Solve the system of linear equations using elimination.
-5x + 3y = -19
-x – 3y = -11
What the first person said
The points in the table lie on a line. What is the slope of the line?
X
-8
-2
4
10
у
8
1
-6
-13
Complete the statement to show an equivalent ratio. ) 18:10 is equivalent to ? : 5.
Answer:
9
Step-by-step explanation:
[tex] \frac{18}{10} = \frac{?}{5} \\ \\? = \frac{18 \times 5}{10} \\ \\? = \frac{90}{10} \\ \\ ? = 9[/tex]
Answer:9
Step-by-step explanation:because if you divide 10 by 2 it’s 5 and if you divide 18/2 it’s 9
For a dinner party, a catering company charges a set fee $150 plus $20 per person. How much will it cost for 35 people to attend the event?
Answer:
$700 for 35 people but if you want to add the fee it will be $850
Factorise the following:
a) x^2 - 5x - 6
b) x^2 + 3x – 40
c) x^2 - 7x - 30
Answer:
a) (x+6)(x-1)
b) (x+8)(x-5)
c) (x+3)(x-10)
Step-by-step explanation:
The final answer would always have to be two brackets with x and the relevant variables.
x²: You know the possible factors that can be multiplied together would be x and x. Each factor would have to be in different brackets, so we get (x + smth else)(x +smth else)
When factorising quadratic expressions, you need to find the correct pair of factors, that when multiplied together, becomes the constant of the expression. They also need to become the middle term when they are multiplied with the term in the bracket and then added together.
Possible factors for a):
1. 1 × 6 = 6
2. 2 × 3 = 6
You know 1 - 6 = -5, so we shall use the factors 6 and 1.
(x+6)(x-1) = x² -x + 6x - 6
= x² + 5x - 6
Thus, (x+6)(x-1) is the answer.
Possible factors for b):
1. 1 × 40 = 40
2. 2 × 20 = 40
3. 4 × 10 = 40
4. 5 × 8 = 40
You know 8 - 5 = 3, so we shall use the factors 8 and 5.
(x+8)(x-5) = x² -5x + 8x - 40
= x² + 3x - 40
Thus, (x+8)(x-5) is the answer.
Possible factors for c):
1. 1 × 30 = 30
2. 2 × 15 = 30
3. 3 × 10 = 30
4. 5 × 6 = 30
You know 3 - 10 = -7, so we shall use the factors 3 and 10.
(x+3)(x-10) = x² -10x + 3x - 30
= x² - 7x - 40
Thus, (x+3)(x-10) is the answer.
a)
x² - 5x - 6
= x² + x - 6x - 6
= x(x + 1) -6(x + 1)
= (x - 6) (x + 1)
b)
x² + 3x - 40
= x² + 8x - 5x - 40
= x(x + 8) -5(x + 8)
= (x - 5) (x + 8)
c)
x² - 7x - 30
= x² - 10x + 3x - 30
= x(x - 10) + 3(x - 10)
= (x + 3) (x - 10)
4 days =____ hours
????????????????????????
4 days = 96 hours.......
It’s time to lock down the design details for the redesigned Brick and Egyptian candles. Because of manufacturing constraints, the base length for each candle has to be at least 2 cm and can be no more than 10 cm. Make a recommendation for the base dimensions of each candle. Explain how you determined your base dimensions. Your reasoning does not have to be all math related.
Answer:
THE SMALLEST FORMS:
- smallest prism ---> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3
- smallest pyramid number one ---> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3
- smallest pyramid number two ---> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 2^2 - sqrt(2)^2 = 4 - 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3
- smallest cylinder --> the cylinder of diameter 2 and height also 2 ==> the radius is diameter/2 = 2/2 = 1 ==> the volume is pi*(radius^2)*height = pi*(1^2)*2 = pi*1*2 = 2*pi cm^3
The lesser volume is the volume of the smallest pyramid number two. ==> it's wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.
THE BIGGEST FORMS:
- biggest prism ---> the cube with all sides 10 ==> the volume is 10*10*10 = 1000 cm^3
- biggest pyramid number one ---> the pyramid with base sides 10 and the height also 10 ==> the volume is (1/3)*10*10*10 = 1000/3 cm^3
- biggest pyramid number two ---> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 10^2 - [5*sqrt(2)]^2 = 100 - 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3
- biggest cylinder --> the cylinder of diameter 10 and height also 10 ==> the radius is diameter/2 = 10/2 = 5 ==> the volume is pi*(radius^2)*height = pi*(5^2)*10 = pi*25*10 = 250*pi cm^3
The bigger volume is the volume of the biggest prism (the side-10 cube). ==> it's wax cost is 0.0075 * 1000 $ per candle = 7.5 $ per candle ==> the total cost per candle is 7.5 + 1.6 = 9.1 $ per candle
The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market, you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.
If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.
Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:
Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 - 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 - (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4
The new length is 10-4=6 and the new width is 2+4=6.
Next I would choose the height of the prism (I like prisms :P) to be [the_golden_ratio]*[base_side] which is approximately 1.618 * 6 = 9.708 which I would round up to 10. ==> The volume would be 6*6*10 = 360 cm^3. ==> the cost would be 0.0075*360 + 1.6 = 2.7 + 1.6 = 4.3 $ per candle. And because my candle is so perfect I'd put the profit margin to be 5.69 $ per candle so I can proudly show it in the store with the price of 4.3 + 5.69 = 9.99 $ :)
Raul opened a savings account with 4300. Each week, x, Raul pays the dog sitter 30 from his savings account. Write a function, f(x), that is equal to the amount of money in the account after Raul pays the dog sitter each week.
Given:
Amount in the savings account = 4300
Each week, Raul pays the dog sitter 30 from his savings account.
To find:
The function, f(x), that is equal to the amount of money in the account after Raul pays the dog sitter each week.
Solution:
Let x be the number of weeks.
Raul pays the dog sitter in 1 week = 30
Raul pays the dog sitter in x week = 30x
Remaining amount = Initial amount - Amount he pays the dog sitter
[tex]f(x)=4300-30x[/tex]
Therefore, the required function is [tex]f(x)=4300-30x[/tex].
Best apps for math and science and english anyone of them you have plzzzz.
Answer:
Try khan academy! It’s free and is really good. Has subjects from k-g12!
Step-by-step explanation:
Answer:
slader is great for science and math and for English paper hacker is pretty good
Mrs. Robertson is carpeting her rectangular living room.
The room is 10 feet wide and 15 feet long. What is the
area to be carpeted?
Answer:
150 ft
Step-by-step explanation:
The formula for area is, height x width (h x w) or base x height (b x h)
10 feet is the base and 15 is the height, multiply those and you get 150
2x-2y=-10 Standard to Slope Intercept form
Answer:
y=x-5
Step-by-step explanation:
2x-2y=10
1.) subtract 2x from both sides
-2y=-2x+10
2.) Divide by -2 to get y by itself
y=x-5
Answer:
y= x+5
Step-by-step explanation:
y =mx+b is slope intercept form
!!!I WILL MARK BRAINLIEST! PLZ ANSWER ASAP AND EXPLAIN! VERY IMPORTANT!!
Answer: Check explanation
Step-by-step explanation: (3,-5), because that's the point where the two lines intersect.
Y=-2x+1
Y=-3/2x-1/2
Substitute the Y to get -2x+1=-3/2x-1/2
1/2x=3/2
x = 3
Now plug x into first equation: y=-2*3+1=-5
so the intersection point is (3,-5)
Does the order pair (1,8) satisfy the function y=3x+6 Yes,No
Answer:
yes it does
Step-by-step explanation:
I really need help so please do your thing and help me
Which inequality represents all values of x for which the product below is
defined?
please help very confused
Answer:
C. x ≥ 5
Step-by-step explanation:
You must meet both conditions:
(x -5) ≥ 0 and (x +2) ≥ 0
For the first condition, ...
x ≥ 5 . . . . add 5 to both sides
For the second condition ...
x ≥ -2 . . . . subtract 2 from both sides.
Since both conditions must be met, we must have ...
x ≥ 5
i hope this helps :)
11 ft =____in.
???!!!!!!$$&&&&&??!!!
Answer:
132 inches=11 feet
Step-by-step explanation:
12 inches are in 1 ft
Answer:
11ft = 132 inch
A recipe calls for 3 cups of sugar and 9 cups of water. How many cups of water should be used with 2 cups of sugar? Type your answerin
Answer
6 cups!
Step-by-step explanation:
HELP GIVING AWAY 55 POINTS!!!!
Pete wants to mix 4 quarts of 20% orange juice concentrate with some 60% pineapple juice concentrate to get a 50% punch concentrate for a party. How much of the 60% pineapple juice concentrate should be used? please answer ASAP and explain thought process
Answer:
12 quartsStep-by-step explanation:
Let the amount of pineapple juice be x quarts, the concentration of juice is as following equation:
4*0.2 + x*0.6 = (4 + x)*0.50.8 + 0.6x = 2 + 0.5x0.6x - 0.5x = 2 - 0.80.1x = 1.2x = 12Please help grades due tomorrow. Thanks to anyone
Answer:
57
Step-by-step explanation:
the two supplementary angles are 57, and 123
You want to buy a $25,000 car. The company is offering a 2 % interest rate for 48 months (4 years). What
will your monthly payments be?
O $500.71
O $815.05
O $542.38
$6, 276.06
Can anyone help me with this?
What is 106% of $40?
Answer:
I think it's 42.4 hope this helps
Answer:
42.4 hope this helps
Step-by-step explanation:
Write the quadratic equation in standard form: 5x^2+3=x
Answer:
5x² - x + 3 = 0
Step-by-step explanation:
The standard form of a quadratic equation is
ax² + bx + c = 0 ( a ≠ 0 )
Given
5x² + 3 = x ( subtract x from both sides )
5x² - x + 3 = 0 ← in standard form
jason can travel 24 miles in 1/2 hour. What is his average speed in miles per hour
Answer:
Step-by-step explanation:
If Jason travel 24 miles in 1/2 hour, he will travel 2*24=2*1/2h
48 miles/hour
or
24 miles...............................30 min
? miles in .............................60 min
(60*24)/30=48
Which of the following functions maps 3 to -5?
Of(x) = x + 8
O f(x) = x-5
O f(x) = 4 – x2
O f(x) = -x + 2
Answer:I think it’s B
Step-by-step explanation:
If I get this wrong i’m sorry
Evaluate the following for when x=5
4(x-2)(x-3)+7(x-2)(x-5)-6(x-3)(x-5)
Answer:5x^(2)-21x+4
Step-by-step explanation:
The graph shows the cost of renting skates. Sadie rents a pair of skates at 10 A.M. How much will she pay if she returns the skates by 1 P.M.?
How much will she pay if she returns them at 1:15 P.M.?
1 PM: ??
1:15 PM: ??
Answer: 1 PM = $8
1:15 PM = $9.0
Step-by-step explanation:
a. Since Sadie rents a pair of skates at 10 A.M and returned the skates by 1 P.M, this means the hours spent was 3 hours. Therefore, based on the graph, for 3 hours rented, he will pay $8
The amount that she will pay if she returns them at 1:15 P.M. will be equal to the value of 3 hours 15 minutes which will be:
= $8 + $1.0
= $9.00
Select the correct answer.
What does the abbreviation IPTC stand for in photography?
A
International Photo Transfer Commission
B.
International Press Telecommunications Council
C. Internal Photo Transfer Commission
D.
Internal Protocol Transfer Council
be
E.
International Photography Trade Council
Answer:
International Press Telecommunications Council
Which of the following inequalities matches the graph? (1 point)
-10
-0
10
1. x>-3
2. x<-3
3. y>-3
4. y<-3
Given:
The graph of an inequality.
To find:
The inequality.
Solution:
From the given graph it is clear that the boundary line is a vertical line parallel to y-axis at the distance of 3 units from the left of y-axis. So, the equation of boundary line is
[tex]x=-3[/tex]
Now, the shaded portion lies on the left of the boundary line. It means the values which are less than 0 are included in the solution set.
The boundary line is a dotted line. So, x=-3 is not included in the solution set.
So, the required inequality is
[tex]x<-3[/tex]
Therefore, the correct option is B.
PLEASE HELP, TWENTY POINTS PLUS BRAINLIEST
Write an explicit function to represent the following sequence.
3,9, 27, 81,...