Which statements about quadrilaterals are true? Choose all answers that are correct. A. A square is always also a parallelogram. B. A parallelogram is always also a rectangle. C. A rhombus is always also a trapezoid. D. A rectangle is always also a parallelogram.

Solution: The correct option is second option, i.e., [tex]y=(x+4)^2-1[/tex].

Explanation:

The standard form of the parabola along the y-axis with vertex (h,k) is [tex]y=a(x-h)^2+k[/tex].

Since the turning point is given as [tex](-4,-1)[/tex].

Put these values in the standard form of the parabola.

[tex]y=a(x+(-4))^2+(-1)[/tex]

[tex]y=a(x+4)^2-1[/tex]       .....(1)

The parabola passes through the points (-5,0), (-3,0) and (0,15). It means each point will satisfy the above condition.

Put x = 0 and y = 15 in the equation (1).

[tex]15=a(0+4)^2-1\\16=4^2a\\16=16a\\a=1[/tex]

Put a = 1 in equation (1).

[tex]y=1(x+4)^2-1[/tex]

Therefore, the The correct option is second option, i.e., [tex]y=(x+4)^2-1[/tex].

There will be 1020 students in the school doing household chores for at least two hours every week.

A ratio is a comparison of two attributes of a similar kind.

Based on the random sample, the number of students doing household chores for at least two hours every week =64+3+1 =68

Out of 100, the number of students doing household chores for at least two hours every week = 68

So, out of 1, the number of students doing household chores for at least two hours every week = 68/100

So, out of 1500, the number of students doing household chores for at least two hours every week = (68/100)*1500 =1020

Thus, there will be 1020 students in the school doing household chores for at least two hours every week.

To get more about ratios visit:

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Answer:  Odd multiple of 3.

[tex]3,\ 9,\ 15,\ 21, \ 27, \ 33, \ 39,\ 45,...........[/tex]

Step-by-step explanation:

Given : The greatest common factor of a number n and 6 is 3.

Then, it is clear that n should be a multiple of 3.

Prime factorization of 6 :

[tex]6=2\times3[/tex]

So for n a even number then the greatest common factor will be 6.

Thus , the possible choice for n is a odd multiple of 3.

Hence, the possible whole-number values for n are :

[tex]3,\ 9,\ 15,\ 21, \ 27, \ 33, \ 39,\ 45,...........[/tex]

200 +6m = 500-6m

add 6m to each side

200+12m = 500

subtract 200 from each side

12m = 300

divide both sides by 12

m = 300/12 = 25

 25 minutes

 check:

200+ 25*6 = 200 +150 = 350

500 - 25*6 = 500-150 = 350

Answer: 58 %

Step-by-step explanation:

Let M represents the event of taking medicine, M' represents the event of not taking medicine and C represents the event of clearing skin,

Thus, according to the question,

n(M) = 55,

n(M') = 45,

n(M∩C) = 30,

n(M'∩C)= 22,

⇒ n(C) = n(M∩C) + n(M'∩C) = 30 + 22 = 52

Let S shows the total number of people,

⇒ n(S) = 100

Hence, the probability of cleared skin,

[tex]P(C)=\frac{n(C)}{n(S)}=\frac{52}{100}=0.52[/tex]

And, the probability of cleared skin of that people who took the medicines,

[tex]P(M\cap C)=\frac{n(M\cap C)}{n(S)}=\frac{30}{100}=0.3[/tex]

Thus, the probability that a patient chosen at random from this study took the medication, given that they reported clearer skin,

[tex]P(\frac{M}{C})=\frac{P(M\cap C)}{n(C)}=\frac{0.3}{0.52}=0.57692307692\approx 0.58 = 58\%[/tex]

Answer: 0.58

Step-by-step explanation:

Let A = Event that the patients received the acne medication.

B = Event that the patients did not receive the acne medication.

C = Patient reported  reported clearer skin.

Now,

[tex]P(A)=\dfrac{55}{100}=0.55\ \ ,P(B)=\dfrac{45}{100}=0.45[/tex]

[tex]P(C|A)=\dfrac{30}{55}\ \ , P(C|B)=\dfrac{22}{45}[/tex]

Using Bayes theorem, The probability that a patient chosen at random from this study took the medication, given that they reported clearer skin:

[tex]P(A|C)=\dfrac{P(A)\cdot P(C|A)}{P(A)\cdot P(C|A)+P(B)\cdot P(C|B)}\\\\=\dfrac{0.55\cdot\dfrac{30}{55}}{0.55\cdot\dfrac{30}{55}+0.45\cdot\dfrac{22}{45}}=0.576923076923\approx0.58[/tex]

Hence, the required probability : 0.58

Answer:

m² + 10m + 21

Step-by-step explanation:

(m + 3)(m + 7)

m(m + 7) + 3(m + 7)

m² + 7m + 3m + 21

m² + 10m + 21

Final answer:

The sum of 60 and 84 expressed as a product of their Greatest Common Factor is 144. You determine this by first finding the GCF, which is 12, and then adding the other factors (5 and 7) together and multiplying by the GCF.

Explanation:

To find the sum of the numbers 60 and 84 as a product of their Greatest Common Factor (GCF), you first need to calculate the GCF of the two numbers. The GCF of 60 and 84 is 12. You can divide each number by 12 to find the other factors, which are 5 for 60 and 7 for 84. Therefore, the sum of the numbers can be expressed as the product of their GCF and the sum of these other factors:

60 + 84 = (12 × 5) + (12 × 7)

GCF × (sum of other factors) = 12 × (5 + 7)

Now you can add the other factors:

5 + 7 = 12

Then multiply by the GCF:

12 × 12 = 144

So, the sum of the numbers expressed as a product of their GCF is 144.

2.085 x 10^6 =

 move the decimal 6 places to the right: 2,085,000

see attached picture for solution:

Final answer:

A bisector cuts a line segment or angle into two equal parts, while a perpendicular bisector not only does that but also intersects the line segment at a right angle.

Explanation:

In mathematics, a bisector is a line segment or line that divides an angle or segment into two equal parts. It cuts the angle or segment into two congruent angles or segments. For example, if you have a line segment AB and its bisector is a line segment CD, then CD divides AB into two congruent segments AC and CB.

A perpendicular bisector is a type of bisector that not only divides a line segment into two equal parts, but it also intersects the line segment at a right angle (90 degrees). So, in addition to being equidistant from the two endpoints of the line segment, the perpendicular bisector is perpendicular to the line segment as well.

Answer:

[tex](\frac{1}{2}, \frac{1}{2})[/tex]

Step-by-step explanation:

Since, the coordinates of the midpoint of a line segment having the endpoints [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex] are,

[tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

Here,

[tex]x_1=-2, y_1=2, x_2 = 3, y_2=-1[/tex]

Hence, the coordinates of the midpoint of segment AB are,

[tex](\frac{-2+3}{2},\frac{2-1}{2})[/tex]

[tex](\frac{1}{2}, \frac{1}{2})[/tex]