Traveling at an average rate of between 40 and 50 miles per hour for 3 to 4 hours, select the best estimate for the distance traveled.

The width of the rectangle is: 33m, by Pythagoras theorem.

Now,

given:

TO find: Width of rectangle = ? (say, w)

Finding:

BY Pythagoras theorem, in the rectangle ABCD,

For l = AB, w = BC and d = AC,

=> l² + w² = d²

Ob substituting the values, we get: 56² + w² = 65²

=> w² = 65² - 56²

=> w² = 4225 - 3136

=> w² = 1089

=> w = 33m

Hence, for the given values of rectangle, the width of the rectangle is 33m by Pythagoras Theorem.

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Answer:

3,490,000

Step-by-step explanation:

3,487,967 = (87967) The 7 rounds up so the 8 would become 9.

Answer:

Step-by-step explanation:

Answer:(3,2)

Step-by-step explanation:

The value of the height of the right prism is given by the formula, h = (SA - 2B) / P. It is gained by using the surface area of the right prism.

What is the right prism?

A right prism is a three-dimensional closed figure with 6 faces, 8 corners and 12 edges. It is called a right prism because, in this prism, the angle between the base and the sides is 90 degrees. All the faces of a right prism are rectangular, hence sometimes also called a right rectangular prism.

Calculation of h for the right prism

We know the  surface area of the right prism is given by:

SA = Ph + 2B

Ph + 2B = SA

Subtracting 2B from both sides of the above equation, we have,

Ph + 2B - 2B = SA - 2B

Ph = SA - 2B

Dividing both sides of an equation by P, we get,

(Ph) / P = (SA - 2B) / P

h = (SA - 2B) / P

Hence, the value of h can be found using the formula, h = (SA - 2B) / P

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a. Length of AB = 7 units

Length of CDS = 3 units

Line segment AB and line segment CD are not congruent.

b. Length of AB = 7 units

Length of CD = 7 units

Line segment AB and line segment CD are congruent.

c. Length of AB = 9 units

Length of CD = 7 units

Line segment AB and line segment CD are not congruent.

Given two points on a coordinate plane, where the two points are on a horizontal or vertical line, the distance between the two points is the absolute difference between their coordinates.

a. Given:

A(10, -4)

B(3, -4)

C(-1, 2)

D(-1, 5)

Length of AB = |10 - 3| = |7|

Length of AB = 7 units

Length of CD = |5 - 2| = |3|

Length of CDS = 3 units

Line segment AB and line segment CD are not congruent.

b. Given:

A(-5, 6)

B(-5, -1)

C(-4, 3)

D(3, 3)

Length of AB = |6 - (-1)| = |7|

Length of AB = 7 units

Length of CD = |-4 - 3| = |-7|

Length of CD = 7 units

Line segment AB and line segment CD are congruent.

c. Given:

A(8, 3)

B(-1, 3)

C(5, 10)

D(5, 3)

Length of AB = |8 - (-1)| = |9|

Length of AB = 9 units

Length of CD = |10 - 3| = |7|

Length of CD = 7 units

Line segment AB and line segment CD are not congruent.

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Answer:

The correct answer should be P(1, 7)

They will save $100 if they purchase together rather than separately.

If this week, the store is offering one free window for each purchase of 4, then the price of 5 windows will be just equal to the price of 4.

1 window = $100

5 windows = 4 x $100 = $400

If

Dave needs 7 windows  

Doug needs 8 windows

total they need together = 7+8 = 15 windows.

Buying at the offer of $400/5 windows,

they should buy 3 sets of 5 windows.

3 x 5 = 15

cost when bought together : 3 x $400

cost when bought together : $1200

If they bought separately,

Dave : 7 = 5 + 2

cost = $400 + 2($100)

cost = $600

Doug : 8 = 5 + 3

cost = $400 + 3($100)

cost = $700

cost when bought separately : $600 + $700

cost when bought separately : $1300

compare the two total costs and to determine how much they will save.

$1300 - $1200 = $100

They will save $100 if they purchase together rather than separately.

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The sum of 17 and 3 times x is given by the algebraic expression "17+3x" .

A mathematical construct called an algebraic expression is made up of integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by a rational exponent).

Let us take an expression 4x³+6xy+9 is an algebraic expression. Where

x,y are variables 4 and 6 are co-efficients and 9 is the constant .

In the above statement it is given that the sum of 17 and times x. Here x is a variable.

3 times x equates to 3x and when 17 is added we get the expression 17+3x.

Hence the required algebraic expression is 17+3x

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Answer: Liam is 17

Step-by-step explanation: 17-14= 3. 17 + 14 = 31

The shipment contained 12 tablets and 36 laptops.

An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.

Let x represent the number of tablets and y represent the laptop.

Each tablet cost $375 and each laptop cost $850, hence:

375x + 850y = 35100  (1)

Also:

y = 3x   (2)

From both equations:

x = 12, y = 36

The shipment contained 12 tablets and 36 laptops.

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The highest percentage of teenagers in the sample listed soccer as their favorite sport. this option is correct .

What does a statistical pie chart mean?

In this question pie chart is showing data of games .

So. by observing the chart we can say that ,

the highest percentage of teenagers in the sample listed soccer as their favorite sport.

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The percentage of those who were married were also obese is: 34.7% (147/424; Option B)

Now,

The percentage of number of married participants who were obese is calculated by: dividing the former (147) by the total number of married participants(424)

=> Percentage of married participants who were obese = 147/424.

Hence, The percentage of those who were married were also obese is: 34.7% (147/424; Option B)

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(COMPLETE QUESTION:

A 2009 study analyzed data from the National Longitudinal Study of Adolescent Health. Participants were followed into adulthood. Each study participant was categorized as to whether they were obese (BMI >30) or not and whether they were dating, cohabiting, or married. The table below summarizes the results.

Dating Cohabiting Married Total

Obese 81 103 147 331

Not Obese 359 326 277 962

Total 440 429 424 1293

What percentage of those who were married were obese? (Round your answer to 1 decimal place.)

A. 32.8% (424/1293)

B. 34.7% (147/424)

C. 25.6% (331/1293)

D. 44.4% (147/331))

1. A line segment can be written with just naming it by its end points and a bar above it while the name of a line requires an double-headed arrow mark above its name.

2. For constructing both a perpendicular and an angle bisector, we need to construct two arcs using a compass and their intersection point. A perpendicular bisector divided a line segment into two equal parts whereas an angle bisector divides an angle into two equal parts.

3. A perpendicular bisector can be drawn by drawing two arcs each above and below the line segment and joining using an straight edge.

1. A line and a line segment may sound quite similar however they are very different. A line, in short, is a line that never ends so it's infinite. It's the same for a line segment except at its end it is indicated by dots rather than arrows.

This difference can be seen in naming them too. A line segment is named using the initial and terminal points of the segment. Sometimes we put a 'bar' mark above its name. For example, [tex]\bar{AB}[/tex]

For a line of infinite length, it is named simply as 'line A' or 'line B' or sometimes put a double-headed arrow mark above its name.

2. A perpendicular bisector and an angle bisector are similar because they both require the need to find where two arcs meet. They are different because angle bisectors split into congruent angles meanwhile a perpendicular bisector splits into congruent segments.

Constructing a perpendicular bisector is similar in the sense that both are drawn using straight edge and compass and need to find the intersection point of the arcs. But they are different in their use as perpendicular bisector equally divides a line segment and an angle bisector equally divides an angle.

3. We have an unmarked straightedge and a compass. First put the compass at one end point A of the line. Then stretch the compass to a length more than half of the line segment AB to be bisected. In the next step, draw an arc above and one below the line. Next put the compass on the other end B of the line. Then repeat drawing two arcs, each above and below the line and also intersecting with the previous arcs. Finally join the two points got with a line cutting the line segment AB. This will be the perpendicular bisector of the line AB.

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Solution:

[tex]3(2x+3)[/tex]

Hope this helps!

============================================================

Explanation:

12 = 3*4

15 = 3*5

The GCF of 12 and 15 is 3

LCM of x and y = (x*y)/(GCF of x and y)

LCM of 12 and 15 = (12*15)/(GCF of 12 and 15)

LCM of 12 and 15 = (12*15)/(3)

LCM of 12 and 15 = 60

-------------------

We can confirm this by listing out the multiples of each

multiples of 12 are: 12, 24, 36, 48, 60, 72, ...

multiples of 15 are: 15, 30, 45, 60, 75, ...

-------------------

Since the LCM is 60, this means their schedules line up every 60 minutes, aka 1 hour.

If they arrive together at 9 AM, then their next arrival time together is 10 AM which is the final answer.

Answer:

3.35kg

Step-by-step explanation:

Answer:

Multiply (5,000,000 x 6.7 x 10^-7) = (5 x 10^6) x (6.7 x 10^-7) = (5 x 6.7) x (10^(6 + - 7)) = 33.5 x 10^-1 = 3.35 kg

Step-by-step explanation:

The coordinates of the point B are (-5, 6)

The given parameters are

A = (-8, 6)

Point = (2, 6)

Proportion = 2/3

Because the y coordinates are the same, we can make use of only the x coordinate

So, we have

Point = Proportion * (B - A)

This gives

2 = 2/3 * (B + 8)

Multiply through by 3/2

So, we have

3 = B + 8

Subtract 8 from both sides

B = -5

Hence, the coordinates of the point B are (-5, 6)

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The sales on which Joyce earns commission is the sale beyond $20,000 which is $2,650. So the total pay for a month for Joyce in which her sales is $22,650 is $1748.75.

Joyce is paid $1,550 per month plus a commission of 7.5% on all sales of more than a $20,000 monthly quota. For the given month her sales is $22,650.

Percentage means a number or a ratio represented in the form of fractions of 100. It is represented using the percentage sign ‘%’. The abbreviations used to represent the percentage are ‘pct’ or ‘pc’. In other words, the percentage is defined as how much of one quantity is made by another quantity and it is evaluated in terms of 100.

Total pay of Joyce = Her pay per month + Commission that she gets

Commission she gets is on the sales beyond $20,000.

Here, commission is on $22,650 - $20,000 = $2,650

She gets 7.5% commission. So, her commission is 7.5% * $2,650

=> 75/1000 * $2,650 = $198.75

So, the total pay of Joyce is $1,550 + $198.75

=> $1748.75 for the month.

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The triangle with vertices located at X(-11 , 0), Y(-11 , -8), and Z(-1 , -4) has its centroid located at (-23/3 , -4).

The centroid of a triangle is the point inside the triangle where the three medians intersect. The median of a triangle is the line the connects the midpoint of a side and the opposite vertex.

To get the centroid of a triangle, use the formula given by:

C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]

where C is the centroid of the triangle located at (x , y)

x1, x2, and x3 are the x-coordinate of the vertices of the triangle

y1, y2, and y3 are the y-coordinate of the vertices of the triangle

Let Point 1(x1 , y1) = X(-11 , 0)

Point 2(x2 , y2) = Y(-11 , -8)

Point 3(x3 , y3) = Z(-1 , -4)

Plug in the values in the formula.

C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]

C(x ,y) = [(-11 + -11 + -1)/3 , (0 + -8 + -4)/3]

C(x ,y) = (-23/3 , -12/3)

C(x ,y) = (-23/3 , -4)

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Answer:

The second answer is the correct one I believe

Answer:

second one

Step-by-step explanation:

Evaluating Expressions-

z−5+ x= -7

x = 1, and z = -3

z−5+ x=-3 + (-5) + 1

          = -3-5+1=-7

to assess an algebraic expression way to find the price of the expression while the variable is changed by using a given range.

to evaluating expression, we replacement the given range for the variable within the expression and then simplify the expression the use of the order of operations

What does “Evaluating Expressions” suggest?

Simplification of expressions can be performed with the help of operations’ order. It consists of changing the variable to discover the expression’s fee. The given number is substituted to evaluate expressions. After this, one needs to simplify it primarily based at the order of the operations

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Answer: 2x2x2 or 2 cubed

Step-by-step explanation: 2x2=4 2x4=8

Answer:

0.35

Step-by-step explanation:

3/6=1/2

7/10=0.7

1/2=0.5,0.5×0.7

=0.35

Answer: 7/20

Step-by-step explanation:

3/6*7/10= 0.35

First write down the decimal number divided by 1 like this:

0.35

1

As we have 2 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by 102 = 100, so that there is no decimal point in the numerator

0.35 × 100

1 × 100

=

35

100

Since the greatest common factor of 35 and 100 is 5, we can simplify the fraction and show the same amount

35 ÷ 5

100 ÷ 5

=

7

20

Therefore, 0.35 as a fraction is 7/20

The value of 'x' in the given question is 27°.

Obtuse Angle may be defined as an angle that is greater than 90° and less than 180°. It may be also defined as an angle between a right angle and a straight-line angle.

From the question we can conclude that the given angles are vertically opposite to each other, and vertically opposite angles are always equal to each other.

Vertically opposite angles are formed when two lines are intersecting each other and the angles formed on each side of the intersection point are called vertically opposite angles.

Now according to the question:

[5(x-4)]°=(4x+7)°

Rearranging the terms:

(5x-20)°=(4x+7)°

=>x=27°

Therefore, the value of x is 27°.

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The time for the projectile to hit the ground from the given position is 1.5 s, which is obtained using the concept of time period and velocity of a projectile.

What is a projectile?

A projectile is defined as an object that has the force of gravity as the only force occurring on it. Acceleration in the projectile motion always acts vertically.

Calculation of the time taken by projectile to hit the ground

The given parameters:

The starting velocity of the projectile, u = 48 ft / s

Height of the projectile, h = 190 ft

Model of the projectile path, h(t) = - 16(t)2 + 48t + 190          —-- 1

When the projectile hits the ground, the final velocity, v = 0

differentiating equation 1 w.r.t t, we get,

(dh(t)) / (dt) = - 32t + 48

Putting dh(t) / dt = 0, we have,

- 32t + 48 = 0

32t = 48

t = 48 / 32

t = 1.5 s

Hence, the time taken by the projectile to hit the ground is 1.5 s.

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