Solve the quadratic equation using the method indicated. See attached photo. Thanks in advance!

The group of restrictions used to simulate the issue includes

The issue includes the following information.

The following are the restrictions for modeling the issue: There is a maximum of a five-fold difference between the number of hours Savanah has booked and that John has.

Savanah will provide childcare for at least 40 hours, with no more than meaning it is not larger than that which suggests it is less than, Hence, y<5x

Meaning "at least 40 hours" is "at least 40 hours." 40 hours or more may be expressed as

y ≥ 40 hours

The two necessary restrictions are represented as y< 5x and y=> 40 hours in an inequality model.

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Step-by-step explanation:

a)

[tex]f(x+h) = 4(x+h)+4[/tex]

[tex]f(x+h)=4x+4h+4[/tex]

b)

[tex]f(x+h)-f(x)=4x+4h+4-(4x+4)[/tex]

[tex]f(x+h)-f(x)=4x+4h+4-4x-4[/tex]

[tex]f(x+h)-f(x)=4h[/tex]

c)

[tex]f(x+h)-f(x)h=4x+4h+4-h(4x+4)[/tex]

[tex]f(x+h)-f(x)h=4x+4h+4-4hx+4h[/tex]

[tex]f(x+h)-f(x)h=-4hx+8h+4x+4[/tex]

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

angle = 26 degress

complement angle = ?

Step 02:

26 + x = 90

x = 90 - 26

x = 64

The answer is:

The complement angle is 64 degrees

The result of the multiplication operation yields 7 7/12

From the question, we are to multiply the given fractions. The given fractions are

1 3/4 and 4 2/6

First, we will convert the fractions to improper fractions

Converting 1 3/4 to an improper fraction

1 3/4 = 7/4

Converting 4 2/6 to an improper fraction

4 2/6 = 26/6

Thus,

The multiplication operation becomes

7/4 × 26/6

= 7/4 × 13/3

= 91/12

= 7 7/12

Hence, the product of the given numbers is 7 1/12

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[tex](5x - 23) + (7x - 1) = 180 \\ 5x + 7x - 23 - 1 = 180 \\ 12x - 24 = 180 \\ 12x = 180 + 24 \\ 12x = 204 \\ \frac{12x}{12} = \frac{204}{12} \\ x = 17[/tex]

x=17°

Angles opposite to shorter sides are shorter. Then, the shortest angle is opposed to the shortest side.

Since the shortest side has a length 2.8 and is opposed to the angle A, then the shortes angle is A.

The next shortest side is that opposite to B, which has a length of 3.4.

And finally, the largest side has a length of 4.7 and it's opposite to the angle C.

Therefore, the list of angles from largest to smallest, is:

He must save 21 dollars per week to meet the goal.

Given,

Katie wants to save at least $280

He currently has $112 saved.

If he has 8 weeks left to save.

Solution:

The amount to be saved is $280 - $112 = $168

If he has 8 weeks left to save,

Per week he must save = $168/8

= $21

He must save 21 dollars per week to meet the goal.

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To find the x-intercepts of the function g(x), we must set it equal to 0 and solve for x.

We have the following:

we can use the quadratic formula to get the roots of the polynomial:

therefore, the x-intercepts of the function g(x) are the points (3/4,0) and (-1/4,0)

The values are as follows:

center:  y²/25-x²/25 = 1

transverse axis : b = 5

Vertices:  (0,5) and (0,-5)

Foci: (0,5√2) and (0,-5√2)

Asymptotes: y = x and y = -x

An asymptote is a line being approached by a curve but never touching the curve. i.e., an asymptote is a line to which the graph of a function converges. We usually do not need to draw asymptotes while graphing functions.

Types of Asymptotes:

1) Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k.

2) Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k.

3) Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b.

y² -x² =25 up down hyperbola with (h,k) = (0,0) a = 5 and b = 5

(y-k)²/a²-(x-h)²/b² = 1 is the standard equation of up-down hyperbola.

With semi-axis is a and semi-conjugate axis is b.

and centre (h,k).

Center = (y-0)²/5²-(y-0)²/5² = 1

= y²/25-x²/25 = 1

The axes are a = 5 and b = 5

transverse axis is b = 5

The foci are given by (h, k+c) and (h, k-c), where c = √a²+b²

c = √5²+5² = 5√2

therefore, the foci are (0,5√2) and (0,-5√2).

The vertices are (h, k+a) and (h, k-a)

(h,k) = (0,0) and a = 5 and b = 5

vertices are (0,5) and (0,-5)

Asymptotes are y = x and y = -x.

Therefore, the summary is as follows:

center:  y²/25-x²/25 = 1

transverse axis : b = 5

Vertices:  (0,5) and (0,-5)

Foci: (0,5√2) and (0,-5√2)

Asymptotes: y = x and y = -x

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Given:

v is the given vector.

To find:

Find the direction angle of v.

Formula to find the direction:

From the given vector x and y are:

The value of x coordinate be 0 or -2.

Given,

Vertex of the graph, f(x) = x² + 2x + 2

We have to find the x coordinate.

Here,

f(x) = x² + 2x + 2 is in the form of quadratic equation.

So, we can find x coordinate by using quadratic formula.

Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

Here,

a = 1, b = 2 and c = 2

So,

[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

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

= [tex]\frac{-2(+-)\sqrt{4-8} }{2}[/tex]

= (-2±(-√4)) ÷ 2

= (-2±(-2)) ÷ 2

Solve for.

-2 + (-2) / 2 = -2 -2 / 2 = -4/2 = -2

Solve for,

-2 - (-2) / 2 = -2 + 2 / 2 = 0

That is,

The value of x coordinate be 0 or -2.

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The parabolic equation that passes through the points is y = 29/7x^2 + -27/7x - 342/7

Parabolic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The given parameters are

x-intercepts (-3,0) and (4,0)

Point = (2,-40)

From the definition above, we have the form to be

y = ax^2 + bx + c

Substitute (-3,0) and (4,0)  in the above equation

So, we have

0 = a(-3)^2 + b(-3) + c

0 = a(4)^2 + b(4) + c

This gives

9a -3b + c = 0

16a + 4b + c = 0

Substitute (2,-40) in the above equation y = ax^2 + bx + c

a(2)^2 + b(2) + c = -40

So, we have

4a + 2b + c = -40

The equations become

9a -3b + c = 0

16a + 4b + c = 0

4a + 2b + c = -40

Using a graphing tool, we have

a = 29/7, b = -27/7 and c = -342/7

So, we have

y = ax^2 + bx + c

This gives

y = 29/7x^2 + -27/7x - 342/7

Hence, the equation is y = 29/7x^2 + -27/7x - 342/7

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Answer:

3:7

Step-by-step explanation:

Given:

To Find:

Formula used:

Using the formula, we have

No. of boys = 28 - 16 = 12

Proportion of boys = 12/28 = 3/7

So, proportion of boys = 3:7.

[tex] = x \times 2 + 15 \\ = 2x + 15[/tex]

DOUBLING IT MEANS MULTIPLYING IT BY 2

THEN ADD 15 AS SHOWN ABOVE.

HOPE THIS HELPS

A situation in which positive and negative numbers are used to describe values that have opposite meaning is that John is on top of a mountain that is 2000 above sea level and his friend is diving and is below 2000 feet.

The thing that 0 represents is the addition in the sea level.

Based on the information illustrated, the situation will be that John is on top of a mountain that is 2000 above sea level and his friend is diving and is below 2000 feet.

Therefore, the addition will be:

= 2000 + (-2000)

= 2000 - 2000

= 0

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Answer:

d) division property of =

Step-by-step explanation:

by step 3, the variable x is still being multiplied by 3. In order to isolate x, you must divide by 3 on both sides.

Answer:1,600

Step-by-step explanation:C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

you already have the answer :)

The slope of a line containing P1(3, 7) and P2(6, 9) is 2/3.

Slope, also called as gradient of a line is a value or number that describes both of the directions x and y. It basically tells the steepness of the line.

To find the slope of line, formula given below is used

[tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex] = slope

Here, y2 = 9

          y1 = 7

          x2 = 6

          x1 = 3

Thus, 9 - 7/6 - 3

= 2/3

Therefore, we can conclude that the  slope of a line containing P1(3, 7) and P2(6, 9) is 2/3.

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The distance between MO is 9.

From the question MP is straight line and O & N is points between M & P.

so the total length of line is 15

Need to find MO , To find  MO = MP - (NP - NO)

                                                   = 15 - (8 -2)

                                                  = 15 - 6 = 9

The MO is 9.

To find points in graph :

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The speed from City A to City B is 352 miles/hour.

Given:

Distance for trip = 1600 miles

Distance for return trip = 1600 miles

The round-trip took 8 h 20 min.

Total time taken for both trips = 8 hours 20 minutes = 8 + (1/3) hours = 25/3 hours

It is mentioned that on the return trip, the average speed was 20% faster than the outbound speed.

Let's assume x is the speed for an outbound trip.

So, x + 20% of x is the average speed of the return trip

x + 20% of x = x + 0.2x = 1.2x

Speed for the return trip = 1.2x

Total time = (distance/speed of outbound trip) + (distance/speed of return trip)

⇒ [tex]\frac{25}{3} =\frac{1600}{x} +\frac{1600}{1.2x}[/tex]

⇒ [tex]\frac{25x}{3} =\frac{1600*1.2 +1600}{1.2}[/tex]

⇒ [tex]10x = 3520[/tex]

⇒ [tex]x = 352[/tex]

Therefore, the speed from City A to City B is 352 miles/hour.

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Answer:

  C.  One solution

Step-by-step explanation:

You want to know the number of solutions of a system of equation such that the graph of the linear function touches the graph of the quadratic function at its minimum.

The number of real solutions of the system of equations is equal to the number of points of intersection of their graphs. The problem statement tells you the graphs intersect at one point, so there is one solution.

__

Additional comment

The linear function can only touch the minimum of a quadratic if its graph is a horizontal line.

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Answer:

t > -2/3

Step-by-step explanation:

−8>−3t−10

Step 1: Flip the equation.

−3t−10<−8

Step 2: Add 10 to both sides.

−3t−10+10<−8+10

−3t<2

Step 3: Divide both sides by -3.

−3t/−3 < 2/−3

t > −2/3

We are asked to find the simple interest associated with a principal of 5480 , an annual rate of 0.04 (4%) and at the end of 7 years:

We use the simple interest formula:

I = P r t

in our case: I = (5480) (0.04) (7) = 1534.4

So the interest is: 1534.40

We answer using two decimal places because this is refering to cents of a dollar.

Answer:

1/5,1/6,2/9,3/10

Step-by-step explanation:

hope it helps helps and have a nice day! :)

Using the probability concept, we have that:

a) The probability is of 0.244.

b) The probability is of 0.756.

c) A student given a $1 bill is more likely to have kept the money.

A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.

For item a, we have that out of 11 + 34 = 45 students who were given a $1 bill, 11 spent the money, hence the probability is given as follows:

p = 11/45 = 0.244.

For item b, we have that out of 11 + 34 = 45 students who were given a $1 bill, 34 kept the money, hence the probability is given as follows:

p = 34/45 = 0.756.

For item c, we have that a student given a $1 bill is more likely to have kept the money, as 0.756(kept) > 0.244(spent), which are the two probabilities we found in the previous items.

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Using proportions, it is found that due to the higher proportion of successful trials, Treatment A had the better success rate

A proportion is a fraction of a total amount, and hence it is represented by the sum of the desired amounts divided by the sum of the total amounts.

For Treatment A, we have that:

Hence the proportion of successful trials for Treatment A is given by:

315/357 = 0.8824.

For Treatment B, we have that:

Hence the proportion of successful trials for Treatment B is given by:

289/350 = 0.8257.

The proportion for Treatment A is higher, as 0.8824 > 0.8257, hence it had the better success rate.

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This necklace sold at auction for $11,379,600 in 2011. The percentage of the initial purchase price was represented by the auction price is 2.1%.

Given that,

For $54,000, an actor purchased a pearl, diamond, and ruby necklace for his well-known wife. This necklace sold at auction for $11,379,600 in 2011.

We have to find what percentage of the initial purchase price was represented by the auction price.

Let us take the percentage as x%.

Necklace sold at auction=the percentage multiplied by the actual price

We get,

$11,379,600 =x%($54,000)

x%=$11,379,600/$54,000

x%=2.1%

Therefore, the percentage of the initial purchase price was represented by the auction price is 2.1%.

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