Answer:
b.
Step-by-step explanation:
x-intercepts are found by factoring. We will use standard factoring here since this one is straightforeward and has real zeros as its solutions.
In our equation,
a = 2
b = 2
c = -4
The rules are to take a * c and then find the factors that number, determine which combination of those factors will give you the linear term (the term with the single x on it), and rearrange those signs accordingly. Let's start with that:
Our a * c is 2 * -4 = -8.
We need the factors of |-8|: 1,8 and 2,4
Some combination of those factors needs to give us a +2x. 2,4 will work as long as the 4 is positive and the 2 is negative.
Now we put them back into the equation, the absolute value of the larger number first:
[tex]2x^2+4x-2x-4=0[/tex]
Now group the terms in sets of 2 without moving any of them around:
[tex](2x^2+4x)-(2x-4)=0[/tex]
In each set of parenthesis, pull out what is common to both terms. In the first set, the 2x is common, and in the second set, the 2 is common:
[tex]2x(x+2)-2(x+2)[/tex]
Now what is common between both terms is the (x + 2), so pull that out, grouping what is remaining in its own set of parenthesis:
[tex](x+2)(2x-2)=0[/tex]
To find the zeros, remember that the Zero Product Property tells us that for that equation above to equal zero, one of those factors has to equal zero, so:
x + 2 = 0 or 2x - 2 = 0. Solve both for x:
x = -2 so the coordinate is (-2, 0)
2x - 2 = 0 and
2x = 2 so
x = 1 so the coordinate is (1, 0)
what is the measure arc PD?
a) 35°
b) 90°
c) 110°
d) 180°
Answer:
c) 110°
Step-by-step explanation:
Arc FP is twice the measure of the marked angle, so is 70°. If FD is supposed to be a diameter, then arc FPD is a semicircle (180°) and arc PD is 180° -70° = 110°.
When the two equations are graphed on a coordinate plane, they intersect at two points.
y=3x^2+4x+3
y=−2x+3
What are the points of intersection?
Enter your answers in the boxes.
(_,_) and (_,)
Answer:
(-2, 7) and (0, 3)
Step-by-step explanation:
A graph of the two equations clearly shows the points of intersection.
The equations are conveniently graphed by a graphing calculator (as here) or by a spreadsheet program, on-line graphing tool, or graphing app.
___
Alternate solution
You can set the two values of y equal to each other, then solve for x.
3x^2 +4x +3 = -2x +3
3x^2 +6x = 0 . . . . . subtract the right side expression
3(x)(x +2) = 0 . . . . . factor the equation
x = 0, x = -2 . . . . . . solutions that make the factors zero
y = -2{0, -2} +3 . . . . substitute the values of x into the expression for y
y = {0, 4} +3
y = {3, 7} . . . . . . . . . the values of y corresponding to x = {0, -2}
Then the points of intersection are (0, 3) and (-2, 7).
if f(×)=-5,tgen f(-3)=
Answer:
f(-3) = -5
Step-by-step explanation:
Put -3 where x is and evaluate the expression:
f(-3) = -5
_____
The function describes a horizontal line. It doesn't matter what x is, the value of the function is -5.
15. Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.
Answer:
y = -2(x -1)^2 -2
Step-by-step explanation:
My "work" consists of providing a table of values to a calculator and asking it for a quadratic model. The result is ...
y = -2(x -1)^2 -2
__
If you like to do these "by hand", you can write the model, then solve for its parameters using the given points.
We observe that the first and third points have the same y-coordinate. Then the vertex of the quadratic will be halfway between the corresponding x-values, at ...
h = (-2 +4)/2 = 1
So, one of the parameters of the model is found already. Using the second point and one other, we can find the remaining parameters for our model:
y = a(x -1)^2 +k
for (4, -20) ...
-20 = a(4 -1)^2 +k = 9a +k
for (0, -4) ...
-4 = a(0 -1)^2 +k = a + k
Subtracting the second equation from the first, we get
-16 = 8a
-2 = a . . . . . divide by 8
Substituting this value of a into the second equation, we have ...
-4 = -2 +k
-2 = k . . . . . . add 2
So, our model is ...
y = -2(x -1)^2 -2
A foam kickboard to use for swimming has two identical hand grips.
a. Find the volume of the kickboard
b. One cubic inch of the phone weighs about 0.007 lb. How much does the kickboard weigh?
Answer:
a. 215.6 in^3
b. 1.51 lb
Step-by-step explanation:
The area of each hand grip hole is that of a circle of radius 0.6 in together with a rectangle 2 in long and 1.2 in wide. So, that area is ...
π·(0.6 in)^2 + (2 in)(1.2 in) = (0.36π +2.4) in^2
The area of the kickboard before the hand grip holes are put in is that of a semicircle of radius 5.5 in together with a rectangle 12 in long and 11 in wide. So, that area is ...
(1/2)·π·(5.5 in)^2 + (12 in)(11 in) = (15.125π +132) in^2
Taking the hand grip holes out, the top area of the board is ...
((15.125π +132) -2(0.36π +2.4)) in^2
= (14.405π + 127.2) in^2
___
a. The volume is the product of the area and the thickness, so is ...
((14.405π +127.2) in^2)·(1.25 in) ≈ 215.568 in^3
__
b. The weight of the kickboard is the product of its volume and its density:
(215.568 in^3)(0.007 lb/in^3) ≈ 1.509 lb
To find the volume of the foam kickboard, its length, width, and height are needed. The weight is then calculated by multiplying the volume by the weight per cubic inch. Without specific dimensions, we cannot provide exact answers for the volume and weight.
Explanation:To find the volume of the foam kickboard, we would need its dimensions such as length, width, and height. If we had these measurements, the volume (V) can be calculated using the formula V = length × width × height. Unfortunately, the question does not provide specific dimensions, so we cannot calculate an exact volume without this information.
To calculate the weight of the kickboard, once the volume is determined, you would multiply the volume by the weight per cubic inch of the foam. Assuming we had a volume of V cubic inches, the weight (W) of the kickboard can be found with W = V × 0.007 lb/in3.
For example, if the kickboard's volume was 100 cubic inches, then the weight would be 100 × 0.007 lb/in3 = 0.7 lb.
The graph shown is only a small part of a larger graph. The table shows two additional points that are part of the function but are not shown on the graph.
Do either of the points prevent the function from being a linear function?
A. No, both points indicate this function is linear because the x and yvalues can be substituted into the equation y=mx+b to create a true equation.
B. Yes; Point A prevents this function from being linear because (-12, 16) would only satisfy the function if the function was exponential.
C. Yes; Point B prevents this function from being linear because (12, -16) would only satisfy a function with a variable rate of change.
D. No; both points indicate this function is linear because they both follow the pattern of the line.
Answer:
C. Yes; Point B prevents this function from being linear because (12, -16) would only satisfy a function with a variable rate of change.
Step-by-step explanation:
Point B is not on the line shown in the graph, so the function would have to be non-linear to include point B.
PLEASE HELP 20! POINTS
Given f(x)=4x^2+6x and g(x)=2x^2+13x+15, find(f/g)(x) . Show your work
X1= -3/2
X2= 0
F(x)=4x^2+6x
To find X-intercept/zero, substitute f(x)=0
0=4x^2+6x
Move the constant to the right
4x^2+6x=0
Factor out 2x from the expression
2x(2x+3)=0
Divide both sides of the equation
2x(2x+3)/2=0/2
X(2x+3)=0
When the product of factors equals 0, at least one factor is 0.
X=0
2x+3=0
Next you solve for X by moving the constant to the right
2x=-3
Then divide both sides by 2
X=-3/2
Hope this answers your question.
The result is (f/g)(x) = (4x² + 6x) / (2x² + 13x + 15).
To find (f/g)(x) for the given functions f(x) = 4x² + 6x and g(x) = 2x² + 13x + 15, you need to divide the function f(x) by g(x).
Step-by-Step Solution:
Write down the functions: f(x) = 4x² + 6x and g(x) = 2x² + 13x + 15.Express the division of these two functions: (f/g)(x) = (4x² + 6x) / (2x² + 13x + 15).Simplify the expression if possible by factoring the numerator and the denominator.In this case, neither the numerator nor the denominator can be factored further in a way that simplifies the fraction: 4x² + 6x and 2x² + 13x + 15 do not have common factors.Thus, the simplest form of (f/g)(x) is: (f/g)(x) = (4x² + 6x) / (2x² + 13x + 15).Therefore, (f/g)(x) stands as (4x² + 6x) / (2x² + 13x + 15).
Match the reasons with the statements in the proof to prove DF = EF, given that DEF is a triangle by definition and angles 3 and 4 are equal.
Given:
DEF
3 = 4
Prove:
DF = EF
Answer with explanation:
Given:
In Δ DEF, ∠3=∠4.
To prove:→ DE=E F
Proof:
1. ∠3=∠4------[Given]
2. →∠1 and ∠ 3 are Supplementary to each other.
(a)⇒∠1 + ∠ 3=180°
→∠2 and ∠ 4 are also Supplementary to each other.
(b)⇒∠2 + ∠ 4=180°
--------------------[Exterior sides in opposite rays]
3. From 1 , a and b
⇒∠ 1 = ∠ 2-------[Two Angles Supplementary to equal Angles are equal to each other]
4. [tex]\Bar{DE}=\Bar{E F}[/tex]
If two angles of a Triangle are equal , then side opposite to these angles are equal.
Answer:
Step-by-step explanation:
Explain why x = 3 makes 4x − 1 ≤ 11 true but not 4x − 1 < 11.
In technical translation, 4 x 3 - 1 is less than or equal to 11 (it's equal). 4 x 3 - 1 < 11 is not true because 11 is not less than 11.
Hope this helps!
Explaining why x = 3 satisfies 4x − 1 ≤ 11 but not 4x − 1 < 11:
When x = 3, we can evaluate the inequalities:
For 4x − 1 ≤ 11: 4(3) - 1 ≤ 11, which simplifies to 12 ≤ 11, making it true.
For 4x − 1 < 11: 4(3) - 1 < 11, which simplifies to 12 < 11, making it false.
Therefore, when x = 3, the first inequality is true while the second one is false.
Which function has a vertex at (2, 6)? f(x) = 2|x – 2| – 6 f(x) = 2|x – 2| + 6 f(x) = 2|x + 2| + 6 f(x) = 2|x + 2| – 6
Answer: Second Option
[tex]f (x) = 2 | x-2 | +6[/tex]
Step-by-step explanation:
For a function of the form:
[tex]f (x) = a | x-h | + k[/tex]
The vertex is always at the point (h, k)
In this case we know that the vertex is in the point (2, 6) and [tex]a = 2[/tex]
This means that
[tex]h = 2\\\\k = 6[/tex]
Therefore the function that has its vertivce in the point (2, 6) is:
[tex]f (x) = 2 | x-2 | +6[/tex]
The correct answer is the second
Find a: 2x+2y=a 2y−4a=2x
Answer:
a=4/5y
Step-by-step explanation:
Elevation and depression? Someone help me please
5 x tan 66 = 7.140
your welcome :)
Answer:
11.2Step-by-step explanation:
Which of the following points is a solution of y > |x| + 5?
A. (0,5)
B. (1,7)
C. (7,1)
Answer:
B. (1,7)
Step-by-step explanation:
Answer is B. (1,7)
If x = 1 then
y > 1 + 5
7 > 6
Answer:
(1 , 7) is a solution of y > IxI + 5 ⇒ answer B
Step-by-step explanation:
* Lets revise the absolute value
- IxI = positive value
- IxI can not give negative value
- The value of x could be positive or negative
* Lets solve the problem
∵ y > IxI + 5
∴ y > x + 5 OR y > -x + 5
- Lets check the answers
∵ y > 0 + 5 ⇒ y > 5
- But y = 5, and 5 it is not greater than 5 and there is no difference
between the two cases because zero has no sign
∴ (0 , 5) not a solution
∵ y > 1 + 5 ⇒ y > 6
- Its true y = 7 and 7 is greater than 6
∵ y > -1 + 5 ⇒ y > 4
- Its true y = 7 and 7 is greater than 4
∴ (1 , 7) is a solution
∵ y > 7 + 5 ⇒ y > 12
- But y = 1 and 1 is not greater than 12
∵ y > -7 + 5 ⇒ y > -2
- Its true y = 1 and 1 is greater than -2
* we can not take this point as a solution because it is wrong
with one of the two cases
∴ (7 , 1) is not a solution
What is the y-intercept of the function f(2)=4-5x?
-5
-4
4
5
C. 4
First, rearrange the equation into slope intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. You get y = -5x + 4. This means the y-intercept is 4.
For this case we have a function of the form [tex]y = f (x)[/tex]
Where:
[tex]f (x) = 4-5x[/tex]
To find the y-intercept of the function we must do x = 0.
Then, replacing:
[tex]f (0) = 4-5 (0)\\f (0) = 4-0\\f (0) = 4[/tex]
So, the y-intercep of the function is 4
ANswer:
4
Option C
In the form of a paragraph, explain the difference between a ray and a segment. Include, in your explanation, a physical description of each defined term. Complete your work in the space provided or upload a file that can display math symbols if your work requires it.
Answer:
Step-by-step explanation:
Segment
A segment is a line that has 2 end points. We can measure the segment length. A segment is represented by [tex]\overline{AB}\\[/tex] where A and b are the two end points of the segment.
Ray
A ray is an line that has one end point and one point goes in infinity. We cannot measure ray as it's one end goes to infinity. A ray is represented by [tex]\overrightarrow{AB}[/tex] where A is the end point and B is the infinite point.
Figures of ray and segment are attached.
Pam invested money into a small stock market account. After several years of continued growth, the table below shows how much her investment earned.
Investment Earnings
Years 1 2 3 4 5
Money Earned $31.25 $125 $500 $2,000 $8,000
Which of the following functions would best model the data above?
Answer:
Exponential
Step-by-step explanation:
i took that
What is the length of AC?
A is at -8 and C i5 at 5
-8 to 0 is 8 units and 0 to 5 is 5 units.
8 +5 = 13
AC is 13 units long.
For this case, we have that by definition, the distance between two points any A and B will be the absolute value of the subtraction of their coordinates in the order that is preferred. (the distances can not be negative)
So:
We find the distance from A to a point x located at 0. ENtonces:
[tex]| -8-0 | = | -8 | = 8[/tex]
Now we add the distance from x to C. From point x (located at zero) to point C there are 5 spaces, then:
[tex]8 + 5 = 13[/tex]
Thus, the distance from A to C is 13
Answer:
13
Solve the system below for m and b.
1239 = 94m + b
810 = 61m + b
Answer:
m=13 b=17
Step-by-step explanation:
Answer:
m=13 b=17
hope this helps
what is the difference of scientific notation. 0.00067 - 2.3 x 10^-5
A. 6.47 x 10⁻⁴
B. 6.47 x 10⁻⁵
C. 4.4 x 10⁻⁵
D. 4.4 x 10¹
Answer is letter A
it is the answer
For this case we must find the difference of the following expressions:
[tex]0.00067\\2.3 * 10 ^ {- 5}[/tex]
For the second expression we must run the decimal 5 times to the left, because the exponent is negative, that is:
[tex]0.000023[/tex]
We subtract:
[tex]0.00067-0.000023 = 0.000647[/tex]
Represented in scientific notation we have:
[tex]6.47 * 10 ^ {- 4}[/tex]
Answer:
Option A
1) Given: mLHE=84°
Find: m∠EYL.
2)Given: m∠EYL=72°
Find: m arc EHL, m arc LVE
Answer:
Part 1) The measure of angle EYL is [tex]96\°[/tex]
Part 2) The measure of arc EHL is [tex]108\°[/tex] and the measure of arc LVE is [tex]252\°[/tex]
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs which comprises
Part 1)
Let
x------> the measure of arc LHE
y----> the measure of arc LVE
we know that
[tex]x+y=360\°[/tex]
[tex]x=84\°[/tex]
Find the value of y
[tex]y=360\°-84\°=276\°[/tex]
Find the measure of angle EYL
[tex]m<EYL=\frac{1}{2} (y-x)[/tex]
substitute the values
[tex]m<EYL=\frac{1}{2}(276\°-84\°)=96\°[/tex]
Part 2)
Let
x------> the measure of arc EHL
y----> the measure of arc LVE
we know that
[tex]x+y=360\°[/tex]
[tex]x=360\°-y[/tex] -----> equation A
[tex]m<EYL=72\°[/tex]
[tex]m<EYL=\frac{1}{2} (y-x)[/tex]
substitute
[tex]72\°=\frac{1}{2} (y-x)[/tex]
[tex]144\°=(y-x)[/tex]
[tex]x=y-144\°[/tex] --------> equation B
equate equation A and equation B and solve for y
[tex]360\°-y=y-144\°[/tex]
[tex]2y=360\°+144\°[/tex]
[tex]2y=504\°[/tex]
[tex]y=252\°[/tex]
Find the value of x
[tex]x=252\°-144\°=108\°[/tex]
therefore
The measure of arc EHL is [tex]108\°[/tex]
The measure of arc LVE is [tex]252\°[/tex]
A circle is a curve sketched out by a point moving in a plane. The measure of the arcEHL and arcLVE are 108° and 252° respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
As we can see in the image attached below, the radius of the circle is OE and OL while there is two tangent to the circle Ey and LY. Therefore, the measure of the ∠OEY and ∠OLY is 90°.
A.)
The sum of the angles of a quadrilateral is 360°.
As it is mentioned in the problem the measure of the angle made by arc LHE is 84° which means the measure of ∠EOL is 84°. Therefore, the sum of all the angles can be written as,
[tex]\text{Sum of angles} = 360^o\\\\\angle OEY + \angle OLY + \angle EOL + \angle EYL = 360^o\\\\90^o+90^o+84^o +\angle EYL = 360^o\\\\\angle EYL = 96^o[/tex]
B.)
The sum of the angles of a quadrilateral is 360°.
As it is mentioned in the problem the measure of ∠EYL is 72°. Therefore, the sum of all the angles can be written as,
[tex]\text{Sum of angles} = 360^o\\\\\angle OEY + \angle OLY + \angle EOL + \angle EYL = 360^o\\\\90^o+90^o+ \angle EOL +72^o = 360^o\\\\ \angle EOL= 108^o\\\\ \rm arc EHL=108^o[/tex]
Since a complete circle measures 360°, therefore, the sum of the angles made by arc EHL and arc LVE can be written as,
arcEHL + arcLVE = 360°
108° + arcLVE = 360°
arcLVE = 252°
Thus, the measure of the arcEHL and arcLVE are 108° and 252° respectively.
Learn more about Circle:
https://brainly.com/question/11833983
50 POINTS
Tyrone rolls a standard number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he has rolled 155 sixes. Find the experimental probability of rolling a six, based on Tyrone’s experiment. Round the answer to the nearest thousandth.
Answer:
Step-by-step explanation:
Unless I'm reading this incorrectly, he throws 155 6's.
There are 1000 throws altogether (according to the table)
So the experimental probability is 155/1000 = 0.155
The answer is B. It is a bit tricky to read.
Consider the following claim: if the point (2 + d, y) is on the graph of the function
f(x) = x(x-4), then the point (2 - d, y) is also on the graph.
Use algebra to show that the claim is true
What is the relationship between the line x = 2 and the graph of f(x)? Justify your reasoning.
Please show steps
Answer:
The point (2 - d, y) is on the graph of f(x)
The line x = 2 is the axis of symmetry of the graph of f(x)
Step-by-step explanation:
* Lets explain how to prove that a point lies on a graph Algebraically
- Substitute the value of the x-coordinate of the point in the equation
of the graph the answer must be equal the y-coordinate of the point
- The function is a quadratic because the greatest power of x is 2,
then it represented by parabola
- The parabola has a vertex point (h , k), where h is the x-coordinate
and k is the y-coordinate
- This vertex divides the parabola into two equal parts, then the axis
of symmetry of the parabola is a vertical line passing through it
∴ The equation of the axis of symmetry is x = h
- The vertex of the parabola could be minimum point if the parabola
opened upward or maximum if it opened downward
- The minimum value and the maximum value are the value of k
# Look to the attached figures for more understand
* Now lets solve the problem
∵ f(x) = x(x - 4)
∵ Point (2 + d , y) is on the graph of f(x)
- Replace each x in f(x) by 2 + d
∴ f(2 + d) = (2 + d)(2 + d - 4) ⇒ add 2 and -4
∴ f(2 + d) = (2 + d)(-2 + d)
∵ f(2 + d) = y
∴ y = (2 + d)( -2 + d)
* Multiply them to simplify
∴ y = 2(-2) + 2(d) + d(-2) + d(d) = -4 + 2d - 2d + d²
∴ y = -4 + d²
* Lets do these steps again with point (2 - d , y)
- Replace each x in f(x) by 2 - d
∴ f(2 - d) = (2 - d)(2 - d - 4) ⇒ add 2 and -4
∴ f(2 - d) = (2 - d)(-2 - d)
∵ f(2 - d) = y
∴ y = (2 - d)( -2 - d)
* Multiply them to simplify
∴ y = 2(-2) + 2(-d) - d(-2) - d(-d) = -4 - 2d + 2d + d²
∴ y = -4 + d²
- The value of y of the point (2 - d , y) = the value of y of the point on
the graph
∵ f(2 + d) = f(2 - d)
∵ The point (2 + d , y) is on the graph of f(x)
∴ The point (2 - d , y) is on the graph of f(x)
* It is true the point (2 - d, y) is also on the graph.
* To find the relation between the line x = 2 and the graph of f(x)
lets find the vertex of the parabola
- If f(x) = ax² + bx + c in the general form, where a, b , c are constant
then h = -b/2a, where h is the x-coordinate of the vertex point, a is
the coefficient of x² and b is the coefficient of x
∵ f(x) = x(x - 4) ⇒ multiply the bracket by x to put it in the general form
∴ f(x) = x² - 4x
- Find the value of a and b to find h
∵ a = 1 and b = -4
∵ h = -b/2a
∴ h = -(-4)/2(1) = 4/2 = 2
∴ The x-coordinate of the vertex point = 2
∵ The axis of symmetry of the parabola passing through the
vertex point
∴ The equation of the axis of symmetry of the parabola is x = 2
* The line x = 2 is the axis of symmetry of the graph of f(x)
Answer:
Step-by-step explanation:
AYOOO
a ball is thrown with a slingshot at a velocity of 110ft/sec at an angle of 20 degrees above the ground from a height of 4.5 ft. approximentaly how long does is take for the ball to hit the ground. Acceleration due to gravity is 32ft/s^2
Answer:
[tex]t=2.47\ s[/tex]
Step-by-step explanation:
The equation that models the height of the ball in feet as a function of time is
[tex]h(t) = h_0 + s_0t -16t ^ 2[/tex]
Where [tex]h_0[/tex] is the initial height, [tex]s_0[/tex] is the initial velocity and t is the time in seconds.
We know that the initial height is:
[tex]h_0 = 4.5\ ft[/tex]
The initial speed is:
[tex]s_0 = 110sin(20\°)\\\\s_0 = 37.62\ ft/s[/tex]
So the equation is:
[tex]h (t) = 4.5 + 37.62t -16t ^ 2[/tex]
The ball hits the ground when when [tex]h(t) = 0[/tex]
So
[tex]4.5 + 37.62t -16t ^ 2 = 0[/tex]
We use the quadratic formula to solve the equation for t
For a quadratic equation of the form
[tex]at^2 +bt + c[/tex]
The quadratic formula is:
[tex]t=\frac{-b\±\sqrt{b^2 -4ac}}{2a}[/tex]
In this case
[tex]a= -16\\\\b=37.62\\\\c=4.5[/tex]
Therefore
[tex]t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}[/tex]
[tex]t_1=-0.114\ s\\\\t_2=2.47\ s[/tex]
We take the positive solution.
Finally the ball takes 2.47 seconds to touch the ground
according to the line plot how many more Runners ran 1/3 of a mile for their warm-up than ran 1/4 of a mile
Answer:
2
Step-by-step explanation:
count how many more
Detroit, Michigan covers an area of 142.9 square miles. There are approximately 672,800 people living in Detroit. Grand Rapids, Michigan has an area of 45.3 square miles and has a population of approximately 195,100 people. How many more people, per square mile, live in Detroit verses Grand Rapids? Round to the nearest person per square mil
Answer:
401 people per square mile
Step-by-step explanation:
First find the number of people per square mile in Detroit by dividing people by square miles:
672,800/142.9 = 4708.18754374
Then do the same for Grand Rapids:
195,100/45.3 = 4306.84326711
Subtract:
4708.2-4306.8 = 401.4
Round to the ones place:
401
The number of more people per square mile living in Detroit compared to Grand Rapids is approximately 400.45 people per square mile.
Explanation:To find the number of more people per square mile living in Detroit versus Grand Rapids, we need to find the population density for each city. Population density is calculated by dividing the population by the area. Let's do the calculations:
Detroit population density = Detroit population / Detroit area = 672,800 / 142.9 = 4,706.42 people per square mile
Grand Rapids population density = Grand Rapids population / Grand Rapids area = 195,100 / 45.3 = 4,305.97 people per square mile
To find the difference in the number of people per square mile, we subtract the population density of Grand Rapids from the population density of Detroit. Therefore, the number of more people per square mile living in Detroit compared to Grand Rapids is approximately 400.45 people per square mile.
What’s the indicated angle (also can you maybe show me how to do it please)
Step-by-step explanation:
it is solved in the diagram
David wants to build a rectangular fencing with the 5 identical parts for his animals. He has 780 feet of fencing to make it. What dimensions of each part will maximize the total enclosed area?
Answer:
Step-by-step explanation:
So we're looking at a rectangle split into 5 smaller rectangles. If the height of each rectangle is y and the width of each rectangle is x, then the amount of fencing is:
P = 6y + 10x
And the area of the large rectangle is:
A = 5xy
We know that P = 780:
780 = 6y + 10x
10x = 780 - 6y
5x = 390 - 3y
If we substitute this into our area equation:
A = (390 - 3y) y
A = -3y² + 390y
This is a vertical parabola pointing down, so we know the maximum is at the vertex, which is at -b/(2a). Or, we can use calculus to take the derivative and set to 0.
dA/dy = -6y + 390
0 = -6y + 390
y = 65
Solving for x:
5x = 390 - 3y
5x = 390 - 3(65)
5x = 195
x = 39
So each part will have a width of 39 feet and a height of 65 feet.
A cone shaped block that has a slant height of 6 inches and has a radius of 4 inches . How many square inches of paper would it take the cover the surface?
Answer:
[tex]T.S.A=40\pi in^2[/tex]
Step-by-step explanation:
The total surface area of the cone is
[tex]\pi r^2+\pi rl[/tex]
The radius of the cone is 4 inches.
The slant height of the cone is l=6 inches.
We substitute these values into the formula to obtain;
[tex]T.S.A=\pi \times (4)^2+\pi \times 4\times6[/tex]
[tex]T.S.A=16\pi+24\pi[/tex]
[tex]T.S.A=40\pi in^2[/tex]
Or
[tex]T.S.A=125.7in^2[/tex] to the nearest tenth.
please help, i have no idea how to do this
Answer:
8 square units
Step-by-step explanation:
The figure is a trapezoid. The area of it is given by the formula ...
A = (1/2)(b1 +b2)h
where b1 and b2 are the lengths of the parallel bases and h is the distance between them.
Your figure shows the base lengths to be 5 and 3, and their separation to be 2. Filling the numbers in the formula, we have ...
A = (1/2)(5 +3)(2) = (1/2)(8)(2) = 4·2 = 8
The area of the figure is 8 square units.
_____
The right-pointing arrows on the horizontal lines identify those lines as being parallel. The right-angle indicator and the 2 next to the dotted line indicate the perpendicular distance between the parallel lines is 2 units.
Help! Please help me with these two questions!!
1.What is the volume of below composite figure?
2.What is the value of x?
Answer:
2. area = 504 cm^2
3. x = 30°
Step-by-step explanation:
2. The figure can be divided across the middle into a rectangular bottom part and a triangular top part. The triangle will have a base length of 21 cm and a height of 32 -16 = 16 cm. Its area is ...
triangle area = (1/2)bh = (1/2)(21 cm)(16 cm) = 168 cm^2
The area of the rectangle is the product of its base (21 cm) and height (16 cm). Its area is ...
rectangle area = bh = (21 cm)(16 cm) = 336 cm^2
Then the total area of the figure is the sum of the areas of its parts:
total area = triangle area + rectangle area
= (168 cm^2) + (336 cm^2) = 504 cm^2
A plane figure has no volume. The volume is zero.
__
3. The angle whose measure is 4x is supplementary to the angle marked 60°, so is 180° -60° = 120°. That means ...
4x = 120°
x = 120°/4 = 30° . . . . divide by the coefficient of x
The value of x is 30°.