Answer:
The vertex of f(x) is at (-5,-10).
The function g(x) is decreasing at a rate of 5%.
The zeros of h(x) are at x = -3 and x = 1.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]
Decaying exponential function:
A decaying exponential function has the following format:
[tex]A(x) = A(0)(1-r)^{x}[/tex]
In which A(0) is the initial quantity and r is the decay rate.
Zeros of a function:
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
Vertex of f:
The function f is given by:
[tex]3(x+5)^2 - 10[/tex]
Expanding the calculations to place at the correct format:
[tex]3(x+5)^2 - 10 = 3(x^2 + 10x + 25) - 10 = 3x^2 + 30x + 75 - 10 = 3x^2 + 30x + 65[/tex]
Which means that
[tex]a = 3, b = 30, c = 65[/tex]
The x-value of the vertex is:
[tex]x_{v} = -\frac{30}{2*3} = -5[/tex]
The y-value of the vertex is:
[tex]f(-5) = 3(-5+5)^2 - 10 = -10[/tex]
The vertex of f(x) is at (-5,-10).
Decreasing rate of g(x).
We have that:
1 - r = 0.95
So
r = 1 - 0.95 = 0.05
Which means that the decreasing rate is of 5%.
The zeros of h(x) are
The zeros are
x + 3 = 0 -> x = -3
x - 1 = 0 -> x = 1
So
The zeros of h(x) are at x = -3 and x = 1.
1. What is the coefficient in the expression: 3 + 6x
Answer: 6
Step-by-step explanation:
6 is the only number next to x and is multiplying with it (ex: 6x would be a coefficient but 6+x would not)
Catherine has an unpaid balance on her credit card of $345.38. She has new charges of $195.65 this month and her monthly interest rate on the unpaid balance is 1.75%. What is the total balance on her monthly bill (to the nearest whole cent)?
$561.90
$555.55
$550.50
$570.08
None of these choices are correct.
Answer:
345.38+195.65+((345.38×(0.0175÷12))
=541.53
ill give branilest
help plz hw assignemnt
Answer:
I think its 100.
Step-by-step explanation:
How are you doing?
Find: 1. three quartiles and 2. interquartile range (IQR).
1, 3, 9, 12, 12, 14, 18
The position of Q1 is the 2th number. Q1 is 3.
The position of Q2 is the 4th number. Q1 is 12.
The position of Q3 is the 6th number. Q1 is 14.
IQR is 11.
What are the required values?The first quartile, second quartile and the interquartile range are used to measure the variation of data. Median is a measure of central tendency. Median is the number at the center of the dataset.
Q1 = 1/4 x (n + 1)
1/4 x 8 = 2nd number = 3
Q2 = 1/2 x (n + 1)
1/2 x 8 = 4th number = 12
Q3 = 3/4 x (n + 1)
3/4 x 8 = 6th number = 14
IQR = Q3 - Q1
14 - 3 = 11
learn more about median, please check: https://brainly.com/question/20434777
#SPJ2
pls helpp mee!!!!! pleaseee
Answer:
it is 5 inches squared
Step-by-step explanation:
1 inches. sjwjqkqkwjhed
points showing equivalent relics on the coordinate planeten
Ty
18
15
12
9
3
1 2 3 581 8 9 10 11 12 %
Which ordered pair would represent a ratio that is equivalent to those shown?
O 16, 12)
(9,6)
(8, 12)
O (12,8)
Answer:
Answer: (8,12) Third option
Step-by-step explanation:
Equivalent Ratios
Nardia plotted some points showing equivalent ratios. The points shown in the graph are: (2,3), (4,6), (10,15)
The ratios of the points in the form y:x are:
[tex]\frac{3}{2}[/tex]
[tex]\frac{6}{4}=\frac{3}{2}[/tex]
[tex]\frac{15}{10}=\frac{3}{2}[/tex]
Note all the ratios are equivalent.
From the ordered pairs provided in the choices, only one of them has the same ratio y:x.
Point (12,8) has a ratio:
[tex]\frac{12}{8}=\frac{3}{2}[/tex]
Answer: (8,12) Third option
Need some help with this..
Step-by-step explanation:
1. 22+5x+3=90
2.3+5x+82=180
3. 89=6x+5
4. 4x+3= 43
you can solve them luv
Which statements are true about the graph shown below. There are more than one answer.
Answer:
cant see the choices what the graph is a function
Step-by-step explanation:
Help and you get candy :3
Georgia is making necklaces. Each necklace has 3 blue beads and 5 red beads. How many red beads will she need to make 8 necklaces?
A. 25 red beads
B. 30 red beads
C. 35 red beads
D. 40 red beads
Answer:
40
Step-by-step explanation:
5 x 8 = 40
Find the missing angle measure in the triangle below.
i need help asap due tonight
Answer:
4
Step-by-step explanation:
multiply 10 by w and 3
equation becomes 10w+30=70
subtract 30 by both sides
equation becomes 10w=40
divide both sides by 10
equation becomes w=4
your answer is 4!
Benjamin went shopping for a new video game. The listed price of the video game
was $34, but the price with tax came to $37.40. Find the percent sales tax.
Answer:10%
Step-by-step explanation:
can someone complete it all
Answer:
Here it is
Step-by-step explanation:
#1. 3:4
#2. 3 to 4
#3. 3/4
Find the solution to the equation. URGENT
Answer:
x + 6 + x + 6 + x + 6 + x + 6 + x + 6 x + 6 + x + 6 + x + 6 = 120
aka 8(6 + x) = 120
48 + 8x = 120
you want to get 8x on one side so you will subtract 48 on both sides - whatever you do to obe side you must do on the other side.
8x = 72
now you want the x by its self so to undo multiplication you need to divide, and divide on both sides.
x = 9
Solution: x = 9
Please help me with this question above
Answer:
top to bottom
Step-by-step explanation:
Pls help thanks sooo much
Answer:
Step-by-step explanation:
a. we do first the multiplication 3*4=12
-9-12=-21
b. you do parenthesis first
(-2)^3=-8
(-8)*(-4)= +32
now we have (32)-3=29
c. as you see in the red square we do multiplication first, than division
3*2=6
(-18)/6=-3
2+(-3)=-1
What is 33/88 in simplest form?
Answer:
3/8
divide both by 11
you get 3/8
Question 2 (Essay Worth 3 points)
A circular picture is 8 inches in diameter.
Part A
What is the area of the picture in square inches?
A. 411 square inches
B. 8rt square inches
C. 161 square inches
D. 321 square inches
Part B
A frame that is 2 inches wide surrounds the picture. What is the total area of the picture and the frame in square inches?
A. 41 square inches
B. 120 square inches
C. 361 square inches
D. 40 square inches
What is the graph represents the equation y=1/3x+2
Step-by-step explanation:
step 1. you mean which graph represents the equation y = (1/3)x + 2?
step 2. please provide the graphs - they are missing.
step 3. the equation has a slope of 1/3 which means it goes up one and three to the right.
step 4. the y intercept is 2 so it goes through the point (0, 2).
Please help for brainliest.
Answer:
C
Step-by-step explanation:
(1, 2) indicates that x=1 and y=2
A:
(2)-(1)=1
3(2)-4(1)≠10
B:
-2(2)+5(1)≠-1
C:3(2)+2(1)=84(2)-(1)=7D:
3(2)-(1)≠1
Please help! Find the value of X. Round to the nearest tenth. acellus
9514 1404 393
Answer:
38.2°
Step-by-step explanation:
The law of sines tells you ...
sin(x)/15 = sin(27°)/11
sin(x) = (15/11)sin(27°) . . . . . multiply by 15
x = arcsin((15/11)sin(27°)) ≈ arcsin(0.619078) ≈ 38.2488°
x ≈ 38.2°
_____
Additional comment
In "law of sines" problems, you need to identify a side and opposite angle that you know both values of. Then, you need to identify whether you're looking for an angle or a side, and whether its opposite side or angle is known. If two angles are known, you can always figure the third from the sum of angles in a triangle.
Here, we have angle 27° opposite side 11. We are looking for an angle, and we know its opposite side. This lets us use the ratio formula directly. Since the angle is the unknown, it is useful to write the equation with sines on top and sides on the bottom.
The given angle is opposite the shorter of the given sides, so this triangle has two solutions. We assume that we want the solution that is an acute angle (141.8° is the other solution). That assumption is based on the drawing. Usually, you're cautioned not to take the drawings at face value.
Jason wants to earn money by raking leaves. He buys a rake that costs $30.00. He plans to charge $8.00 for each lawn that he rakes Calculate the amount of profit Jason
will make if he rakes 15 lawns
Answer:
He will make 90 dollars in profit.
Step-by-step explanation:
15 x 8 to find how much he makes. He makes 120 dollars. But we have to count the 30 dollars less he spent by subtracting 120 - 30. You get 90 dollars.
Hope it helps!
Answer:
120 dollars
Step-by-step explanation:
30 dollars times 15 lawns equal 120$
A teacher asked 21 pupils to estimate the height of a building in metres.
The stem-and-leaf diagram shows all 21 results.
6
represents 6.5m
6
5
9
7
0
2
6
8
8
8
3
3
5
7
7
9
9
0
5
5
5
10
8
11
2.
What was the median estimated height?
m
Answer:
I think it's 8.5m,I wish it is correct.
Step-by-step explanation:
:)I wish it helps.
Find the measure of
answer fast pls! <3
+10pts
Answer:
∠A = 88°
Step-by-step explanation:
= 180° - (50° + 38°)
= 180° - 88°
= 92°
∠A + 92° = 180°
∠A = 180° - 92°
∠A = 88°
Drag the cards to create a number that matches these rules. • The number ends in the tenths place. 50 is the nearest ten when rounding 3. 8 4
Find x. (More info in the picture)
Answer:
The answer is 3.
Step-by-step explanation:
3x+2x-13=47 solve for x
please show all the steps
Please help! Doing online because of pandemic!
For line b, d, and e, line d is parallel to line e, and m∠1 = 81°.
Part A: In complete sentences, explain the relationships between all pairs of special angles 1, 2, 3, and 4 created by transversal line b and parallel lines d and e.
Part B: For the given diagram, use the measure of the special angle relationships created by transversal line b and parallel lines d and e to find the measures of ∠2, ∠3, and ∠4.
Answer:
ART A: Angles 1 and 4 are Corresponding Angles. Angles 1 and 3 are Vertical Angles. Angles 1 and 2 are Adjacent Supplementary Angles. Angles 2 and 3 are also Adjacent Supplementary Angles. Angles 3 and 4 are Opposite Interior Angles.
PART B:
<2=99 °
<3=81 °
<4=99 °
Step-by-step explanation:
PART A: Angles 1 and 4 are Corresponding Angles. Angles 1 and 3 are Vertical Angles. Angles 1 and 2 are Adjacent Supplementary Angles. Angles 2 and 3 are also Adjacent Supplementary Angles. Angles 3 and 4 are Opposite Interior Angles.
PART B:
<2=99 °
<3=81 °
<4=99 °
What is the value of the fourth term in a geometric sequence for which ay =
10 and r = 0.5?
Answer:
1.25
Step-by-step explanation:
a = 10 and r = 0.5
The formula for calculating any term in a geometric sequence is a (the first term) times r (the common ratio) raised to the power of n - 1.
In this case n = 4, since we're looking for the fourth term.
so,
Un = ar^n-1
= ar^4-1
= ar^3
U4 = 10 × 0.5^3
= 10 × 0.125
= 1.25
PLS HELP ILL GIVE BRAINLIEST!
Answer:
C = 55
O = 55
CRA = 64
ORT = 64
T = 61
Answer:
C = 55
O = 55
CRA = 64
ORT = 64
T = 61
Step-by-step explanation:
