Answer:
a) x = 12 y = 9
b) x = -2 y = -4
c) x = 6 y = -2
Step-by-step explanation:
a)
Equation 1: 6x - 7y = 9
Equation 2: 3x + 2y = 54
Multiply Equation 2 by 2:
⇒ 6x + 4y = 108
Subtract equations:
6x + 4y = 108
- 6x - 7y = 9
11y = 99
Divide both sides by 11:
⇒ y = 9
Substitute found value of y into Equation 1 and solve for x:
⇒ 6x - 7(9) = 9
⇒ 6x - 63 = 9
⇒ 6x = 72
⇒ x = 12
---------------------------------------------------------------------------------------------------
b)
Equation 1: 4x - 5y = 12
Equation 2: 2x - 3y = 8
Multiply Equation 2 by 2:
⇒ 4x - 6y = 16
Subtract equations:
4x - 6y = 16
- 4x - 5y = 12
-y = 4
Divide both sides by -1:
⇒ y = -4
Substitute found value of y into Equation 1 and solve for x:
⇒ 4x - 5(-4) = 12
⇒ 4x + 20 = 12
⇒ 4x = -8
⇒ x = -2
---------------------------------------------------------------------------------------------------
c)
Equation 1: 4x - 2y = 28
Equation 2: 3x + 3y = 12
Multiply Equation 1 by 3:
⇒ 12x - 6y = 84
Multiply Equation 2 by 4:
⇒ 12x + 12y = 48
Subtract equations:
12x - 6y = 84
- 12x + 12y = 48
-18y = 36
Divide both sides by -18:
⇒ y = -2
Substitute found value of y into Equation 1 and solve for x:
⇒ 4x - 2(-2) = 28
⇒ 4x + 4 = 28
⇒ 4x = 24
⇒ x = 6
What is the balance point for the following data set? 19 80 15 20
The balance point of the dataset is the mean of the dataset
The balance point of the dataset is 20
How to determine the balance point?From the dataset, we have the following frequency table
Data (x) Frequency (f)
15 2
24 1
26 1
The balance point of the dataset is the mean value of the dataset, and the mean is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
This gives
[tex]\bar x = \frac{15 * 2 + 24 * 1 + 26 *1}{2 +1+1}[/tex]
Evaluate the sum
[tex]\bar x = \frac{80}{4}[/tex]
Evaluate the quotient
[tex]\bar x = 20[/tex]
Hence, the balance point of the dataset is 20
Read more about mean at:
https://brainly.com/question/14532771
The number 28,363,775 rounded to the nearest ten thousand is
Answer:
50,000
Step-by-step explanation:
Just put it in the answer lol :p
Answer:
28,360,000
Step-by-step explanation:
The number after the 6 (the ten thousands is 3, so it rounds down to 28, 360, 000.
please give brainliest!
What is the value of n in the equation below?
Answer:
9
Step-by-step explanation:
12ⁿ⁻⁵ = 12⁴
n - 5 = 4
n = 9
You have four $20 bills, ten $5 bills, and twelve $1 bills in your wallet. If you reach into your wallet twice, what is the probability that you will pull out a $1 bill the first time and a $5 bill the second time?
Answer:
2/28 ?
Step-by-step explanation:
if I'm wrong so sorry
Need help on number 10
If tan C is 3/4, find the sin C.
Answer:
sin C = 3/5
Step-by-step explanation:
see image.
It helps to draw a picture. Tan C is the ratio of the OPP/ADJ.
Pythagorean theorem or if you know Pythagorean triples are a shortcut to find the hypotenuse.
Once you know the hypotenuse, use the ratio for sine to solve the question. Sine is OPP/HYP.
see image.
How many factors do numbers of the form p^n and q^m have if p and q are two different prime numbers and m and n are natural numbers?
The only common factor between these two numbers will be 1.
How many factors do these numbers share?
Remember that any number can be decomposed as a product of prime numbers. For example for 18 we have:
18 = 2*3*3
There 18 is written as a product of its prime factors.
Now, for our case of p^n and q^m we will have:
p^n = P = p*p*p...*p n times.
q^m = Q = q*q*q*...*q m times.
Now, notice that because q and p are primes, there is no common factor in these two decompositions. (and we can't decompose it furthermore). Then we conclude that the only factor that these numbers share is the trivial one, which is 1.
If you want to learn more about prime numbers, you can read:
https://brainly.com/question/145452
what is 0.0981 rounded to the nearest tenth of a percent
Answer:
0.1 percent
Step-by-step explanation:
sorry I don't have an explanation. sorry if it's wrong, at least I tried
Answer:
0.1
Explanation:
It's right
The longer leg of a right triangle is 1 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the
triangle.
cm
Length of the shorter leg: 0
Length of the longer leg: 0
Length of the hypotenuse: 0
cm
cm
Answer:
Shorter leg = 20 cm.
Longer leg = 21cm.
Hypotenuse = 29 cm
Step-by-step explanation:
Let the shorter leg be x cm long
Then longer leg = x + 1 and hypotenuse = x + 9 cm long
So by Pythagoras:
x^2 + (x + 1)^2 = (x + 9)^2
0 = x^2 + 18x + 81 - x^2 - (x^2 + 2x + 1)
x^2 + 18x + 81 - x^2 - x^2 - 2x - 1 = 0
-x^2 + 16x + 80 = 0
x^2 - 16x - 80 = 0
(x - 20)(x + 4) = 0
So x = 20 (we ignore the negative root).
So longer leg = 20 + 1 and hypotenuse = 20 + 9.
The length of a rectangular garden is 4 more than three times the width. If the perimeter of the garden 104 feet, what are the dimensions of the garden.
Write your system of equations:
Answer the question being asked:
Answer:
12 ft by 40 ft
Step-by-step explanation:
Let L represent the length and W the width. Then L = 3W + 4.
The perimeter formula is P = 2L + 2W or P = 2(L + W).
Substituting 104 ft for P, we get 104 ft = 2(L + W), which reduces to
52 ft = L + W, or 52 ft = 3W + 4 + W.
Therefore, 52 ft = 4W + 4.
Solving this for W, we get 48 ft = 4W, or W = 12 ft.
Then, because L = 3W + 4, L = 3(12 ft) + 4 = 40 ft = L
The dimensions of the garden are 12 ft by 40 ft.
55% of 70 =
I want to know for my hw
Answer:
38.5
Step-by-step explanation:
70*(0.55) = 38.5
Answer:
Step-by-step explanation:
To find 55% of 70, we need to write an equation.
this equation will be 55x70/100
now, the answer to 55x70 / 100 is
38.5
We get this answer, because 55x70=3850
and 3850 divided by 100 is 38.5
please help! What is 75 % of 62-(98/4)
Answer:
28.13
Step-by-step explanation:
62 - (98/4)
62 - 24.5 = 37.5
75% of 37.5 is 28.125, or 28.13.
Answer:
22
Step-by-step explanation:
98/4 = 24.5
62-24.5 = 37.5
75% of 37.5
= about 22
What is the value of y in the equation 4x +3 y= 23 when x=2 , x=6
Answer:
5, -⅓
Step-by-step explanation:
x = 2:
4x + 3y = 23
3y = 23 - 4(2)
3y = 15
y = 5
x = 6:
4x + 3y = 23
3y = 23 - 4(6)
3y = -1
y = -⅓
Need help, Brainliest if correct only…. dont answer if you don’t know. Thank u!
Answer:
3/1
Step-by-step explanation:
In triangle ABC, the known side is AC, which is equal to 6. The corresponding side to AC from triangle DEF would be FD, which is equal to 2. You divide 6/2 in order to get 3/1.
There should be 2 answers
[tex]|6m-2|=0\\\\\implies 6m-2 =0~~~~~~~~~~~~~;[\text{If}~ |x| = 0 ~\text{then}~ x = 0]\\\\\implies m = \dfrac 26 = \dfrac 13[/tex]
Which of the following best describes the graph below
Answer:
i believe its A
Step-by-step explanation:
Answer:
B. The graph is not a function.
Step-by-step explanation:
We are given the graph of a relation. It is required to determine whether the graph represents a function or not. 'If a vertical line passing through the graph of the relation cuts the graph at at-most one point, then the given graph represents a function else not'. So, if we plot the vertical line 'x = 3' in the figure, we see that, The vertical line drawn crosses the graph at two points A and B as shown below. Thus it would be B
Solve for c
Can you pls help me??
Answer:
5(c+3)=85
divide both sides by 5
c+3=17
taking 3 to the other side gives us -3
c=17-3
c=14
express in the form 1 : n give n as a simplifeid fraction 8 : 6
Answer:
So, Simplified fraction of 8:6 is 4:3.
Choose the multiplication problem that correctly shows partial products.
A) A
B) B
C) C
Answer:
B) B
Step-by-step explanation:
2 times 4 is 8, so in this case the option is option b as none of the other options show this.
In total,
2 * 4 = 8
60 * 4 = 240
240 + 8 = 248
Pablo had $319 in his savings account. He got $28 for helping a neighbor, and he saved all but $11 of it.
How much is in Pablo's savings account now?
A.
$330
B.
$336
C.
$347
D.
$358
Answer:
the correct answer is B. $336
Step-by-step explanation:
you first add 319 and 28. Then, you subtract the product with 11.
To be honest I think the answer is B
Regis leans a 10-foot ladder against a wall. The base of the ladder makes a 65 angle with the ground.
(a)
What is the distance, In feet, from the base of the ladder to the base of the wall? Round to the nearest tenth of a foot.
(b) Regis needs to move the ladder so that it reaches a window 9.6 feet above the ground.
How many feet closer to the building does he need to move the base of the ladder?
The distance, In feet, from the base of the ladder to the base of the wall is 4.2 ft.
He needs to move the ladder 0.1 ft closer to the base of the building.
The situation forms a right angle triangle.
Right angle triangleRight angle triangle has one of its angles as 90 degrees. The sides and angle can be found using trigonometric ratios.
The length of the ladder is the hypotenuse of the triangle formed. Therefore, the distance, In feet, from the base of the ladder to the base of the wall can be calculated as follows;
cos 65° = adjacent / hypotenuse
cos 65° = d / 10
d = 10 × 0.42261826174
d = 4.22618261741
d = 4.2 ft
She needs to move the ladder so it reached a window 9.6 feet above the ground. Therefore, the distance from the base of the ladder and the wall is as follows;
cos 65 = d / 9.6
d = 9.6 × 0.42261826174
d = 4.05696
d = 4.1
Therefore, he needs to move the ladder 0.1 ft closer to the building.
learn more on right angle triangle here: https://brainly.com/question/14988069
for each of the figures, write an absolute value equation that has the following solution set 3 and 7
The solution set 3 and 7 are the true values of the absolute value equation
The absolute value equation that has a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]
How to determine the absolute value equation?The solution sets of the absolute value equation are given as:
x = {3, 7}
Calculate the mean of the solutions
[tex]x_1 = \frac{7 +3}{2}[/tex]
[tex]x_1 = 5[/tex]
Calculate the difference of the solutions divided by 2
[tex]x_2 = \frac{7 - 3}{2}[/tex]
[tex]x_2 = 2[/tex]
The absolute value equation is the represented as:
[tex]|x - x_1| - x_2 = 0[/tex]
Substitute known values
[tex]|x - 5| - 2 = 0[/tex]
Add 2 to both sides
[tex]|x - 5| = 2[/tex]
Hence, the absolute value equation that has the a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]
Read more about absolute value equation at:
https://brainly.com/question/2166748
Can someone help me out!
Answer:
option c
Step-by-step explanation:
This is the net of square pyramid.
Base of the square pryamid is square and all the other face are triangle.
Please help I'll mark brainliest
i need help finding x and y
Answer:
x is 5 and y is 6
Step-by-step explanation
we find 2/3 factors that equal 10. 2 and 3. the only other number that can be added that equals 10 is 5. i apply the same logic to y
Answer:
Y -- 6
X -- 5
Step-by-step explanation:
we first find y by finding the side that is the longest that is parallel to y (16) we also find that two sets of fives are also parallel to y and 16 as seen in the first screenshot. Then to find the missing value we will subtract the 5 two times from 16 to find y. 16 - 5 = 11 - 5 = 6.
we do the same thing to find x, (10 - 2 = 8) (8 - 3 = 5) X = 5
Kala drove 603 miles in 9 hours at the same rate how many miles would she drive in 12 hours
Answer:
804
Step-by-step explanation:
603/9 x 12
67 x 12
804
Answer:
804 miles in 12 hours
Step-by-step explanation:
603/9 which = 67
67*12 which equal 804
don't forget the unit (mph)
A 10-inch tire has a diameter of 10 inches. What is the circumference of these tires?
Answer:
31.4
Step-by-step explanation:
diameter (d) = 10
circumference = (3.14)d
= (3.14)10 = 31.4
circumference = 31.4
A model of Earth is located 7600 meters from the Globe Arena in Sweden’s solar system model. The volume of the model is approximately 3052.08 cubic centimeters. What is the length of the radius of the Earth model?
The length of the radius of the mudel is 9 cm
Step-by-step explanation:[tex]By\ the\ topic[/tex]
[tex]The\ volume\ of\ the\ mudel\primes\ is\ 3052.08{\rm cm}^3[/tex]
[tex]Formula\ for\ the\ volume\ of\ the\ sphere\ is[/tex]
[tex]\frac{4}{3}\pi\ r^3[/tex]
[tex]\frac{4}{3}\pi\ r^3=3052.08[/tex]
[tex]\pi\ r^3=\frac{3}{4}\times3052.08=2289.06[/tex]
[tex]\gamma3=2289.06\div\pi[/tex]
[tex]\gamma=\sqrt{\frac{2289.06}{\pi}}\approx\sqrt{\frac{2289.06}{3.14}}+\sqrt{729}[/tex]
[tex]r=9cm[/tex]
[tex]7hus,\ the\ length\ of\ the\ vadius\ of\ eanth[/tex]
[tex]mudel\ is\ 9\ cm[/tex]
[tex]Application\ of\ the\ volume\ of\ the\ spheve?[/tex]
I hope this helps you
:)
Katie ate dinner at a restaurant. The bill came to $77. If she left an 18% tip, how much was the tip?
Can someone pls help me?
Answer:
$13.86
Step-by-step explanation:
Just multiply 77 by 18 percent as a decimal (.18) to get the answer, which is $13.86
Hopefully this helps- let me know if you have any questions!
Natalie has 112 boxes she left 105 five boxes and she found 20 boxes how much dose she have?
Answer:
27 boxes.
Step-by-step explanation:
This situation can be represented by the equation:
(112 - 105) + 20 = ?
First we subtract 105 from 112:
112 - 105= 7
Now add 20.
7 + 20 = 27
Natalie has 27 boxes now.
can someone plssss help me with this. I WILL MARK BRAINLIEST
Answer:
5 payments
Step-by-step explanation:
First we add up the prices for the lunches and the movies :)
3 x 5 = 15
15 + 9.5 = 24.5
Second we subtract the 24.5 from the 35 :)
35 - 24.50 = 10.5
Now we divide the price of the cd player by the 10.50 to get the total number of payments :)
50/10.5 = 5
Finally to check it one more time, we multiply the 10.5 by 5 and if it equals 50 or over, it is correct!! :D
10.5 x 5 = 52.5!!!
You did it!
Your correct answer is 5 payments!!
Have a great day!!!
Please rate and mark brainliest!!