Answer:
The solution is ([tex]\frac{7}{12}[/tex] , [tex]\frac{67}{6}[/tex])
Step-by-step explanation:
∵ y = 14x + 3 ⇒ (1)
∵ y = 2x + 10 ⇒ (2)
→ Equate equations (1) and (2) to find x
∵ 14x + 3 = 2x + 10
→ Subtract 2x from both sides
∴ 14x - 2x + 3 = 2x - 2x + 10
∴ 12x + 3 = 10
→ Subtract 3 from both sides
∴ 12x + 3 - 3 = 10 - 3
∴ 12x = 7
→ Divide both sides by 12 to find x
∵ [tex]\frac{12x}{12}[/tex] [tex]\frac{7}{12}[/tex]
∴ x = [tex]\frac{7}{12}[/tex]
→ Substitute the value of x in equation (1) or (2) to find y
∵ y = 2([tex]\frac{7}{12}[/tex]) + 10
∴ y = [tex]\frac{7}{6}[/tex] + 10
∴ y = [tex]\frac{67}{6}[/tex]
∴ The solution is ([tex]\frac{7}{12}[/tex] , [tex]\frac{67}{6}[/tex])
Trisha uses 3 cups of sugar for every 4 cups of flour to make a batch of cookies. Which equation could be used to solve x, the number of cups of flour needed for 9 cups of sugar.
Answer: The number of cups of flour needed for 9 cups of sugar = 12.
Step-by-step explanation:
Equation of direct proportion between two quantities x and y :
[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]
Let x= the number of cups of flour needed for 9 cups of sugar.
Put [tex]x_1=4,\ y_1=3,\ y_2=9, x_2=x[/tex]
[tex]\dfrac{4}{3}=\dfrac{x}{9}\\\\\Rightarrow\ x=\dfrac{9\times4}{3}\\\\\Rightarrow\ x=12[/tex]
Hence, the number of cups of flour needed for 9 cups of sugar = 12.
How many solutions does r > 5 have?
Answer: It can have infinite
Step-by-step explanation:
because numbers never finish
Is 2(6-3x)+x equivalent to 2(3x)+x?
Insert brackets to make this calculation correct.
4 - 1 x 2 = 6
Answer:
(4-1)x2=6
Step-by-step explanation:
(4-1)x2=6
(3)X2=6
6=6
Answer:
[4 - 1] x 2 = 6
Step-by-step explanation:
Test out each possible solution.
Problem: 4 - 1 x 2 = 6
#1: [4 - 1] x 2 = 6
4 - 1 is 3.
3 x 2 is 6.
6 = 6 ✅
#2: 4 [-1 x 2] = 6
-1 x 2 is -2.
-2 [tex]\neq[/tex] 6 ❎
Therefore, #1 is correct.
4. If you are given that plq and p || r,
what can you conclude about lines q and r?
State the theorem that justifies that conclusion.
There are 144 students in the school this year. One-quarter of the students have blue
eyes. One-sixth of the students have green/hazel eyes. Seven-twelfths of the students
have brown eyes. How many students have each of the three colours? SHOW ALL
OF YOUR WORK!
Answer:
Blue eyes = 36
green eyes= 24
brown eyes = 84
Step-by-step explanation:
144 divided by 4 is 36
144 divided by 6 is 24
144 divided by 12 is 12 and then multiplied by 7 is 84
hope this helps
penny reads 10 pages in 1/2
hour. What is the unit rate for pages per hour? For hours per page?
Answer:
she would read 20 pages in 1 whole hour
Cardi B is buying a condo built within
a skyscraper. She learned that each floor is 13 feet tall.
Write an expression to represent the height of the skyscraper if it has f
floors, where f is the number of floors.
How tall, in feet, would her condo be in the skyscraper if she was on the 26th floor?
PLEASE HELP... 25 points
Answer:
13f is equation
which is floors times height
Step-by-step explanation:
26*13=338
338 feet tall
Brainliest appreciated!
Answer:
(H)=13f and the height is 338ft
Step-by-step explanation:
height of skyscraper=h
f=floors
height per floor is 13ft...
(H)=13f
(H)=13*f, if f is 26, then to find height multiply 13 by 26
doing this you get 13*26=338ft
If using the method of completing the square to solve the quadratic equation x^2-19x+9=0 which number would have to be added to "complete the square"?
Answer:
90.25Step-by-step explanation:
Given the quadratic equation x^2-19x+9=0 re arranging we have;
x^2-19x+9 - 9=0 -9
x^2-19x = - 9
In order to complete the square we would add a number to both sides and the number will be the square of the half of coefficient of x in the expression as shown.
Coefficient of x = -19
half of coefficient of x = -19/2
square of the half of coefficient of x = (-19/2)²
square of the half of coefficient of x = 361/4
square of the half of coefficient of x = 90.25
Hence the number that would have to be added to "complete the square" is 90.25
Which of the following statements best describes the location of -(-6) on a number liner
A. It is 6 units to the left of 0.
B. It is 6 units to the night 6.
C. It is 6 units to the right of 0.
D. It is 6 units to the left of 6.
Jogging burns 375 calories in 45 minutes. Determine how many calories burned per hour?
Sumiko and Jandella ran the bleachers together today at Poly High School. Sumiko runs these same bleachers every 6 days and Jandella runs them every 16 days. The soonest they will see each other again is in days.
Answer:
48 days
Step-by-step explanation:
Given that :
Sumiko runs bleachers every 6 days
Jandella runs bleachera every 16 days
The soonest they will see each other again is in days can be obtained by getting the lowest common multiple of 6 and 16
Multiples of
6 : 6, 12, 18, 24, 30, 36, 42, 48, 54,...
16 : 16, 32, 48, 64,...
Lowest common multiple of 6 and 16 = 48
Hence, the soonest they'll see each other again is in 48 days
Is 4 to 7 the same as 7 to 4? Explain why or
why not?
Step-by-step explanation:
4 times of 7 (7 + 7 + 7 + 7 = 28) is the same as 7 times of 4 (4 + 4 + 4 + 4 + 4 + 4 + 4 = 28)
4^7 (4 x 4 x 4 x 4 x 4 x 4 x 4 = 16384) is not the same as 7^4 (7 x 7 x 7 x 7 = 2401)
Answer:
Yes. The difference between them are the same. Both have the same number of units between them,
Step-by-step explanation:
4.5/w = 3
what is the W?
Answer:
w=1.5 or w=13.5
Step-by-step explanation:
this is one answer:
multiply w on both sides to leave u with
4.5=3w
divide both sides by 3
[tex]\frac{4.5}{3}=\frac{3w}{3}[/tex]
1.5=w
_____________________
this is the second one if the first one is wrong:
multiply 4.5 on both sides so that the 4.5/w would leave u with just only w alone.
then 3*4.5=13.5
w=13.5
hope dis helps if not then im not dat smart enough ;?
What kind of solution does 3x+5=-2 have?
Answer:
[tex]x = - \frac{7}{3} [/tex]
step by step:
3x+5=-2
move constant to the right-hand side and change it's sign
3x=-2-5
Calculate the difference
3x=-7
Divided both sides of the equation by 3
Please help look at the picture
Answer:
The correct answer would be D
Find the slope and the y-intercept of the line.
y = 8x-1
Answer:
Slope: 8 Y-intercept: -1
Step-by-step explanation:
This equation follows the format of y = mx + b. M would be the slope, b would be the y-intercept.
Does the table show a proportional relationship, if so , what is the value of y when x is 10
Yes, the given table shows a proportional relation with constant of proportionality 1/3.
What are proportional relation?Two variables x and y are in proportional relation if the relation between then is in the form y = k x, where k is the constant of proportionality.
Or we can say for all pairs ( x, y ) , y/x = k , k is constant then the table containing (x, y) values shows a proportional relationship.
From given table
When x= 5 , y =[tex]1\frac{2}{3}[/tex] =5/3
Then, y/x = (5/3)/5 = 1/3 =k
When x =6 , y =2
Then, y/x = 2/6 = 1/3 =k
When x = 7 , y = [tex]2\frac{1}{3}[/tex] = 7/3
Then, y/x = (7/3) /7 = 1/3 =k
When x=8 , y =[tex]2\frac{2}{3}[/tex] = 8/3
Then , y/x = (8/3) / 8 = 1/3 =k
Thus for each pair (x, y) given in the table the ratio y/x is same , this ratio is say k = 1/3
Therefore, for the given table y/ x = k or y =k x with k = 1/3 , and the table shows a proportional relation with constant of proportionality 1/3.
Also, Learn more about proportionality constant from the link below:
https://brainly.com/question/17793140
#SPJ2
Help me<3. Its maph ugggggg brain hurt......*dieing noises*
Step-by-step explanation:
There are several ways to solve this, but the only one I remember how to do is with the pythagorean theorem. The distance between A and B is the same as a hypotenuse of a triangle with a height the absolute value of y1-y2 and a base of the absolute value of x1-x2.
For example, in the first question, the coordinates are (1,2) and (9,8), so we have a triangle with base 8(9 - 1) and 6(8 - 2). Now we just need to plug that into the pythagorean theorem like so:
[tex] {a}^{2} + {b}^{2} = {c }^{2} [/tex]
or plugging our numbers in,
[tex]8^{2} + {6}^{2} = 100[/tex]
The answer is the radical of the answer, in this case 10.
So if this makes sense, go ahead and try to work the next three out on your own, and if you still need help let me know <:
Hope this helps Bucke!
Brendon sells tires at the local auto parts store. He told a customer that the tire width for a new tire was 21.5 centimeters. Which of the following describes the tire width for the new tire? Help please thank you!!!
Answer:
215 mm
Step-by-step explanation:
1 cm = 10 mm
21.5 cm * (10 mm)/(1 cm) = 215 mm
Answer: 215 mm
2. How many solutions does the system have?
y - 4x = -3
2y - 8x = 10
a. one solution
b. two solutions
c. infinitely many solutions
d. no solution
Answer:
no solution both
Step-by-step explanation:
15
The warmest temperature last winter was 17° F. The very next day, the temperature dropped 22° F. What was the actual temperature at the
end of the second night?
°F
Answer:
-5 degrees fahrenheit
Which Figure is a rotation of the Blue Figure?
A
B
C
D
Answer:
a
Step-by-step explanation:
the green figure is the same as the blue figure.
The number of tons of wheat the government can afford to buy if it spends total of $100 million, wheat costs $300 per ton, and it must buy 5 fighter planes at $15 million each.
Total amount, T = $100 million.
Cost of wheat per ton, C = $300 .
Price per fighter plane, c = $15 million.
Now,
Price of 5 fighter planes, P = $( 15 × 5 ) = $75 million.
Amount left = $( 100 - 75 ) = $25 million.
So,
Number of tons of wheat government can buy is :
[tex]n=\dfrac{25\times 1000000}{300}\\\\n = 83333.33\ tons[/tex]
Therefore, number of tons of wheat the government can afford is 83333.33 tons.
Hence, this is the required solution.
136 = -8(1 + 6v)
Help
Answer:
-3
Step-by-step explanation:
136 = -8(1+6v)
136 = -8 - 48v
136 + 8 = -48v
144 = -48v
144/ -48 = v
-3 = v
It rained all day on Mother's Day and the temperature dropped fourteen and seven tenth degrees. The next day the rain stopped and the temperature rose ten and nine tenths degrees. If the temperature at the beginning of Mother's Day was sixty five and eight tenths degrees, what was the temperature at the end of the day after Mother's Day?
PLEASE ANSWER< I WILL GIVE YOU BRAINLIEST
Answer:
62 Degrees
Step-by-step explanation:
65 8/10 - 14 7/10 = 51 1/10
51 1/10 + 10 9/10 = 62
As of July 1, 2014, the population of India was about 1,267,000,000. How can you write this number in scientific notation?
1. Move the decimal point to the right of the first digit. What is the first factor?
Answer:
1) 1.267x10^9
2) 2
Step-by-step explanation:
Michelle drew a purple line that was 1/2 of an inch long then she drew a green line that was 1/6 of an inch long how much longer what is the purple line than the green line
Answer:
[tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given length of purple line = [tex]\frac{1}{2}\ inch[/tex]
Given length of green line = [tex]\frac{1}{6}\ inch[/tex]
To find:
How much longer is the purple line than the green line ?
Solution:
To find the required length, we have to subtract the length of green line from the length of purple line.
i.e.
The required answer =
[tex]\frac{1}{2}-\frac{1}{6}\\\text{Taking LCM of 2 and 6, we get 6}\\\Rightarrow \dfrac{3-1}{6}\\\Rightarrow \dfrac{2}{6}\\\Rightarrow \bold{\dfrac{1}{3}}[/tex]
Therefore, the answer is:
Purple line is [tex]\frac{1}{3}[/tex] of an inch longer than the green line.
(Find common denominator first.)
3/2 + b=7/4
Answer:
b = 1/4
Step-by-step explanation:
Take the given fractions : 3/2 and 7/4 and find a common denominator.We will use 4 as a common denominator.
In order for the denominator of 3/2 to get to 4, you need to multiply by 2.3 × 2 = 6 2 × 2 = 4
New fraction: 6/4Now we have the equation 6/4 + b = 7/4
7/4 - 6/4 = 1/4
Simplify the expression.
Can someone explain to me how to get the answer? Thanks!
Answer:
11x^2+2x+9
Step-by-step explanation:
2+(2+6)⋅x^2+2x+3x^2+7
2+(8)⋅x^2+2x+3x^2+7
2+8x^2+2x+3x^2+7
9+8x^2+2x+3x^2
9+8x^2+2x+3x^2
11x^2+2x+9