Answer:
213.41 mph.
Step-by-step explanation:
Multiply by 3600 ( seconds in an hour) and divide by 5280 (feet in a mile).
= 213.41 mph.
The length of a rectangle is 2 inches less than twice it’s width. If the perimeter of the rectangle is 74 inches, what is the area of the rectangle?
Answer:
341.25in²
Step-by-step explanation:
Width=x
Length=x+2
X+x+x+2+x+2=74
4x+4=74
4x=70
x=17.5
width=x=17.5
length=x+2=19.5
A=LW
A=17.5*19.5
A=341.25in²
Use the Binomial Theorem to expand (x - 4y)³.
Answer:
x^3-64y^3
Step-by-step explanation:
(x-4y)^3
(x)^3-(4y)^3
x^3-64y^3
Hope this helps ;) ❤❤❤
Please Help, i will give brainiest. Please solve the problem about Sara kicking football.
Answer:
20 m
Step-by-step explanation:
The maximum height is given by the vertex form of the equation, that is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
h(t) = - 5t² + 20t ← factor out - 5 from each term
= - 5(t² - 4t)
Using the method of completing the square
add/subtract ( half the coefficient of the t- term)² to t² - 4t
h(t) = - 5(t² + 2(- 2)t + 4 - 4 )
= - 5(t - 2)² + 20 ← in vertex form
with vertex = (2, 20 )
The maximum height is at the value of k = 20
That is the maximum height is 20 m
Please help!! What is 6(4 - y) = 5 + 3?
Answer:
[tex] \boxed{ \boxed{ \bold{ \sf{2.6}}}}[/tex]Step-by-step explanation:
[tex] \sf{6(4 - y) = 5 + 3}[/tex]
Distribute 6 through the parentheses
[tex] \sf{24 - 6y = 5 + 3}[/tex]
Add the numbers
[tex] \sf{24 - 6y = 8}[/tex]
Move constant to right hand side and change it's sign
[tex] \sf{ - 6y = 8 - 24}[/tex]
Calculate
[tex] \sf{ - 6y = - 16}[/tex]
Divide both sides of the equation by -6
[tex] \sf{ \frac{ - 6y}{ - 6} = \frac{ - 16}{ - 6} }[/tex]
Calculate
[tex] \sf{y = 2.6}[/tex]
Hope I helped!
Best regards!!
Answer: Hi!
First, we need to distribute 6 to the terms inside of the parentheses, 4 and -y.
6 * 4 = 24
6 * (-y) = -6y
Our equation now looks like this:
24 - 6y = 5 + 3
We can now combine like terms.
24 - 6y = 5 + 3
5 + 3 = 8
Our equation now looks like this:
24 - 6y = 8
We can now use inverse operations to get rid of 24. Remember, our goal is to isolate the x. The inverse operation for addition (24 is positive) is subtraction, so we subtract 24 on both sides:
24 - 6y = 8
- 24 - 24
Our equation now looks like this:
-6y = -16
Last step! We now use inverse operations to get rid of -6. The inverse operation for multiplication is division (-6 is being multiplied by y); so we divide -6 on both sides.
-6y/-6 = y
-16/-6 = 8/3 = 2 2/3
Our equation now looks like this:
y = 2 2/3
Therefore, your solution is 2 2/3.
Hope this helps!
Which equation represents a circle with a center at (–3, –5) and a radius of 6 units? (x – 3)2 + (y – 5)2 = 6 (x – 3)2 + (y – 5)2 = 36 (x + 3)2 + (y + 5)2 = 6 (x + 3)2 + (y + 5)2 = 36
Answer:
D. is the answer
The equation that represents a circle with a center at (–3, –5) and a radius of 6 units is given by:
[tex](x + 3)^2 + (y + 5)^2 = 36[/tex]
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this problem, we have that:
The center has [tex]x_0 = -3, y_0 = -5[/tex].The radius is r = 6.Hence:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
[tex](x + 3)^2 + (y + 5)^2 = 36[/tex]
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match each account of events with the type of chronology it illustrates. helppp !!
Rayne sold 3 desks at the local trade show. He paid $4.00 to rent the booth. He gave half of his revenue to the carpenter and was left with $185.50. At what price did Rayne sell each desk?
Rayne sell each desk at the price of $125.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given the following information;
The Number of desks sold = 3
The Amount of rent paid = $4
The Amount paid to carpenter = 1/2 of revenue
The Amount left = $185.50
If Rayee gave half of his revenue to the carpenter and then had $185.50 left.
The his revenue before paying the carpenter will be twice what he has left will be;
($185.50 * 2) = $371
Hence, the total revenue from the sale of 3 desk = ($371 + rent)
= (371 + 4)
= $375
Then each desk cost :
$375 / 3 = 125
Hence, Rayne sell each desk at the price of $125.
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The addition is one of the four fundamental mathematical operations. The selling price of each desk is $122.33.
What is Addition?The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
Revenue generated = Revenue left with Rayne + Revenue with carpenter
Since Rayne gave half of his revenue to the carpenter, therefore, both of them will have the same revenue will them
Revenue generated = Revenue left with Rayne + Revenue left with Rayne
Revenue generated = 2(Revenue left with Rayne)
Revenue generated = 2($185.50)
Revenue generated = $371
Also, Rayne paid a booth rent of $4. Therefore, the total revenue generated will be,
Total revenue generated = Revenue generated + $4
= $371 + $4
= $367
Since Rayne sell 3 desks, therefore, the selling price of each desk will be,
Selling price = $367 / 3
= $122.33
Hence, the selling price of each desk is $122.33.
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A teacher wanted to know how well the gifted students in here class perform relative to her other classes. She administers a standardized test with a mean of 50 and a standard deviation of 10. A student scores of 55, what percent of students have a higher score than hers
Answer: 30.85%.
Step-by-step explanation:
Let X denotes the score of random student.
Given: [tex]\mu = 50[/tex] and [tex]\sigma=10[/tex]
We assume that scores are normally distributed.
Then , the probability that a a student score higher than 55:
[tex]P(X>55)=P(\dfrac{X-\mu}{\sigma}>\dfrac{55-50}{10})\\\\=P(Z>0.5) \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.5)\\\\=1-0.6915\ [\text{By p-value table for z}]\\\\= 0.3085[/tex]
Hence, the percent of students have a higher score than hers is 30.85%.
Solve for all values of x in simplest form
Answer:
x = -16/5 or
x = 6/5
Step-by-step explanation:
[tex]-\left|5+5x\right|-9=-20\\\\\mathrm{Add\:}9\mathrm{\:to\:both\:sides}\\-\left|5+5x\right|-9+9=-20+9\\\\Simplify\\-\left|5+5x\right|=-11\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\\\frac{-\left|5+5x\right|}{-1}=\frac{-11}{-1}\\\\\left|5+5x\right|=11\\\\\mathrm{Apply\:absolute\:rule}:\\\\\mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\5+5x=-11\quad \mathrm{or}\quad \:5+5x=11\\\\5+5x=-11\quad :\quad x=-\frac{16}{5}\\\\5+5x=11\quad :\quad x=\frac{6}{5}\\[/tex]
[tex]x=-\frac{16}{5}\quad \mathrm{or}\quad \:x=\frac{6}{5}\\[/tex]
The value of x after solving the expression -|5 + 5x| - 9 = -20 is equal to x = -16/5 or x = 6/5.
What do you mean by algebraic expressions ?
Algebraic expression is an equation which consists of variables and the arithmetic operations such as division , multiplication , etc.
The algebraic expression given is -|5 + 5x| - 9 = -20
We know that a modulus sign is a representation of ran absolute value which has two values either a positive or negative value.\
After solving the expression we get :
-|5 + 5x| - 9 = -20
So , after removing the modulus sign we will get two expressions :
-(-(5 + 5x) - 9 = -20
5 + 5x = -11
or
-(5 + 5x) - 9 = -20
-(5 + 5x) = -11
Solving the two expressions we get the value of x as :
x = -16/5
or
x = 6/5
Therefore , the value of x after solving the expression -|5 + 5x| - 9 = -20 is equal to x = -16/5 or x = 6/5.
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In the library, there are 12x English books, 5x Chinese books and 4x Malay
books. If there are 15 fewer Indian books than Malay books, find the to
number of books in the library in terms of x.
Answer:
25x - 15
Step-by-step explanation:
Indian books = malay books - 15
=4x -15
Total books =
English books + chinese books + malay + indian
= 12x + 5x + 4x + 4x -15
= 25x - 15
Answer:
Step-by-step explanation:
Indian books = 4x - 15
Total books = 12x + 5x + 4x + 4x - 15 {add like terms}
= 25x - 15
Select the inequality that represents the relationship described below.
The sum of three times a number and seven is greater than four times the number.
Answer:
(C) [tex]3x + 7 > 4x[/tex]
Step-by-step explanation:
Let [tex]x[/tex] represent the number that is unknown.
Using the words, we can write out each equation.
"The sum of three times a number and seven" will be adding 7 to 3x. So [tex]3x + 7[/tex].
"is greater than four times the number." will include a greater than sign and then 4 times the number, x. So:
[tex]> 4x[/tex]
Combining these, we get [tex]3x + 7 > 4x[/tex].
Hope this helped!
===============================================
Work Shown:
x = a number (something unknown)
3x = 3 times a number
3x+7 = the sum of 3 times a number and 7
4x = 4 times a number
3x+7 > 4x is the inequality that forms because the "the sum of 3 times a number and 7" portion is greater than the "4 times a number" portion
Given, f(x) = 2x + 7
Find f(3)
f(3) = 13
Step-by-step explanation:f(x) = 2x + 7
replace x with 3
f(3) = 2×3 + 7
= 6 + 7
= 13
which one is greater 24*36 or 18 twenty-fourths doblulded
Answer:
SO 18²⁴ IS GREATER
Step-by-step explanation:
24×36=864
18²⁴=1.3382588×10³⁰
HOPE IT WILL HELP ^_^
Answer:
24*26
Step-by-step explanation:
18/24ths doubled will result in a fraction while 24*26 is going to be an integer (864) much larger than 3/2= (18/24)*2
Tyrone ran 7 laps on he quarter mile track during practice. Which subset of real numbers would include the distance Tyrone ran at practice?
Answer:
Step-by-step explanation:
7 quarter mile laps totals 7/4 miles, or 1 3/4 miles.
1 3/4 miles is between 1 and 2, a subset of real numbers.
Which of the following functions describes the sequence 4, –2, 1, –12, 14, . . .?
Answer:
D. f(1) = 4, f(n) = –1/2f(n – 1) for n > 1
Step-by-step explanation:
We assume your sequence is supposed to be ...
4, -2, 1, -1/2, 1/4, ...
This has no common difference, but it has a common ratio of -1/2. That is, the first term is 4, and each successive term is -1/2 times the previous one. The function is described by the recursive formula ...
f(1) = 4;
f(n) = -1/2·f(n-1)
if the bacteria population is doubling every hour, can you estimate the bacteria population at the time of 10 hours?
Answer:
Bacterial population at the time of 10 hours = 1040000
Step-by-step explanation:
Let the function that defines the bacterial population after 'x' hours is,
p(x) = a(b)ˣ
Where a = Initial population
And 'x' = Duration or time
Since bacterial population is getting doubled every hour,
2a = a(b)¹
b = 2
Therefore, function will be,
p(x) = a(2)ˣ
From the graph attached,
Point (5, 32500) lies on the graph of the function.
32500 = a(2)⁵
a = [tex]\frac{32500}{32}=1015.625[/tex]
Therefore, the function will be,
p(x) = 1015.625(2)ˣ
For x = 10 hours,
p(10) = 1015.625(2)¹⁰
= 1040000 bacteria
-6x^3 -7x^2 +qx - 12 is divisible by 3x-4. There is no remainder. Find the value of q.
If [tex]3x-4[/tex] is a factor of [tex]p(x)=-6x^3-7x^2+qx-12[/tex], then [tex]x=\frac43[/tex] is a root of [tex]p(x)[/tex] so that [tex]p\left(\frac43\right)=0[/tex]:
[tex]-6\left(\dfrac43\right)^3-7\left(\dfrac43\right)^2+q\left(\dfrac43\right)-12=0[/tex]
[tex]\dfrac{4q-116}3=0[/tex]
[tex]4q-116=0[/tex]
[tex]4(q-29)=0[/tex]
[tex]\implies\boxed{q=29}[/tex]
How many solutions are there to the equation below 14x+2=12x
Which table can be created using the equation below? –2 + 4x = y
Answer:
A
Step-by-step explanation:
x y
-5 -22
0 -2
3 10
A particle travels 16.5 km in 30 minutes. What will be the speed of the particle in km / h ?
s=d/t
Step-by-step explanation:
s=16.5/0.5
s=33
33 km/h since 30 min is half an hour
Answer:
[tex] \boxed{ \huge{ \boxed{ \sf{ \bold{33 \: km/h}}}}}[/tex]Step-by-step explanation:
Distance ( d ) = 16.5 km
Time ( t ) = 30 minutes
( To convert minutes to hour , divide the minutes by 60)
Time ( t ) = [tex] \sf{ \frac{30}{60} }[/tex] = [tex] \sf{0.5}[/tex] hours
Now, let's find the speed
Speed = [tex] \sf{ \frac{distance \: travelled \: ( \: in \: km)}{time \: taken \: ( \: in \: hrs)} }[/tex]
plug the values
⇒[tex] \sf{ \frac{16.5}{0.5} }[/tex]
Calculate
⇒[tex] \sf{33 \: km/h}[/tex]
Hope I helped !
Best regards!!
Select all of the following statements that are true. All real numbers are natural numbers. All whole numbers are integers. All integers are whole numbers. All natural numbers are rational numbers. All irrational numbers are dense.
Answer:
All whole numbers are integers. AND All natural numbers are rational numbers.
Step-by-step explanation:
Answer:
The answer is D and E
Step-by-step explanation:
The sum of the measures of the angles of a triangle is 180 degrees the second angle of a triangle is twice the measure of the first angle the third is 20 more than 5 times the first what are the measures of the three angles
Greetings from Brasil...
As said:
1° angle: X
2° angle: 2X
3° angle: 20 + 5X
"...The sum of the measures of the angles of a triangle is 180 degrees..."
(1° angle) + (2° angle) + (3° angle) = 180
X + 2X + (20 + 5X) = 180
X + 2X + 5X = 180 - 20
8X = 160
X = 160/8
X = 20
But the problem asks for the value of each angle. Thus
1° angle: X
as X = 20, so
1° angle: X = 20
2° angle: 2X
as X = 20, so
2° angle: 2.20 = 40
3° angle: 20 + 5X
as X = 20, so
3° angle: 20 + 5.20 = 20 + 100 = 120
The values of the first, second, and third angles are 20°, 40° and 120° respectively.
Let the first angle = x
Let the second angle = 2 × x = 2x
Let the third angle = 20 + (5 × x) = 20+5x
Total angles in the triangle = 180°
Based on the information above, the angles will be calculated thus:
x + 2x + 5x + 20 = 180
Collect like terms
8x = 180 - 20
8x = 160
x = 160/8
x = 20
First angle = 20°
Second angle = 2x = 2 × 20° = 40°
Third angle = 5x + 20 = (5 × 20°) + 20° = 120°
The angles are 20°, 40°, and 120°
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One of the factors of 12 is chosen what’s the probability the chosen factor is 4?
Answer:
1/6
Step-by-step explanation:
There are six factors of 12: 1, 2, 3, 4, 6, and 12.
So the probability that the chosen factor is 4 is 1/6.
Use the tables below to find (p − q)(2). A 2-column table has 3 rows. The first column is labeled x with entries 4, 2, negative 3. The second column is labeled p (x) with entries negative 1, 3, 2. A 2-column table has 3 rows. The first column is labeled x with entries 4, 2, negative 3. The second column is labeled q (x) with entries 1, negative 2, 5. (p – q)(2) =
Composite functions are multiple functions combined to form another function.
The value of the composite function (p - q)(2) is 5
To find (p - q)(2), we make use of the following composite function formula:
[tex](p - q)(x) = p(x) - q(x)[/tex]
Substitute 2 for x in the above formula
[tex](p - q)(2) = p(2) - q(2)[/tex]
From the table entries, we have:
[tex]p(2) =3[/tex]
[tex]q(2) = -2[/tex]
So, the equation becomes
[tex](p - q)(2) = 3 -- 2[/tex]
Rewrite the above equation as:
[tex](p - q)(2) = 3 + 2[/tex]
Take the sum of 3 and 2
[tex](p - q)(2) = 5[/tex]
Hence, the value of (p - q)(2) is 5
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What is the conjugate of 7-8i?
Answer:
7 + 8i
Step-by-step explanation:
Conjugate of 7 - 8i is 7 + 8i
Answer:
Step-by-step explanation:
7+8i
Solve the equation for x (if possible please show work)
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 4}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{3x - 5 = 2x - 9}[/tex]
Move 2x to left hand side and change it's sign
⇒[tex] \sf{3x - 2x - 5 = - 9}[/tex]
Move 5 to right hand side and change it's sign
⇒[tex] \sf{3x - 2x = - 9 + 5}[/tex]
Collect like terms
⇒[tex] \sf{x = - 9 + 5}[/tex]
Calculate
⇒[tex] \sf{x = - 4}[/tex]
Hope I helped!
Best regards!!
Convert 7s seconds to hours Idk which numbers go where for how my teacher does it he cross multiplies and divides and idk which numbers go where please help
Answer:
0.0208333...
Step-by-step explanation:
You would just divide 7 seconds by 3600 seconds (1 hr) and that would be ur answer so in this case it would be 0.0208333...
Answer:
1/48 or 0.02083 hours
Step-by-step explanation:
75s×1 min/60s×1 hour/60 mins so the seconds and minutes cancel out and you are left with 75/3600=1/48 hours
0.4r = 1.6 pls answer ASAP and pls show how to correct
Answer:
r = 4.
Step-by-step explanation:
0.4r = 1.6
4r = 16
2r = 8
r = 4.
0.4(4) = 1.6
1.6 = 1.6
Hope this helps!
please help me with this question
Answer:
422 cm²
Step-by-step explanation:
Surface area of the composite figure = (surface area of the upper cuboid + surface area of lower cuboid) - 2(base area of the lower cuboid)
Surface area of composite figure = [tex] (2(lw + lh + hw)) + (2(lw + lh + hw)) - 2(l*w) [/tex]
Upper cuboid has the following dimensions:
[tex] l = 4, w = 3, h = 8 [/tex]
Lower cuboid has the following dimensions:
[tex] l = 10, w = 7, h = 5 [/tex]
Plug these values into the formula
Surface area of composite figure
[tex] = (2(4*3 + 4*8 + 8*3)) + (2(10*7 + 10*5 + 5*7)) - 2(4*3) [/tex]
[tex] = (2(12 + 32 + 24)) + (2(70 + 50 + 35)) - 2(12) [/tex]
[tex] = (136 + 310) - 24 [/tex]
[tex] = 446 - 24 = 422 [/tex]
Surface area of composite figure = 422 cm²
What is the greatest integer a, such that a^2 + 3b is less than (2b)^2, assuming that b is 5? Please answer and have a nice day!
===================================================
Work Shown:
b = 5
(2b)^2 = (2*5)^2 = 100
So we want the expression a^2+3b to be less than (2b)^2 = 100
We need to solve a^2 + 3b < 100 which turns into
a^2 + 3b < 100
a^2 + 3(5) < 100
a^2 + 15 < 100
after substituting in b = 5.
------------------
Let's isolate 'a'
a^2 + 15 < 100
a^2 < 100-15
a^2 < 85
a < sqrt(85)
a < 9.2195
'a' is an integer, so we round down to the nearest whole number to get [tex]a \le 9[/tex]
So the greatest integer possible for 'a' is a = 9.
------------------
Check:
plug in a = 9 and b = 5
a^2 + 3b < 100
9^2 + 3(5) < 100
81 + 15 < 100
96 < 100 .... true statement
now try a = 10 and b = 5
a^2 + 3b < 100
10^2 + 3(5) < 100
100 + 15 < 100 ... you can probably already see the issue
115 < 100 ... this is false, so a = 10 doesn't work
Answer:
9
Step-by-step explanation:
I just did the question on AOPS, please see the attachment down below.
Hope this helped! :)