19. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is (a) 20 (b) 23 (c) 169 (d) None of these
Answer:
B
Step-by-step explanation:
Let the two numbers be a and b.
The product of the two is 120 and their sum of their squares is 289. In other words:
[tex]\displaystyle ab = 120 \text{ and } a^2 + b^2 = 289[/tex]
And we want to find the sum of the two numbers.
We can use the perfect square trinomial. Recall that:
[tex]a^2 + 2ab + b^2 = (a+b)^2[/tex]
From the first equation, multiply by two:
[tex]2ab = 240[/tex]
Add the two equations together:
[tex](a^2+b^2)+(2ab) = (289)+(240)[/tex]
Simplify and rewrite:
[tex]a^2+2ab+b^2 = 529[/tex]
Factor using the perfect square trinomial pattern:
[tex](a+b)^2 = 529[/tex]
And take the square root of both sides:
[tex]\displaystyle a + b = \pm\sqrt{529} = \pm23[/tex]
Hence, the sum of the two numbers is 23 or -23.
In conclusion, our answer is B.
A lawn in the shape of a trapezoid has an area of 1,800 square meters. The length of one base is 50 meters, and the length of the other base is 40 meters. What is the width of the lawn?
The vertical side of a right triangle measures 6 inches, and the horizontal side measures 8 inches
1.Write the ratio of the distance of the vertical side to the distance of the horizontal side as a reduced fraction
2.If the original triangle were enlarged by 3 times, what would the new dimensions be?
3.Does the ratio of vertical side to horizontal side change when scaling up? Explain.
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Answer:
3/4vertical: 18 in; horizontal: 24 inno changeStep-by-step explanation:
1. The ratio is ...
(6 in)/(8 in) = 6/8 = 3/4
__
2. The scaled dimensions are ...
6 in × 3 = 18 in (vertical side)
8 in × 3 = 24 in (horizontal side)
__
3. You know from your process of reducing the fraction in part 1 that multiplying numerator and denominator by the same value does not change the reduced ratio.
can anyone help me out with this one?
if x = 5, y = 6, and z= 2, is V x2 + y2 + z2 + 50
rational or irrational? Explain.
Answer:
irrational
Step-by-step explanation:
because
5² + 6² + 2² + 50 = 25+36+4+50 = 115
and 115 is not a squared integer or rational number, so that sqrt(115) is one of these numbers with infinite digits after the decimal point but without any repeating pattern.
and that is per definition irrational.
Select all of the answers that are elements of M = {x | x is a month of the year}
Step-by-step explanation:
M={January, February, March, April, May, June, July, August, September, October, November, December}
When solving secθ=−4.2 for 180°≤θ≤360°, how many possible answers are there?
0
1
2
unable to determine
Please help me with number 1 please help ???
Answer:
mean: 26
median: 28
mode: 28
range:19
Step-by-step explanation:
hipe this helped hun
Brandy makes $102 for a eight hour shift at a weekend job how much will he get paid for 30 hours
Answer:
Brandy would be payed $450 for 30 hours
Step-by-step explanation:
102÷8= 15
15×8= 102
15 dollars is what he makes hourly
30 hours× 15= 450
I don’t understand this I don’t know if I’m supposed to draw or what ?
A man drove 13 miles directly east from his home, made a left turn at an intersection, and then traveled 9 miles due north to his place of work. If the road was made as described above, how much shorter would the man’s one-way trip be every day?
Answer:
ANSWER 5.3 miles
See IMAGE FOR SOLUTION
Miguel reads that the average low temperature today is −4.2°F and that the average high temperature is 9.1º F.
Miguel plots the points on the number line to determine the temperature change between these two readings.
What is the temperature change?
° F
Answer: 13.3
Step-by-step explanation:
took on k12 :]
The change in today's temperature between the two readings as measured by Miguel is 13.3°F
Miguel's temperature readings :
Average low temperature = -4.2°F
Avetage high temperature = 9.1°F
The change in temperature is the difference between the two temperature readings :
Average high temperature - Average low temperature
(9.1 - (-4.2))°F
(9.1 + 4.2)°F = 13.3°F
Hence, the change in temperature reading = 13.3°F
Learn more : https://brainly.com/question/2610134
Halo
please help me
Answers with Solution, ok?
The correct answer is letter C. 75. 36m³ :)
Here's the Solution:
V = π r²hV = (3.14) (2m)² (6m)V = (3.14) (4m²) (6m)V = (3.14) (24m³)V = 75.36m³HOPE THIS HELPS. GOODLUCK:)
Which would you measure using inches?
height of a flagpole
length of a driveway
length of a cross-country race course
length of a pen
Answer:
Length of a pen
Step-by-step explanation:
Because it is comparatively smallest than other,
and we use inches method to measure smaller length.
Find the surface area of a cylinder with a base radius of 2 in and a height of 5 in
Answer:
[tex]r = 2 \\ h = 5 \\ a = 2\pi \: rh + 2\pi {r}^{2} \\ = 2\pi \times 2 \times 5 + 2\pi {2}^{2} \\ = 20\pi + 8\pi \\ = 28\pi \\ = 28 \times 3.14 \\ = 87.92 {unit}^{2} \\ thank \: you[/tex]
In the Tigers Football Club, there are 9 players to each coach, while in the Eagles Football Club, there are 17 players to every 2 coaches. If the total number of players and coaches in the two clubs is 232, how many players and coaches are in each club?
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Answer:
Tigers: 8 coaches, 72 playersEagles: 16 coaches, 136 playersStep-by-step explanation:
We can define a "basic unit" of each team to be the minimum number of players and coaches that can have the given ratio. For the Tigers, that is 1 coach and 9 players, for a total of 10 team members. For the Eagles, that is 2 coaches and 17 players, for a total of 19 team members. If we have t basic units of Tigers and e basic units of Eagles, then we want ...
10t +19e = 232 . . . . . the total of players and coaches in the two clubs
We want t and e to be integers, so this is a Diophantine equation. It can be solved any of several ways, including use of the Extended Euclidean Algorithm. Here, we'll make some observations based on "number sense."
The value of e must be an even number between 0 and 232/19 = 12. The product of e and 19 must be a number that ends in 2, because 10t will end in 0, and the sum with 19e must end in 2.
The only multiple of 9 that ends in 2 is 9×8 = 72, so the value of e must be a positive number less than 12 that ends in 8. We must have e=8.
Then t=(232 -8×19)/10 = 8. This tells us there are 8 "basic units" of each team.
The Tigers have 8 coaches and 72 players.
The Eagles have 16 coaches and 136 players.
All equilateral triangles are congruent. State whether the statement is true or false
True
False
Answer:
TRUE
If a triangle has three congruent angles, it is be equiangular. Since congruent angles have congruent sides opposite them, all sides in an equiangular triangle will also be congruent. Therefore, every equiangular triangle is also equilateral
FIRST -CORRECT- ANSWER WILL GET BRAINLIEST!!
Find u.
A. 2√2
B. 2
C. 4
D. √2
Answer:
u=2 root 2
Step-by-step explanation:
All 45 45 90 degree triangles follow the same pattern
5. Given the exponential function f(x) = 4(3)*, find f(0) and f(1).
O A. f(0) = 4; f(1) = 12
O B. f(0) = 4; f(1) = 36
O C. f(0) = 12; f(1) = 36
O D. f(0) = 12: f(1) = 4
Answer:
C
Step-by-step explanation:
The answer is C
9 * (-3/5) ^5
evaluate
pls help :)
Answer:
[tex] - \frac{2187}{3125} [/tex]
Step-by-step explanation:
[tex]9 \times ( \frac{ - 3}{5} )^{5} [/tex]
[tex]( \frac{ - 3}{5} {)}^{5} = \frac{( - 3 {)}^{5} }{ {5}^{5} } [/tex]
[tex] \frac{ - 243}{ {5}^{5} } = - \frac{ 243}{3125} [/tex]
[tex] - 9 \times ( - \frac{243}{3125} )[/tex]
[tex] = - \frac{2187}{3125} [/tex]
Express the relation(3, 5), (4, 6), (3, 8), (2, 4), (1, 3), as a mapping. Then determine the domain and range
Answer:
y
Step-by-step explanation:
Help please hurry I don’t have much time!!!
Answer:
The correct answer is D
Take D
Help please asap first answer get brainliest
Beging you please
Answers:
12. 2 3/5+1 4/6 = (2+1)+(3/5+4/6) = 3+19/15 = 64/15
13. 2/4*4/6 = 8/24 = 1/3
14. 3/4*3/6 = 9/24 = 3/8
15. 2/6*4/6 = 8/36 = 2/9
16. 2/4*1/6 = 2/24 = 1/12
17. 3/4/1/6 = 18/4 = 9/2
18. 3/4/2/4 = 12/8 = 3/2
19. 3/6/4/6 = 18/24 = 3/4
20. 5/7+2/7 = 7/7 = 1
21. 4/5+5/7 = 53/35
22. 3/5+5/5 = 8/5
23. 1/6-1/6 = 0
24. 3/7-2/3 = -5/21
25. 3/5-2/7 = 11/35
Math is?
At least 5 sentences
Answer:
1.The subject which we learn calculation multiplies devide substation etc.
2.Math is a kind of subject which we can practice more from this subject.
3.Math is an example of life process because if we are talent in math then we can solve the many kaild of problem related in our life..
4.Math also help as to increase our bran pour of we try to solve hard to hard problem..
Think you at last math is importent to as
1. In order to complete the square on x^2 – 3x, you would…?
Answer:
(x-1.5)^2 -2.25
Step-by-step explanation:
divide 3 by 2 which is 1.5
(x-1.5)^2 -2.25
help me do this please!
Answer:
m<ABD = 37°
m<DBC = 58°
Step-by-step explanation:
m<ABD + m<DBC = m<ABC
2x + 23 + 9x — 5 = 95
11x + 18 = 95
-18 -18
--------------------
11x = 77
/11 /11
---------------------
x = 7
Now, plug this into the equation for m<ABD and m<DBC to find their values.
m<ABD = 2x + 23
= 2(7) + 23
= 14 + 23
= 37
m<DBC = 9x — 5
= 9(7) — 5
= 63 – 5
= 58
Now, check to see if our values are right or not.
2x + 23 + 9x — 5 = 95
2(7) + 23 + 9(7) — 5 = 95
14 + 23 + 63 – 5 = 95
100 – 5 = 95
95 = 95 CORRECT
Chris rented a truck for one day. There was a base fee of $19.95, and there was an additional charge of 85 cents for each mile driven. Chris had to pay $183.15
when he returned the truck. For how many miles did he drive the truck?
Answer:
he drove 192 miles
Step-by-step explanation:
why bc I did 0.85 x 192= 183.15
so that makes 192 the miles Chris drove
union and intersection of sets
Answer:
The union of two sets contains all the elements contained in either set (or both sets). The union is notated A ⋃ B. The intersection of two sets contains only the elements that are in both sets. The intersection is notated A ⋂ B.
Answer:
UnionThe union of a set A with a B is the set of elements that are in either set A or B. The union is denoted as A∪B. For example, if A is the set {♢,♡,♣,♠} and B is the set {△,♡,♠}, then A∪B={♢,♡,♣,♠,△}.
IntersectionIntersection of two given sets is the largest set which contains all the elements that are common to both the sets. To find the intersection of two given sets A and B is a set which consists of all the elements which are common to both A and B. The symbol for denoting intersection of sets is '∩'.
(X + ____ ) ^2 = _____
Answer: 1/4 first box 33/16 second box
Step-by-step explanation:
look at pictures for AnSwEr
2 A car transporter can carry 13 cars. How many transporters are needed for 340 cars?
Answer:
27 car transporter
Step-by-step explanation:
Number of cars a car transporter can carry= 13
Number of cars there=340
number of transporters needed= 340÷13
= 27