Answer:
f(x) = - ⁴/₉(x - 3)² + 6Step-by-step explanation:
The vertex form of the equation of the parabola with vertex (h, k) is:
f(x) = a(x - h)² + k
So for vertex (3, 6) it will be:
f(x) = a(x - 3)² + 6
y intercept: 2 means f(0) = 2
f(0) = a(0 - 3)² + 6
2 = a(-3)² + 6
2 -6 = 9a + 6 -6
-4 = 9a
a = ⁻⁴/₉
Therefore:
The vertex form of quardatic function with vertex: (3,6) and y intercept: 2 is
f(x) = - ⁴/₉(x - 3)² + 6
The vertex form of the parabola equation is f(x) = -4/9(x - 3)² + 6 if the vertex: (3,6) and y intercept: 2
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
It is given that:
The vertex: (3,6) and y-intercept: 2
As we know,
The parabola equation:
f(x) = a(x - h)² + k
Here (h, k) is the vertex of the parabola and a is the leading coefficient.
f(x) = a(x - 3)² + 6
f(x) = 2 at x = 0
2 = a(0 - 3)² + 6
a = -4/9
f(x) = -4/9(x - 3)² + 6
Thus, the vertex form of the parabola equation is f(x) = -4/9(x - 3)² + 6 if the vertex: (3,6) and y intercept: 2
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Find the cost with sales tax for an item with a purchase price of $7. Assume that the sales tax is 8%, or 0.08 times the price.
Group of answer choices
Answer:
$7.56
Step-by-step explanation:
$7(.08) = .56 in tax
$7 item cost + .56 in tax
V = LWH solve for the variable w
Answer:
w=v/lh
Step-by-step explanation:
HELP WILL GIVE BRAINLYEST
Answer:
Answer is D. 2 & -2
Answer:D
I THINK
Step-by-step explanation:
Hopefully this is the right one
• Which ratios have a unit rate of 5? Choose ALL that apply.
Answer:
6 1/4 and 1 1/4
1 and 1/5
Step-by-step explanation:
These are the only ones I think
[tex]6\frac{1}{4}[/tex] kilometer: [tex]1\frac{1}{4}[/tex] minutes and 1 kilometer: 1/5 minutes has unit rate as 5.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
The given, ratios are:
4/5 km : 5 minutes
[tex]3\frac{1}{10}[/tex] km: 3/10 minutes
1 kilometer: 1/5 minutes
1/3 kilometer: [tex]1\frac{2}{3}[/tex] minutes
[tex]4\frac{1}{2}[/tex] kilometer: 2 minutes
[tex]6\frac{1}{4}[/tex] kilometer: [tex]1\frac{1}{4}[/tex] minutes
We need to check which ratios have 5 as unit rate.
[tex]6\frac{1}{4}[/tex] kilometer: [tex]1\frac{1}{4}[/tex] minutes has unit rate as 5
25/4/5/4
5
1 kilometer: 1/5 minutes
5
Hence, [tex]6\frac{1}{4}[/tex] kilometer: [tex]1\frac{1}{4}[/tex] minutes and 1 kilometer: 1/5 minutes has unit rate as 5.
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What kind of linear relationship can be represented using a table but not a function? Explain. (1 point)
O A horizontal line can be represented using a table but not a function because the slope is undefined
A vertical line can be represented using a table but not a function because the slope is undefined.
O A vertical line can be represented using a table but not a function because the slope is zero.
O A horizontal line can be represented using a table but not a function because the slope is zero
Answer:
The correct option is;
A vertical line can be represented using a table but not a function because the slope is undefined
Step-by-step explanation:
A function, f(x), representing a linear relationship can be presented as follows;
f(x) = m·x + c
Where;
m = The slope = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)
c = The y-intercept
Whereby the line is a vertical line, x₂ = x₁ and x₂ - x₁ =
Therefore;
The slope of a vertical function, m = (y₂ - y₁)/(x₂ - x₁) = (y₂ - y₁)/0 = ∞ from which we have;
f(x) = ∞·x + c = ∞ which is undefined and the vertical line can only be represented using a table but not a function because the slope is undefined
in order to solve for x which trig function would be used cosine sine or tangent
Answer:
Cosine
Step-by-step explanation:
I took the test
In order to solve for x , we use the trigonometric function cosine
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be ΔABC , where ∠B = 90°
Let the side AB be x
So , the adjacent side = x
The angle of the triangle ∠A is = 72°
So , θ = 72°
The hypotenuse AC = 8
And , by trigonometric relations , we get
cos θ = adjacent / hypotenuse
Substituting the values in the equations , we get
cos 72° = x / 8
Multiply by 8 on both sides , we get
x = cos 72° × 8
Now , cos 72° = 0.30901
Substituting the value of cos 72° , we get
x = 0.30901 × 8
x = 2.472
Hence , the value of x is determined by cosine function
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For an activity in class, student used pieces of string to measure road on a map. They used a map scale to determine the distance between two cities. One group measured the distance between Fort Myers and Miami on a Florida state map. The string distance was 7.75 inches, which represents a real-life distance of about 155 miles. Another group measured the distance between Tampa and Orlando on the same map and found that distance to be 4.25 inches. What is the real-life distance to the nearest mile between Tampa and Orlando
Answer:
Step-by-step explanation:
85miles¯\_(ツ)_/¯
Kathryn owns a video store. She rents games for 4 and moves for 4 She must rent at least 84 to make a profit She does not have anymore than 20 games Write and solve the system
Answer:
Katherine will rent at least 64 movies and 20 games to make a profit
Step-by-step explanation:
The given parameters are;
The amount for which she rents games = 4
The amount for which she rents movies = 4
The number of games and movies she most rent to make profit = 84
The number of games she ≤ 20
Let x represent the number of games, let y represents the number movies, we have;
x + y ≥ 84
x ≤ 20
64 ≤ y ≤ 84
The graph of the inequality created with Microsoft Excel showing the feasible region is included
how do you find the value of √a⁴ ??
(ill give brainliest)
Answer:
[tex]a^{2}[/tex]
Step-by-step explanation:
√a^4 is the same as:
√a × √a × √a × √a
group them as 2 pairs of
(√a × √a) × (√a × √a)
which makes
a × a
which is the same as [tex]a^{2}[/tex]
Complete the table using equivalent ratios.
21:6
7:__
__:4
Answer:
7:2
14:4
Step-by-step explanation:
Suppose there are two circles where the radius of one circle is twice the radius of the other circle. Each circle has an arc where the measures of the corresponding central angles are the same. What is the relationship between the arc lengths in the two circles? Explain. (2 points)
Answer:
[tex]L=2l[/tex] where [tex]l,L[/tex] denote arc lengths of two circles
Step-by-step explanation:
Let [tex]l,L[/tex] denote arc lengths of two circles, [tex]r,R[/tex] denote corresponding radii and
[tex]\alpha _1\,,\alpha _2[/tex] denote the corresponding central angles.
So,
[tex]l=r\alpha _1[/tex] and [tex]L=R\alpha _2[/tex]
This implies [tex]\alpha _1=\frac{l}{r}[/tex] and [tex]\alpha _2=\frac{L}{R}[/tex]
As each circle has an arc where the measures of the corresponding central angles are the same, [tex]\alpha _1=\alpha _2[/tex]
[tex]\frac{l}{r}=\frac{L}{R}[/tex]
As radius of one circle is twice the radius of the other circle,
[tex]R=2r[/tex]
[tex]\frac{l}{r}=\frac{L}{2r}\\\frac{l}{1} =\frac{L}{2}\\L=2l[/tex]
Linda's account has a balance of −$45.50. If she owes the bank more than $30, her account gets closed. Which of the following is true about Linda's account?
Answer:
There's no options but it will get closed
Step-by-step explanation:
Answer:
Step-by-step explanation:
-75.5
How many solutions does the nonlinear system of equations graphed below
have?
2. If mZ1 = 71 degrees, find the measure of the other 7 angles.
The measure of the other 7 angles are;
m∠2 = m∠3 = 109°; m∠4 = m∠5 = m∠8 = 71°; m∠6 = m∠7 = 109°
We are given;
m∠1 = 71°
Thus;
m∠1 and m∠2 are angles that form a straight line and as such they are supplementary angles and sum up to 180°
Thus; m∠1 + m∠2 = 180°
71 + m∠2 = 180°
m∠2 = 180 - 71
m∠2 = 109°
Now, m∠2 and m∠3 are alternate angles and as such;
m∠2 = m∠3
Thus; m∠3 = 109°
Similarly,
m∠1 and m∠4 are alternate angles and as such;
m∠1 = m∠4
Thus;
m∠4 = 71°
m∠1 and m∠5 are corresponding angles and as such;
m∠1 = m∠5
Thus;
m∠5 = 71°
m∠2 and m∠6 are corresponding angles and as such;
m∠2 = m∠6
Thus;
m∠6 = 109°
Similar to how angles were gotten earlier, we can say that;
m∠5 = m∠8 = 71°
and m∠6 = m∠7 = 109°
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In Triangle DEF, f = 160 cm, d = 670 cm and ZE=114°. Find the length of e, to the nearest
centimeter.
Answer:
This is an obtuse scalene triangle with the length of E measuring around 749 cm.
<D = 54.754° ≈ 55°
<E = 114°
<F = 11.246° ≈ 11°
Side D = 670 cm
Side E = 749.46937 cm ≈ 749 cm
Side F = 160 cm
Explanation:
When given two sides, and an angle, we can use trigonometry to find the missing angles, and sides.
Given the triangle ∆DEF with side D measuring 670 cm, side F measuring 160 cm, and angle E measuring 117°, we can apply the law of sines to identify the missing information. A & a chronologically refers to the first angle, and side. B & b chronologically refers to the second angle, and side. And C & c chronologically refers to the third angle, and side.
a / Sin (A) = b / Sin (B) = c / Sin (C)
[side 1]. [side 2]. [side 3].
↓ ↓ ↓
sideD/sin(<D) SideE/sin(<E) SideF/sin(<F)
______________________________
670cm / Sin(D) = E cm / Sin(114) = 160 / sin(F).
Since we are only given two sides with an angle measure, we can refer to the law of cosines to figure this one out.
It states that A = arccos(b²+c²-a²/2bc) → cos(A) = b²+c²-a²/2bc
B = arccos(a²+c²-b²/2ac) → cos(B) = a²+c²-b²/2ac
and C = arccos(a²+b²-c²/2ab) → cos(C) = a²+b²-c²/2ab
capital A, B, and C are angles A, B, and C.
lowercase a, b, and c are sides a, b, and c.
Therefore c² = a² + b² − 2ab cos(C),
b² = a² + c² - 2ac cos (B), and a² = b²+c² - 2bc.
SOH CAH TOA.
Since we know this, we can solve for pretty much everything as long as we are given at least 3 variables. Chronologically, because we are solving for side e, we must use b² = a² + c² - 2ac cos (B), because the rest are only variables we are given, making it easy to solve. So b² = 670² + 160² - 2(670 × 160) × cos(114°) = 561704.3362754.
Now take the square root of that to get b by itself, so √561704.3362754.... = 749.4693698046.... ≈ 749
Answer:749
Step-by-step explanation:
S.A.S law or Cosines
e=561704.33628= 749.469= 749
Need help in math ASAP
Answer:
B
Supplementary means they add to make 180 deg, so solve (4x-8)+(2x+2)=180
Answer:
angle a + angle b=180
4x-8+(2x+2)=180
6x-6=180
6x=180+6
x=186/6
{x=31°}
Jason is flying a kite and has 325 feet of kite string out. The angle of elevation between Jason’s hand and the kite string is 58˚. Jason’s hand is 3 feet above the ground. How high is the kite to the nearest tenth?
i need this asap pls
Answer:
The height of the kite is approximately 278.6 feet
Step-by-step explanation:
The length of Jason's Kite string, l = 325 feet
The angle of elevation of the kite string, θ = 58°
The height of Jason's hand, h = 3 feet above the ground
Therefore, we have;
The height of the kite = The vertical component of the length of the kite string + The height of Jason's hand above the ground
The height of the kite = l × sin(θ) + h
Substituting the values, we get
The height of the kite = 325 × sin(58°) + 3 ≈ 278.6 (which is obtained by rounding the answer to the nearest tenth)
The height of the kite ≈ 278.6 feet.
Given the following sequence and an-1 = 12, what is an?
2, 7, 12, 17,...
Answer:
12
Step-by-step explanation:
[tex]a_{n-1}=12\\\\
Plug\: n = n + 1\\\\
a_{n+1-1}=12\\\\
\huge \red {\boxed {a_{n}=12}} \\\\[/tex]
Round each decimal to the nearest tenth
4. 13.392
5. 27.149
6.8.84858
Help!!
Answer:
13.4
27.1
8.8
Step-by-step explanation:
hope that helps
2(-6m - 3) =6(5m - 1) please show work what is m ?
Answer: m=0
Step-by-step explanation: simplify each individual expression first. The left side of the equation is equal to -12m-6, and the right side is equal to 30m-6. Then together, it equals to -12m-6=30m-6. The -6 cancel each other out. M=0
Do the ratios 16 18 and 1 2 form a proportion?
Answer:
no they don't form a proportion
Step-by-step explanation:
16:18/2:2 = 8:9
8:9 and 1:2 are unequal
11/12 - (-10)- 5/6 please help
Answer:
121/12 is the answer your welcome
what is the slope of the line that passes through the points (2,1) and (17,-17)
hi
You have two points A ( X;Y) and B ( X ; Y)
slope is : ( Yb -Ya) / (Xb -Xa )
A(2 ; 1) and B (17 ; - 17)
so : (-17 - 1 ) / (17 -2) = -18/ 15 = - 6*3 / 5*3 = -6/5
3 4 (x−12)=12 whats the answer tehe
Answer:
x= 12 6/17
Step-by-step explanation:
in the equation (m^5/6) (m^1/6)^7 = m^x , what is the value of x that makes the equation true?
The value of x in the equation (m^5/6) (m^1/6)^7 = m^x is 2
What is the law of exponent?The exponents of numbers are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent: a^m×a^n = a^(m+n); a^m÷a^n = a^(m−n);
(am)ⁿ = a^mn.
Given an equation, (m^5/6) (m^1/6)^7 = m^x
Using the law of exponent, we get,
(m^5/6) (m^1/6)^7 = m^5/6*m^7/6
= m^(5/6+7/6)
= m^12/6
= m^2
Hence, the value of x in the equation (m^5/6) (m^1/6)^7 = m^x is 2
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A man wants to cut down a tree in his yard. To ensure that the tree doesn’t hit anything he needs to know the height of the tree. He measures his distance from the tree at 18 meters and the angle of elevation to the tree at 80 degrees. What is the height of the tree to the nearest tenth of a meter?
Answer:
[tex]\boxed {\boxed {\sf 102.1 \ meters}}[/tex]
Step-by-step explanation:
Let's assume the tree forms a right angle with the ground.
The distance from the tree to the man is 18 meters. The angle of elevation, which is 80 degrees, is the angle from where the man is to the top of the tree. We want to find the height of the tree, which we can call x.
Let's draw a diagram. (not to scale)
We can use sine (opposite/hypotenuse), cosine (adjacent/hypotenuse) or tangent (opposite/adjacent). We base the sides off of the elevation angle.
x is opposite the elevation angle and 18 is adjacent to the angle. So, we must use tangent.
[tex]tan(\theta)=opposite/adjacent[/tex]
The angle (θ) is 80. The opposite is x. The adjacent is 18.
[tex]tan(80)=x/18[/tex]
Now, solve for x by isolating it.
x is being divided by 18. The inverse of division is multiplication. Multiply both sides of the equation by 18.
[tex]18*tan(80)=x/18*18[/tex]
[tex]18*tan(80)=x[/tex]
[tex]18*5.67128182=x[/tex]
[tex]102.0830728=x[/tex]
Round to the nearest tenth. The 8 in the hundredth place tells us to round up.
[tex]102.1\approx x[/tex]
The height of the tree is about 102.1 meters.
**diagram is not to scale
Aplica la operación de números enteros que corresponda:
(+148) + (+35) =
(+80) + (-53) =
(-125) X (-42) =
148+35=183
80+(-53)=27
(-125) x (-42)=5250
Need help asap...,..........
Answer:
x2+ 16k+ 64= not factorable with rational numbers
x2+ 7x+ 10= (x+2)(x+5)
These are what I got from your picture, so don't quote me on this the picture wasn't the best.
All I know is that the answer is F. How do I get to the answer F?
Answer:
8 inches on each side
Step-by-step explanation:
There are 180 white lockers in the school. There are 3 white lockers for every 5 blue locker. How many lockers are in the school?
Answer:
There are 480 lockers in school.
Step-by-step explanation:
480
Step-by-step explanation:
180÷3=60
60x5=300
300+180=480