Solve x 2 - 4x - 7 = 0 by completing the square. What are the solutions?

Answer:

The amount of rainfall increases as an exponential function of time.

Step-by-step explanation:

Answer:

C ;
Here is the picture if the letter changes! Sorry, it was hard to screenshot proof!

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EDGE2023; Good Luck :3!!

Answer:

$3.52 or $3.53

Step-by-step explanation:

We know that he is paying $2.35 per pound, and that he is buying 1.5 pounds worth of pears. Simply multiply 2.35 times 1.5 to get your answer, depending on how far you round, which is 3.52 or 3.53.

1 pound = $2.35

Leo bought 1 pound and 0.5 of a pound (half of a pound). To find how much 0.5 of a pound costs divide 2.35 (the cost of one full pound) by two

2.35 ÷ 2 = 1.18

so...

1 + 0.5 = 1.5

and

2.35 + 1.18 = 3.53

Leo spent $3.53 on 1.5 pounds of pears

Hope this helped!

~Just a girl in love with Shawn Mendes

ANSWER

A,B, and C

EXPLANATION

If

[tex]f(g(x))=g(f(x))=x[/tex]

then f and g are inverse functions.

A.

[tex]f(x) = \frac{x + 1}{6} [/tex]

[tex]g(x) = 6x - 1[/tex]

[tex]f(g(x)) = \frac{6x - 1 + 1}{6} = \frac{6x}{6} = x[/tex]

B.

[tex]f(x) = \frac{x - 4}{19} [/tex]

[tex]g(x) = 19x + 4[/tex]

[tex]f(g(x)) = \frac{19x + 4 - 4}{19} = \frac{19x}{19} = x[/tex]

C.

[tex]f(x) = {x}^{5} [/tex]

[tex]g(x) = \sqrt[5]{x} [/tex]

[tex]f(g(x)) = (\sqrt[5]{x})^{5} = x[/tex]

D.

[tex]f(x) = \frac{x}{x + 20 } [/tex]

[tex]g(x) = \frac{20x}{x - 1} [/tex]

[tex]f(g(x)) = \frac{ \frac{20x}{x - 1} }{ \frac{20x}{x - 1} + 20} = \frac{20x}{40x - 20} = \frac{x}{2x - 1} [/tex]

The correct answers are A, B , C

Answer:

Option C) similar; SSS similarity; ΔABC

Step-by-step explanation:

we know that

The SSS similarity state : If the corresponding sides of two triangles are proportional, then the two triangles are similar

In this problem

80/30=56/21=72/27

2.67=2.67=2.67 -----> is true

therefore

The triangles STU and ABC are similar by SSS similarity

Answer:  The correct option is

(C)  similar; SSS similarity; ΔABC.

Step-by-step explanation:  We are given to check whether the pair of triangles in the figure are similar to each other or not.

If so, we are to complete the similarity statement.

From the figure, we note that

the lengths of the sides of triangle STU are

ST = 72, TU = 80 and SU = 56.

And, the lengths of the sides of triangle ABC are

AB = 27, BC = 30 and AC = 21.

So, we get

[tex]\dfrac{ST}{AB}=\dfrac{72}{27}=\dfrac{8}{3},\\\\\\\dfrac{TU}{BC}=\dfrac{80}{30}=\dfrac{8}{3},\\\\\\\dfrac{SU}{AC}=\dfrac{56}{21}=\dfrac{8}{3}.[/tex]

That is,

[tex]\dfrac{ST}{AB}=\dfrac{TU}{BC}=\dfrac{SU}{AC}=\dfrac{8}{3}.[/tex]

Therefore, the corresponding sides of the two triangles are proportional.

Hence, triangle ABC and STU are similar by SSS similarity.

Option (C) is CORRECT.  

They had 54 twos and 62 threes.

54 + 62 = 116 outcomes of either 2 or 3

The probability is the number of outcomes divided by the total number of rolls.

116 / 360 = 0.32

The answer is A.

Answer:

0.32.

Step-by-step explanation:

Prob(Rolling a 2) = number of 2's rolled / total number of rolls

=  54/360 = 0.15

Similarly Prob(rolling a 3) =  62/360 = 0.17.

So the probability of a 2 or a 3 = 0.15 + 0.17 = 0.32.

Answer:

Jameel is 13 and Laitfa is 13 x 2 - 10 = 16

16 + 13 = 29

Step-by-step explanation:

The equation has already been given to us, so we just have to solve it.

According to the question,

L + J = 29

L = 2J - 10

  L

2J - 10  +  J = 29

add 10 both sides

2J + J = 29 + 10 = 39

3J = 39

J = 39/3 = 13

Done!

Answer:

  (-5, -8)

Step-by-step explanation:

The expression can be divided by 2 to give ...

  x² +13x +40

The solutions to this will have a product of 40 and a sum of -13, the opposite of the x-coefficient. All of the offered choices have a product of 40, but only (-5, -8) has a sum of -13.

Answer:

3

Step-by-step explanation:

The number of dogs are 3 if the ratio of dogs to cats at the pet store's 1:3. If there are 6 more cats than Dogs.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

The ratio of dogs to cats at the pet stores is:

1:3

Let's suppose there are x dogs, then cats are 3x

3x = x + 6

2x = 6

x = 3

Thus, the number of dogs are 3 if the ratio of dogs to cats at the pet store's 1:3. If there are 6 more cats than Dogs.

Learn more about the ratio here:

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Answer:

  (B) isosceles

Step-by-step explanation:

An isosceles triangle is one that has two sides of equal length.

___

If the distance between the legs were the same as the leg length, then the triangle would be equilateral. There is nothing in the problem statement suggesting this is the case.

Answer:

Simplify 23x

.

Tap for more steps...

2x3−12=13+56x

Simplify 56x

Step-by-step explanation:

For this case we must solve the following equation:

[tex]\frac {2} {3} x- \frac {1} {2} = \frac {1} {3} + \frac {5} {6} x[/tex]

Subtract [tex]\frac {5} {6} x[/tex] on both sides of the equation:

[tex]\frac {2} {3} x- \frac {5} {6} x- \frac {1} {2} = \frac {1} {3}[/tex]

We add [tex]\frac {1} {2}[/tex] to both sides of the equation:

[tex]\frac {2} {3} x- \frac {5} {6} x = \frac {1} {3} + \frac {1} {2}\\\frac {12-15} {18} x = \frac {2 + 3} {6}\\\frac {-3} {18} x = \frac {5} {6}\\- \frac {1} {6} x = \frac {5} {6}\\[/tex]

We multiply by 6 on both sides of the equation:

[tex]-x = 5[/tex]

We multiply by -1 on both sides of the equation:

[tex]x = -5[/tex]

Answer:

[tex]x = -5[/tex]

Answer:it is 2 since it include3s all possible answers for both heads & tails.

Step-by-step explanation:

you can get a H1-4 & a T1-4 since you have 4 parts one the spinner & 2 things on a coin (Heads & tails) you can just times 4*2 & know that you have 8 possible answers.

Answer:

H-1 H-2 H-3 H-4, T-1 T-2 T-3 T-4

Answer:

yes

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 3, 2), so

(x + 3)² + (y - 2)² = r²

r is the distance from the centre to a point on the circle

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (- 2, 9)

r = [tex]\sqrt{(-2+3)^2+(9-2)^2}[/tex] = [tex]\sqrt{1^2+7^2}[/tex] = [tex]\sqrt{50}[/tex], hence

(x + 3)² + (y - 2)² = 50 ← equation of circle

Substitute (- 10, 3) into the left side of the equation and if equal to the right side then the point lies on the circle

(- 10, 3) : (- 10 + 3)² + (3 - 2)² = (- 7)² + 1² = 49 + 1 = 50

Hence (- 10, 3) lies on the circle

1, 3, 5

You can tell by looking that her science mean is greater than her math mean.

The higher range number means that her scores in math are more varied and spread out than her science scores.

You can tell by looking that the median scores are the same.

Answer:

A, C, E

Step-by-step explanation:

Answer:

b = ±3

Step-by-step explanation:

4b^2-45=-9

Add 45 to each side

4b^2-45+45=-9+45

4b^2 = 36

Divide by 4

4b^2 = 36/4

b^2 =9

Take the square root of each side

sqrt(b^2) = sqrt(9)

b = ±3

Answer:

(y + 1)

Step-by-step explanation:

Given

5y² + 4y - 1

To factorise the quadratic

Consider the factors of the product of the coefficient of the y² term and the constant term which sum to give the coefficient of the y- term

product = 5 × - 1 = - 5 and sum = + 4

The factors are + 5 and - 1

Use the factors to split the y- term

5y² + 5y - y - 1 ( factor the first/second and third/fourth terms )

= 5y(y + 1) - 1(y + 1) ← factor out (y + 1) from each term

= (y + 1)(5y - 1)

Answer:

The child has 6 dimes and 5 quarters.

Step-by-step explanation:

Let q and d represent the number of quarters and of dimes respectively.

Then q + d = 11 (Equation A), and ($0.25/quarter)q + ($0.10/dime)d = $1.85 (Equation B).

Multiply the 2nd equation by 100 to remove the decimal fractions:

25q + 10d = 185 (Equation C)

Now multiply the 1st equation by -10 to obtain -10q - 10d = -110 (Equation D), and combine this result with Equation C:

-10q - 10d = -110

25q + 10d = 185

--------------------------

15q         = 75, and so q = 75/15 = 5.

According to Equation A, q + d = 11.  Replacing q with 5, we get:

5 + d = 11, and so d = 6.

The child has 6 dimes and 5 quarters.

Answer:

B. 34

Step-by-step explanation:

Perimeter= 42+42+x+x

First add the 42 together

42+42 =  84

Then subtract the number away because this was added to the total

152 - 84 = 68

68 is not your missing number

Dividing 68 by 2 which gives you 34

So,

Perimeter = 42+42+34+34 = 152

Answer:

40

Step-by-step explanation:

Just look up the conversion factor and set up the proportion.

1 dm = 1/10 th of a meter

x dm = 4 meters.                  Cross multiply.

1 dm * 4m = x * 1/10 of a meter. Change 1/10 to a decimal.

1 dm * 4 m = x * 0.1 m                  Divide by 0.1

1 dm * 4 m /0.1 m = x

x = 40 dm

Answer:

8

Step-by-step explanation:

13 - 0.75 (12) + 8 (0.5)

13 - 0.75 (12) + 4

13 - 9 + 4

4 + 4

8

Answer:

8

Step-by-step explanation:

Answer:

x=11, y=8/3

Step-by-step explanation:

Consider quadrilateral LMNO. If this quadrilateral MUST BE a parallelogram, then

LM=NO

and

LO=MN

Thus,

[tex]\left\{\begin{array}{l}4x+4=5x-7\\ \\x-7=3y-4\end{array}\right.[/tex]

Solve this system of two equations. From the first equation:

[tex]4x-5x=-7-4\\ \\-x=-11\\ \\x=11[/tex]

Substitute it into the second equation:

[tex]11-7=3y-4\\ \\3y-4=4\\ \\3y=4+4\\ \\3y=8\\ \\y=\dfrac{8}{3}[/tex]

ANSWER

Yes, f is a function.

EXPLANATION

The domain of the relation is D = {xlx is a state in the United States}

The rule is that f(x) ="the state capital"

The relation will be a function if and only if no two elements in the first set have the same image in the second set.

Since no two states will have the same capital, the relation is a function.

Answer:

The area of the base is [tex]10\pi m^2[/tex]

Step-by-step explanation:

The volume of a cylinder is calculated using the formula:

[tex]Volume=\pi r^2h[/tex]

The volume is given to be:

[tex]V=140\pi m^3[/tex]

The height of the cylinder is h=14 meters.

We substitute these values into the formula to obtain;

[tex]140\pi=\pi r^2\times 14[/tex]

Divide both sides by 14.

[tex]\frac{140\pi}{14}=\pi r^2[/tex]

[tex]10\pi=\pi r^2[/tex]

The area of the base is a circle which is [tex]\pi r^2=10\pi m^2[/tex]

Answer:

y = 6x + 28

Step-by-step explanation:

We are to determine the equation of a line whose slope or gradient is 6 and passes through the point (-4, 4)

The slope-intercept form of the equation of the straight line would be given by;

y = mx + c

y = 6x + c

We proceed to use the given point to determine c;'

when x = -4, y = 4

4 = 6(-4) + c

4 = -24 + c

c = 28

The slope-intercept form of the equation of the straight line is thus;

y = 6x + 28

For this case we have that by definicon, the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

They tell us that the slope is 6, then:

[tex]y = 6x + b[/tex]

We substitute the given point, to find the cut point:

[tex]4 = 6 (-4) + b\\4 = -24 + b\\b = 4 + 24\\b = 28[/tex]

Finally:

[tex]y = 6x + 28[/tex]

Answer:

Option D

Answer:

2) 33

Explanation:

First, identify x.

3x+1=17

3x=16

X=16/3

Then substitute x in the expression.

6x+1=?

6(16/3)+1=?

32+1=?

33=?

So, the answer is #2.

When the equation 3x + 1 equals 17, the value of x is 16/3. Substituting this value of x into the expression 6x + 1 results in an answer of 33.

The subject of the question is Mathematics and it appears to be at a High School level. Given the equation 3x + 1 = 17, we can first solve for x by subtracting 1 from both sides resulting in 3x = 16 and then dividing both sides by 3 which gives x = 16/3. Then we can substitute this value of x in the expression 6x + 1 giving us 6*(16/3) + 1 which simplifies to 32 + 1 = 33. So, the value of the expression 6x + 1 is 33 when the value of the expression 3x + 1 is 17.

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Answer:

-6718464

Step-by-step explanation:

-4x-6=24

24x-6=-144

and keep on doing times -6 6 more times

Answer: The sum is 25220

Step-by-step explanation:

1) -4

2) -4*-6 =24

3) 24*6 = 144

4) 114*-6 = -864

5) -864*6 = -5184

6) -5184*-6= 31104

The sum is: 25220

given,

height of triangle(h)=3.5 in.

base of triangle (b)=4 in.

length of side of triangle(s)= 4 in.

length of prism(l)=9 in.

we have,

surface area of traingular prism( A)=bh+2ls+lb

=4×3.5+2×9×4+9×4

=14+72+36

=122 square inches

Answer:

They're right

Step-by-step explanation:

Answer: 0.66 hours per mile

Step-by-step explanation:

You know that in 4 hours Addison walked 6 miles.

Now, you need to calculate the amount of hours she walked in 1 mile.

 Let be "x" the amount of hours she walked in 1 mile.

Then, to calculate the value of "x" you need to multiply 1 mile by 4 hours and divide by 6 miles:

[tex]x=\frac{(1mile)(4hours)}{6miles}\\\\x=\frac{2}{3}\ hours[/tex]

[tex]x[/tex]≈[tex]0.66\ hours[/tex]

Therefore, her walking rate in hours per mile was:

0.66 hours per mile

To solve the problem, we need to find the area of the triangle, and then find 2/3 of that triangle.

The equation to find the area of a triangle is bh1/2 or base*height*1/2.

Now substitute the known values.

24*16*1/2

Solve

24*8

192.

Now, the easiest way to find 2/3 of a number is to divide that number by 3 and multiply the answer by 2.

192/3=64

64*2=128

Omar kept 128 square centimeters of the flag.

Hope this helps!

[tex] \frac{16 \times 24}{2} = \frac{384}{2} = 192[/tex]

192 is the total area of the triangle; since he kept 2/3 of the flag divide the area by three and times it by two:

[tex]192 \div 3 = 64 \times 2 = 128[/tex]

answer is 128cm^2

Answer:

it measures spread around the mean. Because of its close links with the mean, standard deviation can be greatly affected if the mean gives a poor measure of central tendency. Standard deviation is also influenced by outliers one value could contribute largely to the results of the standard deviation.

Step-by-step explanation:

Answer with explanation:

Mean of a data set is defined as sum of all the observation divided by total number of observation.

For, example

Consider the Data set,the cost of five pens,={3,5,8,10,14}

Mean

      [tex]=\frac{3+5+8+10+14}{5}\\\\=\frac{40}{5}\\\\=8[/tex]

Now, Two pens having cost $ 47 and $ 53 is included in the Data set

New data set of Seven pens,={3,5,8,10,14,47,53}

   Mean

      [tex]=\frac{3+5+8+10+14+47+53}{7}\\\\=\frac{140}{7}\\\\=20[/tex]

So, you can see there is variation or Difference between two means.

We can conclude from above two results ,that mean is affected by outlier.

$10.50 a $1.25 is $9.75 then you do $800 / $9.75 which is 82.05 so we round up with any decimal and he would need to sell 83 pies to start making a profit.