Answer: 99 sq., meters.
Step-by-step explanation:
Given: For ice rink, Length = [tex]14\dfrac25\text{meters}=\dfrac{14\times5+2}{5}=\dfrac{72}{5}\text{meters}[/tex]
Width = [tex]6\dfrac78\text{meters}=\dfrac{8\times6+7}{8}=\dfrac{55}{8}\text{meters}[/tex]
Now, Area of ice rink = length x width
[tex]=\dfrac{72}{5}\times\dfrac{55}{8}=\dfrac{9}{1}\times\dfrac{11}{1}=99\text{ sq. meters}[/tex]
Hence, the area of the ice rink Mr.Cunningham built = 99 sq., meters.
When a polynomial 2x^3+3x^2+ax+b is divided by (x-2) leaves remainder 2, and (x+2) leaves remainder -2.Find a and b.
p(x) = 2x³ + 3x² + ax + b when divided by x - 2 and x + 2 leaves the remainders 2 , - 2.
Find:Value of a and b
Solution:✯ g(x) = x - 2
⟹ 0 = x - 2 [ g(x) = 0 ]
⟹ x = 2
★ p(2) = 2(2)³ + 3(2)² + a(2) + b
⟹ - 2 = 2 * 8 + 3 * 4 + 2a + b
⟹ - 2 - 16 - 12 - 2a = b
⟹ - 30 - 2a = b -- equation (1)
Similarly,
✯ g(x) = x + 2
⟹ 0 = x + 2
⟹ x = - 2
★ p( - 2) = 2( - 2)³ + 3( - 2)² + a ( - 2) + b
Substitute the value of b from equation (1).
⟹ 2 = 2 * ( - 8) + 3 * 4 - 2a - 30 - 2a
⟹ 2a + 2a = - 16 + 12 - 2 - 30
⟹ 4a = - 24
⟹ a = - 24/4
⟹ a = - 6
Substitute the value of a in equation (1).
⟹ - 30 - 2( - 6) = b
⟹ - 30 + 12 = b
⟹ - 18 = b
Therefore,
a = - 6
b = - 18.
I hope it will help you.
Regards.
Find the reciprocal of 1/2 .
Answer:
.5
Step-by-step explanation:
1/2 = .5
What is the ratio of the blue shapes to all the shapes in the set below?
A: 4:9
B: 5:9
C: 4:5
D: 5:4
Answer:
B
Step-by-step explanation:
Answer:
B. 5:9
Step-by-step explanation:
what is an evaluated expression for -7+6x-4x+3
Answer:
-4+2x
Step-by-step explanation:
-7+3=-4
6x-4x=2x
Answer:
-4 + 2x
Step-by-step explanation:
-7 + (+3) = -4, which is why i included a -4 in the expression
6x - 4x = 2x, which is why i included a 2x in the expression
Thank you . Explain also, please!
Answer: 1/2
Step-by-step explanation:
1. Find the least common denominator (14) and multiply the numerator as much as the denominator
4/14 + 3/14
2. Add the 2 fractions together
4/14 + 3/14 = 7/14
3. Simplify
7/14 divided by 7 = 1/2
The answer is 1/2
what is 67473 divided by 32
Answer:
2108.53 I think it's that lol
Guys please hurry up I need this answer
Point E(-5.3) and point D(-4,-3) are located on the grid. Which measurement is closest to the distance between point E and point D
in units?
Answer:
10.8 units
Step-by-step explanation:
Step-by-step explanation:
To find the distance between two points, use the distance formula.
What is the equation of the line in slope-intercept form?
Enter your answer in the boxes y= blank x + blank
Answer:
-3 + 4
Step-by-step explanation:
Answer:
y= 3/5x + 3. You go up 3 to where the other point is, then go over 5 to reach it. The y-intercept is 3 because that 3 is on the Y axis
Step-by-step explanation:
4)
The temperature dropped 3 degrees every hour for 3 hours. Write an expression and write an
integer to represent the total temperature change.
Answer:
I think the integer that represents the change in temperature is -15.
Un bloque de 2kg es trasladado a lo largo de la superficie lisa por accion de una fuerza f=40N ¿cual es el trabajo realisado por la fuerza "f"y por la fuersa de gravedad para un recorrido de 6m?
Explicación paso a paso:
Workdone = Fuerza * distancia movida en la dirección de la fuerza
Dado
Fuerza f = 40N
Distancia = 6 m
El trabajo realizado por la fuerza F es:
Trabajo hecho = 40 * 6
Trabajo terminado = 240 Nm
El trabajo realizado por la fuerza de la gravedad es el trabajo realizado por el cuerpo de 2 kg:
W = mg
W = 2 * 10
W = 20N
Trabajo realizado = 20 * 6
Trabajo terminado = 120 Nm
What is 1486.377 rounded to the nearest hundredth?
Answer:
1486.38
Step-by-step explanation:
Answer:
1,486.38
Step-by-step explanation:
A bag contains:
4 blue marbles
2 green marbles
1 red marble
A marble is chosen at random from the bag and not replaced. Then, a second marble is chosen from the bag. What is the probability that the first marble was red and the second marble was green?
A) 1/7
B) 1/21
C) 2/49
D) 2/6
Answer:
it is ether B or D cuz
Step-by-step explanation:
4+2+1=7 marbles
(4/1)+(2/1)+(1/1)=7/21
divide 21 by 7 that would = 3
Find the slope and Y-intercept of parallel lines using only (-4,6)
x^2 - x + 6 = 0
how do I solve that?
-23
Step-by-step explanation:
x2−x+6=0
Step 1: Find discriminant with a=1, b=-1, c=6.
b2−4ac
=(−1)2−4(1)(6)
=−23
Answer:
−23
Answer:
no solution
Step-by-step explanation
[tex]x^{2}-x+6=(x^{2}-2.\frac{1}{2}x+\frac{1}{4})+6-\frac{1}{4}=(x-\frac{1}{2})^{2}+\frac{23}{4}[/tex]
see : [tex](x-\frac{1}{2})^{2}\geq 0 => (x-\frac{1}{2})^{2}+\frac{23}{4}\geq 0+\frac{23}{4}>0[/tex]
but x² - x + 6 =0
=> it is unreasonable
Jaxson was filling his pool. When he started, it already contained 486 gallons. He filled it for 95 minutes with water coming out of a hose at a rate of 8.4 gallons per minute. How many gallons of water are in the pool at the end of 95 minutes.Immersive Reader
Answer:
1284 gallons
Step-by-step explanation:
The swimming pool already contained 486 gallons.
Then, Jaxson filled the pool for 95 minutes, so, the total amount of water in the pool at the end of 95 minutes = 486 + filled amount in 95 minutes.
The rate of filling water is 8.4 gallons per minute. i.e
In 1 minute, the amount of water filled = 8.4 gallons.
So, by using the elementary method, in 95 minutes, the amount of water filled = 8.4 x 95 = 798 gallons.
So, the total amount of water in the pool at the end of 95 minutes
=486 + 798 = 1284 gallons.
What is the slope of this graph?
A. 4
B. −14
C. −4
D. 14
Answer:
14 is the correct answer
Step-by-step explanation:
Answer:
A.4
Step-by-step explanation:
start at the y-intercept and work down
In what quadrant is the point (3, -4) located?
Answer:
quadrant IV
Step-by-step explanation:
In the image, these are where each quadrant is and labelled. If you plot ( 3,-4) on the grid, it will end up in quadrant IV.
two sides of a triangle have lengths 11 and 16 what must be true about the length of the third side
Answer: The third side of the triangle must be greater than the sum of sides 11 and 16.
Step-by-step explanation: "Triangle Inequality Theorem." This theorem states that any side of a triangle must be shorter than the other two sides added together.
Please mark this as the brainliest.
A 10 foot ladder leans against a building that is 8 feet off of the ground. At what height would a 25 foot ladder touch the building if both ladders form the same angle with the ground?
Answer:
19.99feetStep-by-step explanation:
The set up will form a right angles triangle:
First we need to get the angle of elevation of the first ladder using SOH, CAH, TOA
The length of the ladder will be the hypotenuse = 10foot
The opposite will be the height of the building = 8ft
Using Sin(theta) = opposite/hyp
sin Theta = 8/10
theta = sin^{-1}0.8
theta = 53.13°
If the length of the ladder is now 25 foot, the height of the building will be calculated as shown;
sin Theta = h/25
sin53.13 = h/25
h = 25sin53.13
h = 19.99feet
Hence the height of the building will be 19.99feet
The distribution of ages of runners in a marathon is approximately normal. The oldest participant was 80 and the youngest was 13. Which of the following statements is true of the mean and median ages of the runners?
Answer:
The actual ages of all runners are needed to decide.
HELPPPPP!!! FIND VALUE OF A PLEASE!!
WILL MARK BRAINLIEST!!
A line with a slope of -2 passes through point (2,5) and (-3,A)
What is A????
-10
10
-15
15
THANK UUU!!
Answer:
A=15
Step-by-step explanation:
slope=(A-5)/(-3-2)=-2
A-5=-2×-5=10
A=10+5=15
The double number lines show the ratio of yards to miles.
How many yards are in 5 miles?
8800
Step-by-step explanation:
Divide 3520 by 2 to get 1760
Then you multiply 5 by 1760 to get 8800
The PTA is trying to raise money for an end of the year carnival for a local
school. They are selling t-shirts, s, for fundraisers. Their revenue equation is
represented by the equation below. As a reminder, the revenue equation
describes how much money is brought in during the fundraiser: r(s) = - .1552 + 30s
;Answer:
The answer is below
Step-by-step explanation:
The PTA is trying to raise money for an end of the year carnival for a local
school. They are selling t-shirts, s, for fundraisers. Their revenue equation is
represented by the equation below. As a reminder, the revenue equation
describes how much money is brought in during the fundraiser: r(s) = - .1552 +30s
Their expenses equation is represented by: e(s) = 3s + 200.
A. Find the value of r(s) = e(s)
I
B. Explain what this means in the context of the problem.
Solution:
The revenue is the amount of money gotten by selling goods and products while expenses is the amount of money spent to produce the goods or products.
The revenue is given as:
r(s) = - 0.1552 +30s
While the expenses is given as:
e(s) = 3s + 200.
Since r(s) = e(s), therefore:
3s + 200 = -0.1552 + 30s
30s - 3s = 200 + 0.1552
27s = 200.1552
s = 7.4
s ≈ 7
At break even the expenses and revenue are equal to each other.
This means that if 7 t shirts are produced then the PTA would be at break even.
Use the figure for Exercises 13-15. Find the measure of the given angle.
112°
430
33°
1710
b
15. C
13. a
14. b
Answer:
a + 112 + 33 = 180 ( sum of interior angles of tria
or a + 145 = 180 - ngle is 180 degrees)
or a = 180 - 145
or a = 35 .
similarily,
c + 43 + 71 = 180
or c + 114 = 180
or c = 180 - 114
or c = 66 .
and ,
a + 71 + b = 180 ( sum of angles in straight line is or, 35 +71 + b = 180 180 degrees)
or , b + 106 = 180
or, b = 180 - 106
or, b = 74 .
Thank me later.
Find the equation of the line.
Use exact numbers.
Y= X+
HELP ASAP
Step-by-step explanation:
using the graph, we can see that the line goes through points
(0, 5) and (3, -1)
this is all we need
[tex]y = mx + b\\ m = \frac{y_2-y_1}{x_2-x_1} = \frac{5-(-1)}{0-3} = -2[/tex]
[tex]y = mx + b\\5 = -2(0) + b\\b = 5\\y = -2x + 5[/tex]
nwjskjnsfnwkfdnmfdn gsdkjmcfnm vnndfjsngdrmdtnrnmdcvkjdfnvf
Answer:
nwjskjnsfnwkfdnmfdn gsdkjmcfnm vnndfjsngdrmdtnrnmdcvkjdfnvf
Step-by-step explanation:
Have a great day
Answer:
gshspisgsgushd surrfvereeers
Step-by-step explanation:
Solve the problem involving systems of lineas equations
1. Your mother bought 20 kilos of mangoes and apple combined. Mango P60.00 per kilo and apple is P40.00 per kilo. If she paid P 1000.00 for 20 kilos how many kilos of each kind mother bought?
(a) If x is number of kilos of mango and number of kilos of apple, then the equation is:______
(b) Equation for the cost of fruits_______
(c) The system equations are ______ and _________
(d) Solve by any method.
(e) Check if your result will satisfy the problem.
Answer:
x = 10
y = 10
Step-by-step explanation:
60x + 40y = 1000
x + y = 20
a. If x is number of kilos of mango and number of kilos of apple, then the equation is: x + y = 20
b. Equation for the cost of fruits
60x + 40y = 1000
c. The system equations are x + y = 20 and 60x + 40y = 1000
d. Solve by any method.
60x + 40y = 1000 (2)
x + y = 20 (1)
x = 20 - y
Substitute into (2)
60x + 40y = 1000 (2)
60(20 - y) + 40y = 1000
1200 - 60y + 40y = 1000
- 20y = 1000 - 1200
-20y = - 200
y = -200/-20
= 10
y = 10
Substitute y = 10 into (1)
x + y = 20
x + 10 = 20
x = 20 - 10
x = 10
(e) Check if your result will satisfy the problem.
60x + 40y = 1000
60(10) + 40(10) = 1000
600 + 400 = 1000
1000 = 1000
Creating a system of linear equations and solving using elimination method, the number of mangoes and apples purchased is 10.
Let :
Number of apples = a Number of mangoes = bThe system of equations which could be formed :
a + b = 20 - - - - - - (1)40a + 60b = 1000 - - - - - - (2)From (1)
a = 20 - b - - - - - (3)Substitute a = 20 - b into (2)
40(20 - b) + 60b = 1000
800 - 40b + 60b = 1000
Collect like terms
-40b + 60b = 1000 - 800
-20b = - 200
b = 200/20
b = 10
Substitute b = 10 in (3) :
a = 20 - b
a = 20 - 10
a = 10
Therefore, the Number of apples and mangoes purchased is 10
Learn more :https://brainly.com/question/15165519
An arts academy requires there to be 3 teachers for every 63 students and 4 tutors for every 36 students.How many students does the academy have per teacher ? per tutor ? how many tutors does the academy need if it has 63 students ?
A bike rental company charges a $5 service fee and $1 per hour. If this situation is represented as a function, what would be the slope?
Select one:
6
0
1
5
Answer:
The slope would be 1.
Step-by-step explanation:
The slope would be one becuase the equation would be y=1x+5.
Answer:
the equation would be y=x+5
so the slope is 1
Step-by-step explanation: