Answer:
y = 3x + 4
Step-by-step explanation:
Substituting into point-slope form and converting to slope-intercept form,
[tex]y+5=3(x+3) \\ \\ y+5=3x+9 \\ \\ \boxed{y=3x+4}[/tex]
Calculate the perimeter of 5y + 9 (3y+15) cm (7y+3)cm
Answer:
Step-by-step explanation:
assuming that the figure is a triangle with sides (5y + 9) and (3y + 15) and (7y + 3) we find the perimeter by adding everything
5y + 9 + 3y + 15 + 7y + 3 =
15y + 27
or
3(5y+9)
next time put all the data and figures, we are doing you a pleasure, at least put ALL the data.
PLEASE HELP IMMEDIATELY
Use the function f(x) to answer the questions:
f(x) = 5x2 + 2x − 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
For the given function f(x) = 5x² + 2x - 3,
Part A: The x-intercepts of the graph f(x) are: (-1, 0) and (3/5, 0).
Part B: The vertex of the graph of f(X) is going to be a minimum and its coordinates are (-0.2, -3.2).
Part C: The values obtained in the part A and Part B are used for graphing the given function. Since the vertex is minimum, the parabola opens upwards.
How to calculate x-intercepts of a function?The x-intercepts of a function or equation are obtained at y = 0.
Then, on substituting y = 0 in the function gives the x-coordinate i.e., the x-intercept.
How to calculate the coordinates of the vertex of a function?To calculate the x coordinate of vertex(h, k), use the formula mentioned below:
h = -b/2a
When the function is in the form of ax² + bx + c.
Then, to calculate the y-coordinate of the vertex, substitute obtained h value in the place of x in the function.
Thus, the required coordinates of the vertex are obtained as (h, k).
Calculation:It is given that,
f(x) = 5x² + 2x - 3
Part A: Finding the x-intercepts:
Substituting y = 0 i.e., f(x) = 0;
⇒ 5x² + 2x - 3 = 0
On simplifying/factorizing,
⇒ 5x² + 5x - 3x - 3 = 0
⇒ 5x(x + 1) - 3(x +1) = 0
⇒ (5x - 3)(x + 1) =0
∴ x = 3/5 or x = -1
Thus, the x-intercepts are (3/5, 0) and (-1, 0).
Part B: Finding the vertex of the given function:
We have h = -b/2a
From the given function 5x² + 2x - 3; a = 5, b = 2 and c = -3
So, h = -2/2(5) = -1/5 = -0.2
Then, on substituting h = x = -0.2 in the function we get
k = 5(-0.2)² + 2(-0.2) - 3
k = -3.2
Thus, the coordinates of the vertex are (h, k) = (-0.2, -3.2).
Since a > 0 i.e., 5 > 0, the vertex of the graph is going to be minimum and the graph of f(x) opens upwards.
Part C: Steps to graph f(X):
Step 1: Plot the x-intercepts in the coordinate plane
Step 2: Plot the vertex of the function
Step 3: draw a curve line passing through them, opening towards up.
Thus, the graph of the given function is plotted as shown below.
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Jason solved the following equation to find the value for x.
-8.5x-3.5x=-78
X=6.5
Describe how Jason can check his answer.
Please Help its a math question i will mark brainlist !! plsss look at attached image below ...blessings
Answer:
-2
Step-by-step explanation:
Every point would flip over the y axis the same distance it is from the y axis now, but just on the other side of the y axis.
In the original equation, when y = 0, x is 2, so when we flip it over the y axis, it is now at -2 when y = 0.
please help me if you can
The time, t in seconds that it takes a car to travel a quarter-mile when starting from a full stop can be estimated by using the formula:
[tex]t=5.825\sqrt[3]{w/p\\}[/tex]
Where w = weight of the car
p = power delivered by the engine in horsepower (hp)
If the quarter-mile time for a 3,590-pound car is 13.4 s, how much power does its engine deliver? Round to the nearest pound.
Two students solved this problem. Natasha’s answer was 295 hp and Daniel’s was 679 hp. Why was Daniel wrong? Show each step that led Daniel to the wrong answer
Natasha got the power right. The power is 295 hp.
How to calculate power?t = 5.825∛w / p
where,
w = weight of the carp = power delivered by the engine in horsepowerquarter mile time = tTherefore,
t = 13.4 s
p = 3590
13.4 = 5.825∛ 3590 / p
cube both sides
13.4³ = 5.825³ × 3590 / p
2406.104 = 197.645890625 × 3590 / p
cross multiply
2406.104 p = 709548.747344
p = 709548.747344 / 2406.104
p = 294.895294361
p = 295 hp
Therefore, Natasha got the power right
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Use the graph to write the explicit rule of the arithmetic sequence.
Question 19 options:
A)
ƒ(n) = 9 + 2(n – 1)
B)
ƒ(n) = 5 + 3(n – 1)
C)
ƒ(n) = –3 + 2(n – 1)
D)
ƒ(n) = 3 + 2(n – 1)
Answer: D
Step-by-step explanation:
The first term is 3 and the common difference is 2.
Substituting into the explicit formula for an arithmetic sequence gives D as the correct answer.
Solve the equation 3x² = 108.
Answer:
x = 6
Step-by-step explanation:
First we divide both sides by 3 :
x² = 108 ÷ 3
x² = 36
Now we square root both sides :
x = √36
x = 6
Hope this helped and have a good day
Answer:
x = ± 6
Step-by-step explanation:
Quick steps
[tex]3x^{2} =108[/tex]
[tex]x=\sqrt{\frac{108}{3} } =\sqrt{36}[/tex]
[tex]x=[/tex] ±6
A (positive) number has two square roots; one positive and one negative
Hope this helps
A rectangle is 16 cm. in length. Its width is 50% of its length. what is its perimeter?
Answer: 48 cm
Step-by-step explanation:
A perimeter(P) of a rectangle is equal to 2(L + W), or 2L + 2W, so we write the equation as:
1st way:
W = 50%(16) = 0.5 x 16 = 8
P = 2(L + W)
P = 2(16 + 8)
P = 2(24)
P = 48 cm
2nd way:
P = 2L + 2W
P = 2(16) + 2[50%(16)]
P = 2(16) + 2[0.5 X 16]
P = 32 + 2(8)
P = 32 + 16
P = 48 cm
Evaluate the integral, show all steps please!
Answer:
[tex]\dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given indefinite integral:
[tex]\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x[/tex]
Take partial fractions of the given fraction by writing out the fraction as an identity:
[tex]\begin{aligned}\dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A}{x-4}+\dfrac{B}{x+2}\\\\\implies \dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A(x+2)}{(x-4)(x+2)}+\dfrac{B(x-4)}{(x-4)(x+2)}\\\\\implies x+5 & \equiv A(x+2)+B(x-4)\end{aligned}[/tex]
Calculate the values of A and B using substitution:
[tex]\textsf{when }x=4 \implies 9 = A(6)+B(0) \implies A=\dfrac{3}{2}[/tex]
[tex]\textsf{when }x=-2 \implies 3 = A(0)+B(-6) \implies B=-\dfrac{1}{2}[/tex]
Substitute the found values of A and B:
[tex]\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x = \int \dfrac{3}{2(x-4)}-\dfrac{1}{2(x+2)}\:\:\text{d}x[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}[/tex]
If the terms are multiplied by constants, take them outside the integral:
[tex]\implies \displaystyle \dfrac{3}{2} \int \dfrac{1}{x-4}- \dfrac{1}{2} \int \dfrac{1}{x+2}\:\:\text{d}x[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating}\\\\$\displaystyle \int \dfrac{f'(x)}{f(x)}\:\text{d}x=\ln |f(x)| \:\:(+\text{C})$\end{minipage}}[/tex]
[tex]\implies \dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}[/tex]
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For an alternative approach, expand and complete the square in the denominator to write
[tex](x-4)(x+2) = x^2 - 2x - 8 = (x - 1)^2 - 9[/tex]
In the integral, substitute [tex]x - 1 = 3 \sin(u)[/tex] and [tex]dx=3\cos(u)\,du[/tex] to transform it to
[tex]\displaystyle \int \frac{x+5}{(x - 1)^2 - 9} \, dx = \int \frac{3\sin(u) + 6}{9 \sin^2(u) - 9} 3\cos(u) \, du \\\\ ~~~~~~~~~~~~ = - \int \frac{\sin(u) + 2}{\cos(u)} \, du \\\\ ~~~~~~~~~~~~ = - \int (\tan(u) + 2 \sec(u)) \, du[/tex]
Using the known antiderivatives
[tex]\displaystyle \int \tan(x) \, dx = - \ln|\cos(x)| + C[/tex]
[tex]\displaystyle \int \sec(x) \, dx = \ln|\sec(x) + \tan(x)| + C[/tex]
we get
[tex]\displaystyle \int \frac{x+5}{(x - 1)^2 - 9} \, dx = \ln|\cos(u)| - 2 \ln|\sec(u) + \tan(u)| + C \\\\ ~~~~~~~~~~~~ = - \ln\left|\frac{(\sec(u) + \tan(u))^2}{\cos(u)}\right|[/tex]
Now, for [tex]n\in\Bbb Z[/tex],
[tex]\sin(u) = \dfrac{x-1}3 \implies u = \sin^{-1}\left(\dfrac{x-1}3\right) + 2n\pi[/tex]
so that
[tex]\cos(u) = \sqrt{1 - \dfrac{(x-1)^2}9} = \dfrac{\sqrt{-(x-4)(x+2)}}3 \implies \sec(u) = \dfrac3{\sqrt{-(x-4)(x+2)}}[/tex]
and
[tex]\tan(u) = \dfrac{\sin(u)}{\cos(u)} = -\dfrac{x-1}{\sqrt{-(x-4)(x+2)}}[/tex]
Then the antiderivative we found is equivalent to
[tex]\displaystyle - \int \frac{x+5}{(x - 1)^2 - 9} \, dx = - \ln\left|-\frac{3(x+2)}{(x-4) \sqrt{-(x-4)(x+2)}}\right| + C[/tex]
and can be expanded as
[tex]\displaystyle - \int \frac{x+5}{(x - 1)^2 - 9} \, dx = -\ln\left| \frac{3(x+2)^{1/2}}{(x-4)^{3/2}}\right| + C \\\\ ~~~~~~~~~~~~ = - \ln\left|(x+2)^{1/2}\right| + \ln\left|(x-4)^{3/2}\right| + C \\\\ ~~~~~~~~~~~~ = \boxed{\frac32 \ln|x-4| - \frac12 \ln|x+2| + C}[/tex]
10. Ali's crystal ball grants two-fifths of one-fifth of
all wishes. This is ?% of all wishes.
(A)
2
(B)
25
(C) 8
(D) 60
Answer:
C
Step-by-step explanation:
2/5 x1/5 = 2/25 If you divide 2 by 25, you get.08. To change a decimal into a percent, you move the decimal two places to the right to get 8%
I'm thinking of a number. If I add 4 to the number and then multiply the result by 3,the answer is the same as subtracting 5 from the number and then multiplying the result by 2.
(a) in terms of x?
(b) solve the equation n find the number what I'm thinking of
Answer:
x=-22
Step-by-step explanation:
Let's substitute the number you are thinking of with x
(x+4)*3=(x-5)*2
3x+12=2x-10
x+12=-10
x=-22
An online retail company determined that their cost for each day, x, can be determined by the function C(x) = 2x^2 – 20x + 70 and their revenue by the function R(x) = –x^2 + 5x + 18. How many days will it take for the company to earn a profit?
4
5
20
22
Answer:
4
Step-by-step explanation:
revenue has to be greater than cost for a profit
revenue minus cost = profit
2x^2 – 20x + 70 - (–x^2 + 5x + 18) =
2x^2 – 20x + 70 + x^2 - 5x - 18 =
3x^2 – 25x + 52 ≤ 0
(x - 4) (3x - 13) ≤ 0
x ≤ 4
x ≤ 13/3
since its multiple choice you can enter one of the answers where the x is to get the answer
if you don't know what the question is and are short on time this may help
again:
revenue has to be greater than cost for a profit
revenue minus cost = profit
cost is 2x^2 – 20x + 70
revenue is –x^2 + 5x + 18
cost is
2(4)^2 – 20(4) + 70 =
32-80+70 =
102-80 =
22
revenue is
–x^2 + 5x + 18
–(4)^2 + 5(4) + 18
-16+20+18
-16+38
22
--------------------------------
cost is
2(5)^2 – 20(5) + 70 =
20
revenue is
–(5)^2 + 5(5) + 18
18
-------------------------------------
cost is
2(20)^2 – 20(20) + 70 =
470
revenue is
–(20)^2 + 5(20) + 18
-282
------------------------------
cost is
2(22)^2 – 20(22) + 70 =
598
revenue is
–(22)^2 + 5(22) + 18
-356
-----------------------------------------
cost is
2(3)^2 – 20(3) + 70 =
28
revenue is
–(3)^2 + 5(3) + 18
24
-------------------------------------
cost is
2(2)^2 – 20(2) + 70 =
38
revenue is
–(2)^2 + 5(2) + 18
24
Solve the system of equations below using the substitution method. y = 3x − 1y = - 4x 6
Answer:
x = 1; y = 2
Step-by-step explanation:
y = 3x − 1
y = -4x + 6
In the first equation, y = 3x - 1.
Substitute 3x - 1 for y in the second equation.
3x - 1 = -4x + 6
7x = 7
x = 1
Substitute 1 for x in the first original equation.
y = 3x - 1
y = 3(1) - 1
y = 3 - 1
y = 2
Solution: x = 1; y = 2
Point P is on line segment \overline{OQ}
OQ
. Given PQ=x+7,PQ=x+7, OP=4x-10,OP=4x−10, and OQ=4x,OQ=4x, determine the numerical length of \overline{OQ}.
OQ
.
Answer:
Step-by-step explanation:
4x - 10 + x + 7 = 4x
5x - 3 = 4x
-3 = -x
x = 3
4(3) - 10 = 12 - 10 = 2
3 + 7 = 10
10+2 = 12
4(3)= 12
if you could help with all 4 questions that would be great pls answer if you know the RIGHT answer
Step-by-step explanation:
3. B
because the figure to the left of the y-axis yields the one to the right when you reflect it across y = x.
4. C
Flip either of the figures vertically across x = -1 which is their intersection point and you'll get the other.
5. D
it can't be clockwise because the x value of the vertices would have been negative. so it is 270° counterclockwise resulting in ( -y , x )
6. A
Similar to #4 which except this time, you flip it horizontally like how you lay a book or pick it up.
According to the Coase theorem, negative externalities can be internalized if Select one: a. the government takes action to solve the problem. b. property rights are assigned to the party who is being damaged. c. property rights are assigned to either party. d. property rights are assigned to the party who is doing the damage.
Answer:
B. Property right are assigned to the party who is being
What is the name of each of the two blue points in the hyperbola below?
A. Focus
B. Center
C. Vertex
D. Directrix
Geometry: complete this proof (ASAP!!!!! It’s urgent)
Answer:
1. Given.
2. Alternate Interior Angles Theorem.
3. m<2 + m<7 = 180 by definition of supplementary angles. By definition of congruent angles, m<2 = m<4 and m<5 = m<7, therefore m<4 + m<5 = 180 by substitution property of equality. By definition of supplementary angles, <4 is supplementary to <5.
4. Converse of Consecutive Angles Theorem.
. What is the midpoint of a line segment connecting the points (−4,6) and (8,2)?
Use the diagram to answer each part of the question. The image is not drawn to scale.
will mark brainiest if corrects. try ur best!
In the afternoon, the person (who is 1.6 m tall) casts a shadow that is 8 m. The distance along the ground from the person (H) to the tree (G) is 30 m, and the distance from the tree (G) to the building (F) is 105 m. Calculate the height of the tree and the building. Round answers to the nearest tenth of a meter and show all your work.
The height of the tree and the building are 7.6 m and 28.6 m respectively.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Two triangles are similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.
Triangle BGD, CHD and AFD are similar triangles.
CH = 1.6, DH = 8, GH = 30, GF = 105
FH = GF + GH = 105 + 30 = 135
FD = FH + DH = 135 + 8 = 143; GD = 30 + 8 = 38
Hence, using similar triangles:
BG/CH = GD / DH
BG / 1.6 = 38/8
BG = 7.6 m
Also:
building/CH = DF / DH
building / 1.6 = 143/8
building = 28.6 m
The height of the tree and the building are 7.6 m and 28.6 m respectively.
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convert 5.75 hours to minutes
[tex]\boldsymbol{\sf{Therefore \to \ 5.75\not{h}*\dfrac{60 \ min}{1\not{h}} =345 \ min }}[/tex]
5.75 hours is equal to 345 minutes.
Write down the equation for the following
i,Grade 7 students received a total of 88 books from world vision.they received 63 books on Monday and g books on Tuesday
ii,Solve the equation above
Maria wants to take a survey to predict who will win the election for her town’s mayor. Which samples are most likely to be biased? Check all that apply.
The Biased samples that are most likely to be biased are as follows;
The residents of every other house on her street.
The people at the computer store.
At the mall every 100th person from the town’s phone registry.
Every 10th person who walks down the main street in her town.
According to the statement
we have given that the:
Maria wants to take a survey to predict who will win the election for her town’s mayor.
So, For this purpose
Biased sample In epidemiology, a sample of a group that does not equally represent the members of the group.
The above people are selected randomly with no specific characteristics, so it is less likely to be biased.
These people are selected according to specific characteristics; Subscribing to the golf magazine (who tends to be rich and biased in politics).
So, it is more likely to be biased.
The Biased samples that are most likely to be biased are as follows
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Answer:
A: The residents of every house on her street
B: The subscribers to a golf magazine
C: The people at the computer store at the mall
Find the dimensions of a rectangle with area 1,728 m2 whose perimeter is as small as possible
The dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.
Let the dimension of the rectangle be x and y m.
According to the given question.
The area of the rectangle is 1728 square meter.
⇒ x × y = 1728
⇒ x = 1728/y
Since, the perimeter of the rectangle is the sum of the length of its boundary.
Therefore,
Perimeter of the recatngle with dimensions x and y is given by
Perimeter of the rectangle, P = 2(x + y)
⇒ P = 2(1728/y + y)
⇒ P = 3456/y + 2y
Differentiate the above equation with respect to y
⇒ [tex]P^{'} = -\frac{3456}{y^{2} } + 2[/tex]
For the minimum(small) perimeter equate the above equation to 0.
⇒ [tex]-\frac{3456}{y^{2} } + 2 = 0[/tex]
⇒ [tex]2y^{2} =3456[/tex]
⇒ [tex]y^{2} = \frac{3456}{2}[/tex]
⇒ y^2 = 1728
⇒ y = √1728
⇒ y = 41.56 m
Therefore,
x = 1728/41.56
⇒ x = 41.57 m
Hence, the dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.
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pleasee mwa mwa mwa help me
Answer: About (-2.414, 0) and (0.414, 0)
Step-by-step explanation:
Let us graph the equation given and see what the x-intercepts are. These are points where the line intercepts the x-axis. See attached.
This means our x-intercepts are at about (-2.414, 0) and (0.414, 0).
These are also equal to [tex]-1-\sqrt{2}[/tex] and [tex]-1+\sqrt{2}[/tex]
Answer:
[tex]x = \bold{0.414} \textrm{ and } x= \bold{-2.414}[/tex]
Step-by-step explanation:
See attached graph for a visual
The x-intercepts of a graph are where the graph crosses the x-axis ie where the value of y = 0 The equation of the graph is y=-x^{2}-2x+1
Setting y = 0 and solving for the resultant equation will provide the x-intercepts
[tex]0=-x^{2}-2x+1or-x^{2}-2x+1=0[/tex]
Reversing the signs gives us
[tex]x^{2}+2x-1=0[/tex]
This is a quadratic equation of the form [tex]ax^{2}+bx+c=0[/tex] with a = 1, b = 2 and c=-1
For an equation of this form the roots of the equation ie the values of x which satisfy the equation are given by
[tex]\frac{-b\pm\sqrt{{b^{2}-4ac}}}{2a}[/tex]
Substituting we get the two roots as
[tex]x=\frac{-2\pm\sqrt{{2^{2}-4(1)(-1}}}{2}=\frac{-2\pm\sqrt{{4-(-4)}}}{2}x=\frac{-2\pm\sqrt{8}}{2}8 = 4(2)\sqrt{8}=\sqrt{4}\sqrt{2} = 2\sqrt{2}[/tex]
So the two roots are
[tex]x=\frac{-2\pm2\sqrt{2}}{2}[/tex]
Dividing by 2 we get the two roots(x-intercepts) as
[tex]x=-1\pm\sqrt{2}\\\\x_{1}=-1+\sqrt{2} =-1+1.414=\bold{0.414}[/tex]
[tex]x_{2}=-1-\sqrt{2}=-1-1.414=\boldsymbol{-2.414}[/tex]
Translate the sentence into an equation.
15 less than Taryn's age is 20
use the variable a to represent Taryn's age.
answer choices:
a. 20-a = 15
b. 15-a = 20
c. a-15= 20
d. 20-15 = a
Answer: c. a-15= 20
Step-by-step explanation:
The answer is c because a represents her age and 15 less than that would mean that you have to subtract 15 from her age which is represented by a, and then 15 less than a would equal 20, so a-15=20
in a convex hexa
gon the sum of interior is how many times the sum of exterior angles
Answer:
Twice
Step-by-step explanation:
In a convex hexagon the sum of all interior angle is equal to twice of exterior angles.
PLEASE MARK ME AS BRAINLIST
PLEASE HELP IM STUCK
Answer:
y= 2x + 10
Step-by-step explanation:
The variable depends on the $2 so, the green box should be 2
Help help help help help help
Answer:
∠JKL = 98
Step-by-step explanation:
the two small vertical lines on JK & KL means that
JK & KL are the same length which means that
same length means same degrees
∠KJL & ∠KLJ are the same degrees
∠KJL & ∠KLJ are both 41 degrees
triangles are 180
41 + 41 = 82
180 - 82 = 98
How to find ‘x’ if 8.4 % of ‘x’ is 420.
I will mark the first answerer as brainliest
This is reverse percentage
8.4% = 420
÷8.4 both side
1% is now 50
1% =50
x100
100% is 5000
Check:
8.4/100 = 0.084 our decimal multiplier
5000 x 0.084 = 420
Thus, x is 5000
Hope this helps!
