Step-by-step explanation:
arithmetic sequence means that every new term is created by adding a certain constant (here 2) to the previous term.
a27 = -1/2 = a1 + (n-1)×2 = a1 + 26×2 = a1 + 52
a1 = -52 1/2 = -105/2
an = -105/2 + (n-1)×2
Jamie and Raul both work at the Pizza House. Together, they work a total of 15 hours per week. Raul works 3 more than twice the hours as Jamie. How many hours does Jamie work per week?
Enter your answer in the box.
Answer:
Step-by-step explanation:
List the facts phrase by phrase.
Total = 15 hours
Let Raul's hours = x
Let Jamie's hours = y
Total = x + y = 15
x = 3 + 2y
From total, find x
x+ y = 15 Subtract y from both sides.
x = 15 - y Put the value for x in x = 3+ 2y
3 + 2y = 15 - y Subtract 3 from both sides
2y = 15 - 3-y Combine
2y = 12 - y Add y to both sides.
2y + y = 12 Combine
3y = 12
y = 12 / 3
y = 4
Jamie worked 4 hours
Raul worked 11
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the inverse of the line provided on the graph.
Drawing Tools
Click on a tool to begin drawing.
The inverse function will have x intercept additive inverse of this.
Inverse of the line's interceptsx-intercept=-(-5)=5y intercept=1Now
equation of line in intercept form
[tex]\\ \sf\longmapsto \dfrac{x}{a}+\dfrac{y}{b}=1[/tex]
[tex]\\ \sf\longmapsto \dfrac{x}{5}+\dfrac{y}{1}=1[/tex]
[tex]\\ \sf\longmapsto \dfrac{x+5y}{5}=1[/tex]
[tex]\\ \sf\longmapsto x+5y=5[/tex]
Graph attached
The Graph of the inverse of the function is given below.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
From the given graph,
x intercept=-5
y intercept=1
The inverse function will have x intercept additive inverse of this.
The inverse of the line's intercepts
x-intercept = 1
y-intercept = -5
Now
equation of a line in intercept form
x/a + y/b = 1
x/1 +y/-5 = 1
5x - y = 5
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Erin buys 2 packs of potatoes costing £2 each, 3 packs of carrots for £3 per pack, and 3 turnips costing 60p each.
If she pays with a £20 note, how much change would she get in pounds, £
Answer:
£5.20
Step-by-step explanation:
The change is the difference between the amount tendered and the amount owed. The total amount owed is the sum of the costs for each of the items purchased.
change = £20 - 2(£2) - 3(£3) -3(£0.60) = £20 -14.80 = £5.20
Erin gets £5.20 in change.
Guided Practice
Write the equation of the parabola in vertex form. The vertex is (−3, 3) and the parabola passes through the point (4, 150). Create a rough sketch of the graph to use as a visual aid.
A.
y = 3(x + 3)^2 + 3
B.
y = 4(x − 3)^2 + 3
C.
y = 50(x + 3)^2 + 4
D.
y = 3(x − 3)^2 + 3
Answer:
A.
y = 3(x + 3)^2 + 3
Step-by-step explanation:
The vertex form of the equation is y=a(x-h)2 + k
You know that the vertex (h,k) is (-3,3) and a point on the parabola is (4,150). So what you’re needed ing to find is a bc all of the other letters can be replaced into the equation.
First I would put the equation into vertex form using the vertex given in the problem. : y= (x - (-3))2 + (3). Then I would use the ordered pair (4,150) and replace the x and y with those values
150 = a(4 + 3)2 + 3
Now simplify
150 = a (7)2 + 3
150 = 49a + 3 Important: please be sure to square.
147 = 49a
3= a
Next replace a into the formula now leaving x and y alone.
y = 3 (x+3)2 + 3 [Vertex form]
I hope this helps. Have a great day!
Answer:
A. [tex]y = 3(x + 3)^2 +3[/tex]
Step-by-step explanation:
The vertex form is:
[tex]y = a(x - h)^2 + k[/tex]
Where [tex]a[/tex] is the variable that determinate if the parabola is facing up or facing down and [tex]h[/tex] is the [tex]x[/tex] coordinate of the vertex and [tex]k[/tex] is the [tex]y[/tex] coordinate of the vertex.
So with the given values we have:
[tex]150 = a(4 + 3)^2 + 3[/tex]
Then isolate [tex]a[/tex] for find the missing value.
[tex]147 = a49\\\frac{147}{49} = a\\3 = a[/tex]
Then the final answer is [tex]y = 3(x + 3)^2 +3[/tex]
Jill has a pail of water that holds 612 quarts. She needs to give her plants 18 quart each. How many of her plants can she water?
Enter the correct answer in the box.
Answer:
34
Step-by-step explanation:
Answer:
34
Step-by-step explanation:
Because 612 quarts divided by 18 quarts for each plant is 34. So, it's 34 plants.
What is a^2 - 5b + the square root of c if
A= -3
B= 6
C= 16
Answer:
-21
Step-by-step explanation:
What did she do wrong? What can she do to prevent this?
Answer:
y = 8x + 14 (8x is WRONG)
This is how it is supposed to be
y - 2 = 6x + 12
y = 6x + 14
She must combine like terms, not unlike terms
Which of these are prime numbers 5,6,9,13,18
Answer:
5 and 13
Step-by-step explanation:
Answer:
13
is the answer
Hope it help u
Find the value of x 47 and 22
Answer:
111
Step-by-step explanation:
U calculate the 47°&22°and u cut 69° then u put 180-69=111°
Write a proportion relating the side lengths of the triangle to any other triangle that has the line as a hypotenuse, a horizontal length of x units, and a vertical length of y units.
Answer:
y/x = 2 or y = 2xStep-by-step explanation:
The given triangle has:
Vertical segment = 2 unitsHorizontal segment = 1 unitThe ratio (slope) is:
2/1 = 2For any triangle using same line the proportion is:
y/x = 2 ory = 2xWhat’s the answer for both questions?
Answer:
id
Step-by-step explanation:
help help help help Please
Answer:
It rises -4 and runs 6
Step-by-step explanation:
So the slope is -4/6
elena gives following sequence of transformation to show that the two figures are similar by transforming ABCD into EFGD. dialte using center D reflect using the line AE is elenas method correct
Answer:
Elena is incorrect.
Step-by-step explanation:
In the first step, the figures are supposed to be about the same size. But the reflection over AE does not match them together. The correct line must be vertical and it has to go through point D.
If I'm correct, the scale copy should be 2.
∴/therefore, if it doesn't go through point D, Elena is incorrect.
Mark me brainliest if possible, it's always appreciated! ¯\_(ツ)_/¯
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A shopping mall has $3,368 to spend on new tiles for the floor. If each tile costs $8, how
many tiles can the mall buy?
tiles
Answer:
421 tiles
Step-by-step explanation:
3368/8=421
Answer:
421 tiles
Step-by-step explanation:
Divide $3368 by $8 to determine the number of tiles the store can purchase:
$3368/($8 per tile) = 421 tiles
Could anyone help? I’ve watched the videos but they’ve confused me even more
Answer:
for a) you have to draw the graph of y = x - 1 for values from 0 to 7 so you need to make the table in the picture:(see the attached picture) now draw it using the coordinates from the table
but for b) I don't know I tried something but it didn't work.
A plane traveling to new york has 100 seats on board. if there are p passengers on the plane, which expression represents the number of empty seats there are on the plane
Hi math freindAnswer:
Step-by-step explanation:
Weslyes family spent $1,400 on a trip to the Grand Canyon. They spent 30% of the total on a sightseeing helicopter flight. Wesley estimates that his family spent about $450 on the flight
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
In pic
The question is the img. Please answer both if u can
Problem 1
x = number of weeks
y = amount left on gift card (in dollars)
He starts with $100. Then each week he spends $4.99 which means we subtract 4.99x from the 100 mentioned. We form the expression 100 - 4.99x which is the same as -4.99x + 100
The equation y = -4.99x + 100 is in slope intercept form with m = -4.99 as our slope and b = 100 as the y intercept.
Answer: y = -4.99x + 100=======================================================
Problem 2
The y intercept is 100 because it's the starting amount. Mark the point (0,100) on the graph.
We need one more point to form a straight line. Let's say we picked something like x = 4 to plug into the equation found earlier
y = -4.99x + 100
y = -4.99*4 + 100
y = -19.96 + 100
y = 80.04
After x = 4 weeks, Mark has y = 80.04 dollars left on the card. We'll plot the point (4, 80.04). Then we connect those points with a straight line.
Check out the diagram below.The location of (4, 80.04) can be visually marked as (4,80) since it's close enough in my opinion.
Expand the function.
4
f(x)
=
(2x + 3)4
Answer:
16 x ^4 − 96 x^ 3 + 216 x ^2 − 216 x + 81
Step-by-step explanation:
Use the binomial expansion theorem to find each term. ∑
∑The binomial theorem states ( a + b ) n = n ∑ k = 0 n C k ⋅ ( a n − k b k ) . 4 ∑ k = 0 4 ! ( 4 − k ) ! k ! ⋅ ( 2 x ) 4 − k ⋅ ( − 3 ) k
Expand the summation. 4 ! ( 4 − 0 ) ! 0 ! ⋅ ( 2 x ) 4 − 0 ⋅ ( − 3 ) 0 + 4 ! ( 4 − 1 ) ! 1 ! ⋅ ( 2 x ) 4 − 1 ⋅ ( − 3 ) + 4 ! ( 4 − 2 ) ! 2 ! ⋅ ( 2 x ) 4 − 2 ⋅ ( − 3 ) 2 + 4 ! ( 4 − 3 ) ! 3 ! ⋅ ( 2 x ) 4 − 3 ⋅ ( − 3 ) 3 + 4 ! ( 4 − 4 ) ! 4 ! ⋅ ( 2 x ) 4 − 4 ⋅ ( − 3 ) 4
Simplify the exponents for each term of the expansion. 1 ⋅ ( 2 x ) 4 ⋅ ( − 3 ) 0 + 4 ⋅ ( 2 x ) 3 ⋅ ( − 3 ) + 6 ⋅ ( 2 x ) 2 ⋅ ( − 3 ) 2 + 4 ⋅ ( 2 x ) ⋅ ( − 3 ) 3 + 1 ⋅ ( 2 x ) 0 ⋅ ( − 3 ) 4
Simplify each term.
= 16 x ^4 − 96 x^ 3 + 216 x ^2 − 216 x + 81
Bottled water comes in cases of 24 bottles. You need 150 bottles of water for a school event. How many cases of water do you need to buy?
Enter a unit that best describes the number.
Number 24. unit {uh plz help with this part if u can }
Answer:
6.25 is the exact number, but you should round it to 6
Step-by-step explanation:
150/24=6.25.
It also equals 6 if you round it.
2√8 -3√50+√32 AHIHIHI
Answer:
-9.89949493661
Step-by-step explanation:
100 students are interviewed to see which of biology, chemistry or physics they prefer.
41 of the students are girls. 32 of the girls like biology best.
24 of the boys prefer physics.
6 out of the 25 who prefer chemistry are girls.
What percentage of the students prefer biology?
Answer:
48% of students prefer biology
Step-by-step explanation:
The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places.
800 grams = (How many?)
pounds
700 grams = (How many?)
pounds
Answer:
Here they are unrounded
800 grams = 1.7637
700 grams = 1.54324
Step-by-step explanation:
Hope this helps
1) Round 26.728 to the nearest integer
What
Turn into a equivalent form 6x²+13x+5
Answer:
Assuming the questions wants another form of 6x²+13x+5:
(2x+1)(3x+5) would work.
Step-by-step explanation:
Multiply (2x+1)(3x+5) and you'll get 6x^2+13x+5
Round the quantity to th given place value 13.989 to the nearest tenth
Answer:
13.989 rounded to nearest tenth is 14.0.
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
round
Stacy shares 164 peppers equally between 5 of her friends. How many peppers does each friend get? How many are left over?
Answer:
each person gets 32 papers and there are 4 left over
Step-by-step explanation:
Factor completely:
–abc –5ac –4ab –20a
Answer:
[tex]-a(b+5)(c+4)[/tex]
Step-by-step explanation:
[tex]-abc-5ac-4ab-20\\-a(bc+5c+4b+20)\\-a*c(b+5)+4(b+5)\\-a*(b+5)(c+4)[/tex]
The factor of the given expression is -a(b+5)(c+4)
What is factorization?Factorization in maths is the process of breaking down a number or a mathematical object into smaller or simpler factors that can be multiplied together to get the original number or object
Given is an expression, –abc –5ac –4ab –20a, we need to factor it completely,
-abc -5ac-4ab-20
- a(bc +5c+4b+20)
- ac(b+5)+4(b+5)
- a(b+5) (c+4)
Hence, the factor of the given expression is -a(b+5)(c+4)
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What is the greatest common factor of 50, 15, and 10?
Answer:
5
Step-by-step explanation:
you would need to factor each of the number and they are all in the 5 times table
Answer:
GCF = 5
Step-by-step explanation:
Reason being that all are divisible my 5 and 10 cannot be used because it makes a fraction which is not how the GCF can be found.
Math:
50 = 5 * 10 or 25 * 2 or 50 * 1
15 = 5 *3 or 15* 1
10 = 5 * 2 or 10 * 1
Only thing that is the same is 5, thus 5 is the GCF.
identify the types of each triangle
Answer:
Step-by-step explanation:
1. right angled (isosceles)
2. acute (equilateral or equiangular)
3. obtuse
5. acute
Answer:
Triangle number one is a right triangle. Triangle two is an equilateral triangle. Triangle three which is below triangle one is an obtuse triangle. The fourth triangle is an acute triangle.
Step-by-step explanation:
One is a right triangle because it has one right angle.
Two is an equilateral triangle because all of the three angles are 60 degrees.
Three is an obtuse triangle because one of the three angles is more than 90 degrees.
Finally, 4 is an acute triangle because all of the three angles are less than 90 degrees