Answer:
https://www.dasd.org › 4444PDF
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Entering Algebra 2: Answer Key
Find out the values of x and y from the following ordered pairs.
(x + y, 2) = (13, 2x – y)
Answer:
(x, y) = (5,8)
Step-by-step explanation:
Comparing the ordered pairs we get, x+y=13 and 2=2x-y. Solving it we will get, x=5 and y=8
Question 4 of 5
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
Match each explicit formula to its corresponding recursive formula.
(8) = 5(5)(1-1)
(n) = 3 +5(n-1)
(3) = 5+3(1-1)
7(n) = 3(5)(n-1)
$(n) = 5 +5(n-1)
f(1) = 5
(*) = 3;(n - 1), for 3
(1) = 5
(n) = f(n-1) +5, for n?
f(1) = 5
f(n) = f(n-1) + 3, for n?
Given:
The recursive formulae.
To find:
The correct explicit formulae for the given recursive formulae.
Solution:
If the recursive formula of a GP is [tex]f(n)=rf(n-1), f(1)=a, n\geq 2[/tex], then the explicit formula of that GP is:
[tex]f(n)=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
The first recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=3f(n-1)[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of a GP with a=5 and r=3. So, the required explicit formula is:
[tex]f(n)=5(3)^{n-1}[/tex]
Therefore, the required explicit formula for the first recursive formula is [tex]f(n)=5(3)^{n-1}[/tex].
If the recursive formula of an AP is [tex]f(n)=f(n-1)+d, f(1)=a, n\geq 2[/tex], then the explicit formula of that AP is:
[tex]f(n)=a+(n-1)d[/tex]
Where, a is the first term and d is the common difference.
The second recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+5[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an AP with a=5 and d=5. So, the required explicit formula is:
[tex]f(n)=5+(n-1)5[/tex]
[tex]f(n)=5+5(n-1)[/tex]
Therefore, the required explicit formula for the second recursive formula is [tex]f(n)=5+5(n-1)[/tex].
The third recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+3[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an AP with a=5 and d=3. So, the required explicit formula is:
[tex]f(n)=5+(n-1)3[/tex]
[tex]f(n)=5+3(n-1)[/tex]
Therefore, the required explicit formula for the third recursive formula is [tex]f(n)=5+3(n-1)[/tex].
Can someone please help me with this I’m struggling
Answer:
Equation: [tex]70=(x+3)x[/tex]
x = -10 or x = 7
x = 7 (width can't be negative)
x + 3 = 10
Step-by-step explanation:
Represent the width of the rectangle by x. "The length of a rectangle EXCEEDS the width by 3" means the length is 3 LONGER than the width, so the length is represented by the expression x + 3.
Area = (length)(width)
70 = (x + 3)x
Multiply out the right side.
[tex]70=x^2+3x\\x^2+3x-70=0[/tex]
Factor the left side.
[tex](x+10)(x-7)=0[/tex]
Each binomial could equal 0, so
[tex]x+10=0 \text{ or }x-7=0\\x=-10\text{ or }x=7[/tex]
The negative solution does not make sense as the width of a rectangle.
x = 7, making the length, x + 3 = 10
Answer:
Pls mark this as brainiest
Step-by-step explanation:
Area of the rectangle = length x breadth
consider 'x' to be width
therefore length = x+3
area = (x+3)*x
Area = 70 square
x = 7
x+3 = 7+3
= 10
verification
7 x 10
= 70
Question 4(Multiple Choice Worth 4 points)
.
(08.03)Solve the system of equations and choose the correct answer from the list of options.
X + y = -3
y = 2x + 2
a- five over 3, four over 3
b-negative five over 3, negative four over 3
c- negative 3 over 5 negative 3 over 4
D- 3 over 4, 3 over 5
Answer:
Hello,
Answer B (-5/3,-4/3)
Step-by-step explanation:
I am going to use the substitution 's method.
[tex]\left\{\begin{array}{ccc}x+y&=&-3\\y&=&2x+2\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&2x+2\\x+2x+2&=&-3\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&2x+2\\3x&=&-5\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}x&=&-\dfrac{5}{3} \\\\y&=&2*(-\dfrac{5}{3})+2\\\end {array} \right.\\\\\\\boxed{\left\{\begin{array}{ccc}x&=&-\dfrac{5}{3} \\\\y&=&-\dfrac{4}{3}\\\end {array} \right.\\}[/tex]
Find the distance between the
following points using the
Pythagorean theorem: (5, 10)
and (10, 12)
Answer:
[tex]\displaystyle d = \sqrt{29}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]Step-by-step explanation:
*Note:
The distance formula is derived from the Pythagorean Theorem.
Step 1: Define
Identify
Point (5, 10)
Point (10, 12)
Step 2: Find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(10 - 5)^2 + (12 -10)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{5^2 + 2^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{25 + 4}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{29}[/tex]Please help me answer this question.
Answer:
total candy = 54 bags
y=17
x=37
Step-by-step explanation:
5x + 4y = 253
x-y = 20
x = 20+y
5(20+y) + 4y = 253
100 + 9y = 253
9y = 153
y=17
x=37
GIVE FULL STEP BY STEP OF THIS MATHS WORD PROBLEM
Sohanlal is a gardener. He is paid ₹160 daily, find how much money will he
get in the month of September?
Answer:
Step-by-step explanation:
days in september=30
salry paid per day=Rs.160
salary paid in 30 days=160×30=Rs.4800
Answer:
4800
Step-by-step explanation:
In the month of September there are only 30 days. So assuming Sohanlal works the entire month of September we will multiply how much he makes daily which is 160 times the amount of days he works which is 30. this will look like this:
160 × 30 = 4800
6. The right triangles ABC and DEF are
similar. The hypotenuse of AABC
measures 28 cm and the hypotenuse
of A DEF measures 7 cm. If one of the
legs of AABC measures 16 cm, what
does the corresponding leg of ADEF
measure?
F 1 cm
H 12 cm
G 4 cm
J 64 cm
Answer:
G. 4 cm
Step-by-step explanation:
28 divided by 7 equals 4.
So, 16 divided by 4 equals 4, which is the answer.
4 is the multiple that relates AABC to ADEF.
the diagram shows a prism work out the volume???
Answer:
Volume is equal to
L×W×H
=(10×9×7)cm
=90×7
=630
The volume of the prism is 980cm3.
We are given that;
The dimensions= 4*7*9*2*10cm
Now,
A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.
The volume of a rectangular prism=Length X Width X Height
Volume of upper prism;
=5*4*40
=800cm3
Volume of lower prism;
=2*9*10
=180cm3
Total volume= upper volume + lower volume
=980cm3
Therefore, by the rectangular prism the answer will be 980cm3.
Learn more about a rectangular prism;
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Simplify the expression -4^2(3x - 7)
Answer:
−48x+112
Step-by-step explanation:
evatulate: −16 (3−7)
-48+112
Can you answer this math homework? Please!
Answer:
y + 2.3 = 0.45x
y = 0.45x - 2.3
-2y = 4.2x - 7.8
-2(0.45x - 2.3) = 4.2x - 7.8
-0.90x + 4.6 = 4.2x - 7.8
-0.90x - 4.2x = -7.8 - 4.6
-5.1x = - 12.4
x = -12.4 / -5.1
x = 2.4
y + 2.3 = 0.45x
y = 0.45(2.4) - 2.3
y = 1.08 - 2.3
y = -1.2
solution is : (2.4, - 1.2)
Step-by-step explanation:
Complete the missing parts of the
table for the following function. (picture) please answer all asap
Answer:
x=-1 y = 1/3
x = 1 y = 3
x = 3 y = 27
Step-by-step explanation:
y = 3^x
Let x = -1
y = 3^-1 = 1/3^1 = 1/3
Let x = 1
y = 3^1 = 3
Let x = 3
y = 3^3 = 27
the polygons in each pair are similar. find the missing side length.
Given:
The polygon in the given figure are similar.
To find:
The missing side length.
Solution:
We know that the corresponding sides of similar figures are proportional.
The given polygons are similar, so the their corresponding sides are proportional.
[tex]\dfrac{x}{15}=\dfrac{32}{40}=\dfrac{32}{40}[/tex]
So, the missing values in the equation of proportion are 15, 40, 32 respectively.
On solving the above equation, we get
[tex]\dfrac{x}{15}=\dfrac{4}{5}=\dfrac{4}{5}[/tex]
[tex]\dfrac{x}{15}=\dfrac{4}{5}[/tex]
[tex]x=\dfrac{4}{5}\times 15[/tex]
[tex]x=12[/tex]
Therefore, the value of x is 12.
9. what is the measure of QSR
=======================================================
Explanation:
Extend segment MN such that it intersects side ST. Mark the intersection as point A. See the diagram below.
We're given that angle MNT is 72 degrees. The angle TNA is equal to 180-(angle MNT) = 180 - 72 = 108 degrees, since angles MNT and TNA add to 180.
For now, focus entirely on triangle TNA. We see from the diagram that T = 34 and we just found that N = 108. Let's find angle A
A+N+T = 180
A+108+34 = 180
A+142 = 180
A = 180-142
A = 38
So angle NAT is 38 degrees.
----------------------------
Since segment MA is an extension of MN, and because MN || SQ, this means MA is also parallel to SQ.
We found at the conclusion of the last section that angle NAT was 38 degrees. Angles QST and NAT are corresponding angles. They are congruent since MA || SQ. This makes angle QST to also be 38 degrees
----------------------------
The angles QSR and QST are a linear pair, so they are supplementary
(angle QSR) + (angle QST) = 180
angle QSR = 180 - (angle QST)
angle QSR = 180 - 38
angle QSR = 142 degrees
i need help ASAP please
Answer:
reflection over Y axis
Step-by-step explanation:
Answer:
I believe it is D) a reflection over the Y-axis
Step-by-step explanation
it is going over the Y-axis as if it is a sort of mirror, if it were going over the x-axis it would be flipped upside down, if it was A the shape would be going over the original shape. I don't know how to explain C. (I hope this helped and I hope it was correct lol)
28.35 g in an ounce and 2.21 lb in a kilogram. convert 3 kilograms to ounces. Is conversion correct? Explain. please
Answer:
Whether her conversion is correct or not, you can just base it on the true answer. For this problem, we apply the technique of dimensional analysis. You can like units if they both appear on the numerator and the denominator side. The solution is as follows:
Mass in ounces = 3 kg * (1,000 g/ 1 kg) * (1 ounce/28.35 g) = 105.82 ounces
How do you solve this problem?
9514 1404 393
Answer:
-19.2
Step-by-step explanation:
Fill in the given values and do the arithmetic.
[tex]\displaystyle x\ \blacksquare\ y=\frac{x}{y}-xy\\\\4\ \blacksquare\ 5=\frac{4}{5}-4\cdot5=0.8-20\\\\\boxed{4\ \blacksquare\ 5=-19.2}[/tex]
not sure if this makes sense to you guys but if you can help that'd be great. 15 points(all i have left) due today. thank you!!
Answer:
The graph that have 2 lines is for Question 21 and the graph with three lines is for Question 22
Step-by-step explanation:
(6.6 x 10{-2}) (3.3 x 10{-4})
Answer:
17424
Step-by-step explanation:
(6.6 x 10(-2) ( 3.3 x 10(-4))
(6.6 x - 20) ( 3.3 x -40)
(-132) (-132)
=17424
4 raised to power two minus 8u minus 9=0
Answer: u = [tex]\frac{7}{8}[/tex] or 0.875
Step-by-step explanation:
Let us convert this statement to a question
[tex]4^{2}[/tex]-8u-9 = 0
16-8u-9 = 0
-8u = 0+9-16
-8u = -7
u = -7 ÷ -8
u = [tex]\frac{7}{8}[/tex] or 0.875
Dan invests £18790 into his bank account. He receives 5.9% per year simple interest. How
much will Dan have after 2 years? Give your answer to the nearest penny where appropriate.
Answer: £21007.22
Step-by-step explanation:
First, find the interest amount using the formula SI = (P × R × T) / 100.
SI = interest amount P = principle amount = £18790R = interest rate(in percentage) = 5.9T = time(in years) = 2SI = (P × R × T) / 100 = (18790 × 5.9 × 2)/100 = 221722/100 = £2217.22
The total amount = principle amount + interest amount
= £18790 + £2217.22 = £21007.22
Zoe and Hanna share tips in the ratio 3:7
Last week Zoe received £24
How much did Hanna receive last week?
Answer:
56
Step-by-step explanation:
Zoe : hanna
3 7
Zoe got 24
3*8 = 24
so multiply each side by 8
Zoe : hanna
3*8 7*8
24 56
Hanna got 56
what is the formula to calculate VAT percentage
Answer:
Take the gross amount of any sum (items you sell or buy) – that is, the total including any VAT – and divide it by 117.5, if the VAT rate is 17.5 per cent. (If the rate is different, add 100 to the VAT percentage rate and divide by that number.)
Answer:
divide by 117.5 if the rate different, add 100 to the percentage and divide by the number therefore multiply by 100 to get the total
Step-by-step explanation:
the formula to calculate vat percentage
Ben is 4 times as old as Ishaan. 6 years ago, Ben was 6 times as old as Ishaan.
How old is Ishaan now?
Answer:
Ishaan is currently 15 years old.
Step-by-step explanation:
Let B represent Ben's current age and I represent Ishann's current age.
Ben is four times as old as Ishaan. In other words:
[tex]B=4I[/tex]
Six years ago, Ben was six times as old as Ishaan. In other words:
[tex]B-6=6(I-6)[/tex]
Solve for I. Substitute:
[tex](4I)-6=6(I-6)[/tex]
Distribute:
[tex]4I-6=6I-36[/tex]
Subtract 4I from both sides and add 36 to both sides:
[tex]2I=30[/tex]
And divide both sides by two. Hence:
[tex]I=15[/tex]
Ishaan is currently 15 years old.
Answer:
Age of Ishaan = 15 years
Step-by-step explanation:
Let Ishaan's age = x years
Age of Ben = 4 * x = 4x years
6Years ago:
Age of Ishaan = x - 6
Age of Ben = 4x - 6
6 years ago, Ben was 6 times as old as Ishaan
So, Age of Ben = 6 * Ishaan's age
4x - 6 = 6 *(x-6)
4x - 6 = 6x - 36
Add 36 to both sides
4x - 6 + 36 = 6x
4x + 30 = 6x
Subtract '4x' from both sides
30 = 6x - 4x
30 = 2x
2x = 30
Divide both by 2 sides
x = 30/2
x = 15
What type of line is PQ¯¯¯¯¯¯¯¯?
A. median
B. angle bisector
C. side bisector
D. altitude
Answer:
angle bisector
Step-by-step explanation:
Since the line divided the top angle into two equal pieces we call this an angle bisector.
The reliability coefficient of scores in an end of semester examination. If the variance of the exam score is 100. What is the standard error of measurement ?
Answer:
I Will explained you youuuuuu<uuuuuuuuuu
The graph of g(x) is a translation of the function f(x)=x^2. The vertex of g(x) Is located 5units above and 7 units to the right of the vertex of f(x). Which equation represents g(x)
Step-by-step explanation:
The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011. The Riemann hypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.
the length of a rectangle is 8 cm longer than its width. find the dimensions of the rectangle if its area is 108cm
!!no links!!
Answer:
[tex]4+2\sqrt{31}\text{ by } -4+2\sqrt{31}[/tex]
Or about 15.136 centimeters by 7.136 centimeters.
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A = w\ell[/tex]
Where w is the width and l is the length.
We are given that the length is 8 centimeters longer than the width. In other words:
[tex]\ell = w+8[/tex]
And we are also given that the total area is 108 square centimeters.
Thus, substitute:
[tex](108)=w(w+8)[/tex]
Solve for w. Distribute:
[tex]w^2+8w=108[/tex]
Subtract 108 from both sides:
[tex]w^2+8w-108=0[/tex]
Since the equation is not factorable, we can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = 8, and c = -108. Substitute and evaluate:
[tex]\displaystyle \begin{aligned} w&= \frac{-(8)\pm\sqrt{(8)^2-4(1)(-108)}}{2(1)} \\ \\ &=\frac{-8\pm\sqrt{496}}{2}\\ \\ &=\frac{-8\pm4\sqrt{31}}{2} \\ \\ &=-4 \pm 2\sqrt{31} \end{aligned}[/tex]
So, our two solutions are:
[tex]w=-4+2\sqrt{31} \approx 7.136 \text{ or } w=-4-2\sqrt{31}\approx -15.136[/tex]
Since width cannot be negative, we can eliminate the second solution.
And since the length is eight centimeters longer than the width, the length is:
[tex]\ell =(-4+2\sqrt{31})+8=4+2\sqrt{31}\approx 15.136[/tex]
So, the dimensions of the rectangle are about 15.136 cm by 7.136 cm.
Simplify the variable expression by evaluating its numerical part.
p-7+56 - 12
A. p + 51
B. p+37
O c. p-51
D. p + 49
The table below represents the function f, and the following graph represents the function g.
*
-6
un
4
-3
-2.
-1
0
1
f(x) 8
-2
-8 -10
-8
-2
8.
22
у
4
12
6
- 2
2
4
6
2
-4
6
Complete the following statements.
The functions fand g have
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
The known value in the question includes the following
The given table of f(x) and x, from which we have;
The point of the minimum value, which is the vertex = (-3, -10)
The axis of symmetry, of a parabola is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3
The y-intercept, which is the point the graph intercepts with the y-axis or where x = 0 is the point (0. 8)
Over the interval [-6, -3], the average rate of change of f = (-10 - 8)/(-3 -(-6)) = -6
From the graph of g(x), we have;
The axis of symmetry is the line x = -3
The y-intercept = (0, -2)
Over the interval [-6, -3], the average rate of change of g ≈ (6 - (-2))/(-3 -(-6)) = 8/3
Therefore, we have the correct options as follows;
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
Learn more about parabola here;
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