The correct sequence is a. 17, 26, 37.
To determine the next three terms in the sequence, we must first identify the pattern governing the sequence. Let's examine the differences between consecutive terms:
- The difference between the second term (2) and the first term (1) is 1.
- The difference between the third term (5) and the second term (2) is 3.
- The difference between the fourth term (10) and the third term (5) is 5.
- The difference between the fifth term (17) and the fourth term (10) is 7.
We can see that the differences between consecutive terms are increasing by 2 each time. This suggests that the sequence is generated by adding consecutive odd numbers to the previous term. To find the next terms, we continue this pattern:
- The sixth term will be the fifth term (17) plus the next odd number (9), which is 17 + 9 = 26.
- The seventh term will be the sixth term (26) plus the next odd number (11), which is 26 + 11 = 37.
- The eighth term will be the seventh term (37) plus the next odd number (13), which is 37 + 13 = 50.
Therefore, the next three terms of the sequence are 26, 37, and 50, confirming option a as the correct answer.
Mary borrows $5,000 dollars from her mother at a 3% simple interest rate and pays her $600 in interest after t years.
What is the value of t?
2
3
4
5
Answer:
4
Step-by-step explanation:
The simple interest per year is 3% times $5000 which is 150 dollars.
Now, we have the equation 150x = 600.
We solve and get x = 4
Finley's pumpkin had a mass of 6.56.56, point, 5 kilograms (\text{kg})(kg)left parenthesis, start text, k, g, end text, right parenthesis before he carved it. After carving it, the pumpkin had a mass of 3.9\,\text{kg}3.9kg3, point, 9, start text, k, g, end text.
What was the percent decrease in the mass of the pumpkin?
Answer:
There was 40% decrease in the mass of the pumpkin.
Step-by-step explanation:
Given:
Mass of pumpkin before carving = 6.5 kg
Mass of pumpkin after carving = 3.9 kg
Decrease in mass = Mass of pumpkin before carving - Mass of pumpkin after carving = 6.5 kg - 3.9 kg = 2.6 kg
Now to find the percentage decrease in mass we need to divide Decrease in mass with the total mass of pumpkin before carving and then multiply by 100
% Decrease in mass = [tex]\frac{\textrm{Decrese in mass}}{\textrm{Mass of Pumpkin before carving}}\times100 = 40\%[/tex]
Hence, there was 40% decrease in the mass of the pumpkin.
Answer:
40%
Step-by-step explanation:
I had this problem
what is the ratio for the surface areas of the cones shown below, given that they are similar and that the ratio of their radii and altitudes is 5:4?
Answer:
25:16 is the surface area of the cones.
Step-by-step explanation:
Given: The ratio of their radii and altitudes is 5:4.
Area of similar figures are proportional to the squares of their corresponding sides and this ratio is called scale factor.
Let z be the scale factor
∴z= [tex]\frac{5}{4}[/tex]
Now, let x be the surface area of the larger cone
and let y be the surface are of smaller cone.
∴ [tex]z^{2} = \frac{x}{y}[/tex]
next substituting the value of z ,
⇒[tex](\frac{5}{4} )^{2} =\frac{x}{y}[/tex]
∴ [tex]\frac{x}{y} = \frac{25}{16}[/tex]
The ratio for the surface area of cones is 25:16
Answer:
The correct answer is 25:16
Step-by-step explanation:
Ashley went shopping at the mall she spent 2/5 of her money on new shoes and 1/6 of her money on new jeans. What fraction part of her money remain?
Answer: 13/30 remaining
Step-by-step explanation:
well... 1 - 2/5 - 1/6 = 13/30 remaining
we use "1" to denote the money she began with
For a particular event, 709 tickets were sold for a total of $1,780. If students paid $2 per ticket and non students paid $3 per ticket, how many student tickets were sold
Answer:
709
Step-by-step explanation:
Which function equation is represented by the
graph?
f(x) = 20(1.5)^x
f(x) = 20(1.4)^x
f(x) = 20(2.5)^x
f(x) = 20(2.25)^x
please hurry in a test
Answer:
[tex]f(x)=20(2.5^x)[/tex]
Step-by-step explanation:
we know that
The function of the graph is a exponential function of the form
[tex]f(x)=a(b^x)[/tex]
Looking at the graph
we have the points
(0,20) and (1,50)
Remember that if a point lie on the graph, then the point must satisfy the function
Verify each case
For x=1, f(x)=50
case 1) we have
[tex]f(x)=20(1.5^x)[/tex]
For x=1
[tex]f(1)=20(1.5^1)=30[/tex]
so
[tex]30\neq 50[/tex]
therefore
This function is not represented by the graph
case 2) we have
[tex]f(x)=20(1.4^x)[/tex]
For x=1
[tex]f(1)=20(1.4^1)=28[/tex]
so
[tex]28\neq 50[/tex]
therefore
This function is not represented by the graph
case 3) we have
[tex]f(x)=20(2.5^x)[/tex]
For x=1
[tex]f(1)=20(2.5^1)=50[/tex]
[tex]50=50[/tex]
For x=0
[tex]f(0)=20(2.5^0)=20[/tex]
[tex]20=20[/tex]
therefore
This function is represented by the graph
case 4) we have
[tex]f(x)=20(2.25^x)[/tex]
For x=1
[tex]f(1)=20(2.25^1)=45[/tex]
so
[tex]45\neq 50[/tex]
therefore
This function is not represented by the graph
Answer:
f(x)=20(2.5)x
Step-by-step explanation:
did the test and was correct
1/2, 5/2, 12/4, 1/6, 7/8 ordered least to greatest
Answer:
1/6, 1/2, 7/8, 1/6
Step-by-step explanation:
1/6= .1666666667
1/2=.5
7/8=.875
5/2=2.5
1/6 is the smallest number than 1/2 than 7/8 and 5/2 is the greastest number.
Assume that in October of a particular year about 215 billion text messages were sent or received in the US, and the prediction is that in the next month it will be a 13% increase. About how many will be sent or received in November of the same year? Rounded to the nearest tenth of a billion.
Answer:
There will be [tex]243[/tex] billion messages sent or received in November.
Step-by-step explanation:
Given.
Number of text messages sent or received [tex]=215[/tex] billion.
Increment on the very next month [tex]=13\%=\frac{13}{100}=0.13[/tex]
Lets find what is [tex]13\%\ of\ 215[/tex]
⇒[tex]13\%\ of\ 215[/tex]
⇒[tex]0.13\times 215=27.95[/tex]
So we will add this value to our previous months data.
Now
Number of text messages sent in the month of November [tex]=(27.5+215)=242.95[/tex] billion.
Rounding to the nearest tenth the answer will be [tex]243[/tex] billion.
So [tex]243[/tex] billion text messages were sent or received in November.
What is the perimeter?
Answer:
total sum is called perimwter
the perimeter will be the outer border, and in this case we have three semi-circles and one square, well, the semi-circles have a diameter of 7, we can just get the circumference of all 3 semi-circles add them and append the 7 ft at the bottom, Check picture below.
[tex]\bf \textit{circumference of a semicircle}\\\\ C=\cfrac{\pi d}{2}~~ \begin{cases} d = diameter\\[-0.5em] \hrulefill\\ d=7 \end{cases}\qquad \implies \stackrel{\textit{circumference of all 3 semi-circles}}{3\left( \cfrac{\pi 7}{2} \right)\implies \cfrac{21\pi }{2}} \\\\\\ \stackrel{\textit{sum of all borders}}{\cfrac{21\pi }{2}~~+~~7}~~\approx ~~32.99+7~~\approx~~ 39.99[/tex]
Patsy has cheerleading practice every fourth day. She wants to be in the school play, but they have practice every sixth day. If both start on September 5th, what would be the next date she has to choose between cheerleading and play practice? Show your work and explain.
Answer:
September 17th will be the first date that she has to choose between cheerleading and play practice.
Step-by-step explanation:
Least Common Multiple for 4 and 6 is 12 that is LCM(4, 6) = 12
12 days after September 5th is September 17th
Patsy would need to choose between cheerleading and play practice on September 29th, as this is the next date when both practices fall on the same day, calculated by finding the least common multiple of the practice schedules.
Explanation:To determine when Patsy has to choose between cheerleading and play practice, we need to find the least common multiple (LCM) of the two practice schedules, since she has cheerleading every fourth day and play practice every sixth day.
First, list the multiples of both 4 and 6 until we find a common one:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...Multiples of 6: 6, 12, 18, 24, 30, ...The lowest common multiple of 4 and 6 is 12, but since our sequence started on September 5th and 12 is not a multiple of both 4 and 6, we need to keep going. Continuing our list, 24 is the next common multiple but still not satisfying both conditions. At 24 days, the cycle would repeat itself, and Patsy would again have both practices on the same day.
If these practices both start on September 5th, to find the next date she has both practices, we add 24 days to September 5th. Because September has 30 days, adding 24 days to September 5th results in September 29th. Hence, Patsy would need to choose between cheerleading and play practice on September 29th.
Use synthetic division to evaluate f(x)=3x3+x2−5x−14 when x=−2 .
To evaluate f(x)=3x3+x2−5x−14 when x=−2, use synthetic division to divide the polynomial by -2 and find the resulting value.
Explanation:To evaluate f(x) = 3x^3 + x^2 - 5x - 14 when x = -2, we can use synthetic division. First, set up the synthetic division table with -2 as the divisor and the coefficients of the polynomial as the dividend.
Perform the synthetic division by bringing down the first coefficient, multiplying it by the divisor and adding it to the next coefficient, then continuing the process until you reach the last coefficient. The result in the last row of the table will be the evaluated value of the polynomial.
In this case, the evaluated value of f(x) when x = -2 is 0.
Final answer:
To evaluate f(x)=3x^3+x^2-5x-14 when x=-2, use synthetic division to divide the polynomial by x + 2.
Explanation:
To evaluate f(x)=3x^3+x^2-5x-14 when x=-2, we can use synthetic division. First, write the coefficients of the polynomial in order: 3, 1, -5, -14. The divisor will be x - (-2), which simplifies to x + 2. Set up the synthetic division table and perform the division. The result will be the quotient and the remainder. In this case, the quotient is 3x^2 - 5x - 7 and the remainder is -20.
make x the subject of the formula.
pls help urgently. I will mark as brainliest
Answer:
see explanation
Step-by-step explanation:
Given
(bx + a)(ax + b) = (ax² + b)b ← distribute parenthesis on both sides
abx² + a²x + b²x + ab = abx² + b² ( subtract abx² from both sides )
a²x + b²x + ab = b² ( subtract ab from both sides )
a²x + b²x = b² - ab ← factor out x from each term on the left side
x(a² + b²) = b² - ab ← divide both sides by (a² + b²)
x = [tex]\frac{b^2-ab}{a^2+b^2}[/tex]
Answer:
x = -b/a
Step-by-step explanation:
(bx + a)(ax + b) = (ax^2 + b)(b) needs to be muliplied out as a first step to solving for x:
abx^2 + b^2 + a^2x + ab = abx^2 + b^2
Notice that abx^2 shows up on both sides of this equation, so we can cancel it out:
b^2 + a^2x + ab = b^2
Also, b^2 shows up on both sides, so we can also cancel the b^2 terms:
a^2x + ab = 0
Dividing both sides by a, we get ax + b = 0
and so ax = -b,
which means that x = -b/a
How to put this promble in standard notation
3.25x10
Answer:
multiply both 3.25 and 10 by 100
or
multiple 3.25 by 10 then multiply by 10
Solve for x(.07)+x=14.70
Answer:
[tex]\large\boxed{x=13\dfrac{79}{107}\approx13.74}[/tex]
Step-by-step explanation:
[tex]x(0.07)+x=14.70\qquad\text{combine like terms}\\\\(0.07+1)x=14.70\\\\1.07x=14.70\qquad\text{divide both sides by 1.07}\\\\x=\dfrac{14.70}{1.07}\\\\x=\dfrac{14.70\cdot100}{1.07\cdot100}\\\\x=\dfrac{1470}{107}\\\\x=13\dfrac{79}{107}\approx13.74[/tex]
Given ∠ABE = 45° and ∠EAB = 63° in ΔABE and∠MNP= 72° and ∠NMP = 63° in ΔMNP. Are the two triangles, ΔABE and ΔMPN similar? If so, by what criterion?
Answer:
Yes ,we can prove the two triangles are similar by angle angle test.
Step-by-step explanation:
Given:
∠ABE = 45°
∠EAB = 63° and
∠MNP= 72°
∠NMP = 63°
To Prove:
ΔABE ~ ΔMPN
Proof:
In a Triangle sum of the angles of a triangle is 180°
In ΔMPN
∴ ∠MNP + ∠NMP + ∠MPN = 180°
Substituting the given values we get,
[tex]72+63+\angle MPN = 180\\135 + \angle MPN = 180\\\angle MPN = 180-135\\\angle MPN = 45[/tex]
∠MPN = 45° ..........................( 1 )
Now,for triangles to be similar
minimum two angles should be congruent i.e AA test.all the three sides should be proportional i.e SSS testIn Δ ABE and Δ MPN
∠ ABE ≅ ∠ MPN = 45° ……….{From ( 1 ) and Given}
∠ EAB ≅ ∠ NMP = 63° ………...{Given}
Δ ABE ~ Δ MPN ….{Angle-Angle test}
..........Proved
write the pair of fractions as a pair of fractions with a common denominator 3/4 and 2/5
Answer:
The common denominator [tex]\frac{15}{20}[/tex] and [tex]\frac{8}{20}[/tex]
Step-by-step explanation:
To find the common denominator:
We have to find the LCD of the denominators.Then multiply the fraction with the digit obtained from dividing the LCD with the denominator of the fraction concerned.Here is the work:
LCD of [tex](4,5)[/tex] is [tex](4\times 5)=20[/tex].
So we will divide [tex]20[/tex] with [tex]4[/tex] and then with [tex]5[/tex] the quotient will further be put into the fraction.
So
[tex]\frac{20}{4}=5[/tex] will make the fraction [tex]\frac{3}{4}[/tex] as [tex]\frac{3\times 5}{4\times 5} =\frac{15}{20}[/tex].
Similarly
[tex]\frac{20}{5}=4[/tex] will make the fraction [tex]\frac{2}{5}[/tex] as [tex]\frac{2\times 4}{5\times 4} =\frac{8}{20}[/tex].
Hence with common denominators the fraction can be written as [tex](\frac{15}{20}),(\frac{8}{20})[/tex].
PLEASE AWNSER THIS QUESTION ASAP ;((
Answer:
Yes then no
Step-by-step explanation:
A linear function is of the form y=mx+b, where b and m are constants(not variables). Since the input is the radius, we make that x. The circumference is πd, or 2πr, so if we plug in 2π for m, circumference for y, and 0 for b, this works. The area is πr², which would mean that m would have to be πr. Since r is not a constant, this does not work.
7(8+4k)+12 What is the answer?
Answer:
68+28k
Step-by-step explanation:
Xintercept for the quadratic function f(x)=x²-8x
Answer:
x=0 and x=8
Step-by-step explanation:
The x-intercept is on the x-axis, so we must find x when y=0. f(x) is basically y and y=0, so 0=x^2-8x= x(x-8). For x(x-8) to equal 0, either x is equal to 0 (x=0) or x-8 is equal to 0 (so x is equal to 8). So the two intercepts are x = 0 and x = 8.
I hope this helped! :)
Which of the sets of ordered pairs represents a function? (5 points) A = {(1, −5), (8, −5), (8, 7), (2, 9)} B = {(7, −4), (7, −2), (6, −3), (−9, 5)}
Step-by-step explanation:
For any function,any point in the domain has a unique image in the codomain.
For set [tex]A[/tex]:
[tex]f(8)=-5[/tex] from the point [tex](8,-5)[/tex]
[tex]f(8)=7[/tex] from the point [tex](8,7)[/tex]
For a same point [tex]8[/tex],there are two images.
So,[tex]A[/tex] does not represent a function.
For set [tex]B[/tex]:
[tex]f(7)=-4[/tex] from the point [tex](7,-4)[/tex]
[tex]f(7)=-2[/tex] from the point [tex](7,-2)[/tex]
For a same point [tex]7[/tex],there are two images.
So,[tex]B[/tex] does not represent a function.
The graph of a system of equations with the same slope and the same y-intercepts will have no solutions. (1 point)
Answer:
The statement is false
Step-by-step explanation:
we know that
If a system of equations has two equations with the same slope and the same y-intercept, then both equations represent the same line
so
we have a consistent dependent system
The system has has an infinite number of solutions
therefore
The statement is false
DeShawn is selling tickets to a play. Adult tickets cost $13 each and student tickets cost $9 each. After one day of sales, DeShawn sold 23 tickets and took in a total of $271. How many student tickets did DeShawn sell?
Answer:
The number of student's tickets sold was 7
Step-by-step explanation:
Let
x ----> number of adult's tickets sold
y ----> number of student's tickets sold
we know that
[tex]x+y=23[/tex] ----> [tex]x=23-y[/tex] ---> equation A
[tex]13x+9y=271[/tex] ----> equation B
solve the system by substitution
substitute equation A in equation B
[tex]13(23-y)+9y=271[/tex]
solve for y
[tex]299-13y+9y=271[/tex]
[tex]13y-9y=299-271[/tex]
[tex]4y=28[/tex]
[tex]y=7[/tex]
therefore
The number of student's tickets sold was 7
If D=8 , what is the value of the expression 4+d/2? A.4 B.6 C.8 D.12 E.14
If the question is (4+D)/2 the answer is 6 but if the question is 4+(D/2) the answer is 8. It depends on which way the question is written.
Answer:
the answer is 8
Step-by-step explanation:
If the question is (4+D)/2 the answer is 6 but if the question is 4+(D/2) the answer is 8. It depends on which way the question is written.
The sport boosters club is having a bake sale to buy uniforms. They want to raise $250. They need to rent a booth for $20. How many dozen cookies will they need to sell if they charge $3 per dozen? Which equation could be used to solve this problem
Answer:
3x - 20 = 250
Step-by-step explanation:
Given,
The cost of cookies per dozen = $ 3,
Let x be the number of dozen cookies sold,
So, the cost of x dozen of cookies = x × cost of cookies per dozen
= 3x
Now, the amount of rent = $ 20,
Thus, total earning = cost of x dozen of cookies - rent
= 3x - 20
If $ 250 is needed to raise,
Then total earning = $ 250
⇒ 3x - 20 = 250
Which is the required equation.
What is the slant height, s, of the triangular prism?
Round your answer to the nearest tenth.
HELP ASAP!!!
Answer:
5.4
Explanation:
a²+b²=c²
2²+5²= 4+25
4+25=29
Now we have to square root the 29 which would make the answer 5.4
5.4 is the slant height of the triangular prism.
Application of Pythagoras theorem
The given figure is a triangular based pyramid and in order to determine the slant height, we will apply the pythagoras theorem as shown:
Hypotenuse = s
Opposite = 5
Adjacent = 4/2 = 2
According to the theorem:
hyp² = opp² + adj²
Substitute
s² = 5² + 2²
s² = 25 + 4
s² = 29
s = 5.4
Hence the slant height, s, of the triangular prism is 5.4
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I just need (C) nothing else but C
If you can do it you are amazing!
Answer:
(5,1)
Step-by-step explanation:
Equation of a straight ine in slope intercept form is [tex]y-y_{1} =m\times(x-x_{1} )[/tex]. from that calculate the both equations of straight lines sidewalks1 and sidewalks2 they are x+y=6 and 2x+y=11 on solving both of the equations we get the value of x to be 5 and the value of y to be 1.hence the system of linesr equations intersect at the point (5,1).
3x² + 7x - 5 + 2x²
Simplify
Answer:
3x^2 + 7x - 5 + 2x^2
= 5x^2 + 7x - 5 (a=5, b=7, c=-5)
x = (-b+/- √(b^2 - 4ac))/2a
= (-7+/- √(49+100))/10
= (-7+√149)/10, (-7-√149)/10
Hope this helps!
Problem Page A store is having a sale on jelly beans and trail mix. For 8 pounds of jelly beans and 4 pounds of trail mix, the total cost is $25 . For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $10 . Find the cost for each pound of jelly beans and each pound of trail mix.
Each pound of jelly costs $2.5 and each pound of trail mix costs $1.25
Step-by-step explanation:
Let,
Cost of jelly beans = x
Cost of trail mix = y
According to given statement;
8x+4y=25 Eqn 1
3x+2y=10 Eqn 2
Multiplying Eqn 2 by 2;
[tex]2(3x+2y=10)\\6x+4y=20\ \ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 1;
[tex](8x+4y)-(6x+4y)=25-20\\8x+4y-6x-4y=5\\2x=5[/tex]
Dividing both sides by 2;
[tex]\frac{2x}{2}=\frac{5}{2}\\x=2.5[/tex]
Putting x=2.5 in Eqn 1
[tex]8(2.5)+4y=25\\20+4y=25\\4y=25-20\\4y=5[/tex]
Dividing both sides by 4
[tex]\frac{4y}{4}=\frac{5}{4}\\y=1.25[/tex]
Each pound of jelly costs $2.5 and each pound of trail mix costs $1.25
Keywords: linear equations, subtraction
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Between which two ordered pairs does the graph of f(x) = one-halfx2 + x – 9 cross the negative x-axis?
Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction
(–6, 0) and (–5, 0)
(–4, 0) and (–3, 0)
(–3, 0) and (–2, 0)
(–2, 0) and (–1, 0)
The graph of the quadratic function f(x) = 0.5x² + x - 9 crosses the negative x-axis between the ordered pairs (-7,0) and (-6,0), and between (-2,0) and (-1,0).
Explanation:The graph of the quadratic function f(x) = 0.5x² + x - 9 crosses the negative x-axis at those x-values that make the function equal to zero. To find these, we solve for x in the equation 0.5x² + x - 9 = 0 using the quadratic formula x = -b ± √(b² - 4ac) / 2a.
Here, a = 0.5, b = 1 and c = -9. Substituting these into the formula gives x = -1 ± √(1 + 36) / 1 = -1 ± √(37) / 1. The two possible solutions are approximately -7.06 and +5.06. Therefore, the ranges of x-values crossing the negative x-axis are between the ordered pairs (-7,0) and (-6,0), as well as between (-2,0) and (-1,0).
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The function f(x) = one-halfx2 + x - 9 intersects the negative x-axis between the ordered pairs (-4, 0) and (-3, 0) and also between (-3, 0) and (-2, 0) when solved using the quadratic formula.
Explanation:The question concerned is a quadratic function, specifically, it wants to know where f(x) = one-halfx2 + x – 9 intersects with the negative x-axis. The x-axis is the line where y = 0, so we need to solve the equation 0.5x² + x - 9 = 0 to locate the roots. By applying the quadratic formula, x = [-b ± sqrt(b² - 4ac)] / (2a), we substitute our coefficients into the equation to get: x = [-1 ± sqrt((1)² - 4*0.5*(-9))] / (2*0.5). This will lead to two solutions, x = -2 and x = -3. Hence, the function f(x) = one-halfx2 + x – 9 intersects the negative x-axis between the ordered pairs (-4, 0) and (-3, 0) and also between (-3, 0) and (-2, 0).
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Question is in the photo. check all that apply. please help ASAP
Answer:
[tex]x-2x-6=8x+12-x-4\\-x-6=7x+8[/tex]
Step-by-step explanation:
Given:
The equation is;
[tex]x-2(x+3)=4(2x+3)-(x+4)[/tex]
Now we need to simplify this equation we get;
Step 1: We need to simplify all the terms which are in brackets we get,
[tex]x-2x-6=8x+12-x-4[/tex]
Step 2: Now we need to simplify all variable term and non variable term we get:
[tex]-x-6=7x+8[/tex]
Answer:
These two equivalent equations Katrina has used
[tex]x - 2x - 6 = 8x + 12 - x - 4\\-x - 6 = 7x + 8\\[/tex]
Step-by-step explanation:
Given :
[tex]x - 2(x + 3) = 4(2x + 3) - (x + 4)\\[/tex]
Applying distributive property that is [tex]A\times (B +C) = A\times B + A\times C[/tex] we get
[tex]x - 2x + 3\times -2 = 4\times 2x + 4\times 3 - x - 4\\[/tex]
[tex]x - 2x - 6 = 8x + 12 - x - 4\\-x - 6 = 7x + 8\\[/tex]