Answer:
z = [20/sqrt(3][cos(-2π/3) + isin(-2π/3)]
Step-by-step explanation:
Polar form is
r(cos(theta) + isin(theta))
r = sqrt[(-10/sqrt3)² + (10)²]
r = sqrt(400/3)
r = 20/sqrt(3)
tan^-1[10 ÷ (10/sqrt(3))] = π/3
Theta: -π + π/3 = -2π/3
z = [20/sqrt(3][cos(-2π/3) + isin(-2π/3)]
each set of orther pairs (x, y) represents a relashionship with imput, x, and output, y. which relatonship is a function? a. {(0,1), (0,2), (0,3)} b. {(1,1), (2,2), (3,3)} c. {(1,1),(2,1),(3,1)} d. {(1,1),(2,2),(2,-2)} e. {(1,-1),(2,-2).(3,-3)}
Answer:
b, c, e
Step-by-step explanation:
A function has unique x-values (inputs). Several of the relations here are functions:
a. {(0,1), (0,2), (0,3)} . . . repeated x-value of 0, not a function
b. {(1,1), (2,2), (3,3)} ... function
c. {(1,1),(2,1),(3,1)} ... function
d. {(1,1),(2,2),(2,-2)} . . . repeated x-value of 2, not a function
e. {(1,-1),(2,-2).(3,-3)} ... function
Circle Z is shown. Line segments Z T, Z U, and Z V are radii of the circle. Line segment U X goes through point X and is a diameter. Line segment W Y goes from one side to the opposite side and intersects line segment U X at point S. Line segment W X is a secant. Angle X W X is 42 degrees, angle W S Y is 100 degrees, and angle T Z U is 79 degrees. Complete the statements about circle Z. A central angle, such as angle of circle Z, is an angle whose vertex is and whose sides are radii of the circle. Angle is not a central angle of circle Z. The degree measure of an arc is the degree measure of the central angle that intercepts it. The measure of is degrees.
Answer:
1. uzv
2. the center of the cirle
3. WSX
4. equal to
5. 79
Step-by-step explanation:
Answer:
b a d a b
Step-by-step explanation:
z^4=-625 please help!!!!!!!!!
Answer:
-5
Step-by-step explanation:
sqrt(625) = 25
sqrt(25) = 5
Since 625 is -625, the answer is -5
1 point
#17: A rectangular shape has an area of 150 square units. The sides of the
rectangle measure (x + 3) and (x - 2). What is the value of x? (Type the final
answer as x=# without any space. Example: x=35 If there are two possible
values of x, write the final answer as follows: x=35 and x=36) *
Answer:
The only possible value of x is 12
Step-by-step explanation:
The rectangular shape has an area of 150 square units. The sides of the rectangle measures (x + 3) and (x - 2). The value of x can be computed below
area of a rectangle = length × breadth
area = 150 unit²
The sides are (x + 3) and (x - 2)
Therefore,
(x + 3)(x - 2) = 150
x² -2x + 3x - 6 = 150
x²+ x - 6 = 150
x²+ x - 6 - 150 = 0
x²+ x - 156 = 0
(x - 12)(x + 13) = 0
Therefore,
x = 12 or x = -13
It cannot be - 13 because the sides cannot result to negative . We are left with only 12.
x = 12
The only possible value of x is 12
The value of x is 12
The dimensions of the rectangle are given as:
Length = x + 3Width = x - 2The area is given as:
Area = 150The area of a rectangle is:
[tex]Area = Length \times Width[/tex]
So, we have:
[tex](x + 3)(x -2) = 150[/tex]
Expand
[tex]x^2 + 3x - 2x - 6 = 150[/tex]
[tex]x^2 + x - 6 = 150[/tex]
Subtract 150 from both sides
[tex]x^2 + x - 156 = 0[/tex]
Factorize the above equation
[tex](x + 13)(x - 12) = 0[/tex]
Solve for x
[tex]x = -13[/tex] or [tex]x =12[/tex]
The value of x cannot be negative.
So, the value of x is 12
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A rectangular prism with a volume of 6 cubic units is filled with cubes with side lengths of 1\2 unit.
How many 1/2 unit cubes does it take to fill the prism?
Answer:
Well, Your best answer will be is 48. Because, If the side length is 1/2, cube it to find the volume of the cube. Then divide 6 by 1/8. Remember that if you are dividing a fraction, you multiply by the reciprocal, in this case 8. 6 times 8 is 48. Good Luck!
A stick 1 meter long casts a shadow 1.2 meters long. A building casts a shadow 17 meters long. How tall is the building (to 2 decimal places)
Answer:
14.17m
Step-by-step explanation:
1 / 1.2 = x / 17
x = 17 / 1.2 = 14.1666667 -> 14.17m
14.17m tall is the building (to 2 decimal places).
What is after the decimal point?Digits after the decimal point. The position of the digit to the right of the decimal point of the number is written in decimal notation. For example, 0.079 has 0 decimal places, 7 decimal places, and 9 decimal places.
Rounding a decimal number to two decimal places is the same as rounding to one-hundredth of the second decimal place. For example, 2.83620364 can be rounded from 2.84 to two decimal places, and 0.7035 can be rounded from 0.70 to two decimal places.
1 / 1.2 = x / 17
x = 17 / 1.2 = 14.1666667 -> 14.17m
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Marissa claims that stacking 6 blocks with dimensions of One-half times 1 times 1 will give the same volume as stacking 9 blocks with dimensions of One-third times 1 times 1. Which statements about her claim are true? Check all that apply.
A. Six of the one-half cubes would have a volume of 3 cubic units.
B. Nine of the one-third cubes would have a volume of 6 cubic units.
C. Since One-half and One-third do not have common factors, stacks of one-half
cubes and stacks of third-cubes could never have the same volume.
D. Three of the one-third cubes will make 1 unit cube.
E. Two of the one-half cubes will make 1 unit cube.
F. Both stacks will have a volume of 3 cubic units.
Answer:
(A)Six of the one-half cubes would have a volume of 3 cubic units.
(D)Three of the one-third cubes will make 1 unit cube.
(E)Two of the one-half cubes will make 1 unit cube.
(F)Both stacks will have a volume of 3 cubic units.
sorry you havent gotten an answer until two weeks later
Answer:
The answers are A D E F
Step-by-step explanation:
Hope I helped and stay safe out there <3
At the park, there is a triangular sandbox with base = 12ft and height = 4ft. A drawing of the sandbox is shown above. Brie wants to make another, similar sandbox at home with base=8ft.
Your question is not clear, but it looks as though you want to know how Brie can make a similar sandbox with base = 8ft.
Answer:
For Brie to make a similar sandbox, he must use a base = 8ft, and height = (8/3)ft
Step-by-step explanation:
It is possible for Brie to make a similar triangular sandbox with base = 12ft and height = 4ft.
All he must ensure is that the ratio of base to height of the original sandbox is the same ratio of base to height of the one he is trying to make.
The original sandbox is 12:4
Because he wants to use a base = 8ft, the sandbox he is trying to make is 8:x
Where x is the height of the sandbox he is trying to make.
Then for these sandboxes to be similar, the ratio 12:4 = 8:x
=> 12/4 = 8/x
12x = 8 × 4
12x = 32
x = 8/3
The height must be (8/3)ft
How many solutions does the system have? 6x-y=-1 6x+y=-1
Answer:
One
Step-by-step explanation:
What show variability a dot plot or a box plot
dot plot shows variability
lmk if this helps
Where is the dot plot so we can help
In Mrs. Smith’s enrichment class, 25% of the students are boys. There are 7 boys in the class. How many total students are in Mrs. Smith’s enrichment class?
Answer:28
Step-by-step explanation: 25% is 1/4 so you can multiply 7 and 4 to get 28
Use the two equations from questions 1 and 2 to figure out how many
jerseys Bill would need to order for the price from 'Top Print' to be less
than from "Print It'. Explain how you figured it out.
Answer: multiply u would get 50
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
trust the process
What is a series?
A sequence of numbers separated by commas.
A sequence of numbers summed together.
Numbers that are put in a group.
Answer:
A sequence of numbers summed together
Step-by-step explanation:
A series of numbers is nothing else but the sum of the various numbers or elements of a sequences.
Keenan wants to make a paperweight at pottery class. He designs a pyramid-like model with a base area of 80 square centimeters and a height of 7.5 centimeters. The density of the clay he is using is 1.7 grams per cubic centimeter. What is the weight of Keenan’s paperweight?
Answer: Weight of project: 340 grams
Step-by-step explanation:
It's a simple geometry problem to be honest. So you want to start off with the equation for the volume of a pyramid which is 1/3BH where B=Base and H= Height.
So it should look like this 1/3(80)(7.5)= 200cm 2 x 7.5g = 340 Grams
Answer:
340 is correct
Step-by-step explanation:
Got it one khan
5/6k=4/7 what does k equal?
[tex]\text{Solve for k:}\\\\\frac{5}{6}k=\frac{4}{7}\\\\\text{You can multiply both sides by 6/5, cancelling the 5/6 on the left}\\\\\frac{6}{5}*\frac{5}{6}k=\frac{4}{7}*\frac{6}{5}\\\\k=\frac{4}{7}*\frac{6}{5}\\\\\text{Multiply across}\\\\\boxed{k=\frac{24}{35}}[/tex]
Which line best models line one?
please help me, I need to find this out fast!!
A. X=4
B. Y=4
C. X=4Y
D. Y=X+4
Answer:
A
Step-by-step explanation:
The equation of a vertical line parallel to the y- axis is
x = c
where c is the value of the x- coordinates the line passes through.
Here the line passes through all points with an x- coordinate of 4, thus
x = 4 → A
The length of a rectangle is twice the width. The perimeter is 126 centimeters.
Which system of equations will determine the length, L, and the width, W, of the rectangle?
А.)L+2 = W
2L+ 2W = 126
B.)L+W = 2
LW = 126
C.)L=2W
21+ 2W = 126
D.)W = 2L
L+ 2W = 126
E.)2L = W
L+ W = 126
Final answer:
Choose the equations L = 2W and 2L + 2W = 126 to determine the length and width of the rectangle accurately that is option C is the correct answer
Explanation:
The correct system of equations to determine the length, L, and the width, W, of the rectangle is:
L = 2W
2L + 2W = 126
This system reflects the relationship between the length and the width given that the length is twice the width and the perimeter is 126 centimeters.
3. Nina has $20.14 in her purse. She buys lunch
for $9.67. How much does she have left?
Answer:
Nina has $10.47 left.
Step-by-step explanation:
$20.14 minus $9.67 is $10.47
Answer:
$10.47
Step-by-step explanation:
Nina has $20.14.If she uses $9.67 for lunch then she would be left with($20.14-$9.67) which is equal to $10.47......
Evaluate.
64: (48 – 42)
Answer:
32:3
Step-by-step explanation:
64:(48-42)
Note that 64:(48-42)
Can also be written as 64/(48-42)
So let's solve (48-42) first
=6
So 64/(48-42)=64/6
64/6
Divide both by 2
32/3
So let's convert back to ratio
32:3
Therefore the final answer is 32:3
What type of triangle is shown below?
Answer:
obtuse
Step-by-step explanation:
Answer:
Obtuse
Step-by-step explanation:
A triangle is obtuse when there is one angle that is greater than 90
Using the dimensions of a new scale drawing created using a scale factor of 0.15, find the dimensions of the original rectangle.
Width:
Length:
Answer:
Width- 15.8 ft.
Length- 32 ft.
To find the dimensions of the original rectangle when given the dimensions of a new scale drawing using a scale factor of 0.15, divide the corresponding dimensions of the scale drawing by 0.15.
Explanation:The scale factor of 0.15 means that the new dimensions in the scale drawing are 0.15 times the original dimensions. To find the dimensions of the original rectangle, divide the corresponding dimensions of the scale drawing by 0.15.
Let's say the width and length of the new scale drawing are 10 units and 15 units, respectively. To find the original width and length, divide 10 by 0.15 and 15 by 0.15.
The original width would be 66.67 units (10 / 0.15) and the original length would be 100 units (15 / 0.15).
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9x-4 (x-3)+72
what is X?
Answer:
x = 12
Step-by-step explanation:
9*x-4*(x-3)-(72)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(9x - 4 • (x - 3)) - 72 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
5x - 60 = 5 • (x - 12)
Answer:
I think answer is 16.8....
945 times 134 is equal to what
945*134=126630
if you line them up and then multiply like that it makes it easier or just use a calculator i guess
what is the probability of tossing a standard coin and having it land on head three times in a row?
Answer:
the probability of a coin landing on heads 3 times in a row is 1/8 or 0.125 or 12.5%
Step-by-step explanation:
the chance of landing heads once is 1/2, for it to be 2 times in a row its 1/4, and 3 times in a row its 1/8, basically every time you want to do it in a row you multiply 1/2, so for example for this question you multiply 1/2 by however times you want the coin to land on heads in a row, (1/2) X(1/2)X(1/2)
Gabriel wants to send a parcel to Italy.
His parcel is a cuboid with dimensions 10 cm, 20cm and 40 cm.
He looks at the prices of two companies,
We Deliver and GoParcels.
Not drawn
to scale
We Deliver
Total cost: Sum, in cm, of the 3 dimensions * £0.80 Find the cost or sending th
parcel with each company.
GoParcels
Give each of your answers
Total cost: Total area, in cm, of all 6 faces x £0.02 pounds (2).
Find the cost of sending the parcel with both the companies is the same - £56.00.
Given:
Parcel dimensions: 10 cm, 20cm and 40 cm
1. We Deliver:
Total cost = (Sum of the 3 dimensions) * £0.80
Total cost = (10 cm + 20 cm + 40 cm) * £0.80
Total cost = 70 cm * £0.80
Total cost = £56.00
So, the cost of sending the parcel with We Deliver is £56.00.
2. GoParcels:
Total cost = (Total area of all 6 faces) * £0.02
Total area = 2 * (10 cm * 20 cm + 20 cm * 40 cm + 40 cm * 10 cm)
= 2 * (200 cm² + 800 cm² + 400 cm²)
= 2 * 1400 cm²
= 2800 cm²
Total cost = 2800 cm² * £0.02
Total cost = £56.00
So, the cost of sending the parcel with GoParcels is also £56.00.
Therefore, the cost of sending the parcel with both companies is the same, and it is £56.00.
14. It costs a pool cover manufacturer $0.15 per square foot for the material they use to make pool covers. If a certain circular pool requires a cover with a 24-foot diameter, find the cost for the material
The area of the pool cover is calculated using the formula for the area of a circle, πr². After finding the area, it is multiplied by the cost per square foot to find the total cost of the material, which is approximately $67.86.
Explanation:To calculate the cost of material required to cover a pool, we first need to calculate the area of the pool cover. Since the pool is circular and has a diameter of 24 feet, the radius would be half of the diameter, which is 12 feet. The formula to calculate the area of a circle is πr², so the area of the pool cover would be π*12² which equals approximately 452.39 square feet.
Next, knowing that the cost of the material per square foot is $0.15,we multiply the area by the cost per square foot, 452.39*.15 would give us approximately $67.86. Therefore, the cost of the material for the pool cover is about $67.86.
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2k−12−2=−4 what does k equal i think its 10 but im not sure
Answer:
k=5
Step-by-step explanation:
2k-12-2=-4
2k-14=-4
+14 +14
2k=10
divide by 2 to cancel the k
k=5
Answer:
k= 5
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Help ASAP ! Show work
Answer:
Step-by-step explanation:
Using formula [tex]a^{2} + b^{2} =c^{2}[/tex]
a= 650
b= 800
and c is the unkown
A dress that costs & dollars is on sale for 25% off. Which expressions represent the sale price, in dollars, of the
dress? Select all that apply.
A
0.25%
B 0.75*
C 1.250
D x(1 -0.25)
E 2 – 0.25
Ex – 0. 75x
Answer:
D
Step-by-step explanation:
because its dividing X by .25
Write the equation of the line that passes through the given points.
(2,7.5) and (0, -1.5)
Answer:
y=4.5x +1.5
Step-by-step explanation:
First find your slope using y₂-y₁/x₂-x₁. In this case, your slope should come out to be 4.5. Now put your slope into slope-intercept form to get y=4.5x+b. Now to find the intercept, substitute any of the original coordinates in for x and y. I chose to use (2,7.5); the equation should now read 7.5= 2(4.5)+b. Solve the equation to get b=1.5. Now substitute everything back to slope-intercept form to get y=4.5x +1.5.
Hope this helps!
To find the equation of the line passing through (2, 7.5) and (0, -1.5), you first determine the slope m = 4.5 by using the slope formula. The y-intercept b is -1.5 as the line intersects the y-axis at (0, -1.5). Therefore, the equation of the line is y = 4.5x - 1.5.
Explanation:To write the equation of the line that passes through the given points, (2, 7.5) and (0, -1.5), you first need to find the slope (m) and the y-intercept (b) of the line. The slope is found using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula gives:
m = (7.5 - -1.5) / (2 - 0) = 4.5
The y-intercept b is simply the y-coordinate of the point where the line intersects the y-axis. Since one of the given points is (0, -1.5), which lies on the y-axis, the y-intercept is -1.5.
Substituting m and b into the slope-intercept form gives the equation of the line:
y = mx + b => y = 4.5x - 1.5
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