Answer:
-3x-3=-3(x+1)
opening the bracket and collecting like terms, we have
-3x+3x=-1+3
thus, no solution
Consider this expression.
x^2 + x - 72
Replace the values of a and b to rewrite the given expression.
( x + a )( x + b )
Answer:
Step-by-step explanation:
Hello, first we can develop (x+a)(x+b)
[tex](x+a)(x+b)=x(x+b)+a(x+b)=x^2+bx+ax+ab=x^2+(a+b)x+ab[/tex]
We know that this should be equal to
[tex]x^2+x-72[/tex]
So, we can identify the coefficients of the like terms
1 = 1 (terms in [tex]x^2)[/tex]
1 = a + b (terms in x)
-72 = ab (constant term)
72 is 8 * 9 so, -72=9*(-8)
and we have 9 - 8 =1
so, a = 9 and b = -8
[tex]\Large \boxed{\sf \bf \ x^2+x-72=(x+9)(x-8) \ }[/tex]
Thank you
We are to consider the given expression:
x² + x - 72
The above expression is a quadratic expression and the objective is to determine its roots in form of (x + a) (x + b)
In form of (x + a) (x + b), the values of the expression x² + x - 72 in form of (x + a) (x + b) are 9 and -8 respectively.
From the given expression;
x² + x - 72
So; we will look for two factors of 72 in such a way that if those factors are multiplied together; they will give -72 and the addition of those two numbers will give +1.
So, the factors of 72 are:
1, 2, 3, 6, 8, 9, 12, 36, 72From the above factors;
the multiplication of (-8) × (9) will give us = -72and the addtion of -8 + 9 = +1∴
Our factors are: (-8) and (9)
From x² + x - 72, we have:
x² + (-8x) + (9x) - 72 = 0
(x² - 8x) + (9x -72) = 0
Opening the brackets by factorization;
x(x -8) + 9(x -8) = 0
(x + 9) or (x - 8) = 0
(x + 9) (x - 8) = 0
Recall that, we are to replace the values of a and b with the roots derived from the expression x^2 + x - 72.
Therefore, we can conclude that the values of a and b are 9 and -8 respectively.
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toss two dice. the probability of rolling an even number on both sides is 1/2x1/2= 1/4. predict in 120 tosses how many times an even number will appear on both dice?
Answer:
Chances of both even number = 30 times
Step-by-step explanation:
Given:
Chances of both even number = 1/4
Total number of tosses = 120
Find:
How many times both dice show even number
Computation:
Chances of both even number = [Chances of both even number][Total number of tosses]
Chances of both even number = 1/4 [120]
Chances of both even number = 30 times
The present value of R8052.55 received in 5 years at 9% interest is
Answer:
The present value of a bond is calculated by discounting the bond's future cash payments by the current market interest rate. In other words, the present value of a bond is the total of: The present value of the semiannual interest payments, PLUS. The present value of the principal payment on the date the bond maturaes.Calculate the present value investment for a future value lump sum return, based on a constant interest rate per period and compounding. This is a special instance of a present value calculation where payments = 0. The present value is the total amount that a future amount of money is worth right now.John says 1/3 is smaller than 1/8 because 3 is less than 8. Jane
says 1/3 is greater than 1/8 because the pieces are bigger. Who is
right? How do you know?
Answer:
Jane is correct
Step-by-step explanation:
100 divide by 3 is 33.333 recurring
100 divided by 8 is 12.5
El recibo del servicio de celular del mes de abril facturó un monto de S/52,50 por un consumo de 69 minutos; y el del mes de mayo, facturó S/32 por un consumo de 28 minutos. El monto que cobran cada mes incluye un costo fijo por mantenimiento y un precio establecido por minuto de consumo. ¿Cuántos minutos se debería consumir como máximo para pagar menos de S/30 el siguiente mes?
Answer:
x = 24 minutos
Step-by-step explanation:
Llamaremos "y" el costo fijo mensual y "x" la cantidad de minutos consumidos al mes, según lo cual:
El enunciado del problema establece que la facturación en pesos es igual a un costo fijo y más el consumo en minutos del mes, entonces
En Abril 52,50 = y + b*x ⇒ 52,5 = y + 69*b
y en Mayo 32 = y + b*x ⇒ 32 = y + 28*b
Así obtuvimos un sistema de dos ecuaciones con dos incógnitas, que resolveremos y obtendremos los valores de b y de y
y = 52,50 - 69*b
32 = ( 52,50 - 69*b ) + 28*b
- 20,50 = - 41*b
b = 0,5
y y = 52,5 - 69*0,5
y = 18
Entonces la ecuación de facturación es :
F(x) = 18 + 0,5*x
Para pagar como máximo 30 pesos en el mes siguiente
F(x) = 30 = 18 + 0,5*x
30 - 18 = 0,5*x
x = 24 minutos
A ladder leans against a vertical wall of
height 5 m. If the foot of the ladder is
12 m away from the wall, calculate
the length of the ladder.
Answer: 13m
Step-by-step explanation:
Use Pythagorean theorem: a²+b²=c²
5²+12²=c²
25+144=c²
c²=169
c=13 (even if it is true that there are positive and negative solution, but length cannot be negative)
Given:
A ladder is leant against a wall of height 5m.The foot of ladder is 12m away from the wall.To Find:
The length of ladder.Concept Used:
We will use Pythagoras Theorem.Answer:
Here given
Vertical height = 5m.Base = 12m.Here the length of ladder is equal to hypotenuse of ∆ so formed.
Now in a right angled ∆ ,
=> (hypotenuse)² = (pependicular)²+(base)².
=> h ² = (12m)²+(5m)²
=> h² = 144m² + 25m².
=> h² = 169m².
=> h = √169m².
=> h = 13m.
Hence the required answer is 13m.
The florist makes the greatest number of identical arrangements with the lilies and the daisies. Which combination describes the arrangements?
Answer:
12 arrangements with 5 lilies and 3 daisies
Step-by-step explanation:
17.9% of what number is 14.857?
Answer:
83
Step-by-step explanation:
.179 of x = 14.857
x = 14.857/.179
x = 83
Laura orders 50 m² of concrete paving slabs. The slabs cost £16.75 per m². How much do the slabs cost in total
Answer:
£837.5
Step-by-step explanation:
If she has 50 m² and it costs £16.75 for every m² of concrete, 50 × 16.75 = £837.5.
How do i answer these questions
Answer:
well basically for the first question it gives you
The rate that increases. which is 0.03 per second
And that R = 48 inches at time.
and T= 0.
The question wants you to determine the volume of the balloon at the time and find the volume when t= 300 seconds. so just replace 0 to 300.
Suppose Katie places $4000 in an account that pays 18% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding. (a) Find the amount in the account at the end of 1 year. (b) Find the amount in the account at the end of 2 years
Answer:
A) $48,720 B) $97,440
Step-by-step explanation:
A)
185 of 4000 = 720
12 months per year
4000 times 12 + 720
48000 + 720 = $48,720
B) 48,720 times 2 = $97,440
*wow she has a bunch of dough*
chika left his house by 7.05pm and returned by 1.00pm. How long did he spend outside his house
Answer:
Step-by-step explanation:
7.05 p.m we can call it as 19.05
and 1.00 p.m means 13.00
so time from 19.05 to 24.00 is = 24.00-19.05= 4.55 hr
from 24.00 to 13.00 is = 13.00 hr
so total hr is 4.55 + 13.00= 17.55 hr
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. If the value of the test statistic is 4.99 what is the conclusion of the test? Use significance level of 1%.
A. proportions have changed significantly
B. proportions have not changed significantly
C. test is inconclusive
D. None of these alternatives is correct.
Answer:
Proportions have not changed significantly ( B )
Step-by-step explanation:
GIVEN DATA :
Test statistic = 4.99
significance level = 1% = 0.01
k ( number of groups ) = 3
will we use the chi-squared test to determine the degree of freedom
which is : k-1 = 3 - 1 = 2
looking at the chi-square table to determine the critical value of the test
at significance level = 0.01 and degree of freedom = 2 the critical value = 9.21
Comparing the test value ( 4.99 ) and the critical value ( 9.21 ) it can seen that the test value < critical value which is a condition for not rejecting null hypothesis of the test.
therefore we won't reject the null hypothesis
Write 645,300 in expanded form using exponents
Answer:
Step-by-step explanation:
(6 x 10^5) + (4 x 10^4) + (5 x 10^3) + (3 x 10^2)
A box contains 65 balls numbered from 1 to 65. If 9 balls are drawn with replacement, what is the probability that at least two of them have the same number
Answer:
Probabilty= 7.66*10^-3
Step-by-step explanation:
A box contains 65 balls numbered from 1 to 65.
9 balls are drawn with replacement.
Probabilty of selecting a number = 1/65
Probabilty of selecting a number
= 0.0154
Probabilty of at least 2 numbers out of 9 selected to have Same number
Probabilty= 9C2(0.0154)^2(0.9846)^7
Probabilty= 7.66*10^-3
Evaluate function f(x) = 5x - 3 f(5) =
Answer:
f(5) = 22
Step-by-step explanation:
When we want to solve for f(x) = 5x - 3 when x is 5, all we have to do is plug in 5 as x into the equation.
f(x) = 5x - 3
f(5) = 5(5) - 3
5 * 5 = 25
25 - 3 = 22
f(5) = 22
I hope this helps you!
Roger bowled 7 games last weekend. His scores are 155, 165, 138, 172, 127, 193 , 142. What is the RANGE of Roger's scores?
Answer:
66
Step-by-step explanation:
To find the range, find the difference between the smallest and largest values
The largest value is 193 and the smallest is 127
193 - 127
= 66
The range of Roger's score after he bowled 7 games last weekend is 66
Range is the difference between the highest and the lowest be score in a distribution.Given scores:
155, 165, 138, 172, 127, 193 , 142
The highest score is 193
Lowest score is 127
Range = Highest score - Lowest score
= 193 - 127
= 66
Therefore, the range of Roger's score after he bowled 7 games last weekend is 66
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5.8 -28.37 compute
HELP PLEASE
Select the correct answer.
Over which interval of the domain is function m
negative?
Answer:
C, (6, ∞)
Step-by-step explanation:
The x intercept is 6, and it continues downward for infinity. :) I had this question on my assignment today and it was right!
Interval of the domain for which function is negative is equals to ( 6, ∞).
What is function?" Function is defined as relation between two variable is such that for all the inputs there is exactly one output."
Standard equation of the line
y = mx + b
b = y-intercept
m = slope
According to the question,
For the given line in graph,
y- intercept = 4
x- intercept = 6
Therefore ,
For the function y = mx + b we have,
b = 4
y = mx + 4
Substitute the value of x- intercept in the function y = mx +4 we get,
when x = 6 , y= 0
[tex]0 = m(6) + 4\\\\\implies m= \frac{-4}{6}\\ \\\implies m= \frac{-2}{3}[/tex]
Function [tex]y = \frac{-2}{3}x+ 4[/tex]
Interval of the domain is function is negative.
[tex]y < 0 \\\\\implies \frac{-2}{3}x+ 4 < 0\\\\\implies -2x + 12 < 0\\\\\implies -2x < -12\\\\\implies 2x > 12\\\\\implies x > 6[/tex]
Interval of the domain is function is negative is ( 6, ∞).
Hence, Option (C) is the correct answer.
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9. Find the area of rectangle.
2x
A=
5x?
please help
Answer:
[tex] \boxed{\sf Area \ of \ rectangle = 10x^3} [/tex]
Given:
Length of rectangle = 5x²
Width of rectangle = 2x
To Find:
Area of rectangle
Step-by-step explanation:
[tex]\sf Area \ of \ rectangle = Length \times Width[/tex]
[tex] \sf = 5 {x}^{2} \times 2x[/tex]
[tex] \sf = 5 \times 2 {x}^{2 + 1} [/tex]
[tex] \sf = 5 \times 2 {x}^{3} [/tex]
[tex] \sf = 10 {x}^{3} [/tex]
Answer:
[tex]\huge\boxed{Area\ of\ Rectangle = 10x\³}[/tex]
Step-by-step explanation:
Area of Rectangle = Length * Width
Where Length = 2x and Width = 5x²
Area of Rectangle = (2x)(5x²)
Area of Rectangle = 10x³
Evaluate 14.8 - 0.72
Answer:
the answer is 14.08
Step-by-step explanation:
pt 2 7-7 Please helppp If you guys want lol ill do 7 moreeee LOL
Answer:
c = 72
Step-by-step explanation:
8
x ___c__ = 9 x 8
8
c = 72
Hi there! Hopefully this helps!
--------------------------------------------------------------------------------------------------
Answer: c = 72~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]\frac{c}{8} = 9[/tex]
Multiply both sides by 8.
[tex]c = 9 \times 8[/tex]
Multiply 9 and 8 to get, you guessed it, 72!Which statement is true about this equation? 3(-y + 7) = 3(y + 5) + 6 A. The equation has one solution, y = 0. B. The equation has one solution, y = -1. C. The equation has no solution. D. The equation has infinitely many solutions.
Answer:y=0 So its A
Step-by-step explanation:3(-y+7)=3(y+5)+6
We move all terms to the left:
3(-y+7)-(3(y+5)+6)=0
We add all the numbers together, and all the variables
3(-1y+7)-(3(y+5)+6)=0
We multiply parentheses
-3y-(3(y+5)+6)+21=0
We calculate terms in parentheses: -(3(y+5)+6), so:
3(y+5)+6
We multiply parentheses
3y+15+6
We add all the numbers together, and all the variables
3y+21
Back to the equation:
-(3y+21)
We get rid of parentheses
-3y-3y-21+21=0
We add all the numbers together, and all the variables
-6y=0
y=0/-6
y=0
Answer:
y = 0
Step-by-step explanation:
NEED TO SHOW ALL WORK) For each of the equations given below, use the triangle method to solve for the
desired variable.
Answer:
1) [tex]a=\dfrac{F}{m}[/tex]
2) [tex]m=\dfrac{p}{v}[/tex]
Step-by-step explanation:
1) The given equation is
[tex]F=ma[/tex]
We need to solve this for a.
In the given triangle place single variable i.e., F, on the top and variables in the product in the bottom (order of m and a does not matter) as shown in the below figure.
Using the triangle and the operations (× and ÷), we get
[tex]F=ma[/tex]
[tex]a=\dfrac{F}{m}[/tex]
[tex]m=\dfrac{F}{a}[/tex]
Therefore, the required answer is [tex]a=\dfrac{F}{m}[/tex].
2) The given equation is
[tex]p=mv[/tex]
We need to solve this for m.
In the given triangle place single variable i.e., p, on the top and variables in the product in the bottom (order of m and v does not matter) as shown in the below figure.
Using the triangle and the operations (× and ÷), we get
[tex]p=mv[/tex]
[tex]m=\dfrac{p}{v}[/tex]
[tex]v=\dfrac{p}{m}[/tex]
Therefore, the required answer is [tex]m=\dfrac{p}{v}[/tex].
the weight of earth is about 66 metric ton what is the standard form of 6,600,000,000,000,000,000,000, metric tone
WILL GIVE BRAINLIEST THANKS AND 5 STARS FOR CORRECT ANSWER Desmond ran a lemonade stand in front of his house for the fans walking to the football game. On the first Saturday, he sold 80 cups of lemonade. The second Saturday was cold and rainy so he sold only 70% of what he had sold the previous Saturday. How many cups did he sell on the second Saturday?
Answer:
56
Step-by-step explanation:
First, convert the 70% so that we can use it with the 80 cups. To do this, convert the percent to a decimal by moving the decimal 2 spaces to the left:
70% → 70.00 → 0.70 → 0.7
70% percent can be seen as 0.7. Multiply this by 80:
[tex]80*0.7=56[/tex]
So, 70% of 80 is 56. Desmond sold 56 cups on the second Saturday.
:Done
i need help asap !!!!!!
Answer:
B. ZJ = 85
C. KH = 68
Step-by-step explanation:
Given that ZK, ZL, ZM are perpendicular bisectors of ∆GHJ, they form a circumcenter which is equidistant from the vertices of ∆GHJ. According to the circumcenter theorem, ZH = ZG = ZJ = 85.
Also each median formed is equal. This means: KH = GH, LH = LJ, MG = MJ
Since HG = 136, KH = ½ of 136 = 68.
The two options that are true are:
B. ZJ = 85
C. KH = 68
Simplify (7 + 1)2 - (11 +32) 4.
O A. 59
O B. 17
O C. -3
O D. -13
the 32 is an exponent. so it’s 3 to the second power.
help !
Answer:
59
Step-by-step explanation:
I think your equation is supposed to look like this:
(7 + 1)² - (11 + 3²)/4
Follow PEMDAS to solve (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)
(7 + 1)² - (11 + 9)/4
(8)² - (20)/4
64 - (20)/4
64 - 5
59
Question 2 (1 point)
Saved
A year ago, Rebecca purchased 100 shares of Havad stock for $20 per share.
Yesterday, she placed a limit order to sell her stock at a price of $33 per share before
the market opened. The stock's price opened at $23 and slowly increased to $26 in
the middle of the day, before declining to $22 by the end of the day. The stock did
not pay any dividends over the period in which Rebecca held it. Given Rebecca's
initial investment of $ 20 per share, her return is
Answer:
Her return is [tex]R = 0.10[/tex]
Step-by-step explanation:
From the question we are told that
The number of shares purchased is [tex]n = 100 \ shares[/tex]
The cost price of each share is [tex]x = \$ 20[/tex]
The limit order is [tex]y = \$ 33[/tex]
The first market price for each share is [tex]k = \$ 23[/tex]
The second market price for each share is [tex]u = \$ 26[/tex]
The third market price for each share is [tex]w = \$ 22[/tex]
Generally the limit order would not be executed given that it is higher than the market opening and closing price.
Considering Rebecca's initial investment of $ 20 per share, her return is mathematically evaluated as
[tex]R = \frac{w + d - x}{x}[/tex]
Here d stands for the dividend but since we are told that the stock did not pay any dividend
[tex]R = \frac{22 + 0 - 20}{20}[/tex]
[tex]R = 0.10[/tex]
The sum of two numbers is eight. Using y to represent the smaller number,
translate "three times the larger number" into a variable expression and thenuh
simplify.
Answer:
24 - 3y
Step-by-step explanation:
Since the sum of the two numbers is 8, the larger number is 8 - y.
Three times the larger number: 3 (8 - y).
Simplify using Distributive property: 3 (8 - y) = 24 - 3y.
So the answer is 24 - 3y