Let's let w = the width of the rectangle. If the length is 10 yards less than 3 times the width, then the length is 3w - 10.
How do we find the area? Length times width, right?
So, we have w(3w - 10) = 77. Distributing, we get 3w2 - 10w = 77.
We need to put it all on one side, so we subtract 77 from both sides.
3w2 - 10w - 77 = 0
Now, we have to factor the left side. To do this, we multiply 3(-77) = -231. What are two factors of -231 that add up to -10? How about -21 and 11? -21(11) = -231 and -21 + 11 = -10.
This may not be how you are taught, but we are now going to split -10w into -21w + 11w and plug that into our equation.
Sooooo, now we have 3w2 - 21w + 11w - 77 = 0
Next, we are going to look at the first two terms, 3w2 - 21w. What is common between the two? 3w. Factoring out 3w, we get 3w(w - 7).
Now, the second two terms, 11w - 77. What is common? 11. Factoring out 11, we get 11(w - 7).
Putting all of that together, we now have 3w(w - 7) + 11(w - 7) = 0.
I can explain why and make it more confusing, so I'll just tell you that, since the w - 7 is the same in both parentheses, we keep that as one set of parentheses and combine what's in front into a second set of parentheses.
So, we have (w - 7)(3w + 11) = 0
Lastly, for the left side to equal 0, then either w - 7 and/or 3w + 11 has to equal 0, right?
We pull each out and set them equal to 0.
w - 7 = 0
w = 7
If we plug in 7, we get (7-7)(3(7) + 11) = (0)(21+11) = 0(32) = 0, which is what we want.
3w + 11 = 0
3w = -11
w = -11/3
If we plug -11/3 into the same equation, we'd get 0, again what we want. However, we can't have a negative length! Therefore, -11/3 is out as an answer.
Our width is 7. Since the length is 3w - 10, we plug in 7 and get 3(7) - 10 = 21 - 10 = 11.
Let's check. Length times width = 7(11) = 77. Check!
Solve for x. Justify which angle relationships
you used.
The value of x in the quadrilateral is 112 degrees and the angle relationship is vertical angles.
How to find angles in a quadrilateral?A quadrilateral is a plane figure that has four sides , and also has four corners or vertices. The sum of angles in a quadrilateral is 360 degrees. Examples of quadrilateral are parallelograms, rectangle, square, rhombus etc.
The quadrilateral above has two diagonals that intersect each other. The diagonal AC and BD intersect each other at a points.
The relationship formed are vertically opposite angles. Vertically opposite angles are congruent.
Hence, the sum of angles in a point is 360 degrees.
Let's find x as follows;
2x + 68 + 68 = 360
2x = 360 - 136
2x = 224
x = 224 / 2
x = 112 degrees.
Therefore,
x = 112 degrees
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A pump fills a pool at a constant rate. At the end of 12 minutes it has filled 3 gallons of water. Which table represents the relationship between the number of minutes and the number of gallons of water in the pool?
The table D represents the relationship between the number of minutes and the number of gallons of water in the pool.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given:
A pump fills a pool at a constant rate.
At the end of 12 minutes,
it has filled 3 gallons of water.
From the given choices:
The table D represents the relationship between 12 minutes and 3 gallons of water in the pool.
Therefore, the table D is the correct table.
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La reducción de la ecuación 7a - 9b + 6a - 4b quedaría de la siguiente forma:
23a-31b
13a-13b
13a13b
12a-12b
La expresión se puede simplificar para obtener:
7a - 9b + 6a - 4b = 13a - 13b
¿Como simplificar la expresion?Queremos simplificar la siguiente expresión:
7a - 9b + 6a - 4b
Primero, podemos reordenar los terminos así obtenemos:
7a - 9b + 6a - 4b = 7a + 6a - 9b - 4b
Ahora podemos usar a y b como factores comunes, entonces obtendremos:
7a + 6a - 9b - 4b = (7 + 6)a + (-9 - 4)b
= 13a - 13b
Esa es la opcion correcta.
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PLEASE HELP !!!!!!!!!
A seamstress used 4 meters of string to make 20 bows. She used _ of a meter for each bow
Answer:
1/5
Step-by-step explanation:
20/4=5
The reciprocal of 5 = 1/5
The natural numbers are a subset of all of the following sets except the integers numbers whole numbers real numbers irrational numbers
Answer: irrational numbers
Step-by-step explanation:
By definition, natural numbers are rational numbers.
Graph the functions f(x) = -6x+2 and g(x) =-2^x^+^2 + 6 whst are the solutions of the equation -6x+2=-2^x^+^2 +6
The solution of the system of equation -6x + 2 = -2^{x + 2} + 6 is equal to the ordered pair (0, 2).
How to graph the solution to this system of inequalities?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
f(x) = -6x + 2 ......equation 1.
g(x) = -2^{x + 2} + 6 ......equation 2.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (0, 2)
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The owner increases the sale price by the same percent that you found in part a when he buys jackets for $45 and sells them. How many jackets must the owner buy for the total jacket sales to be at least $250?
Answer:
5 jackets
Step-by-step explanation:
Answer:
The owner must buy 6 jackets
Step-by-step explanation:
$45x [tex]\geq[/tex] $250
x [tex]\geq[/tex] 250/45
x [tex]\geq[/tex] 5.55555.....
There can't be a decimal amount of jackets
What are the coordinates of point B?
50 points not to each im low on points?
slope
it has 3 on side and i have done this plenty of tjmes to know
The Singh family ordered a large pizza with a diameter of 16 inches for dinner. If one of the members of the family ate one eighth of the pizza, how many square inches of pizza are remaining? Use 3.14 for π.
A. 200.96 square inches
B. 175.84 square inches
C. 100.48 square inches
D. 25.12 square inches
Answer:
B. 175.84 square inches
Step-by-step explanation:
The pizza is shaped like a circle
Area of a circle = π r² where r is the radius
r = d/2 where d = diameter
Here d = 16 in
r = 16/2 = 8
Total area of pizza = π · 8² = 64 π
If 1/8th of the pizza was consumed balance = 1-1/8 = 7/8
7/8 of the total area = 7/8 x 64π = 56π = 175.84 square inches
This is the area of the remaining portion of the pizza
K
Factor out the greatest common factor.
3x³+18x²-12x
3x³ +18x²-12x=(Type your answer in factored form.)
The greatest common factor is 3x.
What is Greatest Common Factor?A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common.
For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4.
Given:
3x³+18x²-12x
First, factorize each term of Expression
3x³ = 3. x . x . x
18x² = 3 . 3 . 2. x .x
12x =
So, 3x³+18x²-12x
= 3. x . x . x + ( 3 . 3 . 2. x .x ) - (2 . 2. 3 . x)
= 3x ( 3x² + 6x - 4)
Hence, the GCF is 3x.
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3 is the same as the sum of times a number and -3
A. 3+ (-3)
B.
3+ (-3x)
C. 3+ (-x) = -3
-
D. 3+ (-¹/2) = - 3x
-
The equation is 3 = 3x + (-3) which represents the given statement "3 is the same as the sum of times a number and -3".
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
Let the x represents the number.
The statement is given in the question, as follows:
3 is the same as the sum of times a number and -3
As per the given statement, we can write the algebraic form as
3 = 3x + (-3)
Thus, the equation is 3 = 3x + (-3) which represents the given statement.
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please help
You charged $800 on a credit card and it has an interest rate of 12% APR. You make a payment of $200, how much is your TOTAL BALANCE after one month?
1. $600
2. $672
3. $608
4. $896
The interest charge after one month can be calculated by multiplying the balance by the monthly interest rate, which is 12% divided by 12 months, or 0.12 / 12 = 0.01. The balance after one month would be:
$800 * (1 + 0.01) = $808
The total balance after one month and after making a $200 payment would be:
$808 - $200 = $608
So, the answer is $608.
i need help hurry pls
The value of w = 16. The number 24 has a place value of two due to the presence of two full sets of tens.
What is meant by value?The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value.Value is concerned with how much something is worth, whether in monetary terms or in terms of significance. It can mean "identify how much something is worth" like a reward valued at $200 or it can indicate "hold something in high esteem" like "I value our friendship."The occurrence of two complete sets of tens gives the number 24 its place value of two.Let the be ST = RU = PQ
S T = w, RU= -3w + 44, and PQ = -5w + 68
Then by simplifying the above equation we get,
(w) + (-3w + 44) + (-5w + 68) = 0
w - 3w + 44 - 5w + 68 = 0
Group like terms
w - 3w - 5w + 44 + 68 = 0
Add similar elements: w - 3w - 5w = -7w
-7w + 44 + 68 = 0
Add the numbers: 44 + 68 = 112
-7w + 112 = 0
Move 112 to the right side
-7w = -112
Divide both sides by -7
[tex]$\frac{-7 w}{-7}=\frac{-112}{-7}[/tex]
Then we get,
w = 16
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The value of w in the given trapezoid is 18.4.
What are the properties of trapezium?The following characteristics apply to a trapezium:
Similar to other quadrilaterals, the trapezium's four angles add up to 360°.
Two of a trapezium's sides are parallel, whereas the other two aren't.
Regular trapezium diagonals are divided by one another.
In a trapezium, the mid-length segment's is equal to half the total length of the parallel bases.
A trapezium created by two parallel sides and one non-parallel side has two pairs of neighbouring angles that add up to 180 degrees.
We know that the length of the mid-segment is equal to half the sum of the parallel bases, in a trapezium.
Thus,
TS +PQ = 1/2 (UR)
w - 5w + 68 = 1/2 (-3w + 44)
2(-4w + 68) = -3w + 44
-8w + 136 = -3w + 44
136 - 44 = -3w + 8w
92 = 5w
w = 18.4
Hence, the value of w in the given trapezoid is 18.4.
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Find P(x)=1−2x2−3x3+4x
when x=2
Answer:
-75
I hope this helps,but I think to answer this question you have to replace the x with 2
6. Calculate the total monthly cost including another
$300 per month for taxes and another $150 per
month for insurance
Answer:
450 plus whatever other costs there are if there are any
Step-by-step explanation:
300+150=450 so it is 450 plus any other ammount of money you must pay if any
Find the equation, in standard form, of the line passing through the point (0,-3) and parallel
to x-5y = 75.
The equation in standard form when the line is passing through point (0,-3) and parallel to x - 5y = 75 is 5y - x + 15
What is equation of a straight line ?
Equation of straight line as follows , y = mx + b
where m is the slope of line.
Given equation ,
x - 5y = 75
and the points are (0,-3)
First lets find the slope of a line
we get,
x - 5y = 75
5y = x - 75
y = 1/5 x - 15
m = 1/5
Here the point (0,-3) and slope m = 1/5
Therefore,
The equation of the line
y + 3 = 1/5 (x-0)
5y + 15 = x
5y - x + 15
Therefore, The equation in standard form when the line is passing through point (0,-3) and parallel to x - 5y = 75 is 5y - x + 15
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Please use the law of sines to show me how to solve the triangle please. Thank you .
Answer:
its 47.8 degrees
Step-by-step explanation:
y=-4/5x-2 standard form
Answer:
[tex] y = - \frac{5}{4}x - \frac{5}{2} [/tex]
Step-by-step explanation:
Don't know if it's right but yeah that's what I got.
first interchange x and y second swap the the sides of the equationthird multiply both sides of the equation by 55th move the constant to the right-hand side and change its sign Divide both sides of the equation by -4Find the value of c. Round to the nearest tenth
The value of x is 24.2.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
From the figure,
Base = 22
Hypotenuse = x
Cos Ф = Base / Hypotenuse
Now,
Cos 24 = 22 / x
0.91 = 22/x
x = 22/0.91
x = 24.18
x = 24.2
Thus,
x is 24.2.
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help!!!!!!!!!!!!!!!!!!!!!!!!
''The planets farthest from the Sun have the coolest surface temperatures" is the accurate statement.
Which statement accurately describes the relationship between the surface temperature of the planets and their distances from the Sun?The amount of energy received from the Sun decreases with increasing distance, so the planets farthest from the Sun receive the least energy and therefore have the coolest surface temperatures.
This can be seen in our solar system, where the outer planets (Mars, Jupiter, Saturn, Uranus, and Neptune) are colder than the inner planets(Mercury, Venus, and Earth)
Therefore, the statement "The planets farthest from the Sun have the coolest surface temperatures" is accurate.
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The graph shows the location of the entrance to a state park. Each unit on the graph represents 1 kilometer. Rodrigo uses the graph to locate a waterfall. The waterfall is located 3 kilometers to the left and 4 kilometers down from the park entrance. Rodrigo says the ordered pair for the waterfall is (3,9). Use the drop-down menus to explain Rodrigo's error.
The location of the waterfall on the graph will be (3,1). Instead of going down down, Rodrigo goes 4 units upward direction.
How to interpret Cartesian Coordinates?Coordinates are defined as a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x-axis (horizontal) and y-axis are the two axes that make up a coordinate plane (vertical).
Given that the location of the entrance is at (6, 5).
To reach the waterfall, you need to go 3 km to the left and 4 km down from the park entrance.
The x-coordinate decreases to the left side of a point and increases to the right side of a point.
The y-coordinate decreases to a downward point and increases upward a point.
The x-coordinate of the waterfall is 6 - 3 =3
The y-coordinate of the waterfall is 5 - 4 = 1.
The coordinate that represents the location of a point is (3,1).
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Find the value of c. Round to the nearest tenth
The value of the x for the given triangle is 30.67.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given a right triangle,
the base angle is 61° and the length of the base is 17
using tangent to find the value of x
tanФ = perpendicular/base
here base = 17
perpendicular = x
Ф = 61°
tan61 = x/17
x = 17tan61
x = 30.67
Hence the value of x is 30.67.
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The points O(4,4), P(-4,0), Q(-2,-4), and R(6,0) form quadrilateral OPQR.
On solving the provided question, we can say that none of the segments are parallel or perpendicular, and they are all different lengths. The image is a quadrilateral scalene figure.
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
FG: slope: -4/5, length: √41 ≈ 6.40
GH: slope: -5, length: √26 ≈ 5.10
HI: slope: -1, length: 3√2 ≈ 4.24
IF: slope: 4, length: √17 ≈ 4.12
None of the segments are parallel or perpendicular, and they are all different lengths. The image is a quadrilateral scalene figure.
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Equation of the thine that passes through the point (-6,-8) and is parallel to the line x-2y=6
The rquired equation of the line is x + 2y = - 10
Slope-intercept form of a line:The slope-intercept form of a line is given by
y = mx + cWhere m = slope and c = y-intercept
Note: The slope of two parallel lines will have the same slope
Here we have
The point (-6, -8) and the line x - 2y = 6 --- (1)
Let the equation y = mx + c ---- (2) is the equation of the line that passes through (-6, -8) and parallel to x - 2y = 6
As we know the parallel lines will have the same slope
=> Slope of line (1) = Slope of line (2)
Here x - 2y = 6
=> 2y = - x + 6
=> y = -x/2 + 3 which is in the form of y = mx + c
=> Slope of line = - 1/2
Therefore, the Slope of lines (2) = -1/2
=> y = (-1/2)x + c
=> 2y = -x + 2c --- (3)
Given that line passes through (-6, -8)
=> 2(-8) = - (-6) + 2c
=> - 16 = + 6 + 2c
=> 2c = -10
=> c = -5
=> y = -x/2 + (-5)
=> y = -x/2 - 5
=> 2y = - x - 10
=> x + 2y = - 10
Therefore,
The required equation of the line is x + 2y = - 10
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together, teammates Pedro and Ricky got 2665 base hits last season. Pedro had 275 more hits than Ricky. How many hits did each player have?
The number of hits by each player are 1195 and 1470 hits, respectively
How to determine the number of hits by each playerLet's call the number of hits that Ricky got "x".
Then, Pedro got x + 275 hits.
The total number of hits for both players is x + (x + 275) = 2665
Solving for x, we get 2x + 275 = 2665
Subtracting 275 from both sides,
We get 2x = 2665 - 275 = 2390
Dividing both sides by 2,
We get x = 2390 / 2 = 1195
So Ricky got 1195 hits and Pedro got 1195 + 275 = 1470 hits.
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Find the measure of the three missing angles in the parallelogram below.
The measure of the angles of the parallelogram are: x = 90 degrees, y= 122degress and z=90 degrees
What is a parallelogram?A parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides
Remember that the opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
This implies that y + 58 = 180
Making y the subject of the relation
y=180-58
y=122⁰
Also, since the other two opposite angles are not given, then it means that x=y = 180/2 = 90
this therefore means that x= 90, y= 122 and z= 90 degrees
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Lisa is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.25 . If the flight is on time, the probability that her luggage will make the connecting flight is 0.8 , but if the flight is delayed, the probability that the luggage will make it is only 0.65. Suppose you pick her up at the Denver airport and her luggage is not there. What is the probability that her first flight was delayed?
Answer:
The probability is 0.33
Step-by-step explanation:
Please find the attachment for detail
Mrs. Mortlock uses a calculator program to select students at random to answer questions during class. Each of the 28 students in her class is equally likely to be chosen every time she runs the program. Suppose Mrs. Mortlock runs the program for five different questions.
(a) In how many different ways can the program select which students will answer the five questions?
(b) How many of the selections in part (a) include 5 different students?
a) 17210368 different ways can the program select which students will answer the five questions
b) 11,793,600 different ways.
What is Permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Given:
Each of the 28 students in her class is equally likely to be chosen every time she runs the program.
a) The number of ways can the program select which students will answer the five questions
= [tex]28^5\\[/tex]
= 17210368
b) using Permutation
[tex]P^{28}_2[/tex] = 28! / (28-5)!
= 28! / 23!
= 28 x 27 x 26 x 25 x 24 x 23! / 23!
= 11,793,600
So, there are 11,793,600 different ways.
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I'll give you brainliest and extra points if it's right! :)
Answer:
Answers Below
Step-by-step explanation:
[tex]area = \frac{1}{2} (p \times a)[/tex]
[tex]perimeter = 5s[/tex]
The ratio of the side lengths, yellow to green
We see yellow is 36 and green is 60, so we just put that slash mark in between as indicated in the directions, giving us
36/60. We can reduce this to it's simplistic form of 3/5
The ratio of the perimeters, yellow to green.
To find the perimeter, we multiply the side by 5
Yellow; 36x5= 180
Green; 60x5= 300
We put that ratio slash... 180/300. Reducing it comes out to 90/150 > 30/50 > 3/5 also...
And that's because the polygons are similar.
Since the polygons are similar... what would be the ratio for the areas...
Yep, 3/5
Last is to find the area of the green.
The yellow is 45 and the ratio is 3/5. We can write the equation as a ratio
[tex] \frac{45}{x} = \frac{3}{5} [/tex]
Now if we cross multiply;
[tex](45)(5) = 3x > 3x = 225[/tex]
Last but not least, divide by 3
[tex]x = 75[/tex]
Making the area of the green 75