Step-by-step explanation:
this creates a right-angled triangle, with the pure coordinate changes being the legs, and the actual distance being the Hypotenuse (the side opposite of the 90° angle).
and so, we can use Pythagoras :
distance² = leg1² + leg2² = 300² + 500² =
= 90000 + 250000 = 340000
distance = sqrt(340000) = sqrt(10000×34) = 100×sqrt(34) =
= 583.0951895... km ≈ 583 km
I need help with this math question ASAP. someone PLEASE help me
Answer:
[tex]xy^2+2x-4y^2[/tex][tex];-58[/tex]
Step-by-step explanation:
First, align the same terms next to each other so that combining like terms will be easier.
Remember like terms have the same variables and powers. To combine like terms, all you have to do is add/subtract the coefficients (the numbers in from of the variables).
[tex]2xy^{2} +2xy^{2} -3xy^{2} +3x-x-4y^{2}[/tex]
[tex]2xy^{2} +2xy^{2} -3xy^{2} =xy^{2}[/tex]
[tex]3x-x=2x[/tex]
And [tex]-4y^{2}[/tex] stays the same because there is no term that has [tex]y^{2}[/tex].
So, we have [tex]xy^{2} +2x-4y^{2}[/tex].
Now to evaluate for x= -2 and y= -3 you have to plug them into the simplified expression.
[tex](-2)(-3)^{2} +2(-2)-4(-3)^{2}[/tex]
According to PEMDAS we first solve the exponents: [tex](-2)(9) +2(-2)-4(9)[/tex]
Then we multiply:
[tex](-18) +(-4)-36[/tex]
Add/subtract:
-58
he altitude to the hypotenuse of a triangle with angles of 30 and 60 degrees is 3 units. what is the area of the triangle, in square units? express your answer in simplest radical form.
The area of the triangle is 6√3 square units.
What is the hypotenuse of a triangle?A triangle with a right angle or two perpendicular sides is referred to as a right triangle, a right-angled triangle, or perhaps more formally as an orthogonal triangle (formerly known as a rectangle triangle). Trigonometry's foundation is the relationship between the right triangle's sides and other angles.
According to the given data:The ratios of a given object's sides 30°-60°-90° triangle are 1 : √3: 2.This information allows us to calculate the lengths of something like the triangle's orthogonal sides.
3(2/√3) = 2√3 . . . . side AB in the attached figure.
And also:
2·3 = 6 . . . . . . . . . . side AC in the attached figure.
Then the area of the triangle is:
A = 1/2bh
A = 1/2(6)(2√3) = 6√3 . . . . square units.
the area of the triangle 6√3 square units.
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Which is 3 groups of 5?
3 + 5
5 - 3
3 × 5
5 ÷ 3
Answer: 3 groups of 5 = 5 + 5 + 5 = 15. 5 groups of 3 = 3 + 3 + 3 + 3 + 3 = 15. 3 groups of 5 has the same answer as 5 groups of 3! So, 3 x 5 = 5 x 3. This means that when you multiply 2 numbers, the order of the numbers (which number is first and which is second) does not matter, the answer will still be the same. Multiplication Terms
Step-by-step explanation: I hopes this helps.
help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
Each side is 2 centimeters.
Hope this helps :)
Step-by-step explanation:
A square has sides that are all equal. So in this case the area is 4 square centimeters, and in order to find that we had to multiply 2 sides in which they are equal to each other. All the sides were 2 centimeters. We get 2 sides and multiply to get the area of the square chip.
2 cm × 2cm = 4 square centimeters
what is the answer for J(-3,2) and K(9,2)
The distance between points J(-3,2) and K(9,2) is 12 units.
What is distance?The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given:
The given points are
J(-3,2) and K(9,2)
[tex]x_{1} =-3\\\\x_{2} =9\\\\y_{1} =2\\\\y_{2} =2[/tex]
According to given question we have
By the use of distance formula we have
[tex]\sqrt{(x_{2} -x_{1} )^{2}+ (y_{2} -y_{1} )^{2}} \\\\=\sqrt{(9 -(-3) )^{2}+ (2 -2 )^{2}}\\\\=\sqrt{(12 )^{2}}\\\\=12[/tex]
Therefore, the distance between points J(-3,2) and K(9,2) is 12 units.
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Distance between is missing in question
Mr. Johnston supports a young tree by using a stake and a string forming a right angle with the ground.
60 in.
33 in.
What is the length of the string? Round to the nearest tenth.
Answer:68.48
Step-by-step explanation:a²+b²=c² a=60 b=33 so 60²+33²=4689 and take the square root of that which equals 68.48
write the index notation of 3*3*3*3
Answer:
[tex]3^{4}[/tex]
Step-by-step explanation:
Because 3x3x3x3
3 multipily by 4 times as it's same number
Find the average rate F(x)=7x-12 from -2 to 3
The average rate of given function F(x) = 7x -12 from -2 to 3 is equal to 7.
As given in the question,
Given function F(x) = 7x -12
x₁= -2
x₂ =3
Average rate of the function F(x) is
= {F(x₂) - F(x₁)}/ (x₂ - x₁)
= [7(3)-12 - {7(-2)-12}]/ [3-(-2)]
=(21-12+14+12)/ 5
=35/5
=7
Therefore, the average rate of given function F(x) = 7x -12 from -2 to 3 is equal to 7.
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Which is the correct answer
Answer:
b
Step-by-step explanation:
(x-8)(x+2)= x^2 - 6x - 16
- Find BC if B(8, -7) and C(-4, -2).
The line segment BC has a length of 13 units.
What is the length of a line segment?
In this question we know the locations of the two ends of a line segment. The procedure consists in calculating the vector behind the line segment and later determing its magnitude by Pythagorean theorem. If we know that B(x, y) = (8, - 7) and C(x, y) = (- 4, - 2), then the length of the line segment BC is:
BC = (- 4, - 2) - (8, - 7)
BC = (- 12, 5)
BC = √[(- 12)² + 5²]
BC = 13
The line segment BC has a length of 13 units.
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A runner’s times (in minutes) in three races are 6.9, 6.6, and 6.5. The runner will run two more races and wants the average time of all five races to be less than 6.8 minutes. Describe the average time needed in the two races to achieve this goal. The average time in the two races must be less than minutes.
The average time in two races must be less than 7 minutes.
Given,
Runner's times in three races = 6.9 minutes, 6.6 minutes, 6.5 minutes.
Runner will run two more races.
The average time of all five races = less than 6.8 minutes
We have to find the average time needed in the two races:
Now,
(6.9 + 6.6 + 6.5 + x + y) / 5 < 6.8
Here, x and y are the time in two races.
Let's assume the average as 6.5 which is less than 6.8.
Then,
(6.9 + 6.6 + 6.5 + x + y) / 5 = 6.5
(6.9 + 6.6 + 6.5 + x + y) = (6.5 × 5)
x + y = (6.5 × 5) - (6.9 + 6.6 + 6.5)
x + y = 32.5 - 20
x + y = 12.5
Now, we have to find the average of two races:
That is, (x + y) / 2 = 12.5 / 2 = 6.25.
Above is a solution required by an assumption. By this solution we came to know that the average of two races must be less than 7 minutes.
So, let's conclude like:
The average time in the two races must be less than 7 minutes.
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[tex]\frac{x}{2}=\frac{4}{x} -1[/tex]
[tex]\fbox{x = - 4} \: \sf or \: \fbox{ x = 2}[/tex]
Step-by-step explanation:
[tex] \frac{x}{2} = \frac{4}{x} - 1[/tex]
multiply whole equation with 2x,
[tex] \hookrightarrow\frac{x}{2} \times 2x = ( \frac{4}{x} \times 2x) - (1 \times 2x)[/tex]
[tex]\hookrightarrow {x}^{2} = 8 - 2x[/tex]
Rearranging above equation and making a quadratic equation,
[tex]\hookrightarrow {x}^{2} + 2x - 8 = 0[/tex]
Comparing above equation with, ax²+bx+c,
a =1, b=2, c= -8
Using formula,
[tex]x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
Substituting the given values,
[tex]x = \frac{ - 2 ± \sqrt{ {2}^{2} - 4 \times 1 \times ( - 8)} }{2 \times 1}[/tex]
[tex]x = \frac{ - 2 ± \sqrt{ 4+32} }{2}[/tex]
[tex]x = \frac{ - 2 ± 6 }{2}[/tex]
[tex]x = \frac{ - 2 + 6}{2} = \frac{4}{2} = 2[/tex]
or
[tex]x = \frac{ - 2 - 6}{2} = \frac{ -8}{2} = - 4[/tex]
[tex] \fbox{x = -4} \: \sf or \: \fbox{ x = 2}[/tex]
[tex]\sf \small \pink{Thanks }\: \green{for} \: \blue{joining} \: \orange{brainly } \: \red{community}![/tex]
five years ago, john was twice peters age. peter is now x years old and john is now y years old.
a) write an equation to illustrate the relation between John's age and Peter's age five years age.
b) this year, the total of their ages is 28 years old. use this information to determine John's age in three years.
c) use substitution to justify that your answers to part (a) are correct.
please help
Answer:
Step-by-step explanation:
a)
Peter now = x years old
John now = y years old
Five years ago
y-5 = 2(x-5)
y-5 = 2x-10
y = 2x-5
b)
x+y=28
y=28-x
Therefore
2x-5 = 28-x
3x = 33
x = 11
y = 28 - (11)
y = 17
Therefore
In three years time John will be:
17 + 3 = 20
c)
y-5 = 2x-10
Lefthand side:
(17)-5 = 12
Righthand side:
2(11)-10=22-10=12
Therefore
Lefthand side =Righthand side
YAY!
3(z - 1) - 1/2 (4z + 10) = 4 (z - 3/2) + 10
Answer:
z = -4
Step-by-step explanation:
Let's solve the problem,
→ 3(z - 1) - 1/2 (4z + 10) = 4 (z - 3/2) + 10
→ 3z - 3 - 2z - 5 = 4z - 6 + 10
→ z - 8 = 4z + 4
→ 4z - z = -4 - 8
→ 3z = -12
→ z = -12/3
→ [ z = -4 ]
Hence, the value of z is -4.
Derek is going to lay grass in a
rectangular space that measures
8 by 33 feet. Find the total area
that will be covered by grass.
Answer:
264 square ft
Step-by-step explanation:
8*33=264
the right triangle shown below with hypotenuse 13 inches long and vertical leg 5 inches long is rotated 360c around the vertical leg to form a right circular cone. what is the volume of this cone, in cubic inches?
The cone has a volume of (D) 288in3.
What do we mean by volume?A volume is a unit of measure of occupied three-dimensional space. It is frequently quantified numerically using SI-derived units (such as cubic meters and liters) or various imperial modules (such as the gallon, quart, and cubic inch). The definition of volume is related to the definition of length (cubed). The volume of a container is generally recognized to be its capacity; that is, the quantity of fluid (gas or liquid) that it can hold, rather than the amount of space that it occupies.To find the volume:
Given:
Radius = 6 inheight =?g = 10 inVolume =?Formula:
Volume of a cone = πr²h / 3The Pythagorean theorem is used to calculate height.
height² = 10² - 6² = 100 - 36 = 64 height = 8The volume of the cone:
Volume = π(6)²(8) Volume = π(36)(8) Volume = 288π in³Therefore, the volume of the cone is (D) 288in³.
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The complete question is given below:
Right triangle ABC, shown, has a vertical leg 6 inches long and a hypotenuse 10 inches long. If the triangle was rotated 360 degrees around the vertical leg to form a right circular cone, what would be the volume of this cone, in cubic inches?
A. 32
B. 96
C. 128
D. 288
E. 384
Solve the "or" inequality
7x-14 ≥0 or 4x+5 ≤ -3
The value of the inequality is a x ≥2 or x ≤ -2.
According to the statement
We have to find that the value in the inequality.
So, For this purpose, we know that the
Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
From the given information:
7x-14 ≥0 or 4x+5 ≤ -3
The value of the inequality is a :
7x-14 ≥0 or 4x+5 ≤ -3
x ≥14/7 or x ≤ -3-5/4
x ≥2 or x ≤ -8/4
x ≥2 or x ≤ -2.
So, The value of the inequality is a x ≥2 or x ≤ -2.
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12.5% complete question a painting crew reported that a job is 35 completed. what fraction of the job remains to be done?
Answer:
13/20
Step-by-step explanation:
I hope this helps, have a great day :)
we both play a game where we flip a coin. you win if 3 heads appear, i win if 3 tails appear. what is the expected number of flips for the game to end.
Answer:
9
Step-by-step explanation:
9 because 3x3=9
Solve for x in the diagram below.
Answer:
x = 6
Step-by-step explanation:
From the above diagram, we can deduce that:
5x + (x + 54) = 90 (Sum of Acute Angles)
Now, we can solve for x using this equation.
[tex]5x + (x + 54) = 90 \\ 6x + 54 = 90 \\ 6x + 54 - 54 = 90 - 54 \\ 6x = 36 \\ x = \frac{36}{6} \\ x = 6[/tex]
A square pyramid has a base with a side length of 6 meters. If the
slant height of the pyramid is 5 meters, what is the surface area of the
pyramid?
m²
Answer:
96
Step-by-step explanation:
?
The surface area of the square pyramid with length of the base 6m and slant height of the pyramid 5m is 96 m².
A square pyramid is a 3-D geometrical figure with the base of the shape of square and four triangular faces from each side of the square joining together at the top to form vertex.
The surface area of a square pyramid is given as:
Base area of the square face + 1/2 (perimeter of base × slant height)
Since square base has side of length 6m and the slant height of the pyramid is 5m then surface area is given by;
Surface area = (6×6) + 1/2 (4×6×5)
=> 36 + 1/2 (120)
=> 36 + 60
=> 96 m²
Thus, surface area of square pyramid is 96 m².
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A linear function is shown on the graph.
a linear function beginning with closed circle at 0 comma 2 and ending with a closed circle at 4 comma 6
What is the domain of the function?
{x | 0 ≤ x ≤ 4}
{x | 0 < x < 4}
{y | 2 ≤ y ≤ 6}
{y | 2 < y < 6}
Answer:
A) {x | 0 ≤ x ≤ 4}Step-by-step explanation:
The x-coordinates form the domain.
We know the x-coordinates of the end points of the line, the first numbers in pair of coordinates:
x = 0 and x = 4Also, since both points are closed circles, the endpoints are included.
So the domain is the interval between 0 and 4, both inclusive.
This is shown as:
{x | 0 ≤ x ≤ 4}The matching answer choice is A.
The domain of the function includes all x-values from 0 to 4, including both 0 and 4.
So, the correct answer is option A: {[tex]{x | 0 \leq x \leq 4}\\[/tex]}.
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. In this case, the function begins with a closed circle at (0, 2) and ends with a closed circle at (4, 6), which means that the function is defined at these specific points.
Since the function is a linear function, it represents a straight line.
A linear function is continuous, and it extends indefinitely in both directions.
Therefore, any x-value between 0 and 4 will also be defined by the linear function.
In mathematical notation, we can represent the domain as:
Domain: {x | 0 ≤ x ≤ 4}
This means that the domain of the function includes all x-values from 0 to 4, including both 0 and 4.
So, the correct answer is option A: {[tex]{x | 0 \leq x \leq 4}\\[/tex]}.
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complete question:
A linear function is shown on the graph.
a linear function that passes through the points (0, 2) and (4, 6)
What is the domain of the function?
[tex]{x | 0 \leq x \leq 4}\\{x | 0 < x < 4}\\{y | 2 \leq y \leq 6}\\{y | 2 < y < 6}[/tex]
graph is attached
What's the answer to this question
From calculating the percentages we can say that 43 more students went on Friday than Saturday.
Percentage is defined as quantity per hundred. Percentage is calculated by dividing the given number by the total number and multiplying it by 100.
From the survey we can see that 550 students were supposed to go on Friday. But it is given that 18 percent students did not go to the festival.
Number of students who went = 550 - (18% of 550 )
Therefore students = 550 - 99 =451 students
Again from the survey we can see that 480 students were supposed to go on Saturday . But it is given that 15 percent students did not go to the festival.
Number of students who went =480 - (15% of 480 )
Therefore students = 480 - 72 = 408 students
Therefore the number of more students who went on Friday than Saturday is 451-408 = 43 students
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7) Danice went to the grocery store and purchased 3 packets of noodles, 5 packets of cookies, and 2 packets of dry fruits. If the cost of each packet of noodles, cookies, and dry fruits is $2. $20 and 50 respectively. What is the total amount paid by Danice?
Answer: $206
Step-by-step explanation:
n=packets of noodles.
c=packets of cookies.
d=packets of dry fruit.
2n+20c+50d=
2(3)+20(5)+50(2)=
6+100+100=
6+200=$206
Find the value of x.
(4x+8) =
Answer:
Step-by-step explanation:
(4x+8)
4(x+2)
If p < 0, q > 0, and p + q = r, which statement about r is true? A number line shows p to the left of 0 and q to the right of 0, with q closer to 0 than p. |r| = |q| r > 0 r < 0 |r| > |q|
The correct option is r < 0 for the given inequalities of p < 0, q > 0, and p + q = r.
What is defined by the number line?You can select any point as "0," and all positive numbers will be to the right of the "0," and all negative numbers will be to the left of the "0." A line of infinite length, the points of which correspond to real numbers based on their distance in a negative or positive position from a point randomly chosen as zero.A number line is a straight line to numbers at equal intervals or sections along its length. A number line could be extended in any direction indefinitely and is typically represented horizontally.For the given inequalities;
p < 0, q > 0, and p + q = r;
As, we know that if p < 0; then it hold the negative value.
And for q > 0, it have the positive values.
Because -negative(P) was closer to zero than Positive q, let's say p = -10 and q = 5.
p + q = r
Put the values;
r = -10 + 5 = -5,
r = -5
Therefore, r < 0 is the correct condition for the given inequalities.
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Find an equivalent fraction for the decimal number. In your final answer, include all of your work.
0. 61
61/100 is the equivalent fraction for the given decimal number.
A decimal number then has two components: a whole number part and a fractional part. The decimal place value system for the whole part of a decimal number is the same as the whole number value system. However, we get the fractional part of the decimal number as we move toward the right after the decimal point.
A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator. It shows the total number of equal parts the whole is divided into or the total number of the same objects in a collection.
for converting a decimal into a fraction we need to multiply and divide the decimal by the 10^n where n is the number of digits after the decimal.
61/100 is the equivalent fraction for the given decimal number.
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A die is rolled twice.
What is the probability of rolling a 3 followed by a 2?
chance of 3 is 1/6 and chance of 2 is 1/6 so finale answer is 1/36
An elevator can carry 15 adults or 20 children at one time during the course of a day the elevator Carries a full passenger load 52 times if all the passengers were children how many more people would the elevator carry than If all the passengers were adults
An elevator can carry 15 adults or 20 children at one time during the course of a day the elevator Carries a full passenger load 52 times if all the passengers were children 260 more people would the elevator carry than If all the passengers were adults.
52 trips[tex]\times[/tex]15 adults = 780 adults for the course of a day
52 trips[tex]\times[/tex] 20 children = 1,040 children for the course of a day
The elevator can carry 1040-780=260 more children than adults in a day
A vehicle that travels in a vertical shaft to transport people or cargo between floors of a multistory structure is an elevator, also known as a lift. The majority of contemporary elevators are moved by electric motors through a network of wires and sheaves with the help of a counterweight (pulleys).
Traction elevators come in two varieties: gearless traction and gearless traction. The most sophisticated option is a gearless traction elevator, which operates the hoisting mechanism using counterweights and has a wheel that is directly connected to the engine.
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when constructing a congruent line segment does the ray needed for the construation have to be shorter than the line segment
The condition for two line segments to be congruent is that they must have equal length.
What is a line segment?
A geometrical figure which is a part of a straight line having two unique endpoints is called a line segment. Each point on the line segment lies within the two given endpoints
Explanation of the fact that for the two given line segments to be congruent, they must have the same length
The given statement is False. Because two line segments are said to be congruent if and only if they have exactly the same length. If we construct a ray shorter than the line segment, then both will never be congruent according to the properties of congruence. So, for these two to become congruent, they must have the same length.
Hence, we obtain that the two line segments are congruent if they have exactly the same length.
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