Answer:
The correct answer is Option 1: a1 = -2, an = an-1 + 5
Step-by-step explanation:
A recursive formula is a formula that uses previous term in order to calculate the next term in a sequence.
In case of arithmetic sequence, the next term is obtain by adding a specific number to the last term.
This can be written as:
[tex]a_n = a_{n-1}+d[/tex]
Here
a_n is the terms we are calculating
a_{n-1} is the previous term and d is the common difference.
If we compare the given options, we can see that only option 1 matches with the general form of recursive formula
an = an-1 + 5
Here
5 is the common difference
Hence,
The correct answer is Option 1: a1 = -2, an = an-1 + 5
What is the solution to the system of equations shown below. Show work
X-5y = 11 3x-5y=11
Answer:
The solution to the system of equations will be:
[tex]x=0,\:y=-\frac{11}{5}[/tex]
Step-by-step explanation:
Given the expression
[tex]x - 5y = 11[/tex]
[tex]3x - 5y = 11[/tex]
solving the expression
[tex]\begin{bmatrix}x-5y=11\\ 3x-5y=11\end{bmatrix}[/tex]
Multiplying x-5y = 11 by 3: 3x-15y=33
so
[tex]\begin{bmatrix}3x-15y=33\\ 3x-5y=11\end{bmatrix}[/tex]
and
[tex]3x-5y=11[/tex]
[tex]-[/tex]
[tex]\underline{3x-15y=33}[/tex]
[tex]10y=-22[/tex]
now solving 10y = -22 for y
[tex]10y=-22[/tex]
divide both sides by 10
[tex]\frac{10y}{10}=\frac{-22}{10}[/tex]
simplify
[tex]y=-\frac{11}{5}[/tex]
For 3x-5y=11 plug in y = -11/5
[tex]3x-15\left(-\frac{11}{5}\right)=33[/tex]
[tex]3x+15\cdot \frac{11}{5}=33[/tex]
[tex]3x+33=33[/tex]
Subtract 33 from both sides
[tex]3x+33-33=33-33[/tex]
Simplify
[tex]3x=0[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=\frac{0}{3}[/tex]
Simplify
[tex]x=0[/tex]
Thus, the solution to the system of equations will be:
[tex]x=0,\:y=-\frac{11}{5}[/tex]
Michelle has fifteen more than two times as many pieces of candy as her sister. Which expression represents the number of pieces of candy that Michelle has if the variable c represents the number of pieces of candy that her sister has?
The expression which represents the number of pieces of candy that Michelle has will be y = 2c + 15.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
Michelle has fifteen more than two times as many pieces of candy as her sister.
Then the expression which represents the number of pieces of candy that Michelle has will be
If the variable c represents the number of pieces of candy that her sister has. Then we have
Let y be the number of candy that Michelle has.
Then we have
y = 2c + 15
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A scanner scanned 56 photos in 7 minutes. If it scans photos at a constant rate, it can scan_ photos in 27 minutes. This is equivalent ratios. What is the answer for the blank spot guys? I need help fast!
Answer:
the answer would be 216 in 27 minutes.
Answer: 216
Step-by-step explanation:
If the scanner is able to scan 56 photos in 7 minutes, then it scans 8 photos in 1 minute. Under this rule of 8:1, then it can scan 216 photos in 27 minutes.
In a school of 400 students, 55% are females. How many of the students are female?
Answer:
220
Step-by-step explanation:
400 x .55 = 220
A, B and C are three similar shapes.
The surface area of shape A is 4 cm2
.
The surface area of shape B is 25 cm2
.
The ratio of the volume of shape B to the volume of shape C is 27 : 64.
Work out the ratio of the height of shape A to the height of shape C.
Simplify your answer, and give it in the form A : C.
+explanation pleasee :)
============================================================
Explanation
Shape A has surface area 4 cm^2
Shape B has surface area 25 cm^2
The ratio of the surface areas, from A to B, is 4:25
Apply the square root to both parts and we get 2:5 as the ratio of the corresponding sides. If shape A has a height of 2, then shape B will have a corresponding height of 5. I recommend drawing out two squares with these properties to see that their areas form the ratio mentioned above.
The ratio of the volume of shape B to shape C's volume is 27:64. Apply the cube root to both parts to get 3:4. This means if the height of shape B is 3, then the corresponding height on shape C is 4.
-----------------------
We found these ratios for the sides
A:B = 2:5B:C = 3:4The goal is to find the ratio A:B:C which ties all three shapes together showing how they all connect in terms of their corresponding sides.
Note how in A:B = 2:5 we have B = 5, but in B:C = 3:4 we have B = 3. We cannot combine the two ratios in this form since the B terms don't match.
The good news is that we can apply scaling to get the B values to match up
The ratio 2:5 is equivalent to 6:15 after multiplying both parts by 3
The ratio 3:4 is equivalent to 15:20 after multiplying both parts by 5.
The multipliers 3 and 5 are used because note how 15 is the LCM of those previous B values mentioned.
-----------------------
After scaling those ratios, we have
A:B = 6:15B:C = 15:20From here, we can quickly see that A:B:C = 6:15:20. This is possible because the '15's match up for the B terms.
If shape A has a height of 6, then shape B has a height of 15, and C has a height of 20. All of these heights correspond to one another.
Then we just erase out the B part to conclude A:C = 6:20 which reduces to A:C = 3:10 after dividing both parts by 2.
2. Find the perimeter of the new figure.
4.5 ft
31.5 ft
a family has a monthly budget of $2,400 how much money is spent on each category? 44% is spent on housing
Answer: See explanation
Step-by-step explanation:
Here's the complete question:
A family has a monthly budget of $2,400. How much money is spent on each category? 44% is spent on housing. 23% is spent on food. 6% is spent on clothing. 17% is spent on transportation. The rest is put into savings.
Housing = 44%
Food = 23%
Clothing = 6%
Transportation = 17%
Savings = 1 - (44% + 23% + 6% + 17%) = 10%
Amount spent on Housing = 44% × $2400 = 0.44 × $2400 = $1056
Amount spent on Food = 23% = 23% × $2400 = 0.23 × $2400 = $552
Amount spent in Clothing = 6% = 6% × $2400 = 0.06 × $2400 = $144
Amount spent on Transportation = 17% = 17% × $2400 = 0.17 × $2400 = $408
Savings = 10% = 10% × $2400 = 0.1 × $2400 = $240
Sandy ate 1/6 of a candy bar. John ate 3/4 of it. How much more of the candy bar did John eat than Sandy?
Explain how you solved.
step by step plesae AM TIMED
Answer:
John ate 7/12 more of the candy than Sandy.
Step-by-step explanation:
3/4 is equivalent to 9/12.
1/6 can be expressed as 2/12.
Step 3: 9/12 - 2/12 = 7/12.
Now that they have the same denominators, perform the subtraction process.
Then,John ate 7/12 more of the candy than Sandy.
What is the equation of the line perpendicular to y= 1/2x + 3 passing through the point (-3,4)?
42 mm
56 mm
What is the length of the hypotenuse?
Answer:
70 mm
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
c² = 42² + 56² = 1764 + 3136 = 4900 ( take the square root of both sides )
c = [tex]\sqrt{4900}[/tex] = 70
3. A flat screen television has a diagonal length of 40
inches. The base is 34 inches across. What is the
height of the television? Round your answer to the
nearest tenth.
ANSWER FAST
On the grid draw the graph of X+Y=6 for values of X between -2 and 3.
See the picture the red line.
It's wrong anyone know?
Answer:
-2 Because i did the test and got a 100% on it
The approximate number of blood cells B
passing through an animal's major artery
4
each millisecond is given by B = 17m3,
where m is the animal's mass in kilograms.
Find the number of blood cells passing
through a 243 kg bear's major artery
each millisecond
Answer:
[tex] m = \frac{ \sqrt[3]{243b} }{17} [/tex]
what is the range of the function g(x)=|x-12|-2?
Answer:-14
Step-by-step explanation:
Answer:
{y | y > 12}
Step-by-step explanation:
just took the test
The graph of y=|x| Is reflected across the x-axis and then scaled vertically by a factor of 3/8?
Answer: y= -3/8|x|
Step-by-step explanation: so D oh khan academy
The function after reflection is y= -3/8 |x|
What is Translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
A transformation known as a translation involves shifting each point in a figure by the same amount and in the same direction.
Given:
y= |x|
So, reflection for x axis
y= -|x|
and, scaled vertically by a factor of 3/8
y= -3/8 |x|
Hence, the function after reflection is y= -3/8 |x|
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On a map, Hamad is standing at (10, -11). His friend Saif is standing at
(1, -11). In which direction and How many steps Hamad will move to reach Saif? Explain
The coordinates of triangle DEF are D(4,2), E(7,2), and F(6,8). If you translate triangle DEF 4 units right and 3 units down, what are the coordinates of E'?
Answer:
E’ is (11,-1)
Step-by-step explanation:
Here, we want to get the new coordinates of E
The translation is 4 units right ( add 4 to x-value) and 3 units down ( subtract 3 from y-value)
So for E, we have
(7 + 4, 2-3)
= (11, -1)
Can someone help me?
Step-by-step explanation:
there, hope it helps! :)
Which Fraction Is Equal To 1/6 + 1/6 +1/6
Answer:
3/6=1/2
Step-by-step explanation:
1/6+1/6+1/6=3/6
The most simplified answer is 1/2
The fraction 1/6 + 1/6 +1/6 is equals to the 1/2 after adding them all.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
= 1/6 + 1/6 +1/6
Taking LCM of 6, 6, and 6 is 6
= (1+1+1)/(6)
= 3/6
Divide by 3 on numerator and denominator.
=1/2
Thus, the fraction 1/6 + 1/6 +1/6 is equals to the 1/2 after adding them all.
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Un movil que ha partido de reposo inicia un M.R.U.A al cabo de 8seg, cambia su rapidez a 60m/seg. Hallar la distancia recorrida por el movil. Hacer grafica
Answer:
La distancia recorrida por el móvil es 240 metros.
Step-by-step explanation:
Puesto que el móvil experimenta movimiento rectilíneo uniformemente acelerado, la distancia recorrida es determinada por las siguientes ecuaciones cinemáticas:
[tex]\Delta x = v_{o}\cdot t + \frac{1}{2}\cdot a\cdot t^{2}[/tex] (1)
[tex]v = v_{o} + a\cdot t[/tex] (2)
Donde:
[tex]\Delta x[/tex] - Distancia recorrida, medida en metros.
[tex]v_{o}[/tex] - Velocidad inicial, medida en metros por segundo.
[tex]v[/tex] - Velocidad final, medida en metros por segundo.
[tex]a[/tex] - Aceleración, medida en metros por segundo al cuadrado.
[tex]t[/tex] - Tiempo, medido en segundos.
En (2) despejamos el tiempo:
[tex]a = \frac{v-v_{o}}{t}[/tex]
Si aplicamos esta ecuación en (1):
[tex]\Delta x = v_{o}\cdot t + \frac{1}{2}\cdot \left(\frac{v-v_{o}}{t} \right)\cdot t^{2}[/tex]
[tex]\Delta x = v_{o}\cdot t + \frac{1}{2}\cdot (v-v_{o})\cdot t[/tex]
[tex]\Delta x = \frac{1}{2}\cdot v_{o}\cdot t+\frac{1}{2}\cdot v\cdot t[/tex]
[tex]\Delta x = \frac{1}{2}\cdot (v_{o}+v)\cdot t[/tex] (3)
Si sabemos que [tex]v_{o} = 0\,\frac{m}{s}[/tex], [tex]v = 60\,\frac{m}{s}[/tex] and [tex]t = 8\,s[/tex], entonces la distancia recorrida es:
[tex]\Delta x = \frac{1}{2}\cdot \left(0\,\frac{m}{s}+60\,\frac{m}{s}\right) \cdot (8\,s)[/tex]
[tex]\Delta x = 240\,m[/tex]
HELP PLS ASAP
-3(3x - 5y - 9) + 7x + 7 =
Answer:
8..
Step-by-step explanation:
-3x-5y=61
7x-5y=-9
-10x=70
x=-7
y=-8..
a goalie makes 28 saves in 4 games what is the unit rate saves per game?
Answer:
7 saves per game
Step-by-step explanation:
*URGENT* I NEED HELP QUICK
I would say D
Hope I helped :)
This year Martin's income is 1/4 greater than his income from Last year. If s represents his income from last year, what is his income this year?
Answer: 1 1/4s or 1.25s
Step-by-step explanation:
From the question, we are informed that this year Martin's income is 1/4 greater than his income from last year. We are further told that his income from last year is represented by s.
Therefore, hus income this year will be:
= s + (1/4 × s)
= s + 1/4s
= 1 1/4s or 1.25s
Answer:
it is 1/4s
Step-by-step explanation:
Five cats each ate 1/5 of canned food and 1/5 cup of dry food. How much food did they eat altogether?
Answer:
2
Step-by-step explanation:
With regards to the above, we can sum up the foods ate together by the 5 cats, then we have;
= 1/5 + 1/5
= 2/5
Then we can multiply the value above by the 5 cats
= 2/5 × 5
= 10/5
= 2
The cats eat 2 foods together.
Please help I am not soo good at math
Answer:
D
Step-by-step explanation:
Answer: X = 300
So it would be "D"
4. Which expression is equivalent to the expression below?
Select all that apply.
-⅖ ( 15 - 20D +5C)
A. –30 + 40d – 10c
B. –6 + 8d – 2c
C. –2c + 8d – 6
D. 6 – 8d + 2c
Answer:
B
Step-by-step explanation:
The equivalent expression for the expression -2/5(15 - 20d + 5c) is
-6 + 8d - 2c
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
-2/5 x (15 - 20d + 5c)
= -2/5 x 15 + 2/5 x 20 - 2/5 x 5c
= -2 x 3 + 2 x 4 - 2c
= -6 + 8d - 2c
Thus,
The equivalent expression is -6 + 8d - 2c.
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How much money was put into the account at the beginning?
On a map 3 inches = 20 miles if the distance between two cities on the map is 15 inches how many miles apart are they
Answer:
100 miles is the answer
Step-by-step explanation:
3 inches = 20 miles
15/3 = 5
5 x 20
= 100 miles
========================================================
Work Shown:
(3 inches)/(20 miles) = (15 inches)/(x miles)
3/20 = 15/x
3*x = 20*15
3x = 300
x = 300/3
x = 100
Therefore, 15 inches on the map correspond to 100 miles in real life.
-------------------
We could approach the problem like this:
3 inches = 20 miles
5*(3 inches) = 5*(20 miles)
15 inches = 100 miles
In the second step, I multiplied both sides by 5 to turn the "3 inches" into "15 inches".
how much is 6/9 + 36/9 to a mixed
number
Answer:14/15 + 42/11
Step-by-step explanation:
