Evaluate (precalculus)

The range of a function is the set of y-values the function contains. Thus, in this case, the range would be the set of values under the y column, as this represents the y-values the function produces.

We see "2, 3, 4, 2" under the y column. Since we are establishing a set of values, we are going include all the values under the column, which includes 2, 3, and 4. We are not going to repeat the second 2 because it isn't necessary, as 2 is already in the set thus.

Thus, the final set for the range of the function is {2, 3, 4}, or Choice A.

Answer:

The length of side KM is [tex]\sqrt{109}[/tex] units.

Step-by-step explanation:

Given information:  KLMN is a trapezoid, ∠N= ∠KML, FD=8, LM:KN=3:5, F∈ KL, D∈ MN , ME ⊥ KN KF=FL, MD=DN, [tex]ME=3\sqrt{5}[/tex].

From the given information it is noticed that the point F and D are midpoints of KL and MN respectively. The height of the trapezoid is [tex]3\sqrt{5}[/tex].

Midsegment is a line segment which connects the midpoints of not parallel sides. The length of midsegment of average of parallel lines.

Since LM:KN=3:5, therefore LM is 3x and KN is 5x.

[tex]\frac{3x+5x}{2}=8[/tex]

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

[tex]x=2[/tex]

Therefore the length of LM is 6 and length of KN is 10.

Draw perpendicular on KN form L and M.

[tex]KN=KA+AE+EN[/tex]

[tex]10=6+2(EN)[/tex]                (KA=EN, isosceles trapezoid)

[tex]EN=2[/tex]

[tex]KE=KN-EN=10-2=8[/tex]

Therefore the length of KE is 8.

Use pythagoras theorem is triangle EKM.

[tex]Hypotenuse^2=base^2+perpendicular^2[/tex]

[tex](KM)^2=(KE)^2+(ME)^2[/tex]

[tex](KM)^2=(8)^2+(3\sqrt{5})^2[/tex]

[tex]KM^2=64+9(5)[/tex]

[tex]KM=\sqrt{109}[/tex]

Therefore the length of side KM is [tex]\sqrt{109}[/tex] units.

The answer is [tex]\sqrt{70}[/tex]

Answer:

y =  8x + 6

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 and y is the y-coordinate of a point on the line.

m  = 8

Y-intercept = 6

y = mx + c   ⇒ y =  8x + 6

Answer:

X-intercept:(-4/3,0)

Y-intercept:(0,-3/2)

Step-by-step explanation:

The x-intercept is (-4/3, 0) and the y-intercept is (0, -3/2).

To find the x-intercept of the equation 8y= -9x-12, we substitute y with 0 and solve for x. This gives us:

8(0) = -9x-12

0 = -9x-12

-9x = 12

x = -12/9

x = -4/3

Therefore, the x-intercept is (-4/3, 0).

To find the y-intercept, we substitute x with 0 and solve for y. This gives us:

8y = -9(0)-12

8y = -12

y = -12/8

y = -3/2

Therefore, the y-intercept is (0, -3/2).

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Anna earns $8.50 per hour babysitting. For 3, 3.5 and 4 hours of work, she will earn $25.50, $29.75, and $34.00 respectively.

Anna earns $8.50 per hour for babysitting. To calculate her earnings, we simply need to multiply the number of hours she worked by her hourly rate.

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[tex]f(x)=x^2-2x-8;\ g(x)=\dfrac{1}{4}x-1\\\\f(x)=g(x)\iff x^2-2x-8=\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4x^2-8x-32=x-4\qquad\text{subtract x from both sides}\\\\4x^2-9x-32=-4\qquad\text{add 4 to both sides}\\\\4x^2-9x-28=0\\\\4x^2-16x+7x-28=0\\\\4x(x-4)+7(x-4)=0\\\\(x-4)(4x+7)=0\iff x-4=0\ \vee\ 4x+7=0\\\\x=4\ \vee\ 4x=-7\\\\\boxed{x=4\ \vee\ x=-\dfrac{7}{4}}[/tex]

Answer:

450

Step-by-step explanation:

Answer:

(2i,0) (-2i,0)

(1,0) (-1,0).

Step-by-step explanation:

The graph below shows that there are only 2 real solutions at x = 1 and x = - 1

Expressed as points, these two are (1,0) and (-1,0). However that is not the complete answer. There are 2 complex points.

y = x^4 + 3x^2 - 4

y = (x^2 - 1)(x^2 + 4)

These two binomials can be equated to 0

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

Answer:

48 min  

Step-by-step explanation:

1 h = 60 min

It takes 60 min to go 65 mi.

Time = 52 × 60/65

Time = 48 min

Answer:

48min

Step-by-step explanation:

I used this question and got it right on my test. :)

Answer:

60

Step-by-step explanation:

The required result is 60 when 480 is divided by 8, with no remainder.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

To divide 21,900 by 25, we can perform long division as follows:

  8 ) 480 ( 60

     - 480

     ________

          0

When we divide the first digit of 480 (which is 4) by the divisor 8, which gives us 60 with a remainder of 0.

Therefore, 480 divided by 8 is 60, with no remainder.

To learn more about the division operation click here :

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The complete question would be as:

What is the result when 480 is divided by 8 long division?

sorry, put the wrong answer and cant delete

Answer:

4/15 distance

Step-by-step explanation:

We can use ratio's to solve this, putting distance over time

1/5 distance          x distance

----------------   = ----------------------

3/4 hour                 1 hour

Using cross products

1/5 * 1 = 3/4 x

1/5 = 3/4 x

Multiply by 4/3 to isolate x

1/5 * 4/3 = 4/3 * 3/4x

4/15 = x

The train can travel 4/15 of the distance in 1 hour

Answer:

option A

-2x + 4y = 4

-3x + 6y = 6

Step-by-step explanation:

In option A, if the student multiply the first equation by 3 and the second equation by -2, then the equations become

-6x+12y = 12 and

6x-12y =-12

If she adds both equations, she will get 0 = 0

This means that the system has infinite number of solutions.

Hence, the student could have started with equations -2x + 4y = 4 and -3x + 6y = 6.

Answer:

4, 2, 1, [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex], .....

Step-by-step explanation:

Fifth term (a₅) =  [tex]\frac{1}{4}[/tex]

Common ratio (r) = [tex]\frac{1}{2}[/tex]

n = 5

The formula to find the [tex]n^{th}[/tex] term of a geometric sequence is

a₅ = a₁r⁽ⁿ⁻¹⁾

=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})^{(5-1)}[/tex]

=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})^{(4)}[/tex]

=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})*(\frac{1}{2})*(\frac{1}{2})*(\frac{1}{2})[/tex]

=> [tex]\frac{1}{4}[/tex] = a₁* [tex]\frac{1*1*1*1}{2*2*2*2}[/tex]

=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{16})[/tex]

Flip the sides of the equation

a₁*[tex](\frac{1}{16})[/tex] = [tex]\frac{1}{4}[/tex]

Multiply both sides by 16

a₁*[tex](\frac{1}{16})[/tex]*16 = [tex]\frac{1}{4}[/tex]*16

Cancelling out the 16's from the top and bottom of the left side

a₁ = [tex]\frac{16}{4}[/tex]

=> a₁ = 4

So, first term of the geometric sequence is 4.

Common ratio = [tex]\frac{1}{2}[/tex]

Second term = First term * Common ratio

                      = 4* [tex]\frac{1}{2}[/tex]

                      = [tex]\frac{4}{2}[/tex]

                      = 2

Third term = Second Term * Common ratio

                  = 2 * [tex]\frac{1}{2}[/tex]

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

                  = 1

Fourth term = Third Term * Common ratio

                    = 1 * [tex]\frac{1}{2}[/tex]

                    = [tex]\frac{1}{2}[/tex]

Fifth term (given) = [tex]\frac{1}{4}[/tex]

So, the geometric sequence would be

4, 2, 1, [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex], .....

To change the story from first person to third person point of view, first-person pronouns like 'I', 'me', and 'we' should be changed to third-person pronouns such as 'they', 'he', 'she', or the friends' names.

To change the point of view of the story from first person to third person, it is necessary to change the pronouns used in the narration. If the original story used first-person pronouns such as I, me, and we, these would need to be changed to third-person pronouns such as they, he, she, or the friends' names to reflect the third person point of view.

For example, a sentence that originally reads "We went to the park after school" would change to "They went to the park after school" in the third person point of view. This shift enables the story to be told as if an outside observer is describing the events that happen to the group of friends, rather than the friends themselves narrating the story.

Final answer:

The value of any number raised to the power of 1 is the number itself, as it implies a single multiplication of the number by 1.

Explanation:

The value of a number raised to the power of 1 is always the number itself. This is because an exponent represents how many times to multiply the number by itself. When the exponent is 1, you are simply multiplying the number by 1, which does not change its value.

For example:

Answer:

D) -2

Step-by-step explanation:

Answer:

D- -2

Hope this helps :)

[tex]y=3-2x\\\\4x-y=4x-(3-2x)=4x-3+2x=6x-3\\\\\text{Put}\ x=-5+6i\ \text{to the expression}\ 6x-3:\\\\6(-5+6i)-3\qquad\text{use distributive property}\\\\=(6)(-5)+(6)(6i)\\\\=-30+36i\\\\Answer:\ \boxed{4x-y=-30+36i}[/tex]

Answer:

$7. Based on the assumption that both offices paid the same amount for delivery, the difference in the total cost paid is due to the difference in the number of turkey sandwiches ordered, which is 4. The cost of each sandwich is a quarter of this difference in cost.

Step-by-step explanation:

In mathematical working, the explanation above can be written in the form of equations, where we work to solve the value of a variable. In this case, we are interested to find the value of t.

Define variables:

Let the cost of a turkey sandwich be $t while the delivery fee be $d.

Form 2 equations:

Assuming that the sandwich stores charges the same delivery fee for both offices,

4t + d= 33 -----(1)

8t + d= 61 -----(2)

Solve by elimination:

(2) - (1):

4t= 61 - 33

4t= 28

Divide both sides by 4:

t= 7

Thus, each turkey sandwich adds $7 to the cost of the delivery.

To find out how much each turkey sandwich adds to the cost of delivery, we need to determine the cost of delivery in both cases and subtract it from the total price paid by each office.

To find out how much each turkey sandwich adds to the cost of delivery, we need to determine the cost of delivery in both cases and subtract it from the total price paid by each office.

For the first office, they paid $33 for 4 turkey sandwiches. Let's assume the cost of delivery is 'x'. So the equation to represent the total cost is: 4x + 33 = total cost.

Similarly, for the second office, they paid $61 for 8 turkey sandwiches. Let's assume the cost of delivery is 'y'. So the equation to represent the total cost is: 8y + 61 = total cost.

Now we can solve both equations to find the values of 'x' and 'y' which will represent the cost of delivery. Once we have those values, we can calculate how much each turkey sandwich adds to the cost of delivery by dividing the cost of delivery by the number of turkey sandwiches ordered.

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Answer:

Step-by-step explanation:

1.  <3 = <4                                      1 Given

2.  <2 <3 are supplementary      2.  non common   sides in  opposite  rays

3. <2 + <3 = 180                             3.  Definition of supplementary angles

4.  <2 + < 4 = 180                              4  substitution

5.  <1 = <4                                       5  Opposite angles are equal

6 <2 + <1 = 180                                6     Substitution

7.  <1, <2 are supplementary            7.  Definition of supplementary angles

The only word I am not sure of is the last word in 2

Answer:

16

Step-by-step explanation:

We want to divide 1/2 pound in 8 equal parts

1/2 dividend by 8/1 is the same as  

1/2 multiplied by 1/8 =1•1/2•8=1/16

Each package will weigh 1/16 of a pound  

Or 1 ounce since 1 pound = 16 oz

Answer: Kate expression: 2(50-t)

2 : represents twice,

50 : represents Initial number of tickets Kate has,

t : The lost tickets

50-t : represents Number of ticket Kate has After loosing t tickets

Jack expression: 100 - 2t

100 : Twice of initial ticket Kate has,

t :  The lost tickets

2t : represents twice of the lost tickets,

100-2t : represents Final number of ticket Kate has.

Step-by-step explanation:

Since, According to the question,

Initially Kate has 50 tickets.

She lost tickets = t

And, after losing t ticket she has tickets = 50 - t

But, His father doubled the amount, Thus she has final tickets = 2(50-t)= 2×50 -2× t = 100 - 2t  

Final answer:

Kate's expression, 2(50−t), represents the number of tickets she has now by doubling the tickets she had left after losing some. Jack's expression, 100−2t, represents the number of tickets Kate has now by subtracting twice the number of tickets she lost from the total number of tickets she initially had.

Explanation:

Kate wrote the expression 2(50−t) to find the number of tickets she has now. In this expression, t represents the number of tickets she lost. The expression is simplified as follows: multiply 2 by the quantity (50−t). This means that Kate's dad doubled the tickets she had left after losing some tickets.

Jack's expression, 100−2t, also determines the number of tickets Kate has now. In this expression, t represents the number of tickets she lost. The expression is simplified as follows: subtract 2 times the quantity t from 100. This means that Jack found the number of tickets Kate has by subtracting twice the number of tickets she lost from the total number of tickets she initially had.

Answer:

First box: 6x

Second box: 24

Step-by-step explanation:

9(16)=6x

144 = 6x   | divide by 6

144/6 = 6x/6

24 = x

Answer:

m = 1

Step-by-step explanation:

Given ->  3m + 5 = 8

Subtraction -> 3m = 3

Division -> m = 1

Answer:

m= 1

Step-by-step explanation:

3m +5 = 8     Substract 5 to both sides

 3m = 3         Divide 3 in both sides

  m = 1

Answer:

The correct option is A.

Step-by-step explanation:

The given inequality is

[tex]y\leq -2x[/tex]

The sign of inequality is ≤, it means the points on relation line lie in the solution set.

The related equation of the inequality is

[tex]y=-2x[/tex]

At x=0,

[tex]y=-2(0)=0[/tex]

At x=1,

[tex]y=-2(1)=-2[/tex]

Plot the points (0,0) and (1,-2) on a coordinate plane.

The sign of inequality is ≤, it means we have shade below the line.

The point (-2,4) and (3,-6) are in solution set because,

[tex]4\leq -2(2)\Rightarrow 4\leq 4[/tex]            (True)

[tex]-6\leq -2(3)\Rightarrow -6\leq -6[/tex]           (True)

Therefore option A is correct.

The points (1,2) and (1,3) are not in the solution set because,

[tex]2\leq -2(1)\Rightarrow 2\leq -2[/tex]            (False)

[tex]3\leq -2(1)\Rightarrow 3\leq -2[/tex]           (False)

Therefore options B,C and D are incorrect.

Answer:  (1,2) (-2,-4)

Step-by-step explanation:

Answer:

The scale factor used was 1/2

hope this helped

Step-by-step explanation:

Answer:

2 1/2

Step-by-step explanation:

You divide and there are 2 two’s that can go into 5 with a remainder of 1

Answer: 2 1/2

Step-by-step explanation:

divide 5/2

you get 1 as a remainder and two at the top

2 1/2

[tex]\left\{\begin{array}{ccc}2x+3y=17\\x+5y=19&|\text{multiply both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+3y=17\\-2x-10y=-38\end{array}\right}\qquad\text{add both sides of equations}\\.\qquad\qquad-7y=-21\qquad\text{divide both sides by (-7)}\\.\qquad\qquad \boxed{y=3}\\\\\\\text{Substitute the value of y to the second equation}\\\\x+5(3)=19\\\\x=15=19\qquad\text{subtract 15 from both sides}\\\\\boxed{x=4}\\\\Answer:\ x=4\ and\ y=3.[/tex]