Answer:
scalene
Step-by-step explanation:
We know it isn't a right triangle because it doesn't satisfy the Pythagorean Theorem (9² + 16² ≠ 17²). Because the lengths of the sides are all different, it can't be an equilateral (all equal sides) or an isosceles (2 equal sides) either. Therefore, it is a scalene triangle (all 3 sides different). Hope this helps!
Assume y varies directly as x.
If y = 7 when x = 3, find x when y = 21.
Answer:
X=9
Solution is in the picture above.
What is the range of possible sizes for side x?
8.8
Answer:
The size of side x can range from 0.5 < x < 16.5.
The size of side x cannot take on values 0 and 16.5, but it ranges between those two values for side x to complete a triangle with those two other sides.
Step-by-step explanation:
Complete Question
What is the range of possible sizes for side x? One Side is 8.5 the other is 8.0.
Solution
With the logical assumption that the three sides are to form a triangle
Let the two sides given be y and z
And the angle between y and z be θ
The angle θ can take on values from 0° to 180° without reaching either values.
As θ approaches 0°, (x+z) becomes close to equaling y. (x + z) < y
It can never equal y, because θ can never be equal to 0°, if a triangle is to exist.
Hence, x > (z−y)
x > 8.5 - 8.0
x > 0.5
As θ approaches 180°, x approaches the sum y+z, θ can never equal 180° if a triangle is to exist, so x never equals (y+z).
Hence x < (y+z)
x < 8 + 8.5
x < 16.5
Hope this Helps!!!
Given a right triangle with leg a = 6 and hypotenuse c = 10. Find the three heights, the three medians, the three bisectors, and the radii of the inscribed and circumscribed circles.
Answer:
The three heights are 4.8, 6, 8The three medians are 5, 2√13, √73The three angle bisectors are (24/7)√2, 3√5, (8/3)√10The radii of the incircle and circumcircle are 2 and 5, respectivelyStep-by-step explanation:
a) The other leg of the right triangle is ...
b = √(10² -6²) = √64 = 8
The area of the triangle is ...
A = 1/2bh = 1/2(6)(8) = 24
Then the height to the long side is ...
h = 2A/c = 48/10 = 4.8
The three heights are 4.8, 6, 8.
__
b) The medians to the hypotenuse is half its length, because that is also the radius of the circumcircle: 10/2 = 5.
The medians to the legs are computed from the Pythagorean theorem:
median to "b" = √(4² +6²) = √52 = 2√13
median to "a" = √(3² +8²) = √73
The three medians are 5, 2√13, √73.
__
c) The angle bisectors to the legs can be found in a fashion similar to the medians, using the angle bisector theorem to locate the point of intersection on the leg.
The angle bisector to "b" divides it into segments in the ratio 6:10, so the point of intersection is 6/(6+10)×8 = 3 units from the right angle. Then its length is ...
bisector to "b" = √(6² +3²) = √45 = 3√5
The angle bisector to "a" divides it into segments in the ratio 8:10, so the point of intersection is 8/(8+10)×6 = 8/3 units from the right angle. Then its length is ...
bisector to "a" = √(8² +(8/3)²) = (8/3)√10
I find it easier to compute the bisector to the hypotenuse by considering the hypotenuse to be a line with x- and y-intercepts at 8 and 6. Then its equation can be 3x+4y=24, and its intersection with the line y=x will be x = y = 24/7. The length of the segment to that point is ...
bisector to "c" = (24/7)√2
The three angle bisectors are (24/7)√2, 3√5, (8/3)√10.
__
d) The radius of the inscribed circle can be found from the formula ...
r = √((s-a)(s-b)(s-c)/s) . . . . where s is the semiperimeter = 24/2 = 12
r = √(2×4×6/12) = 2
The hypotenuse is the diameter of the circumscribed circle, so the radius of that circle is c/2 = 5.
The radii of the incircle and circumcircle are 2 and 5, respectively.
What is the y-coordinate of the point that divides the directed
line segment from J to K into a ratio of 2:3?
K(8,11)
J(-3,1)
*7
*-6
*5
*-5
Answer:
(D)5
Step-by-step explanation:
Given the point J(-3,1) and K(8,11).
The line segment that divides the segment from J to K in any given ratio can be determined using the formula.
[tex]P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n} ,\dfrac{my_2+ny_1}{m+n}\right)[/tex]
In the given case:
[tex](x_1,y_1)=(-3,1), (x_2,y_2)=(8,11)[/tex], m:n=2:3
Since we are to determine the y-coordinate of the point that divides JK into a ratio of 2:3, we have:
[tex]\dfrac{my_2+ny_1}{m+n}=\dfrac{2*11+3*1}{3+2}\\\\=\dfrac{22+3}{5}\\\\=\dfrac{25}{5}\\\\=5[/tex]
The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3 is 5.
The correct option is D.
Answer:
The answer is actually C(5) not D
Step-by-step explanation:
What is the value of 7 in number 3,407,215
Answer:
7=7000
Step-by-step explanation:
To determine what the digit 7 means in 3,407,215, if we put 3,407,215 into the place value chart, we can see that the 7 appears in the units column of the thousands period.
So the digit 7 in this number means 7 thousands.
Image below.
8. Simplify the rational expression.
3x-27
3x + 3
Answer:
below
Step-by-step explanation:
3(x-9)
3(x+1)
divide by a gcf and place it outside the parenthesis.
find the area of this parallelogram
Answer:
Area of this parallelogram A = base x height = 11 x 6 = 66 (cm2)
Hope this helps!
:)
In Hocking County, the population is 28,547 people of which 11,504 are obese. What percentage of Hocking County residents are obese? Round percentage to one decimal place.
Answer:
hi there
40.3
Step-by-step explanation:
28547=100%
11504=R
11504 x 100=1150400/28504
1150400/28504=40.29 = 40.3
11504/28547 = 0.40x 100 = 40 %
Factor 24 j − 16 24j−1624, j, minus, 16 to identify the equivalent expressions.
Answer:
8(3j-2)
Step-by-step explanation:
Given the expression: 24j−16
We are required to factor the expression.
The GCD of 24 and 16 is 8. We therefore divide both terms of the expression by 8.
[tex]8(\dfrac{24j}{8}-\dfrac{16}{8})\\\\=8(3j-2)[/tex]
An equivalent expression therefore is: 8(3j-2)
Find m∠TUL.
m∠TUV = 167°
m∠TUL = (x + 11)°
m∠LUV = (11x)°
A) 18°
B) 20°
C) 22°
D) 24°
Step-by-step explanation:
Actual graph for this problem is attached below
m∠TUV = 167°
m∠TUL = (x + 11)°
m∠LUV = (11x)°
m∠TUV= m∠TUL+ m∠LUV
now plug in the angles for each
m∠TUV= m∠TUL+ m∠LUV
[tex]167= x+11 +11x[/tex]
solve the equation for x
[tex]167= x+11 +11x\\167=11 +12x[/tex]
Subtract 11 from both sides
[tex]156=12x[/tex]
divide both sides by 12
x=13
m∠TUL = (x + 11)°
m∠TUL = (13+ 11)° = (24)°
answer:
24°
Sporting Equipment, Inc. makes two types of balls: Soccer balls and Cork balls. The making of each soccer ball and cork ball requires 3 hours and 4 hours of production time, respectively. For the next month, the total production hours of 500 are available. Also, the combined production quantity for these two balls must be at least 150 units. The objective for this linear programming model is to fulfil the given production requirements at a minimum cost. The production cost for each Soccer ball is S7 and each Cork ball is $9.
1. Formulate the problem, using the following decision variables:
S = number of Soccer balls manufactured
C = number of Cork balls manufactured
2. The objective function is:
A. Maximize 9S + 7C
B. Minimize 7S + 9C
C. Minimize 9S + 7C
D. Maximize 7S + 9C
3. The constraint equation for the production hours is:
A. 3S + 4C >= 500
B. 4S + 3C <= 500
C. 4S + 3C <= 500
D. 3S + 4C <= 500
4. The constraint equation for the combined production quantity is:
A. S + C <= 150
B. S + C >= 150
C. S + C = 150
D. S + C =/150
5. If the company produces 100 soccer balls and 50 cork balls, the cost of production is:
a. $1250 b. $1350 c. $1150 d. $2000
Answer:
2) B). Minimize 7S + 9C
3) D) . 3S + 4C ≤ 500
4) B). S + C ≥ 150
5) C) $1150
Step-by-step explanation:
The company makes two types of balls, the balls and their costs are written below:
Soccer ball, S = $7
Cork ball, C = $9
Production time of each ball:
Soccer ball = 3 hours
Cork balls = 4 hours
2) To find the objective function.
Since the cost of each soccer ball is $7 and S balls are produced, the total cost of soccer balls is 7S.
Similarly, the cost of each cork ball is $9 and C balls are produced, total cost is 9C.
The objective function maximize profits and minimizes losses. Here, the objective for this linear programming model is to fulfil the given production requirements at a minimum cost.
Therefore the objective function here is: Minimize 7S+9C
3)The constraint equation for the production hours.
To produce one soccer ball, 3 hours are needed, i.e 3S, to produce one Cork ball 4 hours are needed, i.e 4C.
Since we are given a maximum productin time of 500 hours, the constraint equation for the production hours would be:
3S + 4C ≤ 500
4) Since we are told the combined production quantity for these two balls must be at least 150 units, the constraint equation for the combined production quantity is:
S + C ≥ 150
5)Since each soccer ball costs $7, 100 soccer balls would cost:
7*100 = $700
Similarly, since each Cork ball costs $9, 50 cork balls would cost:
9*50 = $450
Therefore the total cost of production would be:
$700 + $450 = $1,150
Note: Question number 1 isn't a question, it's an expression.
What is the circumferance of a sphere
Answer:
Circumference of a sphere = 6.2857 (R)
Step-by-step explanation:
Circumference of a sphere is approximately 2[tex]\pi[/tex] times of the given radius.
Assume:
Radius of the sphere (r) = R
Find:
Circumference of a sphere = ?
Computation:
⇒ Circumference of a sphere = 2[tex]\pi[/tex]r
⇒ Circumference of a sphere = 2 × [tex]\frac{22}{7}[/tex] × R
⇒ Circumference of a sphere = 2 × 3.1428 × R
⇒ Circumference of a sphere = 6.2857 (R)
there were 632 animals gathered at the river. a herd of 187 elephants and 266 zebras left the river area. how many animals were still at the river?
Answer: There was a total of 173 animals left by the river
Step-by-step explanation:187+266 = 453
You subtract 453 from the total number of animals which is 632
632-453 = 179
A bag contains 6 green chips, 8 red chips, and 3 blue chips. If you draw two chips without replacement, what is the probability that both chips are the same color?
Answer:
2/17
Step-by-step explanation:
you add up all the chips and then the two chips =2
6+8+3=17
so 2/17
in the coordinate plane, ABCD has vertices with coordinates A(1,-1), B(-5,3), C(-3,6),
and D(3,2)
Answer:
C
Step-by-step explanation:
Which Function is shown in the Graph?
Answer:
A is the correct answer
Step-by-step explanation:
Hope i helped :)
A greenhouse contained both 6-inch high geraniums and 3 inch high geraniums. The 6-inch high geraniums were taken out of the greenhouse in early spring and grew at a rate of 1 inch per week. The 3 inch high geraniums remained in the greenhouse and grew at a rate of 1 (1/2) inches per week. After the 6-inch high geraniums were taken outside, in how many weeks were both groups of geraniums the same height.
Answer:
6 weeks
Step-by-step explanation:
Let the number of weeks be x.
Then we have an equation:
6 + 1*x = 3 + 1 1/2 x6 + x = 3 + 1.5x1.5x - x = 6 - 30.5x = 3x = 3/0.5x = 6 weeksSo after 6 weeks both 6-inch and 3-inch geraniums will have same height
PLZ HELP ME
The graph shows the solution to which system of inequalities?
A) y < -2x + 4 and y < 2x + 4
B) y < -2x + 4 and y ≤ 2x + 4
C) y > -2x + 4 and y ≤ 2x + 4
D) y ≤ -2x + 4 and y ≤ 2x + 4
Answer:
see below
Step-by-step explanation:
The shading is below the line in both cases. The dashed line has negative slope, so the inequality associated with it is ...
y < -2x +4 . . . . . . note that the < symbol has no "or equal to"
The solid line has positive slope, so its inequality is ...
y ≤ 2x +4
Both these inequalities are found in choice B.
Suppose that the function f(x)=2x + 6 Represents the number of cars to drive by an ex minutes how many cars will drive by in 4 minutes
Answer:
14
Step-by-step explanation:
Put 4 where x is in the function and do the arithmetic.
f(4) = 2(4) +6 = 8+6 = 14
14 cars will drive by in 4 minutes.
4x-k=17 solve for x
Answer:
k = -17 + 4x
Step-by-step explanation:
Simplifying
4x + -1k = 17
Reorder the terms:
-1k + 4x = 17
Solving
-1k + 4x = 17
Solving for variable 'k'.
Move all terms containing k to the left, all other terms to the right.
Add '-4x' to each side of the equation.
-1k + 4x + -4x = 17 + -4x
Combine like terms: 4x + -4x = 0
-1k + 0 = 17 + -4x
-1k = 17 + -4x
Divide each side by '-1'.
k = -17 + 4x
Seaside Bike Shop rents bikes for $10 plus $4 per hour. Jack paid $30 to rent a bike. Which equation, when solved for x, gives the number of hours he rented the bike?
You don’t list the options but you need to multiply the hourly rate by the number of hours (x) and add that to the few to find the total so the equation would be:
Total = 4x +10
You are told the total was $30 so you can solve for x:
30 =3x + 10
Subtract 10 from both sides:
20 = 4x
Divide both sides by 4:
X = 5 hours
What is the average?
3 4 5 8
Answer: 5
Step-by-step explanation:
3+4+5+8 = 20/4 = 5
Your round trip drive to school is 3 7/10 miles.how many miles do you drive to and from school in 5 days?
Answer:
18 1/2 miles
Step-by-step explanation:
3 7/10 * 5
Change to an improper fraction
(10* 3 + 7)/10 * 5
37/10 *5
Rewriting
37 * 5/10
37/2
Changing back to an mixed number
2 goes into 37 18 times with 1 left over
18 1/2
r = the number of racks
s = the number of shoes
Which of the variables is independent and which is dependent?
Answer:
number of shoes is independent, number of racks is dependent
Step-by-step explanation:
the number of racks does not affect the number of shoes but if there are a lot of shoes, the number of racks will increase.
Last week, Maria bought k pounds of cherries at the regular price of $2.75 per pound. This week, cherries were on sale for 20 percent off, and maria bought twice as many pounds as she bought last week, which of the following is the total in dollar, Maria paid for the cherries last week and this week
Answer:
$7.15k
Step-by-step explanation:
So the first week, she used $2.75k
Then, you can calculate the amount for one pound the next week by doing 0.8 * 2.75 = 2.2
So the second week she used 2 * 2.2 * k = $4.4k
$4.4k + $2.75k = $7.15k
Might be wrong so check it.
Caitlin ran 1,680 feet on monday and 2,340 feet on Tuesday how many yards did she run in those two days
Answer:
4020
Step-by-step explanation:
Mr. Toshiro manages a company that supplies a variety of domestic and imported nuts to supermarkets. He received an order for 120 bags of cashews, 310 bags of walnuts, and 60 bags of Brazil nuts. The prices per bag for each type are $29, $18, and $21, respectively. Represent the number of bags ordered and the cost as vectors.
Answer:
n = 120i + 310j + 60k
p = 29i + 18j + 21 k
Total cost = $10,320
Step-by-step explanation:
Let n and p represent the vectors for number of products and prices respectively.
Also, the coordinates i,j and k represent cashews, walnut and Brazil nut respectively.
The vector form of the total number of bags ordered and the cost are;
n = 120i + 310j + 60k
p = 29i + 18j + 21 k
We can obtain the total cost by obtaining the dot product of the two vectors.
Total cost = n.p = (120i + 310j + 60k).(29i + 18j + 21 k)
C = 120×29 + 310×18 + 60×21
C = $10,320
Enter numbers in the blanks to complete the sentences.
Answer:
For The First Line the answer is 0
For the second line the answer is 0,0
Step-by-step explanation:
I put the picture :)
Enter numbers in the blanks to complete the sentences.
For equations in the form y=kx, if x=0, then y= 0
So the point, 0 then the other box is 0 must be on the graph of every equation in the form y=kx.
I got this correct if this doesn't help I also put the picture that I got it correct :)
Maria, an experienced shipping clerk, can fill a certain order in 9 hours. Jim, a new clerk, needs 11 hours to do the same job. Working together, how long will it take them to fill the order
Answer:
4 19/20 hours or 4 hours , 57 minutes
Step-by-step explanation:
Given
In 9 hours Maria can fill a certain order let Say X
In 9/9 hours Maria can fill X/9 of the order
in 1 hour Maria can fill X/9 of the order
__________________________________
In 11 hours Jim can fill a certain order let Say X
In 11/11 hours Maria can fill X/11 of the order
in 1 hour Maria can fill X/11 of the order
_____________________________________________
Therefore total order filled by them in one hour will sum of individual work done by them in one hour.
Mathematically,
total order filled by Jim and maria in one hour = work done by Jim in one + work done by Maria in one hour
total order filled by Jim and maria in one hour = 1/11 + 1/9
=> [tex]1/11 + 1/9 \\=> (9 + 11)/11*9\\=> 20/99[/tex]
=>20/99 of certain order is filled by both of them in one hour.
=>Total order is one. Hence, to get 1 from 20/99 we need to multiply it with its reciprocal (i.e 99/20) as 20/99 *99/20 = 1
now
=>20/99 of certain order is filled by both of them in 1 hour.
=>multiplying both order and hour with 99/20 we have
20/99 *99/20 of certain order is filled by both of them in 1* 99/20 hour
Thus total order is filled by them in 99/20 hours = 4 19/20 hours.
1 hour has 60 minutes
so 19/20 has 60*19/20 minutes = 57 minutes.
Working together, Jim and Maria will take 4 hours , 57 minutes to fill the order.
Round 43.597 to nearest hundred