Answer:
780
Step-by-step explanation:
Let x be the original price
x - x*72% is the new price
x - .72x = 218.40
.28x = 218.40
Divide each side by .28
.28x/.28 = 218.40/.28
x =780
For f(x) = 3x + 1 and g(x) = x2 - 6, find (f + g)(x).
Answer:
x^2+3x-5
Step-by-step explanation:
f(x) = 3x + 1
g(x) = x^2 - 6,
(f + g)(x)= 3x + 1 +x^2 - 6,
Combine like terms
= x^2+3x-5
Answer:
[tex] {x}^{2} + 3x - 5[/tex]
Step-by-step explanation:
[tex]f(x) = 3x + 1 \\ g(x) = {x}^{2} - 6 \\ (f + g)(x) = (3x + 1) + ( {x}^{2} - 6) \\ = 3x + 1 + {x}^{2} - 6 \\ = {x}^{2} + 3x - 5[/tex]
When solving the system of equations, which expression could be substituted for r in the first equation?
3r + 2t = 15
r = 4 – t
Answer:
4-t
Step-by-step explanation:
We use the second equation and r = 4-t
every time we see r in the first equation replace it with 4-t
Any help, I would highly appreciate it
Answer:
B
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle x(b-c) = y+x[/tex]
And that:
[tex]2b=3c=7[/tex]
And we want to find the value of y / x.
To start, subtract x from both sides in the first equation:
[tex]x(b-c) -x = y[/tex]
Divide both sides by x:
[tex]\displaystyle \frac{x(b-c)-x}{x}=\frac{y}{x}[/tex]
Simplify:
[tex]\displaystyle (b-c)-1 = \frac{y}{x}[/tex]
Next, in the second equation, divide everything by two:
[tex]\displaystyle b = \frac{3}{2} c = \frac{7}{2}[/tex]
Substitute:
[tex]\displaystyle \left(\frac{3}{2} c - c \right) - 1= \frac{y}{x}[/tex]
Simplify:
[tex]\displaystyle \frac{1}{2} c - 1 = \frac{y}{x}[/tex]
From the modified second equation, we can multipy both sides by 1/3:
[tex]\displaystyle \frac{1}{2} c = \frac{7}{6}[/tex]
Substitute:
[tex]\displaystyle \left(\frac{7}{6}\right) -1 = \frac{y}{x}[/tex]
Subtract:
[tex]\displaystyle \frac{y}{x} = \frac{7}{6} - \frac{6}{6} = \frac{1}{6}[/tex]
Therefore, our answer is B.
Becky bikes 6 miles in 24 minutes. At the same rate, how many miles would she bike in 60
minutes?
Answer:
10 miles
Step-by-step explanation:
6 in 24 min 6÷24=4
60÷6 =10
=======================================================
Here's one approach:
(6 miles)/(24 minutes) = (x miles)/(60 minutes)
6/24 = x/60
6*60 = 24*x
360 = 24x
24x = 360
x = 360/24
x = 15
She travels 15 miles in 60 minutes (aka 1 hour). So we can say her speed is 15 mph.
-----------------------------
Here's another approach:
If she travels 6 miles in 24 minutes, then her unit rate is distance/time = 6/24 = 1/4 = 0.25 miles per minute.
So if she travels for 60 minutes, then she'll cover a distance of 60*0.25 = 15 miles
find the missing side of the triangle
Answer:
25
Step-by-step explanation:
[tex]a^2 + b^2 = c^2[/tex]
[tex]24^2 + 7^2 = x^2[/tex]
[tex]576 + 49 = x^2[/tex]
[tex]x ^ 2 = 625[/tex]
[tex]x = 25[/tex]
Answer:
Using Pythagoras theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]
[tex](x)^{2} =(24)^{2}+(7)^{2}[/tex]
[tex]x^{2} =576+49=625[/tex]
[tex]x=\sqrt{625} =25[/tex]
[tex]x=25[/tex]
OAmalOHopeO
Find the missing side of triangle
Answer:
30.
Step-by-step explanation:
x^2 = 24^2 + 18^2
x^2 = 576 + 324 = 900
x = sqrt900 = 30.
The graph of f(x) = |x| is transformed to g(x) = |x + 1| – 7. On which interval is the function decreasing?
(–∞, –7)
(–∞, –1)
(–∞, 1)
(–∞, 7)
Answer:
(−∞,−1) interval is is the function decreasing..Step-by-step explanation:
Given : The graph of f(x) = |x|f(x)=∣x∣ is transformed to g(x) = |x+1|-7g(x)=∣x+1∣−7To find : On which interval is the function decreasing?Solution :First we plot the graph of both the functions, The graph of f(x) = |x|f(x)=∣x∣ is shown with black line.The graph of g(x) = |x+1|-7g(x)=∣x+1∣−7 is shown with violet line. The graph shows the interval over which it is increasing or decreasing.As we notice it is increasing on the interval (-1,\infty)(−1,∞)Decreasing on (-\infty,-1)(−∞,−1)Therefore, (-\infty,-1)(−∞,−1) interval is the function decreasing. please markse as brainliests please for my effort...The function [tex]g(x) =|x + 1| - 7[/tex] decreases at interval [tex](-\infty, -1)[/tex]
The parent function is given as:
[tex]f(x) =|x|[/tex]
The transformed function is given as:
[tex]g(x) =|x + 1| - 7[/tex]
Both functions are absolute value functions, and an absolute value function is represented as:
[tex]y=a| x-h |+k[/tex]
Where, the vertex of the function is:
[tex]Vertex = (h,k)[/tex]
By comparing [tex]y=a| x-h |+k[/tex] and [tex]g(x) =|x + 1| - 7[/tex], we have:
[tex](h,k) = (-1,-7)[/tex]
[tex]a= 1[/tex]
Because (a) has a positive value (i.e. 1) and (h) is negative, then the vertex represents a minimum.
This also means that, the function will decrease from infinity, till it gets to the x-coordinate of the vertex.
Hence, the function [tex]g(x) =|x + 1| - 7[/tex] decreases at interval [tex](-\infty, -1)[/tex]
Read more about transformation at:
https://brainly.com/question/5757291
Find the 17th term of an arithmetic sequence whose first term is 12 and whose common difference is 6. Type answer as an integer (no decimals).
Answer:
Step-by-step explanation:
n17 = ?
n = 17
d = 6
a1 =12
a17 = a1 +(n - 1)d
a17 = 12 + (17 - 1)*6
a17 = 12 + 16*6
a17 = 12 + 96
a17 = 108
Lydia has half of her investment in stock paying a 7% dividend and the other half in a stock paying 13% interest. If her total annual interest is $410, how much does she have invested?
Answer:
$4,100
Step-by-step explanation:
Interest = principal * rate * time
Let entire principal = amount invested = p
Investment A :
Rate, r = 7%, principal = p/2, time, = 1
Investment B :
Rate, r = 13%, principal = p/2, time = 1
Total interest = $4.10
(p/2 * 0.07 * 1) + (p/2 * 0.13 * 1) = 410
0.035p + 0.065p = 410
0.1p = 410
p = 410 / 0.1
p = $4100
The perimeter of a rectangular park is 300 feet. The length of the park is 10 feet longer than the width.
Find the length of the park.
What is the length of the park?
feet=?
Answer:
80 ft
Step-by-step explanation:
width = w
length = w+10
Perimeter of a rectangle
P = 2(l+w)
300 = 2(w+10+w)
300 = 2(2w+10)
Divide by 2
300/2 = 2/2(2w+10)
150 = 2w+10
Subtract 10
150-10 = 2w+10-10
140 = 2w
Divide by 2
140/2 = 2w/2
70 = w
l = w+10
l = 70+10
w = 80
If m2 DOC = 44º and m2 COB = 80°,
find the measure of the indicated arc
in circle o.
mCB = [?]°
Answer:
80°
Step-by-step explanation:
m<COB = 80°, it's the central angle for arc CB,
so mCB = 80°
Solve for a.
a
2
8
a =
✓ [?]
Pythagorean Theorem: a2 + b2 = c2
Enter
Answer: [tex]a=\sqrt{60}[/tex]
Step-by-step explanation:
To solve for a, we want to use Pythagorean Theorem as provided int eh problem. a and 2 are the legs while 8 is the hypotenuse.
[tex]a^2+2^2=8^2[/tex] [exponent]
[tex]a^2+4=64[/tex] [subtract both sides by 4]
[tex]a^2=60[/tex] [square root both sides]
[tex]a=\sqrt{60}[/tex]
Now we know that [tex]a=\sqrt{60}[/tex].
9. An equation representing the height of a burning candle is H = 2(9 - 2t), where
H is the height of the candle in cm and
t is the amount of time that the candle has been burning in minutes.
How long will it take for the candle to burn down to a height of 4 cm?
a. 2 min
b. 3.5 min
C. 5.5 min
d. 7 min
Answer:
H= 4cm
we want t
4=2(9-2t)
2=(9-2t)
-7=-2t
t=3.5 minutes
CAN SOMEBODY PLEASE HELP ME
Answer: AS = 46
Step-by-step explanation:
Since we know that a circumcenter is equidistant from all three vertices, we know that segment BS is congruent to segment CS which is congruent to segment AS. By the definition of congruent segments, BS = AS. Since BS is 46, we know that AS will also be 46.
pls answer quickly before 3:30
Two tangents drawn to a circle from a point outside it, are equal in length.prove it.
At noon, Garrett left Magnolia and headed North at 10 kph. At 2 p.m., Ben left Magnolia and headed North. If Ben was 15 km ahead of Garrett at 7 p.m., how fast was Ben
traveling?
Choose one answer.
O
a. 17 kph
o
b. 12 kph
c. 21 kph
Ο Ο
d. 16 kph
Answer:
Step-by-step explanation:
This is simple, but the extra numbers given in the form of the specific times might throw you off.
If Garrett leaves at noon and at 7 Ben is some distance ahead of him, that means that Garrett has been driving for 7 hours. Ben left at 2, so at 7 pm he has been driving for 5 hours. That's part of what's confusing. We'll put that in a table to hopefully make things easier:
d = r * t
G 7
B 5
We also know that Garrett is driving at 10 km/h, so:
d = r * t
G 10 * 7
B r 5
The r is because Ben's rate is our unknown. Look at the top of the table. That is the formula we are going to use to solve this problem: d = rt.
If Garrett drives for 7 hours at 10 km/hr, then the distance he has traveled is 70 km (that's found by multiplying the rate of 10 km/h by the time of 7 hours). Ben's rate, along those same lines of reasoning, is 5r. Fill that in:
d = r * t
G 70 = 10 * 7
B 5r = r * 5
Ok now the table is filled out. Let's look at the rest of the problem. It says that at 7 pm Ben's distance is 15 km more than Garrett's distance. The words "more than" indicate addition. In words that is
"Ben's distance is Garrett's distance plus 15 km" which translates to, mathematically speaking:
5r = 70 + 15 and
5r = 85 so
r = 17
Ben's rate is 17 km/h, choice a.
7.2b + 6.5 > 4.8b – 8.1
Answer:
[tex]7.2b+6.5>4.8b-8.1[/tex]
Multiply both sides by 10
[tex]72b+65>48b-81[/tex]
Subtract both sides by 65
[tex]72b>48b-146[/tex]
Subtract both sides by 48b
[tex]24b>-146[/tex]
Divide both sides by 24
[tex]b>-\frac{73}{12}[/tex]
OAmalOHopeO
Please decide !!!!!!!!
9514 1404 393
Answer:
6 pours
Step-by-step explanation:
Here are two 6-step solutions. The four digits represent the contents of the 9,5,4,2 containers (in that order) after a single pour. The starting condition is 9000.
Solution 1:
7002 — 9 > 27200 — 2 > 53240 — 9 > 43510 — 4 > 53312 — 5 > 23330 — 2 > 4Solution 2:
5040 — 9 > 45400 — 4 > 51440 — 9 > 41530 — 4 > 51332 — 5 > 23330 — 2 > 9Which statement can be modeled by x + 3 < 12?
Julie has 3 notebooks. Together, Mary and Julie have less than 12
notebooks
Sam sold 3 mobiles. To earn a prize, Sam must sell atleast 12 mobiles.
Frank has 3 hats. Frank and his brother Peter have more than 12 hats.
Sandy walked 3 miles yesterday. She must walk more than 12 miles.
Answer:
Step-by-step explanation: i think in my own word x+3<12 is A because it said julie only 3 notebook togerther it make itt less than 12notebook
The entrance fee to a local waterpark is $34 per person. At the waterpark, you can rent a raft for $1.50 per hour. Which expression is equivalent to the amount it would cost Leah for h hours in the park if she rented a raft?
Answer: 34+1.50h
Step-by-step explanation:
Algebraic Equation:
The entrance fee to the waterpark is the intial cost for Leah to get in the park. The amount of hours that Leah will spend at the park is a variable.
You need to add the intial cost and the variable amounts together.
34+h
You put the h in the equation because you don't know how long Leah will spend on the raft. You will be multiply by the rate per hour for a raft.
34+1.50h
Therefore the cost for Leah is 34+1.50.
34 + 1.50h
Therefore, Leah’s cost is 34 + 1.50h.
Rectangle ABCD is similar to rectangle JKLM. AB = 12, BC = 8, CD = 12, DA = 8, and JK = 15. What is the scale factor from JKLM to ABCD? Reduce all answers.
Answer:
4/5 or 0.8
Step-by-step explanation:
this problem description is not very precise. it leaves out the definition what corners or sides of JKLM correspond to corners and sides of ABCD.
I assume J and K correlate to A and B, and JK is a long side of JKLM.
so, we are going from JKLM to ABCD.
that means we are going from larger to smaller (as JK = 15 and therefore larger than AB = 12).
what is the scale factor to go from 15 to 12 ?
15 × x = 12
x = 12/15 = 4/5 or 0.8
What is the translation from the preimage to the image in the graph?
Answer:
(x, y ) → (x + 4, y - 1 )
Step-by-step explanation:
Consider the coordinates of K and K'
K (- 3, 5 ) , K' (1, 4 )
x- direction : - 3 → 1 is + 4 units to the right
y- direction : 5 → 4 is - 1 units down
translation rule is (x, y ) → (x + 4, y - 1 )
Find the Measure of one interior angle for each polygon
Answer:
5 corners : 108 degrees
6 corners : 120 degrees
Step-by-step explanation:
there are (at least) 2 different views to get the result :
officially (usually the teachers' preferred method) you consider a polygon as a combination of non-overlapping triangles. a polygon with n corners or edges we can split into n-2 such triangles.
each triangle has an angle sum of 180 degree.
so, the polygon angle sum is (n-2)×180 degrees.
and each (internal) angle is then (n-2)×180/n
n = 5 : (5-2)×180/5 = 3×36 = 108 degrees
n = 6 : (6-2)×180/6 = 4×30 = 120 degrees
the second approach (I prefer) goes after the external angles of the polygon.
the sum of all external angles in any polygon is 360 degrees (a full circle).
for n corners/edges each external angle is 360/n.
and the internal angle is then the complement to 180 degrees = 180 - 360/n
n = 5 : 180 - 360/5 = 180 - 72 = 108 degrees
n = 6 : 180 - 360/6 = 180 - 60 = 120 degrees
I will be marking brainliest please help me with these questions.
Answer/Step-by-step explanation:
1. To find the area of the shaded region, you'd find the area of the white rectangular shape, next, find the area of the whole triangular shape, then find the difference of their areas to get the area of the shaded region. Thus, the formula to use would be:
Area of shaded region = area of triangle - area of rectangle
Area of shaded region = ½*base*height - length*width
1. a. Volume of triangular prism = area of triangular base * height of prism
Volume of triangular prism = ½bh * H
Where,
b = 6 m
h = 4 m
H = 8 m
Substitute
Volume of prism = ½*6*4*8
Volume of prism = 96 m³
b. Volume of sphere = ⁴/3πr³
Where,
r = 9 cm
Substitute
Volume = ⁴/3*π*9³
Volume = ⁴/3*π*729
Volume ≈ 3,053.6 cm³ (nearest tenth)
2. Use Pythagorean theorem to find the height of the cone
radius of the cone (r) = ½(16) = 8 cm
Slant height (l) = 11 cm
height (h) = ?
Using Pythagorean theorem, we have:
h = √(l² - r²)
Substitute
h = √(11² - 8²)
h = √(57)
h ≈ 7.5 cm (nearest tenth)
b. Volume of the cone = ⅓πr²h
where,
r = 8 cm
h = 7.5 cm
Volume = ⅓*π*8²*7.5
Volume = 502.7 cm³ (nearest tenth)
In an arithmetic sequence, the first term is 5 and the third term is -5. What is the 20th term?
Answer:
-115
Step-by-step explanation:
Thus with the sequence /question numbers are reducing by 5 .
Help ! With step by step solution
Answer:
the correct answer is C
Step-by-step explanation:
first step you change the x and y powers to the square root(showing in the pic).
second the number outside of the parenthesis times the numbers inside the parenthesis and then you just figure it out how it works...
Solve for both x and y in the parallelogram below.
Answer:
x is 14 and y is 13
Step-by-step explanation:
[tex]{ \sf{(4y - 5) = (3y + 8)}} \\ { \sf{y = 13}}[/tex]
[tex]{ \sf{(x + 12) = 2y}} \\ { \sf{x + 12 = 2(13)}} \\ { \sf{x + 12 = 26}} \\ { \sf{x = 14}}[/tex]
4y-5=3y+8( opposite sides of parallelogram are equal)
or, 4y-5-3y=8
or, 4y-3y=8+5
.•. y=13
now,
x+12=2y
x+12=2*13
x=26-12
.•. x=14
What are the simplest forms for red, blue, and green line
Answer:
Red line: y=-1/2x+1 Blue line: y=-1/3x-2 Green line: y=x
Step-by-step explanation:
f(x) red line m=-1/2 b=1
g(x) blue line m=-1/3 b=-2
h(x) green line m=1 b=0
When a potential difference across a resistor is 2.0 V with a current of 1.5 A. What is its resistance?
V = IR
2 = 1.5 x R
R = 2 / 1.5
R = 1 1/3 ohms
Hope this helps!
