Use the function, to match each key feature listed below.

The equation of the line which passes through (4, 1) in slope - intercept form is y = 1/2x - 1

The equation of a line takes the form:

y = Slope (x) + y - intercept

The slope is already given as 1 / 2 and we have a point on the line. This point can be substituted into the equation of a line to find the value of the y - intercept.

y = Slope (x) + y - intercept

1 = 1/2 (4) + y - intercept

y - intercept = 1 - 2

y - intercept  = - 1

The equation of the line will then be:

y = 1/2x - 1

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The transformation is applied to ΔABC to get the ΔA'B'C' is vertical translation of 6 units downwards.

The triangle has the vertices  A(-2, 3), B(2, 1), and C(1, 0)

They are transformed such that:

A(-2, 3)→A'(-2,-3)

B(2, 1)→B'(2,-5)

A(-1, 0)→A'(-2,-6)

Now, if we pay close attention, we can notice that A's y-coordinate is 6 less than A's.

Similar to A, B and C have coordinates that are 6 units lower than the object's coordinates but with the same x-coordinate.

This demonstrates that the graph undergoes a vertical translation; the graph is translated 6 units lower since the new ordinates are 6 units smaller.

A transformation, or f: X→X', is a function that maps to itself. The transformation will result in the pre-image X becoming the image X'. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, may be used in this transformation.

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The most appropriate design for the study would be the experiment. We must apply the new repellent to a group of 5 dogs and the popular repellent to another group of 5 dogs. This will allow us to establish if the new repellent is more effective.

The most appropriate research design for this case is the experiment because it will allow us to check if our hypothesis is true.

The research design of experiment should be implemented as follows. First of all we must apply the new repellent to a group of 5 dogs and in parallel, we must apply the popular repellent to another 5 dogs. After a while we must examine them to check the effects of the repellent.

In this way we will know if the new repellent is more effective than the popular repellent. Additionally, we can establish how effective it is taking into account that we used a population of 5 dogs.

This design would benefit my research because it allows me to establish whether my hypothesis is true. Additionally, it allows me to establish how much more effective one repellent is than the other.

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If a waste bin is in the shape of a cylinder. the diameter of the base is 20cm and the height is 25cm. The volume of the waste bin is: 7,853.98 cm³.

Using this formula to find the volume

Volume (v) = π (d/2)² h

Where:

d= diameter =  20 cm

h = height =25 cm

Let plug in the formula

Volume (v) = π × (20/2)² × 25

Volume (v) = π × 100 × 25

Volume (v) = 7,853.98 cm³

Therefore 7,853.98 cm³ is the volume.

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Answer:

42 rotten tomatoes would likely be found in 14 boxes.

Step-by-step explanation:

Since [tex]\frac{12}{4} = \frac{3}{1}[/tex] , there are 3 rotten tomatoes in every box.

[tex]\frac{3 * 14}{1 * 14} = \frac{42}{14}[/tex]

3 * 14 = 42, so 14 boxes contain 42 rotten tomatoes.

Answer: 9.1

Step-by-step explanation:

1. Pythagorean Theorem

a^2+b^2=c^2

(9)^2+(1)^2=c^2

2. Solve

81+1=c^2

82=c^2

3. Solve for c

[tex]\sqrt{82}[/tex]=[tex]\sqrt{c}[/tex]

c=9.05

4. Round

c=9.1

El promedio de los números enteros 3, 8, 9 y 12 es igual a 8. (Opción correcta: Cierto)

En este problema tenemos un conjunto de cuatro números enteros positivos, del cual debemos comprobar si el promedio uniforme es igual a 8. El promedio uniforme es definido por la siguiente operación:

[tex]\bar {x} = \frac {1}{n} \cdot \sum \limits_{i = 1}^{n} x_{i}[/tex]

Donde:

Si sabemos que n = 4, x₁ = 3, x₂ = 8, x₃ = 9 y x₄ = 12, entonces el promedio uniforme del conjunto de datos es:

[tex]\bar {x}[/tex] = (3 + 8 + 9 + 12) / 4

[tex]\bar x[/tex] = 8

El promedio del conjunto de datos, correspondiente a los números enteros positivos 3, 8, 9 y 12, es igual a 8.

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Answer: they both go up in cents by 5s.  they may not be only five but five's.  Therefore, they are adding by 5s and that is the linear relationship

Step-by-step explanation:

4 minutes is equivalent to 240 seconds.

There is 60 seconds in a minute.

60x4 = 240.

Answer:

240 Seconds.

Step-by-step explanation:

1 Minute is 60 Seconds, SO 4 x 60 = 240!

Step-by-step explanation:

Formula for distance travelled:

x= ut + 1/2at^2

x is 1.4km, convert this to m since acceleration is in m, = 1400m

u is initial velocity, in this case assume 0

a is acceleration, = 4m/s^2

t is unkown and what we want to find out

Substitute value into formula,

1400 = 0t + 1/2(4)t^2

1400 = 2t^2

t^2 = 1400/2

t^2 = 700

t = 26.458s

Formula for acceleration:

a = (v-u)/t

at= v-u

Substitute value,

4(26.458) = v - 0

v = 105.832 m/s

Answer:

1008cm^2

Step-by-step explanation:

Please see photo

Answer:

D: (neg infinity, pos infinity)

R: [-2, pos infinity)

Step-by-step explanation:

The resulting equation of isolation and substitution is  9y⁴-466 y² + 5481 = 0

Given:

{x² + y² = 25

{x²/16 - y²/9 = 1

Zach isolated  x² in the first equation, we have:

x² + y² = 25

x² = 25- y²

Zach then substituted the x² into the second equation:

x²/16 - y²/9 = 1                           (put x² = 25- y²)

(25- y²)²/16 - y²/9 = 1                (Expand the bracket)

(625- 50y²+y⁴)/16 - y²/9 = 1      The LCM of 9 and 16 is 144

( 9(625- 50y²+y⁴) - 16 y² ) /144 = 1         Cross multiply

9(625- 50y²+y⁴) - 16 y² = 144

5625 - 450y² + 9y⁴-16 y² = 144

9y⁴-466 y² + 5625 = 144

9y⁴-466 y² + 5625-144 = 0

9y⁴-466 y² + 5481 = 0  

Therefore, the resulting equation is  9y⁴-466 y² + 5481 = 0

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Answer:

c) 9/14

Step-by-step explanation:

Given problem,

→ (1/7) + (1/2)

Let's solve the problem,

→ (1/7) + (1/2)

→ (2/14) + (7/14)

→ (2 + 7)/14

→ 9/14

Hence, answer is 9/14.

A student ran 6% of the journey.

In this question, we have been given the distance between two village is 8km a student walk from one village to the other he walk most of the way buy runs the last 480metres.

We know that 1 km = 1000 meters

So, 8 km = 8000 meters

So, the percent of the journey he ran,

480/8000 * 100

= 6%

Therefore, A student ran 6% of the journey.

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They achieved 26.9 miles per gallon approximately with that car in this trip.

Given that the initial odometer reading is = 87236.2 miles

Final odometer reading after trip is = 87626.2 miles

So the distance of the total trip is = 87626.2-87236.2 = 390 miles

They used 14.5 gallons of gas on the tri[p.

So the mileage is = 390/14.5 = 26.9 miles per gallon approximately.

Their car achieved 26.9 miles per gallon approximately.

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what the question............

Answer:

f(x) = -3x+1

Step-by-step explanation:

every straight graph has an equation f(x) = m * x + b

when the graph goes up when you look at it from left to right, m is a positive number. when it goes down, then m is negative.
the value of m you can read when you go 1 to the right and then count how many you need to go up/down to meet the graph. in this picture, you need to go down 3.
So m = -3
b is how many you habe to go up (+) or down (-) from the center point 0
so in this case you see on the picture that the graph is hitting the y line on 1

so your equation is -3x + 1

Answer: 11.74

Step-by-step explanation:

4.33+4.33+1.54*1.54+11.74

A rectangle has two pairs of equal sides.

The ratio of the volume of the cylinder to the volume of the sphere = 3:1

Let take the volume of a closed cylinder as V1.

And take the volume of a closed sphere as V2.

And the radius of the cylinder = radius of the sphere = r

Height of the cylinder = h

If height of the cylinder is four times the radius of the cylinder  which means h = 4r

Volume of the closed cylinder V1 = π × r^2 × h

if h = 4r

Then V1 = π × r × r × 4r

V1= 4π × r^3

Volume of the closed cylinder V1= 4π × r^3

Volume oh the sphere V2 = 4/3 × π × r^3

The ratio of the volume of the cylinder to the volume of the sphere

= V1 / V2 = V1 : V2

V1 : V2 = (4π × r^3) ÷ (4/3 × π × r^3)

V1 : V2 = 4 ÷ 4/3 = 4/1 × 3/4 = 3/1 = 3 : 1

The ratio of the volume of the cylinder to the volume of the sphere = 3:1

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The new price for the car when there's an increase of 6% is $35616.

Given that the dealership increased the price of a certain car by 6% and the original price was $33,600.

The new price will be:

= Original price + Increase in price

= $33600 + (6% × $33600)

= $33600 + $2016

= $35616

The new price is $35616.

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Answer:

[tex]P(x)=x^3-3x^2+16x-48[/tex]

Step-by-step explanation:

Given information:

For any complex number  [tex]z=a+bi[/tex], the complex conjugate of the number is defined as  [tex]z^*=a-bi[/tex].  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if P(x) is a polynomial with real coefficients, and 4i is a root of f(x)=0, then its complex conjugate -4i is also a root of P(x)=0.

Therefore, the polynomial in factored form is:

[tex]P(x)=1(x-3)(x-4i)(x-(-4i))[/tex]

[tex]P(x)=(x-3)(x-4i)(x+4i)[/tex]

Expand the polynomial:

[tex]P(x)=(x-3)(x^2+4ix-4ix-16i^2)[/tex]

[tex]P(x)=(x-3)(x^2-16(-1))[/tex]

[tex]P(x)=(x-3)(x^2+16)[/tex]

[tex]P(x)=x^3+16x-3x^2-48[/tex]

[tex]P(x)=x^3-3x^2+16x-48[/tex]

Answer:

The y-intercept would be zero, if the original equaion equaled zero.

Step-by-step explanation:

y + [tex]\frac{3}{7}[/tex]x = 0  ?  Subtract [tex]\frac{3}{7}[/tex]x from both sides

y = [tex]\frac{-3}{7}[/tex] x + 0

The value of the variable in the given ordered pairs: (1,y) and (x,3) are x = -1 and y = -7.

An equation is an expression that shows the relationship between two or more numbers and variables.

We have to find the values of the variable in the given ordered pairs: (1,y) and (x,3).

Equation is 6x + 1.2y = −2.4

For ordered pairs: (1,y)

6(1)+1.2y =-2.4

1.2y=-8.4

y=-7

For Pair (x,3)

6(x)+1.2(3) =-2.4

6x = -6

x=-1

Hence, the value of the variable in the given ordered pairs: (1,y) and (x,3) are x = -1 and y = -7.

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Answer:

x = 6

Step-by-step explanation:

x + 2(4x-6) = 42

x + 8x - 12 = 42

9x = 42 + 12

9x = 54

9/9 x = 54/9

x = 6

Answer:

hope this helps!!!

It depends on how accurate you want to be, but two straight lines between 0° and 30° and 30° and 90° will not be too bad for Sine.

Thus for angles less than 30°

sinx≈x/60

and for angles greater than 30°

sinx≈(30+x)/120

For Cosine you use the identity

cosx=sin(90−x)

And for Tangent you use the identity

tanx=sinxcosx

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Answer:

Step-by-step explanation:

given:

line f:  y+3 = [tex]\frac{1}{6}[/tex](x-2)

line g:   P1=(x1,y1) = ( -6,1)    and parallel to  f  ( same slope)

use point-slope, again  

y-y2 = m(x-x1)

y-1=[tex]\frac{1}{6}[/tex](x-(-6))

y-1 =[tex]\frac{1}{6}[/tex](x+6)

y-1 = [tex]\frac{1}{6}[/tex]x +1

y = [tex]\frac{1}{6}[/tex]x + 1 +1

y = [tex]\frac{1}{6}[/tex]x + 2   ( in slope intercept form  y= mx+b)

This is not a prime factorization.

The correct prime factorization is [tex]2^5*3*5^4*11^2[/tex]

=======================================================

Further Explanation:

The expression your teacher gave you is not a prime factorization because the 8 isn't prime.

8 = 2*2*2 = [tex]2^3[/tex]

If we replace 8 with [tex]2^3[/tex], then we go from

[tex]2^2*3*5^4*8*11^2[/tex]

to

[tex]2^2*3*5^4*2^3*11^2[/tex]

and that rearranges to

[tex]2^2*2^3*3*5^4*11^2[/tex]

Then we can simplify the [tex]2^2*2^3[/tex] portion to get [tex]2^5[/tex] since we add the exponents while keeping the base '2' the same.

We therefore end up with

[tex]2^5*3*5^4*11^2[/tex]

as the correct prime factorization. Each base (2,3,5,11) is a prime number.

---------------

As a check, use your calculator to type in

2^2*3*5^4*8*11^2

and also

2^5*3*5^4*11^2

and you should get the result of 7,260,000 each time. Since we get the same result, this confirms 2^2*3*5^4*8*11^2 = 2^5*3*5^4*11^2