Answer:
We are given
We are also given and , which allows us to rewrite the equation as
(I substituted every "b" with "a" and every "c" with "9").
The solutions to this quadratic equation are -25 and 7. We discard -25 because a side with negative length would make no sense.
The required measure of side a of the rectangular prism is a = 9.3 meters.
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
Here,
SA = 2ab + 2bc + 2ac
434 = 2a² + 14a + 14a
434 = 2a² + 28a
2a² + 28a - 434 = 0
a² + 14a - 217 = 0
a² + 14a + 49 - 49 - 217 = 0
(a + 7)² = 266
a = 9.3 or a = -23.3
Since the negative measure of length can be neglected.
a = 9.3 = b
Thus, the required measure of side a of the rectangular prism is a = 9.3 meters.
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Factor completely. 5x2 - 2x - 7
Answer:
(5x-7)(x+1)
Step-by-step explanation:
Here, we want to factor the given polynomial
That would be;
5x^2-7x+5x-7
= 5x^2+5x-7x-7
= 5x(x + 1) -7(x + 1)
= (5x-7)(x+ 1)
K is the midpoint of PQ, P has
coordinates (-9,-4), and K
has coordinates (-1, 6). What
are the coordinates of Q?
A (-5, 1) C (-11,8)
B (5, 10) D (7.16)
Answer:
Coordinates of Q [tex](x_2,y_2) \:are\: \mathbf{(7,16)}[/tex]
Option D is correct option.
Step-by-step explanation:
We are given:
K is the midpoint of PQ
Coordinates of P = (-9,-4)
Coordinates of K = (-1,6)
We need to find coordinates of Q [tex](x_2,y_2)[/tex]
We will use the formula of midpoint: [tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
We are given midpoint K and [tex]x_1,y_1[/tex] the coordinates of P we need to find [tex]x_2,y_2[/tex] the coordinates of Q.
[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\(-1,6)=(\frac{-9+x_2}{2},\frac{-4+y_2}{2})\\[/tex]
Now, we can write
[tex]-1=\frac{-9+x_2}{2}, 6=\frac{-4+y_2}{2}\\Simplifying:\\-2=-9+x_2\:,\: 12=-4+y_2\\-2+9=x_2\:,\: 12+4=+y_2\\x_2=7\:,\:y_2=16[/tex]
So, we get coordinates of Q [tex](x_2,y_2) \:are\: \mathbf{(7,16)}[/tex]
Option D is correct option.
The sum of two consecutive even integers is 118 what are the integers
Answer:
58 and 60
Step-by-step explanation:
well if we say that x is the first integer
then we have that the next one is
x+2
so we have
[tex]x+(x+2)=118\\\\2x+2=118\\\\2x=116\\\\x=58[/tex]
and the other one is
[tex]x+2=58+2=60[/tex]
Answer:
suppose one of our integers is x. then the next one would be x+2(because they are consecutive). so the equation looks like this :
x + ( x + 2 ) = 118 then we'll have : 2x+2 = 118 then : 2x = 116 .
so x would be 58 and the next one would be 60
Step-by-step explanation:
BRAINLIEST IF U ANSWER!!! BTW I WILL BE CHECKING IF THE ANSWER IS CORRECT ONLY IF ITS CORRECT BRIANLIEST ANSWER WITHIN 30 MINS!!! The value of a baseball player's rookie card began to increase once the player retired. When he retired in 2000 his card was worth $4.23 The value has increased by $2.92 each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2010 ?
Answer:
Relationship: [tex]y =2.92x+4.23[/tex]
They are not proportional
The value is $33.43
Step-by-step explanation:
Given:
[tex]x = years[/tex]
[tex]y = amount[/tex]
When he retired, the expression is:
[tex](x_1,y_1) = (0,4.23)[/tex]
and the rate (m) is:
[tex]m = 2.92[/tex]
Solving (a): The relationship between y and x
This can be solved using the following point-slope formula:
[tex]y - y_1=m(x-x_1)[/tex]
Substitute values for x1, y1 and m
[tex]y - 4.23=2.92(x-0)[/tex]
[tex]y - 4.23=2.92(x)[/tex]
Make y the subject
[tex]y =2.92(x)+4.23[/tex]
[tex]y =2.92x+4.23[/tex]
Solving (b): Are they proportional?
No, they are not
A proportional relationship is expressed as:
[tex]y = mx[/tex]
By comparing this to [tex]y =2.92x+4.23[/tex]; they have different format
Solving (c): Value in 2010?
First, we determine the value of x in 2010
2000; x = 0
2001; x = 1
---
--
-
2010; x = 10
Substitute 10 for x in [tex]y =2.92x+4.23[/tex]
[tex]y = 2.92*10+4.23[/tex]
[tex]y = 29.2+4.23[/tex]
[tex]y = 33.43[/tex]
what s the domain for d(x)=850(0.94)x
Given:
The function is
[tex]d(x)=850(0.94)^x[/tex]
To find:
The domain of the function.
Solution:
Domain is the set of input values.
We have,
[tex]d(x)=850(0.94)^x[/tex]
It is an exponential function, with initial value 850 and decay factor 0.94 because 0.94<1.
The exponential functions are defined for all real values of x. So, the domain of exponential function is always the set of all real numbers.
Therefore, the domain of the function d(x) is the set of all real numbers, i.e., R.
Explain how to find rate of change from a table.
(6 x 10^2)\(3x10^-5)
the answer is 2 x 10^7 :D
quack quack quack (hopefully this helps)
Answer: 20,000,000 or 2 × 10^7
Step-by-step explanation:
(6 × 10²) ÷ (3 × 10^-5)
(6 × 100) ÷ (3 × 0.00001
)
600 ÷ 0.00003
20,000,000
or
2 × 10^7
Hope this helped!
Help with this please. I’d appreciate if you showed the steps and the answer. Thanks a lot!
[tex]\boxed{\boxed{\pink{\bf \leadsto Hence \ the \ horizontal \ distance \ is \ 11.47 \ feet . }}}[/tex]
Step-by-step explanation:Given that Scott is using a 12 foot ramp . And the height of the truck is 3.5 feet from the ground. And we need to find the horizontal distance of the ramp reaches the ground of the truck .
Here will be a formation of a right angled triangle in which the
Ramp will be hypontenuse.Height will be perpendicular .Base distance will be base .On using Pythagoras Theorem ,
[tex]\red{\bf \implies base^2+perpndicular^2=hypontenuse^2}\\\\\bf\implies (12 ft )^2 = base^2 + (3.5 ft )^2\\\\\bf\implies 144ft^2 = base^2+12.25 ft^2 \\\\\bf\implies base^2 = 144ft^2-12.25ft^2 \\\\\bf\implies base^2 = 131.75 ft^2\\\\\bf\implies base=\sqrt{131.75ft^2}\\\\\bf\implies\boxed{\red{\bf base = 11.47 ft }}[/tex]
★ Hence the horizontal distance is 11.47 feet .
Aldrine is buying coffee for his coworkers. He orders small and large coffees. Small coffees
cost $3 and large coffees cost $5. He spent $30 and ordered eight cups of coffee in total.
Write a system of equations that represents the situation
How many of each coffee did he buy? How do you know?
Let small cups = S
Large cups = L
They bought a total of 8 cups, so S + L = 8
Rewrite as S = 8-L (1st equation)
Then you also have
$3S + $5L = $30 (2nd equation)
Replace the S in the second equation with the first equation:
$3(8-L) + $5L = $30
Simplify:
24 - 3L + 5L = 30
Combine like terms:
24+2L = 30
Subtract 24 from both sides:
2L = 6
Divide both sides by 2:
L = 3
They bought 3 large cups
Since they bought a total of 8 cups, that means they bought 5 small cups ( 8-3=5)
Large = 3 cups, Small = 5 cups
⚠️HELP⚠️MY HW IS DUE IN 10 MINS
A water tank is being filled with water. Before water is pumped in, the water level in the tank is 11 inches high. After 20 minutes, the water level is 56 inches high.
If "t" represents the time in minutes, and "h" represents the water level, which of the following equations can be used to model this situation?
A. h=2.25t + 11
B. h=2.25t - 11
C. h=11t + 2.25
D. h=45 + 11t
Answer:
Step-by-step explanation:
so coz there was already 11 inches but after 20min the tank is 56inch so wht u do is this
45+11t if im right
11. Find the sum of all prime numbers between 50
and 60.
A. 109
B. 110 -0. 112 D. 122
Answer:
[tex]C.112[/tex]
Step-by-step explanation:
[tex]First,\\Lets\ list\ out\ all\ the\ primes\ between\ 50\ and\ 60:\\53,59\\Hence,\\By\ adding\ them\ we\ get:\\53+59\\=112[/tex]
Object A has 50 kg while Object B has 75 kg. They were pushed with the same amount of force. Which will have greater acceleration
Answer:
Object A will have greater acceleration.
Step-by-step explanation:
Given that,
The mass of object A = 50 kg
The mass of object B = 75 kg
They were pushed with the same amount of force.
We know that, the force acting on an object is given by :
F = ma
Here F is same for both mass
[tex]m_1a_1=m_2a_2[/tex]
Mass and acceleration have inverse relation. It means the object whose mass is less will have greater acceleration. Hence, the acceleration is greater for object A.
1,5,25,61.....
What's following number?
Given:
1,5,25,61.....
To find:
The following number.
Solution:
We can see a pattern in the given sequence.
[tex](-1)^2+(0)^2=1+0=1[/tex]
[tex](1)^2+(2)^2=1+4=5[/tex]
[tex](3)^2+(4)^2=9+16=25[/tex]
[tex](5)^2+(6)^2=25+36=61[/tex]
Using this pattern the next term is the sum of squares of 7 and 8.
[tex](7)^2+(8)^2=49+64=113[/tex]
Therefore, the next number is 113.
pleasee helpppppppp this needs donee
Answer:
-23
Step-by-step explanation:
firstly u need to substitute a to 1/4 and b to 6
16(1/4) to the power of 2 - 4(6) equal to -23
ASAP Analyze the Error: What is the error in the way the calculation of the slope of the two points is set up and/or solved? Please be specific.
Answer/Step-by-step explanation:
Given two points on a line, (-4, 10) and (0, 2), the slope of the line is calculated as follows:
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (-4, 10) = (x_1, y_1) [/tex]
[tex] (0, 2) = (x_2, y_2) [/tex]
Plug in the values
[tex] slope (m) = \frac{2 - 10}{0 - (-4)} [/tex]
[tex] slope (m) = \frac{-8}{4} = -2 [/tex]
Slope = -2
The wrong formula was used. Slope is supposed to be change in y over change in x. Rather the difference of each coordinates was solved and divided by each other, which makes the whole calculation wrong.
Five friends attend a matinee movie and spend $8 per ticket. They also purchase a small bag of popcorn each. The friends spend a total of $62.50. Let x be the price of a small bag of popcorn.
Which equation represents the situation?
62.50 + 8x = 40
40 + 8x = 62.50
40 + 5x = 62.50
62.50 + 5x = 40
Answer:
40+5x=62.50
Step-by-step explanation:
8 friends 5 dollars is 40 dollars. Each popcorn bag is 2.5
40+5(2.5)=62.5
40+12.5=62.5
Answer:
62.50 + 8x = 40
Brailest plez and ill give you brainiest!
Step-by-step
A population of rabbits is tripling every week. If the population starts with 5 rabbits, how many rabbits will there be at the end of 7 weeks?
Answer:
10,935 bunnies at the end of 7 weeks
Step-by-step explanation:
5 x 3 = 15
^ x 3 = 45
^ x 3 = 135
^ x 3 = 405
^ x 3 = 1,215
^ x 3 = 3,645
^ x 3 = 10,935
I may be way off, forgive me, but I hope this helps anyway, have a good day!!
The perimeter of a rectangular carpet is 34 feet. The length of the carpet is one foot shorter than twice the width a) Write and solve an equation to solve for the variable. b) Find the area of the carpet.
please help
Answer:
a.) 3x = 18 (where x = width)
b.) Area = 66 squared feet
Step-by-step explanation:
2{x + (2x-1)} = 34
3x - 1 = 17
x = 6 feet
length = 11 feet
Area = x (2x -1)
Solve the compound inequality: n+1<=-3 or -4n<-8
Answer:
-4n<-8 the answer for this is (n>2)
n+1<=-3 the answer for this is (n<=-4)
The value of n is less than equal to negative 4 and greater than 2. n ≤ –4 and n > 2.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequalities are given below.
n + 1 ≤ –3 …1
–4n < –8 …2
On solving equation 1, we have
n + 1 ≤ –3
n ≤ –4
On solving equation 2, we have
–4n < –8
n > 2
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factorize the following
2mh+3mk-2nh-3nk
Answer:
(2h + 3k) (m - n)
Step-by-step explanation:
factor by pairing: pair and factor the first two terms, then pair and factor the remaining two; there should be one factor which duplicates
m is common factor of 1st pair: m(2h+3k)
n is common factor of 2nd pair: n(2h+3k)
answer is one of the duplicate factors (2h+3k) times terms not contained in parentheses (m+n)
Answer:
[tex](2h+3k)(m-n)[/tex]
Step-by-step explanation:
[tex]2mh+3mk-2nh-3nk[/tex]
Just look at the common terms
[tex]2mh-2nh-3nk+3mk = 2h(m-n)-3k(n-m) = 2h(m-n)+3k(m-n)[/tex]
By grouping we have
[tex]2h(m-n)+3k(m-n) =\boxed{(2h+3k)(m-n)}[/tex]
John is 5 years older than Samantha and Samantha is twice as old as Tim. If the
sum of their ages is 95, how old is John?
The age of John is 41 years.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
John is 5 years older than Samantha and Samantha is twice as old as Tim.
And, The sum of their ages is 95.
Now,
Let the age of Tim = x
Then, Age of Samantha = 2x
And, Age of John = 2x + 5
Since, The sum of their ages is 95.
So, We can formulate;
⇒ x + 2x + (2x + 5) = 95
⇒ 5x + 5 = 95
Subtract 5 both side, we get;
⇒ 5x + 5 - 5 = 95 - 5
⇒ 5x = 90
Divide by 5, we get;
⇒ x = 18
Thus, The age of John = 2x + 5
= 2 × 18 + 5
= 36 + 5
= 41
Therefore, The age of John is 41 years.
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Can anyone please help me with this attachment?
If you can't read my writing, this is the questions:
'Calculate the perimeter of this sector.
Give your answer in terms of pi.'
Answer:
Perimeter of the sector = (36 + 8π) cm.
Step-by-step explanation:
Formula to find the of an arc of the circle is,
Length of the arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]
Here, θ = central angle formed by the arc
r = radius of the circle
Therefore, length of the arc given in the picture = [tex]\frac{80}{360}(2\pi) (18)[/tex]
= 8π cm
Perimeter of the sector = Sum of all sides of the sector
= Length of radius + length of the arc + length of radius
= 18 + 8π + 18
= (36 + 8π) cm
Perimeter of the sector is (36 + 8π) cm.
STOP PUTTING WRONG ANSWERS
Answer:
why did you put this as a question? you seriously could have just saved some points and commented it on a question you know
Step-by-step explanation:
A town spends 43% of its annual budget on education.
If the town’s budget is one million dollars, how much will be spent on education?
Answer:
430,000 dollars will be spent on education.
Step-by-step explanation:
np
(GEOMETRY) What is the length of the radius of the circle?
Answer:
[tex]r=\frac{5}{2}\sqrt{2}[/tex]
Step-by-step explanation:
Triangles And Circles
If a right triangle is inscribed in a circle (or the circle is circumscribed around the right triangle), then the hypotenuse of the triangle is the diameter of the circle.
The right triangle has both legs of known lengths, thus the hypotenuse (the diameter of the circle is):
[tex]d^2=5^2+5^2[/tex]
[tex]d^2=25+25=50[/tex]
[tex]d=\sqrt{50}[/tex]
Since 50=2*25:
[tex]d=5\sqrt{2}[/tex]
Thus the radius of the circle is:
[tex]r=\frac{d}{2}[/tex]
[tex]r=\frac{5\sqrt{2}}{2}[/tex]
[tex]\boxed{r=\frac{5}{2}\sqrt{2}}[/tex]
Find the slope of the line that passes through the two points below.
(3,6) and (10,4)
Answer:
Slope: -2/7
Step-by-step explanation:
Slope is change in y over change in x.
(4-6)/(10-3)
= -2/7
13 A scout group has a raffle to raise money for charity,
There is I prize to be won in the raffle.
Laura buys 12 raffle tickets.
A total of 350 raffle tickets are sold.
Find the probability that Laura does not win the prize.
(Total for Question 13 is 2 marks)
Answer:
29%
Step-by-step explanation:
The probability that Laura does not win the prize is 0.9657
What is Probability?
The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
The value of probability lies between 0 and 1
Given data ,
Let the probability that Laura wins be = P ( x )
So , the probability that Laura does not win is = 1 - P ( x )
Let the total number of raffle tickets to be sold is = 350 raffle tickets
The number of tickets Laura bought = 12 raffle tickets
Therefore , the probability that Laura wins the prize =
number of tickets Laura bought / total number of raffle tickets
The probability that Laura wins the prize P ( x ) = ( 12/350 )
Now ,
The probability that Laura does not win is = 1 - P ( x )
The probability that Laura does not win = 1 - ( 12/350 )
The probability that Laura does not win = ( 350 - 12 ) / 350
The probability that Laura does not win = 338 / 350
The probability that Laura does not win = 0.9657
Hence , The probability that Laura does not win the prize is 0.9657
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3 of 6
Sushil, Natasha & Fiona share some money in the ratio 1:4:2
In total, Sushil and Fiona receive £39
How much does Natasha get?
Answer:
Amount got by Natasha = £52
Step-by-step explanation:
Given that:
Ratio of Sushil, Natasha and Fiona's share = 1:4:2
Amount of money received by Sushil and Fiona = £39
Let,
x be the number of times.
x+2x = 39
3x = 39
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{39}{3}\\x=13[/tex]
Share of Natasha = 4x = 4(13) = £52
Hence,
Amount got by Natasha = £52
Twenty less than a number is at least 15
Answer:
what??
Step-by-step explanation:
Answer:
n - 20 ≥ 15
n ≥ 35
Step-by-step explanation:
a number could be greater than or equal to 35 and be a solution
Solve for the variable c in this equation:
3a(b+c)=d
A) c= d-3ab/3a
B) c=d+3ab/3a
C) c=d-3b/3a
D) c=d+3b/3a
Answer:
if it's me I would pick etherbc are d I holp it helps