Given:
Three integers, a, b, and c, where c is a positive integer.
The product of a and b is 6.
The product of a and c is -4.
The product of b and c is -6.
To find:
The values of a,b and c.
Solution:
According to the given information:
[tex]ab=6[/tex] ...(i)
[tex]ac=-4[/tex] ...(ii)
[tex]bc=-6[/tex] ...(iii)
From (ii), we get
[tex]a=-\dfrsc{4}{c}[/tex] ...(iv)
From (iii), we get
[tex]b=-\dfrsc{6}{c}[/tex] ...(v)
Putting [tex]a=-\dfrsc{4}{c}[/tex] and [tex]b=-\dfrsc{6}{c}[/tex] in (i), we get
[tex]\dfrac{-4}{c}\times \dfrac{-6}{c}=6[/tex]
[tex]\dfrac{24}{c^2}=6[/tex]
[tex]\dfrac{24}{6}=c^2[/tex]
[tex]4=c^2[/tex]
Taking square root on both sides, we get
[tex]\pm \sqrt{4}=c[/tex]
[tex]\pm 2=c[/tex]
It is given that c is a positive integer. So, it cannot be negative and the only value of c is [tex]c=2[/tex].
Putting [tex]c=2[/tex] in (iv), we get
[tex]a=-\dfrsc{4}{2}[/tex]
[tex]a=-2[/tex]
Putting [tex]c=2[/tex] in (v), we get
[tex]b=-\dfrsc{6}{2}[/tex]
[tex]b=-3[/tex]
Therefore, the values of a,b,c are [tex]a=-2,b=-3,c=2[/tex].
The sides of a triangle are in the extended ratio of 3 : 4:10. If the length of the
shortest side is 9 in., what is the perimeter of the triangle?
Answer:
51cm
Step-by-step explanation:
9 divided by 3 is 3inches
3 inches is 1 share
3 plus 4 plus 10 is 17
17 times 3 is 51
The length of the triangle is 9, 12, and 30. Then the perimeter of the triangle will be 51 inches.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The perimeter of the triangle is determined by adding together all of its sides.
The sides of a triangle are in the extended ratio of 3:4:10. If the length of the shortest side is 9 in.
Let x be the canceled value from the ratio. Then we have the ratio will be 3x: 4x: 10x.
The value of the variable 'x' is given as,
3x = 9
x = 9 / 3
x = 3
Then the other sides of the triangle will be
4x = 4 (3) = 12 in
10x = 10 (3) = 30 in
Then the perimeter of the triangle will be calculated as,
P = 9 + 12 + 30
P = 51 inches
The length of the triangle is 9, 12, and 30. Then the perimeter of the triangle will be 51 inches.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ2
Find the area of the rectangle.
A = [? ] cm2
6 cm
9 cm
Answer:
54 cm2
Step-by-step explanation:
A = l * b
A = 6 * 9
A = 54
Please mark my answer as brainliest for further answers:)PPPPPPPPPPPPPPPPPPLLLLLLLLLLLLLLLLLLLLLLLZZZZZZZZZZZZZZZZZZZZZ HELP I NEED ALL 3 QUESTIONS ANSWERED
1. a. The image's dilated side lengths on each side:
AB = CD = 45cm.
BD = AC = 24cm.
2. a. Equal ratios exist between the lengths of matching sides. The ratio is the same as the dilation's scale factor.
b. The image is a dilation of the original image.
c. The scale factor = 4.
3. a. The image is a dilation of the original image.
b. The scale factor = 2.
What do you mean by scale factor?A scale factor, often referred to as a conversion factor, is a numerical value that is used to alter a figure's size without altering its shape. The scale factor can be calculated if both the dimensions of the original and the dilated (increased or lowered) figure are known. The basic formula for calculating a figure's scale factor is given as,
Scale factor is equal to the division between the dimensions of the new and old shapes.
In the first figure, the sides are given as:
AB = 15cm
BD = 8cm
Scale factor = 3
Now, using the scale factor formula:
Scale factor = New dimensions/Old dimensions
⇒ 3 = New dimension/15
⇒ New dimension of AB = 45cm.
Similarly, new dimension of BD = 24cm.
In the second figure, as the lengths of corresponding sides have equal ratios. Both the figures are similar. The image is the dilation of the original figure as the lengths of corresponding sides have equal ratios. The ratio is the same as the dilation's scale factor. So, the scaler factor here is 4.
Now in the last figure we can see that the coordinates of A', B', C' and D' are exactly half of that of the coordinates of A, B, C and D.
The ratio of the coordinates is 2:1.
Therefore, the scale factor = 2.
To know more about scale factor, visit:
https://brainly.com/question/27895074
#SPJ1
Math problem help please
Answer:
I say B.
Step-by-step explanation:
sorry if I'm wrong. Have a nice day :)
Help???? I don’t know which one it is
Answer:
A
Step-by-step explanation: Rreminder be happy and stay confident <3
Please answer this quick
Answer:
Third choice: 1/3
Step-by-step explanation:
You have a 2/6 chance of not landing on a positive, since 2 numbers are negative. Only spinning once so nothing else needs to be done. Simplify to get 1/3.
Carlos wants to go on a road trip to Jacksonville, Florida.
For every gallon of gas, his car travels m miles
He will travel 500 miles to Jacksonville.
Gas costs $3.65 per gallon.
Which expression shows how much Carlos will spend for gas on the trip to Jacksonville?
a) 500(3.65m) c) 3.65(m/500)
b) 3.65(500/m) d) 500(1/3.65m)
QUICK PLEASE!
b)3.65(500/m)
Hope this helps
76.57143 nearest tenth
Answer:
76.6
Step-by-step explanation:
so the nearest tenth is 76.57143
Answer:76.6
Explanation:
For brainiest:):):):):)
Answer:
254.34
Step-by-step explanation:
Area of a circle = pi*r² So the radius is diameter/2 which is 9, so the area is pi*81 which is 254.34
14. 254.47
EXPLANIACTION
A=(3.14/4) * 18^2
What is the answer for x?
Answer:
x = 7°
Step-by-step explanation:
Sum of All angles = 180°
Form an equation
180 - 90 - 36 = 7x + 5
54 = 7x + 5
Subtract 5 from both sides
49 = 7x
x = 49/7
x = 7
Can some one help me its due today please help im struggling!!!
Answer:
Problem 27: 35
Step-by-step explanation:
This is because 7 times (Multiplied) by 9-4 is 35. We get here by doing 9-4=5. This problem then turns into 7(5)
Plz helppp I’m not so smart:)
Step-by-step explanation:
I think you will get x this way:
x=180°-140°
x=40°
CAN I PLEASE HAVE SOME HELP
Answer:
I am pretty sure it's A and I am very sorry if I'm wrong
Step-by-step explanation:
The way I would think about this question is this: because Jordan only wants to work a maximum of 40 hours, he can work 40 hours or less. Which is described as an equation in the top equation of letter A. And because he also wants to make $250 or more, the bottom equation in A would work as well.
I hope that makes sense! Please ask me in the comments if you want more explanation on it
help please lol :)))))))
What is the measure of each interior angle of the regular polygon pictured below? If necessary, round to the nearest tenth.
Answer:
144
Step-by-step explanation:
The measure of each interior angle formula:
[tex]\frac{180(n-2)}{n} \\\\\frac{180(10-2)}{10} \\\\\frac{180(8)}{10} \\\\\frac{1440}{10} \\\\144[/tex]
Answer:
135
Step-by-step explanation:
deltamath
Which choice is equivalent to the quotient below?
I think it’s B. ?
PLEASE HELP!!
The choice equivalent to the quotient below is option D. 2.
What is Square Root?Square root of a number is the value such that the value when multiplied to itself two times gives the original number.
It is denoted by the symbol √.
For example, square root of 16 is 4 since 4 × 4 = 16
Given expression is
√100 / √25
We have to find the square root of each of the value and then divide it.
We know that,
100 = 10 × 10
So 100 = 10²
So,√100 = 10
Similarly,
25 = 5 × 5
So √25 = 5
Substituting the values,
√100 / √25 = 10 / 5 = 2
Hence the quotient is 2.
To learn more about Square roots, click here :
https://brainly.com/question/29286039
#SPJ7
7(m-6),when m=8
Answer please
Answer:
14
Step-by-step explanation:
7(8−6)
7(8−6)
=14
Hope it helps :)
Emily's snack allowance at school exceeds $7. Her snack allowance is one-fourth of her monthly allowance. Write and solve an inequality to determine a, what could be Emily's monthly allowance?
Answer:
x>28
Step-by-step explanation:
x>7
4x>28
If t represents the amount of time Neda has spent typing the second letter, which equation states the rule used to determine the number of words, W, Neda has typed today?
Answer:
W = t + 200
Step-by-step explanation:
Number of words typed in the first letter = 200
The relationship between the total words typed, W and the number of seconds, t spent on the second letter :
W = number of words typed in first letter + t
W = 200 + t
Choosing any pair of values from the table :
W = 245 ; t = 45
W = 200 + 45
W = 245
Therefore, the number of words, W typed today can be represented as
W = 200 + t
if it is exactly 8:00, How long does it take for the hands of the clock to be pointed in the same direction
Answer:
Hey! do not go to brainly for this, sometimes brainly can be no help and people will scam for points, or maybe try to hack you (pt virus) with those links saying the answers there.. I am not saying this for points but go to https://www.varsitytutors.com/basic_geometry-help/how-to-find-the-distance-between-clock-hands for that
Step-by-step explanation:
So don't waste your time on brainly finding answers, you can run out of points fast, some people wont answer at all.
Evaluate the expression shown for x = 12.
Negative StartFraction 5 over 6 EndFraction x + 7
Negative 15 and StartFraction 5 over 6 EndFraction
–3
9 and two-thirds
18 and StartFraction 1 over 6 EndFraction
Answer: It is -3
Step-by-step explanation:
Answer:
the person above deserves brainliest its correct on e d g e n u i t y 2 0 2 0
Step-by-step explanation:
does anyone know the answer for this problem :P
Answer:
A: 6x^2 + 19x + 3
Step-by-step explanation:
6x + 1 (x +3)
use the foil method so first do 6x(x) and you get 6x^2 then 6x(3) + x(1) and you get the 19x then you just do 3(1) and you get your answer which as stated above is 6z^2 + 19x + 3
Q Review / Finish Test
Tools -
ABC
Question 3
Theo is an athletic trainer who works with high school football and baseball players. This clients, 40% play football, and the rest play baseball. Of the students who play football, 30% are on the varsity team,
while 50% of Theo's baseball clients are on the varsity team. What percent of Theo's clients are on the varsity team?
The percentage of Theo's clients are on the varsity team will be 27%
What will be a percent of Theo's clients are on the varsity team?It is given in the question that
clients, 40% play football
clients, 60% play Baseball
Of the students who play football, 30% are on the varsity team,
50% of Theo's baseball clients are on the varsity team.
So clients who play football and are on the varsity team will be
[tex]0.4\times 0.3=0.12[/tex] = 12%
And clients who play baseball and are on the varsity team will be
[tex]0.6\times 0.5=0.15[/tex]=15%
The total percent of the varsity team will be =12+15=27%
Thus the percentage of Theo's clients are on the varsity team will be 27%
To know more about percentage follow
https://brainly.com/question/19247356
3x +2 for x=5
Help me
Answer:
15 + 2=
17
Step-by-step explanation:
Answer: 3 x 2 + 13 x - 10
Step-by-step explanation:
:)
please tell the function equation as well too
Answer:
A = Rate of change is y = 4x
This is because it is set up as y/x and for the graph B = y = 3x.
Function A is greater in change than Function B
Because if you substitute x for 1.
A would be 4.
B would be 3.
Symbolize and solve Equations
Amy and Stephanie were playing a number game. Amy picked a number and told Stephanie that if she added 8 to the number and
multiplied the sum by 4, it would equal 12. Which equation could Stephanie use to find the number, x?
A. 4(X + 8) = 12
B .4+(x+8)=12
C. 4(x)+8=12
D. 8(x + 4) = 12
Bacteria are the most common example of exponential growth. Select a number between 2 and 10 to represent the hourly growth rate of a certain bacteria. For example, selecting the number 8 would mean that the amount of bacteria will be 8 times greater after every hour.
a. Suppose you start with one single bacterium. Make a table of values showing the number of bacteria that will be present after each hour for the first six hours using the hourly growth rate that you selected. Then determine how many bacteria will be present once 24 hours have passed.
b. Explain why this table represents exponential growth.
c. Using this example, explain why any nonzero number raised to a power of zero is equal to one.
d. Write a rule for this table.
e. Suppose you started with 100 bacteria, but they still grew by the same growth factor. How would your rule change? Explain your answer.
Answer:
bh
Step-by-step explanation:
Answer:
Answers are below
Step-by-step explanation:
Hour 0 1 bacterium
Hour 1 3 bacterium
Hour 2 9 bacterium
Hour 3 27 bacterium
Hour 4 81 bacterium
Hour 5 243 bacterium
Hour 6 729 bacterium
After 24 hours, the number of the bacterium will reach 282,429,536,481.
B) This table represents exponential growth because of the number of bacterium always being multiplied by 3.
C) The reason that any number to the zero power is one is that any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.
D) Y = 1 + 3 to the power of x
E) The rule would change by having all of the numbers multiplied by 100 since there is 100 bacterium at Hour 0.
What is the distance between the points (3, 4) and (3, -7)
Answer:
distance is estimated 11
Which phrase from the text most clearly explains the main idea of the third paragraph? (5 points)
Memory uses general knowledge
Other memories and other stories
When telling a friend about the event
Rather than the actual participant
Answer:
is there an image of the story?
Answer:
A. Memory uses general knowledge
I deeply apologize if it's wrong but that's just what I think.
Also, I just took the test with this question and I'm pretty sure I got it correct.
can someoneone help me with please i have to sent it today
Writing A story
Read the task below.
Your English teacher has asked you to write a story for your school magazine
The story must begin with this sentence:
It all began when Hayley was woken up by a loud noise.
Your story must include:
• an open window
• a broken vase
Write your story.
Answer:
I was asleep in bed one night when, suddenly, a loud noise woke me. I did not know what it was I searched around for a few minutes, but I couldn't find where the sound was coming from, but on the floor, I saw a broken wase, and i decided to throw it away in the open window next to me... My house was very far out, hidden behind trees, and darkness was around me. Ahhh! The sound was repeating again and again so I decided to rush over to my phone to call the police. but then I realized that was just not any sound, but it was a cry for help. The police said they will send over a rescue worker to help me, to help them, whoever it is. I went downstairs to find something sharp something that could help me or at least scare away the person here.
Step-by-step explanation:
Hope you like it xD It is not 100% finished so probably you can finish it, i wrote an introduction for you) good luck