Answer:
18w+8
Step-by-step explanation:
[tex]2(4 + 9w) \\ = 2(4) + 2(9w) \\ 8 + 18w \\ = 18w + 8[/tex]
Answer:
8+18w [tex]\huge\checkmark[/tex]
Step-by-step explanation:
Hi! Hope you are having an amazing day! :)
Distribute 2 by multiplying everything inside the parentheses by 2:
[tex]\huge\mathrm{2(4+9w)}[/tex]
[tex]\huge\mathrm{8+18w}[/tex] (Answer)
Hope you find it helpful.
Feel free to ask if you have any doubts.
[tex]\bf{-MistySparkles^**^*}\star[/tex]
the 15 chihuahua puppies ate 63 cups of food last week if each puppy ate the same amount of food how many cups of puppy food did each puppy eat
Answer:4.2 cups
Step-by-step explanation:
Just do 63 cups, divided by the 15 puppies which equals 4.2 cups! pls mark brainliest
Answer:
4.2 cups
Step-by-step explanation:
I am in the assiment and i just got it right on the assiment
This figure shows how to create a six-pointed star from twelve equilateral triangle tiles: [asy]
size(7cm);
pair cis(real magni, real argu) { return (magni*cos(argu*pi/180),magni*sin(argu*pi/180)); }
for(int i=90;i<450;i+=60) {
pair c=cis(1.2,i);
path p=c-cis(1,i)--c-cis(1,i+120)--c-cis(1,i-120)--cycle;
fill(p,orange+white);
draw(p);
pair c=cis(2.4,i);
path p=c+cis(1,i)--c+cis(1,i+120)--c+cis(1,i-120)--cycle;
fill(p,orange+white);
draw(p);
};
label("$\longrightarrow$",(4,0));
pair x=(8,0);
real s=sqrt(3);
path p=x+cis(s,0)--x+cis(3,30)--x+cis(s,60)--x+cis(3,90)--x+cis(s,120)--x+cis(3,150)--x+cis(s,180)--x+cis(3,210)--x+cis(s,240)--x+cis(3,270)--x+cis(s,300)--x+cis(3,330)--cycle;
fill(p,orange+white);
draw(p);
[/asy] If each of the original tiles has a perimeter of $10$ cm, what is the perimeter of the final star in cm?
Answer:
40 cm
Step-by-step explanation:
Each point of the final 6-pointed star has 2/3 of the perimeter of the equilateral triangle. So, the 6 points have a total perimeter of ...
6(2/3)(10 cm) = 40 cm
The perimeter of the final star is 40 cm.
Answer:
40
Step-by-step explanation:
The star has $12$ sides. Each side is one-third of the perimeter of a triangular tile, or $\frac{10}3$ cm. So the perimeter of the star is
$$12\cdot\frac {10}3 = 4\cdot 10 = \boxed{40\text{ cm}}.$$
Alternatively, consider that the original tiles are composed of $12$ triangles with $3$ sides each, which have $12\cdot 3 = 36$ sides in all. Only $12$ of those $36$ sides make up the perimeter of the star. $12$ is one-third of $36,$ so the perimeter of the star is one-third of the total perimeter of the tiles. The tiles have a total perimeter of $10 \cdot 12=120\text{ cm},$ so the perimeter of the star is $\frac{120}3 = 40$ cm.
Without using a calculator, convert the fraction to a decimal
Answer:
what's the fraction though?
The temperature at midnight is shown. The outside temperature decreases 2.3 C over the next two hours. What is the outside temperature at 2 A.M. ?
Answer:
Outside temperature at 2 A.M = -33.2°C
Step-by-step explanation:
Given:
Temperature at 12:00 midnight (outside) = -30.9°C
Rate of decreases = - 2.3°C per two hour
Find:
Outside temperature at 2 A.M
Computation:
Outside temperature at 2 A.M = Temperature at 12:00 midnight (outside) + Rate of decreases
Outside temperature at 2 A.M = -30.9°C + (- 2.3°C)
Outside temperature at 2 A.M = -33.2°C
Pls someone explain this to me
Thank u.
Answer:
a) a= 60
c) a= 135
d) a= 40
f) a= 115
g) a= 37
i) a= 130
Step-by-step explanation:
If you see a little square at the angle, this means that the angle is a right angle, which means that it is 90°.
Let's look at Q5a.
a) a° +30°= 90°
a°= 90° -30°
a°= 60°
a=60
Questions 5b has the same concept.
The sum of the angles on a straight line is 180°. The abbreviation used for this is (adj. ∠s on a str. line).
Let's look at Q5c.
c) a° +45°= 180° (adj. ∠s on a str. line)
a°= 180° -45°
a°= 135°
a= 135
Question 5d uses the same concept too.
Let's look at Q5d.
d) 90° +50° +a°= 180° (adj. ∠s on a str. line)
a°= 180° -90° -50°
a°= 40°
a= 40
Vertically opposite angles are equal. The abbreviation written for this is (vert. opp. ∠s).
Use this for questions 5f and 5g.
f) a°= 115° (vert. opp. ∠s)
a= 115
g) a°= 37°
a= 37
The sum of angles on a point is 360°. This will help you solve questions 5h and 5i.
i) 140° +90° +a° = 360° (∠s at a point)
a° +230°= 360°
a°= 360° -230°
a°= 130°
a= 130
which one is correct?
Answer:
[tex] (x+4)^2=4[/tex]
Step-by-step explanation:
[tex]x^2+8x+12=0\\
\implies (x^2+8x+16)+12=16\\
\implies (x+4)^2=16-12\\
\implies \boxed{(x+4)^2=4}[/tex]
Answer:
(x +4)^2 = 4
Step-by-step explanation:
if we add 4 to the expression x^2 + 8x + 12 we will have a perfect square which is shown as (x +4)^2
so (x +4)^2 = 4 is equivalent to the expression x^2 + 8x + 12
Is my answer correct?
Answer:
Your answer is correct
Step-by-step explanation:
SAS triangle is proven through b option.
Hope this helps....
Have a nice day!!!!
plz help ASAP! last question thank u
Answer:
The correct Option is Option A
Step-by-step explanation:
A survey of athletes at a high school is conducted, and the following facts are discovered: 28% of the athletes are football players, 25% are basketball players, and 24% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that they are either a football player or a basketball player
Answer: 0.29 or 29%
Step-by-step explanation:
Given :
Probability that the athletes are football players : P(football ) = 0.28
Probability that the athletes are basketball players : P(basketball) = 0.25
Probability that the athletes play both football and basketball: P( both football and basketball ) = 0.24
Now, using formula
P(either football or basketball)= P(football )+ P(basketball+ P( both football and basketball )
⇒P(either football or basketball)= 0.28+0.25-0.24 = 0.29
Hence, the probability that they are either a football player or a basketball player = 0.29 .
prove that (3-4sin^2)(1-3tan^2)=(3-tan^2)(4cos^2-3)
Answer:
Proof in the explanation.
Step-by-step explanation:
I expanded both sides as a first step. (You may use foil here if you wish and if you use that term.)
This means we want to show the following:
[tex]3-9\tan^2(\theta)-4\sin^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]
[tex]=12\cos^2(\theta)-9-4\cos^2(\theta)\tan^2(\theta)+3\tan^2(\theta)[/tex].
After this I played with only the left hand side to get it to match the right hand side.
One of the first things I notice we had sine squared's on left side and no sine squared's on the other. I wanted this out. I see there were cosine squared's on the right. Thus, I began with Pythagorean Theorem here.
[tex]3-9\tan^2(\theta)-4\sin^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]
[tex]3-9\tan^2(\theta)-4(1-\cos^2(\theta))+12\sin^2(\theta)\tan^2(\theta)[tex]
Distribute:
[tex]3-9\tan^2(\theta)-4+4\cos^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]
Combine like terms and reorder left side to organize it based on right side:
[tex]4\cos^2(\theta)-1+12\sin^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
After doing this, I since that on the left we had products of sine squared and tangent squared but on the right we had products of cosine squared and tangent squared. This problem could easily be fixed with Pythagorean Theorem again.
[tex]4\cos^2(\theta)-1+12\sin^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
[tex]4\cos^2(\theta)-1+12(1-\cos^2(\theta))\tan^2(\theta)-9\tan^2(\theta)[/tex]
Distribute:
[tex]4\cos^2(\theta)-1+12\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
Combined like terms while keeping the same organization as the right:
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
We do not have the same amount of the mentioned products in the previous step on both sides. So I rewrote this term as a sum. I did this as follows:
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
Here, I decide to use the following identity [tex]\cos\theta)\tan(\theta)=\sin(\theta)[/tex]. The reason for this is because I certainly didn't need those extra products of cosine squared and tangent squared as I didn't have them on the right side.
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\sin^2(\theta)-9\tan^2(\theta)[/tex]
We are again back at having sine squared's on this side and only cosine squared's on the other. We will use Pythagorean Theorem again here.
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\sin^2(\theta)-9\tan^2(\theta)[/tex]
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8(1-\cos^2(\theta))-9\tan^2(\theta)[/tex]
Distribute:
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8+8\cos^2(\theta)-9\tan^2(\theta)[/tex]
Combine like terms:
[tex]12\cos^2(\theta)-9+3tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)[/tex]
Reorder again to fit right side:
[tex]12\cos^2(\theta)-9+4\cos^2(\theta)\tan(\theta)+3\tan^2(\theta)[/tex]
This does match the other side.
The proof is done.
Note: Reordering was done by commutative property.
We want to factor the following expression:
(x+4)^2 -4y^5 (x+4) + 4y10
We can factor the expression as (U – V)2 where U and V are either constant integers or single-variable
expressions.
1) What are U and V?
Answer:
U = x + 4 and V = 2y^5.
Step-by-step explanation:
Square root of (x + 4)^2 = x + 4
Square root of 4y^10 = 2y^5
U = x + 4 and V = 2y^5.
(U - V)^2 = U^2 - 2UV + V^2
= (x + 1)^2 - 2 (2y^5 (x + 1) + 4y^10
= (x + 1)^2 - 4y^5 (x + 4) + 4y^10
Answer:
U = x + 4 and V = 2y^5.
Step-by-step explanation:
i think the answer. . .is the second one please correct me if i'm wrong
Answer: You are correct, it is the second option.
Step-by-step explanation:
Volume of a cylinder formula is: pi*r^2*h. The diameter is 6 and the radius is half the diameter so we get r=3. The height is 10 inches, so h=10. pi(3)^2(10) is the volume of the vase.
Volume of a sphere (marbles) formula is: 4/3*pi*r^3
The marbles have a diameter of 3 so 3/2=1.5. r=1.5.
The volume of the marbles is 8(4/3*pi*1.5^3).
Then you subtract the volume of the marbles from the volume of the vase to find the volume of the water in the vase.
pi(3)^2(10) - 8(4/3pi(1.5)^3)
Hope this helps. :)
Answer:
You are absolutely correct, second option is the correct answer.
Step-by-step explanation:
Diameter of vase = 6 inches
Therefore, radius r = 3 inches
Diameter of marbles = 3 inches
Radius of marbles = 1. 5 inches
Height of water h = 10 inches
Volume of water in the vase = Volume of vase - 8 times the volume of one marble
[tex] = \pi r^2h - 8\times \frac{4}{3} \pi r^3 \\\\
= \pi (3\: in) ^2(10\: in) - 8( \frac{4}{3} \pi (1.5\: in) ^3) \\\\[/tex]
Please answer this IQ maths question and tell method please
1) if 32 and 43 makes 35 , then 76 and 15 makes ______?
a)69 (b) 92 (c) 94 (d) 78
2)(3,6,11) and (13, 10,7) then (15,?,3) find the missing one
Answer:
3
3+3=6
3+3+5=11
13
13-3=10
10-3=7
15
15-7=8
8-5=3
32+43=75
75-40(highest ten)=35
76+15=91
91-70=21
Which property justifies the following equation? 7[6+5+(-6)] = [6+(-6)+5] A.distributive B.commutative C.associative D.identity
Which of the following is the graph of f(x) = x2 + 3x − 4? graph of a quadratic function with a minimum at 2, negative 9 and x intercepts at negative 1 and 5 graph of a quadratic function with a minimum at 3, negative 4 and x intercepts at 1 and 5 graph of a quadratic function with a minimum at 2.5, negative 2.4 and x intercepts at 1 and 4 graph of a quadratic function with a minimum at negative 1.5, negative 6.2 and x intercepts at 1 and negative 4
Answer:
x intercepts at -4 and 1,
with a minimum at (-1.5, -6.25)
Step-by-step explanation:
(x + 4)(x - 1) = 0
x = -4, 1
min = -b/2a = -3/2(1) = x = -1.5
y = (-1.5)² + 3(-1.5) - 4 = -6.25
Answer:
graph of a quadratic function with a minimum at negative 1.5, negative 6.2 and x intercepts at 1 and negative 4
Step-by-step explanation:
The graph shows the minimum is (-1.5, -6.25) and the x-intercepts are a -4 and 1. This matches the last description.
__
The x-coordinates of the offered minima are all different, so it is sufficient to know that the axis of symmetry is the line ...
x = -b/(2a) = -3/(2(1)) = -1.5 . . . . . . . for quadratic f(x) = ax² +bx +c
This is the x-coordinate of the minimum.
I need domain and range
Answer:
-3 and infinity
Step-by-step explanation:
genetic experiment with peas resulted in one sample of offspring that consisted of green peas and yellow peas. a. Construct a % confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations? a. Construct a % confidence interval. Express the percentages in decimal form. nothingp nothing (Round to three decimal places as needed.) b. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations? No, the confidence interval includes 0.25, so the true percentage could easily equal 25% Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%
Complete Question
A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 164 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?
Answer:
The 95% confidence interval is [tex]0.2392 < p < 0.3108[/tex]
No, the confidence interval includes 0.25, so the true percentage could easily equal 25%
Step-by-step explanation:
From the question we are told that
The total sample size is [tex]n = 432 + 164 =596[/tex]
The number of offspring that is yellow peas is [tex]y = 432[/tex]
The number of offspring that is green peas is [tex]g = 164[/tex]
The sample proportion for offspring that are yellow peas is mathematically evaluated as
[tex]\r p = \frac{ 164 }{596}[/tex]
[tex]\r p = 0.275[/tex]
Given the the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 5\% = 0.0 5[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1- \r p )}{n} }[/tex]
=> [tex]E = 1.96 * \sqrt{\frac{0.275 (1- 0.275 )}{596} }[/tex]
=> [tex]E = 0.0358[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p - E < p < \r p + E[/tex]
=> [tex]0.275 - 0.0358 < p < 0.275 + 0.0358[/tex]
=> [tex]0.2392 < p < 0.3108[/tex]
HELP!!! Let U be the set of students in a high school. The school has 800 students with 20 students on the gymnastic team and 10 students on the chess team. Select the Venn diagram if three students are on both teams.
Answer:
Step-by-step explanation:
this app is useless don't use it for math probs it doesn't help at all just stay on your work hoped this helped
a 6 foot tall man casts a shadow that is 9 ft long. At the same time, a tree nearby casts a 48 ft shadow. how tall is the tree
Answer:
32 ft tall
Step-by-step explanation:
Since a 6 ft man casts a shadow 9 ft long, the shadow is 3/2 of the actual object/person.
SINCE THE TREE'S SHADOW IS AT THE SAME TIME, THE HEIGHT IS THE SAME RULE.
We know the tree's shadow is 48 ft.
--> 48/3 = 16
16 x 2 = 32
32 ft tall
Hope this helps!
Answer: 32ft tall
Step-by-step explanation:
BRAINLIEST, 5 STARS AND THANKS IF ANSWERED CORRECTLY.
A quadratic equation with a negative discriminant has a graph that..
A. touches the x-axis but does not cross it
B. opens downward and crosses the x-axis twice
C. crosses the x-axis twice.
D. never crosses the x-axis.
Answer:
never crosses the x-axis.
Step-by-step explanation:
A quadratic equation with a negative discriminant has a graph that - never crosses the x-axis.
Answer:
The graph of a quadratic equation that has a negative discriminant is the one that never intersect x-axis. The graph of a quadratic equation that has a zero discriminant is the one that intersect x-axis at only one point. To be clearer, it can be seen in the attached image.
Step-by-step explanation:
Answer D
3 sides of the triangle are consecutive odd numbers. What is the smallest possible perimeter of the triangle ?
Answer:
8
Step-by-step explanation:
The there smallest consecutive odd numbers are 1,3 and 5
Therefore the smallest possible perimeter of such triangle = 8
Given the equation −2x − 13 = 8x + 7, which order of operations completely solves for x? (1 point) Add 2x, then subtract 8x, lastly subtract 7 Add 2x, then add 13, lastly divide by 10 Subtract 8x, then add 13, lastly divide by −10 Subtract 8x, then add 2, lastly add 13
Step-by-step explanation:
We have given an equation −2x − 13 = 8x + 7
We need to find the operations that is used to find the value of x. It can be done by the following ways.
Subtract 8x on both the sides of the equation
−2x − 13 -8x= 8x + 7 -8x
-10x-13 = 7
Add 13 on both the sides of the equation,
-10x-13+13 = 7+13
-10x=21
Divide by -10 on both sides
[tex]x=\dfrac{-20}{10}\\\\x=-2[/tex]
Hence, the correct option is "Subtract 8x, then add 13, lastly divide by −10"
Which point on the number line best represents√57?
Answer:
8.
Step-by-step explanation:
[tex]\sqrt{57} =\sqrt{3 * 19}[/tex]
Since this cannot be further simplified, we will calculate the square root of 57 with our calculators.
We find that the square root of 57 is 7.549834435, and since the tenths place is a 5, we will round up to the next whole number. So, the point on the number line that best represents the square root of 57 is 8.
Hope this helps!
Which expression gives the length of the transverse axis of the hyperbola
shown below?
X
У
Focus
Focus
O AY
O B. X-y
O c. xt
O D. X+ y
Answer:
Option (B)
Step-by-step explanation:
From the picture attached,
F1 and F2 are the focii of the hyperbola.
Point P(x, y) is x units distant from F1 and y units distant from the other focus F2.
By the definition of a hyperbola,
"Difference between the distances of a point from the focii is always constant and equals to the measure of transverse axis."
Difference in the distances of point P from focii F1 and F2 = (x - y) units
This distance is equal to the length of the transverse axis = (x - y) units
Therefore, Option (B) will be the answer.
Answer:
x-y
Step-by-step explanation:
What is the area of a circle with a radius of 35 inches?
in 2
(Use 3.14 for Pi.)
Answer:
3846.5 in.
Step-by-step explanation:
πr² = (3.14)(35)² = 3846.5 in.
Factorise 6x2 - x - 2
Answer:
[tex] \boxed{\sf (3x - 2)(2x + 1)} [/tex]
Step-by-step explanation:
[tex] \sf Factor \: the \: following: \\ \sf \implies 6 {x}^{2} - x - 2 \\ \\ \sf The \: coefficient \: of \: {x}^{2} \: is \: 6 \: and \: the \: constant \\ \sf term \: is \: - 2. \: The \: product \: of \: 6 \: and \: - 2 \\ \sf is \: - 12. \\ \sf The \: factors \: of \: - 12 \: which \: sum \: to \\ \sf - 1 \: are \: 3 \: and \: - 4. \\ \\ \sf So, \\ \sf \implies 6 {x}^{2} - 4x + 3x - 2 \\ \\ \sf \implies 2x(3x - 2) + 1(3x - 2) \\ \\ \sf \implies (3x - 2)(2x + 1)[/tex]
Answer:
[tex] \boxed{(2x + 1)(3x - 2)}[/tex]Step-by-step explanation:
[tex] \mathsf{ {6x}^{2} - x - 2}[/tex]
Write -x as a difference
[tex] \mathsf{6 {x}^{2} + 3x - 4x - 2}[/tex]
Factor out 3x from the expression
[tex] \mathsf{3x(2x + 1) - 4x - 2}[/tex]
Factor out -2 from the expression
[tex] \mathsf{3x(2x + 1) - 2(2x + 1)}[/tex]
Factor out 2x + 1 from the expression
[tex] \mathsf{(2x + 1)(3x - 2)}[/tex]
[tex] \mathcal{Hope \: I \: helped!}[/tex]
[tex] \mathcal{Best \: regards!}[/tex]
What is the value of $a$ if the lines $2y - 2a = 6x$ and $y + 1 = (a + 6)x$ are parallel?
Answer:
a=-3
Step-by-step explanation:
the sum of n and the sum of 8 and 6"
Answer:
Its 14
Step-by-step explanation:
8+6=14
Answer:
The answer is 16
08
+ 06
----------
16
Hope it helps ;)
Please mark as brainliest
If x = -12, y = -3; find xy² ?
Find the value of xy².
Solution:-xy²
★ Substituting the values of x and y ,we get :
⇒ -12 × ( -3 )²
⇒ -12 × 9
⇒ -108
What is a21 of the arithmetic sequence for which a7=−19 and a10=−28? A. -35 B. 35 C. -58 D. -61
Answer:
a21 = -61
Step-by-step explanation:
[tex]a_{n}=a_{1}+(n-1)d[/tex]
[tex]-19=a_{1}+(7-1)d[/tex]
[tex]-28=a_{1}+(10-1)d[/tex] (subtract to eliminate a₁)
9 = -3d
d = -3
-19 = a₁ + (6)(-3)
-1 = a
a21 = -1 + (21 - 1)(-3)
= -61
Answer:
-61 (Answer D)
Step-by-step explanation:
The general formula for an arithmetic sequence with common difference d and first term a(1) is
a(n) = a(1) + d(n - 1)
Therefore, a(7) = -19 = a(1) + d(7 - 1), or a(7) = a(1) + d(6) = -19
and a(10) = a(1) + d(10 - 1) = -28, or a(1) + d(10 - 1) = -28
Solving the first equation a(1) + d(6) = -19 for a(1) yields a(1) = -19 - 6d. We substitute this result for a(1) in the second equation:
-19 - 6d + 9d = -28. Grouping like terms together, we get:
3d = -9, and so d = -3.
Going back to an earlier result: a(1) = -19 - 6d.
Here, a(1) = -19 - 6(-3), or a(1) = -1.
Then the formula specifically for this case is a(n) = -1 - 3(n - 1)
and so a(21) = -1 - 3(20) = -61 (Answer D)
