Answer:
18 + √3
Step-by-step explanation:
The product of a surd and its conjugate gives a rational number. Hence;
(18 - √3) (18 + √3)
=324 + 18√3 - 18√3 - 3
=321
A rational number does not contain any surd, hence the answer.
Answer: cube root 1/18 & cube root 12
Find the area of the following shape. Show all work
Best way to solve this is by using
[tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]
[tex]where \: s = \frac{a + b + c}{2} [/tex]
s=(12+8+17)/2
=18.5
using the formulae
area =43.5
Autumn runs a farm stand that sells peaches and grapes. Each pound of peaches sells
for $2 and each pound of grapes sells for $4. Autumn sold 35 more pounds of grapes
than pounds of peaches and made $200 altogether. Graphically solve a system of
equations in order to determine the number of pounds of peaches sold, 2, and the
number of pounds of grapes sold, y.
Answer:
She sold 10 pounds of peaches and 45pounds of grapes
Step-by-step explanation:
X= pounds of peaches
x+35=pounds of grapes
2x+4(x+35)=200
2x+4x+140=200
6x=200-140
6x=60
x=10
She sold 10 pounds of peaches and 45pounds of grapes. (Sorry, can’t help you graph it.)
ALGEBRAIC EXPRESSION 11. Subtract the sum of 13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7. 12. From the sum of x 2+ 3y 2 − 6xy, 2x 2 − y 2 + 8xy, y 2 + 8 and x 2 − 3xy subtract −3x 2 + 4y 2 – xy + x – y + 3. 13. What should be subtracted from x 2 – xy + y 2 – x + y + 3 to obtain −x 2+ 3y 2− 4xy + 1? 14. What should be added to xy – 3yz + 4zx to get 4xy – 3zx + 4yz + 7? 15. How much is x 2 − 2xy + 3y 2 less than 2x 2 − 3y 2 + xy?
Answer:
Explained below.
Step-by-step explanation:
(11)
Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).
[tex][(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z[/tex]
Thus, the final expression is (-11x + y - 12z).
(12)
From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).
[tex][(x^{2} + 3y^{2} - 6xy)+(2x^{2} - y^{2} + 8xy)+(y^{2} + 8)+(x^{2} - 3xy)] - [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[x^{2} + 3y^{2} - 6xy+2x^{2} - y^{2} + 8xy+y^{2} + 8+x^{2} - 3xy]- [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[4x^{2}+3y^{2}-xy+8]-[-3x^{2} + 4y^{2} - xy + x - y + 3]\\=4x^{2}+3y^{2}-xy+8+3x^{2}-4y^{2}+xy-x+y-3\\=7x^{2}-y^{2}-x+y+5[/tex]
Thus, the final expression is (7x² - y² - x + y + 5).
(13)
What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?
[tex]A=(x^{2} - xy + y^{2} - x + y + 3) - (-x^{2}+ 3y^{2}- 4xy + 1)\\=x^{2} - xy + y^{2} - x + y + 3 +x^{2}- 3y^{2}+ 4xy -1\\=2x^{2}-2y^{2}+3xy-x+y+2[/tex]
Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).
(14)
What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?
[tex]A=(4xy-3zx + 4yz + 7)-(xy - 3yz + 4zx) \\=4xy-3zx + 4yz + 7 -xy + 3yz - 4zx\\=3xy-7zx+7yz+7[/tex]
Thus, the expression is (3xy - 7zx + 7yz + 7).
(15)
How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?
[tex]A=(2x^{2} - 3y^{2} + xy)-(x^{2} - 2xy + 3y^{2})\\=2x^{2} - 3y^{2} + xy-x^{2} + 2xy - 3y^{2}\\=x^{2}-6y^{2}+3xy[/tex]
Thus, the expression is (x² - 6y² + 3xy).
land and sea corporation has just purchased some shoreline property, and according to their calculations it will cost 2.5 times as much to develop the land as much as it did to buy it. If land and sea believe it will end up spending a combined total of $13,457,500 on both the land and its developments, how much must be the land alone have cost?
Answer:
5,383,000 / *improvments cost 8,074,500
Step-by-step explanation:
if 2.5 is by 'times' then,
13,457,500 / 2.5 =
5,383,000
Which means the cost of the land is 5,383,000
To check just multiply:
5,383,000 x 2.5 = 13,457,500
*Extra
13,457,500 - 5,383,000
= the cost of improvements = 8,074,500
Hope this helps, and have a good day :)
Answer:
$3,845,000
Step-by-step explanation:
Land cost = lDevelopment cost = dTotal cost = $13,457,500As per given:
d= 2.5 lThen total is:
l+2.5l= 134575003.5l= 13457500l= 13457500/3.5l= $3845000Cost of the land alone is $3,845,000
The fuel efficiency of one type of car is recorded in a scatterplot where the amount of gas used, x (in gallons), is paired with the distance traveled, y (in miles), for various trips. The equation for the line of best fit for the data is y = 28x. How can the y-intercept and slope of this line be interpreted
Answer:
The answer can be interpreted by the distance moved by each gallon :))
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
Just took it. Edg 2020. Hope this helps :)
what is the coefficient of the variable in the expression 4-3x
As per the question,
We have to find what's the coefficient.
Let's start to seperate the expression.
Here,
x is the variable,
4 is a number.
-3 is also a number.
4, -3x
The number with x here is -3 in (-3x) as the coefficient is (-3) in the given equation.
Answer:
Hey there!
Rearrange the expression to: -3x+4
The coefficient would be -3.
Let me know if this helps :)
Diagram shows helicopter H flying towards an island P
When the helicopter is 100 m above sea level, the pilot sees a man fishing from boat Q. Given the angles of depression of the island P and boat Q from H are 22° and 61.5° respectively.
Calculate the distance, in M, of PQ
Please help me to explain :(
Answer:
193.21 m
Step-by-step explanation:
make a vertical line down from the helicopter that is 100m
tan 61.5 = 100/x x = 54.3 (distance from the point directly below helicopter to boat)
tan 22 = 100/x x = 247.51 (distance from the point directly below helicopter to the island
247.51 - 54.3 = 193.21 (distance from boat to island)
Which statement correctly compares
1–201 and
1512
ol-201 = 151
ol-201 < 51
l-201 > 151
Answer:
Option B.
Step-by-step explanation:
Consider the correct question is "Which statement correctly compares
1. -201 and 151
-201 = 151
-201 < 51
-201 > 151"
The given numbers are -201 and 151. We need to compare these numbers.
We know that all negative numbers are less than positive numbers.
So,
-201 < 151
If both numbers are negative, then the larger negative number is the smaller number.
Therefore, the correct option is B.
Use slope-intercept form to graph each system of equations and solve each system.
Answer:
(0,3), graph is attached.
Step-by-step explanation:
We know that the first equation will increase 2 points in y for every 1 x, since the constant next to x is 2. We also know it's y-intercept will be 3.
As for the second equation, we know it will have no y and instead run through the y=3 line, crossing every value of x.
Graphing this, we see that these lines intersect at (0,3) so that's the solution to this system.
Hope this helped!
A power failure on the bridge of a Great Lakes freighter has resulted in the ship's navigator having to do her own calculations. She measures the angle between the ship's course and a lighthouse on shore as 32°. After the ship has travelled 1500 m, she measures the angle to be 72°. Determine if the ship was closer to or farther from the lighthouse at the second sighting, and by what distance. (4 marks)
It is impossible to measure the length of a particular swamp directly. Kendra put a stake in the ground and measured from the stake to opposite ends of the swamp, the results being 410 m and 805 m. She measured the angle between the distances to be 57°. What is the length of the swamp? (4 marks)
Answer:
1) The ship is closer
2) 675.73 m
Step-by-step explanation:
1) The given parameters are;
The initial angle between the ship's course and the lighthouse = 32°
The final angle between the ship's course and the lighthouse = 72°
The distance traveled by the sip between he two positions = 1500 m
Therefore we have a triangle formed between the distance covered by the ship and the two distances of the ship from the lighthouse, a and b
Where;
a = The initial distance fro the lighthouse
b = The final distance fro the lighthouse
The angles of the triangle are
32°, (180 - 72) = 108° and 180 - 32 - 108 = 40°
By sine rule we have;
1500/(sin(40)) = a/(sin(108)) = b/(sin(32)) =
Therefore, a = sin(108°) × 1500/(sin(40°)) = 2219.37 m
b = (sin(32°)) × 1500/(sin(40°)) = 1236.61 m
Therefore, a > b
The initial distance fro the lighthouse > The final distance fro the lighthouse, which shows that the ship is closer
2) By cosine rule we have
a² = b² + c² - 2× b×c×cos(A)
Where the given measurements by Kendra are;
410 m and 805 m with an included (in between) angle of 57°, we have;
Let b = 410 m, c = 805 m, and A = 57°, we have;
a² = 410^2 + 805^2 - 2× 410×805×cos(57 degrees) = 456608.77 m²
a = The length of the stream = 675.73 m.
How to do this question plz answer me step by step plzz plz plz plz plz plz plz plz
Answer:
288.4m
Step-by-step explanation:
This track is split into a rectangle and two semi-circles.
We can find the length of the semi-circles by finding its circumference with the formula [tex]2\pi r[/tex].
[tex]2\cdot3.14\cdot30\\188.4[/tex]
However this is half a circle, so:
[tex]188.4\div2=94.2[/tex].
There are two semi-circles.
[tex]94.2\cdot2=188.4[/tex]
Since there are two legs of 50m each, we add 100 to 188.4
[tex]188.4+100=288.4[/tex]m
Hope this helped!
Answer:
Step-by-step explanation:
To solve for the perimeter, we first look at the rectangle in the middle. the length is 50m, and there are two sides to it, so: 50 * 2 = 100m for the top and bottom of the track.
For the circle, we can see the diameter is 30m. To solve for the circumference, we need to use the formula 2πr.
15 * 2π ≈ 94.2477796077
We add that to 100m and get:
194.2477796077
HELP ASAP
[tex]Given that $33^{-1} \equiv 77 \pmod{508}$, find $11^{-1} \pmod{508}$ as a residue modulo 508. (Give an answer between 0 and 507, inclusive.)[/tex]
===================================================
Work Shown:
[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]
Notice how 33*77 = 2541 and 11*231 = 2541
[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.
So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]
Does someone know how to solve this?
Answer:
6 quarts
Step-by-step explanation:
8 bags
--------
2 quarts
Multiply top and bottom by 3
8*3 bags
--------
2*3 quarts
24 bags
--------------
6 quarts
Answer:
6
Step-by-step explanation:
2 quarts of iced tea = 8 tea bags.
x quarts of Iced tea = 24 tea bags
=> 2/8 = x/24
=> Multiply the extremes and means
=> 8x = 48
=> 8x / 8 = 48 / 8
=> x = 6
6 quarts of iced tea can be made with 24 tea bags.
If 2x+5=8x, then 12x=?
Answer:
[tex]\boxed{10}[/tex]
Step-by-step explanation:
[tex]2x+5=8x[/tex]
[tex]\sf Subtract \ 8x \ from \ both \ sides.[/tex]
[tex]2x+5-8x=8x-8x[/tex]
[tex]-6x+5=0[/tex]
[tex]\sf Subtract \ 5 \ from \ both \ sides.[/tex]
[tex]-6x+5-5=0-5[/tex]
[tex]-6x=-5[/tex]
[tex]\sf Divide \ both \ sides \ by \ -6.[/tex]
[tex]\displaystyle \frac{-6x}{-6} =\frac{-5}{-6}[/tex]
[tex]\displaystyle x =\frac{5}{6}[/tex]
[tex]\sf Evaluate \ 12x.[/tex]
[tex]\displaystyle 12 \cdot \frac{5}{6} =\frac{60}{6} =10[/tex]
Answer:
10
Step-by-step explanation:
2x+5=8x: First, you are going to subtract 2x from both sides of the equation.
5=6x: Now divide 6x from each side of the equation.
x=5/6: now plug in 5/6 by multiplying this number by 12.
Your final answer should be 10.
A traveler explores the regions of Mexico. She travels from Sonora to Colima, and
Colima to Tamaulipas. Write two inequalities that represent the two possible distances
from Tamaulipas back to Sonora.
Answer:
809mi
Step-by-step explanation:
There are two ways to travel form Tamaulipas to Sorona. The first if the direct route from Sorona to Tamaulipas which is 809mi. The another route is to travel to Colima from Sorona and then travel to Tamaulipas from Colima. This is the long distance routes in which there are two destination points. The direct route is shorter in length therefore preferable.
Jonah will cover a cube in wrapping paper. Each edge of the cube is 25 cm long. What is the least amount of
wrapping paper he needs to cover the cube?
15 625 square centimeters
25 square centimeters
37.5 square centimeters
42 25 square centimeters
Save and Exit
Next
Subm
MO
Answer:
3750 cm²
Step-by-step explanation:
To find the answer, we need to find the surface area of the cube. The surface area formula for a cube is 6a² where a = the length of an edge. We know that a = 25 so the surface area is 6 * 25² = 6 * 625 = 3750 cm².
Answer:
37.5 hopefully this is the answer you were looking for!
Step-by-step explanation:
You have been saving $12 each week for many weeks. One day, you decide to count your savings and find that you have $384. Write and solve a multiplication equation to find how many weeks w you have been saving.
Answer:
Hope I helped! Brainleist!
Step-by-step explanation:
you get $12/week
and you have $
your equation is
y=12x
now...
y = 384
so
384=12x
x= 32
I NEED HELP ON THIS QUESTION!!!!! I WILL GIVE BRAINLIEST TO THE BEST ANSWER!!!!
Answer:
D
Step-by-step explanation:
Both are exponential decay.
Answer:
D.Step-by-step explanation:
f(0) = 24, f(1) = 6 and f(2) = 0 means f(x) > 0 in (0,2)
and f(0) > f(1) > f(2) means f is decreasing in (0,2)
g(0) = 15 and g(2) = 0 means g(x) > 0 in (0,2)
and g(0) > g(2) means g is decreasing in (0,2)
What is the value of this expression? (the best answer receives a brainiest)
Answer:
answer is D
Step-by-step explanation:
2^4=16
16+(16-12)=20
over
(6+9)/(7-4)
15/3=5
so the new equation is 20/5=4
Answer:
D. 4
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Exponents
[tex]\frac{16 + (16 -3(4))}{(6+9)/(7-4)}[/tex]
Step 2: Parenthesis
[tex]\frac{16 + (16 -12)}{15/3}[/tex]
Step 3: Parenthesis
[tex]\frac{16 + 4}{15/3}[/tex]
Step 4: Divide
[tex]\frac{16 + 4}{5}[/tex]
Step 5: Add
[tex]\frac{20}{5}[/tex]
Step 6: Divide
4
Peter attempted to use the divide-center method to find the line of best fit on a scatterplot.
What was his mistake?
He had a different number of points to the left of the vertical line than to the right of the vertical line.
He had a different number of points above the line of best fit than below the line of best fit.
He didn’t approximate the center of the cluster located on the left side of the vertical line and of the cluster located on the right side of the vertical line.
He didn’t connect the centers of the clusters on the left side and right side of the vertical line to produce the line of best fit.
Answer:
He had a different number of points to the left of the vertical line than to the right of the vertical line.
Step-by-step explanation:
Divide-center method is the method which involves dividing the data on the graph into two equal parts and then fin the line of best fit. The center of each group is approximated and then a line is constructed between two centers which is estimated as line of best fit.
I NEED HELP PLEASE I GIVE 5 STARS !
Answer:
C. 2[tex]\sqrt{29}[/tex]
Step-by-step explanation:
Square root of 116 is 10.7703296
Square root of 29 is 5.38516481, but as it is multiplied by 2, it becomes 10.7703296
Solve for h. 3/7=h/14-2/7
Answer:
h = 10
Step-by-step explanation:
Given
[tex]\frac{3}{7}[/tex] = [tex]\frac{h}{14}[/tex] - [tex]\frac{2}{7}[/tex]
Multiply through by 14 to clear the fractions
6 = h - 4 ( add 4 to both sides )
10 = h
Answer:
10
Step-by-step explanation:
We start out with 3/7 = h/14 - 2/7
add 2/7 to both sides:
(5/7) = h/14
Multiply both sides by 14 to get rid of the fraction:
h = 10
Which graph represents the solution set of this inequality?
10c + 5 < 45?
Answer:
see below
Step-by-step explanation:
10c + 5 < 45
Subtract 5 from each side
10c + 5-5 < 45-5
10c < 40
Divide by 10 on each side
10c/10 < 40/10
c < 4
Open circle at 4 and the line going to the left
When computing the standard deviation, does it matter whether the data are sample data or data comprising the entire population? Explain. Yes. The formula for s is divided by n, while the formula for σ is divided by N − 1. Yes. The formula for s is divided by n − 1, while the formula for σ is divided by N. No. The formula for both s and σ is divided by n − 1. No. The formula for both s and σ is divided by N.
Answer:
Yes. When computing the sample standard deviation, divide by n −1. When computing the population standard deviation, divide by N
Step-by-step explanation:
Priya, Han, and Mai each measured one of the circular objects from earlier. Priya says that the bike wheel is 24 inches. Han says that the yo-yo trick is 24 inches. Mai says that the glow necklace is 24 inches. 1. Do you think that all these circles are the same size? 2. What part of the circle did each person measure? Explain your reasoning.
Answer:
Yes they are of the same size since they have the same number and standard unit of measurement (i.e 24 inches).
Each person measures the circumference of the circle.
Step-by-step explanation:
Given that :
Priya, Han, and Mai each measured one of the circular objects from earlier.
Priya says that the bike wheel is 24 inches.
Han says that the yo-yo trick is 24 inches.
Mai says that the glow necklace is 24 inches.
Do you think that all these circles are the same size?
Yes they are of the same size since they have the same number and standard unit of measurement (i.e 24 inches).
What part of the circle did each person measure?
Each person measures the circumference of the circle.
The circumference also known as the perimeter of the circle is denoted by :
C = 2π r
The circumference of a circle is the distance round the edges of the circle.
Given that C = 24
24 = 2π r
r = 24/(2π)
r = 3.8 inches
This confirms the claim that all the circle are of the same size since they possess the same radius.
Answer:
The person who answered first is WRONG
Step-by-step explanation:
I did this and these are the answers the teacher gave me:
the circles are NOT the same size
and they are measuring by diameter, radius, and circumfrence
5
What is the equation, in point-slope form, of the line that
is parallel to the given line and passes through the point
(-3, 1)?
4
3
2
(-3, 1)
42.27
1
5 4 3 2 1
2 3 4 5 x
y-1=-{(x+3)
y-1=-{(x + 3)
y-1= {(x + 3)
y-1= {(x + 3)
(-2, 4)
Answer: [tex]y-1=\dfrac32(x+3)[/tex]
Step-by-step explanation:
Slope of a line passes through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]
In graph(below) given line is passing through (-2,-4) and (2,2) .
Slope of the given line passing through (-2,-4) and (2,2) =[tex]\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}[/tex]
Since parallel lines have equal slope . That means slope of the required line would be .
Equation of a line passing through (a,b) and has slope m is given by :_
(y-b)=m(x-a)
Then, Equation of a line passing through(-3, 1) and has slope = is given by
[tex](y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)[/tex]
Required equation: [tex]y-1=\dfrac32(x+3)[/tex]
Find the amplitude of y = -2 sin x
Answer:
Amplitude = 2
Step-by-step explanation:
The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x). The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.
Cheers.
when a 200 g solution A and 400g of saline solution B are mixed a 6% salt solution is created also when a 400g of saline solution A and 200g of solution B are mixed 7% salt is created find what percent concentration of saline and saline b solution are
Answer:
A = 8%, B = 5%
Step-by-step explanation:
Let
a=concentration of solution A (in percent)
b=concentration of solution B (in percent)
Given
2a+4b = 0.06*(2+4) ...........(1)
4a+2b = 0.07*(4+2) ...........(2)
2(1) - (2)
4a-4a +8b-2b = 6 (2*0.06-0.07)
6b = 6(0.05)
b = 0.05 .............(3)
Substitute (3) into (1) and solve for a
2a+4(0.05) = 0.36
2a = 0.16
a = 0.08
Sandra spotted the sailboat from the shore and measured the angle from the waterline to the top of the boats mast to be 7° if the top of the mask is 23 feet above the water how far is the middle of the sailboat from the shore? Estimate your answer to the nearest tenth.
Answer:
The middle of the sailboat is approximately 268.8 feet from the shore.
Step-by-step explanation:
Let the distance from shore to the middle of the boat be represented by x, the angle of elevation of Sandra from the shore to the top of the boat mast is 7°. Applying the required trigonometric function to this question, we have;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan 7° = [tex]\frac{23}{x}[/tex]
⇒ x = [tex]\frac{23}{Tan 7^{0} }[/tex]
= [tex]\frac{23}{0.12279}[/tex]
= 268.7515
∴ x = 268.8 feet
The middle of the sailboat is approximately 268.8 feet from the shore.
Select the equivalent expression,
(9^6*7^-9)^-4 =?
Choose 1 answer:
А
9^24*7^-36
B
9^24/7^36
C
7^36/9^24
Answer:
c
Step-by-step explanation:
The expression (9⁶ x 7⁻⁹)⁻⁴ is equivalent to expression 7³⁶ / 9²⁴. Then the correct option is D.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The expression is given below.
⇒ (9⁶ x 7⁻⁹)⁻⁴
Simplify the expression, we have
⇒ (9⁻⁶ x 7⁹)⁴
⇒ 9⁻²⁴ x 7³⁶
⇒ 7³⁶ / 9²⁴
Then the correct option is D.
More about the equivalent link is given below.
https://brainly.com/question/889935
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