Answer:
(6b + 5)(b + 1).
Step-by-step explanation:
6b² + 3b + 8b + 5
= 6b^2 + 11b + 5
= 6b^2 + 6b + 5b + 5
= 6b(b + 1) + 5(b + 1) b + 1 is common so:
= (6b + 5)(b + 1)
Answer:
( 6b + 5 ) ( b + 1 )
Step-by-step explanation:
6b² + 3b + 8b + 5
6b²+ 11b + 5
6b²+ 5b + 6b + 5
( 6b + 5 ) ( b + 1 )
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
what is the missing length? help plssss
========================================
Work Shown:
LK = 65
LR = 52
RK = LK - LR = 65 - 52 = 13
The triangles are similar, so the corresponding sides form equal ratios
LK corresponds to RK as they are both on the same side
LK/RK is one ratio and it is equal to MK/SK
----------------
LK/RK = MK/SK
65/13 = 60/x
65x = 13*60 ... cross multiply
65x = 780
x = 780/65 ... divide both sides by 65
x = 12
SK = 12
Answer:
12
Step-by-step explanation:
RK = 65- 52= 13
similar triangle (∆RKS and ∆LKM)
[tex] \frac{13}{65} = \frac{x}{60} [/tex]
[tex]x = \frac{60 \times 13}{65} [/tex]
[tex]x = 12[/tex]
pls help!!
will give the brainliest!
Need explanation
Urgent!!!
Answer:
h=4 and k=-4....
Step-by-step explanation:
hopevit helps you
Step-by-step explanation:
[tex]A^2= \begin{bmatrix} 4 & 0 \\ 4 & 4 \end{bmatrix}[/tex]
Equate this to $hA + kI$
Thus,
[tex] A^2= h \begin{bmatrix} 2 & 0 \\ 1 & 2 \end{bmatrix} + k \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}[/tex]
Hence we have the following equations (by equating corresponding terms on both sides):
$2h+k=4$
$h=4$
Solve these to get $h=4$ and $k=-4$
-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]
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! :)
the 3rd and the 4th terms of an arithmetic progression are 6and30 respectively determine the common term,first term and the 10th term
Answer:
first term= -42
common difference= 24
10th term= 174
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
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 ;) ❤❤❤
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!
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:
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%.
Here is a number line with some points labeled. Type the answers into the boxes below. a. Write the number
A as a fraction.
B as a decimal
C as a decimial and a fraction
Answer:
A = 2/4
B = 1.25
C = 11/4 , 2.75
Step-by-step explanation:
solve 36x^2+23=60x using quadratic formula
Answer:
x₁ = 0.6
x₂ = 1.07
Step-by-step explanation:
36x² + 23 = 60x
36x² - 60x + 23 = 0
x = {-(-60)±√((-60²)-(4*36*23))} / (2*36)
x = {60±√(3600-3312)} / 72
x = {60±√288) / 72
x = {60±16.97) / 72
x₁ = {60-16.97} / 72 = 43.03/72 = 0.6 aprox.
x₂ = {60+16.97} / 72 = 76.97/72 = 1.07 aprox.
verify:
x₁
36*0.6² + 23 = 60*0.6
36*0.36 + 23 = 36
13 + 23 = 36
x₂
36*1.07² + 23 = 60*1.07
36*1.145 + 23 = 64.2
41.2 + 23 = 64.2
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)
In Point-Slope Form, what is the equation of the line perpendicular to y = -8x - 5 that passes through (2,-4)
Answer:
line: y = (1/8)x - 17/4
Step-by-step explanation:
To find perpendicular of line (negative reciprocal the given slope)
y = -8x-5
Perpendicular slope = (1/8)x
-4 = (1/8)(2) + b
-4 = 1/4 +b
Multiply everything by 4 to make it eaiser
-16 = 1 -+4b
-17 = 4b
b = -17/4
Which of the following equations is quadratic? (a) x1x² + 1) = 0
(b) 5(4x + 2) = 3
(c) (x+3)(x + 4) = 5
Answer:
(c) (x+3)(x+4)=5
Step-by-step explanation:
It's in factored form, and you would use the method of finding the perfect square to get the equation set to zero and find the solutions.
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!!
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!
How many solutions are there to the equation below 14x+2=12x
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
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.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ5
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.
Learn more about Addition here:
https://brainly.com/question/14092461
#SPJ2
convert the repeating decimals to fractions
1:) repeating 7
?
16/9
Step-by-step explanation:1,7777777777777 =
= 1,(7)
= (17 - 1)/9
= 16/9
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°
Read related link on:
https://brainly.com/question/15348675
Write a justification for each step given that EG=FH
Answer:
Option (C)
Step-by-step explanation:
Statements Reasons
1). EG = FH 1). Given information
2). EG = EF + FG 2). Segment addition postulate
3). FH = FG + GH 3). Segment addition postulate
4). EF + FG = FG + GH 4). Definition of congruent segments
5). EF = GH 5). Subtraction property of equality
Therefore, reasons given in Option (C) will be the answer.
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.
I AM GONNA CRY PLEASE PLEASE HELP ME
You invest $5,000 dollars in an account at 1.6% interest and interest is compounded
annually (once a year).
a) Write an equation that shows the amount of money you have after x years.
b) How much money would you have after 15 years?
Part (a)
Answer: y = 5000(1.016)^x------------------
Explanation:
You use the compound interest formula
A = P(1 + r/n)^(n*t)
where
A = final amount after t yearsP = amount deposited (principal) = 5000r = decimal form of interest rate = 0.016n = number of times we compound per year = 1t = number of years = x, some unknown numberAfter plugging those values in, you would go from A = P(1 + r/n)^(n*t) to
A = P(1 + r/n)^(n*t)
A = 5000(1 + 0.016/1)^(1*x)
A = 5000(1.016)^x
Since you're using x for the input, it's possible your teacher wants you to use y for the output. So replace A with y to get y = 5000(1.016)^x
==============================================
Part (b)
Answer: 6344.18 dollars--------------------------
Explanation:
Plug x = 15 into the equation we found back in part (a). Use your calculator to simplify. Round to the nearest hundredth which is rounding to the nearest penny.
y = 5000(1.016)^x
y = 5000(1.016)^15
y = 6344.1818561953
y = 6344.18
Answer:
girlie u gotta chill
Step-by-step explanation:
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.
Learn more about algebraic expression here :
https://brainly.com/question/2164351
#SPJ2
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
A student took a survey of the class. There are 42 students in the class. The student surveyed favorite foods. 10 said hamburgers, 22 said pizza, 8 said french fries, and 2 said salad. Which percentage of the class chose pizza?
Answer:
52.38%
Step-by-step explanation:
Given that,
Total number of students in the class is 42
Out of 42, 10 like hamburgers, 22 like pizza, 8 like french fries, and 2 like salad.
We need to find the percentage of the class chose pizza. There are 22 student who like to have pizza. Required percentage is given by :
[tex]P=\dfrac{22}{42}\times 100\\\\P=52.38\%[/tex]
So, 52.38% of students chose pizza.