f(x)=−2x+16
g(x)=4x+10
please give me the intersection points

Answers

Answer 1

Answer:

(1, 14)

Step-by-step explanation:

The intersection is when both functions have same coordinates

f(x) = g(x)

Substitute to get

- 2x + 16 = 4x + 104x + 2x = 16 - 106x = 6x = 1

The y- coordinate is

y = - 2(1) + 16 = -2 + 16 = 14

So the intersection point is (1, 14)

Answer 2

Answer:

(1, 14)

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=-2x+16\\g(x)=4x+10\end{cases}[/tex]

Substitute the function notation for y to create a system of equations:

[tex]\begin{cases}y=-2x+16\\y=4x+10\end{cases}[/tex]

To find the points of intersection of the given functions, solve the system of equations.

Multiply the first equation (function f(x)) by 2:

[tex]\implies 2y=-4x+32[/tex]

Add this to the second equation (function g(x)) to eliminate x:

[tex]\begin{array}{r l}4x+10 & = y\\+ \quad -4x+32 & = 2y\\\cline{1-2} 42 & = 3y\end{array}[/tex]

Solve for y:

[tex]\implies 3y=42[/tex]

[tex]\implies y=14[/tex]

Substitute the found value of y into one of the equations and solve for x:

[tex]\implies 4x+10=14[/tex]

[tex]\implies 4x=4[/tex]

[tex]\implies x=1[/tex]

Therefore, the point of intersection of the given functions is (1, 14).


Related Questions

What is the volume of a sphere with a radius of 9.1 ft, rounded to the nearest tenth of a cubic foot?

Answers

The volume of the sphere with a radius of 9.1ft is 3256.55cubic feet.

We have given that, the radius of the sphere is 9.1ft.

We have to determine the volume of the sphere

What is the formula for the volume of the sphere?

The volume of the sphere  is given by

[tex]V=\frac{4}{3}\pi r^3[/tex]

r is the radius of the sphere

V- is the volume of the sphere

So use the given value in the formula so that,

[tex]V=\frac{4}{3}\pi (9.1)^3[/tex]

[tex]V=3156.55082 ft^3[/tex]

Therefore the volume of the sphere with a radius of 9.1ft is 3256.55cubic feet.

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Answer:3156.6

Step-by-step explanation:

What is an equation of the line that passes through the points (−3,−4) and (-4, -6)

Answers

Answer:

[tex]\Large\boxed{\sf{y=2x+2}}[/tex]

Step-by-step explanation:

Use the slope formula.

SLOPE FORMULA:

[tex]\Rightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

y2=(-6)y1=(-4)x2=(-4)y1=(-3)

[tex]:\Longrightarrow \sf{\dfrac{-6-\left(-4\right)}{-4-\left(-3\right)}}[/tex]

Solve.

[tex]\sf{\dfrac{-6-\left(-4\right)}{-4-\left(-3\right)}=\dfrac{-6+4}{-4+3}=\dfrac{-2}{-1}=2}[/tex]

The slope is 2.

Use the slope-intercept form.

SLOPE-INTERCEPT FORM:

[tex]\sf{y=mx+b}[/tex]

X=slopeB=y-intercept.The y-intercept is 2.

y=2x+2

Therefore, the final answer is y=2x+2.

I hope this helps, let me know if you have any questions.

[tex]\text{Given that,}\\\\(x_1,y_1) =(-3,-4)~~ \text{and}~~ (x_2,y_2) = (-4,-6)\\\\\text{Slope,}~m = \dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{-6+4}{-4+3} = \dfrac{-2}{-1} =2\\ \\\text{Equation of line,}\\\\~~~~~y-y_1 = m(x-x_1)\\\\\implies y+4=2(x+3)\\\\\implies y =2x+6-4\\ \\\implies y= 2x+2[/tex]

Graph =−2+5 y = − 2 x + 5 and =−12−3 y = − 1 2 x − 3 . Are the lines parallel, perpendicular, or neither?

Answers

Answer:

They are neither,they intersect but not at a 90 degree angleStep-by-step

explanation: hope this helps :)

equivalent expression to −5.55−8.55c+4.35c

Answers

-5.55-8.55c+4.35c 2nd and 3rd term is like term we can connect. -digit have to larger number than +digit so the sign will be negative
-5.55-4.2c there is no like term to connect
Hence this is the answer

Simplify the following expression

(x^0 y^2/3 z^-2)^3/2 divided by (x^2z^1/2)^-6

Answers

[tex]\dfrac{\left(x^0 y^{\tfrac 23} z^{-2} \right)^{\tfrac 32}}{\left(x^2 z^{\tfrac 12} \right)^{-6}}\\\\\\=\dfrac{1\cdot \left( y^{\tfrac 23}\right)^{\tfrac 32} \cdot \left(z^{-2} \right)^{\tfrac 32}}{\left(x^2 \right)^{-6} \cdot \left( z^{\tfrac 12} \right)^{-6}}~~~~~~~~~~~~~~~~~~;\left[(ab)^m = a^m b^m\right]\\\\\\=\dfrac{y^{1} \cdot z^{-3}}{x^{-12} \cdot z^{-3}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[(a^m)^n = a^{mn}\right]\\\\\\=\dfrac{y}{x^{-12}}\\\\\\[/tex]

[tex]=\dfrac{y}{\tfrac 1{x^{12}}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-m} = \dfrac 1{a^m} } \right]\\\\\\=yx^{12}[/tex]

If you flipped a fair coin 18 times, about how many times would you expect heads to appear? please ansewr i need help

Answers

Answer:

1/2, or around 9 times

Step-by-step explanation:

since a fair coin has 2 sides, that makes you have 2 possible outcomes. Heads and tails, 2 sides, makes it 50-50 so you would expect to get around 9 heads because 50% or 1/2 of 18 is 9. Hope this helps

How can i find the circumference of a circle if I already know it's area?

Answers

Answer:

With the area you can find the radius and then substitute the radius in the circumference formula

Solve. 5y + 42 − y = 34

Answers

Answer:

The answer is y= -2

Step-by-step explanation:

(Arrange according to the like terms first)

5y-y+42= 34

4y+ 42-34= 0

4y+ 8= 0

4y= -8

∴ y= -8/4=-2

So, y= -2

Hope it will help.

Answer:

y = -2

Step-by-step explanation:

question : 5y + 42 − y = 34

⇒ 5y + 42 − y = 34

•shifting the +42 to the right side :

⇒ 5y - y = 34 - 42

⇒ 4y = -8

•shifting the 4 to the right side :

⇒ y = -8/4

⇒ y = -2 Answer...

hope that helps...

HELP I REALLY NEED HELPPPPP

Answers

[tex]\bold{ANSWER:}[/tex]

Answer:

100 degrees

Step-by-step explanation:

If x-3=6, what is the value of x?
Group of answer choices

x=2

x=3

x=6

x=9

Answers

Answer:

x=9

Step-by-step explanation:

9-6=3

what is the volume of the triangular prism

A) 12 cm
B) 18
C) 24
D) 48

Answers


Remember the formula for calculating volume is: Volume = Area by height. V = A X h.
For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.
So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h

What is the value of x2(7−x)+2 when x=5?

Answers

substitute the value of x for 5

(5)^2(7-5)+2

square 5 to get 25(7-5)+2

minus 7 and 5 to get 25(2)+2

multiply 25 and 2 to get 50 + 2

add the equation to get 52

so, the value of the equation is 52

hope this helped!

A pistol is accidentally discharged vertically upward at a height of 3 feet
above the ground. If the bullet has an initial muzzle velocity of 200 feet
per second the path of the bullet is modeled by
h (t) = -16t² + 200t + 3.
A. How long does it take for the bullet to reach its maximum height.
Round to nearest hundredth.
B. What is the maximum height?
C. How long will it take for it to hit the ground?
D. When will the bullet be 403 feet above the ground?

Answers

The maximum height the bullet will reach is 627 ft. The time(from the point when bullet was fired) it will take the bullet to hit the ground is 12.51 sec approx. The time when the bullet will be 403 ft above the ground are 2.475 sec and 10.02 sec approx.

How to obtain the maximum value of a function?

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

For this case, the height of the bullet from the ground is modeled by the equation:

[tex]h(t) = -16t^2 + 200t + 3[/tex]

where height is in meters and time is in seconds. And t is the time in seconds passed from the point of time when the bullet was fired.

A) Finding maximum height reached by the bullet:

Finding its first and second rate with respect to the variable 't', we get:

[tex]\dfrac{d(h(t))}{dt} = h'(t) = -32t + 200\\\\\dfrac{d^2(h(t))}{dt^2} = h''(t) = -32 < 0[/tex]

Thus, the second rate is negative no matter what the value of 't' is. So all the critical points would be corresponding to maxima.

Now, finding the critical points by equating the first rate = 0, we get:

[tex]h'(t) = 0\\\\-32t + 200 = 0\\\\t = \dfrac{200}{32} = 6.25 \: \rm sec.[/tex]

Due to only one critical point, and that each critical point is maxima, we have the value of h(t) globally maximum when t = 6.25

Putting t = 6.25 in the function h(t), we get the maximum height achieved by the bullet as:

[tex]h(t) = -16t^2 + 200t + 3\\h(6.5) = -16(6.5)^2 + 200(6.5) + 3 = 627 \: \rm ft[/tex]

B) Finding the time it will take the bullet to fall on the ground

When the bullet will fall on the ground, the value of h(t) would be 0.

Putting h(t) = 0, and finding the values of 't' for which this is true, we get:

[tex]h(t) = -16t^2 + 200t + 3\\0 = -16t^2 + 200t + 3\\\\16t^2 -200t -3 =0\\\\t = \dfrac{-(-200) \pm \sqrt{ (-200)^2 - 4(16)(-3)}}{2(16)}\\\\t \approx \dfrac{200 \pm 200.479}{32}\\\\t \approx -0.0149 \: \rm sec., t \approx 12.51 \: sec.[/tex]

Bullet will fall only after it is shot, so time taken for the bullet to fall compared to the time when its shot would be greater, so time passed (t here) would be positive.

Thus, at approx t = 12.51 sec, the bullet will fall on the ground.

C) When will the bullet be at 400 ft of height from the ground?

At  t = 0, bullet was at 3 ft, and therefore, whenever bullet will reach 400 ft, the time t would be > 0.

Putting h(t) = 400, we get:
[tex]h(t) = -16t^2 + 200t + 3\\400 = -16t^2 + 200t + 3\\\\16t^2 -200t +397 =0\\\\t = \dfrac{-(-200) \pm \sqrt{ (-200)^2 - 4(16)(397)}}{2(16)}\\\\t \approx \dfrac{200 \pm 120.797}{32}\\\\t \approx 2.475\: \rm sec., t \approx 10.02\: sec.[/tex]

These both values are true. The time when t = 2.475 approx, the bullet would be going up, passing by 400 ft height, and when t = 10.02 approx, the bullet would be coming down, passing by 400 ft height.

Thus, the maximum height the bullet will reach is 627 ft. The time(from the point when bullet was fired) it will take the bullet to hit the ground is 12.51 sec approx. The time when the bullet will be 403 ft above the ground are 2.475 sec and 10.02 sec approx.

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Given the graph of the function f(x), find each of the following.
† y
a. f(-4) 2
b.
f(0) O
C.
f (2) -1
d. f (5) -1

Answers

Answer:

a) 2 ; b) 0; c) -2 ; d) -1

Step-by-step explanation:

a) f(-4)=2 ;

b) f(0)=0;

c) f(2)= -2 ;

d) f(5)= -1

A=2 b=0 hopes this helps

Which point is located at - 1/6

Answers

Answer:

Point C

Step-by-step explanation:

it is negative, so we can already eliminate points A and B so which leaves us with C and D. It is a fraction that is greater than -1 so that eliminates point D, so the remaining point is our final answer.

Answer:

Point C

Step-by-step explanation:

Step 1:  What point is located at -1/6

We can see that the arrow pointing up showcases us going positive and the arrow pointing down showcases us going negative.  0 gives us the middle point between negatives and positives. We can see that there are 6 ticks between each whole number.  Therefore, if we go 1/6 of a tick down in the negative direction we would get point C.

Answer: Point C

PLease help me w this q.8

Answers

Answer:

B

Step-by-step explanation:

Angle 1 and angle  3 are alternate interior angles.

A fair die is rolled 5 times. What is the probability of having no 1 and no 4 among the rolls? Round your answer to three decimal places. ​

Answers

Answer:

0.132

Step-by-step explanation:

Rolling a die is an independent event.

Chance of not rolling a 1 or 4 is 4/6 or 2/3

[tex]\frac{2}{3} ^5 = \frac{32}{243} = 0.13168[/tex]

anyone know the answer i really need help?

Answers

Answer:

8

Step-by-step explanation:

HOPE THIS HELPS! PLS GIVE ME BRAINILIEST PLSSSSSSSSSSSSSSSSSSS!

5 objects of any size that are in
the shape of a rectangular prism.
You can find these items anywhere
around your house. You could use a
tissue box, shoe box, cereal box,
any snack food box, etc.
Ruler that has inches.

help

Answers

To make a triangular prism we need cardboard, glue and scissors.

What is a triangular prism?

A triangular prism is a geometric shape characterized by:

It has three sides.It is a polyhedron.It has a triangular base and three faces that join it with another base.Its sides are rectangular.

How to make a triangular prism out of cardboard?To make a triangular prism out of cardboard we must draw two equilateral triangles on the cardboard.Then we must draw three rectangles that have the same height as the length of the sides of the triangle.Subsequently, we must cut out all the shapes we draw, a total of five figures.Then we must paste the three rectangles on each side of the triangles.Once we glue the three rectangles to one of the triangles, we assemble the prism by joining the other side of the rectangles to the other triangle.

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Please help!!!!!

Two chords intersect within a circle to form an angle whose measure is 53 degrees. If the intercepted arcs are represented by 3x + 3 and 10x -14, find the measure of the LARGER of these two arcs.

A. 106
B. 76
C. 9
D. 30

Answers

Answer:

76degrees

Step-by-step explanation:

Using the theorem which states that the vertex of the angle inside a circle is half the sum of the measured intercepted arcs. Hence;

Angle at the vertex = 53 degrees

Half the sum of intercepted arcs = 1/2(3x+3+10x-14)

Half the sum of intercepted arcs = 1/2(13x-11)

Equating to  the vertex to find x

1/2(13x-11) = 53

13x - 11 = 2 * 53

13x - 11 = 106

13x = 106 + 11

13x = 117

x = 117/13

x = 9

For the arc 3x + 3

= 3(9) + 3

= 27 + 3

= 30degrees

For the arc 10x - 14

= 10(9) - 14

= 90 - 14

= 76degrees

Hence the measure of the larger of the two arcs is 76degrees

Please help me, I feel so idiotic right now

Answers

Answer:

a)  $8.80

b)  40%

Step-by-step explanation:

Part (a)

Given:

Original price = $22Discounted price = $13.20

Original price - discounted price

= $22 - $13.20

= $8.80

Part (b)

percentage = (amount discounted ÷ original price) x 100

                    = (8.80 ÷ 22) x 100

                    = 40%

Find the value of x to the nearest tenth.​

Answers

Answer:

x ≈ 16.2

Step-by-step explanation:

tan56° = [tex]\frac{24}{x}[/tex] ( multiply both sides by x )

x × tan56° = 24 ( divide both sides by tan56° )

x = [tex]\frac{24}{tan56}[/tex] ≈ 16.2 ( to the nearest tenth )

A rectangular painting has a length of 24 inches and a width of 7 inches. What is the length of the diagonal of the painting in inches? Enter your answer in the box.

Answers

Pythagorean theorem
a^2 + b^2 = c^2
(24)^2 + (7)^2 = c^2
625inches
sqrt 625 =25

25 inches.

Answer: 25 inches

Step-by-step explanation:

24² + 7² = 625

Square root of 625 = 25

-
Solve the system of equations – 2z – 2y = -24 and 3z – 2y = -33 by
combining the equations.
-
( 2z -2y =-24)
– 32 -2y =-33)
-
-
-22 -2y = -24
-32 -2y -33
0 - 0 Y=
You must answer all questions above in order to submit.
P

Answers

Answer:

z = -1.8, y = 10.2

Step-by-step explanation:

- 2z -2y = -24 (EQ 1)

3z - 2y = -33 (EQ 2)

Change one of the equations to it's opposite (Turning a negative number to a positive/or the other way around)

Let's target the equation that can leave us with the simplest question to solve

-2z + -2y = -24

-3z + 2y = 33

-5z = 9

(Dividing and switching the negative sign over)

z = -1.8

Plug in Z to solve for y.

-2(-1.8) - 2y = -24

3.6 - 2y = -24

-2y = -20.4

y = 10.4

Find the solution of the system of equations.

x-y=-3
-8x+y=45

Answers

Answer:

x = 17, y = 28

Step-by-step explanation:

1. Isolate for x in "x - y = -3, -8":

x - y+y = -3, -8+y

x = -11 + y

2. Substitute "x = -11 + y" in for x in the second expression:

-11 + y + y = 45

3. Simplify:

-11 + 2y = 45

4. Isolate y:

-11+11 +2y = 45+11

2y = 56

[tex]\frac{2y}{2} = \frac{56}{2}[/tex]

y = 28

5. Substitute the new y-value into the first equation:

x = -11 + 28

x = 17

hope this helps!

Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.

Answers

Answer:

∆The lateral surface area of cylinder =417.62 mm²

Step-by-step explanation:

Diameter = 7

Radius = 7/2

Lateral Surface Area of cylinder = 2πrh

=> 2× π × 7/2 × 19

=> 38 × 7/2 × π

=> 133 × π { taking π as 3.14}

=> 133× 3.14

=> 417.62 mm²

What is the lateral area of the cone

Answers

[tex]\bold{ANSWER:}[/tex]

45.74 ft^2

[tex]\bold{EXPLANATIONS:}[/tex]

write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
28:7

Answers

The answer is 4/1 you just have to divide 7 from both numbers and then you will get 4/1

Answer:

[tex] \frac{4}{1} [/tex]

Step-by-step explanation:

[tex]writing \: as \: a \: fraction \: the \\ numerator = 28 \\ denominator = 7 \\ as \: a \: fraction \: it \: is \: \: \frac{28}{7} \\ dividing \: numerator \: and \: denominator \: by \: four \\ = \frac{4}{1} \\ hope \: this \: helps \\ please \: rate \: and \: mark \: brainliest[/tex]


What is the area of the unshaded part of the
rectangle to the right?
A. 19,000 ft²
B. 45,000 ft²
C. 28,000 ft²
D. 26,000 ft²

Answers

the answer is 82 million

please help me find the answe asap

Answers

Answer:

B

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

this year's mean = [tex]\frac{7+3.3+2}{3}[/tex] = [tex]\frac{12.3}{3}[/tex] = 4.1

last year's mean = [tex]\frac{5.3+1.6+2.4}{3}[/tex] = [tex]\frac{9.3}{3}[/tex] = 3.1

difference = 4.1 - 3.1 = 1

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