Answer:
sqrt.(a) * absolutevalue(b)
Step-by-step explanation:
You do abs value when you have an even exponent with an odd exponent result from b^2 to b^1.
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Answer: Hello there!
Well, the square root is the inverse function of the square potential.
This is if you have [tex](\sqrt{x} )^{2} = x[/tex] and [tex]\sqrt{x^{2} } = +-x[/tex]
A interesting part of the square root is that (-4)*(-4) = 16, and 4*4 = 16, so the solutions for [tex]\sqrt{16}[/tex] are -4 and 4. For this is that you see a +- symbol in the second equation.
Now, if you have the number [tex](a*b)^{2}[/tex]
Now, we put this inside a square root: [tex]\sqrt{(a*b)^{2} } = +-a*b[/tex]
So the solutions for the square root of (a*b)^2 are a*b and - a*b.
Ying Zyiyu covered the first 300 miles of a trip going at 60 mph and the last hundred going at 40 mph. What was his average speed for the entire trip?
Answer:
53 1/3 mph
Step-by-step explanation:
Speed equals distance over time.
She covered 300 miles in 60mph, which took 5 hours.
(300/60=5 )
She also covered 100 miles in 40mph, which means she took 2.5 hours.
(100/40=2.5)
So the total distance is 400miles and the total time is 7.5 hours.
s=d/t substitute values which gives you 400/7.5 which equals 53 1/3 mph
Which table of ordered pairs represents a proportional relationship?
Answer:
The correct option is 3.
Step-by-step explanation:
We need to find a table of ordered pairs that represents a proportional relationship.
Proportional relationship: It means y-values are proportional to x-values.
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is constant of proportionality.
For table 1,
[tex]\frac{y_1}{x_1}=\frac{8}{4}=\frac{2}{1}[/tex]
[tex]\frac{y_2}{x_2}=\frac{11}{7}[/tex]
[tex]\frac{2}{1}\neq \frac{11}{7}[/tex]
Table 1 does not represents a proportional relationship.
Similarly,
For table 2,
[tex]\frac{25}{5}\neq \frac{49}{7}[/tex]
Table 2 does not represents a proportional relationship.
For table 3,
[tex]\frac{3}{6}=\frac{5}{10}=\frac{7}{14}=\frac{1}{2}[/tex]
Table 3 represents a proportional relationship.
For table 4,
[tex]\frac{6}{3}\neq \frac{11}{8}[/tex]
Table 4 does not represents a proportional relationship.
Only table 3 represents a proportional relationship. Therefore the correct option is 3.
What equation has the steepest graph ?
Answer:
B
Step-by-step explanation:
for a linear equation y = mx + b,
the steepness of the graph is denoted by the slope, m
The larger the absolute number of the slope, the steeper it is
in this case it is quite clear that B has the largest absolute number for m.
i.e abs (-10) = 10
What value of x is in the solution set of 3(x-4)>5x+2?
3(x - 4) > 5x + 2
First you must distribute the 3 to the numbers inside the parentheses
(3 * x) + (3 * (-4)) > 5x + 2
3x + (-12) > 5x + 2
3x - 12 > 5x + 2
Now you must combine like terms
3x goes with 5x
^^^To do this subtract 3x to both sides of the equation
(3x - 3x) - 12 > (5x - 3x) + 2
0 - 12 > 2x + 2
-12 > 2x + 2
-12 goes with 2
^^^To do this subtract 2 to both sides
-12 - 2 > 2x + (2 - 2)
-14 > 2x + 0
-14 > 2x
Isolate x by dividing 2 to both sides
-14/2 > 2x/2
-7 > x
Hope this helped!
~Just a girl in love with Shawn Mendes
A hamburger bun merchant can ship 8 large boxes or 10 small boxes of hamburger buns into a carton for shipping. In one shipment, he sent a total of 96 boxes of hamburger buns. If there are more large boxes than small boxes, how many cartoons did he ship?
56 large boxes and 40 small boxes.
Step-by-step explanation:To solve this problem, we need to use the concept of multiples. By definition, a multiple of a number is that number multiplied by an integer. For instance, 3, 6, 9, 12 are multiples of 3. So let's do a chart and list the multiples of large and small boxes:
[tex]\begin{array}{cccccccccc}Number\,of\,boxes & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\\Large & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72\\Small & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90\end{array}[/tex]
From this, our goal is to select the number of small and large boxes such that the sum is 96 boxes of hamburger burns and the number of large boxes is greater than the number of small boxes. From the table, the correct solution is:
56 large boxes and 40 small boxes, and this meets our requirement, because 56 + 40 = 96 and 56 > 40
Lin multiplies 7/8 times a number.the product is less than 7/8 . Which could be Lin’s number ?
Answer:
Any number less than 1
Step-by-step explanation:
Let x be the number Lin multiplies by 7/8. So, we have:
(7/8)*x < 7/8
We need to find the possible values for x. Lets start by dividing both sides of our inequality by (7/8) in order to get x alone on the left side.
(7/8)*x / (7/8) < (7/8)/(7/8)
Reordering:
(7/8) / (7/8) * x < (7/8)/(7/8)
As any number divided by itself (except from 0) is equal to 1:
x < 1
So, the number that Lin multiplied by 7/8 MUST be less than 1. This is evident, as any positive number multiplied by a number less than 1 will decrease, doesn't matter if its a negative or positive number.
So, such number is less than 1. Any number less than 1 could be Lin's number.
Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4. f(x) = −16x2 f(x) = 16x2 f(x) = − x2 f(x) = x2
Answer:
[tex]f(x)=-\frac{1}{16} x^2[/tex]
Step-by-step explanation:
We are to derive the equation of the parabola with a focus at [tex](0, -4)[/tex] and a directrix of y = 4.
We know that a parabola is the locus of all the points as long as the distance from the fixed point on the parabola to the fixed line directrix is kept same.
This parabola is facing downwards. So assuming any point on the parabola to be [tex](x,y)[/tex].
Distance from focus [tex](0,-4)[/tex] to [tex](x,y)[/tex] = [tex]\sqrt{(x-0)^{2} +(y+4) ^{2}}=\sqrt{x^{2}+ (y+4)^{2}}[/tex]
Distance from [tex](x,y)[/tex] to directrix [tex](y=4)[/tex] = [tex]\left | y-4 \right |[/tex]
Equating these distances as they are equal:
[tex]\sqrt{x^{2}+ (y+4)^{2}}=\left | y-4 \right |[/tex]
[tex]{x^{2}+ (y+4)^{2}=(y-4)^{2}[/tex]
[tex]x^2+y^2+8 y +16 = y^2 - 8 y+16[/tex]
[tex]x^2 = -8 y - 8 y= -16 y[/tex]
[tex]x^2= - 16 y[/tex]
So the equation of the parabola is [tex]f(x)=-\frac{1}{16} x^2[/tex].
Answer:
The equation of the parabola is y = -1/16 x²
Step-by-step explanation:
* Lets revise some facts about the parabola
- Standard form equation for a parabola of vertex at (0 , 0)
- If the equation is in the form x² = 4py, then
- The axis of symmetry is the y-axis, x = 0
- 4p equal to the coefficient of y in the given equation to
solve for p
- If p > 0, the parabola opens up.
- If p < 0, the parabola opens down.
- Use p to find the coordinates of the focus, (0 , p)
- Use p to find equation of the directrix , y = - p
* Lets solve the problem
∵ The focus at (0 , -4)
∵ The coordinates of the focus are (0 , p)
∴ p = -4
∵ The directrix is y = 4
∵ The equation of the directrix , y = - p
∴ -p = 4 ⇒ p = -4
∵ the equation is in the form x² = 4py
∵ p = -4
∴ x² = 4(-4)y
∴ x² = -16y ⇒ divide both sides by -16
∴ y = -1/16 x²
* The equation of the parabola is y = -1/16 x²
In an '80% off' sale, an oven was £112. Work out the original price.
Answer:520
Step-by-step explanation:
Suppose the original prize is=x
If the discount is of 80%,the selling prize is of 20%
20% of x=112
20x/100=112
X=520
Its the original prize...
Answer:
£560
Step-by-step explanation:
80% off means that the sale price is 20% of the original price.
The original price is represented by 100%
Divide the sale price by 20 to find 1% then multiply by 100 to obtain the original price
original price = [tex]\frac{112}{20}[/tex] × 100 = £560
C is the center of the circle. Find the length of QPR
Answer:
30
Step-by-step explanation:
The length from one point on the edge of a circle to the middle will always be the same otherwise it isn't a circle. If QC is the same as CR than 15 and 15 would get you 30.
Answer:
70.686
Step-by-step explanation:
In order to know the length of QPR, we have to notice that QR=1/4 of the perimeter of the circle (circumference), then QPR= 3/4 of the perimeter of the circle.
Remember:
Circumference of a circle= 2[tex]\pi[/tex]*radius
Where:
[tex]\pi[/tex]= 3.1416 (its a constant value)
radius=15
Circumference of a circle=2*3.1416*15=94.248
Then:
QPR= 3/4 of the circumference of the circle
QPR= 3/4*94.248
QPR= 70.686
10. One number is 5 times another number, and
their sum is -60. What is the lesser of the two
numbers?
F. -5
G. -10
H. -12
1 -48
Answer:
G. -10
Step-by-step explanation:
Let one number = x
Let the second one = y
Equations
y = 5x
x + y = -60
Solution.
Put 5x in for y in the second equation.
x + 5x = -60 Combine like terms on the left
6x = -60 Divide by 6
6x/6 = -60/6 Do the division
x = -10
So one of the numbers is minus 10
What is the approximate probability of choosing an orange marble and a green marble
Answer:
Step-by-step explanation:
It depends on how many green and orange marbles their are...If their is 30 marbles in a bag and 10 of them are orange and green it would be 10/30 divide both of them by 10 and you would get 1/3 But that is just an example.
Hope my answer has helped you in any way!
Answer:0.04444
Step-by-step explanation:
Number of red balls = 5
Number of orange balls = 2
Number of yellow balls = 1
Number of green balls = 2
Therefore total number of balls = 10.
Probability of getting a ball =
P(choosing orange ball) =
After picking an orange ball, we are left with 9 balls
P ( choosing a green ball) =
P(choosing an orange marble and a green marble) =
0.04444 is the approximate probability of choosing an orange marble and a green marble.
write an expression to find the area and perimeter of the rectangle:
L=
[tex] {2x}^{2} - x + 3[/tex]
W=
[tex] {4x}^{2} + 2x - 1[/tex]
Answer:
Step-by-step explanation:
the area is :A= L×W
A= (2x²-x+3)(4x²+2x-1).....calculate
the perimeter is : P= 2(L+W)
P= 2(2x²-x+3)+(4x²+2x-1))....calculate
Charles is on a 8 1/2 mile bike ride. He stops for a rest after he’s gone 5 2/5 miles. How much farther does he still have to go?
Answer:
31/10 or 3 1/10 more miles.
Step-by-step explanation:
=
(17 × 5) - (27 × 2)
2 × 5
Answer:
[tex]3\frac{1}{10}[/tex] miles
Step-by-step explanation:
The total distance of Charles bike ride is = [tex]8\frac{1}{2}[/tex] miles
He has covered the distance = [tex]5\frac{2}{5}[/tex] miles
We will subtract his covered distance from total distance.
He still have to go = [tex]8\frac{1}{2}[/tex] - [tex]5\frac{2}{5}[/tex]
= [tex]\frac{17}{2}[/tex] - [tex]\frac{27}{5}[/tex]
= [tex]\frac{85-54}{10}[/tex]
= [tex]\frac{31}{10}[/tex]
= [tex]3\frac{1}{10}[/tex] miles
He still have to go [tex]3\frac{1}{10}[/tex] miles
The rate (gallons per day) at which a pond loses water due to evaporation from one day after observation has started is give by w(t)=1/T2 (squared).
where t is the number of days after the first day. suppose we want to find out what the trend is for the total change in gallons in the pond. (Fill in the following table)
t is the number of days after the first day, and w is the number of gallons.
T: 1 2 10 50 100 200 500 1000
w(t): ? ? ? ? ? ? ? ?
Answer: see table below
Step-by-step explanation:
[tex]\left\begin{array}{c|l}T&\qquad w(t)\\1&\dfrac{1}{1^2}=1\implies 1.00\\\\2&\dfrac{1}{2^2}=\dfrac{1}{4}\implies 0.25\\\\10&\dfrac{1}{10^2}=\dfrac{1}{100}\implies 0.01\\\\50&\dfrac{1}{50^2}=\dfrac{1}{2500}\implies 0.0004\\\\100&\dfrac{1}{100^2}=\dfrac{1}{10000}\implies 0.0001\\\\200&\dfrac{1}{200^2}=\dfrac{1}{40000}\implies 0.000025\\\\500&\dfrac{1}{500^2}=\dfrac{1}{250000}\implies 0.000004\\\\1000&\dfrac{1}{1000^2}=\dfrac{1}{100000}\implies 0.000001\\\end{array}\right[/tex]
the national flag of scotland has a white diagonal on a blue backround Tracy is sewing a scottish flag she knows that the length of one diagonal will be 15 feet and the flag will be 9 feet high to the nearest foot how long will the scottish flag be
Answer:
12 feet
Step-by-step explanation:
By Pythagoras theorem, a²+b²=c², where c represents the diagonal and a and b represents the other sides of a right angled triangle
As a flag is a rectangle, the two triangles cut would be right angled triangles
Therefore, a²+9²=15²
a²+81=225
a²=144
a=√144
a=12 feet
Final answer:
To calculate the length of the Scottish flag, the Pythagorean theorem is applied. With a diagonal (hypotenuse) of 15 feet and a height of 9 feet, the length is found to be 12 feet.
Explanation:
The question involves calculating the length of the Scottish flag given the length of one diagonal and the flag's height. To find the length of the Scottish flag, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here, we know the length of the diagonal (hypotenuse) is 15 feet and the height (one side) is 9 feet.
Let x be the length of the Scottish flag (the other side of the right-angled triangle). According to the Pythagorean theorem, [tex]x^2 + 9^2 = 15^2.[/tex]
Solving for x, we get:
[tex]x^2 + 81 = 225[/tex][tex]x^2 = 225 - 81[/tex][tex]x^2 = 144[/tex][tex]x = \sqrt144[/tex]x = 12Therefore, the length of the Scottish flag will be 12 feet to the nearest foot.
Determine the best method to solve the system of equations. Then solve the system.
7x-2y=8
5x+2y=4
Answer:
x=1 y = -1/2
(1,-1/2)
Step-by-step explanation:
7x-2y=8
5x+2y=4
I would use elimination since we have 2y in one equation and -2y in the other
7x-2y=8
5x+2y=4
--------------------
12x = 12
Divide each side by 12
12x/12 = 12/12
x =1
The substitute back into equation 2
5(1) +2y = 4
5 +2y = 4
Subtract 5
5-5+2y = 4-5
2y = -1
Divide by 2
2y/2 = -1/2
y = -1/2
Answer:
The best method is the elimination method. The solution is (1, -1/2).
Step-by-step explanation:
7x - 2y = 8
5x + 2y = 4
12x = 12
x = 1
7(1) - 2y = 8
7 - 2y = 8
-2y = 1
y = -1/2
Make sure to write the answer in the form of an ordered pair.
Note: Alternative methods are graphing and the substitution method.
It is about a 425-mile drive from San Jose to
Los Angeles down CA-1, and about a 320-
mile drive from San Jose to Santa Barbara
along the same route.
If you stop in Santa Barbara, you can take a
walk along the water front, or visit the Santa
Barbara Zoo.
How far is the drive from
Santa Barbara to Los Angeles?
Answer:
105
Step-by-step explanation:
425 - 320 = 105 miles
Final answer:
The drive from Santa Barbara to Los Angeles is 105 miles, which is the difference between San Jose to Los Angeles (425 miles) and San Jose to Santa Barbara (320 miles).
Explanation:
The question asks how far it is to drive from Santa Barbara to Los Angeles. To determine this distance, we utilize the total distance from San Jose to Los Angeles and subtract the distance from San Jose to Santa Barbara. Starting with the overall distance of San Jose to Los Angeles, which is 425 miles, we deduct the San Jose to Santa Barbara distance of 320 miles. This calculation will provide us with the distance from Santa Barbara to Los Angeles.
By subtracting 320 miles from 425 miles, we find that the distance from Santa Barbara to Los Angeles is 105 miles.
if the diameter of a circle is 7/8 of an inch what is its radius
Answer:
r = 7/16 inch
Step-by-step explanation:
The radius is 1/2 of the diameter
r = 1/2 d
r =1/2 (7/8)
r = 7/16 inch
f(x) = 4x2 + 1 and g(x) = x2 - 5, find (f+ g)(x)
Answer:
Step-by-step explanation:
(f + g)x translates into a more readable f(x) + g(x) so all you do is
f(x) + g(x) = 4x^2 + 1 + x^2 - 5
f(x) + g(x) = 5x^2 - 4
Answer:3x^2+6
Step-by-step explanation: I'm not really good at math but the correct answer is 3x^2+6
If x+4/4 =y+3/3 then y/3=
Answer:
x/4
Step-by-step explanation:
(y+3)/3=y/3+3/3=y/3+1
So to find y/3 in your equation all we would need to do is subtract 1 on both sides giving:
(x+4)/4-1
This can be simplified
x/4+4/4-1
x/4+1-1
x/4+0
x/4
Answer: x/4
convert 9.25% to fraction form
Answer:
[tex]\frac{37}{400}[/tex]
Step-by-step explanation:
9.25% as a fraction would be [tex]\frac{9.25}{100}[/tex], since a percentage is always out of 100.
Multiply the fraction by 100 to convert the decimal into fraction form
[tex]\frac{9.25}{100} \rightarrow\frac{925}{10000}[/tex]
Reduce to the simplest terms
[tex]925\div25=37\\\\ 10000\div25=400\\\\ \frac{37}{400}[/tex]
12b−17b−b how solve this?
Answer:
-6b
Step-by-step explanation:
In this question, its simple math,how?
All the terms are alike, so just apply subtraction method;
[tex]=12b-17b-b\\\\\\\\=12b-18b\\\\=-6b[/tex]
For this case we have the following expression:
[tex]12b-17b-b=[/tex]
We have that by definition of Law of the Signs of the Sum that: Equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the greater is placed. So:
[tex]-5b-b =\\-6b[/tex]
Answer:
-6b
Somebody help this is algebra
Answer:
2 is your answer
Step-by-step explanation:
If h(x)= 5 then 5= 2x +1
so 5 = 2x + 1
-1 -1 on both sides
then 2x = 4
2 2 divide by 2
which x = 2
Hope my answer has helped you!
The surface area (SA) of a cube with a as the length of each of its sides is given by the formula . If the surface area is known, how can you rewrite the formula to find its side?
Answer:
Step-by-step explanation:
1 surface area of the cube is s*s.
There are 6 faces on such a cube.
Area = 6*s^2 Divide by 6
Area/6 = 6s^2 / 6 Do the divsion
Area/6 = s^2
s = sqrt(area/6)
At the beginning of March, Janet opened a checking account with her first paycheck of $153.82. During the month, she withdrew $40 from the ATM, wrote a check for $54.12 to pay for her cell phone, deposited a check for $215.70, transferred $75.00 to her savings account, and had a debit of $130 for sports equipment.
Answer:
$ 70.4
Step-by-step explanation:
Data:
The opening balance = $ 153.82
Withdrawal made = - $ 40
Check for payment = - $ 54.12
Deposited a check for payment = + $ 215. 70
Transferred amount to the savings = - $ 75.00
Debit for the sports equipment = -$ 130
The total amount left will be = $ (153.82- 40-54.12+ 215.70-75-130)
= $ 70.4
Answer:
The account balance is $70.40.
Explanation:
Please make the brainliest :)
The digits 1,2,3 and 4 are used to make a 3 digit number. Each digit can be repeated. What is the total number of 3 digit numbers that can be made using these digits?
Answer:
24 ways
Step-by-step explanation:
4P3 = 4*3*2
=24
Final answer:
The total number of three-digit numbers that can be made using the digits 1, 2, 3, and 4 with repetition allowed is 64. This is computed by multiplying the number of digit options available for each place value in a three-digit number (4 options each for hundreds, tens, and ones).
Explanation:
To determine the number of possible three-digit numbers that can be created using the digits 1, 2, 3, and 4, with the possibility of repeating digits, we need to consider that each place value (hundreds, tens, and ones) can be filled by any of the four digits available.
Therefore, for the hundreds place, there are 4 options (1, 2, 3, or 4). The same is true for the tens and ones place, since repetition is allowed, giving 4 options for each. We calculate the total number of combinations by multiplying the number of options for each place value:
Hundreds place: 4 options
Tens place: 4 options
Ones place: 4 options
The total number of possible numbers is 4 (for the hundreds) × 4 (for the tens) × 4 (for the ones) = 64 numbers.
what is 123,456,789 times 2 divided by 4
Answer:
61728394.5
Step-by-step explanation:
Using order of operations, you can either perform the multiplication first or the division first.
123,456,789 × 2 / 4 =
123,456,789 / 2 =
61728394.5
Answer:
61,728,394.5
Step-by-step explanation:
Remember to follow PEMDAS & left->right rule.
In this case, they are multiply & divide, so you can solve through left - > right rule:
123,456,789 x 2 = 246,913,578
246,913,578/4 = 61,728,394.5
61,728,394.5 is your answer.
~
Simplify the expression –3(x + 3)2 – 3 + 3x. What is the simplified expression in standard form?
–3x2 – 18x – 27
–3x2 – 15x – 30
–3x2 + 3x + 6
–3x2 + 3x – 30
Answer:
[tex]-3x^2-15x-30[/tex]
Step-by-step explanation:
The given expression is [tex]-3(x+3)^2-3+3x[/tex].
We expand to obtain:
[tex]-3(x^2+6x+9)-3+3x[/tex].
We apply the distributive property to get:
[tex]-3x^2-18x-27-3+3x[/tex].
Group and combine the like terms;
[tex]-3x^2-18x+3x-27-3[/tex].
[tex]-3x^2-15x-30[/tex].
This polynomial expression is in standard form because it is descending powers of x.
The simplification of the algebraic expression in standard form is -3x² - 15x - 30
What is an algebraic expression?An algebraic expression is the expression of mathematical variables with their coefficients(numbers), integers, and arithmetic operations. The simplification of algebraic expression usually follows a pattern such as;
opening the bracketstaking like terms and solving the like terms separately.From the given algebraic expression, we have:
= -3(x + 3)² - 3 + 3x
Let's expand the above terms in the bracket, we have:
= -3(x² +6x + 9) - 3 + 3x
= -3x² - 1x - 27 - 3 + 3x
By rearrangement, we have:
= -3x² - 18x + 3x - 27 - 3
= -3x² - 15x - 30
Learn more about algebraic expression here:
https://brainly.com/question/4344214
Serena counts her calories over several days. What is her total caloric intake given these values: 1,405; 1,219; 1,119; 1,353.
For this case we add the quantities of calories consumed per day, that is:
[tex]1,405 + 1,219 + 1,119 + 1,353 = 5,096[/tex]
So Serena consumed 5,096 calories in 4 days. If we want to know the average calorie content per day, we divide the amount obtained by 4:
[tex]\frac {5,096} {4} = 1,274[/tex]
ANswer:
5,096 total calories
Consumes on average 1,274 calories per day.
While driving from his house to the beach, Cameron passed a sign the read “beach 21 miles.” If the distance from Cameron’s house to the beach is 46 miles, how many miles had Cameron already traveled?
Answer:
Step-by-step explanation:
46-21=25
Answer: 25 miles
Step-by-step explanation:
Given : The distance is remaining to travel to reach the beach from the sign = 21 miles
The distance between the beach and his house = 46 miles
Now, the distance Cameron traveled already is given by :-
[tex]\text{Total distance-Remaining distance}\\\\=46-21=25\text{ miles}[/tex]
Hence, Cameron already traveled 25 miles.