Solve x2 - 4x - 7 = 0 by completing the square. What are the solutions?

Answer:

3 apples / 4 people

3/4

to check divide fractions

Multiply reciprocal

3/1 x 4/1

3/1 / 1/4 = 3/4

3/4 x 4 = 12/4 = 3 apples

3/4 is the answer

Hope this helps

Step-by-step explanation:

Answer:

3,360

Step-by-step explanation:

We calculate the number of permutations for this problem where the order in which we accommodate people matters to us as follows:

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

where n is the total number of options we have; the total number of members: [tex]n=16[/tex]

and r is the number of places or positions we are considering which in this case are the President position, the Vice president position and the treasurer position ⇒ 3 positions in total ⇒ [tex]r=3[/tex]

substituting n and r in the formula:

[tex]P=\frac{16!}{(16-3)!} \\\\P=\frac{16!}{13!} \\\\P=3,360[/tex]

A president, a Vice President, and a treasurer can be selected from the members in 3,360 ways

Answer:

five dollars and forty cents

5.40$

Step-by-step explanation:

90+6%= 95.40

Answer:

Step-by-step explanation:

The probability that a dentist recommend Colgate is;

P = 1/2 = 0.5

The probability that a dentist doesn't recommend Colgate is;

P' = 1 - P = 1 -0.5 = 0.5

Of 10 sample dentists, the probability that exactly 8 dentists recommend Colgate toothpaste is;

8 will recommend and two will not recommend it.

P(X) = P^8 × P'^2

P(X) = (0.5)^8 × (0.5)^2

P(X) = 0.0039 x 0.25

P(X) = 0.00098 = 0.098%

Answer: B

Step-by-step explanation:

For this problem, to solve for x, you want to move all like terms to one side.

[tex]\frac{1}{4}x-\frac{1}{2}x=\frac{7}{8} +\frac{1}{8}[/tex]

Now that you have moved like terms to one side, you can directly add and subtract to combine like terms.

[tex]-\frac{1}{4} x=1[/tex]

x=-4

Answer:

[tex]x = - 4[/tex]

Second answer is correct

Step-by-step explanation:

[tex] \frac{1}{4} x - \frac{1}{8} = \frac{7}{8} + \frac{1}{2} x \\ \frac{1}{4} x - \frac{1}{2} x = \frac{1}{8} + \frac{7}{8} \\ \frac{1x - 2x}{4} = \frac{8}{8} \\ - \frac{1}{4} x = 1 \\ - 1x = 1 \times 4 \\ - 1x = 4 \\ x = - 4[/tex]

hope this helps you

Answer:

a. 50 turns

b. 0.0114 A

c. 0.25 A, 10 V

Step-by-step explanation:

Given:-

- The required current ( Is ) = 0.5 A

- The required voltage ( Vs ) = 5 V

- Transformer is 100% efficient ( ideal )

- The number of turns in the primary coil, ( Np ) = 2200

- The Voltage generated by power station, ( Vp ) = 220 V

Find:-

a. The number of turns in the secondary coil of the transformer

b. The current supplied by the power station

c. The effect on output current and voltage when the number of turns of secondary coil are doubled.

Solution:-

- For ideal transformers that consists of a ferromagnetic core with two ends wounded by a conductive wire i.e primary and secondary.

- The power generated at the stations is sent to home via power lines and step-down before the enter our homes.

- A household receives a voltage of 220 V at one of it outlets. We are to charge a phone that requires 0.5 A and 5V for the process.

- The outlet and any electronic device is in junction with a smaller transformer.

- All transformers have two transformation ratios for current ( I ) and voltage ( V ) that is related to the ratio of number of turns in the primary and secondary.

                     Voltage Transformation = [tex]\frac{N_p}{N_s} = \frac{V_p}{V_s}[/tex]

Where,

                 Ns : The number of turns in secondary winding

- Plug in the values and evaluate ( Ns ):

                           [tex]N_s = N_p*\frac{V_s}{V_p} \\\\N_s = 2200*\frac{5}{220} \\\\N_s = 50[/tex]

Answer a: The number of turns in the secondary coil should be Ns = 50 turns.

- Similarly, the current transformation is related to the inverse relation to the number of turns in the respective coil.

                  Current Transformation = [tex]\frac{N_p}{N_s} = \frac{I_s}{I_p}[/tex]

Where,

                 Ip : The current in primary coil

- Plug in the values and evaluate ( Ip ):

                        [tex]I_p = \frac{N_s}{N_p}*I_s\\\\I_p = \frac{50}{2200}*0.5\\\\I_p = 0.0114[/tex]  

Answer b: The current in the primary coil should be Ip = 0.0114 Amp.

- The number of turns in the secondary coil are doubled . From the transformation ratios we know that that voltage is proportional to the number of turns in the respective coils. So if the turns in the secondary are doubled then the output voltage is also doubled ( assuming all other design parameters remains the same ). Hence, the output voltage is = 2*5V = 10 V

- Similary, current transformation ratio suggests that the current is inversely proportional to the number of turns in the respective coils. So if the turns in the secondary are doubled then the output current is half of the required ( assuming all other design parameters remains the same ). Hence, the output current is = 0.5*0.5 A = 0.25 A

Answer:

37 years difference.

Step-by-step explanation:

K = Kissi

k = Age of Kissi

E = Esinam

e = Age of Esinam

L = Lariba

l = Age of Lariba

k + e + l = 147

K : E

3 : 5 → (×3) → 12 : 15

E : L

3 : 5 → (×5) → 15 : 25

K : E : L

12 : 15 : 25

12 + 15 + 25 = 52

147/52 = 2.8269...

K is the young since out of the three part ratio, 12 is the smallest and likewise, L is the oldest.

k = 12 × 2.8269... = 33.923... → 34 y/o

e = 15 × 2.8269... = 42.40... → 42 y/o

l = 25 × 2.8269... = 70.673... → 71 y/o

∴ The difference between the youngest and oldest is:

71 - 34 = 37

Answer:

[tex]F=\frac{s^2_1}{s^2_2}=\frac{0.2^2}{0.126^2}=2.520[/tex]

Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_1 -1 =10-1=9[/tex] and for the denominator we have [tex]n_2 -1 =20-1=19[/tex] and the F statistic have 9 degrees of freedom for the numerator and 19 for the denominator. And the P value is given by:

Now we can calculate the p value with this probability:

[tex]p_v =P(F_{9,19}>2.520)=0.043[/tex]

Using a significance level of 5% we see that the p value is lower than this value and we have enough evidence to reject the null hypothesis and we can conclude that the variation for the new process is lower than the new one.

Step-by-step explanation:

Information given

[tex]n_1 = 10 [/tex] represent the sampe size old

[tex]n_2 =20[/tex] represent the sample size new

[tex]s_1 = 0.2[/tex] represent the sample deviation for old

[tex]s_2 = 0.126[/tex] represent the sample deviation for new

The statistic is given by:

[tex]F=\frac{s^2_1}{s^2_2}[/tex]

Hypothesis to test

We want to test if the new process is less variable than the old, so the system of hypothesis are:

H0: [tex] \sigma^2_1 \leq \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 >\sigma^2_2[/tex]

The statistic is given by:

[tex]F=\frac{s^2_1}{s^2_2}=\frac{0.2^2}{0.126^2}=2.520[/tex]

Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_1 -1 =10-1=9[/tex] and for the denominator we have [tex]n_2 -1 =20-1=19[/tex] and the F statistic have 9 degrees of freedom for the numerator and 19 for the denominator. And the P value is given by:

Now we can calculate the p value with this probability:

[tex]p_v =P(F_{9,19}>2.520)=0.043[/tex]

Using a significance level of 5% we see that the p value is lower than this value and we have enough evidence to reject the null hypothesis and we can conclude that the variation for the new process is lower than the new one.

Answer:

4 hours.

Step-by-step explanation:

Well we can simply divide 32 by 8 and we get 4 hours:

32 miles ÷ 8 miles = 4 hours

It takes the cyclist 4 hours.

Answer:

  4 hours

Step-by-step explanation:

As every speed limit sign tells you, ...

  speed = miles/hours

Solving for time and using generic distance units, we get ...

  time = distance/speed

Filling in the given values, we have ...

  time = 32 km/(8 km/h) = (32/8) h = 4 h

It takes the cyclist 4 hours to travel 32 km.

Answer:

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Step-by-step explanation:

.....

Answer:

400

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Answer:

The diameter of the smallest circular opening through which the box will fit  is 5.7 cm to the nearest tenth

Step-by-step explanation:

The dimensions of the rectangle are :

height: 4 cm

length: 10 cm

breadth: 4 cm

The diameter of the smallest circular opening through which the box will fit will be equals to the diagonal of a face of the rectangular box.

The face we will try to fit in first will determine the diagonal that we will calculate.

Let us try to fit in the right side of the rectangular box. The face we will have at that side is a square of 4 cm by 4 cm which is formed by the height and the width of the box.

We can calculate the diagonal using Pythagoras Theorem:

diagonal = [tex]\sqrt{height^{2}+ breadth^{2}}= \sqrt{4^{2}+4^{2}}=5.657 \approx 5.7cm[/tex] to the nearest tenth

Answer:

The number of days the cat food will last is 8 days.

Step-by-step explanation:

In this case, it it provided that Grandmother bought enough cat food for her four cats to last for 12 days.

Assume that each cat consumes x portions of food each day.

Then the four cats will consume, 4x portions of food each day.

Then in 12 days the amount of food consumed by the 4 cats will be:

Total amount of cat food = 12 × 4x

                                          = 48x.

Now, it is provided that she on her way home she brought back two stray cats.

Then the six cats will consume, 6x portions of food each day.

Compute the number of days the cat food will last as follows:

[tex]\text{Number of days the cat food will last}=\frac{\text{Total amount of cat food}}{\text{Amount of food consumed each day}}[/tex]

                                                           [tex]=\frac{48x}{6x}\\\\=\frac{48}{6}\\\\=8[/tex]

Thus, the number of days the cat food will last is 8 days.

Given:

2x -3 > 11 -5x

Simplify both sides:

2x - 3 > -5x + 11

Add 5x to both sides:

2x - 3 +5x > -5x + 11 +5

7x - 3 > 11

Add 3 to both sides:

7x - 3 +3 > 11 + 3

7x > 14

Divided 7 to both sides:

[tex]\frac{7x}{7}[/tex] > [tex]\frac{14}{7}[/tex]

x > 2

Answer:

Any number greater than 2 would be the answer. In Edg, choose 4! Choosing 2 would be incorrect in their system.

Step-by-step explanation:

Answer:

5 / (x+4)      x ≠2 x≠-4

Step-by-step explanation:

5(x-2)/(x-2)(x+4)

The denominator cannot be zero so x ≠2 x≠-4

Cancel like terms in the numerator and denominator

5 / (x+4)      x ≠2 x≠-4

Answer:

This can be written as d + 16 because plus means addition.

Answer:

10 successful throws

Step-by-step explanation:

40 free throws

25% (25)

40 x 0.25 = 10

Answer: a) S'(1) = 136; S'(2) = 104; S'(4) = 76;

b) S''(1) = -38; S''(2) = -26; S''(4) = -2

Step-by-step explanation:

a) S' means first derivative;

[tex]\frac{d}{dt}[/tex](6t³ - 45t² +180t +130) = 6t² - 50t + 180

S'(1) = 6.1² - 50.1 + 180

S'(1) = 136

S'(2) = 6.2² - 50.2 + 180

S'(2) = 104

S'(4) = 6.4² - 50.4 + 180

S'(4) = 76

b) S'' is the second derivative of S:

[tex]\frac{d^2}{dt^2}[/tex](6t² - 50t + 180) = 12t - 50

S''(1) = 12.1 - 50

S''(1) = -38

S''(2) = 12.2 - 50

S"(2) = -26

S"(4) = 12.6 - 50

S"(4) = -2

c) Derivative is the rate of change of a function. The first derivative is the slope of the tangent line to the graph if the function in a determined point, while the second derivative measures how the rate of change is changing.

Analysing the values, we can conclude that the sales of the product after t months is decreasing at a rate of 12.

Answer:

A. x-1 and x-5

Step-by-step explanation:

zeros are 1 and 5

so the factors are:

x-1 and x-5

Option A is correct

Answer:

the line just goes straight up the y-axis. so, place your dot at -3 and draw the line straight up

Step-by-step explanation:

The line is shifted downward by 3 units from the x-axis, and the slope of the line is zero. The intercept of the line is at (0, -3).

The collection of all coordinates in the planar of the format [x, f(x)] that make up a variable function's graph.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The equation of the line is given below.

y = –3

The line y = –3 is parallel to the x-axis.

The slope of the line is zero.

The line is shifted downward by 3 units from the x-axis.

The intercept of the line is at (0, -3).

The graph of the line y = –3 is given below.

More about the graph of the function link is given below.

https://brainly.com/question/9834848

#SPJ2

Answer:

After 121 passes, there will be 11 cups facing up

Step-by-step explanation:

Given that:

Peter initially  lines up 121 cups facing down in a straight line from left to right and consecutively labels them from 1 to 121.

We can have an inequality ; i.e 1 ≤ n ≤  121; if n represents the divisor including n itself for which n  = odd number. Thus at the end of this claim, the cup will be facing up.

On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.)

For each divisor on the ith pass of n;

[tex]i \ th \ pass \ = \ n \ \to \ p |n[/tex]  since we are dealing with possibility of having an odds number:

Thus; [tex]p =i[/tex] and [tex]i^2 = n[/tex]  where ; n = perfect square.

Thus ; we will realize that between 1 to 121 ; there exist 11 perfect squares. Therefore; as a result of that ; 11 cups will definitely be facing up after 121 passes

Answer: scalene and right

Step-by-step explanation:

Answer:

20 total

Shelves 3 shelves /20 total=0.15=15%

Signs 2/20=0.10=10%

Benches 6/20=0.30=30%

Tablet Holders 9/20=0.45=45%

Step-by-step explanation:

Answer:

Shelves: 15%

Signs: 10%

Benches: 30%

Tablet Holders: 45%

Step-by-step explanation:

Shelves: [tex]\frac{3}{3+2+6+9} =\frac{3}{20} =\frac{15}{100} =[/tex] 15%

Signs: [tex]\frac{2}{3+2+6+9} =\frac{2}{20} =\frac{10}{100} =[/tex] 10%

Benches: [tex]\frac{6}{3+2+6+9} =\frac{6}{20} =\frac{30}{100}=[/tex] 30%

Tablet Holders: [tex]\frac{9}{3+2+6+9} =\frac{9}{20} =\frac{45}{100} =[/tex] 45%

Step-by-step explanation:

-8x + 4 > 5 - 3x

-8x + 3x > 5 - 4

-5x > 1

x > 1 / - 5

Answer: 4/3

Step-by-step explanation:

As you know this graph is a lemniscate

[tex]4\int\limits^1_0 {x\sqrt{1-x^{2} } \, dx =\frac{4}{3} =1.33$[/tex]

Answer:

-3 =n

Step-by-step explanation:

11(n – 1) + 35 = 3n

Distribute

11n -11 +35 = 3n

Combine like terms

11n +24 = 3n

Subtract 11n from each side

11n +24 -11n = 3n -11n

24 = -8n

Divide each side by -8

24/-8 = -8n/-8

-3 =n

Answer: n=-3

Step-by-step explanation:

11n-11+35=3n

24=-8n

n=-3

Answer:

Step-by-step explanation:

factor out the numerator and demoninator

(m-2)(m-1)/m(m-1)

= (m-2)/m

Answer:

Sample space: [tex]\Omega=\{1,2,3,4,5,6\}[/tex]

Event of rolling the number 1 3, or 4 : A={1,3,4}

Step-by-step explanation:

When you roll a number cube with faces labeled from 1 to 6 once.

The possible outcomes are: 1,2,3,4,5 or 6.

Therefore, the sample space of this event is:

Given the event of rolling the numbers 1, 3, or 4.

Now we are required to give the outcomes for the event of rolling number 1,3 or 4.  Let's call the event A. The set of possible outcomes for A has all the numbers 1, 3 and 4 as follows

Answer:

D. G(x) = |x| + 7

Step-by-step explanation:

→For the function G(x) to shift upwards, there needs to be a number being added to the whole function.

→The answer isn't "A," because the 1 is being subtracted, making it shift downwards 1 unit, not upwards.

→The answer isn't "B," because adding the 2 there would cause the function to shift to the left for 2 units, not upwards.

→The answer isn't "C," because 10 is being multiplied, which would cause the function to narrow, and not shift upwards.

This means the correct answer is "D," because the 7 is being added, making the function shift upwards 7 units.

Answer:

A = 19.6 ft²

Step-by-step explanation:

A = πr²            Use this equation to find the area of the circle

A = π(2.5)²      Multiply

A = π(6.25)     Multiply

A = 19.6 ft²