Find the distance between the two points in simplest radical form. (7,−1) and (9,−9)
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (7, -1) and (9, -9). Substitute:
[tex]d=\sqrt{(9-7)^2+(-9-(-1))^2}=\sqrt{2^2+(-8)^2}=\sqrt{4+64}=\sqrt{68}\\\\=\qrt{4\cdot17}=\sqrt4\cdot\sqrt{17}=\boxed{2\sqrt{17}}[/tex]
The distance between the points (7, -1) and (9, -9) is calculated using the distance formula and simplifies to [tex]2\sqrt{17}[/tex] units.
To find the distance between two points in simplest radical form, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]. For the points (7, -1) and (9, -9), the calculation is as follows:
First, find the difference in the x-coordinates: 9 - 7 = 2.
Next, find the difference in the y-coordinates: -9 - (-1) = -8.
Now, square each difference: (2)^2 = 4 and (-8)^2 = 64.
Add these squares together: 4 + 64 = 68.
Finally, take the square root of the sum: [tex]\sqrt{68}[/tex].
This radical simplifies to [tex]\sqrt{4 * 17} = 2\sqrt{17}[/tex], which is in simplest radical form.
Therefore, the distance between the points (7, -1) and (9, -9) is [tex]2\sqrt{17}[/tex] units.
Bob wants to distribute his fish and plants without any left over. 5 tanks 18 plants 24 fish
The problem is that Bob cannot evenly distribute his 24 fish and 18 plants across 5 tanks due to left over quantities when the numbers are divided.
Explanation:The problem presented is a math problem requiring the use of division and balance. It involves Bob trying to evenly distribute his 24 fish and 18 plants across 5 tanks. An effective way is to divide the quantities of fish and plants by the number of tanks. Therefore, if there are 5 tanks, 24 fish would be divided by 5, giving 4 fish with 4 left over, and 18 plants divided by 5 gives 3 plants each with 3 left over. This indicates that an even distribution is not possible with these numbers, because there would always be a excess quantity of fish and plants beyond what can be put in the 5 tanks.
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To distribute the fish and plants without any leftover, divide the total number of fish and plants by the number of tanks.
Explanation:To distribute the fish and plants without any leftover, Bob needs to divide them equally among the tanks. To find out how many fish and plants should be in each tank, we need to divide the total number of fish and plants by the number of tanks.
Number of fish in each tank = 24 fish / 5 tanks = 4 fish per tank.
Number of plants in each tank = 18 plants / 5 tanks = 3.6 plants per tank. Since we can't have a fraction of a plant, we can round it up to 4 plants per tank or distribute the leftover plant evenly among the tanks.
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what is the first step of solving the equation 2/3x + 1/3x + =5
Answer:
I would combine like terms
Step-by-step explanation:
2/3x + 1/3x + =5
The first step would be to combine like terms
2/3 x + 1/3 x = x
solve for 7 + y = -2 -3x
Answer:
y = -3x-9
Step-by-step explanation:
To solve for y, we need to subtract 7 from each side
7-7 + y = -2-7 -3x
y = -3x-9
For x:
[tex]-2-3x=7+y[/tex] add 2 to both sides
[tex]-3x=9+y[/tex] divide both sides by (-3)
[tex]\boxed{x=-3-\dfrac{1}{3}y}[/tex]
For y:
[tex]7+y=-2-3x[/tex] subtract 7 from both sides
[tex]\boxed{y=-9-3x}[/tex]
-x+3y=12 and y=6x+21 system of substitution
Answer:
(x, y) = (- 3, 3)
Step-by-step explanation:
given the 2 equations
- x + 3y = 12 → (1)
y = 6x + 21 → (2)
Substitute y = 6x + 21 into (1)
- x + 3(6x + 21) = 12 ← distribute
- x + 18x + 63 = 12
17x + 63 = 12 ( subtract 63 from both sides )
17x = - 51 ( divide both sides by 17 )
x = - 3
Substitute x = - 3 into (2) for y
y = (6 × - 3 ) + 21 = - 18 + 21 = 3
solution is (- 3, 3 )
Help with #5 please no idea at all
Answer:
associative property of multiplication
Step-by-step explanation:
Associative property of multiplication states that (a x b) x c = a x (b x c).
5 * (sqrt(9) *4) = (5* sqrt(9) ) *4
Brainliest + Points!
A target is made of a yellow square inside of a green square. What is the theoretical probability that a dart will hit the green square if the side length of the yellow square is 4, and the side length of the green square is 8?
A.
0.25
B.
0.5
C.
0.75
D.
0.8
The green square is the larger square, the total area for the target would be 8 x 8 = 64 square units.
The area of the smaller yellow square would be 4 x 4 = 16 square units.
The green area would be the difference between the total target area and the yellow area: 64 - 16 = 48 square units.
The probability of hitting the green area = 48 / 64 = 0.75
The answer is C.
can someone please tell me what r^2 - 9 = is?
Answer:
The answer is (r + 3)(r - 3)
Step-by-step explanation:
There need to be two number that add together to get 0
and two number that multiply together to get -9
3 + -3 = 0
3 · -3 = -9
= (r + 3)(r - 3)
Manuel finished his English assignment in 1/2 hours. Then he completed his chemistry assignment in 2/5 hours. What was the total amount of time Manuel spent doing these two assignments?
Answer:
9/10 hours
Step-by-step explanation:
You want the total of 1/2 hours and 2/5 hours.
AdditionAddition of fractions is accomplished by converting them to values that have a common denominator.
1/2 = 5/10
2/5 = 4/10
Then the sum is ...
1/2 +2/5 = (5/10) +(4/10) = (5 +4)/10 = 9/10
Manuel spent 9/10 hours on the two assignments.
__
Additional comment
Equivalently, you can convert the fractions to decimals and add them that way:
1/2 +2/5 = 0.5 +0.4 = 0.9 . . . . . 9/10 hours
Your calculator can tell you what the sum is.
The jones family drove 336 miles to their vacation destination. Mr. Jones drove for 2 hours, Mrs. Jones drove for 1.4 hours, and Marcus drove the remaining 1.25 hours. To the nearest tenth, what was the average rate of speed in miles per hour for the Jones’ family trip?
Answer:
first, you add the hours driven then you divide.
2+1.4+1.25=4.65
336/4.65=72.3
Step-by-step explanation:
PLEASE!!!!!!!!!!!! HELPPPP!!!!!!!!!!!!!!!!!!
Which of the following inequalities matches the graph?
graph of an inequality with a solid vertical line through the point (5, 0) and shading to the left of the line
x less than or equal to 5
x greater than or equal to 5
y less than or equal to 5
y greater than or equal to 5
The graph described by the student shows a solid vertical line through the point (5, 0), with shading to the left. This corresponds to the inequality 'x less than or equal to 5'.
Explanation:The student is asking about a graph of an inequality which features a solid vertical line that passes through the point (5, 0). The graph has shading to the left of this line. A vertical line in coordinate geometry represents all points where the x-coordinate is a specific value, and if the shading is to the left, it indicates that the x-values are less than or equal to that specific value of the vertical line.
Therefore, the correct inequality that matches the described graph is x less than or equal to 5 (`x ≤ 5`). The other options do not correctly represent a vertical line or the indicated shading direction.
use the law of cosines to find each missing side round to the nearest tenth
Answer:
13.1
Step-by-step explanation:
yes
Darrien purchases some clothes for a total of $26.50, before tax. Sales tax in his state is 5 percent. What is the total price he has to pay for the clothes? Step 1: (Original Price)(Tax Percent) = Amount of Tax Step 2: Original Price + Amount of Tax = $
Answer:
$27.83
Step-by-step explanation:
26.50 x .05 = 1.325 (round up to 1.33 since the 5 is 5 or greater)
26.50 + 1.33 = 27.83
Amount of tax will be 1.33
Answer:
27.83
Step-by-step explanation:
In Iowa, the format for license plates is 2 numbers followed by 4 letters. However the letters I, O, W, A are not allowed and also the use of repeats is not allowed either. How many license plates are available?
Answer:
32291999
Step-by-step explanation:
Step 1
We will use the fundamental counting principle to work out the total number of possible plates. The fundamental principle of counting states that if a process can be completed in k steps, and that there are [tex]n_1[/tex] steps to complete the first step, [tex]n_2[/tex] steps to complete the second step and [tex]n_k[/tex] stepts to finish the kth step, then there are [tex]n_1\times n_2 \times ....\times n_k[/tex] ways to complete the steps.
Step 2
In this step we figure out the number of ways to complete each step given that no repetitions are allowed. Note that this will include the plate that has I,O,W,A.
The first step can be carried out in 10 ways because there are 10 digits.
The second step can be carried out in 9 ways because we are not allowed to repeat any digits.
The third step can be carried out in 26 ways as there are 26 letters of the alphabet.
The fourth step can be carried out in 25 ways because no repeats are allowed.
the fifth step can be carried out in 24 ways because two of the letters will already have been used.
The sixth step can be carried out in in 23 ways because three letters have been used already.
Step 3
The third step is to use the fundamental counting principle with the values listed in step 3. We will also subtract 1 from whatever value we get because we would have counted the combination with I,O,W,A in it. This calculation is shown below,
[tex]10\times 9\times 26\times 25\times 24\times 23-1=32291999[/tex]
To calculate the total number of available license plates in Iowa based on specific formats and restrictions.
License Plate Combination Calculation:
Since the format is 2 numbers followed by 4 letters, with restrictions on certain letters and repeat use, we calculate the possibilities step by step:
For numbers: 10 choices for each position, so 10×10 = 100 possibilities.
For letters: After considering the restrictions, we have 22 choices for the first letter, 21 for the second, 20 for the third, and 19 for the fourth, resulting in 22×21×20×19 = 155,760 possibilities.
Finally, multiplying the possibilities for numbers and letters gives us the total number of available license plates: 100 × 155,760 = 15,576,000.
Find the selling price of each item Cost of a sled:99.50 Markup:95%
Answer:
Take wholesale cost and multiply it by 95%, then add to the original value
another way, just multiply by 1.95
Retail cost: 1.95*($99.50) = $194.03
Amir drove from Jerusalem to the lowest place on earth, the Dead Sea.
The statement is true. Amir did indeed drive from Jerusalem to the Dead Sea, which holds the distinction of being the lowest point on Earth in terms of land elevation.
True. Amir drove from Jerusalem to the Dead Sea, which is indeed the lowest place on Earth in terms of land elevation. The Dead Sea is a remarkable geographical feature located in the Jordan Rift Valley and is renowned for its extreme salinity, making it one of the saltiest bodies of water on Earth. The surface of the Dead Sea lies approximately 430 meters (1,410 feet) below sea level, and its shores border both Jordan to the east and Israel and the West Bank to the west.
Jerusalem, on the other hand, is situated on a plateau in the Judaean Mountains, and the drive from Jerusalem to the Dead Sea involves descending from higher elevations down to the low-lying area where the Dead Sea is located. This journey provides travelers with a striking transition from the elevated terrain around Jerusalem to the uniquely low and buoyant waters of the Dead Sea.
The Dead Sea's remarkable location and its high salinity levels have made it a popular destination for tourists seeking the therapeutic benefits of its mineral-rich mud and the sensation of effortlessly floating on its surface. This natural wonder's status as the lowest place on Earth is well-documented and contributes to its global renown.
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The question probable may be:
Amir drove from Jerusalem to the lowest place on earth, the Dead Sea. True or false.
How much more expensive is it to buy a ticket in New york than in Atlanta?
The table shows the average baseball ticket price for three anerican cities
A)$12.86
B)$14.17
C)$5.25
D)$8.92
Table: locations. Average price
Atlanta. $14.42
New York. $28.59
Los Angeles. $19.67
Answer:B
Step-by-step explanation:
May you help me out someone
Answer:
x = 4 1/2 or 4.5 cm
Step-by-step explanation:
We know the perimeter of the rectangle is given by the formula
P =2(l+w)
19 = 2(2.5 + (2.5+x))
Simplifying
19 = 2( 5+x)
Distribute
19 = 10 + 2x
Subtract 10 from each side
19-10 = 10-10 + 2x
9 = 2x
Divide each side by 2
9/2 = 2x/2
4.5 = x
which lists all the integer solutions of the equation |x| <3
a 0 1 and 2
b 0 1 2 and 3
c -2 -1 0 1 and 2
d -3 -2 -1 0 1 2 and 3
Answer:
c -2 -1 0 1 and 2
Step-by-step explanation:
abs (x) < 3
Absolute value equations have 2 solutions, one positive and one negative ( remember to flip the inequality when taking the negative solution).
x<3 and x>-3
-3 <x<3
The integer solutions are -2,-1,0,1-2
We do not include 3 because there is no equals sign on the inequality.
A 10.5 ounce package costs $2.98 A 27.8 ounce package costs $8.99 which is the better deal based on the unit price. Round your answers to the nearest cent.
Final answer:
After calculating the cost per ounce for both packages, the 10.5-ounce package, with a unit price of $0.284 per ounce, is the better deal compared to the 27.8-ounce package, which has a unit price of $0.323 per ounce.
Explanation:
To determine which package has the better unit price, you calculate the cost per ounce for each package and compare them. First, divide the total cost of each package by the number of ounces it contains.
For the 10.5-ounce package at $2.98:
$2.98 ÷ 10.5 ounces = approximately $0.284 per ounce
For the 27.8-ounce package at $8.99:
$8.99 ÷ 27.8 ounces = approximately $0.323 per ounce
Now, compare the unit prices. The 10.5-ounce package has a lower unit price of $0.284 per ounce compared to the 27.8-ounce package with a unit price of $0.323 per ounce, making the 10.5-ounce package the better deal based on unit price.
What is the answer to linear equation: 5 - 5w = 6
Answer: [tex]w=-\frac{1}{5}[/tex]
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
1. You have the following equation given in the problem above:
[tex]5 -5w= 6[/tex]
2. Then, you need to solve for [tex]w[/tex], as you can see in the following steps:
[tex]5-5w=6\\-5w=6-5\\-5w=1\\w=-\frac{1}{5}[/tex]
3. Therefore, as you can see, the value of [tex]w[/tex] is:
[tex]w=-\frac{1}{5}[/tex]
Identify the percent amount and base in this problem.150 is 25 percent of what number.
let's say that number is "x", so that is then the 100%.
if 150 is 25%, what is "x"?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 150&25 \end{array}\implies \cfrac{x}{150}=\cfrac{100}{25}\implies \cfrac{x}{150}=4\implies x=600[/tex]
Write the equation of the line that passes through (3, 4) and (2, –1) in slope-intercept form.
ANSWER: [tex]y=9x-23[/tex]
EXPLANATION:
We can use the slope-formula to find the slope.
[tex]\text{Slope Formula:} \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\frac{4+5}{3-2} =m\\\\\frac{9}{1} = m\\\\9=m[/tex]
Now that we have the slope, we can plug in one of the x and y values into the slope-intercept formula to find b.
[tex]\text{Slope-Intercept Formula}:y=mx+b\\\\4=9(3)+b\\\\4=27+b\\\\-23=b[/tex]
The equation of the line that passes through (3, 4) and (2, -1) is [tex]y=9x-23[/tex]
What comes after 90 cents in coins?
Answer: 100 cents making it 1 dollar
Answer:
91 Cents
Step-by-step explanation:
The next and lowest coin is a penny.
90 + 1 = 91
Why do you first combine like terms and then use the distributive property to solve 8(5x+9x+6)=160
Final answer:
To solve 8(5x+9x+6)=160, we first combine like terms to simplify the expression within the parentheses to 14x+6, and then use the distributive property to further simplify and solve the equation. This order of operations ensures clarity and accuracy in solving the equation.
Explanation:
The question involves solving the algebraic expression 8(5x+9x+6)=160. The first step in simplifying and solving an equation like this is to combine like terms within the parentheses. Combining like terms (5x+9x) simplifies the expression inside the parentheses to 14x+6. This simplification makes the equation easier to manage and understand. The next step is to use the distributive property which allows us to multiply the number outside the parenthesis (in this case, 8) by each term inside the parenthesis individually (14x and 6). After distributing, we get 112x + 48 = 160, from which we can solve for x by isolating the variable.
The order of operations is crucial here; combining like terms before using the distributive property ensures the equation remains manageable and reduces the potential for errors. After these steps, we can subtract 48 from both sides and divide by 112 to find the value of x that satisfies the equation.
A line has a slope of -5 and passes through the point (2, 2). An equation for this line is
A) y = 2x + 2
B) y = 2x - 5
C) y = -5x - 2
D) y = -5x + 12
Answer:
The equation of the line has a slope of -5 and passes through the point (2, 2) is y = -5x + 12 .
Option (D) is correct.
Step-by-step explanation
The equation of the line
y = mx + c
where m is the slope and c is the y - intercept .
As given
A line has a slope of -5 and passes through the point (2, 2).
The slope of the line is -5.
m = -5
Put in the equation of the line
y = -5x + c
Put x = 2 and y = 2
2 = -5 × 2 + c
2 = - 10 + c
2 + 10 = c
12 = c
Put the value of c in the y = -5x + c
y = -5x + 12
Therefore the equation of the line has a slope of -5 and passes through the point (2, 2) is y = -5x + 12 .
Option (D) is correct.
To find the equation of the line with slope -5 passing through (2, 2), use the point-slope form and simplify to get y = -5x + 12. Therefore, the correct answer is option D.
To find the equation of the line with a slope of -5 that passes through the point (2, 2), we can use the point-slope form of the equation of a line:
y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passes through.
Substituting the given values:
y - 2 = -5(x - 2)
Simplify this equation:
Distribute the -5: y - 2 = -5x + 10Add 2 to both sides to solve for y: y = -5x + 12Therefore, the equation of the line is y = -5x + 12, so the correct answer is option D.
Write the sentence as an equation.
384 subtracted from the quantity 35 times q is q times 225, decreased by 189
Answer:
35q-384 = 225q-189
Step-by-step explanation:
since its 384 subtracted from 35 times q it will be 35q-384 and then it says "is" which is an equal sign (=) and then q times 225 which is 225q decreased by 189 which is 225q-189 so it will be 35q-384 = 225q-189
Simple questions points!!! :)
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Answer questions 3-6
Answer:
3. aₙ = -9n +7
4. d = -2.4
5. a₆ = 45
6. aₙ = 133 + 4n
Step-by-step explanation:
Question 3.
a₁ = -2; aₙ = aₙ₋₁ - 9
The explicit rule for an arithmetic sequence is
aₙ = a₁ + d(n -1 )
d = aₙ - aₙ₋₁
aₙ = aₙ₋₁ - 9 Subtract aₙ₋₁ from each side
aₙ - aₙ₋₁ = -9
d = -9
For this sequence,
aₙ = -2 – 9(n - 1) Remove parentheses
aₙ = -2 - 9n + 9 Combine like terms
aₙ = -9n + 7
===============
Question 4
d = aₙ - aₙ₋₁
a₂ - a₁ = 6.2 – 8.6 = -2.4
a₃ - a₂ = 3.8 – 6.2 = -2.4, etc.
The common difference is
d = -2.4
===============
Question 5
aₙ = 8n – 3 Substitute the value of n
a₆ = 8×6 – 3
a₆ = 48 - 3
a₆ = 45
============
Question 6
a₁ = 137; d = 4
aₙ = a₁ + d(n -1 )
aₙ = 137 + 4(n -1 )
aₙ = 137 + 4n -4
aₙ = 133 + 4n
WEATHER The equation y=0.2x +3.5 can be used to find the amount of accumulated snow y in inches x hours after 5 P.M. on a certain day. Identify the slope and y- intercept of the graph of the equation and explain what each represents.
Answer:
Slope (m) = 0.2 and y-intercept (b) = 3.5.
Slope represents here the increase in snow 0.2 inches per hour and y-intercept represents here the initially 3.5 inches snow was there.Step-by-step explanation:
We are given weather equation y=0.2x +3.5 for finding the amount of accumulated snow y in inches x hours after 5 P.M. on a certain day.
We need to identify the slope and y- intercept of the graph of the equation .
Let us compare given equation y=0.2x +3.5 by slope-intercept form y=mx+b, we get
Slope (m) = 0.2 and y-intercept (b) = 3.5.
Slope represents here the increase in snow 0.2 inches per hour and y-intercept represents here the initially 3.5 inches snow was there.A 15 ft ladder leans against the side of a house. The top of the ladder is 13 ft off the ground. Find x, the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree.
Answer:
x= 60.1 degrees
Step-by-step explanation:
The triangle forms a right angle triangle
Opposite side of angle x = 13 ft
Hypotenuse of the triangle = 15
We know the opposite side and the hypotenuse
So we use trigonometric formula sin(x)
[tex]sin(x) = \frac{opposite}{hypotenuse}[/tex]
[tex]sin(x) = \frac{13}{15}[/tex]
When we move 'sin' to the other side it becomes 'sin^-1'
[tex]x=sin^{-1}(\frac{13}{15})[/tex]
x = 60.073565
Answer:x = 60.073565
Step-by-step explanation: