Which represents the solution(s) of the graphed system of equations, y = x2 + x – 2 and y = 2x – 2

Answer:

The approximate value of arc cos(0.87) is 29.54°

Step-by-step explanation:

we know that

The arc cosine of x is defined as the inverse cosine function of x

so

if y=cos(x)

then

arc cos (y)=x

In this problem we have

y=0.67

so

x=arc cos(0.87)

using a calculator

x=29.54°

So, the approximate value of arccos(0.67) is about 0.84108 radians.

To approximate arccos(0.67) using a calculator, we find it to be approximately 0.84108 radians. This value represents the angle whose cosine is 0.67. Arccos, or inverse cosine, returns the angle in radians between 0 and π (approximately 3.14159) whose cosine is the input value. In this case, 0.67 is the cosine of the angle 0.84108 radians. This angle is commonly used in trigonometric calculations, such as determining the angle of a vector or solving geometric problems involving cosine functions.Let's use a calculator to find the approximate value of arccos(0.67).

Using a calculator:

[tex]arccos(0.67) \approx 0.84108 radians[/tex]

Answer:

A person drinks 4.52 cups per hour

Step-by-step explanation:  

No of work days = 5

No of hours in day = 10

No of hours in week = 10*5= 50 hours

Total cups consumed = 226

No of cups consumed per hour = Total no of cups/ Total week  hours            

                                                     = 226/50

                                                     = 4.52 cups/ hour

Answer:

The option A,D and E are correct.

Step-by-step explanation:

Given: 2x^3-250x^2

Factor : 2x^2(x-125)

So, GCF = 2x^2

Now a = 1 and b= 5

we know that a^3-b^3 = (a-b)(a^2+ab+b^2)

(x)^3 - (5)^3 = (x-5)(x^2+5x+25)

So, the option A,D and E are correct.

Answer:

$1720.00

Step-by-step explanation:

55.75 + 9.65 = 65.40

65.40 x 26.3 = 1720.02

Answer:

So first blank=6

Second blank=0

Third blank=-5

Fourth blank=6

Step-by-step explanation:

It is a horizontal line so the equation is just going to be

[tex]y=\text{ whatever y-coordinate they gave you in that one point}[/tex].

So it will be [tex]y=6[/tex]

We are going to do the point-slope form too as I requested.

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex].

We have m=0 since you said the slope was 0 and since it said your have a horizontal line (which means the slope slope or m is 0).

You also that it contains the point [tex](-5,6)=(x_1,y_1)[/tex].

So our line in point-slope form is [tex]y-6=0(x-(-5))[/tex].

Answer:

axis of symmetry is [tex]x=\frac{-9}{2}[/tex].

The ordered pair of the vertex is [tex](\frac{-9}{2},\frac{-145}{4})[/tex].

Step-by-step explanation:

Your function is a quadratic.

Compare [tex]x^2+9x-16[/tex] to [tex]ax^2+bx+c[/tex].

You should see that [tex]a=1,b=9,c=-16[/tex].

The x-coordinate of the vertex or the axis of symmetry since the axis symmetry goes through the vertex can be found by computing [tex]\frac{-b}{2a}[/tex].

So here we go!

The axis of symmetry is [tex]x=\frac{-9}{2(1)}=\frac{-9}{2}[/tex].

When you write your axis of symmetry be sure to write it as an equation.

That is the axis of symmetry is [tex]x=\frac{-9}{2}[/tex].

Now that was also the x-coordinate of your vertex.  To find the corresponding y-coordinate of the vertex, plug your value for [tex]x[/tex] into

[tex]y=x^2+9x-16[/tex].

[tex]y=(\frac{-9}{2})^2+9(\frac{-9}{2})-16[/tex]

Put into calculator:

[tex]y=\frac{-145}{4}[/tex] when [tex]x=\frac{-9}{2}[/tex]

The ordered pair of the vertex is [tex](\frac{-9}{2},\frac{-145}{4})[/tex].

Answer:

Vertex: [tex](h,k)\rightarrow(-4.5,-36.25)[/tex]

Axis of symmetry: [tex]x=-4.5[/tex]

Step-by-step explanation:

First I'll find the axis of symmetry. This formula lets us find the a.o.s: [tex]x=\frac{-b}{2a}[/tex].

In [tex]x^2+9x-16[/tex], the values of a, b, and c are:

We only need a and b to find the axis of symmetry. Substitute these values into the formula.

Simplify this fraction.

The axis of symmetry of this quadratic function is x = -4.5.

Now to find the vertex, we have to take into account that this quadratic is in standard form, making it a little harder. We have to convert this function into vertex form.

Start by changing f(x) to 'y' and adding 16 to both sides.

Use the completing the square formula: [tex](\frac{b}{2} )^2[/tex]

Keep the balance by adding 20.25 on the left side and adding it on the right side of the equation.

Combine like terms.

Factor the right side of the equation. Ask yourself, "What two numbers multiply to 20.25 (c) and add up to 9 (b)?" These two numbers are 4.5 and 4.5. Rewrite the right side with factors.

Isolate y by subtracting 36.25 from both sides of the equation.

Now this quadratic function is in vertex form, making it super simple to find the vertex using [tex](h, k)[/tex].

Vertex form of a quadratic is:

Compare [tex]y=(x+4.5)^2-36.25[/tex] with the original vertex form and find where h and k are. Those are the x (h) and y (k) values of the vertex.

Since the original vertex form has x - h, the h value in [tex]y=(x+4.5)^2-36.25[/tex] would be a negative since two negatives make a positive. The k value would stay "normal"---negative would mean it is a negative and positive would mean it is a positive number.

Therefore the h value is -4.5, and the k value is -36.25.

The ordered pair of the vertex is [tex](-4.5, -36.25)[/tex].

Answer:

A

Step-by-step explanation:

If you reflect over line A both pentagons are equally spaced in proportion to the line

The pentagon is reflected over the line A.

Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.

Here given are two pentagons on left and right.

The pentagon on the left is a reflection of the pentagon on the right.

This means that both the pentagons should be proportionally spaced from the line.

If we consider the line of reflection as B, the the pentagon on the right is nearer to the line compared to that on the left.

If we consider line D as the line of reflection, then pentagon on the left is nearer to the line compared to that on the right.

So if line A is the line of reflection, the both pentagons are equally spaced from the line.

Hence line A is the line of reflection.

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Answer:

x^2-16 goes with (x+4)(x-4)

x^2+10x+16 goes with (x+8)(x+2)

Step-by-step explanation:

The first one you got wrong is known as a difference of squares.

To factor a difference of squares, a^2-b^2, you just write it as (a-b)(a+b) or (a+b)(a-b) would work too.

So x^2-16=(x-4)(x+4) or (x+4)(x-4).

Let's check (x+4)(x-4) using foil!

First: x(x)=x^2

Outer: x(-4)=-4x

Inner: 4(x)=4x

Last: 4(-4)=-16

----------------------Add

x^2-16

Bingo! (x+4)(x-4) definitely corresponds to x^2-16.

Here are more examples of factoring a difference of squares:

Example 1:  x^2-25  = (x+5)(x-5)

Example 2: x^2-81   = (x+9)(x-9)

Example 3: x^2-100 =(x+10)(x-10)

Onward to the next problem:

x^2+10x+16

When the coefficient of the leading term of a quadratic is 1, all you have to do is find two numbers that multiply to be c=16 and add up be b=10.

Those numbers would be 8 and 2

because 8(2)=16 and 8+2=10.

So the factored form of x^2+10x+16 is (x+2)(x+8) or (x+8)(x+2).

Here is another example of when the leading coefficient of a quadratic is 1:

Example 1:  x^2+5x+6=(x+2)(x+3) since 3(2)=6 and 3+2=5.

Example 2: x^2-x-6=(x-3)(x+2) since -3(2)=-6 and -3+2=-1.

Answer:

[tex]x=k=117\°[/tex]

Step-by-step explanation:

Givens

AB || CD

EF || GH

These parallels gives us certain pair of angles which are congruent.

The given angle 63° is congruent with its corresponding angles. The image attached shows all corresponding angles that are equal to 63° (red angles).

Basically,

[tex]x+63=180[/tex] and [tex]k+63=180[/tex], by suplementary angles and straight angle definition.

Then, solving for [tex]x[/tex] and [tex]k[/tex], we have

[tex]x=180-63\\x=117\°[/tex]

[tex]k=180-63\\k=117\°[/tex]

Therefore, both angles are equal to 117°.

The measure of each angle are:

Given:

AB || CD

EF || GH

As, the lines are parallel and parallel line have following properties

So, <m = 63 {Corresponding angle}

Now, <m + <n = 180 {Linear pair}

63 + <n =180

<n =180 - 63

<n = 117

and, <k = 63 {Vertical opposite angle}

and, <k = <x = 63  {Corresponding angle}

and, <w = <x = 63  (alternate Interior angle}

and, <p = <w = 63 {Vertical opposite angle}

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The circumcenter O, formed by the intersection of the perpendicular bisectors of sides AB and BC, is equidistant from all vertices, with OA = OB = OC. Here option B is correct.

In a triangle, the circumcenter is the point where the perpendicular bisectors of its sides intersect. In this case, the circumcenter O is formed by the intersection of the perpendicular bisector of side AB and the perpendicular bisector of side BC.

The circumcenter is equidistant from all three vertices, making OA, OB, and OC equal, and these distances represent the radius of the circumcircle.

This line not only bisects side AB but also intersects with the perpendicular bisector of side BC at the circumcenter O. The equality of OA, OB, and OC ensures that the circumcircle passes through all three vertices of the triangle, making it a significant point in the context of the triangle's geometry. Here option B is correct.

Answer:

126 units

Step-by-step explanation:

the lateral area of a regular pyramid with a square base of 126 units has a slant height of 9 units and base side lengths of 7 units.

Answer:

168.558

Step-by-step explanation:

       168.58

34√5731.0

    -34 ↓3

     23 3

    -204 ↓1

       28  1

     - 272 ↓0

       19  0

       -170  ↓0

         20 0

        -170  ↓0

           30 0

          -272 ↓0

            28  0

and just goes on..

Answer:

see explanation

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, -4) and (x₂, y₂ ) = (3, - 1)

d = [tex]\sqrt{(3-0)^2+(-1+4)^2}[/tex]

  = [tex]\sqrt{3^2+ 3^2}[/tex]

  = [tex]\sqrt{9+9}[/tex]

  = [tex]\sqrt{18}[/tex] = 3[tex]\sqrt{2}[/tex] ≈ 4.24 ( to 2 dec. places )

Answer:

1010

Step-by-step explanation:

There are a whole class of questions that rely on the method to this one.

First add up what you know

1270 + 1150 + 870 + 1450 = 4740

Now add on the 5th month (which you don't know. Call it x)

4740 + x

Divide by 5

(4740 + x)/5 = 1150 and that is your equation    

Solution

Multiply both sides by 5

5*(4740 + x) / 5 = 1150 * 5

4740 + x = 5750

Subtract 4740 from both sides

4740 - 4740 + x = 5750 - 4740

x = 1010

Which seems kind of low, but that's what the numbers come to.

Answer:

A 54

Step-by-step explanation:

RC = 126

WC = 72

RC = WC + RW

126 = 72+RW

Subtract 72 from each side

126-72 = 72-72+RW

54 = RW

Answer: First option

[tex]RW=54[/tex]

Step-by-step explanation:

Notice in the image that the distance from R to C is equal to 126.

Then we write:

[tex]RC = 126[/tex]

Also note that the distance between W and C is 72.

We know that:

[tex]RC=RW + WC[/tex]

In this case we want to find RW, so we solve the equation for RW

[tex]RC-WC=RW + WC-WC[/tex]

[tex]RC-WC=RW[/tex]

[tex]RW=RC-WC[/tex]

Now we substitute the values of RC and WC into the equation

[tex]RW=126-72[/tex]

[tex]RW=54[/tex]

Answer:

39 meat patties

Step-by-step explanation:

Given,

The Big Burger recipe calls for 3 meat patties, 2 slices of cheese and 4 pickles,

That is, the ratio of meat patties, cheese and pickles in the recipe = 3 : 2 : 4

Let in a recipe,

Meat patties = 3x, Cheese = 2x, pickles = 4x

Where, x is a positive real number,

If there are 52 pickles,

⇒ 4x = 52 ⇒ x = 13

Hence, meat patties = 3 (13) = 39

Answer:

C. 1307 ft

Step-by-step explanation:

Given:

Angle = 48.4 degrees

Height, opposite side= 1472 feet

his distance from the Empire State Building, base=x

Now as per the trigonometric ratios:

Tan∅= Opposite/base

tan(48.4)= 1472/x

x=1472/(1.13)

x=1302.65

his distance from the Empire State Building is 1302.65 feet!

Answer:

The correct answer is option C.

Step-by-step explanation:

Height of Empire State Building = 1,472 feet

Angle formed by the line segment from the point of ground on which Dante is positioned to the top of the building is  48.4°.

Distance of Dante from the Empire State Building =?

In the fig ,ΔABC

AB = 1,472 feet, BC = ? , θ= 48.4°

[tex]\tan\theta =\frac{Perpendicular}{base}[/tex]

[tex]\tan 48.4^o=\frac{AB}{BC}[/tex]

[tex]BC=\frac{AB}{\tan 48.4^o}=\frac{1,472 feet}{1.1263}=1,306.9 feet\approx 1,307 feet[/tex]

Distance of Dante from the Empire State Building is 1,307 feet.

Answer:

For    [tex]x^x > 500,000[/tex]  [tex]x=7[/tex]

For  [tex]x^{(-x)} > 500,000[/tex]  [tex]x=-7[/tex]

Step-by-step explanation:

We need to find the smallest positive whole number that satisfies the inequality:

[tex]x^x > 500,000[/tex]

We tested with x = 6

[tex]6^6=46,656\\\\46,656 > 500,000[/tex]

Inequality is not met because  [tex]46,656 < 500,000[/tex]

We test with the following integer x = 7

Then we have that:

[tex]7^7=823,543\\\\823,543 > 500,000[/tex]

Then the smallest positive integer that will make  [tex]x^x > 500,000[/tex]  is 7 because Inequality is met.

In the same way the largest negative integer that will make  [tex]x^{(-x)} >500000[/tex] is [tex]x=-7[/tex] Beacuse   [tex]7^{-(-7)}=823,543>500,000[/tex]

Answer:

Smallest positive integer value for [tex]x^x>500000[/tex] is,

x = 7,

Largest negative integer value for [tex]x^{-x}>500000[/tex] is,

x = -8

Step-by-step explanation:

If [tex]x^x>500000[/tex]

By graphing calculator,

[tex]x>6.83[/tex]

Thus, the smallest possible positive integer value of x is 7,

Now,

[tex]x^{-x}>500000[/tex]

Possible negative integer values of x are -6, -7 and -8,

If x = -6, -7, and -8,

[tex](-6)^{6}=46656[/tex]

[tex](-7)^{7}=-823543[/tex]

[tex](-8)^{8}=16777216[/tex]

[tex]\because 16777216 > 500000[/tex]

Thus, the largest negative integer value of the inequality [tex]x^{-x}>500000[/tex] is,

x = -8.

[tex]34+3\cdot5=34+15=49[/tex]

Hope this helps.

r3t40

Answer:

[tex]\huge \boxed{49}\checkmark[/tex]

Step-by-step explanation:

Order of operations

PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

Do multiply first.

[tex]\displaystyle 34+3\times5[/tex]

[tex]\displaystyle 3\times5=15[/tex]

Add from left to right to find the answer.

[tex]\displaystyle 34+15=49[/tex]

[tex]\huge \boxed{49}[/tex], which is our answer.

Hope this helps!

Answer:

3

Step-by-step explanation:

3 is the greatest possible number of stops she made at traffic lights.

A distance-time graph suggests how the distance an item has traveled in a given time. it's far a simple line graph that denotes distance as opposed to time findings the graph. Distance is plotted on the Y-axis.

In a distance-time graph, the gradient of the line is equal to the velocity of the object. The more the gradient (and the steeper the road) the faster the object is transferring.

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Answer:

1) 95

2) -12

3) 7

4) 1,700

5) 57

6) 3,070

Answer:

3x - 5

Step-by-step explanation:

Perform the indicated multiplication.  We get:

7x - 14 - 4x + 9.

Combining like terms, we get 3x - 5

Answer:

B. A(w)=w∧2+4w

Step-by-step explanation:

Let the width of the rectangle be w.

The length is  4 feet longer than the width= w+4

Area of a rectangle= length× width

A=L×W

=(w+4)×w

Opening the brackets gives the:

A=w²+4w

Therefore the expression for the area in terms of width is A(w)=w∧2+4w

Answer:

4800 miles

Step-by-step explanation:

The probability that the number is formed greater than 600 is [tex]\frac{1}{2}[/tex].

Probability is the chance that something will happen, or how likely it is that an event will occur.

The formula for the probability is

[tex]P(E) = \frac{number \ of \ favorable \ outcomes }{Total\ number\ of\ outcomes}[/tex]

Where,

P(E) is the probability of any event.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

The formula for the permutation is given by

[tex]^{n} P_{r} = \frac{n!}{(n-r)!}[/tex]

Where,

[tex]^{n} P_{r}[/tex] is the permutation

n is the total number of objects

r is the total number of objects to be selected

According to the given question.

We have total four numbers 2, 4, 6, 7.

So,

The total number of three digits can be formed using these four numbers = [tex]^{4} P_{3}[/tex] = [tex]\frac{4!}{(4-3)!} =\frac{4\times 3\times 2\times 1}{1}[/tex][tex]=24[/tex]

Now, for making three digits number which are greater than 600 by using 2, 4, 6, 7 without repetition is given by

Number of ways for filling hundred place is 2 (either 6 or 7).

Number of ways for filling tens place is 3 (if 6 is placed at hundred place then remaining numbers are 7, 2, 4 and if 7 is place at hundred place then remaining numbers are 6, 2, 4).

Number of ways for filling one place is 2(because only 2 number are left).

Therefore, the total numbers of three digits can be formed by using these numbers 2, 4, 6, and 7

[tex]= 2\times 3\times 2\\=12[/tex]

So,

the probability that the number is formed greater than 600

= [tex]\frac{total\ three\ digits\ numbers\ which\ are \ formed \ by\ using\ 1,\ 2, \ 3, \ and\ 4\ which\ are\ greater\ than\ 600 }{Total \ three\ digits\ numbers\ formed\ by \ using \ 1,\ 2,\ 3,\ and \ 4}[/tex]

[tex]= \frac{12}{24}[/tex]

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

Therefore, the probability that the number is formed greater than 600 is [tex]\frac{1}{2}[/tex].

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Answer:

Step-by-step explanation:

The number of customers carrying cash=45% = 0.45

The number of customers carrying checks= 44% =0.44

The number of customers carrying both = 31% = 0.31

So,

To find the probability we will write the expression:

cash+checks-cash or checks(both)=cash and checks

0.45+0.44-both=0.31

0.45+0.44-0.31=both

0.58=both....

Answer:

<AED = 60

Step-by-step explanation:

Since triangle ADE is similar to triangle ABC

Angle ADE equals angle ADC

The angles of a triangle add to 180 degrees

<A + <ADE + <AED = 180

36 + 84+ <AED = 180

Combine like terms

120 + <AED = 180

Subtract 120 from each side

120-120 +<AED = 180-120

<AED = 60

Answer:

58°

Step-by-step explanation:

Since DE and BC are parallel, ADE will be equal to ABC.

So ADE is 84°.

And, the sum of the angles of a triangle is 180°. So AED will be equal to 180-(38 + 84),which is 58°

[Only if Angle A is 38°]

Answer:

110.5 units²

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = [tex]\frac{1}{2}[/tex] product of diagonals, that is

A = 0. 5 × MK × JL = 0.5 × 13 × 17 = 110.5

The area of the rhombus will be 110.5 square units.

The area of the rhombus can be calculated by half of the product of its two diagonals.

Here given,

JKLM is a rhombus.

The length of its diagonals will be MK=13

JL=17

The diagonal MK and JL intersect each other by 90° at point O.

Now the rhombus is divided by 4 right-angled triangle,

Area of the rhombus will be 4 times of the right-angled triangle ΔMJO

Area of the rhombus= 4*Area of right-angled triangle ΔMJO

=4*(1/2)*MO*JO

= 4*(1/2)*(MK/2)(JL/2)

=(1/2)*MK*JL

=(1/2)*the product of its two diagonals

=(1/2)*13*17

=110.5 Square unit

Therefore the area of the rhombus will be 110.5 square units.

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Answer:

The zeros are x=1, x=-6

Step-by-step explanation:

f(x) =x^2+5x-6

Factor:  What two numbers multiply to -6 and add to 5

-1 *6 = -6

-1 +6 = 5

f(x) = (x-1) (x+6)

Using the zero product property

0 = (x-1) (x+6)

  x-1 =0  x+6=0

x=1         x=-6

The zeros are x=1, x=-6

Answer:

A.  d = 0.75.

Step-by-step explanation:

The z-score =( x - m) / d  where m = the mean and d = the standard deviation.

So we have

(3 - m) / d = 1

3   -  m =  d.............(1)

and

(3.75 - m) / d = 2

3.75 - m = 2d....... (2)

Subtract (2) - (1):

0.75 = d.

Answer: A 0.75

Step-by-step explanation:

Formula for z-score :

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

, where x= random variable

[tex]\mu[/tex] = Population mean

[tex]\sigma[/tex] = Standard deviation

As per given , we have

[tex]+1=\dfrac{3-\mu}{\sigma}\\\\\Rightarrow\ \sigma=3-\mu\\\\\Rightarrow\ \mu=3-\sigma---(i)[/tex]

[tex]+2=\dfrac{3.75-\mu}{\sigma}\\\\\Rightarrow\ \mu=3.75-2\sigma---(ii)[/tex]

From (i) and (ii) , we have

[tex]3-\sigma=3.75-2\sigma\\\\\Rightarrow\ 2\sigma-\sigma=3.75-3\\\\\Rightarrow\ \sigma=0.75[/tex]

Hence, the standard deviation of the length of candy bars produced at Carl's Candies is 0.75.

Thus , the correct answer is A.  0.75.