Answer:
2x⁴+x³-x²+54x+56
Step-by-step explanation:
Given the expression length of dylan room = (x² – 2x + 8) and width = (2x² + 5x – 7), assuming the shap of the room is rectangular in nature, the formula for calculating area of a triangle is given as;
Area of rectangle = Length *Width
Area of the rectangle = (x² – 2x + 8)(2x² + 5x – 7)
Area of the rectangle = x²(2x² + 5x – 7) - 2x (2x² + 5x – 7) + 8(2x² + 5x – 7)
= (2x⁴+5x³-7x²)-(4x³+10x²-14x)+(16x²+40x-56)
expanding the bracket
= 2x⁴+5x³-7x²-4x³-10x²+14x+16x²+40x-56
Collecting the like terms;
= 2x⁴+5x³-4x³-7x²-10x²+16x²+40x+14x+56
= 2x⁴+x³-x²+54x+56
Hence, the expression that represents the area (lw) of Dylan's room is 2x⁴+x³-x²+54x+56
Answer:
2x^4+ x^3 - x^2 + 54x - 56 expression represents the area of Dylan’s room
Step-by-step explanation:
C on edge :)
HELP ME PLEASSSSEE On a winter morning, the temperature before sunrise was -10℉. The temperature then rose by 1℉ each hour for 7 hours before dropping by 2℉ each hour for 3 hours. What was the temperature, in degrees Fahrenheit, after 10 hours?
Answer:
3 degrees F
Step-by-step explanation:
if the temperature rose 1* for 7 hours, times 1 by 7. which is 7 and add to -10. which is -3. then, since the temperature rose by 2* for 3 hours, times 2 by 3 which is 6 and add to -3, which is 3.
i hope this helped?
Ozzie's Mother bought an assortment of greeting cards while she was at the bookstore. She bought twice as many birthday cards as anniversary cards. She bought 2 fewer anniversary cards than general greetings cards, but 2 more anniversary cards than get well cards. If she bought 2 get well cards, how many cards did she buy in all?
Brainlist
Answer:
20
Step-by-step explanation:
2 get well cards
4 anniversary cards
6 greeting cards
8 birthday cards
Eight people are going for a ride in a boat that seats eight people. One person will drive, and only three of the remaining people are willing to ride in the two bow seats. How many seating arrangements are possible?
Answer:
720 seating arrangments
Step-by-step explanation:
There are eight people but driver is always the same so we only have to deal with combinations of the other 7 seats.
the combination of the five seats has 5! times 2 combinations for each of the 3 passengers willing to ride in the two boat seats thus the total number of different seating arrangements is 5! times 3! or 720
hope this helps :)
Using the Fundamental Counting Theorem, it is found that there are 5760 possible seating arrangements.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
For the driver, there are 8 outcomes, hence [tex]n_1 = 8[/tex].For the bow seats, there are [tex]n_2 = 3 \times 2 = 6[/tex] outcomes.For the other 5 seats, there are [tex]n_3 = 5![/tex] possible outcomes.Hence:
[tex]N = 8 \times 6 \times 5! = 5760[/tex]
There are 5760 possible seating arrangements.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
If the quadratic formula is used to solve 2x^2 - 3x - 1 = 0, what are the solutions?
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
[tex]2x-3x-1=0\\(2x-3x)+(-1)=0\\-x-1=0\\-x-1+1=0+1\\-x=1\\\frac{-x}{1}=\frac{1}{-1}\\ x=-1[/tex]
I'LL GIVE BRAINLIEST AND THANKS -SOLVE THE QUADRATIC EQUATION
Answer:
x = -1.47, 1.14
Step-by-step explanation:
Quadratic Formula: [tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
We are given a = 3, b = 1, and c = -5. Simply plug it into the Quadratic Formula:
Step 1: Plug in variables
[tex]x=\frac{-1+/-\sqrt{1^2-4(3)(-5)} }{2(3)}[/tex]
Step 2: Solve
[tex]x=\frac{-1+/-\sqrt{1+60} }{6}[/tex]
[tex]x=\frac{-1+/-\sqrt{61} }{6}[/tex]
Step 3: Plug into calculator to evaluate into decimals
You should get x = -1.46837 and 1.13504
Answer:
1.13 and -1.46
Step-by-step explanation:
Our quadratic equation is: 3x²+x-5=0
The method we will use is te dicriminant method
let Δ be the discriminant:
a= 3b= 1c= -5Δ = b²-4*a*c
Δ= 1²-4*3*(-5)Δ= 1+60Δ=6161 is a positive number so we have solutions x and x':
x= (-b-√Δ)/2*a = (-1-√61)/2*3 = [tex]\frac{-1-\sqrt{61} }{6}[/tex] = -1.46 x'= (-b+√Δ)/2*a = (-1+√61)/2*3 =[tex]\frac{-1+\sqrt{61} }{6}[/tex] = 1.13so the two solutions are :
-1.46 and 1.13
4x-5 - 2x-1
___ ____
2 6
Reduce the following expression into a single fraction.
Answer:
[tex]\frac{5x - 8}{3}[/tex]
Step-by-step explanation:
Find the LCM of the denominators and then solve:
[tex]\frac{4x - 5}{2} - \frac{2x - 1}{6} \\\\[/tex]
[tex]\frac{4x - 5}{2} - \frac{2x - 1}{6} \\\\\frac{3(4x - 5) - 2x - 1}{6} \\\\\frac{12x - 15 - 2x - 1}{6}\\\\\frac{10x - 16}{6}\\\\ \frac{2(5x - 8)}{2 * 3} \\\\ \frac{5x - 8}{3}[/tex]
Joe earned x dollars the first day he worked in December, where x is an integer. For each day after the first that he worked in December, Joe earned twice the amount he earned on the previous day. Did Joe earn less than $35 on the 4th day he worked in December?
(1) Joe earned more than $120 in total for the first five days he worked in December.
(2) Joe earned less than $148 on the 6th day he worked in December.
Answer:
1. Always translate the question stem, set up equations (limit the number of variables) and breakdown the question stem of possible
2. Never overlook the constraints the question provides.
Now the question stem tells us that on the
1st day Joe earned = x
2nd day = 2x
3rd day = 4x
4th day = 8x
Question stem: Did Joe earn less than $35 on the 4th day -----> 8x < 35 ----> x < 4.375
Since x is an integer, the question becomes 'Is x <= 4
Statement 1 : Joe earned more than $120 in total for the first five days he worked in December.
x + 2x + 4x + 8x + 16x > 120
31x > 120 ---> x > 3.9....
This gives us both a YES and a NO since x can be 4 or any integer greater than 4
Statement 2: Joe earned less than $148 on the 6th day he worked in December
32x < 148 ----> x < 4.625
Since x is an integer, x <=4. Sufficient.
hope this helps
-lvr
this is 69 points if you answer please help
Answer:
see below
Step-by-step explanation:
Angle C is equal to the 1/2 the difference of the two arcs
C = 1/2 ( large DC - small DC)
Large DC = ( 360 - 5x - 2) sum of a circle is 360 degrees
Small DC = 5x-2 the central angle is equal to the intercepted arc
C = 1/2 ( 360 - 5x-2 - ( 5x -2)) Angle Formed by Two Intersecting Chords
C = 1/2 ( 360 - 2 ( 5x-2))
Distributing the 1/2
C = 180 - (5x-2)
Replacing the C with 2x+7
2x+7 = 180 - (5x-2)
Add 5x-2 to each side
2x+7 +5x-2 = 180
Antonio is correct
Combine like terms
7x +5 = 180
7x = 175
Divide by 7
x =25
Then solve for A = 5x-2
A = 5*25-2
= 125-2
= 123
List the coordinates of FOUR vertices that create the feasible region on the graph. Submit your answer in the form of FOUR ordered Pairs (x, y)
Answer:
(500,0) , (300,0), (200,200) and (300,200)
Step-by-step explanation:
The region of the graph we are concerned with is that small portion which is shaded.
We need the coordinates that bounds this portion of the graph.
These coordinates are four in number and they are as identified by noticing the four points that surround the portion then making tracings from these points to the x and y axes respectively.
We proceed as follows;
The four points we are looking at in no particular order are;
(500,0) , (300,0), (200,200) and (300,200)
The points having coordinates that have y = 0 are those that are domiciled on the x-axis
We have two of these points which are on the x-axis.
ASAP!!! THIS WORTH 50 POINTS!
Answer:
90 16-oz cases and 30 20-oz cases will maximize resin and time use120 16-oz cases will maximize profitStep-by-step explanation:
Let x represent the number of cases of 16-oz cups produced.
Let y represent the number of cases of 20-oz cups produced.
The limitation imposed by available production time is ...
x + y ≤ 15·8 = 120 . . . . maximum number of cases produced in a day
The limitation imposed by raw material is ...
14x +18y ≤ 1800 . . . . . maximum amount of resin used in a day
__
The point of intersection of the boundary lines for these inequalities can be found using substitution:
14(120- y)+18y = 1800
4y = 120 . . . . . subtract 1680, simplify
y = 30
x = 120 -30 = 90
This solution represents the point at which production will make maximal use of available resources. It is one boundary point of the "feasible region" of the solution space.
__
The feasible region for the solution is the doubly-shaded area on the graph of these inequalities. It has vertices at ...
(x, y) = (0, 100), (90, 30), (120, 0)
The profit for each of these mixes of product is ...
(0, 100): 25·0 +20·100 = 2000
(90, 30): 25·90 +20·30 = 2850 . . . . uses all available resources
(120, 0): 25·120 +20·0 = 3000 . . . . maximum possible profit
The family can maximize their profit by producing only 16-oz cups at 120 cases per day.
Answer:
90 16-oz cases and 30 20-oz cases will maximize resin and time use
120 16-oz cases will maximize profit
Step-by-step explanation:
Sarah serves at a restaurant and makes 20% of what she sells as tips. Her base salary is $10.20an hour. Each hour she sells an average of $60 of food and drinks. She also makes time and a half when she works over 8 hours during a single shift. Her work week contains three 10-hour shifts, one 5-hour shift, and one 11-hour shift. Using the same income deductions as stated in the previous question, what is Sarah’s annual gross income and annual net income.
Sara works 46 hours per week
9 hours are overtime and 37 hours are regular time
pay rate at time and a half: 10.20∗1.5=15.30
regular hours plus overtime pay
37∗10.20=377.40
9∗15.30=137.70
Income due to tips
Total hours worked∗60per hour∗20%
46∗60∗.20=552
Weekly Income=Hourly income + tips
Weekly Income=377.40+137.70+552.00
Weekly Income=1067.10
Annual income=Weekly income∗52
Annual income=55489.20
A container weighs 78.1 kg when it is filled with some cement. The same container weighs 25.5 kg when it is filled with some sand. The mass of the cement is 5 times as heavy as the mass of the sand. Find the mass of the container
Container + cement = 78.1
Container + sand = 25.5
Difference( cement - sand) = 78.1 -25.5 = 52.6
4 x Sand = 52.6
Sand = 52.6/4 = 13.15
Container = 25.5 - 13.15 = 12.35 kg
Nora bought a car last year so that she could drive to work after school. She spent $250 last year for gas. This year she spent $295. Disregarding other factors, what is the inflation rate? 18% 19% 20% 21%
Answer:
here,
money spent in 1st year =$250
money spent in 2nd year=$295
total inflated amount=$295- $250
=$45
Then,
inflation rate= ($45/ $250)×100%
=18%
Corey owns a 50 acre vineyard and every year, depending upon conditions, worries about flooding. Corey wants rainfall amounts to be at most 12 inches per year. Which model is correct?
A: X Greater than or equal to 12?
B: X less than or equal to 12?
C: X less than 12?
Answer:
B: X less than or equal to 12
x≤12
Step-by-step explanation:
Corey owns a 50acre vineyard
Corey wants rainfall amounts to be at most 12 inches per year
Let rainfall=x
Corey wants amount of rainfall (x) to be at most 12 inches per year
x is at most 12 inches per year
In inequality, the appropriate symbol representing “at most” is the “less than or equal to”
(≤) symbol
So, substituting the symbol
We have,
x≤12
B: X less than or equal to 12
What is the answer to 99,200 + 10(18/2)?
Answer:
99,290
Step-by-step explanation:
99,200 + 10(18/2)
= 99,200 + 10(9)
= 99,200 + 90
= 99,290
Which is the length of the hypotenuse of the right triangle? Round your answer to the nearest tenth of a centimeter.
Hint: Pythagorean Theorem: a^2+ b^2 = c^2
Answer:
Length of hypotenuse of given triangle
= sqrt(356) (exact value)
= 18.87 (to 2 decimal places)
Step-by-step explanation:
Using the pythagorean Theorem,
The hypotenuse
c = sqrt(a^2+b^2)
= sqrt(16^2+10^2)
= sqrt(356) (exact value)
= 18.87 (to 2 decimal places)
The length of the hypotenuse of the right triangle is approximately
18.9 cm.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (the base and the height in this case).
Plugging in the given values, we get:
c² = 16² + 10²
c² = 256 + 100
c² = 356
c ≈ 18.9
Rounding the answer to the nearest tenth of a centimeter, we get:
c ≈ 18.9 cm
Therefore,
The length of the hypotenuse of the right triangle is approximately
18.9 cm.
Learn more about the Pythagorean theorem here:
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Find the point Q along the directed line segement from point R (-3, 3) to point S(6, -3) that divides the segment in the ratio 2:1.
Answer:
Step-by-step explanation:
m : n = 2 : 1
R (-3, 3 ) ; x1 = -3 & y1 = 3
S(6 , -3) ; x2 = 6 & y2 = -3
Formula for the point that divides a line m:n = [tex](\frac{mx_{2}+nx_{1}}{m+n} , \frac{my_{2}+ny_{1}}{m+n})[/tex]
[tex]Q(\frac{2*6+1*(-3)}{2+1}, \frac{2*-3 + 1*3}{2+1})\\\\\\Q(\frac{12-3}{3} , \frac{-6+3}{2+1})\\\\\\Q(\frac{9}{3} , \frac{-3}{3})\\\\[/tex]
=Q(3, -1)
Answer:
D.) (3,-1)
Step-by-step explanation:
I got it correct on founders edtell
HURRY I NEED IT NOW!!! What is the solution to this system of equations? x + 2 y = 4. 2 x minus 2 y = 5. (3, Negative 5 and one-half) (3, one-half) no solution infinitely many solutions
Answer:
(3, 1/2)
Step-by-step explanation:
set the equation up
x+2y=4
2x-2y=5
then solve
The correct option is B.[tex](3,\frac{1}{2})[/tex]
Given equations,
[tex]x+2y=4.....(1)\\2x-2y=5.....(2)[/tex]
The standard form for linear equations in two variables is [tex]Ax+By=C[/tex].
On comparing equation 1 and equation 2 with the standard form we get,
[tex]a_{1}=1, b_{1}=2, c_{1}=4\\a_{2}=2, b_{2}=-2,c_{2}=5[/tex]
Here,
[tex]\frac{a_{1} }{a_{2} } =\frac{1}{2} \\[/tex] and [tex]\frac{b_{1} }{b_{2} } =\frac{2}{-2} =-1[/tex]
Since [tex]\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }[/tex], So the given system of equation has a unique solution.
Now Adding equation 1 and 2 we get,
[tex]3x=9\\x=3[/tex]
putting the value of x in equation 1 we get,
[tex]3+2y=4\\2y=1\\y=\frac{1}{2}[/tex].
Hence the required solution of equation is [tex](3,\frac{1}{2})[/tex]. the correct option is B.[tex](3,\frac{1}{2})[/tex]
For more details follow the link:
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Question 8 of 10
A T-shirt vendor is thinking about changing the number of T-shirts he brings to
an event. To make sure he doesn't run out, he plans to bring more of the size
most likely to be sold.
The table shows the number of T-shirts of each size sold at his last event and
the number he had for sale.
Sold
Number for sale
180
Small
126
Medium
220
270
284
315
Large
X-Large
95
135
Which size should he bring more of?
A. Small
B. Medium
C. Large
D. X-Large
Large-size shirts should be brought more of which is more likely to be sold.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Sales Sold
Small 180 126
Medium 220 270
Large 284 315
x-large 95 135
Now,
The percentage of small size sold.
= 126/180 x 100
= 70%
The percentage of medium size sold.
= 220/270 x 100
= 81.5%
The percentage of large size sold.
= 284/315 x 100
= 90%
The percentage of x-large size sold.
= 95/135 x 100
= 70%
Thus,
Large-size shirts are sold more.
Learn more about expressions here:
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Please answer it in two minutes
Answer:
36.33
Step-by-step explanation:
The given figure is pentagon
The sum of angles of polygon is (2n-4)*90 where n is number of sides of polygon
for pentagon number of sides is 5
thus, n = 5
\
sum of angles of pentagon = (2*5-4)*90 = 6*90 = 540
Given angles of pentagon
t, 149 , t+144, 3t -11 , t+40
Thus, sum of all these angles should be equal to 540
t + 149 + t+144 + 3t -11 + t+40 = 540
=> 6t + 322 = 540
=> 6t = 540 - 322 = 218
=> t = 218/6 = 36.33
Thus, t = 36.33
Segment BD is parallel to segment CE. If AB = 4, AC = 6, and AD = 7, what is AE?
Answer:
B. 10.5Step-by-step explanation:
If BD║CE then ΔADB and ΔAEC a similar triangles
so:
[tex]\frac{AE}{AD}=\frac{AC}{AB}\\\\\frac{AE}{7}=\frac{6}{4}\\\\AE=\frac32\cdot7\\\\AE=\frac{21}2\\\\AE=10.5[/tex]
To measure a stone face carved on the side of a mountain, two sightings 700 feet from the base of the mountain are taken. If the angle of elevation to the bottom of the face is 35degreesand the angle of elevation to the top is 38 degrees,what is the height of the stone face
Answer:
Height of stone face is : 56.7 ft
Step-by-step explanation:
Kindly refer to the attached image for the diagram of the given conditions and values.
Let C be the base of mountain.
D be the point from where two sightings are taken.
AB be the stone face.
Angle of elevations:
[tex]\angle BDC =35^\circ\\\angle ADC =38^\circ[/tex]
To find:
Height of stone face = ?
AB = ?
Solution:
We can use trigonometric function of tangent here in two triangles [tex]\triangle BCD\ and\ \triangle ACD[/tex]:
[tex]In\ \triangle BCD :[/tex]
[tex]tan(\angle BDC) = \dfrac{Perpendicular}{Base} = \dfrac{BC}{CD}\\\Rightarrow BC = 700 \times tan35 ..... (1)[/tex]
[tex]In\ \triangle ACD :[/tex]
[tex]tan(\angle ADC) = \dfrac{Perpendicular}{Base} = \dfrac{AC}{CD}\\\Rightarrow AC = 700 \times tan38\\\Rightarrow AB +BC = 700 \times tan38\\\\\text{Using equation (1):}\\\Rightarrow AB + 700 \times tan 35 = 700 \times tan 38\\\Rightarrow AB = 700 \times tan 38-700 \times tan35\\\Rightarrow AB = 700 \times (tan 38-tan35)\\\Rightarrow AB = 700 \times 0.081\\\Rightarrow AB = \bold{56.7}\ ft[/tex]
So, Height of stone face is : 56.7 ft
pls say me the 12th qns
Answer:
Step-by-step explanation:
12) p & q are parallel lines , n is transversal
4z = 108 { corresponding angles are congruent}
Divide both sides by 4
z = 108/4
z = 27°
n & m are parallel lines , p is transversal
3y = 4z { corresponding angles are congruent}
3y = 4 * 27
y = [tex]\frac{4*27}{3}[/tex]
y = 4*9
y = 36°
n & l are parallel lines, q is transversal
6x = 108 { corresponding angles are congruent}
x = 108/6
x = 18°
Help me pls, it’s for right now
Answer:
c
Step-by-step explanation:
Please help ASAP. Determine an equation of a quadratic function with the characteristics of its graph. Coordinates of the vertex: V(5,4) ; y intercept 79
Answer: y = 3(x - 5)² + 4
Step-by-step explanation:
Use the Vertex form: y = a(x - h)² + k to find the a-value
Given: (x, y) =(0, 79) and (h, k) = (5, 4)
79 = a(0 - 5)² + 4
79 = 25a + 4
75 = 25a
3 = a
Input a = 3 and (h, k) = (5, 4) into the Vertex form:
y = 3(x - 5)² + 4
1. What number comes next in this sequence?
483, 759, 264, 837,?
A) 487
B) 592
C) 375
D) 936
Please answer ASAP 15 points for this one
Select the correct answer. Write (21 − 4i) − (16 + 7i) + 28i as a complex number in standard form. A. 5 + 39i B. 5 + 17i C. 5 − 39i D. 5 − 17i
Answer:
b. 5 + 17i
Step-by-step explanation:
solve the simultaneous equation
y=x+3
y=7x+1
I'll mark you BRAINLIEST
Answer:
x = 1/3 , y = 10/3
Step-by-step explanation:
Solve the following system:
{y = x + 3 | (equation 1)
y = 7 x + 1 | (equation 2)
Express the system in standard form:
{-x + y = 3 | (equation 1)
-(7 x) + y = 1 | (equation 2)
Swap equation 1 with equation 2:
{-(7 x) + y = 1 | (equation 1)
-x + y = 3 | (equation 2)
Subtract 1/7 × (equation 1) from equation 2:
{-(7 x) + y = 1 | (equation 1)
0 x+(6 y)/7 = 20/7 | (equation 2)
Multiply equation 2 by 7/2:
{-(7 x) + y = 1 | (equation 1)
0 x+3 y = 10 | (equation 2)
Divide equation 2 by 3:
{-(7 x) + y = 1 | (equation 1)
0 x+y = 10/3 | (equation 2)
Subtract equation 2 from equation 1:
{-(7 x)+0 y = -7/3 | (equation 1)
0 x+y = 10/3 | (equation 2)
Divide equation 1 by -7:
{x+0 y = 1/3 | (equation 1)
0 x+y = 10/3 | (equation 2)
Collect results:
Answer: {x = 1/3 , y = 10/3
Answer:
[tex]\boxed{x=\frac{1}{3} }[/tex]
[tex]\boxed{y=\frac{10}{3} }[/tex]
Step-by-step explanation:
[tex]y=x+3\\y=7x+1[/tex]
Plug y as x+3 in the second equation.
[tex]x+3=7x+1\\7x-x=3-1\\6x=2\\x=\frac{1}{3}[/tex]
Plug x as 1/3 in the second equation.
[tex]y=7(\frac{1}{3} )+1\\y=\frac{7}{3}+1\\y=\frac{10}{3}[/tex]
By visual inspection, determine the best-fitting regression model for the
scatterplot.
Need help ASAP please
Answer:
its a! sorry im so late
Step-by-step explanation:
HELP!!!!!
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Enter the correct answer.
Answer:
1
Step-by-step explanation:
identify two points on the graph:
1. (0, 4)
2. (-2, 2)
use slope formula: (y² - y¹) / (x² - x¹)
1. (2 - 4) / (-2 - 0) = -2 / -2 = 1
slope = 1