Answer:
7
Step-by-step explanation:
2x^2 - 7x - 4 = 45
2x^2 - 7x - 49 = 0 : subtract 45 from both sides
Quadratic formula:
x = (7 ± sqrt(7^2 - 4*2*-49) ) / 4
x = (7 ± sqrt(49 - -392)) / 4
x = (7 ± sqrt(441)) / 4
x = (7 ± 21) / 4
x = (7 + 21) / 4 OR x = (7 - 21) / 4
x = 28 / 4 OR x = -14 / 4
x = 7 as it is the only positive answer
3. Consider the sequence,-8, -5, -2, 1, ...
a) Determine the explicit formula for the general term, 1,, of this sequence in simplified
form. (2 marks)
b) Use this formula to determine the value of t20. (1 mark)
c) Algebraically determine which term has a value of 40. (1 mark)
Answer:
a) [tex]a_n=3\,n-11[/tex]
b) [tex]a_{20}=49[/tex]
c) term number 17 is the one that gives a value of 40
Step-by-step explanation:
a)
The sequence seems to be arithmetic, and with common difference d = 3.
Notice that when you add 3 units to the first term (-80, you get :
-8 + 3 = -5
and then -5 + 3 = -2 which is the third term.
Then, we can use the general form for the nth term of an arithmetic sequence to find its simplified form:
[tex]a_n=a_1+(n-1)\,d[/tex]
That in our case would give:
[tex]a_n=-8+(n-1)\,(3)\\a_n=-8+3\,n-3\\a_n=3n-11[/tex]
b)
Therefore, the term number 20 can be calculated from it:
[tex]a_{20}=3\,(20)-11=60-11=49[/tex]
c) in order to find which term renders 20, we use the general form we found in step a):
[tex]a_n=3\,n-11\\40=3\,n-11\\40+11=3\,n\\51=3\,n\\n=\frac{51}{3} =17[/tex]
so term number 17 is the one that renders a value of 40
plz help me if you can
Answer:
Hey there!
These triangles can be proved congruent by the HL Theorem.
Hope this helps :)
Hey Mate!!
Your answer will be HL Theorem.
Because, Since the triangles overlap, their hypotenuses are the same side and therefore congruent by the reflexive property. This means the triangles are congruent by a hypotenuse, leg and right angle. This is known as HL.
☆ Good Luck ☆
♡ Comments down ♡
By ◇~Itsbrazts ◇~
Jillian has three different bracelets (X, Y, and Z) to give to her friends as gifts in any order she prefers. If bracelet Y is chosen first, in how many ways can Jillian give out the bracelets?
Answer:
B. 2
Step-by-step explanation:
ed2020
If Y bracelet is chosen first then there will be only two ways to give out the bracelets.
What are permutation and combination?
When the order of the arrangements counts, a permutation is a numerical approach that establishes the total number of alternative arrangements in a collection.
The number of alternative configurations in a collection of things when the order of the selection is irrelevant is determined by combination.
Given that Jillian has three bracelets
X, Y, and Z
Said that Y has chosen first
The remaining bracelets are X and Z
Number of ways
[Y] X, Z [Y] Z, XIt means there are only two ways to give out bracelets.
Hence "If Y bracelet is chosen first then there will be only two ways to give out the bracelets".
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Cal's go cart has a gas tank with the dimensions shown below. He uses a gas can that holds 1 liter of gas, to fill the go cart tank. 1 liter = 100cm to the power of 3. How many full gas cans will it take to fill the go cart's gas tank?
Answer:
8 cans
Step-by-step explanation:
[tex]V=lwh\\l=40\\w=25\\h=8\\V=(40)(25)(8)\\V=(1000)(8)\\V=8000^3\\\frac{8000^3}{1000^3} =8[/tex]
Since the volume is 8000 cm³ and 8000 cm³ divided by 1000 cm³ is equal to 8, the total cans it will take to fill up the go cart is 8 cans.
Note:
I know this is really late but this to help people for future references
Consider the points P(5,5,1) and Q(13,13,3).
a. Find PQ with right arrow and state your answer in two forms: (a,b,c) and ai+bj+ck.
b. Find the magnitude of PQ with right arrow.
c. Find two unit vectors parallel to PQ with right arrow.
Answer:
a) [tex]\overrightarrow{PQ} = (8,8, 2)[/tex] or [tex]\overrightarrow{PQ} = 8\,i + 8\,j + 2\,k[/tex], b) The magnitude of segment PQ is approximately 11.489, c) The two unit vectors associated to PQ are, respectively: [tex]\vec v_{1} = (0.696,0.696, 0.174)[/tex] and [tex]\vec v_{2} = (-0.696,-0.696, -0.174)[/tex]
Step-by-step explanation:
a) The vectorial form of segment PQ is determined as follows:
[tex]\overrightarrow {PQ} = \vec Q - \vec P[/tex]
Where [tex]\vec Q[/tex] and [tex]\vec P[/tex] are the respective locations of points Q and P with respect to origin. If [tex]\vec Q = (13,13,3)[/tex] and [tex]\vec P = (5,5,1)[/tex], then:
[tex]\overrightarrow{PQ} = (13,13,3)-(5,5,1)[/tex]
[tex]\overrightarrow {PQ} = (13-5, 13-5, 3 - 1)[/tex]
[tex]\overrightarrow{PQ} = (8,8, 2)[/tex]
Another form of the previous solution is [tex]\overrightarrow{PQ} = 8\,i + 8\,j + 2\,k[/tex].
b) The magnitude of the segment PQ is determined with the help of Pythagorean Theorem in terms of rectangular components:
[tex]\|\overrightarrow{PQ}\| =\sqrt{PQ_{x}^{2}+PQ_{y}^{2}+PQ_{z}^{2}}[/tex]
[tex]\|\overrightarrow{PQ}\| = \sqrt{8^{2}+8^{2}+2^{2}}[/tex]
[tex]\|\overrightarrow{PQ}\|\approx 11.489[/tex]
The magnitude of segment PQ is approximately 11.489.
c) There are two unit vectors associated to PQ, one parallel and another antiparallel. That is:
[tex]\vec v_{1} = \vec u_{PQ}[/tex] (parallel) and [tex]\vec v_{2} = -\vec u_{PQ}[/tex] (antiparallel)
The unit vector is defined by the following equation:
[tex]\vec u_{PQ} = \frac{\overrightarrow{PQ}}{\|\overrightarrow{PQ}\|}[/tex]
Given that [tex]\overrightarrow{PQ} = (8,8, 2)[/tex] and [tex]\|\overrightarrow{PQ}\|\approx 11.489[/tex], the unit vector is:
[tex]\vec u_{PQ} = \frac{(8,8,2)}{11.489}[/tex]
[tex]\vec u_{PQ} = \left(\frac{8}{11.489},\frac{8}{11,489},\frac{2}{11.489} \right)[/tex]
[tex]\vec u_{PQ} = \left(0.696, 0.696,0.174\right)[/tex]
The two unit vectors associated to PQ are, respectively:
[tex]\vec v_{1} = (0.696,0.696, 0.174)[/tex] and [tex]\vec v_{2} = (-0.696,-0.696, -0.174)[/tex]
a 4 times the sum of 3 & 5 is subtracted
from
rom 35
Lines m and n are parallel, as shown in the diagram below. What are the measures of angles A and B?
Answer:
a = 55° and b = 60°
Step-by-step explanation:
→ Remember 2 key points about angles
Angles in a triangle add up to 180°Alternate angles are equal→ Angle a is alternate to 55° so using the 2nd point,
a = 55°
→ Remember the fact that angle in a triangle add up to 180°
55° + 65° + b = 180°
→ Collect the whole numbers
120° + b = 180°
→ Minus 120° from both sides to isolate b
b = 60°
The solution is : the measures of angles A and B are:
A = 55° and B = 60°
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
We know that 55+ b+ other angle = 180 since they make a straight line
The other angle = 65 since they are alternate interior angles
55+ B+ 65 = 180
Combine like terms
120 + B = 180
B = 60
A + B + 65 = 180
interior angles of a triangle must equal 180 degrees
A +60+ 65 =180
Combine like terms
A +125 = 180
A = 55
Hence, The solution is : the measures of angles A and B are:
A = 55° and B = 60°
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6. A psychology professor of a large class became curious as to whether the students who turned in tests first scored differently from the overall mean on the test. The overall mean score on the test was 75 with a standard deviation of 10; the scores were approximately normally distributed. The mean score for the first 20 students to turn in tests was 78. Using the .05 significance level, was the average test score earned by the first 20 students to turn in their tests significantly different from the overall mean?
Answer: Z is less than Zc ∴ 1.342 < 1.96
Therefore, Null hypothesis is not Rejected.
There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.
Step-by-step explanation:
Given that;
U = 75
X = 78
standard deviation α = 10
sample size n = 20
population is normally distributed
PROBLEM is to test
H₀ : U = 75
H₁ : U ≠ 75
TEST STATISTIC
since we know the standard deviation
Z = (X - U) / ( α /√n)
Z = ( 78 - 75 ) / ( 10 / √20)
Z = 1.3416 ≈ 1.342
Now suppose we need to test at ∝ = 0.05 level of significance,
Then Rejection region for the two tailed test is Zc = 1.96
∴ Reject H₀ if Z > Zc
and we know that Z is less than Zc ∴ 1.342 < 1.96
Therefore, Null hypothesis is not Rejected.
There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.
Testing the hypothesis, it is found that since the p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.
At the null hypothesis, we test if the mean is of 75, that is:
[tex]H_0: \mu = 75[/tex]
At the alternative hypothesis, we test if the mean is different of 75, that is:
[tex]H_1: \mu \neq 75[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
X is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation.n is the size of the sample.For this problem, we have that:
[tex]X = 78, \mu = 75, \sigma = 10, n = 20[/tex]
The value of the test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{78 - 75}{\frac{10}{\sqrt{20}}}[/tex]
[tex]z = 1.34[/tex]
Since this is a two-tailed test, the p-value of the test is P(|z| < 1.34), which is 2 multiplied by the p-value of z = -1.34.
Looking at the z-table, z = -1.34 has a p-value of 0.0901.
2(0.0901) = 0.1802
The p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.
A similar problem is given at https://brainly.com/question/15535901
Match the system with the amounts of solutions. pls
From top to bottom, the answers are
no solutionsone solutioninfinitely many solutionsone solution==============================================
Explanation:
The first system of equations has each equation with the same slope 2, but different y intercepts. This indicates we have parallel lines. Parallel lines never cross, so there are no solutions. A solution is where the two lines cross.
The second system of equation has one solution where the two lines cross. This is because the slopes are different
The third system has infinitely many solutions. We have the same line graphed out twice. One line is directly on top of the other to yield infinitely many intersection points.
The fourth system is similar to the second system. Different slopes lead to exactly one solution. The y intercept doesn't affect the number of solutions (whether its 0, 1 or infinitely many)
For each equation shown, they are in the form y = mx+b with m as the slope and b as the y intercept.
What is angle ac? Round to the nearest hundredth. HURRY
Answer:
AC = 20°
Step-by-step explanation:
180° (total angle amount of a triangle) - 70° + 90° (right angle) = ac
AC = 20°
Hope this helps!
y > -x + 2
y < 3x - 2
Which graph represents the system of inequalities?
Answer:
C
Step-by-step explanation:
When an equality has a ≤, or ≥ sign (greater than/less than or equal to), the line will be solid. When an equality has a <, or > sign(greater than/less than), the lines will be dotted. As we can see, both of the inequalities given have <, or >, meaning they must both have dotted lines. Since one of the lines in D is solid, the correct answer is C.
Answer:
c is right answer, you can download desmo to solve the graph questions easily
Find the length of AB , given A(5,-2) and B(-3,-4)
Answer:
sqrt(68) is the length.
Step-by-step explanation:
For this you will use the distance formula, sqrt((x2-x1)^2+(y2-y1)^2)
So for this it is sqrt((5+3)^2+(-2+4)^2)
sqrt(64+4)
sqrt(68)
8.246
Choose the Δ that seems to be congruent to the given one. [D - top left] [C - top right] [E - center] [A - bottom left] [B - bottom right] ΔBEC ≅ Δ AEB AED ABD (You guys are probably not gonna get to this in time so I'm putting this out there for the future of you that are gonna need it :) )
Answer:
Δ BEC ≅ Δ AED
Step-by-step explanation:
Consider triangles BCA and ADB. Each of them share a common side, AB. Respectively each we should be able to tell that AD is congruent to BC, and DB is congruent to CA, so by SSS the triangles should be congruent.
_________
So another possibility is triangles BEC, and AED. As you can see, by the Vertical Angles Theorem m∠BEC = m∠ADE, resulting in the congruency of an angle, rather a side. As mentioned before AD is congruent to BC, and perhaps another side is congruent to another in the same triangle. It should be then, by SSA that the triangles are congruent - but that is not an option. SSA does is one of the exceptions, a rule that is not permitted to make the triangles congruent. Therefore, it is highly unlikely that triangles BEC and AED are congruent, but that is what our solution, comparative to the rest.
Δ BEC ≅ Δ AED .... this is our solution
1. 2² X 5⁵ 2⁴ 2. (6⁵)² 6⁷ 3.(2x7)⁵ 7⁴ toloong
Answer:
1. 2⁶
2. 6⁷
3. 14⁵
Step-by-step explanation:
We assume and apply the laws of logarithms and indices in the problems above.
1. Product Rule Law: which states that
loga (MN) = loga M + loga N
Where 2² X 5⁵ = 2²+⁵ = 2⁷
2. The Power rule: in which (6⁵)² = 6⁵+² = 6⁷
3. (2x7)⁵ = (14)⁵ or 5 log 14
Which of the following have the property that a(x)=a−1(x)? I. y=x II. y=1/x III.y=x^2 IV. y=x^3 A. I and II, only B. IV, only C. I, II, and III D. I, only
Answer:
Correct answer:
A. I and II
Step-by-step explanation:
First of all, let us have a look at the steps of finding inverse of a function.
1. Replace y with x and x with y.
2. Solve for y.
3. Replace y with [tex]f^{-1}(x)[/tex]
Given that:
[tex]I.\ y=x \\II.\ y=\dfrac{1}x \\III.\ y=x^2 \\IV.\ y=x^3[/tex]
Now, let us find inverse of each option one by one.
I. y = x, a(x) = x
Replacing y with and x with y:
x = y
x = [tex]a^{-1}(x)[/tex] = [tex]a(x)[/tex] Hence, I is true.
II. [tex]y =\dfrac{1}{x}[/tex]
Replacing y with and x with y:
[tex]x =\dfrac{1}{y}[/tex]
[tex]x=\dfrac{1}{a^{-1}(x)}[/tex]
[tex]\Rightarrow a^{-1}(x) = \dfrac{1}{x}[/tex]
[tex]a^{-1}(x)[/tex] = [tex]a(x)[/tex] Hence, II is true.
III. [tex]y =x^{2}[/tex]
Replacing y with and x with y:
[tex]x =y^{2}\\\Rightarrow y = \sqrt x\\\Rightarrow a^{-1}(x) = \sqrt{x} \ne a(x)[/tex]
Hence, III is not true.
IV. [tex]y =x^{3}[/tex]
Replacing y with and x with y:
[tex]x =y^{3}\\\Rightarrow y = \sqrt[3] x\\\Rightarrow a^{-1}(x) = \sqrt[3]{x} \ne a(x)[/tex]
Hence, IV is not true.
Correct answer:
A. I and II
If f(x)=k (square root)2+x, and f^-^1 (-15)=7, what is the value of k
There's a bit of ambiguity in your question...
We know that [tex]f^{-1}(-15)=7[/tex], which means [tex]f(7)=-15[/tex].
I see three possible interpretations:
• If [tex]f(x)=k\sqrt2+x[/tex], then
[tex]f(7)=-15=k\sqrt2+7\implies k\sqrt2=-22\implies k=-\dfrac{22}{\sqrt2}=11\sqrt2[/tex]
• If [tex]f(x)=k\sqrt{2+x}[/tex], then
[tex]f(7)=-15=k\sqrt{2+7}\implies -15=3k\implies k=-5[/tex]
• If [tex]f(x)=\sqrt[k]{2+x}[/tex], then
[tex]f(7)=-15=\sqrt[k]{2+7}\implies-15=9^{1/k}\implies\dfrac1k=\log_9(-15)[/tex]
which has no real-valued solution.
I suspect the second interpretation is what you meant to write.
Consider the y-intercepts of the functions:
f(x) = |x – 1] + 2
g(x) =
(x + 3)
h(x) = (x + 1) -3
1
What is the ordered pair location of the greatest y-intercept of the three functions?
Answer:
+3, 0
Step-by-step explanation:
y-intercept for f(x) is when x = 0, so it is +1, 0
y-intercept for g(x) is when x = 0, so it is +3, 0
y-intercept for h(x) is when x = 0, so it is -2, 0
The y-intercept of a function is the point where x = 0.
The ordered pair that represents the greatest y-intercept is (0,3)
The functions are given as:
[tex]\mathbf{f(x) = |x - 1| + 2}[/tex]
[tex]\mathbf{g(x) = (x + 3)}[/tex]
[tex]\mathbf{h(x) = (x + 1) - 3}[/tex]
Set x = 0, and solve the functions
[tex]\mathbf{f(x) = |x - 1| + 2}[/tex]
Substitute 0 for x
[tex]\mathbf{f(0) = |0 - 1| + 2}[/tex]
[tex]\mathbf{f(0) = |- 1| + 2}[/tex]
Remove absolute brackets
[tex]\mathbf{f(0) = 1 + 2}[/tex]
[tex]\mathbf{f(0) = 3}[/tex]
[tex]\mathbf{g(x) = (x + 3)}[/tex]
Substitute 0 for x
[tex]\mathbf{g(0) = (0 + 3)}[/tex]
[tex]\mathbf{g(0) = 3}[/tex]
[tex]\mathbf{h(x) = (x + 1) - 3}[/tex]
Substitute 0 for x
[tex]\mathbf{h(0) = (0 + 1) - 3}[/tex]
[tex]\mathbf{h(0) = 1 - 3}[/tex]
[tex]\mathbf{h(0) = - 2}[/tex]
Hence, the ordered pair that represents the greatest y-intercept is (0,3)
Read more about ordered pairs at:
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evaluate:
(5-6)^2 x (4+3)
Answer:
7
Step-by-step explanation:
( -1 ) ^ 2 = 1 * ( 4 + 3 ) 1 * ( 4 + 3 ) = 71 * 7 = 7i Hope this helps
Answer:
7Step-by-step explanation:
[tex] {(5 - 6)}^{2} \times (4 + 3)[/tex]
Calculate the difference
[tex] = {( - 1)}^{2} \times (4 + 3)[/tex]
Add the numbers
[tex] = {( - 1)}^{2} \times 7[/tex]
Evaluate the power
[tex] = 1 \times 7[/tex]
Any expression multiplied by 1 remains the same
[tex] = 7[/tex]
Hope this helps...
Best regards!!
A rectangular playground has an area of 180 square yards. The length of the playground is 3 yards longer than the width. Find the length of the playground.
A)15 yards
B)18 yards
C)12 yards
D)13 yards
Answer: The length is 15 yards so the answer is A.
Step-by-step explanation:
If the length is 3 more than the width the we will represent it by the equation L = w+3 where w is the width and to find the area of a rectangle, we need to multiply the length by the width. so the length is w+3 and the width is w so
w(w+3) = 180 solve for the w
w^2 + 3w = 180 subtract 180 from both sides
w^2 + 3w -180 = 0 find two numbers that their product is -180 and add to 3.
the number 12 and -15 works out because -12*15= -180 and -15+ 12 =3
We will now have a new quadratic equation as
w^2 - 12w + 15w - 180 = 0 factor by grouping
w(w-12) 15(w-12)= 0 factor out w-12
(w-12)(w+15) = 0 set them both equal zero.
w -12 = 0 or w+15= 0
w = 12 or w = -15
Since we know that -15 can't represent a distance, then 12 is the width .
So if we are to find the length and it gives us the information that the length is 3 yards more that the width then we will add 3 to the width to equal the length.
L= 12 +3
L = 15
The length of the rectangular playground is 15 yards. The correct answer would be an option (A).
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
Since the length is 3 more than the width
So, we will represent it by the equation L = W+3 ...(i)
A rectangular playground has an area of 180 square yards
So, L × W = 180
Substitute the value of equation (i), and we get
W(W+3) = 180
W² + 3W = 180
W² + 3W -180 = 0 ...(i)
Solving the above quadratic equation, we get the values of W :
W = 12 and W = -15
Take positive value because dimensions can't be negative.
Substitute the value of W = 12 in equation (i), and we get
L = 12 + 3 = 15
Therefore, the length of the playground is 15 yards.
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12)
Solve the problem.
12) A commercial building contractor is trying to decide which of two
projects to commit her company to.
Project A: a profil of $50,000 with a probability of 0.6, a profit of $90,000
with a probability of 0.3, and a profit of $10,000 with a probability of 0.1.
Project B: a profit of $100,000 with a probability of 0.1, a profit of $64,000
with a probability of 0.7, and a loss of $20,000 with a probability of 0.2.
Find answer lines 1 & 2)the expected profit for each & (answer line 3
which project should be selected.
Answer:
Project A : $58,000
Project B: $52800
Project A should be selected as it has a higher expected profit value than project B
Step-by-step explanation:
Given the following:
PROJECT A:
Profit : ---------50000--90,000--10,000
Probability: ----0.6-------0.3--------0.1
PROJECT B:
Loss of 20,000 = -20,000 in profit terms
Profit : -----100,000--64,000--(-20,000)
Probability: ----0.1-------0.7--------0.2
Expected profit:
Profit value * probability of profit
Expected profit on project A:
[(50000*0.6)+(90000*0.3)+(10000*0.1)
30000 + 27000 + 1000 = $58000
Expected profit on project B:
[(100000*0.1)+(64000*0.7)+(-20000*0.2)
10000 + 44800 - 4000 = $50800
Project A should be selected as it has a higher expected profit value than project B
How do the functions compare over the interval The exponential grows at approximately half the rate of the quadratic. The exponential grows at approximately the same rate as the quadratic. The exponential grows at approximately twice the rate of the quadratic. The exponential grows at approximately four times the rate of the quadratic. Mark this and return
Answer:
Correct Option: B
Step-by-step explanation:
Linear functions are the type of functions that are applied to model occurrences that rise or fall at a constant proportion. These sorts of functions are polynomial functions with a maximum exponent of one on the variable. The graphs of these kind of functions are in the form of a line.
Exponential functions are the type of functions that have the variable in exponent form. The growth rate or decline rate is either slow than quick or quick than slow.
Quadratic functions are of the form f (x) = ax² + bx + c. The graph of this function is in the form of a parabola. The graph first increases, hit a maximum, then decreases or decreases, hit a minimum, then increases.
From the provided graphs it can be seen that, the exponential function grows at approximately the same rate over the interval 0 ≤ x ≤ 1 as the quadratic function.
Answer:
bbb
Step-by-step explanation:
solve for e.
0.75(8 + e) = 2 - 1.25e
Answer:
e = -2
Step-by-step explanation:
Well to solve for e in the following equation,
.75(8 + e) = 2 - 1.25e
We need to distribute and use the communicative property to find e.
6 + .75e = 2 - 1.25e
-2 to both sides
4 + .75e = -1.25e
-.75 to both sides
4 = -2e
-2 to both sides
e = -2
Thus,
e is -2.
Hope this helps :)
if x^2=20 what is the value of x will give brainliest for answer
Answer:
x² - 20 = 0
Using the quadratic formula
[tex]x = \frac{ - b± \sqrt{( {b})^{2} - 4ac } }{2a} [/tex]
a = 1 b = 0 c = -20
So we have
[tex]x = \frac{ - 0 ± \sqrt{ {0}^{2} - 4(1)( -20)} }{2(1)} \\ \\ x = \frac{± \sqrt{80} }{2} \\ \\ x = \frac{±4 \sqrt{5} }{2} \\ \\ \\ x = ±2 \sqrt{5} \\ \\ \\ x = 2 \sqrt{5} \: \: \: or \: \: \: x = - 2 \sqrt{5} [/tex]
Hope this helps you.
Question 4 of 8
Consider the recursive function of an arithmetic sequence below.
f(1) = 3
f(n) = f(n − 1) + 4, for n = 2, 3, 4,...
What is the 6th term of the sequence?
19
23
27
22
Submit
Answer:
[tex]\large \boxed{\sf \ \ 23 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]a_1=f(1)=3\\\\a_2=f(1)+4=3+4=7\\\\a_3=f(3)=a_2+4=7+4=11\\\\a_4=a_3+4=11+4=15\\\\a_5=a_4+4=15+4=19\\\\a_6=a_5+4=19+4=23[/tex]
So the answer is 23.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Write an equation for the line that is parallel to the given line and that passes through the given point. y=34x−9;(−8,−18)
Answer:
Step-by-step explanation:
eq. of line parallel to y=34x-9 is y=34 x+k
∵ it passes through (-8,-18)
∴-18=34×-8+k
k=-18+272
k=254
so reqd. eq. is y=34 x+272
Name the postulate or theorem you can use to prove...
Bus A and Bus B leave the bus depot at 7 am. Bus A takes 25 minutes to do its route and bus B takes 40 minutes to complete its route. At what time are they both back at the bus depot together? Give your answer as a 12-hour clock time.
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Explanation:
List out the multiples of 25 to get {25, 50, 75, 100, 125, 150, 175, 200}
Do the same for the multiples of 40 to get {40, 80, 120, 160, 200}
We see that the lowest common multiple (LCM) is 200
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Another way to get the LCM is to multiply 25 and 40 to get 25*40 = 1000. Then divide this over 5 as this is the GCF between the two original numbers. We end up with the same LCM since 1000/5 = 200.
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There's a third way to get the LCM
List out the prime factorization of each value
25 = 5*5
40 = 2*3*5
Note how we have the unique factors of 2, 3 and 5. Circle the unique factors such that we highlight the ones that occur the most. We have 2 occur once, 3 occur once, and 5 occurs twice. We have circled one 2, one 3, and two 5's. They multiply out to 2*3*5*5 = 8*25 = 200
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Whichever method works for you, the LCM is 200. This means that every 200 minutes, we have bus A and bus B arrive at the depot at the same time. Their cycles line up at the 200 minute mark.
Convert this to hours,minutes format.
200 minutes = 180 minutes + 20 minutes
200 minutes = 3 hours + 20 minutes
200 minutes = 3 hrs, 20 min
We can represent "3 hrs, 20 min" in 12-hour clock notation by writing 3:20
Add this onto 7:00, which is 7 AM and we get
(7:00) + (3:20) = (7+3):(00+20) = 10:20 AM
We have started at 7 AM and fast forwarded 3 hours and 20 minutes to arrive at 10:20 AM.
find the quotient of and express it in the simplest form
Answer:
No answer can be found
Step-by-step explanation:
There isn't any value to find and express in simplest form lol.
what is the measures of ∠x
Answer:
x = 64
Step-by-step explanation:
∠ HIA and ∠ LJK are corresponding angles and congruent, thus
∠ HIA = 60°
The sum of the 3 angles in Δ HIA = 180° , thus
x = 180 - (60 + 56) = 180 - 116 = 64
find the coordinates of the point first whose abscissa is -5 and ordinate is 4
Answer:
The coordinate of the point is (-5, 4)
Step-by-step explanation:
In a regular two dimensional graph, the abscissa is the horizontal or x - axis while the y-axis which is the vertical axis is referred to as the ordinate
Abscissa and ordinate are used in mathematics to indicate the coordinate of a point in a two dimensional coordinate system, where the abscissa and ordinate are placed in between a parenthesis, with the abscissa being on the left and the ordinate on the right separated by a comma.