The solutions of the equations -x² + 4x +3 = 0 are


A. (x = -3) and (x = -1)
B. (x = 1) and (x = 3)
C. (x = -2 -√7) and (x = -2 + √7)
D. (x = 2 -√7) and (x = 2 + √7)

can someone explain this pls​

Answer: 3 x minus 3 + 4 = 2 minus x minus 3

              3 x + 1 = negative x minus 1

Step-by-step explanation:

             A and D. Edge 2020

The required equation that Samuel used is 3x -3 + 4 =2- x -3. option A is correct.

Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use, is to be determined.

The equation is the relationship between variables and represented as[tex]y = ax +b[/tex]  is an example of a polynomial equation.

Given equation is [tex]3(x-1) +4 =2 -(x+3)[/tex]
Simplification of the above equation,
opening the parenthesis on both sides
step 1⇒ 3x - 3 + 4 = 2 - x - 3
step 2⇒ 3x + 1 = -x - 1
Transposition of -x to the left side and +1 to the right side
step 4 ⇒ 3x +x = -1 -1
                  4x = -2
Transposition of 4 to the denominator of -2.
step 5⇒ x = -2/4
               x = -1/2

Thus , Step 1 3x -3 + 4 =2- x -3 is the equivalent equation used by the samuel.

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Answer:

45

Step-by-step explanation:

10/4x3=7.5

8/4x3=6

6x7.5=45yards

Answer:

D

Step-by-step explanation:

the inscribed angle intersects an arc that twice the measure of the arc interested by the central angle. The inscribed angle's arc measures 144° and the central angle's arc measures 72°

>central angle and the arc the intersected arc are equal i.e they are both 72°

>the inscribed angle is half of the measure of the intersected arc i.e since the inscribed angle is 72° the arc interested is 144°

Answer:

[tex]\boxed{d = 54 yards}[/tex]

Step-by-step explanation:

Formula for diagonal is as follows:

[tex]d = \sqrt{l^2+w^2}[/tex]

Where d is diagonal, l is length (50 yards) and w is width (20 yards)

[tex]d = \sqrt{(50)^2+(20)^2}[/tex]

[tex]d = \sqrt{2500+400}[/tex]

[tex]d = \sqrt{2900}[/tex]

d = 53.85 yards

d ≈ 54 yards

Answer:

[tex]\boxed{\mathrm{54 \: yards}}[/tex]

Step-by-step explanation:

The shape of the pool is a rectangle.

The diagonal of a rectangle can be found through a formula by using Pythagorean theorem.

[tex]d^2=l^2 +w^2[/tex]

[tex]d=diagonal\\l=length\\w=width[/tex]

The length is given 50 yards, and width is given 20 yards. Find the diagonal.

[tex]d^2 =50^2 +20^2[/tex]

[tex]d^2 =2500+400[/tex]

[tex]d^2 =2900[/tex]

[tex]d=\sqrt{2900}[/tex]

[tex]d \approx 53.851648[/tex]

[tex]d \approx 54[/tex]

Answer:

(3, 13)

Step-by-step explanation:

The curve decreases from x = 3 to x = 13.

Answer: (3, 13)

Answer: 40/41

Step-by-step explanation:

The cosine can be represented as adjacent/hypotenuse.  Thus, the cosine of C is 40/41

Answer:

Solution,

BC = 40

AC = 41

Now,

[tex]cos \: theta \: = \frac{adjacent}{hypotenuse} [/tex]

[tex]cos \: c \: = \frac{bc}{ac} [/tex]

Plugging the values

[tex]cos \: c \: = \frac{40}{41} [/tex]

Hope this helps..

Good luck on your assignment..

Answer:

[tex]\boxed{\sf y=6}[/tex]

Step-by-step explanation:

There are 5 identical squares.

The area of one square is [tex]\sf s^2[/tex].

[tex]\sf{y^2 } \times \sf{5}[/tex]

[tex]\sf 5y^2[/tex]

The area of the whole shape is 180 cm².

[tex]\sf 5y^2=180[/tex]

Solve for y.

Divide both sides by 5.

[tex]\sf y^2=36[/tex]

Take the square root on both sides.

[tex]\sf y=6[/tex]

Answer:

Step-by-step explanation:

let the parabola be y=a(x+5)²+0

or y=a(x+5)²

∵ it passes through (-3,1)

1=a(-3+5)²

4a=1

a=1/4

so parabola is y=1/4(x+5)²

Answer:

14

Step-by-step explanation:

7x2=14

Answer:

(2, 2), (5, 3), (9, 4), and (13, 5).

Step-by-step explanation:

The inverse of a function makes it so that the x-values become y-values, and y-values become x-values.

The current coordinates are (2, 2), (3, 5), (4, 9), and (5, 13).

If the function were inversed, the coordinates would be (2, 2), (5, 3), (9, 4), and (13, 5).

Hope this helps!

Answer:

Step-by-step explanation:

Hello,

First of all, we know that the solution of the following equation

   [tex]ax^2+bx+c=0[/tex]

are

   [tex]\dfrac{-b\pm\sqrt{b^2-4ac}}{2a} \ \text{ when } \Delta=b^2-4ac \geq 0[/tex]

I would suggest that you try to apply this formula first and check the solution only after you try.

Let's apply it in this case, we have:

[tex]a=4\sqrt{5} \\ \\ b=-24 \\ \\ c= -9\sqrt{5}[/tex]

[tex]\Delta=b^2-4ac=24^2+4*9*5=1296 \\ \\ \sqrt{\Delta}=36 \ \text{ and the solutions are } \\ \\ \\ x_1=\dfrac{24-36}{8\sqrt{5}}=\dfrac{-12}{8\sqrt{5}}=\boxed{\dfrac{-3}{2\sqrt{5}}} \\ \\x_2=\dfrac{24+36}{8\sqrt{5}}=\dfrac{60}{8\sqrt{5}}=\boxed{\dfrac{15}{2\sqrt{5}}}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The cost C, of hosting the banquet with the services of Caterer One is;

C = $ 45·n

The cost C, of hosting the banquet with the services of Caterer Two is;

C = $250 +  $ 28·n

The cost C, of hosting the banquet with the services of Caterer Three is;

C = $500 +  $ 20·n

Step-by-step explanation:

The information includes;

The amount available to the group for the banquet = $120

The number of people attending the banquet = n

The cost incurred in hosting the banquet = C

The major costs in hosting the banquet are hall rental and caterer

The cost per caterer are as follows;

Caterer One

The cost per person including the hall = $45

Therefore, the cost incurred, C, in hosting the banquet using caterer one is equal;

C = n × $45 = $ 45·n

Caterer Two

The hall rental = $250

The cost per person = $28

Therefore, the cost incurred, C, in hosting the banquet using caterer two is equal;

C = $250 +  n × $28 = $250 +  $ 28·n

Caterer Three

The hall rental = $500

The cost per person = $20

Therefore, the cost incurred, C, in hosting the banquet using caterer three is equal;

C = $500 +  n × $20 = $500 +  $ 20·n.

Answer:

The cost C, of hosting the banquet with the services of Caterer One is;

C = $ 45·n

The cost C, of hosting the banquet with the services of Caterer Two is;

C = $250 +  $ 28·n

The cost C, of hosting the banquet with the services of Caterer Three is;

C = $500 +  $ 20·n

Step-by-step explanation:

The information includes;

The amount available to the group for the banquet = $120

The number of people attending the banquet = n

The cost incurred in hosting the banquet = C

The major costs in hosting the banquet are hall rental and caterer

The cost per caterer are as follows;

Caterer One

The cost per person including the hall = $45

Therefore, the cost incurred, C, in hosting the banquet using caterer one is equal;

C = n × $45 = $ 45·n

Caterer Two

The hall rental = $250

The cost per person = $28

Therefore, the cost incurred, C, in hosting the banquet using caterer two is equal;

C = $250 +  n × $28 = $250 +  $ 28·n

Caterer Three

The hall rental = $500

The cost per person = $20

Therefore, the cost incurred, C, in hosting the banquet using caterer three is equal;

C = $500 +  n × $20 = $500 +  $ 20·n.

Answer:

Step-by-step explanation:

 This problem brothers on selection without repetition, so we will be using permutation to solve this problem.

Given

n= 12 ,which is  the number we are choosing from

r= 3, which is the number of committee(president, vice-president, and​ secretary-treasurer.)

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

Substituting we have

[tex]= \frac{12!}{(12-3)!}\\\\ = \frac{12!}{(9)!}\\\\= \frac{12*11*10*9!}{9!}[/tex]

[tex]= 12*11*10= 1320[/tex]

Answer:

the numbers of cars pf various colors in a parking lot

Answer:  The speed of a car as it changes during a time.

B is the best example of continuous data.

Step-by-step explanation:  The contrast between the definitions of continuous data  vs. discreet data is that discrete data is counted, continuous data is measured.

A speedometer measures speed continuously, time is measured continuously.

Time can, however, be reported as discreet measurements in situations where that kind of data is needed. (not in this question)

A Number of cars is discreet.

Data from different workers or different days is not continuous.

Answer:

iii) 5.7

iv) 27.85

vii) 0.609

viii) 40.0709

Step-by-step explanation:

hope this helps

Answer:

x= 24, y= 33°

Step-by-step explanation:

MJ is part of the diameter of the circle and there is right angle between the diameter and HK

As the diameter and HK are perpendicular, HM=MK and mHJ= mJK

So,

and

Answer:

8(6-x)

Step-by-step explanation:

Both 48 and 8 can be divisible by 8.

48 ÷ 8 = 6

8 ÷ 8 = 1

Therefore you get the answer 8(6-x)

as the simplest form.

Hope this helps.

The 210 angles in the standard position are shown in figure (A) option (A) is correct.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that:

The measure of the angle:

= 210 degrees

The reference angle can be defined as the angle formed between the terminal side and the x-axis, known as the reference angle.

The angle between the x-axis and the y-axis is 90 degrees.

The angle between the y-axis and the negative x-axis is 90 degrees.

The angle between the negative x-axis and the arrow shown in the coordinate plane is 30 degrees.

Thus, the 210 angles in the standard position shown in figure (A) option (A) is correct.

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Answer:

7625597484987 ways

Step-by-step explanation:

Given the following :

Number of ball(k) = 9

Number of bins (n) = 27

How many different ways are there to distribute these 9 balls among the 27 bins.

Here, the balls have different labels (1 to 9)

The bins are also distinguishable, therefore each ball can go into any of the 27 distinct bins.

Therefore, the different ways are there to distribute these 9 balls among the 27 bins equals = n^k

27^9 = 7625597484987 ways.

Answer:

hello:

Step-by-step explanation:

If f(x) = -8x - 6 and g(x) = x+8 ,  (f • g) (- 7)= f(g(-7))

but g(-7)=-7+8=1

(f • g) (- 7)= f(1) =-8(1)-6 =-14

Answer:

1/5 or 20%

Step-by-step explanation:

This problem can be easily solved by finding the probability of her picking one matching pair to leave in the suitcase (which results in pulling out exactly two matching pairs)

For the first sock, it does not matter what sock she picks.

For the second sock, there is only 1 out of the 5 socks left that would match the first one picked. Therefore, the probability that she pulls out exactly two matching pairs is 1/5 or 20%

I hope this helps you

Answer:

950.33 ft³

Step-by-step explanation:

The volume of a cylinder is denoted by: V = πr²h, where r is the radius and h is the height.

Here, the radius is r = 5.5 ft and the height is h = 10 ft. Plug these into the formula:

V = πr²h

V = π * 5.5² * 10 ≈ 950.33 ft³

The answer is thus 950.33 ft³.

~ an aesthetics lover

Complete question :

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in:

a. More than 20 minutes? b. For 20 minutes or less

Answer: 0.0764 ; 0.9236

Step-by-step explanation:

Mean (m) = 15 minutes

Standard deviation (sd) = 3.5

Z - score :

Z = (x - m) / sd

A) more than 20 minutes

P(X > 20) ; x = 20

Z > (20 - 15) / 3.5 = 5/3.5 = 1.429

P(z > 1.429) = 0.5 - P(0<z<1.43)

Using the z-table: 1.43 = 0.4236

0.5 - 0.4236 = 0.0764

2) 20 minutes or less :

P(X <= 20) ; x = 20

Z < (20 - 15) / 3.5 = 5/3.5 = 1.429

P(z < 1.429) = 0.5 + P(0<z<1.43)

Using the z-table: 1.43 = 0.4236

0.5 + 0.4236 = 0.9236

Answer:

Rhombus.

Step-by-step explanation:

A rhombus is a  quadrilateral, meaning that it has four lateral sides. A Rhombus is a 2-dimensional shape, and has two lines of symmetry.  A Rhombus has a rotational symmetry of order two, and the opposite sides are parallel. Also, the opposite angles in Rhombus are equal. Th diagonals of a Rhombus bisect each other at a right angle.

Other quadrilateral shapes includes the Rectangle, Parallelogram, and the Kite.

Answer:

5

Step-by-step explanation:

(0.000064)^5/6 divided by (0.00032)^6/5

(0.00032)^6/5=(0.000064)

and

(0.000064)^6/5=(0.00032)

so now we have (0.00032) divided by (0.000064)

which is 5!

hope this helps!

Answer: yes

Step-by-step explanation: no

Answer:

Option (C).

Step-by-step explanation:

To check a graph whether it's a function or not we use a vertical line test. In this test first we draw a vertical line on the given graph. If this line intersects the graph at more than one point, the graph is not a function.

In the given parabola, opening upwards passes the vertical line test.

Therefore, this graph shows a function.

Option (C) will be the answer.

Option  (c) Yes; the graph passes the vertical line test. And

(d) Yes; there are no y-values that have more than one x-value are correct options. Hence, a given graph is a function.

This is a graph of [tex]y = x^2[/tex]

Which is a graph of parabola.

To determine the given graph is a function or not, we do a vertical line test.

The vertical line test says that if a vertical line intersects a graph more than once, then that graph is not a function. And in this case, y-values have more than one x-values.

Let’s draw a vertical line in the given graph  (attached below)

We see that the vertical line touches the graph only at once. That’s why it is a function, and so there are no y-values that have more than one x-value.

Hence, the given graph is a function and option (3) and (4) are correct options.

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Answer:

A

Step-by-step explanation:

We know that because the second plane flies 15 miles less, it has to be either A or B, because they have -15 at the end.

It cannot be B, because in B, the second plane has a -w in the equation. However, in the word problem, the second plane flies with the wind, not against it. Therefore, it must be A.