Geometry

9. find x (click to see photo)

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).

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.

Step-by-step explanation:

it is solved in the diagram

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

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.

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.

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

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.

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

Answer:

a=4/5y

Step-by-step explanation:

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°.

Answer:

m=13 b=17

Step-by-step explanation:

Answer:

m=13 b=17

hope this helps

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

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°.

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

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.

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.

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.

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.

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

Answer:

2

Step-by-step explanation:

count how many more

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

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.

Number 2,3,5 are true

Answer:

Exponential

Step-by-step explanation:

i took that

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

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.

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:

5 x tan 66 = 7.140

your welcome :)

Answer:

Step-by-step explanation:

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.

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:

Therefore, (f/g)(x) stands as (4x² + 6x) / (2x² + 13x + 15).

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

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.