Answers
so you already have the slope=-6/5 and the intercept is 3
y=-(6/5)x+3
Related Questions
Find the surface area of a regular pentagonal prism with side length 8, altitude 20, and apothem approximately 5.5
Answers
The surface area of a regular pentagonal prism can be found by calculating the area of the pentagonal bases and the area of the rectangular sides and then summing those areas together.
Explanation:Calculating the Surface Area of a Regular Pentagonal Prism
To find the surface area of a regular pentagonal prism with given dimensions, we need to calculate the area of two components: the area of the pentagonal bases and the area of the rectangular sides (also called the lateral faces). We are given that the side length (s) of the pentagon is 8 units, the prism's altitude (h), or height, is 20 units, and the apothem (a) is approximately 5.5 units.
Firstly, the area of a pentagon (Apentagon) is calculated using the formula Apentagon = ½ * perimeter * apothem, where the perimeter (P) of a regular pentagon is the side length multiplied by 5. Thus, the area of one pentagonal base is ½ * 5 * 8 * 5.5. Next, to find the entire area of the two pentagonal bases, we multiply this result by 2.
The area of each of the rectangular sides can be found by multiplying the side length by the prism's altitude. Since there are 5 identical rectangular sides in a regular pentagonal prism, their total area is 5 * 8 * 20.
Adding these two results together gives us the total surface area of the prism. So, the formula for the surface area is Total Surface Area = (2 * ½ * 5 * 8 * 5.5) + (5 * 8 * 20).
What is the next number of 2 7 8 3 12 9
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Answer with Step-by-step explanation:
We are given a pattern
2 7 8 3 12 9
and we are asked to find the next term of this pattern
2+1=3
7+5=12
and 8+1=9
We can view this pattern in the set of three numbers and then, the next three are formed by adding one, five & one, respectively.
See these COLUMNS of groups of three:
2 3 4
7 12 17
8 9 10
Hence, next number in the pattern is:
4
The formula can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an object that has fallen 25 feet. Round your answer to the nearest tenth.
Answers
The formula:
v1^2-v0^2=2aS
where
v0=initial velocity (0 if object falls from rest), ft/s
v1=velocity reached after falling a distance S, ft/s
S=distance from initial position, positive downwards (for falling objects), ft
a=acceleration due to gravity, 32.2 ft/s^2 in imperial units
So substituting numbers, assuming initial velocity is zero (from rest), then
S=25 ft
v1^2-0^2=2*32.2*25
v1^2=1610
v1=sqrt(1610)
=40.1 ft/s
this box can be packed with 48 unit cubes the edge length each unit cube is 1 meter what is the voume of the box
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Answer:
48 cubic meters.
Step-by-step explanation:
48x1
unit meter is cubic meters
Write 337,060 in expanded form using exponents
Answers
Write 935.97 in expanded form
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hope it helps
Pamela is 13 years older than Jiri. The sum of their ages is 53 what is Jiri's age?
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p=j+13
Then you are told that the sum of their ages is 53 so:
p+j=53
We already know from the first statement that p=j+13, this makes p+j=53 become:
(j+13)+j=53 so we combine the two j's on the left side
2j+13=53 subtract 13 from both sides
2j=40 divide both sides by 2
j=20
So Jiri is 20 years old.
The solution is: Jiri is 20 years old.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
Pamela is 13 years older than Jiri so:
p=j+13
Then you are told that the sum of their ages is 53 so:
p+j=53
We already know from the first statement that p=j+13, this makes p+j=53 become:
(j+13)+j=53 so we combine the two j's on the left side
2j+13=53 subtract 13 from both sides
2j=40 divide both sides by 2
j=20
So Jiri is 20 years old.
Hence, The solution is: Jiri is 20 years old.
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2^-1 ∙ 2^-4 is what?
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When the power is minus just flip the number and make it denominator and make the power positive
(a^b)(a^c)=a^(b+c)
In this case:
(2^-1)(2^-4)
2^(-1-4)
2^-5 which is equal to:
1/(2^5)
1/32
Preston goes on a camel safari in Africa. They travel 5 km north, then 3km east and then 1 km north again. What distance did he cover? What was his displacement?
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what was his displacement? well, he has a north displacement of 6, 5 + 1, and a horizontal displacement of 3, check picture below.
so, his total displacement is "c" northeast.
The total distance Preston covered on his camel safari is 9 km, and his displacement is 6.71 km toward the northeast.
Determining Distance and Displacement
To answer the student's question about Preston's journey during his camel safari, we need to consider the definitions of distance and displacement.
Distance is the total length of the path traveled regardless of direction. In Preston's case, he traveled 5 km north, then 3 km east, and then 1 km north again. Therefore, the total distance covered is the sum of these individual distances
Displacement, on the other hand, measures the change in position from the starting point to the final point and is direction-dependent. It is a vector quantity with both magnitude and direction. To find the displacement, we can represent Preston's movement on a coordinate system with north being the positive y-direction and east being the positive x-direction.
From the starting point, moving 5 km north and then 1 km north results in a total of 6 km in the positive y-direction.
The magnitude of the displacement can be calculated using the Pythagorean theorem:
√((6 km)² + (3 km)²) = √(36 km² + 9 km²) = √(45 km²) = 6.71 km (rounded to two decimal places)The direction of the displacement would be to the northeast. Therefore, Preston's displacement is 6.71 km toward the northeast.
How do I answer this question?
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In a glide reflection, what comes first and what comes second?
first the glide, and second another glide
first the glide, and second a reflection
first the reflection, and second another reflection
first the reflection, and second a glide
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In a glide reflection, the reflection comes first and the glide comes second.
Explanation:In a glide reflection, first the reflection is applied, and second a glide is performed. The reflection is a transformation that flips the shape across a line of reflection, while the glide is a transformation that slides the shape along a vector. The combination of the reflection and glide creates a glide reflection.
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A pilot can travel 540 miles with the wind in the same amount of time as 380 miles against the wind. Find the speed of the wind if the pilots speed in still air is 230 miles per hour.
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540/(230+w)=380/(230-w)
540(230-w)=380(230+w)
124200-540w=87400+380w
124200-920w=87400
-920w=-36800
w=40
So the wind speed is 40 miles per hour.
A cylinder has a base area of 169π cm2 . Its height is 4 cm more than the radius. Identify the volume of the cylinder. Round to the nearest tenth, if necessary.
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Answer:
V = 9025.8 cm3
Step-by-step explanation:
Ricky is filling an 8 inch by 4 inch by 4 1/2 inch rectangular box with packing peanuts. The peanuts are cubes that come in two different sizes ,1 cubic inch and 1/8 inch .How many peanuts of each size are needed to fill the box?
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8 of the 1/8 inch=1 of the 1 cubic inch
He could do 144 and 0
143 and 8
142 or 16
Or just keep following the pattern... Hope that helped
“the sum of eight and twice w”
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Sum is +
twice w=2w
Sum of 8 and 2w
8+2w
hope this helps:)
please mark thanks and brainliest:)
Answer:
the expression is [tex]8+2w[/tex]
Step-by-step explanation:
WE need to write the expression for the given statement
“the sum of eight and twice w”
Expression represents the terms that contains variables and operations. the variable we use for the expression is 'w'
Difference represents the subtraction operation.
Sum represents the addition operation.
twice 'w' means 2 times w that is 2w
the sum of 8 and 2w
For sum we use '+'
so ,the expression becomes [tex]8+2w[/tex]
how do write an equation to represent a real world situation?
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Rewrite the equation in standard form and identify a, b, and c. 2x^2 + 6x - 9 = 3x^2 - 11x - 7
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Subtract 2x^2 from both sides
6x - 9 = x^2 - 11x - 7
Substract 6x from both sides
-9 = x^2 - 17x - 7
Add 9 to both sides
0 = x^2 - 17x + 2
a = 1
b = -17
c = 2
Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?
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[tex] \frac{2}{3}x-3 \geq y[/tex]
to plot the pairs (x, y) for which the inequation holds, draw the line [tex]y=\frac{2}{3}x-3[/tex]
then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.
we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.
inequation 2:
[tex]y+ \frac{2}{3}x\ \textless \ 4 [/tex]
[tex]y\ \textless \ - \frac{2}{3} x+ 4 [/tex]
draw the lines
i) [tex]y=\frac{2}{3}x-3[/tex] use points (0, -3), (3, -1)
ii)[tex]y=- \frac{2}{3} x+ 4 [/tex] use points ( 0, 4), (3, 2)
let's use the point P(3, 3) to see what region of the lines need to be coloured:
[tex]\frac{2}{3}x-3 \geq y[/tex] ;
[tex]\frac{2}{3}(3)-3 \geq 3[/tex]
[tex]2-3 \geq 3[/tex], not true so we color the region not containing this point
[tex]y+ \frac{2}{3}x\ \textless \ 4 [/tex]
[tex](3)+ \frac{2}{3}(3)\ \textless \ 4 [/tex]
[tex]3+ 5\ \textless \ 4 [/tex] not true, so we color the region not containing the point (3, 3)
The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.
Answer:
in other words b
Step-by-step explanation:
ΔABC has three sides with these lengths: AB = 9, BC = 40, and CA = 41. What is the value of cos C?
Answers
40*40 = 1600
9* 9 = 81
so a^2 = b^2 + c^2
1681 = 1600 + 81
1681 = 1681 ...it's right triangle
CA = 41 = Hypo.
cosC = Adj / Hypo
cosC = BC / CA = 40/41
answer
cosC = 40/41
Answer:
The correct answer is
C 40/41
Step-by-step explanation:
What is a ratio equivalent to 8/10 with lower terms
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In this case the gcf is 2 so you divide both 8 and 10 by 2, and you get 4/5.
Based on the historical record what is the empirical probability that the city will be hit by a tornado
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what is the product x 2-16/2 x+8 . x3-2x2+x/x2+3x-4
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------------- * ---------------------
2x+8 x^2 + 3x -4
(x+4)(x-4) x (x - 1)(x - 1)
= ----------------- * ----------------------
2(x+4) (x + 4)(x - 1)
x(x- 4) (x - 1)
= -----------------
2 (x + 4)
Answer:
A on Edge 2021
[tex] \frac{x(x - 4)(x - 1)}{2(x + 4)} [/tex]
a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, how many miles from earth is the star?
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3.4 * 5.87х10^12 miles
In a case whereby a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, the number of miles from earth the star is can be expressed as [tex]3.4 * 5.87 * 10^12 miles[/tex]
How can the number of miles be calculated?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given that star=3.4 light years from earth
1 light years= [tex]5.87*10x^{12} miles[/tex]
The number of miles from earth is
[tex]3.4 * 5.87 *10^{12} miles\\\\=3.4 * 5.87 * 10^12 miles[/tex]
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Write the quadratic function in the form g(x)= a (x-h)^2 +k . Then, give the vertex of its graph. g(x)=3x^2+30x+72
Writing in the form specified: g(x)= ___
Vertex:___
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is a perfect square trinomial
now, let's take a closer look at the middle guy
is just 2 * guy on the left * guy on the right
so the middle term is just the product of the two terms of the binomial, without the exponent, or square rooted, and 2
alrite... that said.... now let's do some grouping
[tex]\bf g(x)=3x^2+30x+72\implies g(x)=(3x^2+30x)+72 \\\\\\ g(x)=3(x^2+10x)+72\implies g(x)=3(x^2+10x+\boxed{?}^2)+72[/tex]
so hmm we're missing the guy on the right there... who may that be?
well, we know the middle term is 10x, wait a minute, 10x is just 2 * 5 * x
so, if the guy on the left is "x", the other guy must be "5", 2*5*x = 10x
now, what we do is, we add 5²
however, bear in mind that, all we're doing is, borrowing from our very good friend Mr Zero, 0
so, if we add 5², we also have to subtract 5², so +5² - 5²
let's do so
[tex]\bf g(x)=3(x^2+10x)+72\implies g(x)=3(x^2+10x\boxed{+5^2-5^2})+72 \\\\\\ \textit{let's take out the negative from the group} \\\\\\ g(x)=3(x^2+10x+5^2)+\boxed{3(-5^2)}+72 \\\\\\ g(x)=3(x^2+10x+5^2)-75+72\implies g(x)=3(x+5)^2-3 \\\\\\ g(x)=3[x-(-5)]^2-3[/tex]
[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} y=a(x-{{ h}})^2+{{ k}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ \begin{array}{lcclll} g(x)=3[x-&(-5)]^2&-3\\ &\uparrow &\uparrow \\ &h&k \end{array}[/tex]
The length of the hypotenuse is:
0.
1.
2.
4.
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divide the base by the sin of the opposite angle
base = 2
opposite angle = 30 degrees
2/sin(30) = 4
x = 4
A student was asked to use the formula for the perimeter of a rectangle, P = 2l + 2w, to solve for l. The student came up with an answer, P -2w=2l. What error did The student make? Explain. Then solve for l
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A road crew spread 1 1/3 tons of gravel evenly over 8 feet of road.how many tons of gravel did they spread on each foot of road?
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What are the spherical coordinates of the point whose rectangular coordinates are (4,1,4)?
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The spherical coordinates for the given rectangular coordinates (4,1,4) can be calculated using formulas for the transformation. They approximately yield (sqrt(33), 0.505, 1.540).
Explanation:In mathematics, we can convert rectangular coordinates to spherical coordinates using given formulas. Here, we have the rectangular coordinates (4,1,4). The transformation from rectangular to spherical involves three-step calculations:
First, calculate the radial coordinate, r, which is the distance from the origin to the point. It is given by r = sqrt(x^2 + y^2 + z^2).Second, find the polar angle, theta, measured relative to the vertical z-axis. It is given by cos(theta) = z/r.Lastly, find the azimuthal angle, phi, measured relative to the x-axis. It is given by cos(phi) = x/(r*sin(theta)).
Applying the formulas, we get: r = sqrt(4^2 + 1^2 + 4^2) = sqrt(33), theta = cos^-1(4/sqrt(33)) which is approximately 0.505, and phi = cos^-1(4/sqrt(33)*sin(0.505)) which is approximately 1.540.
So, the spherical coordinates of the point whose rectangular coordinates are (4,1,4) are approximately (sqrt(33), 0.505, 1.540).
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A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=52t-16t^2 . What is the maximum height that the ball will reach? Do not round your answer.
Height: ________Feet
Answers
We know that in this case the vertex is at a maximum height because the leading coefficient is negative. If it were positive, then the vertex would be at the lowest point, in other words, they would ask you to solve for the lowest point. In this case we are solving for the highest point.
Primarily, we can use the axis of symmetry formula to solve for the x-coordinate of the vertex which demonstrates the time the object takes to reach its apex. Once we find the t or the x-coordinate, we can plug it back into the equation to solve for the h or height.
Axis of symmetry formula: -b/ 2a
(b) is 52 in this case. (a) is -16 in this case. Just plug the numbers in but be mindful of the signs included in the formula.
-(52)/ 2(-16) = -52/-32
The quotient would be a terminating decimal: 1.625
Therefore, the time it takes for the ball to reach its highest point would be 1.625 seconds. Now you can plug this number back in as a substitution for the variable t and you can solve for h.
h = -16(1.625)^2 + 52(1.625)
h = -16(2.640625) + 84.5
h= -42.25 + 84.5
h = 42.25
Therefore, the maximum height that the ball will reach in 1.625 seconds is 42.25 feet.
The maximum height would be 42.25 feet that the ball will reach.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
A vertical upward throwing of a ball Its height h after t seconds (in feet) is given by the function h(t) = 52t - 16t²
Here h(t) = 52t - 16t²
Differentiate with respect to t to get maximum height
h'(t) = 52 - 2 × 16t
h'(t) = 52 - 32t
In this position, the acceleration would be zero,
So 0 = 52 - 32t
32t = 52
t = 52/ 32
t = 1.625
Substitute the value of t = 1.625 in the given function,
⇒ h = 52(1.625) - 16(1.625)²
⇒ h = 84.5 - 42.25
⇒ h = 42.25
Therefore, the maximum height would be 42.25 feet that the ball will reach.
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Which if the following is the smallest value 0.79, 2.40, 3.00007, 0.424, or 100?
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hope this helps
The smallest value is 0.424
-----------------------------------------------------------------------------
You might think that 0.79 is the smallest one but it also has 0 which is not written. 0.790 is bigger than 0.424
I hope that helps!