When multiplying the same base with exponents, you keep the base the same and then you add the exponents, so for this question you do:
10^3 x 10^6
10^9
Which of the following best describes the relationship between (x + 1) and the polynomial x2 - x - 2?
A. It is impossible to tell whether (x + 1) is a factor.
B. (x + 1) is not a factor.
C. (x + 1) is a factor.
Answer:
C
Step-by-step explanation:
to factor x² - x - 2
consider the factors of the constant term which sum to give the coefficient of the x-term.
the factors are - 2 and + 1 since - 2 × 1 = - 2 and - 2 + 1 = - 1
x² - x - 2 = (x - 2)(x + 1), hence (x + 1) is a factor
The relationship between (x + 1) and the polynomial x² - x - 2 is that ( x + 1) is a factor of x² - x - 2.
What is a polynomial?A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a non negative integral power.
How to know whether there is any relation between (x + 1) and the polynomial x² - x - 2?The given polynomial is x² - x - 2.
Here we should try to factorise the polynomial.x² - x - 2
= x² - 2x + x - 2
= x( x - 2) + 1( x - 2)
=( x - 2) ( x + 1)
So we can see that, ( x + 1) is a factor of x² - x - 2.
So, option C is correct.
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What is the probability the spinner will land on a dotted region?
A- 25%
B- 33%
C-37.5%
D- 50%
Dotted Regions Include- 25%, 12.5%, and 12.5%
Stripped Regions Include- 12.5%, and 25%
White Region Includes- 12.5%
The probability for the spinner landing on the dotted region is 1/2.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lies in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
The probability for the given case is evaluated as,
P(Spinner lands on dotted region) = Total space for dotted region/100
= (25 + 12.5 + 12.5)/100
= 50/100
= 1/2
Hence, the probability that the spinner will land on a dotted region is 1/2.
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ILL GIVE BRAINLIEST ANSWER IN 5 MIN
Which of the sets of ordered pairs represents a function?
A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}
B = {(4, 2), (3, −2), (9, 4), (11, −3)}
Select one:
a. Only A
b. Only B
c. Both A and B
d. Neither A nor B
Answer:
D.
Step-by-step explanation:
Function does not have duplication of a number.be
The A choice contains duplicates of both 2 and -2.
The B choice contains a duplicate of 4.
Therefor, it must be D.
==============================================
Which of the sets of ordered pairs represents a function?
A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}
B = {(4, 2), (3, −2), (9, 4), (11, −3)}
Select one:
a. Only A
b. Only B
c. Both A and B
d. Neither A nor B
X varíes directly with y and z. X =1200 when y =20 and z=30 find x when y=10 and z=20
Answer:
Value of x = 400
Step-by-step explanation:
Joint variation states that describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them.
Given: x varies directly with y and z.
i.e [tex]x \propto y[/tex] and [tex]x \propto z[/tex]
then we have the joint variation as;
[tex]x = k yz[/tex] ......[1] where k is the constant variation.
Substitute the value of x =1200 when y =20 and z = 30 to solve for k;
[tex]1200 = k (20)(30)[/tex]
Simplify:
[tex]1200 = 600k[/tex]
Divide both sides by 600 we get;
[tex]k = 2[/tex]
Now, substitute k =2 , y =10 and z = 20 to find x;
Using [1] we have;
[tex]x = 2 \times (10)(20) = 2 \times 200[/tex]
Therefore, the value of x is, 400
Answer:
x = 400
Step-by-step explanation:
given that x varies directly with y and z the the equation relating them is
x = kyz ← k is the constant of variation
to find k use the given condition x = 1200 when y = 20 and z = 30
k = [tex]\frac{x}{yz}[/tex] = [tex]\frac{1200}{20(30)}[/tex] = 2, thus
x = 2yz is the direct variation equation
when y = 10 and z = 20, then
x = 2 × 10 × 20 = 400
A 63 kg object needs to be lifted 7 meters in a matter of 5 seconds. Approximately how much horsepower is required to achieve this task?
A. 1.16 hp
B. 864.36 hp
C. 441 hp
D. 0.59 hp
Answer:
1.16 horse power. Option A.
Step-by-step explanation:
Work done = m g h = 63 * 9.81 * 7 = 4326.21 joules
Power = 4326.21 / 5 = 865.24 Watts
1 Horse power = 746 watts so the answer is 865.24 / 746 = 1.16 HP to nearest hundredth.
Answer:
1.16 hp
Step-by-step explanation:
A car salesperson earns 5.8% commision on every car sold. How much commision will the salesperson earn on the sale of a 28,400 car?
Answer:
1647.2
Step-by-step explanation:
5.8% times 28,400 = 1647.2
5.8% = 5.8/100 = .058
so .058 times 28,400 = 1647.2
Final answer:
To find the commission, convert the rate to decimal by dividing by 100 then multiply by the sale price. A salesperson earns 5.8% commission, resulting in $1,647.20 for a $28,400 car.
Explanation:
To calculate the commission a car salesperson earns on the sale of a car, you first need to understand that commission is a percentage of the sale price they receive as their payment. In this case, the salesperson earns a 5.8% commission on each car sold. To find out how much commission they would earn on a $28,400 car, the following calculation is performed:
Sale price of car = $28,400
Commission rate = 5.8%
First, convert the commission rate from a percentage to a decimal by dividing by 100:
5.8% / 100 = 0.058
Next, multiply the sale price by the decimal commission rate:
$28,400 x 0.058 = $1,647.20
Therefore, the commission earned on the $28,400 car is $1,647.20.
Order the numbers 0.64,
2/3 , 65%, and
7/10 from least to greatest. (3 points)
Answer:
.64 < 65 % < 2/3 < 7/10
Step-by-step explanation:
To order all the numbers from least to greatest, but all the numbers in the same form (fraction, decimal, or percent). I will put them all in decimal form so that I can compare them.
0.64, .64
2/3 , =.666666repeating
65% = 65/100 = .65
7/10 = .7
.64< .65<.6666repeating<.7
but we need to put them in their original form
.64 < 65 % < 2/3 < 7/10
Brainliest + Points!
Please show work!
A target is made of a blue square inside of a red square. The blue square has an area of 64 square units, and the red square has an area of 196 square units.
Assuming it hits the target, what is the probability that a dart will land in the red region?
A.
0.25
B.
0.33
C.
0.67
D.
0.75
Answer:
C
Step-by-step explanation:
The target area is shown in the attached picture.
We want to figure out probability of hitting red region.
The area of the figure is the area of the red square, which is 196.
Area of red region is area of whole square (196) minus area of blue square (64). So we have:
Area of red region = 196 - 64 = 132
Probability of hitting red region is 132 divided by total, which is 196.
[tex]\frac{132}{196}=0.67[/tex]
Answer choice C is right.
Debbie cut cord to sixths she is five of the pieces to make necklaces she used equal length of the remaining cord for each of four bracelets what fraction of the original cord did Debbie use for each bracelet
Answer:
¹/₂₄
Step-by-step explanation:
Debbie used ⅚ of the cord for necklaces.
That left ⅙ of the cord for four bracelets.
Each bracelet used:
Fraction of cord = ⅙ ×¼ = ¹/₂₄
Debbie used ¹/₂₄ of the cord for each bracelet.
If the area of a rectangle is 8x^2+10x-3 and it’s width is 2x+3 what is the perimeter of this rectangle?
Answer:
192
Step-by-step explanation:
Blue's Berry Farm charges Percy a total of $24.75 for entrance and 2.5 kilograms of strawberries. The entrance fee is $6, and the price for each kilogram of strawberries is constant. The total cost C for picking strawberries is a function of x, the kilograms of strawberries picked. Write the functions formula. C=
Answer:
C = 6 + 7.5 x
Step-by-step explanation:
Given,
The amount is $24.75 for entrance and 2.5 kilograms of strawberries.
⇒ Entrance fee + 2.5 kilograms of strawberries = $24.75
Since, Entrance fee = $ 6,
And, the price for each kilogram of strawberries is constant.
⇒ $ 6 + 2.5 × 1 kilograms of strawberries = $24.75
⇒ 2.5 × 1 kilograms of strawberries = 18.75
⇒ 1 kilograms of strawberries = $ 7.5.
Thus, the cost of x strawberries = 7.5 x
Also, the total charge for x strawberries = Entrance fee + the cost of x strawberries
= 6 + 7.5 x
⇒ C = 6 + 7.5 x
Which is the required function formula.
What is the supplement of a 47 angle?
Answer:
133° angle
Step-by-step explanation:
Note that "supplement" means 180°.
To find the supplement of the angle given (47°), subtract the given measurement with the total supplementary measurement.
180 - 47 = 133
The supplement of a 47° angle is 133°.
~
What is the solution to the following system? 3x+3y=10
-9x-9y=-30
Answer:
Infinite number of solutions.
Step-by-step explanation:
We have the equations,
1. 3x+3y=10
2. -9x-9y= -30
Now, if we multiply equation 1 with -3, we will obtain equation 2.
i.e. -3×(3x+3y)= -3×10
i.e. -9x-9= -30
So, we see that both the equations are same.
The equation 3x+3y=10 will have solution for many values of x and y.
Hence, the system will have infinite number of solutions.
Answer:
Infinite Solution
Step-by-step explanation:
Given :
[tex]3x+3y=10[/tex] -----(A)
[tex]-9x-9y = -30[/tex] ------(B)
To Find : Solution of the given system of equations
Solution :
We will solve it by using substitution method
Finding the value of x from equation (B)
⇒[tex]-9x-9y = -30[/tex]
⇒[tex]-9x= -30+9y[/tex]
⇒[tex]x= \frac{-30+9y}{-9}[/tex]
⇒[tex]x= \frac{-10+3y}{-3}[/tex]
Putting this value of x in equation (B)
⇒ [tex]3( \frac{-10+3y}{-3})+3y=10[/tex]
⇒[tex]10-3y+3y = 10[/tex]
⇒[tex]10= 10[/tex]
Since x and y both gets eliminated from the equation we got 10 = 10
Since the equations represent the same line.
If a consistent dependent system that has an infinite number of solutions
Hence there is infinite solution .
A plane has 360360 total seats, which are divided into economy class and business class. For every 13 seats in economy class, there are 5 seats in business class.
How many seats are there in each class?
Answer:
There are 260 seats in the economy class and 100 seats in the business class. A plane has 360 total seats, which are divided into economy class and business class. For every 13 seats in economy class, there are 55 seats in business class.
The lunch special at Jimmy John’s costs $5.60. The math club has $50.40 in its treasury. How many lunch specials can the club buy? Write and solve an inequality. Show your work
They can afford 9. You work it out by dividing 50.40 / 5.60
The math club can buy at most 9 lunch specials from Jimmy John's with the money in its treasury.
To determine how many lunch specials the math club can buy, we need to divide the total amount of money in the treasury by the cost of one lunch special. Let's denote the number of lunch specials the club can buy as \( n \).
The cost of one lunch special is $5.60, which can be written as a fraction of dollars as[tex]\( \frac{560}{100} \)[/tex]to make the calculations easier. The total amount of money in the treasury is $50.40, which can similarly be written as [tex]\( \frac{5040}{100} \).[/tex]
Now, we set up the inequality to find the maximum number of lunch specials \( n \) that can be bought without exceeding the treasury's funds:
[tex]\[ \frac{560}{100}n \leq \frac{5040}{100} \][/tex]
To solve for \( n \), we divide both sides of the inequality by the cost of one lunch special:
[tex]\[ n \leq \frac{\frac{5040}{100}}{\frac{560}{100}} \][/tex]
[tex]\[ n \leq \frac{5040}{560} \][/tex]
[tex]\[ n \leq 9 \][/tex]
Since \( n \) must be an integer (you can't buy a fraction of a lunch special), the math club can buy 9 lunch specials at most. Any more than that, and they would not have enough money. Thus, the maximum number of lunch specials the club can buy is 9."
The radius of the circle whose equation is (x + 4)² + (y - 2)² = 36 is
Answer: 6
The equation given to you is in the form (x-h)^2 + (y-k)^2 = r^2
The right hand side 36 is in the place of r^2, so r^2 = 36 leading to r = 6 after you apply the square root to both sides.
find the length of side x in simplest radical form with a rational denominator
Answer:
[tex]\dfrac{10\sqrt{3}}{3}[/tex]
Step-by-step explanation:
You want the length of the hypotenuse in a 30°-60°-90° right triangle with long leg 5.
RatioThe ratios of side lengths in a 30°-60°-90° triangle is ...
1 : √3 : 2
Multiplying these values by 5/√3 gives ...
5/√3 : 5 : 10/√3
That is, the length of the side marked X is 10/√3.
RationalizeThe denominator can be rationalized by multiplying the fraction by 1 in the form of (√3)/(√3):
[tex]X = \dfrac{10}{\sqrt{3}}=\dfrac{10}{\sqrt{3}}\times\dfrac{\sqrt{3}}{\sqrt{3}}\\\\\\\boxed{X=\dfrac{10\sqrt{3}}{3}}[/tex]
What is the equation in slope intercept form of the line that is perpendicular to the given line and passes through the point (-4,-3)
Answer:
b no is the right answer i think
How long (to the nearest foot) is Kentucky Avenue between c street and d street?
Answer:
Kentucky Avenue is 575 ft between C street and D street
Step-by-step explanation:
x / (460 ft) = (1000 ft) / (800 ft)
Divide the right side:
x / (460 ft) = 1.25
To solve for "x", multiply both sides by 460 ft:
(460 ft) [x/(460)] = (460) (1.25)
x = 575 ft
Hope this helped :)
Cecily is comparing two checking accounts. Checking account A has a monthly fee of $16 and a per-check fee of $0.08, while checking account B has monthly fee of $14 and a per-check fee of $0.12. She want to know how many checks she would need to write per month for the accounts to charge the same amount in fees.
Part 1: If x represents the number of checks Cecily writes per month, what expression represents the monthly fee in dollars charged by checking account A?
Part 2: What equation can be set up to solve for the number of checks Cecily would need to write per month for the accounts to charge the same in fees?
Answer:
(1) 0.08x + 16
(2) 0.08x + 16=0.12x + 14
Step-by-step explanation:
Checking account A has a monthly fee of $16 and a per-check fee of $0.08
Per check fee is a constant rate that is 0.08
Let x represents the number of checks Cecily writes per month
1 check fee = 0.08
x checks fee = 0.08x
monthly fee is $16 , we add that as well
So total monthly fee charges for account A is
0.08x + 16
checking account B has monthly fee of $14 and a per-check fee of $0.12.
1 check fee = 0.12
x checks fee = 0.12x
monthly fee is $14 , we add that as well
So total monthly fee charges for account B is
0.12x + 14
(2) To find number of checks write per month for the accounts to charge the same in fees
WE set both expression , account A = account B
0.08x + 16=0.12x + 14
Subtract 0.12x on both sides
-0.04x + 16 = 14
Now subtract 16 on both sides
-0.04x = -2
Divide by -0.04 on both sides
So x= 50
Find the slope of the line that passes through the pair of points.
(-40.86,5.6) and (0.86,4.2)
simplify
Answer:
-.033557047
Step-by-step explanation:
Slope = (y2-y1)/ (x2-x1)
= (4.2 - 5.6)/(.86- 40.86)
= -1.4/ (.86 + 40.86)
= -1.4/41.72
-.033557047
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-40.86, 5.6) and (0.86, 4.2). Substitute:
[tex]m=\dfrac{4.2-5.6}{0.86-(-40.86)}=\dfrac{-1.4}{0.86+40.86}=-\dfrac{1.4}{41.72}=-\dfrac{140}{4172}\\\\=-\dfrac{140:4}{4172:4}=-\dfrac{35}{1043}=-\dfrac{35:7}{1043:7}=-\dfrac{5}{149}[/tex]
Answer: The slope = - 5/149Can someone walk me through this? (Geometry - Triangle Congruence Proof using SAS Theorem)
Answer: sample
Step-by-step explanation:
Help plz
Eleven students are lined up at the drinking fountain. Every other student is a boy. The first, third, fifth, and seventh students are boys. Which other ones are boys?
Answer:
The 9th and 11th students are also boys.
Step-by-step explanation:
Every other student is a boy. Since the 7th student is a boy this means the 8th student is a girl.
You can also think of it with odd numbers. Every odd numbered student is a boy.
How would I solve 5(x -2) =2x +16?
Answer: First, multiply 5 by x-2 to get 5x-10. We now have 5x-10=2x+16. Subtract 2x on both sides: 3x-10=16. Add 10 to both sides: 3x=26. Lastly, divide by 3x to isolate x: x=8.6666667
Please help me with number 2,3,4,5,6 THANK YOU
Answer:
I will help you with question number 2.
48:
12*4
Step-by-step explanation:
12*4=48
what is the ratio of 36 dm to 6 m
Answer:
Step-by-step explanation:
Ratio means division. 36 dm / 6 dm = 6. Cancel out dm.
As a ratio, it would technically be 6:1
A coffee maker costs $124.46. It is marked down 40%.
What is the final price of the coffee maker after it is marked down?
Hi There!
Step-by-step explanation:
40% = 0.4
124.46 * 0.4 = $49.784 (Discount)
124.46 - 49.784 = $74.676 (Sale Price)
74.676 = 74.68
Answer:
$74.676 or $74.68
Hope This Helps :)
Answer:
The cost would be $74.68
Step-by-step explanation:
To find this amount, multiply the original price by the percentage you would be paying. Since the mark down is 40%, we know that the amount paid is 60%. So multiply that by the original cost.
$124.46 * 60% = $74.68
Write an equation of the line that is perpendicular to -x + y = 5 and passes through the point (2, -5). A) y = x - 7 B) y = x - 5 C) y = x - 3 D) y = -x - 3
Answer:
D) y = -x - 3
Step-by-step explanation:
Step 1. Find the slope (m₁) of the original line
The equation for the original line is
-x + y = 5 Add x to each side
y = x + 5
slope = m₁ = 1
Step 2. Find the slope (m₂) of the perpendicular line
m₂ = -1/m₁ Substitute the value of m₁
m₂ = -1/1
m₂ = -1
====================
Step 3. Find the equation for the perpendicular line
y = mx + b Substitute the value of m₂
y = -x + b
The line passes through (2, -5).
-5 = -2 + b Add 2 to each side
b = -3
y = -x - 3
In the image, below the graph of your original equation is the red line.
The blue line passing through (2, -5) is the perpendicular line.
Given 4x =
a + b/8c
, rearrange the equation for a, in terms of b, c, and x
To rearrange the equation for a, subtract b/8c from both sides: a = 4x - b/8c.
Explanation:To rearrange the equation for a, we start with the given equation 4x = a + b/8c. First, we isolate a by subtracting b/8c from both sides, giving 4x - b/8c = a. Therefore, the equation for a in terms of b, c, and x is a = 4x - b/8c.
A turtle crawls 3 yards in an hour. How far will it crawl in 2 hours?
Answer:
It will crawl 6 yards in 2 hours. If you can, please mark me the brainliest :)
Step-by-step explanation:
3 yards an hour * 2 hours = 6 yards per hour.
Answer: 2hrs = 120 mins
1km = 100,000cm
120 x 38 = 4560cm