For this case we have that the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
We have the points:
[tex](x_ {1}, y_ {1}) = (5, -2)\\(x_ {2}, y_ {2}) = (- 7,3)[/tex]
Substituting:
[tex]d = \sqrt {(- 7-5) ^ 2 + (3 - (- 2)) ^ 2}\\d = \sqrt {(- 7-5) ^ 2 + (3 + 2) ^ 2}\\d = \sqrt {(- 12) ^ 2 + (5) ^ 2}\\d = \sqrt {144 + 25}\\d = \sqrt {169}\\d = 13[/tex]
Thus, the distance between the points is 13
Answer:
[tex]d = 13[/tex]
Solve the following system using the Substitution method:
x - y = -4
x - 2y = -6
(3 points, 2 for work, 0.5 for each part of the solution (x,y))
Answer:
(x, y) = (-2, 2)
Step-by-step explanation:
We are given the following two equations which we are to solve using the substitution method:
[tex]x - y = -4[/tex] --- (1)
[tex]x - 2y = -6[/tex] --- (2)
From equation (1):
[tex]x = y-4[/tex]
Substituting this value of x in (2) to get:
[tex]x = [tex]x - 2y = -6\\\\(y-4)-2y=-6\\\\-y=-6+4\\\\-y=-2[/tex][/tex]
y = 2
Substituting the value of y in (1) to get x:
[tex]x - y = -4[/tex]
[tex]x - 2 = -4[/tex]
[tex]x = -4 + 2[/tex]
x = -2
Therefore, (x, y) = (-2, 2).
a regulat pentagon has side lenghts of 5.8cm and apothem of 4cm. calculate its perimeter and area
PENTA = 5.
a regular polygon has all equal sides, so if one side is 5.8, all are, so the perimeter for this pentagon with 5 sides is 5.8 + 5.8 + 5.8 + 5.8 + 5.8 = 29.
[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} p=perimeter\\ a=apothem\\ \cline{1-1} p=29\\ a=4 \end{cases}\implies A=\cfrac{1}{2}(4)(29)\implies A=58[/tex]
Ivan has a right rectangular prism with a square base. The height of the prism is twice the length of the base.
Which shapes can be obtained as a horizontal or vertical slice through the prism? Select all that apply.
A. a rectangle
B. a triangle
C. a parallelogram (with no right angles)
D. a square
E. a pentagon
pls answer ASAP!!!
thank you!
a rectangle and a square
A rectangle & a square
Nelly has a large rectangular postcard that is 9 inches long and 4 inches wide. What is the area of the postcard?
The answer is probably 36
Answer:
The answer is 36 inches
Step-by-step explanation:
Since the rectangle is 9 inches long and the length is 4 inches wide and you need to find the area the formula is A=L*W so you would multiply 9 and 4 which gives you 36
Find the height of the pyramid if the volume and the area are 90 cu. ft. and 30 sq. ft., respectively. A. 9 ft. B. 0.999 ft. C. 1 ft. D. 270 ft.
Answer:
A. 9 ft
Step-by-step explanation:
Given that volume of the pyramid = 90 cu. ft.
Given that area of the base of the pyramid = 30 sq. ft.
Now we need to find about what is the height of the pyramid.
So plug the given values into formula of the volume of the pyramid
[tex]volume=\frac{1}{3}\left(Base\ Area\right)\left(Height\right)[/tex]
[tex]90=\frac{1}{3}\left(30\right)\left(Height\right)[/tex]
[tex]90=\left(10\right)\left(Height\right)[/tex]
[tex]\frac{90}{10}=Height[/tex]
[tex]9=Height[/tex]
Hence correct choice is A. 9 ft
Find the volume of the cylinder. 30 POINTS :0!!
Formula: V = PI x r^2 x H
Volume = 3.14 x 4^2 x 10
Volume = 3.14 x 16 x 10
Volume = 3.14 x 160
Volume = 160π or 502.4 units^3
To find the volume of a cylinder, we use the formula represented below.
Volume = [tex]\pi[/tex][tex]r^{2}[/tex]h
Notice that our cylinder has a radius of 4 and a height of 16, so we can plug these numbers into our formula.
Image provided.
HELP!!! Simplify: (3x − 2y) − (4x + 5y).
this is 7th grade math
btw.
Answer: =−x−7y
Step-by-step explanation:
First, Distribute the Negative Sign:
=3x −2y+ −1(4x+5y),
=3x+ − 2y + − 1(4x) + −1 (5y),
=3x+ −2y + −4x + −5y
Then, Combine Like Terms:
=3x+−2y+−4x+−5y
=(3x+−4x)+(−2y+−5y)
Finally you get the answer :
= −x + −7y
* Hopefully this helps:) Mark me the brainliest:)!!
∞ 234483279c20∞
Answer:
-x - 7y
Step-by-step explanation:
First, get rid of the parentheses by multiplying them out. Multiply them by one for them to go away.
Now, you have 1(3x - 2y) - 1(4x + 5y).
Now simplify, and it's 3x - 2y - 4x - 5y (Yes, -5y! It's beause -1 * 5y = -5y. The sign is supposed to change).
Ok. The next is easy: Identify your matching variables.
3x , -4x and -2y , -5y
So, we're going to assume x comes before y in the new equation, as that's how it is alphabetically, and that's it.
-x - 7y.
Hope this helps!
Circular flower bed is 17 m in diameter and has a circular Samick around it is that to meters wide find the area of the sidewalk in square meters use 3.14 for pi
Answer:
26.69 square meters
Step-by-step explanation:
A=r(3.14)
A= 8.5(3.14)
A=26.69 meters
What is the answer to
3ab-9ab+7ab
Answer:
ab
Step-by-step explanation:
Since the terms all have the variable ab then they are like terms.
Collect them by adding/subtracting the coefficients
ab(3 - 9 + 7)
= 1ab = ab ← the 1 is assumed
The expression 3ab - 9ab + 7ab simplifies to ab by combining like terms.
Explanation:The student is asking to simplify the algebraic expression 3ab - 9ab + 7ab. This involves combining like terms. As all terms are multiples of ab, we can add and subtract them as coefficients:
3ab - 9ab + 7ab = (3 - 9 + 7)ab = 1ab = ab
The rules followed here are analogous to the rules of arithmetic addition and subtraction. This concept is fundamental as it provides a foundation for simplifying expressions and solving equations in algebra.
In a function y= .08 + 5, y represents the cost of water per gallons and x represents the number of gallons. How much does the cost of water increase for every gallon? A. X B. .08 C. 5.00 D. 5.08
Answer:
B. 0.08
Explanation:
The general form of a linear equation is:
y = mx + c
where:
m is the slope or the rate of change (increase or decrease)
c is the y-intercept or the initial value
Therefore, in a linear equation, the slope simply gives us the rate of change of the function (increase/decrease)
Now, the given equation is:
y = 0.08x + 5
Comparing the given equation with the general form, we will find that:
m = 0.08
Therefore, the cost of water increase for every gallon (rate of change) is 0.08
Hope this helps :)
What is the measure of secant DE?
Answer:
[tex]ED=32\ units[/tex]
Step-by-step explanation:
we know that
Applying the Intersecting Secant Theorem
[tex]AC*BC=EC*DC[/tex]
substitute the values
[tex](16+5)*(5)=(ED+3)*(3)[/tex]
Solve for ED
[tex](21)*(5)=(ED+3)*(3)[/tex]
[tex]35=(ED+3)[/tex]
[tex]ED=35-3=32\ units[/tex]
the vertex form of the equation of a parabola is y=(x-5)2+16. what is the standard form of the equation
Answer:
y = x² - 10x + 41
Step-by-step explanation:
The standard form of a quadratic is ax² + bx + c : a ≠ 0
Given
y = (x - 5)² + 16 ← expand (x - 5)²
= x² - 10x + 25 + 16
= x² - 10x + 41 ← in standard form
Answer: [tex]y=x^2-10x+41[/tex]
Step-by-step explanation:
The standard form of a quadratic function is:
[tex]y=ax^2+bx+c[/tex]
You need to remember the square of a binomial:
[tex](a-b)^2=a^2-2ab+b^2[/tex]
Applying the above, you get:
[tex]y=(x-5)^2+16[/tex]
[tex]y=(x^2-2(x)(5)+5^2)+16[/tex]
Simplify the expression:
[tex]y=x^2-10x+25+16[/tex]
Now you need to add the like terms.
THerefore, you get:
[tex]y=x^2-10x+41[/tex]
What is the mean for the data set?
412, 428, 475, 462, 481, 407, 420, 467, 472, 408
Express your answer as a decimal to the nearest tenth.
Enter your answer in the box.
P.S not actually asking just giving the answer to others who come across this question.
The answer to your question is 443.2 as the mean is the average
Which number is irrational
Answer:
sqrt(17)
Step-by-step explanation:
sqrt(49) = 7 rational
.06060606 (repeating) = 2/33 rational
1/6 rational
sqrt(17) irrational
What is the length of YZ
Answer:
D = 48
Step-by-step explanation:
because if AB is 24, YZ is the double, so YZ is 48
what is the cross section of a rectangular prism
Answer:
The cross section is just at the center of the rectangle. Sorry if I couldn't be of more help but good luck.
Step-by-step explanation:
Which of the following reasons completes the proof in line 2?
A.) Definition of parallelogram.
B.)If both pairs of opposite sides are =, then a parallelogram.
C.) All quadrilaterals are parallelograms.
Answer:
B: If both pairs of opposite sides are =, then a parallelogram.
Step-by-step explanation:
If was right on my assignment
Quadrilateral ABCD is a rhombus and parallelogram.
What is a rhombus?A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus.
Given, in a quadrilateral ABCD,
AB= BC = CD = DA
Since A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.
A Quadrilateral is a Parallelogram, if any of this is possible in a Quadrilateral
One Pair of Opposite Sides are equal and Parallel.Opposite sides are equal.Diagonals Bisect each other.One Pair of Opposite sides are parallel and Opposite angles are equal.Opposite sides are Parallel.Definition of a parallelogram.
All quadrilaterals are parallelograms.
If both pairs of opposite sides are equal.
Therefore, Quadrilateral ABCD is a rhombus and parallelogram.
Learn more about rhombus here:
https://brainly.com/question/29283762
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What is the value of X
Answer:
B. 8
Step-by-step explanation:
The sum of all exterior angles of pentagon is equal to 360°. There are such exterior angles: 62°, 66°, 77°, 59°, (12x)°. Thus, the sum
[tex]62^{\circ}+66^{\circ}+77^{\circ}+59^{\circ}+(12x)^{\circ}=360^{\circ},\\ \\264^{\circ}+(12x)^{\circ}=360^{\circ},\\ \\(12x)^{\circ}=360^{\circ}-264^{\circ},\\ \\(12x)^{\circ}=96^{\circ},\\ \\x^{\circ}=8^{\circ}.[/tex]
need help asap!!!
The probability of winning a game is 75%. How many times should you expect to win if you play 60 times?
(A)15
(B)45
(C)5
(C)30
Answer:
B.) 45
Step-by-step explanation:
All that is needed to solve this problem is .75*60. Whenever there is a percentage, , just move the decimal place up two :).
A hammer is 1 foot long a car is 15 feet long and shovel is 4 feet long which statement is correct? Choose all that apply’s
Answer:
Tationia Rolon
Step-by-step explanation:
Here
Solve the system of equations.
- 3x + 2y = 56
- 5x - 2y = 24
X = ?
Y= ?
X=-10 and Y=13, look at the image attached to see the solution
Answer:
x = -10
y = 13
Step-by-step explanation:
- 3x + 2y = 56 ------ Equation 1
- 5x - 2y = 24 ------ Equation 2
Equation 1 + Equation 2.
-8x = 80
x = -10
Substitute x = - 10 into Equation 1.
-3(-10) + 2y = 56
30 + 2y = 56
2y = 26
y = 13
Find the area of Diameter of 8.42
Answer:
55.68 square units
Step-by-step explanation:
To fond the area of a circle of diameter 8.42, we are using the area formula for a circle:
[tex]A=\frac{1}{4} \pi d^{2}[/tex]
where
[tex]A[/tex] is the area of the circle
[tex]d[/tex] is the diameter of the circle
We know from our problem that the diameter of our circle is 8.42, so [tex]d=8.42[/tex]. Replacing the values in our formula:
[tex]A=\frac{1}{4} \pi d^{2}[/tex]
[tex]A=\frac{1}{4} \pi (8.42)^{2}[/tex]
[tex]A=55.68[/tex] square units
We can conclude that the area of a circle of diameter of 8.42 units is 55.68 square units.
Answer:
[tex]A\ =55.65 \: square units[/tex]
step-by-step explanation :
Area of a circle with diameter 8.42
The area of a circle is given as
[tex]A\ =\pi ({ \frac{d}{2} })^{2} [/tex]
where d is the diameter.
Substituting into the formula :
[tex]d = 8.42 \: unts \: [/tex]
[tex]\pi = 3.14[/tex]
This implies that,
[tex]A\ =3.14 \times ({ \frac{8.42}{2} })^{2}[/tex]
We simplify to obtain :
[tex]A\ =55.65 \: square units[/tex]
The equation y=1/3x is the boundary line for the inequality y>=1/3x. Which sentence describes the graph of the inequality?
Answer: Third option
The region shaded above a solid boundary line
Step-by-step explanation:
The limit for inequality [tex]y\geq\frac{1}{3}x[/tex] is the line [tex]y=\frac{1}{3}x[/tex].
Note that the inequality includes all values of y that are greater than or equal to the function [tex]f(x)=\frac{1}{3}x[/tex]. . This means that the region includes all values of y that are above the line [tex]f(x)=\frac{1}{3}x[/tex]. .
Remember that inequality includes values that are greater than or equal to the line [tex]f(x)=\frac{1}{3}x[/tex], therefore all values belonging to the limit line [tex]f(x)=\frac{1}{3}x[/tex], are also part of the region. This is represented by delimiting the region with a solid line
Finally the answer is the third option
Identify the mapping diagram that represents the relation and determine whether the relation is a function.
Answer:
line graph and it is a function
Step-by-step explanation:
It shows a specific spot on the map
The mapping diagram is a function because each element in the domain is mapped to exactly one element in the range.
The mapping diagram that represents the given relation is:
(-3, -6)
(-1, -6)
(5, -6)
(8, -6)
This is because each element in the domain (the x-values) is mapped to exactly one element in the range (the y-values).
Is the relation a function :
Yes, the relation is a function. A function is a relation in which each element in the domain is mapped to exactly one element in the range.
In this case, each x-value is mapped to exactly one y-value.
Example:
(-3, -6) is a function because -3 is mapped to exactly one y-value, which is -6.
(5, -6) is a function because 5 is mapped to exactly one y-value, which is -6.
Conclusion:
The mapping diagram that represents the given relation is a function.
For similar question on mapping diagram.
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Complete question : 1. Identify the mapping diagram that represents the given relation and determine whether the relation is a function. {(–3, –6), (–1, –6), (5, –6), (8, –6)}
Solve by using the square root property. Write your answer in simplest radical form.
Answer: X = t or minus 4 square root 3 and X= 4 square root 3 Explanation: add 48 on both sides bring down x squared = 48 take the square root on both sides you get X= t or - 4 square root 3 and X=4 square root 3) Animex yw
Answer:
x = ±4√3
Step-by-step explanation:
Given: x² = 48, find x. Note that we must take the square root of both sides, and that there are 2 roots (solutions) because this is a second order equation.
√x² = ±√48
48 is not a perfect square, but it does factor into 16 (a perfect square) and 3 (not a perfect square).
Thus, x = ±4√3 (the last answer choice)
Which expression is equivalent to x(x + 9) + 20 x + 5 ?
A) x + 4
B) x + 5
C) x − 4
D) x − 5
Final answer:
The expression x(x + 9) + 20x + 5 is equivalent to x² + 29x + 5.
Explanation:
To simplify the expression x(x + 9) + 20x + 5, we can distribute the x to both terms inside the parentheses:
x * x + x * 9 + 20x + 5
This simplifies to:
x² + 9x + 20x + 5
Combining like terms, we get:
x² + 29x + 5
Therefore, the expression x(x + 9) + 20x + 5 is equivalent to x² + 29x + 5.
Which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number and four”?
Answer:
You never gave any options, but the right answer is 3-(x+1)=1/2(3x+4)
Step-by-step explanation:
Answer:
3 - (n - 1) = (1/2)(3n - 4)
Step-by-step explanation:
Next time, please share the possible answer choices. Thank you.
"three minus the difference of a number and one"
can be represented algebraicallyl as 3 - (n - 1), where n is the number.
"one-half of the difference of three times the same number and four” can be represented by (1/2)(3n - 4).
The desired equation is thus:
3 - (n - 1) = (1/2)(3n - 4)
If Melissa estimates she would read 250 but she read 290 what is the percent error
Answer: 13.8%
Step-by-step explanation:
Percent error = approximate-exact/exact x 100
250-290/290 x 100 = |-13.8| = 13.8%
The product of binomial and a trinomial is x^3+3x^2-x+2x^2+6x-2.
Answer:
x = -2 or x = sqrt(13)/2 - 3/2 or x = -3/2 - sqrt(13)/2
Step-by-step explanation:
Solve for x:
x^3 + 5 x^2 + 5 x - 2 = 0
The left hand side factors into a product with two terms:
(x + 2) (x^2 + 3 x - 1) = 0
Split into two equations:
x + 2 = 0 or x^2 + 3 x - 1 = 0
Subtract 2 from both sides:
x = -2 or x^2 + 3 x - 1 = 0
Add 1 to both sides:
x = -2 or x^2 + 3 x = 1
Add 9/4 to both sides:
x = -2 or x^2 + 3 x + 9/4 = 13/4
Write the left hand side as a square:
x = -2 or (x + 3/2)^2 = 13/4
Take the square root of both sides:
x = -2 or x + 3/2 = sqrt(13)/2 or x + 3/2 = -sqrt(13)/2
Subtract 3/2 from both sides:
x = -2 or x = sqrt(13)/2 - 3/2 or x + 3/2 = -sqrt(13)/2
Subtract 3/2 from both sides:
Answer: x = -2 or x = sqrt(13)/2 - 3/2 or x = -3/2 - sqrt(13)/2
Which statement correctly compares the slopes of the two functions?
ANSWER
B. Function g has slope 3 which makes it steeper
EXPLANATION
The function f(x) has equation:
3x-y=6
We slope for y to get:
-y=-3x+6
y=3x-6
The slope of this function is 3.
The function g(x) passes through (-2,1) and (0,5).
The slope is
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
[tex]m = \frac{5- 1}{0 - - 2} [/tex]
[tex]m = \frac{4}{2} = 2[/tex]
Function g has slope 3. Hence it is steeper.
The statement which correctly compares the slopes of two functions is:
Function f(x) has a slope 2, which makes is steeper than g(x)Step-by-step explanation:If the slope of a function has a greater absolute value as compared to other then that function is steeper than the other.
Here we have a function f(x) as:
[tex]3x-y=6[/tex]
On changing to slope-intercept form of a line
i.e. y=mx+c
where m is the slope of the line and c is the y-intercept of the line we have:
[tex]f(x)=y=3x-6[/tex]
i.e. the slope of function f(x) is: 3
The function g(x) is a graph that passes through (-2,1) and (-1,3)
The equation for y=g(x) is given by:
[tex]y-1=\dfrac{3-1}{-1-(-2)}\times (x-(-2))\\\\\\y-1=\dfrac{2}{-1+2}\times (x+2)\\\\\\i.e.\\\\\\y-1=\dfrac{2}{1}\times (x+2)\\\\\\i.e.\\\\\\y=2x+4+1\\\\\\i.e.\\\\\\y=2x+5[/tex]
( since we used a concept of a line passing through two-point (a,b) and (c,d) is given by the equation:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex] )
Hence, the slope of function g(x) is: 2
The absolute value of slope of function f(x) is greater than function g(x)
( since 3>2 )
Hence, we get function f(x) is more steeper.