Answer:
{x,y}={60,35}
Step-by-step explanation:
// Solve equation [2] for the variable x
[2] x = y + 25
// Plug this in for variable x in equation [1]
[1] (y +25) + y = 95
[1] 2y = 70
// Solve equation [1] for the variable y
[1] 2y = 70
[1] y = 35
// By now we know this much :
x = y+25
y = 35
// Use the y value to solve for x
x = (35)+25 = 60
Answer:
x=57
y=38
Step-by-step explanation:
(1): x+y=95
(2): y=2/3x
substitute y=(2/3)x in equation (1):
x+(2/3)x=95
Multiply both sides by 3
3x+2x=285
5x=285
Divide both sides by 5
x=285/5
x=57
substitute x=57 in equation (2):
y=2/3×57=38
hence: x=57 , y=38
A rectangles length is 8 feet longer than twice its width. The rectangles perimeter is 316 feet. Find the rectangles length and width.
The rectangles length is ______ feet, and its width is_____feet.
Answer:
length= 108 feet,
width= 50 feet
Overview of steps:
Define variablesForm two equations using given informationSolve for one variable through substitution/ eliminationSolve for the other variable through substitutionWorking:
Let the length and the width of the rectangle be L and W feet respectively.
L= 2W +8 -----(1)
Perimeter= 2(length) +2(width)
316= 2L +2W
2L +2W= 316
Divide both sides by 2:
L +W= 158 -----(2)
Substitute (1) into (2):
2W +8 +W= 158
Simplify:
3W +8= 158
3W= 158 -8
3W= 150
Divide both sides by 3:
W= 150 ÷3
W= 50
Substitute W= 50 into (1):
L= 2(50) +8
L= 100 +8
L= 108
Thus, the rectangle's length is 108 feet, and its width is 50 feet.
The cafeteria sold 15 more turkey sandwiches than ham sandwiches. They sold 63 sandwiches in all. How many ham sandwiches did the cafeteria sell?
Answer:
48
:)
Step-by-step explanation:
63-15 = 48
48+15= 63
help pls don’t know what i’m doing
Step-by-step explanation:
since the polynomial is in the form
+x² - nx - m
we know that we are looking for 2 factors of x (to create x²).
and they must be in the form of
(x + a)(x - b)
to create the negative "m" at the end.
and "b" must be larger than "a" to create the negative "n" in the middle.
let's do the multiplication and compare the parts with our actual expression :
(x + a)(x - b) = x² - bx + ax - ab = x² + (a - b)x - ab
so, we know now in numbers that
-ab = -44
ab = 44
and
a - b = -7
a = b - 7
the short solution here is trial and error with the factors of 44 :
44 = 1×44 = 2×22 = 4×11
ah, only one combination has a difference of the factors of 7 or -7 : 4 and 11.
since b has to be larger (as a - b = -7), we have a = 4 and b = 11
and the factorization of our original expression is
f(x) = (x + 4)(x - 11)
FYI
if there is not such a short list of options to try, we can also go the full formal way :
we can use the second equation as identity in the first equation and get
(b - 7)b = 44
b² - 7b = 44
b² - 7b - 44 = 0
by the way, it is not surprising that it looks the same way as the original expression in x, because the factorization uses exactly the zero solutions for the original expression.
anyway, the formal solution to a quadratic equation of
ax² + bx + c = 0 is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = b (the variable of our equation above)
a = 1
b = -7
c = -44
b = (7 ± sqrt((-7)² - 4×1×-44))/(2×1) =
= (7 ± sqrt(49 + 176))/2 = (7 ± sqrt(225))/2 =
= (7 ± 15)/2
b1 = (7 + 15) / 2 = 22/2 = 11
b2 = (7 - 15) / 2 = 8/2 = 4
based again on the original equations and the fact that b has to be the larger number, we get again (of course) that b1 is the valid solution and
b = 11 and a = 4
For a standard normal distribution, find the approximate value of p (negative 0.78 less-than-or-equal-to z less-than-or-equal-to 1.16). use the portion of the standard normal table below to help answer the question. z probability 0.00 0.5000 0.16 0.5636 0.22 0.5871 0.78 0.7823 1.00 0.8413 1.16 0.8770 1.78 0.9625 2.00 0.9772 22% 66% 78% 88%
The z-probability for the condition -0.78 ≤ z ≤ 1.16 is 66%.
What is a z-score?
A z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
It is given that
-0.78 ≤ z ≤ 1.16
We have to find the p-value corresponding to -0.78 ≤ z ≤ 1.16.
This means, p(-0.78 ≤ z ≤ 1.16)
p(0.78≤ z ≤1.16) can be written as p(z ≤ 1.16) - p(z ≤ -0.78)
p(0.78≤ z ≤1.16) = p(z ≤ 1.16) - (1-p(z ≤ 0.78))
p(0.78≤ z ≤1.16) = p(z ≤ 1.16) -1 + p(z ≤ 0.78)
From the standard normal table,
p(z ≤ 1.16)=0.87698
p(z ≤ 0.78)=0.78230
So, p(0.78≤ z ≤1.16)= 0.87698-1+0.78230
p(0.78≤ z ≤1.16) = 0.65928≈0.66 i.e 66%
Therefore, the z-probability for the condition -0.78 ≤ z ≤ 1.16 is 66%.
To get more about standard normal distribution visit:
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Answer:
66%
Step-by-step explanation:
hopes this helps!! have an amazing day <3
ILL GIVE BRAINLIEST #20 please, how do I know if it’s similar or not? Is it similar
Answer:
Step-by-step explanation:
20.
itis not similar as ratio of corresponding sides is not equal.
4/2=2
6/4=3/2
8/6=4/3
2≠3/2≠4/3
Which expressions are equivalent to the one below? Check all that apply.
9^x
Answer: B, C, E, and F.
Step-by-step explanation: All these answers I picked all simplify to 9^x. A and D both don't simplify to that as both are 27^x.
Hope this helps! :)
Factor the following polynomials by finding a GCF
Answer:
Step-by-step explanation:
To factor out a GCF from a polynomial we first need to identify the GCF of all the terms, this is the part that goes in front of the parenthesis, then we divide each term by the GCF, the answer is what is left inside the parenthesis. This is shown in the following examples Example 3. 4x2−20x+16 4x2 −20x16GCF is4, divide each term by4
Urgent. Please show all work
Answer:
[tex]\displaystyle f'(x) = \frac{4}{x^2}[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Differentiation
DerivativesDerivative NotationThe definition of a derivative is the slope of the tangent line: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x) = -\frac{4}{x}[/tex]
Step 2: Differentiate
[Function] Substitute in x: [tex]\displaystyle f(x + h) = -\frac{4}{x + h}[/tex]Substitute in functions [Definition of a Derivative]: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{-\frac{4}{x + h} - \big( -\frac{4}{x} \big)}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{4}{x(x+ h)}[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle f'(x) = \frac{4}{x(x+ 0)}[/tex]Simplify: [tex]\displaystyle f'(x) = \frac{4}{x^2}[/tex]∴ the derivative of the given function will be equal to 4 divided by x².
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
After years of smoking, the most powerful influence for their continuing to smoke is: Please help for Health and make sure you're right
A. To ease anxiety or stress.
B. To satisfy their desire for the taste of a cigarette.
C. To give their hands something to do.
D. Their addiction to nicotine.
Answer:
D. Their addiction to nicotine.
Explanation:
Nicotine is a type of drug which makes it tough for smokers to stop smoking and this is what makes them attracted most. The more nicotine you inhale, the better you feel - giving pleasure. Nicotine is harmful for the body and increases possibility of heart attack.
can someone pls help
Answer 48°
l hope na tama ang sagut ko
80 points. Help please.
4. Test the residuals of two other points to determine how well the line of best fit models the data.
Slope is y = 1x + 2
Answer:
[tex]\red{ \rule{10pt}{9999999pt}}[/tex]
Step-by-step explanation:
[tex]\red{ \rule{10pt}{999999pt}}[/tex]
You did it! please don't delete
Abdul has a rope that is 6 meters long. He cuts away a piece that is 2.39 meters long. How long is the remaining piece of rope?
6 - 2.39 = 3.61 meteres remaining for the rope
find the volume of the solid
Kyle has a notebook for each of his 13 classes he puts 5 stickers on each notebook there are 10 stickers on each sheet how many sheets of stickers will Kyle need?
[tex][Hello,BrainlyUser][/tex]
[tex]\left[Here\; your \;Answer\; below}\right][/tex]
Answer:
7
Step-by-step explanation:
Given;
Kyle has 13 notebooks (1 for each class) and he puts 5 stickers on each one
Solve;
If Kyle wants to put 5 stickers on each of his 13 classroom notebooks, then we simply multiply 5*13 to find out how many stickers he will use in total.
5 * 13 =65
Kyle used 65 stickers total.
Then, to find out how many sheets he used, we will simply divide the total amount of stickers (T) by the amount of stickers on a sheet (S).
T = 65
S = 10
65/10 = 6.5
Thus, He will need 7 sheets, but will only use 6 and a half sheets.
[CloudBreeze]
The school drama club sold 2,400 tickets to a play and made $9,000 from the ticket sales. Student tickets,
X, were $3 and adult tickets, y, were $5.
Create a system of two equations to represent this situation.
Hi!
Given:
total tickets = 2,400 total profit = 9,000student tickets cost $3adult tickets cost $5x = student ticketsy = adult ticketsThe first equation we can make can use the total number of tickets. The total number of tickets would be equal to the number of student tickets plus the number of adult tickets, correct? Therefore:
[tex]x+y=2400[/tex]
Now, the second one can use the profit and the price of each ticket. The number of student tickets multiplied by 3 (for the price) plus the number of adult tickets multiplied by 5 would be equal to the total profit. Hence:
[tex]3x+5y=9000[/tex]
Therefore, your system of equations is:
[tex]x+y=2400[/tex]
[tex]3x+5y=9000[/tex]
If 12 out of 15 people recycle aluminum cans, how many people out of 1 million would you expect to recycle? ( Answer fast please!! Due in 20 minutes thank you !)
Answer:
800,000 people
Step-by-step explanation:
20 emails in 5 minutes……. Unit rate
What are the area and perimeter of the figure? Include the units in your answers (units, square units, or cubic units). The area is . The perimeter is . Skip to navigation
Answer:
howdy, I THINK it's 27
Step-by-step explanation:
because I searched it up
help hurry! 10 points
Can someone help me with this?
Answer:
Example 1 = ?
Example 2 = x = 3.22
Example 3 = 10.963 = x
Example 4 = ?
Twelve trees are equally spaced along one side of a straight road. The distance from the first tree to the sixth tree is 60 feet. What is the distance in feet between the first and last trees?
Answer:
120 feet
Step-by-step explanation:
because 60 feet x2 is 120
The distance between the first and the last tree is 132 feet.
What is an Arithmetic Progression?An arithmetic progression(A.P.) is a series, where the difference between consecutive numbers is constant.
The first term of an A.P. is denoted by a, and the common difference is denoted by d.
The nth term of an A.P. series is found using the formula:
aₙ = a + (n-1)d.
The sum of n terms of an A.P. series is found using the formula:
Sₙ = (n/2)(2a + (n-1)d)
How do we solve the given question?We are said that every tree is equally spaced. So the distance between the trees is in arithmetic progression.
With the first tree being at 0 feet from itself, our a = 0.
The distance from the first tree to the sixth tree is 60 feet, so we can say that the 6th term is 60
6th term = a + 5d
or, 60 = 0 + 5d
or, d = 60/5 = 12 feet.
To find the distance between the first tree and the last tree(12th tree), we will find the 12th term of the series,
12th term = a + (12-1)d = 0 + 11(12) = 132 feet.
∴ The distance in feet between the first and last tree is 132 feet.
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Calculate the volume. Round your answers to the nearest tenth if necessary.
Answer:
need to see problem please
Find the missing value for x.
Answer:
x is 62 degrees i think
Step-by-step explanation:
wow how do i know how to do this. ANYWAYS:
since it says that the whole two angels is 152 and that one of the angles is 90 degrees we can write the equation:
90 + x = 152
x = 62
you may ask "but thats the degree of the angle next to 90.." but it is also x because it is parallel (i think thats the word)
Write a+5 as a difference.
Answer:
+(a-5)
Step-by-step explanation:
Take out the positive sign as a common factor and change the middle positive sign to negative.
abcdef is a regular hexagon of side 6 cm. Find the area of the shaded region.
Answer:
36√3 cm2 is the answer you should be expected
Lamar filled a measuring cup with 3 cups of vegetable oil. Then he poured 1 4/5 cups of the oil into a frying pan. How much oil is left in the measuring cup?
Answer:
1, 1\5 left
Step-by-step explanation:
need rn! worth 25 points!!!
~Shoto Todoroki here~
Use the form a cos(bx−c)+d
to find the amplitude, period, phase shift, and vertical shift.
Amplitude: 3/4
Period: 2π/3
Phase Shift: None
Vertical Shift: 4
hope this helps :D
If f(1) = 0, what are all the roots of the function f (x) = x cubed 3 x squared minus x minus 3? Use the Remainder Theorem. X = –1, x = 1, or x = 3 x = –3, x = –1, or x = 1 x = –3 or x = 1 x = –1 or x = 3.
All the roots of the provided function If f(1) is equal to the zero are -3, -1 and 1.
What is polynomial?
Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).
The function given in the problem is,
[tex]f(x)=x^3+3x^2-x-3[/tex]
If f(1) = 0
[tex]f(1)=(1)^3+3(1)^2-(1)-3\\f(1)=1+3-1-3\\f(1)=0[/tex]
Thus, (x-1) is one of the factor of polynomial. Equate the polynomial equal to the zero, to find other roots as,'
[tex]x^3+3x^2-x-3=0\\x^2(x+3)-1(x+3)=0\\(x+3)(x^2-1)\\(x+3)(x+1)(x-1)=0[/tex]
Equate all the groups to zero to find the roots as,
[tex]x+3=0, x=-3\\x+1=0, x=-1\\x-1=0, x=1[/tex]
Hence, all the roots of the provided function If f(1) is equal to the zero are -3, -1 and 1.
Learn more about polynomial here;
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Answer: B
Step-by-step explanation:
Every angle in the polygon is a right angle. The area of the polygon is 426 in2
What is the length of the left side of the polygon? Show your work
Plss help
The length of the missing side of the polygon with an area of 426 inches² is 31 inches.
PolygonPolygon is a 2-dimensional shape. They are made of straight lines.
Therefore,
area of the polygon = 426 inches²
The composite figure can be divided into two rectangle. Therefore,
area = area of rectangle 1 + area of rectangle 2
area of rectangle = lw
where
l = lengthw = widthTherefore,
let
the unknown side = x
426 = 26 × 11 + (26 - 19) (x - 11)
426 = 286 + 7x - 77
426 + 77 - 286 = 7x
7x = 217
x = 217 / 7
x = 31
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Write an equation for each line.
Answer:
Step-by-step explanation:
Equation of blue line:
blue line is parallel to y-axis
⇒ x = 5
Equation of green line:
Green line is parallel to x-axis.
y = 2
Equation of red line:
At y-intercept x = 0. Point on red line is (0,5)
So, y-intercept = 5
y = mx + b Here, m is slope any b is y-intercept.
y = mx + 5
Now, choose any other point in red line. ((1,7)
Substitute this value in the above equation and we can find m
7 = m*1 + 5
7 - 5 = m
m = 2
y = 2x + 5
Equation of black line:
Black line and red line are parallel and so, they have same slope.
y = 2x + b
y-intercept (0,-6) ; b = -6
y = 2x - 6