Answer:
1. A. and C.2. C.Step-by-step explanation:
[tex]1.\\\bold{YES}\\A.\ (x+5)^2=49\iff x+5=\pm\sqrt{49}\\\\x+5=\pm7\qquad\text{subtract 5 from both sides}\\\\x=-13\in\mathbb{Q}\ or\ x=2\in\mathbb{Q}\\\\C.\ x^2=81\iff x=\pm\sqrt{81}\\\\x=\pm9\in\mathbb{Q}\\\\\bold{NOT}\\B.\ x^2=12\to x=\pm\sqrt{12}\notin\mathbb{Q}\\D.\ (x-1)^2=20\to x-1=\pm\sqrt{20}\notin\mathbb{Q}[/tex]
[tex]\bold{YES}\\C.\\x^2+12x+36=0\\\\x^2+2(x)(6)+6^2=0\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+6)^2=0\iff x+6=0\qquad\text{subtract 6 from both sides}\\\\x=-6\\\\\bold{NOT}\\A.\\3x^2+x-2=0\\3x^2+3x-2x-2=0\\3x(x+1)-2(x+1)=0\\(x+1)(3x-2)=0\iff x+1=0\ \vee\ 3x-2=0\\\text{two different solutions}\\B.\\x^2-15x+36=0\\x^2-12x-3x+36=0\\x(x-12)-3(x-12)=0\\(x-12)(x-3)=0\iff x-12=0\ \vee\ x-3=0\\\text{two different solutions}[/tex]
1 a. A van moves with a
constant speed of 118
km/h, How far can it
travel in 2 hours
15 minutes?
Show your working out
As we know distance equals speed multiplied by time
118*2.25=265.5
Therefore the car can travel 265.5km in 2 hours 15 minutes with the speed of 118km/h
The van can travel approximately 265.5 kilometers in 2 hours and 15 minutes.
To find out how far the van can travel in 2 hours and 15 minutes, we need to use the formula:
Distance = Speed × Time
Given:
- Speed of the van = 118 km/h
- Time = 2 hours 15 minutes
First, let's convert the time to hours:
2 hours 15 minutes = 2 + 15/60 hours
= 2.25 hours
Now, we can use the formula to calculate the distance:
Distance = 118 km/h × 2.25 hours
Distance ≈ 265.5 km
Therefore, the van can travel approximately 265.5 kilometers in 2 hours 15 minutes.
write a compound interest function to model the following situation. then find tbe balance after the given number of years.
$5,400 invested at a rate of 2.4%, compounded monthly; 5 years
Answer:
[tex]\$6,087.75[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=5\ years\\ P=\$5,400\\ r=0.024\\n=12[/tex]
substitute in the formula above
[tex]A=\$5,400(1+\frac{0.024}{12})^{12*5}[/tex]
[tex]A=\$5,400(1.002)^{60}=\$6,087.75[/tex]
what is the median of the following string of values 16, 95, 3, 37, 97, 13, 27,42,64,14
Answer:
32
Step-by-step explanation:
put the numbers in order from less to greatest
3,13,14,16,27,37,42,64,95,97
the middle numbers are 27 and 37
27+37 is 64
64 divided by 2 is 32
First put the numbers in order from least to greatest
3, 13, 14, 16, 27, 37, 42, 64, 95, 97
Median means middle so find the middle number by deleting the least and greatest number in each "layer"
3, 13, 14, 16, 27, 37, 42, 64, 95, 97
13, 14, 16, 27, 37, 42, 64, 95
14, 16, 27, 37, 42, 64
16, 27, 37, 42
27, 37
You have two numbers left. To find the middle take the mean of these two numbers, by adding them together then dividing the sum by two
27 + 37 = 64
64 / 2 = 32
32 is the median!!!
Hope this helped!
A circle is the collection of points in a plane that are the same distance from a given point in the plane. true or false
true
any given point in a circle is equal distance from the center
Answer: TRUE.
Step-by-step explanation:
It knows that the distance "d" between any two points is equal to [tex]\sqrt{(x-x_0)^2-(y-y_0)^2}[/tex].
In a circle the distance between a point that belongs to the circumference and the center ([tex]x_0,y_0[/tex]) is always the same. Then:
[tex]\sqrt{(x-x_0)^2-(y-y_0)^2}[/tex] is always equal to a constant called "r".
This is:
[tex]\sqrt{(x-x_0)^2-(y-y_0)^2}=r[/tex]
Square both sides of the equality:
[tex](\sqrt{(x-x_0)^2-(y-y_0)^2})^2=r^2[/tex]
[tex](x-x_0)^2-(y-y_0)^2=r^2[/tex]
Note that we obtain the General equation of a circle.
This prove that if the distance between a given point in the plane and a collection of points is equal, then the equation of a circle is obtained.
Therefore, the statement "A circle is the collection of points in a plane that are the same distance from a given point in the plane." is true.
What is the best estimate for the percent of students scoring greater than 92 on at test?
Answer:
80
Step-by-step explanation:
Find the area of the kite!!! HELP PLEASE!!!!
A. 24 units^2
B. 54 units^2
C. 33 units^2
D. 36 units^2
ANSWER
C. 33 units^2
EXPLANATION
The area of a kite is half times product of the diagonals.
The diagonals are
3+3=6 units
and
9+2 =11 units.
The area of the kite is
[tex] = \frac{1}{2} \times 11 \times 6[/tex]
[tex] = 11 \times 3[/tex]
[tex] = 33 {units}^{2} [/tex]
The correct choice is C
Ruth bought cutter s and screwdrivers to upgrade the computers in her company. A cutter costs 15.2$ and a screw driver costs $2. She bought a total of 29 tools and spent 150.40$. how many of each tool did ruth buy?
Answer:
The number of cutters is 7
The number of screw drivers is 22
Step-by-step explanation:
Let
x-----> the number of cutters
y----> the number of screw drivers
we know that
x+y=29 ----> equation A
15.2x+2y=150.40 ----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (7,22)
see the attached figure
therefore
The number of cutters is 7
The number of screw drivers is 22
What is the area of this trapezoid?
A. 14 m2
B. 18 m2
C. 21 m2
D. 35 m2
Answer:
b
Step-by-step explanation:
yes
Answer:
B
Step-by-step explanation:
If we draw another vertical line on the other side, we can split this into a rectangle and two triangles. The width of the rectangle is 5 m, so the base of the triangle on the left is 1 m, just like the triangle on the right.
The area is therefore the sum of the areas of each shape:
A = Arectangle + 2Atriangle
A = (5 m)(3 m) + 2(½ (1 m)(3 m))
A = 18 m²
Simplify to create an equivalent expression. −5(1−5k)−4(2k+5)\qquad{-5(1-5k)-4(2k+5)}−5(1−5k)−4(2k+5)
17k−25 is the answer.
How do you recognize if an expression is an equivalent?Expressions are equal if they may be simplified to the same 0.33 expression or if one of the expressions can be written just like the other. similarly, you can additionally determine if two expressions are equal when values are substituted in for the variable and both arrive at an equal solution.
How do you write an equivalent expression in a trendy shape?Algebraic expressions are equal in the event that they constantly lead to the same result whilst you evaluate them, irrespective of what values you substitute for the variables. For instance, if x = three, then x + x + 4 = three + three + 4 = 10 and 2x + 4 = 2(3) + four = 10 additionally.
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PLEASE HELP 10 POINTS
Answer:
Step-by-step explanation:
Sample space {1,2,3,4,5,6}
3 to 6: {3,4,5,6}
My punctuation may not be the same as yours, but that is what they are asking for.
A spinner has 4 equal sections: red, white, blue, and green. John spins the spinner and tosses a
coin. Which shows the sample space for spinning the spinner and tossing the coin?
A, B, C, or D
Answer:
Step-by-step explanation:
The sample space should show all the possible outcomes.
The first option includes all 4 colors and both head and tails.
The second option is missing tails as an outcome.
The third option is missing blue.
The fourth option is missing tails.
So it must be the first one.
A rectangular stained glass window is 2 feet by 4 feet. A clear glass border is constructed around the stained glass window. The width of the border is equal and was made out of 7 square feet of clear glass. What is the width of the border?
The width of the border around the stained glass window is approximately 1.15 feet, calculated by subtracting the stained glass area from the total area including the border.
To find the width of the border, we need to subtract the area of the stained glass window from the total area including the border.
Given:
- Length of stained glass window = 4 feet
- Width of stained glass window = 2 feet
- Area of stained glass window = [tex]\(4 \times 2 = 8\)[/tex] square feet
- Total area including the border = Area of stained glass window + Area of border = 8 + 7 = 15 square feet
Let's denote the width of the border as x feet.
The total length including the border is 4 + 2x feet, and the total width including the border is 2 + 2x feet.
The area of the total window with the border is the product of its length and width:
(4 + 2x)(2 + 2x) = 15
Expanding this equation:
8 + 4x + 4x + 4x^2 = 15
8 + 8x + 4x^2 = 15
4x^2 + 8x - 7 = 0
Now, let's solve this quadratic equation using the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
Where a = 4, b = 8, and c = -7.
[tex]\[x = \frac{{-8 \pm \sqrt{{8^2 - 4 \times 4 \times (-7)}}}}{{2 \times 4}}\][/tex]
[tex]\[x = \frac{{-8 \pm \sqrt{{64 + 112}}}}{8}\][/tex]
[tex]\[x = \frac{{-8 \pm \sqrt{{176}}}}{8}\][/tex]
[tex]\[x = \frac{{-8 \pm 4\sqrt{{11}}}}{8}\][/tex]
[tex]\[x = \frac{{-2 \pm \sqrt{{11}}}}{2}\][/tex]
Since the width cannot be negative, we take the positive root:
[tex]\[x = \frac{{-2 + \sqrt{{11}}}}{2} \approx 1.15 \text{ feet}\][/tex]
Therefore, the width of the border is approximately 1.15 feet.
What is the area of trapezoid?
Answer:
141.12 cm^2
Step-by-step explanation:
A = 1/2 (b1+b2)h where b1 = 10.2, b2 = 12.2 and h = 12.6
so
A = 1/2(10.2 + 12.2) * (12.6)
A = 1/2(22.4)(12.6)
A = 141.12 cm^2
Answer:
A≈141.12
A=a+b/2(h)
The slope of a line is 1/3 . What is the slope of a line perpendicular to this line?
-3
-
3
Answer:
perpendicular is the opposite, so -3
Answer:
FIRST OPTION: -3
Step-by-step explanation:
By definition, if two lines are perpendicular to each other, then their slopes are negative reciprocals.
In this case you can observe that that the slope of the line is [tex]\frac{1}{3}[/tex] and you know that the other line is perpendicular to this line. Therefore, their slopes are negative reciprocals.
This means that:
If [tex]slope_1=\frac{1}{3}[/tex] ,then [tex]slope_2=-3[/tex]
This matches with the first option.
Solve for F in terms of K:
[tex]K=\frac{5}{9}(F+459.67)[/tex]
The value of F in terms of K is (9K - 2298.67)/5.
What is Function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Here, given function:
K = 5/9 (F + 459.67)
9K = 5(F + 459.67)
9K = 5F + 2298.67
9K - 2298.67 = 5F
F =(9K - 2298.67)/5
Thus, the value of F in terms of K is (9K - 2298.67)/5.
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To solve for F in terms of K, you can use the equation F = (9/5)(K) - 459.67.
Explanation:To solve for F in terms of K, we need to isolate F on one side of the equation.
Step 1: Start with the given equation:
K = (5/9)(F + 459.67)
Step 2: Multiply both sides of the equation by 9/5 to undo the multiplication on the right side:
(9/5)(K) = F + 459.67
Step 3: Simplify the left side:
(9/5)(K) = F + 459.67
Step 4: Subtract 459.67 from both sides to isolate F:
(9/5)(K) - 459.67 = F
Therefore, F in terms of K is given by the equation F = (9/5)(K) - 459.67.
Apply the distributive property in reverse to create am equivalent expression
1.) 16a+8b=______
2.) 25g+15=_______
3.) 24f+16=________
1. 8(2a+b)
2. 5(5g+3)
3. 8(3f+2)
The reverse of the distributive property involves factoring out the Greatest Common Factor (GCF) from the terms of the expression. For example, 16a + 8b becomes 8(2a + b), where 8 is the GCF.
The reverse of the distributive property involves factoring out the Greatest Common Factor (GCF) from each term in the expression to create an equivalent expression. Here's how it's done step-by-step:
Identify the GCF for all the terms in the expression.
Factor the GCF out of each term, which is essentially dividing each term by the GCF.
Write the factored expression in the form of the GCF multiplied by the remaining terms added together.
Applying this process:
For 16a + 8b, the GCF is 8, so the equivalent expression is 8(2a + b).
For 25g + 15, the GCF is 5, so the equivalent expression is 5(5g + 3).
For 24f + 16, the GCF is 8, so the equivalent expression is 8(3f + 2).
What is the lateral area of the cone to the nearest whole number. The figure is not drawn to scale 40M 60M
Answer:
48984 m^2
Step-by-step explanation:
The height(h) of cone is given by: 50 m.
Diameter of cone is: 240 m.
Also radius(r) of cone is:240/2=120 m.
The lateral surface(S) area is given by:
The lateral area of the cone comes out to be 48984 m^2.
What is lateral area?
The formula of the lateral area of cone is given by, area = pi×r×L
The amount of territory occupied by the curved surface area of a cone is known as the lateral surface area.
The lateral surface area of a cone is also in the three-dimensional plane because it is a three-dimensional form. The shape of a cone is created by stacking and rotating several triangles around an axis. Since a cone has a flat base so it has curved surafce area as well as total surface area. A cone's lateral area is measured in square units, such as cm2, m2, in2, and so on.
Given,
Height of cone : 50m
Diameter of cone: 240m
so,it's radius will be 120m
L = [tex]\sqrt{r^{2}+h^{2}}[/tex]
L = [tex]\sqrt{120^{2} +50^{2} }[/tex]
L = 130
since,Area = pi×r×L
=3.14×120×130
=48984m^2
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6. A new car has an MSRP of $29,999, and it comes with a premium package priced at
$2500, a navigation package priced at $500, and a destination charge of $700. What is the
sticker price of this car?
Answer:
it is 33,699
Step-by-step explanation:
you add the MSRP, then the other charges
The sticker price of the car is $33,699.
Explanation:The sticker price of the car can be calculated by adding the MSRP, premium package, navigation package, and destination charge. The MSRP is $29,999, the premium package is $2500, the navigation package is $500, and the destination charge is $700.
The sticker price is calculated as follows:
Add the MSRP and the premium package: $29,999 + $2500 = $32,499Add the navigation package: $32,499 + $500 = $32,999Add the destination charge: $32,999 + $700 = $33,699Therefore, the sticker price of the car is $33,699.
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Help me guys pls ❤️❤️
Determine the angle measure of the following angles ?
1) b =
2) m=
3) h=
4) g=
5) i=
6) j=
Answer
1) [tex]b=101\degree[/tex]
2) [tex]m=50\degree[/tex]
3) [tex]h=79\degree[/tex]
4) [tex]g=101\degree[/tex]
5) [tex]i=51\degree[/tex]
6) [tex]j=130\degree[/tex]
Explanation
From the diagram,
[tex]b=101\degree[/tex], corresponding angles are equal.
From the diagram, m=k, corresponding angles are equal.
But k+130=180, angles on a straight line sum up to 180 degrees.
This implies that k=180-130=50
[tex]\therefore m=50\degree[/tex]
From the diagram ; [tex]h+101=180\degree[/tex],angles on a straight line sum up to 180 degrees.
[tex]\implies h=180-101\degree[/tex]
[tex]\implies h=79\degree[/tex]
From the diagram, [tex]g=101\degree[/tex] vertically opposite angles are equal.
From the triangular portion;
i+h+m=180. sum of interior angles of a triangle.
This implies that:
i+79+50=180
i+129=180
i=180-129
[tex]i=51\degree[/tex]
Finally
[tex]j=130\degree[/tex], vertically opposite angles are equal.
Answer:
Part 1) ∠b=101°
Part 2) ∠m=50°
Part 3) ∠h=79°
Part 4) ∠g=101°
Part 5) ∠i=51°
Part 6) ∠j=130°
Step-by-step explanation:
Part 1) ∠b
we know that
∠b=101° ------> by corresponding angles
Part 2) ∠m
we know that
∠m=∠k ------> by corresponding angles
and
∠k+130°=180° -----> by supplementary angles
∠k=180°-130°=50°
therefore
∠m=50°
Part 3) ∠h
we know that
∠h+101°=180° -----> by supplementary angles
∠h=180°-101°=79°
Part 4) ∠g
we know that
∠g=101° -----> by vertical angles
Part 5) ∠i
we know that
The sum of internal angles of a triangle must be equal to 180 degrees
so
∠h+∠m+∠i=180°
substitute the values and solve for ∠i
79°+50°+∠i=180°
∠i=180°-129°=51°
Part 6) ∠j
we know that
∠j=130° -----> by vertical angles
The volume of a rectangular box can be found using the formula lwh where l represents the length, w represents the width, and h represents the height of the box. What is the volume of a box with the following dimensions?
I = 4 centimeters
W= 5 centimeters
H=6 centimeters
Answer:
120 cm^3
Step-by-step explanation:
volume = lwh
I = 4 centimeters
w = 5 centimeters
h = 6 centimeters
volume = (4 cm)(5 cm)(6 cm)
volume = 120 cm^3
some time ago restaurant claim that it could prepare your hamburger 128 ways how many condiments do you need in order to be able to prepare 128 different hamburgers
Answer:
128
Step-by-step explanation:
To create 128 different hamburgers with multiple combinations of condiments, you would need 7 different condiments. This is due to the fact that each condiment presents 2 possibilities, on the burger or not, and 2 to the power of 7 equals 128.
Explanation:In this scenario, each condiment represents an option that can be either included or excluded. This means that, for each condiment, there are 2 possibilities (it's either on the burger, or it's not). The question implies that the number of possible combinations equals 128, which is 2 to the power of 7.
So, to create 128 different hamburgers, the restaurant must offer 7 different condiments. This is because 2 (possibilities for each condiment) to the power of 7 (condiments) equals 128.
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Consider the gender and class make-up of students at a large university by gender and status as given in the table.
What is (Female | Undergraduate)? Give your answer to three decimal places.
Answer:
0.589
Step-by-step explanation:
THis is a conditional probability question. Let's look at the formula first:
P (A | B) = P(A∩B)/P(B)
" | " means "given that".
So, it means, the "Probabilty A given that B is equal to Probability A intersection B divided by probability of B."
So we want to know P (Female | Undergraduate ). This in formula is:
P (Female | Undergraduate) = P (Female ∩ Undergraduate)/P(Undergraduate)
Now,
P (Female ∩ Undergraduate) means what is common in both female and undergraduate? There are 43% female that are undergrads. Hence,
P (Female ∩ Undergraduate) = 0.43
Also,
P (Undergraduate) is how many undergrads are there? There are 73% undergrads, so that is P (undergraduate) = 0.73
plugging into the formula we get:
P (Female | Undergraduate) = P (Female ∩ Undergraduate)/P(Undergraduate)
=0.43/0.73 = 0.589
this is the answer.
Which of the following equations has solutions of 3 ± Square root 5 ?
(x - 5)2 = 3
(x - 3)2 = 5
(x + 3)2 = 5
(x + 5)2 = 3
Answer:
I think it is C. I am not sure
The correct equation that has solutions of 3 ± √5 is (x - 3)² = 5.
The solutions of the equation are given as 3 ± √5 To find an equation that has these solutions, we would look for an equation in the form (x - a)^2 = b, where the solutions to x can be found using the square root property x = √b + a or x = -√b + a. In this case, we are looking for an equation where a is 3 and b is 5 to fit the solutions provided.
Examining the options provided:
(x - 5)² = 3 does not meet the criteria(x - 3)² = 5 is the correct equation(x + 3)² = 5 does not meet the criteria(x + 5)² = 3 does not meet the criteriaTherefore, the equation with solutions of 3 ± √5 is (x - 3)² = 5.
A six sided number cube labeled from 1 to6 is rolled what is the probability of getting a multiple of two or multiple of three? 1/2 5/6 1/6 2/3
Answer:
2/3
Step-by-step explanation:
The cube has the following numbers written on its faces;
1, 2, 3, 4, 5, 6
Among these numbers, the multiples of 2 and 3 are;
2, 3, 4, 6 .
The probability of rolling a multiple of 2 or 3 is thus;
4/6 = 2/3
Which is the required probability
PLEASE HELPS
A shoe factory produces 1.81 × 104 pairs of shoes each month. Estimate how many pairs of shoes the factory will produce if it maintains that rate for 10 years. (There are 1.2 × 102 months in 10 years.)
1. Estimate each coefficient: 1.81 ≈ 2
1.2 ≈ 1
2. Write the product: (2 × 104)(1 × 102)
The shoe factory would make approximately
____ ×106 pairs of shoes in 10 years.
Please fill in the blank thx!!!
Answer:
The answer is 2
Step-by-step explanation:
we know that
step 1
Estimate each coefficient:
1.81 ≈ 2
1.2 ≈ 1
step 2
Write the product:
[tex](2*10^{4})(1*10^{2})=(2*1)*10^{4+2}=2*10^{6}[/tex] pairs of shoes in 10 years.
Answer:
the answer is two 2
Step-by-step explanation:
LMN and QRS are similar. Find the value of X.
x+5/30 = 50/75
x+5/10 = 2
x+5 = 20
x = 15
3/5y + 2/9 = 5/8 - 2/5y + 5/8
Answer:
y = 37/36
Step-by-step explanation:
let's take a peek at the denominators hmmmm 5, 9, 8 hmmmm we can get an LCD of simply their product, well, that'd be 360, so then, let's multiply both sides by the LCD of 360 to do away with the denominators and proceed.
[tex]\bf \cfrac{3}{5}y+\cfrac{2}{9}=\cfrac{5}{8}-\cfrac{2}{5}y+\cfrac{5}{8}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{360}}{360\left( \cfrac{3}{5}y+\cfrac{2}{9} \right)=360\left( \cfrac{5}{8}-\cfrac{2}{5}y+\cfrac{5}{8} \right)} \\\\\\ 72(3y)+40(2)=45(5)-72(2y)+45(5) \\\\\\ 216y+80=225-144y+225\implies 216y+80=450-144y \\\\\\ 216y=370-144y\implies 360y=370\implies y=\cfrac{370}{360}\implies y=\cfrac{37}{36}[/tex]
1. In ABC, C is a right angle and BC = 11. If B = 30°, find AC. (1 point)
PLEASE HELP I HAVE ONE DAY TO COMPLETE THE CONNECTION PRECALCULUS B UNIT 8: SEMESTER EXAM! I would do ANYTHING PLEASE?!
Answer:
[tex]AC=\frac{11\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Given that triangle ABC is a right angle triangle. Where angle C is a right angle. Also we have been given that BC = 11, B = 30°. Now we need to find the value of AC.
Apply formula:
[tex]\tan\left(\theta\right)=\frac{opposite}{adjacent}[/tex]
[tex]\tan\left(B\right)=\frac{AC}{BC}[/tex]
[tex]\tan\left(30^o\right)=\frac{AC}{11}[/tex]
[tex]\frac{1}{\sqrt{3}}=\frac{AC}{11}[/tex]
[tex]\frac{11}{\sqrt{3}}=AC[/tex]
[tex]AC=\frac{11}{\sqrt{3}}[/tex]
or
[tex]AC=\frac{11}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}[/tex]
or
[tex]AC=\frac{11\sqrt{3}}{3}[/tex]
Hence final answer is [tex]AC=\frac{11\sqrt{3}}{3}[/tex].
Find the series shown.
7 + 9 + 11 + 13 + 15
11 + 13 + 15 + 17 + 19
11 + 13 + 15 + 17 + ...
7 + 9 + 11 + 13 + ...
Answer:
C [tex]11+13+15+17+...[/tex]
Step-by-step explanation:
Consider the series
[tex]\sum\limits_{n=3}^{\infty}(2n+5)[/tex]
The nth term of series is [tex]a_n=2n+5[/tex]
The bottom index tells you that n starts changing from 3, so
[tex]a_3=2\cdor 3+5=11\\ \\a_4=2\cdot 4+5=13\\ \\a_5=2\cdot 5+5=15\\ \\a_6=2\cdot 6+5=17\\ \\...[/tex]
Thus, the sum of all terms is
[tex]11+13+15+17+...[/tex]
how do I solve this
plz help
Well it depends. If your radical is wrapped around the entire expression, then your answer would be 3xy²z²√10xz, but if your radical is ONLY wrapped around 90, then your answer would be 3√10x³y⁴z⁵ [radical wrapped ONLY around 10]. So, with the way this is written, although it is simple to figure this out, it is difficult to find the answer you are looking for.