Graph the image of this figure after a dilation with a scale factor of 1/2 centered at the point (-3,0)

Answer: choice A. 40 liters

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

Explanation:

x = number of liters of the 50% alcohol solution

If we have x liters of 50% alcohol, then we have 0.50*x liters of pure alcohol. This is added to 0.90*40 = 36 liters of pure alcohol (from the 90% solution).

So far we have 0.50*x + 36. This expression represents the total amount of pure alcohol. We want a 70% solution, so we want 70% of the total 40+x meaning 0.50*x + 36 is to be set equal to 0.70*(40+x) and we solve for x as shown below

0.50*x + 36 = 0.70*(40+x)

0.50*x + 36 = 0.70*(40)+0.70*(x)

0.50*x + 36 = 28+0.70*x

36 - 28 = 0.70*x - 0.50x

8 = 0.20x

0.20x = 8

x = 8/0.20

x = 40

So that is why the answer is choice A. 40 liters

Answer:  1.4 f or [tex]1f +\frac{4f}{10}[/tex]

Step-by-step explanation:

Since, According to the question,

The snowfall in February in Delphine's house had = f cm

Again according to the question,

In March, Delphine's house had 40% more snowfall than in February.

Therefore, The snowfall in March in Delphine's house had = 140% of The snowfall in February in Delphine's house had

= 140 % of f

= [tex]\frac{f\times 140}{100}[/tex]

= 1.4 f cm

= 1 f + 0.4 f

= [tex]1 f + \frac{4f}{10}[/tex] cm

Answer:

It should be c & e

Answer:

B & D

Step-by-step explanation:

The quadratic formula can be used to solve for x for any quadratic. Recall a quadratic is any function whose highest exponent known as degree is 2. Looking at the answer selections, A has one term with exponent 3. This isn't possible in the formula. Looking at answer C, the term with exponent 2 has the same coefficient on each side of the equal sign. When it is rearranged these will cancel out no exponent of 2 will be in the equation anymore. Only B & D work after being rearranged and simplified

The two equations after simplifying will give quadratic equations are:-

x ²-6x-7=2x² and 5x²-3x+10=2x².

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Solving for the quadratic equation:-

Option B:-

x ² -   6x   -   7  =   2x²

- 2x²   +   x ² -   6x   -   7  =  0

x ²  +  6x  +  7  =  0

Option D:-

5x²   -   3x   +   10  =    2x².

5x²  -  2x². -   3x   +   10  =   0

3x²  -   3x  +  10  =  0

Therefore two equations after simplifying will give quadratic equations are- x ²-6x-7=2x² and 5x²-3x+10=2x².

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Final answer:

To find how many cups of flour are needed for every dozen muffins made, set up a ratio using the given information, and solve for x.

Explanation:

To find how many cups of flour are needed for every dozen muffins made, we can set up a ratio using the information given in the question. We know that to make 1 1/2 dozen muffins, 3 1/2 cups of flour are needed. So we can set up the ratio:

1 1/2 dozen muffins : 3 1/2 cups of flour = 1 dozen muffins : x cups of flour

To solve for x, we can cross multiply, and divide:

(1 1/2) * x = (1) * (3 1/2)

x = (1 * 3 1/2) / (1 1/2) = 7/2 cups of flour

Therefore, for every dozen muffins made, 7/2 cups of flour are needed.

Answer: Alternate Interior Angles Theorem (choice B)

If you have two parallel lines, and cut them with a third line, then you'll form two pairs of alternate interior angles. Alternate interior angles are angles that that are on the inside of the parallel "train tracks", but they are on opposite sides of the transversal line.

9.915 mi and that's all and that helped friend me please thanks stay pretty

Answer:

9.91 miles

Step-by-step explanation:

Refer the attached figure

Forest Ranger at point A observes the fire at angle of 41° north of east i.e.∠CAB = 41°

The distance between the two rangers is 15 miles i.e. AB = 15 miles

Forest Ranger at point B observes the fire at at 56° north of west. i.e.∠CBA= 56°

Now we are supposed to find who is closest to the fire

So, we are supposed to find the length of AC and BC

So, first calculate ∠ACB

We will use angle sum property of triangle

Angle  sum property of triangle  : Sum of all angles of triangle is 180°

So, ∠CBA+∠ACB+∠CAB =180°

56°+∠ACB+41° =180°

97°+∠ACB =180°

∠ACB =180°-97°

∠ACB =83°

Now to find  AC and BC we will use law of sines

[tex]\frac{a}{sin A}=\frac{b}{Sin B}=\frac{c}{SinC}[/tex]

Refer the attached figure

[tex]\frac{AC}{sin 56}=\frac{BC}{Sin 41}=\frac{15}{Sin83}[/tex]

So, [tex]\frac{BC}{Sin 41}=\frac{15}{Sin83}[/tex]

[tex]BC=\frac{15}{Sin83} \times Sin 41[/tex]

[tex]BC=9.91478[/tex]

[tex]\frac{AC}{sin 56}=\frac{15}{Sin83}[/tex]

[tex]AC=\frac{15}{Sin83} \times sin 56[/tex]

[tex]AC=12.5289[/tex]

So, BC< AC

So, the ranger who is closest to fire is at a distance of 9.91 miles .

So, Option 1 is true

Answer:

L = V / WH

Step-by-step explanation:

Solve for L: V = LWH

To solve, all you have to do is get L on its own on one side.

Because the only operation used in this equation is multiplication, only one operation is needed to solve it: division. Just divide both sides by WH to isolate L.

V / WH = LWH / WH

V / WH = L

[tex]LWH=V\qquad\text{divide both sides by}\ WH\neq0\\\\\boxed{L=\dfrac{V}{WH}}[/tex]

Answer:

4

Step-by-step explanation:

UPC (Universal Product Code) is a numeric symbol used in retail products. UPC has two variants, an 11 digit UPC Type A bar code and and 6 digit UPC Type E bar code.

The given UPC code 78007305233 is an 11 digit UPC Type A bar code.

1) From the right to the left, starting with odd position, we need to assign the odd/even position to each digit.

0 E 0 E 0 E 0 E 0 E 0                [0 stands for Odd, E stands for Even]

7 8 0 0 7 3 0 5 2 3 3

2) Summing up all digits in the odd positions and multiplying the result by 3

(7+0+7+0+2+3)*3 = 19 * 3 = 57

3) Summing up all digits in the even positions

8+0+3+5+3 = 19

4) Summing up the results of step three and four

57 + 19 = 76

5) Now, divide the result of the fourth step by 10. The check digit would be the number which adds the remainder to 10. In our case, upon dividing, 76 by 10 we get the remainder 6. The check digit is the result of 10-6 = 4.

Answer:

1) 7/6 or 1 1/6     2)7/55 of a foot longer      3) 13/4 or 3 1/4 cups of milk

4) 56/5 or 11 1/5 feet

Step-by-step explanation:

Let's go over this.

1) If the question asks how much cereal George eats in all, then you must add.

To do this, we must find 2/3 + 1/2. Also, we need to find the common denominator, so that is 6. 2/3 x 2= 4/6. 1/2 x 3= 3/6. Now, it is easier to add. 4/6 + 3/6= 7/6, or 1 1/6.

2) We must find the common denominator again. This is 55, since this is the LCM of 11 and 5. 3/11 x 5= 15/55. 2/5 x 11= 22/55. Now, since the orange fish is longer, 22/55 - 15/55 = 7/55 of a foot longer.

3) This is simple. 13/8 "doubled" is the same as 13/8 x 2, or 13/8 x 2/1. 13 x 2 = 26, and 8 x 1 =8. Our fraction will be 26/8, and we can simplify this to 13/4, or 3 1/4 cups of milk.

4) We can convert these two fractions to improper fractions. 2 1/3 = 7/3, and 4 4/5= 24/5. 7/3 x 24/5= 7 x 24/3 x 5 which is 168/15. The fully simplified fraction is 56/5, or 11 1/5 feet.

5) We must divide 2 1/2 and 4. 2 1/2 = 5/2, and 5/2 divided by 4 is the same thing as 5/2 x 1/4, which is 5/8 of a candy bar.

6) For this problem, we need to find the number of friends. We are supposed to divide 4 and 1/2. 4 divided by 1/2 is equal to 4/1 x 2/1, which is 8. Jack can split his candy bar pieces to 8 friends.

I hope this helped!

Final answer:

The unit rate of 2134 meters in 212 hours is approximately 10.063 meters per hour. This calculation involves dividing the total distance by the total amount of time.

Explanation:

To find the unit rate of 2134 meters in 212 hours, we need to calculate how many meters are covered in one hour. The unit rate is computed by dividing the total distance by the total time.

The calculation is as follows:

Unit rate = Total distance / Total time

Unit rate = 2134 meters / 212 hours

Calculating this gives us a unit rate of approximately 10.063 meters per hour. It's important to make sure that the result is reasonable. If you travel a certain distance in a given number of hours, dividing the distance by the time should give you how many meters you travel in one hour, which in this case, it does.

Answer: 320

Step-by-step explanation:

[tex]a_n=a_1(r)^{n-1}\quad \text{where}\ a_1\ \text{is the first term, r is the ratio, n is the term}[/tex]

[tex]a_7=5(2)^{7-1}[/tex]

   [tex]=5(2)^{6}[/tex]

   [tex]=5(64)}[/tex]

   [tex]=320[/tex]

Answer:

The 7th term in Geometric Sequence is 320

Step-by-step explanation:

Given : the geometric sequence whose first term is 5 and whose common ratio is 2.

To Find : 7th term

Solution :

Using the formula of Geometric Sequence :

[tex]a_{n} =a_{1} *r^{n-1}[/tex]    --(A)

Since,

[tex]a_{1}=5[/tex]

r =2

n = 7 (term no. need to calculate)

Putting these values in ---(A)

⇒[tex]a_{7} = 5*2^{7-1}[/tex]

⇒[tex]a_{7} = 5*2^{6}[/tex]

⇒[tex]a_{7} = 5*64[/tex]

⇒[tex]a_{7} =320[/tex]

Hence the 7th term in Geometric Sequence is 320

Final answer:

To determine the number of pairs of female dolphins, the total number of dolphins is divided equally between males and females, resulting in 8 female dolphins. Then, dividing by 2 as they swim in pairs, we find there are 4 pairs of female dolphins.

Explanation:

The question involves dividing the total number of dolphins in the pod by two to find out how many male and female dolphins there are since the pod has an equal number of each gender. Since the females are swimming in pairs, we then divide the number of female dolphins by two to find out how many pairs there are.

There are 16 dolphins in total. Half of them are females, so there are 8 female dolphins. The females swim in pairs, so to find the number of pairs we divide the number of female dolphins by two:

8 females ÷ 2 = 4 pairs of female dolphins.

Use photo math

Hope this helps

Answer:

the answer would be 6.5 pounds

Step-by-step explanation: 19 1/2 divided by three

Answer:

3149/999 = 3  152/999

Step-by-step explanation:

I'll assume the bar is over 152 and there is a typo.

Use a step-by-step calculator (I recommend Symbolab) OR:

Let x equal 3.152...

1000x = 3152.152...

1000x-x = 3152.152... - 3.152...

999x =

3152.152...

-     3.152...

3149

Cancel out the .152...

999x = 3149

Divide by 999 on each side

x=3149/999 = 3 152/999

Answer:

The given number is 3.152.

Notice that this is a rational number without a repetition pattern, that means we just need to divide all digist without the decimal point by 1000, because the number of zeros always depends on the number of decimals, which are three in this case.

[tex]\frac{3152}{1000}[/tex]

Then, we simplfy

[tex]\frac{3152}{1000}=\frac{1576}{500}=\frac{788}{250}=\frac{394}{125}[/tex]

So, the improper fraction equal to 3.152 is 394/125.

The mixed number is [tex]\frac{394}{125}=3\frac{19}{125}[/tex]

NOTES:

Degree: the largest exponent in the polynomial

End Behavior:

Multiplicity (M): the exponent of the zero. e.g. (x - 3)²  has a multiplicity of 2

Relative max/min: the y-value of the vertices.  

Rate of Change: slope between the two given points.

********************************************************************************************

1. f(x) = (x-1)²(x + 6)

a) Degree = 3

b) end behavior:

c) (x - 1)²(x + 6) = 0

   x - 1 = 0                     x + 6 = 0

       x = 1 (M=2)                   x = -6 (M=1)

d) The midpoint between 1 and -6 is -3.5, so axis of symmetry is at x = -3.5

y = (-3.5 - 1)²(-3.5 + 6)

  =  (-4.5)²(2.5)

  = 50.625

50.625 is the relative max

e) see attachment #1

f) The interval at which the graph increases is: (-∞, -3.5)U(1, ∞)

g) The interval at which the graph decreases is: (-3.5, 1)

h) f(-1) = (-1 - 1)²(-1 + 6)

          = (-2)²(5)

          = 20

    f(0) = (0 - 1)²(0 + 6)

          = (-1)²(6)

          = 6

Find the slope between (-1, 20) and (0, 6)

m = [tex]\frac{20-6}{-1-0}[/tex]

   = [tex]\frac{14}{-1}[/tex]

   = -14

********************************************************************************************

2.    y = x³+3x²-10x

         = x(x² + 3x - 10)      

         = x(x + 5)(x - 2)

a) Degree = 3

b) end behavior:

   Coefficient is positive so right side goes to positive infinity

   Degree is odd so left side goes to negative infinity

c) x(x + 5)(x - 2) = 0

   x = 0                     x + 5 = 0                     x - 2 = 0

   x = 0 (M=1)                   x = -5 (M=1)                x = 2 (M=1)

d) The midpoint between -5 and 0 is -2.5, so axis of symmetry is at x = -2.5

y = -2.5(-2.5 + 5)(-2.5 - 2)

  =  -2.5(2.5)(-4.5)

  = 28.125

28.125 is the relative max

The midpoint between 0 and 2 is 1, so axis of symmetry is at x = 1

y = 1(1 + 5)(1 - 2)

  =  1(6)(-1)

  = -6

-6 is the relative min

e) see attachment #2

f) The interval at which the graph increases is: (-∞, -2.5)U(1, ∞)

g) The interval at which the graph decreases is: (-2.5, 1)

h) f(-1) = -1(-1 + 5)(-1 - 2)

********************************************************************************************

3. y = -x(x + 2)(x - 7)(x - 3)

a) Degree = 4

b) end behavior:

   Coefficient is negative so right side goes to negative infinity

   Degree is even so left side goes to negative infinity

c)  -x(x + 2)(x - 7)(x - 3) = 0

  -x = 0                     x + 2 = 0                     x - 7 = 0             x - 3 = 0

   x = 0 (M=1)                 x = -2 (M=1)                x = 7 (M=1)          x = 3 (M=1)

d) The midpoint between -2 and 0 is -1, so axis of symmetry is at x = -1

y = -(-1)(-1 + 2)(-1 - 7)(-1 - 3)

  =  1(1)(-8)(-4)

  = 32

32 is a relative max

The midpoint between 0 and 3 is 1.5, so axis of symmetry is at x = 1.5

y = -(1.5)(1.5 + 2)(1.5 - 7)(1.5 - 3)

  =  -1.5(3.5)(-5.5)(-1.5)

  = -43.3125

-43.3125 is the relative min

The midpoint between 3 and 7 is 5, so axis of symmetry is at x = 5

y = -(5)(5 + 2)(5 - 7)(5 - 3)

  =  -5(7)(-2)(2)

  = 140

140 is the relative max

e) see attachment #3

f) The interval at which the graph increases is: (-∞, -1)U(1.5, 5)

g) The interval at which the graph decreases is: (-1, 1.5)U(5, ∞)

h) f(-1) = -(-1)(-1 + 2)(-1 - 7)(-1 - 3)

          = 1(1)(-8)(-4)

          = 32

    f(0) = -(0)(0 + 2)(0 - 7)(0 - 3)

          = 0

Find the slope between (-1, 32) and (0, 0)

m = [tex]\frac{32-0}{-1-0}[/tex]

   = [tex]\frac{32}{-1}[/tex]

   = -32

Given : (3x² - 2y² + 5x) + (4x² + 12y² - 7x)

Rearranging like terms, we get :

⇒ (3x² + 4x²) + (12y² - 2y²) - 7x + 5x

⇒ 7x² + 10y² - 2x

But, Marcus got the Answer as : 7x² - 10y² - 2x

Marcus combined the terms -2y² and 12y² Incorrectly

Following are the solution to the given expression:

Given:

[tex]\bold{(3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y^2-2x}[/tex]

To find:

Solve equation=?

Solution:

[tex]\to \bold{(3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y^2-2x}[/tex]

Solving the L.H.S part:

[tex]\to \bold{(3x^2-2y^2+5x)+(4x^2+12y^2-7x)}\\\\\to \bold{(3x^2-2y^2+5x+4x^2+12y^2-7x)}\\\\\to \bold{(7x^2+10y^2-2x)}\\\\[/tex]

Solving the R.H.S part:

[tex]\bold{=7x^2-10y^2-2x}[/tex]

Since in this question the [tex]L.H.S \neq R.H.S[/tex] , and when we solve the equation so, except the third choice all were correct.

Therefore, the final answer is " He combined the terms [tex]\bold{-2y^2\ and\ 12y^2}[/tex]incorrectly."

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Answer: 56

Step-by-step explanation: The pattern is 8 x 3.5 = 28, 10 x 3.5 = 35, 12 x 3.5 = 42... so 16 x 3.5 = 56

Answer:

56

Step-by-step explanation:

Answer: 6

The remainder theorem says that if we divide p(x) over x-k, then the remainder is r = p(k)

In this case, we have p(x) = x^2+5 and x-k = x+1 = x-(-1). So k = -1 is plugged into p(x) to get

p(x) = x^2+5

p(-1) = (-1)^2+5

p(-1) = 1+5

p(-1) = 6

That is why the remainder is 6. You can use polynomial long division or synthetic division to confirm this answer.

Answer:

The remainder would be 6.

Step-by-step explanation:

Answer:

Answer in simplified form is:

(sinФ - cosФ)² + (sinФ + cosФ)² = 2

Step-by-step explanation:

Given,

(sinФ - cosФ)² + (sinФ + cosФ)²

This can be simplified as:

(sin²Ф + cos²Ф - 2sinФcosФ) + (sin²Ф + cos²Ф +2sinФcosФ)

We know that : sin²Ф + cos²Ф = 1

So,

( 1 - 2sinФcosФ) + (1 + 2sinФcosФ)

or 1 + 1 -2sinФcosФ + 2sinФcosФ

or 2

Hence we got  (sinФ - cosФ)² + (sinФ + cosФ)² = 2

Answer:

Its more because 9.36 has a bigger beginning then 9.359.

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Answer:

No

Step-by-step explanation:

9.36= 9.360

9.360> 9.359

The hundredeth's place of 9.360 is greater than the hundredth's place of 9.359.

Answer:

Relative Size, S, is 1584.89

Step-by-step explanation:

The equation is [tex]R=log_{10}(S)[/tex]

Where,

It is given that in Richter Scale, an earthquake measured 3.2, so [tex]R=3.2[/tex].

They want to know relative size, S, so we put given information in equation and solve for S:

[tex]R=log_{10}(S)\\3.2=log_{10}(S)[/tex]

Converting to exponential form, we have:

[tex]3.2=log_{10}(S)\\S=10^{3.2}\\S=1584.8932[/tex]

Rounding to nearest hundredth, we have:

[tex]S=1584.89[/tex]

Final answer:

To find the relative size of an earthquake measured at 3.2 on the Richter scale, calculate 10 to the power of 3.2. This results in a relative size of approximately 1584.89 when expressed to the nearest hundredth.

Explanation:

The relationship between the relative size of an earthquake, S, and the measure of the earthquake on the Richter scale, R, is given by the equation log S = R. If an earthquake measured 3.2 on the Richter scale, we can calculate its relative size by finding the antilogarithm (typically the base 10) of the Richter scale magnitude. This means finding 10 to the power of the magnitude.

To find the relative size for an earthquake that measured 3.2 on the Richter scale:

The relative size or seismic-wave amplitude of the earthquake is therefore approximately 1584.89 when expressed to the nearest hundredth.

Answer:78.5

Step-by-step explanation

3.14×r^2

Area of a circle whose radius is 5 meters is 78.55square meter

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry

The formula for area of circle is Area equal to pi r square

A=πr²

The radius is given which is 5 meters

r=5

Substitute the r value in Area of circle formula

A=3.142×5²

We know that five square is twenty five.

=3.142×25

=78.55

Hence  area of a circle whose radius is 5 meters is 78.55square meter.

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Answer:

336 dollars

Step-by-step explanation:

Set up a proportion. Because you know that three pairs of pants costs sixteen dollars, you can put three over sixteen because they are both the same part of the equation, the same part being that they are pairs of pants. Then you set up another proportion, sixty three over x, because you do not know how much sixteen pairs of pants costs. It should look like this. Then you cross multiply and divide.

3                          63

---            =          ----

16                          x

16 times 63 = 1008

1008/3 = 336

Answer:  $336

Answer:

the golf ball travels 4,295.52 inches in 20 seconds

Step-by-step explanation:

the ball spins around 340 revolutions per minute

340 revolutions per 60 seconds

60 seconds = 340 revolutions

1 seconds = [tex]\frac{340}{60} = 5.667[/tex]

so its around 5.7 revolutions in 1 second

1 second = 5.7 revolutions

 20 seconds = 5.7 * 20 = 114 revolutions

In 20 second ball spins 114 revolutions

To find distance traveled in 1 revolution we find the circumference of circle

circumference of circle = 2* 3.14 * r

r is the radius = 6 in

circumference of circle = 2* 3.14 * 6= 37.68 inches

In 1 revolution ball travels 37.68 inches

In 114 revolution ball travels 37.68 * 114 = 4295.52 inches

the golf ball travels 4,295.52 inches in 20 seconds

Answer:

15

Step-by-step explanation:

25 percent of 20 is 5, and 20-5 equals 15.

In a group of 20 students, 15 do not wear glasses.

Answer:

the x-coordinate

Step-by-step explanation:

The slope intercept form is: y = mx + c

where m⇒ slope

          c ⇒ y-intercept

          (x,y) is a point on the graph the  satisfy the equation representing that graph.

∴ x is the x-coordinate of a point on the line.  

[tex]\left\{\begin{array}{ccc}y=6x+2&(*)\\y=x+17&(**)\end{array}\right\\\\\text{Substitute}\ (*)\ \text{to}\ (**):\\\\6x+2=x+17\qquad\text{subtract 2 from both sides}\\6x=x+15\qquad\text{subtract x from both sides}\\5x=15\qquad\text{divide both sides by 5}\\\boxed{x=3}\\\\\text{Put the value of x to the second equation}:\\\\y=3+17\\\boxed{y=20}\\\\Answer:\ \boxed{D.\ (3,\ 20)}[/tex]

Answer:

D ( 3, 20 )   For A pex

Step-by-step explanation:

Answer: A+C = 180 (first answer choice)

This statement is only true if and only if we are dealing with a rectangle (where all four angles are 90 degrees). Otherwise, the statement is false.

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

side notes:

The second statement that AN = NC and DN = NB is true because a parallelogram has its diagonals bisect each other. In other words, the diagonals cut in each other in half.

The third statement that AD = BC and DC = AB is true because opposite sides of a parallelogram are parallel and congruent.

The fourth statement is true because opposite angles of a parallelogram are congruent. If A = C = 90, then A+C = 90+90 = 180 backing up the claim I made earlier, but it's possible that A and C are non-right angles making this parallelogram non-rectangular.

Answer:

m∠A + m∠C = 180

Step-by-step explanation: