Find the Greatest Common Factor of Two or More Expressions
In the following exercises, find the greatest common factor.
3. 72,162

Answer:

[tex]\begin{cases}x=-6\\y=-10\end[/tex]

Step-by-step explanation:

[tex]\begin{cases}-x+3y=-24 \left(1)\right\\-4x+2y=4 \left(2)\right\end[/tex]

Make x the subject in (1)

[tex]x=3y+24 \left(3)\right[/tex]

Sub into (2)

[tex]-4(3y+24)+2y=4\\\\\implies-12y-96+2y=4\\\\\implies10y=-100\\\\y=-10[/tex]

Sub into (3)

[tex]x=-30+24\\\\x=-6[/tex]

Hence

[tex]\begin{cases}x=-6\\y=-10\end[/tex]

Answer:

[tex]\left \{ {{x=-6} \atop {y=-10}} \right. .[/tex]

Step-by-step explanation:

[tex]\left \{ {{-x+3y=-24\ \ (1)} \atop {-4x+2y=4\ \ \ (2)}} \right. \ \ \ \ \\[/tex]

We multiply equation (1) by -4:

-x+3y=-24 |*(-4)

-x*(-4)+3y*(-4)=-24*-(-4)

4x-12y=96.  (3)        ⇒

[tex]\left \{ {{4x-12y=96\ \ (3)} \atop {-4x+2y=4\ \ \ (2)}} \right.[/tex]

We summarize equations (2) and (3):

[tex]-10y=100\ |:(-10)\\y=-10.\\Make\ y \ the\ subject\ in\ (1):\\-x+3*(-10)=-24\\-x-30=-24\\-x=-24+30\\-x=6\ |*(-1)\\x=-6.[/tex]

f(x)=y=√x looks something like this:

(4,2)

(9,3)

(16,4)

Whilst your graph is much higher slope, for lack of better term

Rules of transformation

f(x)+b - function is shifted b units upward (up y-axis)

f(x)-b - function is shifted b units downward (down y-axis)

f(x+b) - function is shifted b units to the left (negative x-axis)

f(x-b) - function is shifted b units to the right (positive x-axis)

-f(x) - function is reflected over x-axis

f(-x) - function is reflected over y-axis

bf(x) - vertical stretch for |b| > 1, vertical shrink for 0< |b| <1

f(bx) - horizontal shrink for |b| > 1, horizontal stretch for 0< |b| <1
**INVALIDATE my answer, as statements were given 10 mins after posted**

Answer:

The graph is translated to the left by 3

Step-by-step explanation:

the equation would be y= sqrt(x)+3

The dust particle is seen to have 400 times more mass than the pollen particle

We will use the scientific notation.

For example, 0, 002 can be written as:

2 × 10³

Where;

3 is the number of times the comma (,) must be run to the right to convert the quantity 0, 002 to 2.

0, 002

0| 0 0 2

0 0| 02 -----------1

0 0 0|2------------2

0 0 0 2| ----------3

Thus, for the given expression:

Powder particle 0.000000778 g

It can be written as: 0.0000008 g = 8 × 10⁻⁷

b = -7

In the same way

Pollen grain of 0.00000000155 g

It can be written as:

0.000000002 g = 2 × 10⁻⁹

To know how big the mass of the dust particle is with respect to the pollen, we have;

(8 × 10⁻⁷)/(2 × 10⁻⁹) = 400

Complete question is;

The table below shows the approximate masses of a dust particle and a grain of pollen.

Dust Particle 0.000000778 g

Grain of Pollen 0.00000000155 g

The mass of a dust particle can be estimated and written in the form a × 10^b, where a = 8 and b =

The mass of a grain of pollen can be estimated and written in the form a × 10^b, where a = 2 and b =

Based on the estimates, the mass of a dust particle is approximately BLANK

times larger than the mass of a grain of pollen.

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Answer:

vertex = (2, - 32 )

Step-by-step explanation:

given a quadratic function in standard form

y = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

given

y = 2(x + 2)(x - 6) ← expand factors using FOIL

   = 2(x² - 4x - 12 ) ← distribute parenthesis

y   = 2x² - 8x - 24 ← in standard form

with a = 2, b = - 8 , then

x = - [tex]\frac{-8}{4}[/tex] = 2

substitute x = 2 into the function for corresponding y- coordinate

y = 2(2 + 2)(2 - 6) = 2(4)(- 4) = 8 × - 4 = - 32

vertex = (2, - 32 )

Answer:

D. 8

Step-by-step explanation:

32^(3/5) is the same as [tex]\sqrt[5]{32}[/tex]^3.

 [tex]\sqrt[5]{32}[/tex] = 2 because 2^5=32

2^3 = 8

Simplify the expression.

Rewrite 32 as 2⁵.

[tex]\bf{\left(2^{5}\right)^{\frac{3}{5} } }[/tex]

Apply the power rule and multiply exponents, (αᵐ)ⁿ=αᵐⁿ.

[tex]\bf{2^{5}^{(\frac{3}{5} )} }[/tex]

Cancel the common factor of 5.

Cancel the common factor.

[tex]\bf{2^{\not{5}}^{(\frac{3}{5} )} }[/tex]

Substitute the expression.

[tex]\bf{2^{3} \ \ \to \ Calculate \ power. }[/tex]

Raise 2 to the power of 3.

We conclude that the correct option is "D".

Answer:

This really needs more information to answer correctly.  What is bria's movement relative to the bus stop?  Is she moving towards it, away, or to the side?

Step-by-step explanation:

Lacking this information, I can only say that as Bria's distance increases as she moves away from the bus stop (an assumption of direction).  Let's say the bus stop is x yards distant in the other direction.   Bria's distance from the bus stop varies from x+80 yards to x+190 yards.  The signs would change if she were moving towards the bus stop.  And they'd be something entirely different if a different angle were involved.

Answer:

Step-by-step explanation:

Perimeter is the sum of lengths of triangles. Hence it's unit in

c

m

. Area has unit

c

m

2

i.e., length squared. So if measurements are in the ratio

3

:

4

, areas are in the ratio

3

2

:

4

2

or

9

:

16

. This is because the two triangles are similar.

A total area is

75

square centimeters, we need to divide it by the ratio

9

:

16

Of which first will be the area of the smaller triangle.

Hence the area of the smaller triangle is

75

×

9

9

+

16

=

75

×

9

25

=

75

3

×

9

25

1

=

27

square centimeters

The area of larger triangle would be

75

×

16

9

+

16

=

3

×

16

=

48

square centimeters

The area of the space under the slide is 2.10 square meters

The diagram in the question is added as an attachment

The vertical distance is represented by h.

So, we have:

sin(70) = h/2

Solve for h

h = 2 * sin(70)

Evaluate

h = 1.88 m

Hence, the vertical distance is 1.88 m

This is calculated using

sin(40) = h/Slide

This gives

sin(40) = 1.88/Slide

Solve for Slide

Slide = 1.88/sin(40)

Evaluate

Slide = 2.92

Hence, the length of the slide is 2.92 m

This is calculated using:

A = 0.5 * h * slide * sin(∅)

Where

∅ = 90 - 40 = 50

So, we have:

A = 0.5 * 1.88 * 2.92 * sin(50)

Evaluate

A = 2.10

Hence, the area of the space under the slide is 2.10 square meters

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Answer:

42 times

Step-by-step explanation:

Here,

4 hits = 7 times

1 hits= 7/4 times

24 hits = 7/4 × 24

= 42 times.

The number of times that the baseball player makes the hit if he hit 24 hits is 42 times, which is an option (a).

Given that:

A baseball player makes 4 hits every 7 times at bat.

It is required to find the number of times that the player hits if he hit 24 hits.

Number of times that 4 hits are made = 7

Number of times that 1 hit is made = 7/4

So, the number of times that 24 hits are made can be found by the following formula.

Using the proportional concept, the number of times, N, is:

[tex]N=\frac{7}{4} \times 24[/tex]

   [tex]=7\times6[/tex]

   [tex]=42[/tex]

Hence, the correct option is (a).

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In general, the greater the between-group variance compared to the within-group variance, the more likely you are to find statistical significance.

Unlike the inside group version, where the focus is on the differences among a population and its implication, the between-organization variant is concerned with finding how the method of corporations differ from each other.

Inside-organization version (on occasion referred to as mistakes organization or error variance) is a time period used in ANOVA tests. It refers to variations because of variations within individual businesses (or ranges). In other words, no longer all of the values within every group (e.g. method) are equal.

With the purpose to examine multiple groups right away, we can study the ANOVA, or analysis of Variance. not like the t-test, it compares the variance within every sample relative to the variance between the samples.

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Answer:

5√3

Step-by-step explanation:

An equilateral triangle is a triangle that has all same 3 measurements of 60°, and since all measurements are same, all sides are also equal too.

Hence, there'll be 3 sides that are 10 units. Since the base is divided into half, each will be 5 for base.

Then apply Pythagoras Theorem where states that:

[tex]\displaystyle{c=\sqrt{a^2+b^2}}[/tex]  or [tex]\displaystyle{c^2=a^2+b^2}[/tex]

where c is hypotenuse, a and b can be defined either adjacent or opposite.

We know that our adjacent is 5 units, opposite is h unit(s) and hypotenuse is 10 units. Apply the theorem:

[tex]\displaystyle{10^2=h^2+5^2}[/tex]

Solve the equation for h-term:

[tex]\displaystyle{100=h^2+25}\\\\\displaystyle{100-25=h^2}\\\\\displaystyle{75=h^2}\\\\\displaystyle{h=5\sqrt{3} }[/tex]

Therefore, the height or value of h is 5√3

The picture is attached for visual reference regarding sides of triangle. If you have any questions, please let me know in the comment!

Answer:

Step-by-step explanation:

The Matching for each transformation is

1. (x,y) → (3x, y)

horizontal stretch by factor 3.

2. (x,y) → (x + 3, y)

translation 3 unit right

3. (x,y) → (x, 3y)

Vertical stretch by factor 3.

4. (x,y) → (x, y + 3)

translation 3 unit up.

5. (x,y) → (3x, 3y)

dilation with Scale factor 3.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

1. (x,y) → (3x, y)

It is horizontal stretch by factor 3.

2. (x,y) → (x + 3, y)

It is translation 3 unit right because the rule for translation for 3 unit right is x - > x + a

3. (x,y) → (x, 3y)

It is Vertical stretch by factor 3.

4. (x,y) → (x, y + 3)

It is translation 3 unit up.

5. (x,y) → (3x, 3y)

It is dilation with Scale factor 3.

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Answer:

o

Step-by-step explanation:

Order of operations. Left-to-Right prevails

P = parenthesis first
E = exponentiation
MD multiplication/division leftmost has higher priority
AS addition/subtraction leftmost first

1st computation: (2 + 2) because of P ==> 3

2nd Computation: 3² = 9

3rd computation (1+2)² = 3² = 9
Answer 9 - 9 = 0

Answer:

a) Call-more is cheaper

b) 60 minutes

Step-by-step explanation:

Call-More: C = 0.40t + 25

Talk-Now:  C = 0.15t + 40

a) Substitute t =  50 minutes in the above equations.

Call-More:

         C = 0.40*50 + 25

            = 20 + 25

        C = 45

 Talk-Now:

          C = 0.15*50 + 40

              = 7.5 + 40

          C  = 47.40

Company Call-more is cheaper than Talk-now.

b) We have to find the conditions under what condition the two companies charge the same.

    Charge of company Call-more = charge of company Talk-now.

                  0.40t + 25 = 0.15t + 40

                            0.40t = 0.15t + 40 -25

                            0.40t = 0.15t + 15

                 0.40t - 0.15t = 15

                             0.25t = 15

                                     [tex]\sf t = \dfrac{15}{0.25}\\\\ t = \dfrac{15*100}{25}\\\\[/tex]

                                     t = 15*4

                                     t = 60 minutes

Two companies charge the same for 60 minutes.

The area of LMNP is 6. 25 π^2

Area of a rectangle = length × width

Circumference = 2 (length + width)

If circumference = 10 π

Let's  find the length and width

10π = 2( L+ W)

10 π = 2(L + W)

10π = 2(L+ W)

L + W = 10π ÷ 2

L + W = 5π

Length = 2. 5π

Width = 2. 5π

Area = 2. 5π× 2. 5π

Area = 6. 25 π^2

Thus, the area of LMNP is 6. 25 π^2

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Answer:

The answer is 6.2

Step-by-step explanation:

The factors of 16 are 1,2,4,8, and 16.

get the sum of the factors which is 31, then divide it to number of the addends which is 5.

31/5 = 6.2

Answer:

B

Step-by-step explanation:

since the slope is 5, 1/5x or -1/5x cannot be the slope. since the slope isn't negative it also cancels out -5x. 5x can be your only slope and that is in answer B.

The next step in the series is option C.

First we are presented by different shapes.

The first shape is a square. This shape has 4 sides.

The next shape is a pentagon, it has 5 sides.

The shape after the pentagon is a hexagon. It has 6 sides.

From here we can see that the shapes follow the pattern , 4, 5, 6 ..., the next shape should be 6 + 1 sides = 7 sides.

Hence the answer is option C.

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

Explanation:

Apply the difference of squares rule

x² - 4y² = 13

x² - (2y)² = 13

(x - 2y)(x + 2y) = 13

Since x and y are positive integers, this means x-2y and x+2y are both integers as well.

The value 13 is prime. Its only factors are 1 and 13

Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:

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

Let's consider case A

We have this system of equations

[tex]\begin{cases}x-2y = 1\\x+2y = 13\end{cases}[/tex]

Add the equations straight down

Therefore we have 2x = 14 solve to x = 7

From here, plug this into either equation to solve for y

x-2y = 1

7 - 2y = 1

-2y = 1-7

-2y = -6

y = -6/(-2)

y = 3

You should get the same result if you used x+2y = 13

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

Since we've found that x = 7 and y = 3, notice how case B is not possible

Example:  x-2y = 13 becomes 7-2(3) = 13 which is false.

Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.

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

Let's check those x and y values in the original equation

x² - 4y² = 13

7² - 4*(3)² = 13

49 - 4(9) = 13

49 - 36 = 13

13 = 13

The answer is confirmed.

Answer:

ok so first they drove 55 for 3 hours so

55*3=165

and then they drove 45 for 2 hours

45*2=90

165+90=255

so in total they drove 255 miles

Step-by-step explanation:

Answer:

255 miles

Step-by-step explanation:

[tex]\boxed{\sf Distance= Speed \times Time}[/tex]

Journey before lunch:

[tex]\implies \sf Distance = 55 \times 3=165\: miles[/tex]

Journey after lunch:

[tex]\implies \sf Distance = 45 \times 2=90\: miles[/tex]

Total miles driven

= distance traveled before lunch + distance traveled after lunch

= 165 miles + 90 miles

= 255 miles

Therefore, the Ramos family drove 255 miles in total.

Answer:

PART A

length of foot = y

length of forearm = x = 17

Equation: y = 0.860x + 3.302

Plug in 17 for x in the equation, and simplify. Remember to follow PEMDAS, first multiply, then combine like terms:

y = (0.860)(17) + 3.302

y = 14.62 + 3.302

y = 17.922

length of foot = y = 17.922 inches long

Applying the inscribed angle theorem, m∠CED = 34°.

According to the inscribed angle theorem, measure of inscribed angle DCE = 1/2(measure of intercepted arc ED).

m(ED) = 180 - 112 [semicircle]

m(ED) = 68°

m∠CED = 1/2(68°) [inscribed angle theorem]

m∠CED = 34°

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Answer:

  D.  all three figures

Step-by-step explanation:

A cube is a rectangular prism that has every edge equal in length to every other edge. This ratio of edge lengths holds for all cubes. Every cube is similar to every other cube.

Cubes with edge lengths of 5 ft, 7 ft, and 10 ft will all be similar. Any pair of corresponding edges of different cubes will have the same ratio.

The rocket will take 2 seconds for the rocket to hit the ground.

We have,

To find the time it takes for the rocket to hit the ground, we need to determine when the height, h, becomes zero (since the ground is at height zero).

Given the equation for the height of the rocket at time t:

h = -4.9t² + 9.1t + 1.4, we can set h to zero and solve for t:

0 = -4.9t² + 9.1t + 1.4

This is a quadratic equation in the form of at² + bt + c = 0,

where a = -4.9, b = 9.1, and c = 1.4.

To solve for t, we can use the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

Substituting the values:

t = (-(9.1) ± √((9.1)² - 4(-4.9)(1.4))) / 2(-4.9)

t = (-9.1 ± √(82.81 + 27.44)) / (-9.8)

t = (-9.1 ± √110.25) / (-9.8)

Now, we have two possible solutions for t:

t₁ = (-9.1 + √110.25) / (-9.8)

t₂ = (-9.1 - √110.25) / (-9.8)

Calculating these values:

t₁ ≈ -0.143

t₂ ≈ 2

Since time cannot be negative, the only meaningful solution is t₂ ≈ 2 seconds.

Thus,

The rocket will take 2 seconds for the rocket to hit the ground.

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Answer:

x = 1

Step-by-step explanation:

A line with undefined slope is a vertical line with equation

x = c

where c is the value of the x- coordinates the line passes through

the line passes through (1, 5 ) with x- coordinate 1 , then

x = 1 ← equation of line

Answer: The first answer choice

Step-by-step explanation:

In the first answer choice, the distance increases for two units, then decreases for three units. The distance then increased for 4 units, stayed level for 3 units, and then decrease slowly for 6 units. The graph exactly follows this trend.

The second answer is immediately wrong because it relates the distance between the car and the concert venue. It never mentioned that the car moved, and the venue obviously can't move.

The third answer says that after the first increase/decrease, Tyler went to go text his friends. However, the graph does not show a flat area after the first increase/decrease.

The fourth answer, like the second answer is immediately wrong because homes and schools can't move.

This is my first response, so I hope it was helpful. :D

Using proportions, it is found that the scale of the drawing is:

1 inch = 12 yards.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The scale is that 144 yards are represented by 12 inches, hence:

144/12 = 12

Then, 1 inch = 12 yards.

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Answer:

  213°

Step-by-step explanation:

Consider the angle measured at the lighthouse between North and the Boat. The lengths given in the problem statement are the lengths of the side opposite that angle, and the length of the hypotenuse of the right triangle shown. The trig function that relates the angle and those sides is ...

  Sin = Opposite/Hypotenuse

The sine of the angle at the lighthouse is ...

  sin(bearing to boat) = (13.5 km)/(24.6 km) = 45/82

The value of the angle is found using the inverse sine function, called the arcsine function:

  bearing to boat = arcsin(45/82) ≈ 33°

The bearing from the boat to the lighthouse is in the opposite direction. It can be found by adding 180° to this angle:

  bearing to lighthouse = 33° +180° = 213°

__

Additional comment

The attached image shows a calculator making this calculation. Note that the angle mode is set to DEG (lower left corner). The arcsine function is usually found as the 2nd function of the Sin key.

The formula for Classical Probability.

The probability of a simple event happening is the number of times the event can happen, divided by the number of possible events. The “math” way of writing the formula is P(A) = f / N.

Without replacing drawn marbles:

Probability of drawing 3 green:

3/10*2/9*1/8=1/120

Probability of drawing 3 black:

4/10*3/9*2/8=1/30

Probability of drawing 3 green:

3/10*2/9*1/8=1/120

Adding these three: 6/120 =5%

If replacing marbles after each draw

Probability of drawing 3 black:

(3/10)^3=9/1000

Probability of drawing 3 green:

(4/10)^3=16/10000

Probability of drawing 3 black:

(3/10)^3=9/1000

Adding these three: 34/1000= 3.4%.

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