Answer: Choice C. p = 250(0.79)^t
Work Shown:
p = a*b^t
p = a*(1+r)^t
p = 250*(1+(-0.21))^t
p = 250(0.79)^t
Note that r = -0.21 is negative to indicate we have exponential decay.
if f(x) = 4x^2 - 3, then what is the remainder when f(x) is divided by x + 3?
Answer:
33
Step-by-step explanation:
x+3=0
x=-3
4(-3)²-3=(4×9)-3
36-3=33
(15xy+30yz)/15y bhoomika sis answer
Answer:
x + 2z
Step-by-step explanation:
[tex]\frac{15xy+30yz}{15y}[/tex] ← divide each term on the numerator by 15y
= [tex]\frac{15xy}{15y}[/tex] + [tex]\frac{30yz}{15y}[/tex]
= x + 2z
Which Experession Is Equivalent To 13-(21)
Karl drove for 4 hours. For part of the trip he drove at 50 miles per hour. For the rest of the trip he drove at 100 miles per hour.
All together he drove 250 miles.
Solve this equation for h to find out how many hours he drove at 50 miles per hour.
250 = 50h + 100(4 - h)
Answer:
3 hours
Step-by-step explanation:
250 = 50h + 100(4 - h)
250 = 50h + 400 - 100h
250 = -50h + 400
-150 = -50h
h = 3
HELP ASAP!!!
The line (y-1)=(2/3)(x+1) contains point (a,-3).
What is the value of a? Show
your work.
[tex]\\ \sf\Rrightarrow y-1=\dfrac{2}{3}(x+1)[/tex]
[tex]\\ \sf\Rrightarrow -3-1=\dfrac{2}{3}(a+1)[/tex]
[tex]\\ \sf\Rrightarrow -4=\dfrac{-2(a+1)}{3}[/tex]
[tex]\\ \sf\Rrightarrow -2(a+1)=-4(3)[/tex]
[tex]\\ \sf\Rrightarrow -2(a+1)=-12[/tex]
[tex]\\ \sf\Rrightarrow a+1=\dfrac{-12}{-2}[/tex]
[tex]\\ \sf\Rrightarrow a+1=6[/tex]
[tex]\\ \sf\Rrightarrow a=6-1[/tex]
[tex]\\ \sf\Rrightarrow a=5[/tex]
When multiplying two negative numbers, what kind of number does one always get for an answer?
Answer:
a positive number
Step-by-step explanation:
-(-) = +
for example, -1 * -1 = 1
Write the quadratic function in vertex form.
y = x2 + 8x + 18 (50 points for brainly)
A. y = (x - 4)2 - 2
B. y = (x - 4)2 + 2
C. y = (x + 4)2 - 2
D. y = (x + 4)2 + 2
Step-by-step explanation:
The Graph of a Quadratic Function
A quadratic function is a polynomial function of degree 2 which can be written in the general form,
f(x)=ax2+bx+c
Here a, b and c represent real numbers where a≠0. The squaring function f(x)=x2 is a quadratic function whose graph follows.
This general curved shape is called a parabola and is shared by the graphs of all quadratic functions. Note that the graph is indeed a function as it passes the vertical line test. Furthermore, the domain of this function consists of the set of all real numbers (−∞,∞) and the range consists of the set of nonnegative numbers [0,∞).
When graphing parabolas, we want to include certain special points in the graph. The y-intercept is the point where the graph intersects the y-axis. The x-intercepts are the points where the graph intersects the x-axis. The vertex is the point that defines the minimum or maximum of the graph. Lastly, the line of symmetry (also called the axis of symmetry) is the vertical line through the vertex, about which the parabola is symmetric.
For any parabola, we will find the vertex and y-intercept. In addition, if the x-intercepts exist, then we will want to determine those as well. Guessing at the x-values of these special points is not practical; therefore, we will develop techniques that will facilitate finding them. Many of these techniques will be used extensively as we progress in our study of algebra.
Given a quadratic function f(x)=ax2+bx+c, find the y-intercept by evaluating the function where x=0. In general, f(0)=a(0)2+b(0)+c=c, and we have
y-intercept (0,c)
Next, recall that the x-intercepts, if they exist, can be found by setting f(x)=0. Doing this, we have a2+bx+c=0, which has general solutions given by the quadratic formula, x=
−b±
√
b2−4ac
2a
. Therefore, the x-intercepts have this general form:
x-intercepts (
−b−
√
b2−4ac
2a
,0) and (
−b+
√
b2−4ac
2a
,0)
Using the fact that a parabola is symmetric, we can determine the vertical line of symmetry using the x-intercepts. To do this, we find the x-value midway between the x-intercepts by taking an average as follows:
x = (
−b−
√
b2−4ac
2a
+
−b+
√
b2−4ac
2a
) ÷2 = (
−b−
√
b2−4ac
−b+
√
b2−4ac
2a
)÷(
2
1
) =
−2b
2a
⋅
1
2
= −
b
2a
Therefore, the line of symmetry is the vertical line x=−
b
2a
. We can use the line of symmetry to find the the vertex.
Line of symmetry Vertex x=−
b
2a
(−
b
2a
,f(−
b
2a
))
Generally three points determine a parabola. However, in this section we will find five points so that we can get a better approximation of the general shape. The steps for graphing a parabola are outlined in the following example.
Example 1
Graph: f(x)=−x2−2x+3.
Solution:
Step 1: Determine the y-intercept. To do this, set x=0 and find f(0).
f(x) = −x2−2x+3 f(0) = −(0)2−2(0)+3 = 3
The y-intercept is (0,3).
Step 2: Determine the x-intercepts if any. To do this, set f(x)=0 and solve for x.
f(x) = −x2−2x+3 Set f(x)=0. 0 = −x2−2x+3 Multiply both sides by −1. 0 = x2+2x−3 Factor. 0 = (x+3)(x−1) Set each factor equal to zero. x+3 = 0 or x−1 = 0 x = −3 x = 1
Here where f(x)=0, we obtain two solutions. Hence, there are two x-intercepts, (−3,0) and (1,0).
Step 3: Determine the vertex. One way to do this is to first use x=−
b
2a
to find the x-value of the vertex and then substitute this value in the function to find the corresponding y-value. In this example, a=−1 and b=−2.
x =
−b
2a
=
−(−2)
2(−1)
=
2
−2
= −1
Substitute −1 into the original function to find the corresponding y-value.
f(x) = −x2−2x+3 f(−1) = −(−1)2−2(−1)+3 = −1+2+3 = 4
The vertex is (−1,4).
Step 4: Determine extra points so that we have at least five points to plot. Ensure a good sampling on either side of the line of symmetry. In this example, one other point will suffice. Choose x=−2 and find the corresponding y-value.
x y Point −2 3 f(−2)=−(−2)2−2(−2)+3=−4+4+3=3 (−2,3)
Our fifth point is (−2,3).
Step 5: Plot the points and sketch the graph. To recap, the points that we have found are
y-intercept: (0,3) x-intercepts: (−3,0) and (1,0) Vertex: (−1,4) Extra point: (−2,3)
Answer:
The parabola opens downward. In general, use the leading coefficient to determine if the parabola opens upward or downward. If the leading coefficient is negative, as in the previous example, then the parabola opens downward. If the leading coefficient is positive, then the parabola opens upward.
All quadratic functions of the form f(x)=ax2+bx+c have parabolic graphs with y-intercept (0,c). However, not all parabolas have x-intercepts.
Here is a `5`-by-`8` grid.
Create a design so that there are `3` times as many unshaded squares as there are shaded squares.
x = number of shaded squares
3x = number of unshaded squares
This is because there are 3 times as many unshaded squares compared to shaded
unshaded = 3*(shaded)
Since there are 5*8 = 40 squares overall, this means,
shaded+unshaded = 40
x+3x = 40
4x = 40
x = 40/4
x = 10
There are 10 shaded squares and 3x = 3*10 = 30 unshaded squares.
So you'll shade in 10 squares in any fashion you prefer.
The base of a rectangle is 3cm more than the height. The perimeter is 26cm. Determine the length of the base in centimeters.
Answer:
Step-by-step explanation:
b = h+3
Perimeter = 2b+ 2h
= 2(h+3) +2h
= 4h+ 6
4h+6 = 26
h = 5 cm
b = h+3 = 8 cm
Math geometry 7th grade (20 points)
Answer:
semoga jawapan ini dapat membantu
help me pls pls pls pls
[tex] \frac{4c}{h} - k[/tex]
Step-by-step explanation:
well that is the answer
Answer:
s = (4C/h) - k
Step-by-step explanation:
C = ((s + k)/4)h
multiply by 4/h
4C/h = s + k
subtract k
s = (4C/h) - k
Solve for h.
2(h − 16) − 16 = –12
h =
Answer:
18
Step-by-step explanation:
2h - 32 - 16 = -12
2h - 48= -12
2h =-12+48
h=36\2
h = 18
Answer:
h = 18
Step-by-step explanation:
Given
2(h - 16) - 16 = - 12 ← distribute and simplify left side
2h - 32 - 16 = - 12
2h - 48 = - 12 ( add 48 to both sides )
2h = 36 ( divide both sides by 2 )
h = 18
How many degrees in a circle
Answer:
360is the answer
Step-by-step explanation:
f(x)=2x^2-5;find when f(x)=-7
Answer:
x=i or no solution exists depending on the user's grade
Step-by-step explanation:
f(x) = 2x^2-5
-7 = 2x^2-5
-2 = 2x^2, x^2=-1, x=i
Answer:
±i = x
Step-by-step explanation:
f(x)=2x^2-5;
f(x)=-7
-7 = 2x^2 -5
Add 5 to each side
-7+5 = 2x^2 -5+5
-2 =2x^2
Divide by 2
-2/2 =2x^2 /2
-1 = x^2
Take the square root of each side
sqrt(-1) = sqrt(x^2)
±i = x
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x = -4
Step-by-step explanation:
[tex]-8x+3=-6x+11\\\\-2x+3=11\\\\-2x=8\\\\x=-4[/tex]
Answer:
x = -4
Step-by-step explanation:
-8x + 3 = -6x + 11
transpose
-8x +6x = 11 - 3
-2x = 8
x = 8/-2
x = -4
88 Decigrams equals 8.8 what
Answer:
8.8 grams
...................
The required 88 Decigrams equals 8.8 grams.
Given that,
To determine 88 Decigrams equals 8.8.
All over the world, most things are in use as of common quantity, so people all over the world agree that they have to follow a common system of measurement and that the common system of measurement is called standard measurement.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole.
here,
10 decigram = 1 gram
88 decigram = 8.8 gram
Thus, the required 88 Decigrams equals 8.8 grams.
Learn more about measurements here:
https://brainly.com/question/4725561
#SPJ2
AB = 6 and AC=13. Find BC.
Answer:
BC = 7
Step-by-step explanation:
AB + BC = AC
Substitute values for the line segments:
6 + BC = 13
Isolate line segment BC by subtracting both sides by 6:
6 - 6 + BC = 13 - 6
0 + BC = 13 - 6
BC = 7
Check your work:
6 + 7 = 13
13 = 13
Correct!
Final grades are often computed using weighted averages. Some college professors use complicated weighted averages. Your college professor tells you he will give a 33%-67% split on grades between tests and homework where whichever average is higher will be the 67%.
What will your final grade be if your homework average is 85 and your test average is 76?
Answer:
≈ 82Step-by-step explanation:
Add 67% of 85 to 33% of 76:
85*0.67 + 76*0.33 = 82.03 ≈ 8267% of 85
[tex]\\ \sf\longmapsto \dfrac{67}{100}\times 85[/tex]
[tex]\\ \sf\longmapsto 85(0.67)[/tex]
[tex]\\ \sf\longmapsto 56.95[/tex]
33% of 76
[tex]\\ \sf\longmapsto \dfrac{33}{100}\times 76[/tex]
[tex]\\ \sf\longmapsto 76(0.33)[/tex]
[tex]\\ \sf\longmapsto 25.08[/tex]
Add both
[tex]\\ \sf\longmapsto 56.95+25.08[/tex]
[tex]\\ \sf\longmapsto 82.03[/tex]
A popular amusement park has had199,792,458 visitors since it opened. Which
number, written in scientific notation, is the
best approximation of the number of visitors?
a) 0.2 x 107 visitors
b) 0.2 x 108 visitors
c) 2.0 x 107 visitors
d) 2.0 x 108 visitors
Answer:
d) 2.0 * 10⁸
Step-by-step explanation:
199,792,458 ≈ 200,000,000 = 2.0* 10⁸
Determine if the following statement is true or false. If false provide a counterexample.
An equation with an integer coefficient will always have an integer solution.
Answer: An equation with an integer coefficient will NOT always have an integer solution.
Explanation: 3x=25⟹x=253 , therefore it is false.
what is the quotient of 5472 and 81?
Enter your answer by filling in the boxes.
[ ] R [ ]
Answer:
67
Step-by-step explanation:
Division:-
[tex]\sf\Large\qquad\quad67\\ \begin{array}{cc} \cline{2 - 2}\sf 81 )&\sf \ 5472\\&\sf -487 \downarrow\\ \cline{2-2}& \sf \ \ \ \ 602\\ &\sf \ - 567 \\ \cline{2-2} & \sf \ \035 \\ \cline{2-2} \end{array}\\\\\\ Divisor \rightarrow 81 \\ \\ Quotient \rightarrow 67\\\\Remainder \rightarrow 35[/tex]
Answer:
[69] R [45}
Step-by-step explanation:
dont worry i got it right guys i did this bc i know there is people like me looking for the answer to this!
i need some help!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
We are dealing with theoretical probability. This means that our probability of said outcome is
[tex] \frac{x}{y} [/tex]
where x is the outcome we want, and y is the total number of outcomes possible.
28. There is 3 triangles out of 6 polygons so the probability is 1/2.
29.There is 1 Pentagon so the probability is 1/6.
30. This is a complement to question 28. A complement is the inverse of the problem. A complement and its original add to 1 so the probability of both getting a triangle is 1/2.
31. There is 4 non quadraletrial so the probability is 2/3.
32. There is 3 figures that has more sides than three so 1/2 is the probability.
33.There is only multi right angles figures so 1/2 is the probability.
34. There is 30 days in April so the probability it's the 29th is
[tex] \frac{1}{30} [/tex]
35. There is 31 days in July and 15 days after the 16th. So the probability
is
[tex] \frac{15}{31} [/tex]
Given m||n, find the value of x. (3x+10) (6x-10)
Answer:
Use the given functions to set up and simplify
( 3x + 10 ) ( 6 x − 10 ) = 18 x^ 2 + 30 x − 100
Can someone please help me!
Answer:
1/6 is the fobability of a polygon
WILL GIVE BRAINLY: VOLUME
The formula for volume is V=lwh. Remember to convert from cubic centimeters to cubic meters.
The formula for volume is
V = Lenght x Width X Height
In your diagram, we have all 3 of these.
Length = 25 cm
Width = 12 cm
Height = 14 cm
To make it easier let's just convert all these to meters.
Length = 0.25 m
Width = 0.12 m
Height = 0.14 m
V = (0.25)(0.12)(0.14)
V = 0.0042 cubic meters
the product of 9 and 4 more than x
Answer:
36-x
Step-by-step explanation:
Hi Monica
Algebra errors to avoid
Answer:
see image
Step-by-step explanation:
The circumference of a circular garden is 113.04 feet. What is the radius of the garden? Use 3.14 for pie and do not round your answer.
Answer:
18 ft
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi *r
113.04 = 2 ( 3.14) * r
113.04 = 6.28 r
Divide each side by 6.28
113.04/6.28 = 6.28r/6.28
18 =r
22) solve for x
A) 7
B) -9
C) -10
D) 10
B
Step-by-step explanation:
AM on total = 1/2
so (x+19)/(x+29)=1/2
2x +38 =x + 29
x=-9
What is 12.3% of 240