{0.0375\times 9}=e^{0.3375}=1.40144[/tex]

[tex]=10500\times \:1.40144\dots[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:10500\times \:1.40144\dots =14715.11589\dots[/tex]

Rounding it to the nearest cents.

=14715.12.

Divide 50 by 22: 2.27272727...

Round up to hundredth and your final answer is 2.27

hope that helps :)

The angle in the dilated figure is the same as the original angle in each case, a fact that should be confirmed by the way the answer choices are shown.

∠A = ∠A'

... 4x -4 = 51 -x

... 5x = 55

... x = 11

∠A = 4·11 -4 = 40 . . . . . . doesn't match any offered choice

___

∠B = ∠B'

... 6x -1 = 4x +21

... 2x = 22

... x = 11

... ∠B = 6·11 -1

... ∠B = ∠B' = 65 . . . . . matches selection D)

_____

∠C = ∠C'

... 8x -13 = 6x +9

... 2x = 22

... x = 11

... ∠C = 6·11 +9 = 75

... ∠C = ∠C' = 75 . . . . . matches selection D)

Answer:

f(-1) = -1 . . . . matches the last selection

Step-by-step explanation:

When evaluating piecewise functions, the first step is to determine the applicable piece. The argument -1 is in the range of the middle definition, (-2, 1). So, the function value is ...

... (-1)³ = -1

the sum of the angles in a triangle = 180°, thus

x + [tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{6}[/tex] x = 180

multiply through by 6

6x + 3x + x = 1080

10x = 1080 ( divide both sides by 10 )

x = 108

the angles are 108°, 54° and 18°

Since all the angles are different and the largest is 108°

The triangle is an obtuse scalene triangle

The measures of the angles of the triangle are approximately 108 degrees, 54 degrees, and 18 degrees. This type of triangle is a scalene triangle, as all of its angles are different.

To find the measures of the angles of a triangle whose angles are x, 1/2x, and 1/6x, we will use the fact that the sum of the angles in a triangle is always 180 degrees. The equation representing this is:

x + 1/2x + 1/6x = 180

Combine like terms:

1.6667x = 180

Then solve for x:

x ≈ 108 degrees

Now plug x into the original angle measures to get:

Angle 1 = 108 degrees

Angle 2 = 1/2x = 54 degrees

Angle 3 = 1/6x = 18 degrees

Lastly, in terms of the type of triangle, this is a scalene triangle because all of its angles are different.

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Into each bowl, he will pour

... (1/3)×(7 1/5) = (1/3)×(6 6/5) = 2 2/5 . . . liters of juice

_____

Here, we have elected to rewrite 7 1/5 as 6 6/5 so each part of the number (whole number, fraction) will be divisible by 3.

You may have been taught to convert 7 1/5 to an improper fraction before doing the multiplication. That method looks like ...

... (1/3)×(36/5) = 12/5 = 2 2/5 . . . . same result

If the angle is 90 degrees, then the complement would be 27, because 90 / 3 = 30, and 30 - 3 = 27. Basically, you divide the angle by 3 and subtract 3 to find the complement if this is the case.

Answer:

22⁰

Step-by-step explanation:

Angle = x

Complement = 90 - x

Given:

x = 3 (90 - x) + 2

x = 270 - 3x + 2

4x = 272

x = 68

Complement = 90 - 68 = 22⁰

ANSWER 1

Note that,

[tex]f(u)=tan^{-1}(u)[/tex]

is the same as

[tex]f(u)=arctan(u)[/tex]

We apply the product rule.

[tex]f(x)=x^2tan^{-1}(x)[/tex]

So we keep the second function and differentiate the first,plus we keep the first function and differentiate the second.

[tex]f'(x)=(x^2)'tan^{-1}(x)+x^2(tan^{-1}(x))' [/tex]

Recall that,

If

[tex]f(u)=tan^{-1}(u)[/tex]

Then,

[tex]f'(u)=\frac{1}{1+u^2}} \times u'[/tex]

This implies that,

[tex]f'(x)=2xtan^{-1}(x)+\frac{x^2}{x^2+1} [/tex]

ANSWER 2

We apply the product rule and the chain rules of differentiation here.

[tex]f(x)=xsin^{-1}(1-x^2)[/tex]

[tex]f'(x)=x'sin^{-1}(1-x^2)+x(sin^{-1}(1-x^2))' [/tex]

Recall that,

If

[tex]f(u)=sin^{-1}(u)[/tex]

Then,

[tex]f'(u)=\frac{1}{\sqrt{1-u^2}} \times u'[/tex]

This implies that,

[tex]f'(x)=sin^{-1}(1-x^2)+x \times \frac{1}{\sqrt{1-(1-x^2)^2}}\times (-2x) [/tex]

[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{1-(1-2x^2+x^4)}} [/tex]

[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{1-1+2x^2-x^4}}[/tex]

[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{2x^2-x^4}}[/tex]

Answer:

1. B) 7

2. B) {y|y ≤ -1}

Step-by-step explanation:

1. Put -4 where x is in the function definition and do the arithmetic.

... 3 - (-4) = 3 +4 = 7

2. If the maximum function value is -1 and the values extend to -∞ from there, then the range is (-∞, -1]. In your notation, that is ...

... {y | y ≤ -1}

B and B

f(x) → 3 - x

to evaluate f(- 4 ) substitute x = - 4 into f(x)

f(- 4 ) = 3 - (- 4 ) = 3 + 4 = 7 → B

the range of a function are the values of y for the function

this function ( probably quadratic ) has a vertex at (0, - 1), that is the y-value is - 1

Since the function opens down then the values of y are tending to negative infinity

so the range of values for y are less than or equal to - 1 to negative infinity

{y | y ≤ - 1 } → B

Answers: The statement that express the same scale are Options B and C.

Solution:

A. 5 cm on the map represents 50 m in Chicago?

Rule of three:

1 cm represents 100 m

5 cm represents    x

x=(5 cm).(100 m) / (1 cm)

x=500 m

5 cm on the map represents 500 m in Chicago.

The statement A doesn't express the same scale.

B. 1 mm on the map represents 10 m in Chicago?

1 mm = 0.1 cm

Rule of three:

1 cm    represents 100 m

0.1 cm represents    x

x=(0.1 cm).(100 m) / (1 cm)

x=10 m

1 mm = 0.1 cm on the map represents 10 m in Chicago.

The statement B expresses the same scale.

C. 1 km in Chicago is represented by 10 cm on the map?

1 km = 1,000 m

Rule of three:

1 cm    represents 100 m

x         represents  1,000 m

x=(1 cm).(1,000 m) / (100 m)

x=10 cm

1 km = 1,000 m in Chicago is represented by 10 cm on the map.

The statement C expresses the same scale.

D. 100 cm in Chicago is represented by 1 m on the map?

100 cm = 1 m

Rule of three:

1 cm    represents 100 m

x         represents  1 m

x=(1 cm).(1 m) / (100 m)

x=0.01 cm

100 cm = 1 m in Chicago is represented by 0.01 cm on the map.

The statement D doesn't express the same scale.

Answer:

a,b,c d is incorrect but a,b,c is right

Step-by-step explanation:

just took the test

Area is the product of length and width. If you assume the dimensions are integers, you are looking for factors of 117 that differ by 4.

117 = 1×117 = 3×39 = 9×13

These last two factors differ by 4, so we know the dimensions of the barn are ...

... 9 ft wide by 13 ft long

32 inches³

the volume V of a pyramid = [tex]\frac{1}{3}[/tex] × area of base × height

area of base = 4² = 16 and h = 6

V = [tex]\frac{1}{3}[/tex] × 16 × 6 = 32

If you want to simplify this, you can add the coefficients of like terms.

... = x²(2+2) +x(4+4) +(-3-3)

... = 4x² +8x -6

_____

Since both of the parts of the sum are the same, this expression can be rewritten using the distributive property:

... = 2(2x² +4x =3)

_____

The sum can also be rewritten to vertex form.

... = 4(x² +2x) -6

... = 4(x² +2x +1) -6 -4(1)

... = 4(x +1)² -10

This is an expression describing a parabola with vertex (-1, -10) and a vertical scale factor of 4. It has roots (x-intercepts) at -1±√2.5.

29°

Consider the right triangle between the plank and the ground

the angle can be found using tangent ratio

tanx° = [tex]\frac{opposite}{adjacent}[/tex]

where adjacent = 18 and opposite = 10

tanx° = [tex]\frac{10}{18}[/tex]

x = [tex]tan^{-1}[/tex]([tex]\frac{10}{18}[/tex]) = 29.0546 ≈ 29°

Answer:

29 degrees to nearest degree.

Step-by-step explanation:

This is the angle whose tangent is  10/18 or 5/9.

this = 29 degrees

Let's form the difference of the two expressions and see what we can learn.

(2y -x) -(2x -y) = 2y -x -2x +y = 3y -3x = 3(y -x)

Since y > x, this is positive, so 2y -x is greater than 2x -y.

Part (a)

The variable y is the dependent variable and the variable x is the independent variable.

Part (b)

The cost of one ticket is $0.75. Therefore, the cost of 18 tickets will be:

[tex]0.75\times 18=13.5[/tex] dollars

Now, we know that Kendall spent her money only on ride tickets and fair admission and that she spent a total of $33.50.

Therefore, the price of the fair admission is: $33.50-$13.50=$20

If we use y to represent the total cost and x to represent the number of ride tickets, the linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission can be  written as:

[tex]y=0.75x+20[/tex]......Equation 1

Part (c)

The above equation is logical because, in general, the total cost of the rides will depend upon the number of ride tickets bought and that will be 0.75x. Now, even if one does not take any rides, that is when x=0, they still will have to pay for the fair admission, and thus their total cost, y=$20.

Likewise, any "additional" cost will depend upon the number of ride tickets bought as already suggested. Thus, the total cost will be the sum of the total ride ticket cost and the fixed fair admission cost. Thus, the above Equation 1 is the correct representative linear equation of the question given.

The yearly membership cost plus the cost per visit was set equal to the non-member cost per visit, and solving the equation gave us the result.

We need to find the number of visits it would take for the total cost of a member and a non-member to be the same if they both use the waterpark at each visit. Let's denote the number of visits as x.

The yearly membership cost is $275, and each visit to the waterpark costs an additional $5 for a member. So, for x visits, the total cost for a member is:

Member cost = $275 + $5x

Non-members pay $6 for parking, $15 for admission to the park, and $9 for the waterpark per visit. Therefore, the total cost for a non-member is:

Non-member cost = ($6 + $15 + $9)x = $30x

Setting both costs equal to find the number of visits where the costs are the same:

$275 + $5x = $30x

Now we solve for x:

$275 = $30x - $5x

$275 = $25x

x = $275/$25

x = 11

Therefore, it would take 11 visits for the total cost to be the same for a member and a non-member if they both use the waterpark at each visit.

Answer: Step 2. She incorrectly squared the numbers.

Solution:

The correct steps are:

1. a^2+7^2=25^2

2. a^2+49=625

3. a^2=576

4. a=24

In which step did Shawna make an error?

Step 2. She incorrectly squared the numbers.

Since, we are given right angled triangle

so, we use pythagoras theorem to find 'a'

step-1:

Using pythagoras theorem

[tex]a^2+7^2=25^2[/tex]

step-2:

we know that

[tex]7^2=7\times 7 =49[/tex]

[tex]25^2=25\times 25 =625[/tex]

so, we get

[tex]a^2+49=625[/tex]

she made error in second step

step-3:

Subtract both sides by 49

[tex]a^2+49-49=625-49[/tex]

[tex]a^2=576[/tex]

step-4:

Take sqrt both sides

we get

[tex]a=24[/tex]

so,

Answer is:

Step 2. She incorrectly squared the numbers.

Answer: C

Step-by-step explanation:

Answer:

OPtion C is correct answer.

Step-by-step explanation:

Given that there is a system of equations as

y =-4x+3 and y =3x+1

Table is prepared with side by side values of y for a given x

From the table we are to find the solution of the system

On analysing the table we find that the difference between two y's is

0.5, -0.2, -0.9, -1.6, -2.3,-3

Hence we select the one which shows minimum difference i.e. -0.2

For this, x = 0.6

When x =0.6, y shows two values as 0.6 and 0.8

So we approximate y value as average of these two i.e. 0.7

So solution is

(0.6, 0.7)

N = 10.79

isolate N by adding 6.47 to both sides of the equation

N = 4.32 + 6.47 = 10.79

The unknown number N in the equation N - 6.47 = 4.32 is found to be 10.79 when we add 6.47 to both sides of the equation.

To solve for the unknown number N in the equation N - 6.47 = 4.32, we must isolate the variable N on one side of the equation. We do this by adding 6.47 to both sides of the equation:

N - 6.47 + 6.47 = 4.32 + 6.47

This simplifies to:

N = 10.79

The unknown number N is therefore 10.79. When providing the final answer, we must make sure that it is reported with the correct number of significant figures, which in this case are three significant figures.

IQR = 6

First locate the median [tex]Q_{2}[/tex] at the centre of the data arranged in ascending order. Then locate the lower and upper quartiles [tex]Q_{1}[/tex] and [tex]Q_{3}[/tex] located at the centre of the data to the left and right of the median.

Note that if any of the above are not whole values then they are the average of the values either side of the centre.

rearrange data in ascending order

15 16 ↓17 17 18 21 22 ↓23 25

                     ↑

[tex]Q_{2}[/tex] = 18

[tex]Q_{1}[/tex] = [tex]\frac{16+17}{2}[/tex] = 16.5

[tex]Q_{3}[/tex] = [tex]\frac{22+23}{2}[/tex] = 22.5

IQR = [tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 22.5 - 16.5 = 6

Final answer:

The interquartile range (IQR) for the given data set is calculated by first arranging the data in ascending order, finding the first and third quartiles (Q1 and Q3), and subtracting Q1 from Q3. The correct IQR for this data set, following this methodology, is 6, not the mistakenly provided 7.

Explanation:

The question asks about calculating the interquartile range (IQR) of a given data set. The IQR is important because it measures the middle 50% spread of data, pinpointing where the bulk of values lie, and helps in identifying potential outliers. To compute the IQR, we first need to organize the data in ascending order, then find the first quartile (Q1) and the third quartile (Q3), and finally subtract Q1 from Q3 (IQR = Q3 - Q1).

For the provided data set: 17, 16, 21, 15, 25, 22, 18, 23, 17:

Arrange data in ascending order: 15, 16, 17, 17, 18, 21, 22, 23, 25.

Find the median (Q2), which is 18 in this case as it's the middle value.

Q1 is the median of the first half (excluding the middle value if odd number of data), so Q1 = 16.5.

Q3 is the median of the second half, hence Q3 = 22.5.

Therefore, IQR = Q3 - Q1 = 22.5 - 16.5 = 6.

Contrary to the mistaken calculation of IQR as 9 - 2 = 7 provided in the reference, the computed IQR for this data set, following the correct methodology, is 6.

There are 5 days to a school week: Monday, Tuesday, Wednesday, Thursday and Friday.

Divide number of school days by 5 to find the number of weeks:

171 / 5 = 34.2 weeks.

The weeks start with Monday, so there would be 35 Mondays. ( 34 full weeks and the partial week would begin with a Monday)

Divide 171 by 7 (as there are 7 days in each week), obtaining 24.4.  There's one Monday in every 7 days, so in 168 days there'd be exactly 24 Mondays, and in 171 days there'd still be exactly 24 Mondays, with 3 days left over.

Assuming one electrician-day is the same as another, the total job is ...

... (18 electricians)×(35 days) = 630 electrician·days

When that work is split among 28 electricians, it can be expected to take ...

... (630 electrician·days)/(28 electricians) = 22.5 days

Every 3 feet is $18. 18 divided by 3 equals 6.

24 divided by 6 equals 4. (So the second one is correct)

30 divided by 6 is 5, so the answer is not 30. it'd be 36.

48 divided by 6 is 8, so it is not 7.

72 divided by 6 is 12. But 6 multiplied by 9 equals 52. So, your answer is 52.

Hoped this helped,

-Anime

(1) QS bisecting <PQR implies <PQS = <SQR

(2) <PQS=45 deg and (1) imply <SQR also = 45 deg

(3) from (2) it follows that <PQR = <PQS + <SQR = 45 + 45 deg = 90 deg and therefore the triangle is right-angled