Answer:
A.
f(x+1)=5/2f(x) with f(1)=3/2
Step-by-step explanation:
So we are looking for a recursive form of
[tex]f(x)=\frac{3}{2}(\frac{5}{2})^{x-1}[/tex].
This is the explicit form of a geometric sequence where [tex]r=5/2[/tex] and [tex]a_1=\frac{3}{2}[/tex].
The general form of an explicit equation for a geometric sequence is
[tex]a_1(r)^{n-1} \text{ where } a_1 \text{ is the first term and } r \text{ is the common ratio}[/tex].
The recursive form of that sequence is:
[tex]a_{n+1}=ra_n \text{ where you give the first term value for } a_1[/tex].
So we have r=5/2 here so the answer is A.
f(x+1)=5/2f(x) with f(1)=3/2
By the way all this says is term is equal to 5/2 times previous term.
Answer:
A
Step-by-step explanation:
Edge 2021
A florist makes a bouquet using 4 roses, 5 carnations, and 3 daffodils.
write the ratio of carnations to daffodils in three different ways.
Answer:
5:3
5 to 3
3/5
There are three ways to write numbers as ratios
As a ratio:
x:y
As a word sentence:
x to y
As a fraction:
x/y
Answer:
The ratio of carnations to daffodils in three different ways are 5/3, 5:3 and 5 to 3.
Step-by-step explanation:
Given information:
Number of roses = 4
Number of carnations = 5
Number of daffodils = 3
We need to write the ratio of carnations to daffodils in three different ways.
The three different ways to write as ratio are
1. Fraction
[tex]\frac{x}{y}[/tex]
2. Ratio using colon
[tex]x:y[/tex]
3. Word form
x to y
The ratio of carnations to daffodils is
[tex]\frac{\text{Number of carnations}}{\text{Number of daffodils}}=\frac{5}{3}[/tex]
It can be written as 5:3 and 5 to 3.
Therefore the ratio of carnations to daffodils in three different ways are 5/3, 5:3 and 5 to 3.
What is the prime factorization of 621?
Answer:
The prime factors of 621 are 3*3*3*23 ....
Step-by-step explanation:
Prime factorization is the process of finding that which prime numbers can be multiplied together to make the original number.
Find the prime factors of 621.
Start with the smallest prime number which is 2. If the number is divisible by 2 then solve further. If not then move to the next prime number.
621 is nor divisible by 2
We move towards the next prime number which is 3.
621 divided by 3 = 207
207 divided by 3 = 69
69 divided by 3 = 23
Now 23 is only divisible by 23 which is also a prime number.
Thus the prime factors of 621 are 3*3*3*23 ....
A famous instance of variation is Newton’s Law of Gravity. It states that the magnitude of the Force, F, of gravitational attraction between two masses, m1 and m2, varies directly with the product of the masses and inversely with the square of the distance, r, between them. Write a variation equation relating F, m1, m2, and r.
[tex]\bf \qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ F=\cfrac{k(m_1\cdot m_2)}{r^2}\leftarrow \textit{F varies directly with a product and inversely with }r^2[/tex]
What is the solution to the equation 1/4x+2=-5/8x-5
Answer:
-8
Step-by-step explanation:
Start by multiplying both sides by 4.
[tex]\frac{1}{4} x+2=-\frac{5}{8} x-5\\x+8=-\frac{5}{2} x-20[/tex]
Next, multiply both sides by 2.
[tex]x+8=-\frac{5}{2} x-20\\2x+16=-5x-40[/tex]
Now, combine like terms.
[tex]2x+16=-5x-40\\7x+16=-40\\7x=-56\\x=-8[/tex]
Answer:
-8 on edg
Step-by-step explanation:
true or false ? The segment ab is congruent to the segment bo
Answer:
True
Step-by-step explanation:
The segment ¯AB¯ is congruent to the segment ¯BC¯ .
The point is in between the circle.
Therefore, they are congruent.
True. The segment AB is congruent to the segment BC.
How to know two line segments are congruent ?If the length of both the line segments are same, then we can say that both the line segments are congruent to each other.
Is the statement true or false ?Here, in the given diagram AC is a chord of the circle centering at O.
B is a point on the chord AC.
The radius of the circle which is perpendicular to AC & passes through B,forms right angle at point B.
Since, AC is a chord of the circle & a radius is perpendicular to AC, the the intersecting point of AC & the radius is midpoint of AC.
So, B is the midpoint of AC.
∴ Line segment AB = Line segment BC
Hence, Segment AB is congruent to segment BC.
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What is the solution of the equation x2 + 8x + 5 = 0?
Answer:
x = -0.683 (3dp)
x = -7.317 (3dp)
Step-by-step explanation:
Step 1: Apply the quadratic formula
(-b±([tex]\sqrt{b^{2}-4ac}[/tex])) / 2a
a = 1 (x²)
b = 8 (8x)
c = 5 (5)
(-8±([tex]\sqrt{8^{2}-4 x 1 x 5}[/tex])) / 2 x 1
Step 2: Simplify
(-8±([tex]\sqrt{44}[/tex])) / 2
Step 3: Solve
You need to replace the ± with first a + and then a -.
(-8+([tex]\sqrt{44}[/tex])) / 2 = -0.683 (3dp) = x
(-8-([tex]\sqrt{44}[/tex])) / 2 = -7.317 (3dp) = x
Hope this helps!
A man walked north 119 feet and then west 120 feet. Find the shortest distance between the start and end points.
Answer:
169 feet
Step-by-step explanation:
(see attached)
Masha had 200 scoops of ice cream and Liz had 180 scoops. After they each ate an equal amount of scoops, the ratio of Masha’s scoops to Liz’s scoops was 3:2. How many scoops did each of them eat?
Answer:
Each of them eat 140 scoops.
Step-by-step explanation:
Let x be the amount eaten by each of them,
Given,
The initial ice cream Masha has = 200 scoops
Final ice cream Masha has = ( 200 - x ) scoops
while the initial ice cream Liz has = 180 scoops,
Final ice cream Liz has = (180-x) scoops,
According to the question,
[tex]\frac{200-x}{180-x}=\frac{3}{2}[/tex]
[tex]400-2x=540-3x[/tex] ( by cross multiplication )
[tex]-2x=140-3x[/tex] ( Subtracting 400 on both sides )
[tex]x=140[/tex] ( adding 3x on both sides )
Hence, each of them eat 140 scoops.
Answer: 140 scoops.
Hope this helped!
Use the quadratic formula to solve the equation
2x^2- 3x+8 = 0
Answer:
Look at pic.
Step-by-step explanation:
Hope this helps!
Using the quadratic formula, the roots of the equation 2x^2 - 3x + 8 = 0 are found to be complex numbers. The roots are: x = 3/4 ± sqrt(-55) / 4.
Explanation:The subject of this question is the solution to the quadratic equation using the quadratic formula. The quadratic formula is used to find the roots of a quadratic equation, which is an equation of the form ax^2 + bx + c = 0.
The quadratic formula is given by: x = [-b ± sqrt(b^2 - 4ac)] / (2a)
For your equation, 2x^2 - 3x + 8 = 0, the values are a = 2, b = -3 and c = 8.
We substitute these values into the quadratic formula:
x = [3 ± sqrt((-3)^2 - 4*2*8)] / (2*2)
After carrying out the operations, we obtain:
x = [3 ± sqrt(9 - 64)] / 4
The term inside the square root is negative, meaning that the roots of the equation are complex numbers:
x = [3 ± sqrt(-55)] / 4
The answer to the equation is: x = 3/4 ± sqrt(-55) / 4
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Michelle is on a secret mission to reclaim artifacts that were recently stolen from the National Museum. The artifacts are located in a private manor just outside the city. The rectangular base of the manor is 60m by 30m.
Help Michelle plan her mission by redrawing the base of the manor by moving points on the grid below.
HELP!!
The drawing should be 10 units in width and 5 units in height.
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
What are problem-solving and examples?Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Learn more about Problem-solving here: brainly.com/question/13818690
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Alex and Alicia are twins. Kevin is 5 years older than the twins. Their ages total 53. How old are the twins?
(Pictures included, pls help)
Carlos draws a transversal, t, on two parallel lines AB and CD, as shown below:
He makes the following table to prove that the alternate interior angles are equal:
Which is The missing justification?
A) Opposite Interior Angles Are congruent when parallel lines are intersecting by a transversal
B) Vertical Angles Formed By Two Intersecting Segments Are Congruent
C) Adjacent Angles Formed By Two Interesting Segments Are Supplementary
D) Opposite Exterior Angles Are Congruent When Parallel Lines Are Intersected By A transversal
Answer:
Option B
Step-by-step explanation:
When two intersecting lines cut each other they form four angles. these two pair of angles are called opposite angles or vertical angles. The vertical angles formed by two intersecting segments are equal.
Thus option B is correct: The vertical Angles Formed By Two Intersecting Segments Are Congruent !
Answer:
B.
Step-by-step explanation:
When you intersect two lines, the angles opposite by the intersection vertex has the same measure. Generally, Those angles are called vertical angles.
In the figure, we have that angle 1 and angle 3 are vertical angles, then both have the same measure. So, the correct option is B) Vertical Angles Formed By Two Intersecting Segments Are Congruent.
Is the following graph linear, nonlinear and/or a relation?
Answer:
B. Linear function and a relation
Step-by-step explanation:
The graph is a straight line and by definition a linear function.
Each point on the line can be expressed as an ordered pair i.e the coordinates (x,y), implying that there is a relation between x and y.
Answer:
B. Linear function and a relation
Step-by-step explanation:
The following terms are defined like so,
Linear: linear functions show up as straigh lines when plotted on a graph
Non-Linear: non-linear functions show up as curvy or wavvy lines when plotted on a graph
Relation: relation graphs have specific outputs for every input, meaning for every x location on the graph there is only one y point.
Based on the definitions above we can determine that the graph in the diagram is both Linear and a Relation, since it is both a straight diagonal line as well as only having one specific y coordinate for every x coordinate. So the answer would be B. Linear function and a relation.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Which is the graph of the equation y-1=2/3(x-3)?
PLEASE ANSWER ASAP
Answer:
Graph #1
Step-by-step explanation:
Compare your
y - 1 = (2/3)(x - 3) to
y - k = m(x - h). We see that k = 1 and h = 3.
Thus, (1, 3) is a point on the graph. This matches Graph #1.
Note: Graph #1 and Graph #3 appear to be the same. Why?
The graph of the equation is:
Graph 1
Step-by-step explanation:The equation is given by:
[tex]y-1=\dfrac{2}{3}\times (x-3)[/tex]
Now, we will see the point through which the graph passes through.
when x=3 we have:
[tex]y-1=\dfrac{2}{3}\times (3-3)\\\\i.e.\\\\y-1=\dfrac{2}{3}\times 0\\\\i.e.\\\\y-1=0\\\\i.e.\\\\y=1[/tex]
i.e. the graph passes through (3,1)
and also when x= -3 we have:
[tex]y-1=\dfrac{2}{3}\times (-3-3)\\\\i.e.\\\\y-1=\dfrac{2}{3}\times -6\\\\i.e.\\\\y-1=2\times -2\\\\i.e.\\\\y-1=-4\\\\i.e.\\\\y=-4+1\\\\i.e.\\\\y=-3[/tex]
i.e. the graph passes through (-3,-3)
The graph which satisfies these two points is: Graph 1
What is the surface area of the figure?
Answer:
0.6625 in²
Step-by-step explanation:
The surface area of this figure will be the area of the base added to area of the triangles
Area of the 4 triangles
Area of a triangle is given by ;
[tex]A=\frac{1}{2} *b*h[/tex]
where b is the base length and h is the height of the triangle
Area of 1 triangle
Given base length as 0.25 inches and height is 1.2 inches.
[tex]A=\frac{1}{2} *0.25*1.2=0.15\\[/tex]
Area of all 4 triangles
- multiply the area of one triangle by 4
- 0.15*4=0.6 in²
Area of the base
The base is a square of length 0.25 inches
Area of a square=length×length
[tex]A=l*l\\A=0.25*0.25=0.0625in^{2}[/tex]
Total surface area
Total surface area= Area of the triangles + Area of the base
[tex]=0.6+0.0625=0.6625in^{2}[/tex]
What is the verbal expression for 3(n+8)
Make n be a number. You must add 8 and the number together then multiply the answer by 3. This means that the verbal expression is:
3 multiplied by the sum of a number and 8.
Hope this helped!
~Just a girl in love with Shawn Mendes
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.
Time (hours) Distance (miles)
4 260
6 390
8 520
10 650
A writer chargers $5 per word plus a startup fee of $50 per article. Write an equation in standard form to represent the total cost, y of a project that is x words long
Answer:
The answer is y=5x+50
Hope this helps!!!
Creamy Brand ice cream costs $5.50 per gallon, How much would it cost you to buy 2.25 gallons of ice cream for a party if the total tax on your order is $0.72?
Answer:
$13.00
Step-by-step explanation:
so you multiply $5.50 by 2.25 gallons
5.50
x 2.25 =
2750+1100+1100= 12.3750
then you round it off which will make your answer $12.38
then to find out how much it will be with the taxes you add $12.38 and .072 to it to make the total for the ice cream $13.00
Karen buys 2 packages of printer paper for $5.79 each, a box of pens for $9.25. a box of paperclips for $2.29, and a
calendar for $12.50. If a 6.25% sales tax is added, what is the total cost of Karen's purchase?
(SHOW WORK)
Answer: I think its $37.84625 according to the working shown :)
Step-by-step explanation:
cost of paper= $5.79, hence 2 is 2 x 5.79= 11.58
pens= $9.25
paperclips= $2.29
calendar= $12.50
Total= 11.58+9.25+2.29+12.50= 35.62
6.25% sales tax on total purchase= 6.25/100 x 35.62= $2.22625
Adding the sales tax: 35.62+2.22625= $37.84625
Answer:
$37.84625
Step-by-step explanation:
(5.79*2)+9.25+2.29+12.50=35.62
tax: 6.25% of total cost:
6.25/100 * 35.62=2.22625
total cost + tax
35.62+2.22625=37.84625
Which number is equal to 10^4?
40
1,000
10.000
40.000
Answer:
10.000
Step-by-step explanation:
10^4 is equal to 10,000.
10^4 to the second power means that you have too add 4 zeros to the end of the number.
Since 10 already has a 0, you would add 3 more.
Therefore, the answer would be 10,000.
10^4 is the same as saying 10 x 10 x 10 x 10, which is equal to 10 000.
Solve for x. Your answer must be simplified. -12x ≤ 44
Answer:
x ≥ - [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Given
- 12x ≤ 44
Divide both sides by - 12, remembering to reverse the inequality sign as a consequence of dividing by a negative quantity, hence
x ≥ [tex]\frac{44}{-12}[/tex] ← note sign reversed
Dividing the numerator/denominator by 4, gives
x ≥ - [tex]\frac{11}{3}[/tex]
Solve this equation. Solve for the letter X
-×=-34
Answer: x=34
Step-by-step explanation: Divide each side by -1 to get rid of the negatives and isolate x. You will get x = 34 as your answer.
What is the name of ostrich's meat?
Answer:
Ostrich meat is a "red meat" similar in color and taste to beef. However, it is lower in fat grams per serving compared to chicken and turkey.
Step-by-step explanation:
Hope this helped??!! :3
So far a total of 48 tickets have been sold for the school play for a total revenue of $220. How many student tickets have been sold? Set up and solve a system of equations to solve the problem.
Adult = $7
Student=$3
Last year you mowed grass and shoveled snow for 10 households. You earned $200 per household
mowing for the entire season and $180 per household shoveling for the entire season. You earn a total of
$1880 last year. Write and solve an algebraic model to determine the number of households you mow and
shovel for
Answer:
what ever it said above
Step-by-step explanation:
What is the x-intercept of the line with the equation y= 1/2 x-3
Answer:
The x intercept is 6
Step-by-step explanation:
To find the x intercept, set y =0 and solve for x
y= 1/2 x-3
0 = 1/2x -3
Add 3 to each side
0+3 = 1/2 x-3+3
3 =1/2x
Multiply each side by 2
2*3 =1/2x*2
6 =x
The x intercept is 6
the number a is a number less than -3. what is the range of possible values of 1/a squared
Answer:
Numbers less than 1/9.
Step-by-step explanation:
We are given a number [tex]a[/tex] and that it is less than -3.
That is [tex]a<-3[/tex].
What is the range of possibles for [tex]\frac{1}{a^2}[/tex]?
So if [tex]a<-3[/tex] then [tex]a^2>9[/tex].
*I knew to flip inequality here because if I square any number less than -3 it was going have a value bigger than 9.
If [tex]a^2>9[/tex], then [tex]\frac{1}{a^2}<\frac{1}{9}[/tex].
*When taking reciprocal flip the inequality.
Let's do a test:
Let's see if we pick a number less than -3 that we get a result that is less than 1/9 after we find the reciprocal of the square of the number we choose.
Let's pick -4.
-4 is less than -3
Square -4, you get 16 and 16>9.
The reciprocal of 16 is 1/16 and 1/16<1/9.
So 1/16 is a number less than 1/9.
Final answer:
The range of possible values for 1/a squared is all positive numbers greater than 0.
Explanation:
The range of possible values of 1/a squared can be determined by considering the range of values for a. Since a is a number less than -3, it means that a is a negative number less than -3. To find the range of possible values for 1/a squared, we need to consider the range of possible values for a squared. Since a squared is the square of a negative number, it will always be positive. Therefore, the range of possible values for 1/a squared is all positive numbers greater than 0.
What is the value of -3+8 when x=4
Solve the compound inequality 6b < 36 or 2b + 12 > 6.
Answer:
all values of b
Step-by-step explanation:
6b < 36 or 2b + 12 > 6.
First solve the one on the left
6b < 36
Divide by 6
6b/6 < 36/6
b <6
Then solve the one on the right
2b + 12 > 6
Subtract 12 from each side
2b+12-12 >6-12
2b >-6
Divide by 2
2b/2 >-6/2
b >-3
b<6 or b >-3
Rewriting
b>-3 or b<6
b > -3 is an open circle at -3 with a line going to the right
b < 6 is an open circle at 6 with a line going to the left
The or means we add the lines together
We have a line going from negative infinity to infinity
all values of b
Answer:
All real numbers b ∈ [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
First we solve the following inequality
[tex]6b < 36[/tex]
Divide by 6 both sides of the inequality
[tex]b<\frac{36}{6}\\\\b<6[/tex]
The set of solutions is:
[tex](-\infty, 6)[/tex]
Now we solve the following inequality
[tex]2b + 12 > 6[/tex]
Subtract 12 on both sides of the inequality
[tex]2b + 12-12 > 6-12[/tex]
[tex]2b> -6[/tex]
Divide by 2 on both sides of the inequality
[tex]\frac{2}{2}b> -\frac{6}{2}[/tex]
[tex]b> -3[/tex]
The set of solutions is:
[tex](-3, \infty)[/tex]
Finally, the set of solutions for composite inequality is:
[tex](-\infty, 6)[/tex] ∪ [tex](-3, \infty)[/tex]
This is: All real numbers [tex](-\infty, \infty)[/tex]