rewrite! Write an new and equivalent equation that is easier to solve
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
Given - an equation in it's general formTo do - convert the given equation into a form that is easy to solveGiven equation -
[tex]\bold{(x + 2) {}^{2} + 4(x + 2) - 5 = 0} \\ [/tex]
solve the parenthesis so as to obtain simpler terms
[tex]\bold{\implies \: ( x {}^{2} + 4x + 4 ) + 4x + 8 - 5 = 0}\\ [/tex]
solve the like terms and you'll obtain the required equation !
[tex]\bold{\implies \: x {}^{2} + 8x - 7 = 0}[/tex]
hope helpful ~
[tex]{\large{\red{\mapsto{\maltese{\underline{\green{\boxed{\blue{\underbrace{\overbrace{\pink{\pmb{\bf{Answer:}}}}}}}}}}}}}}[/tex]
x = -7, -1
Step-by-step explanation:
[tex] \sf {(x + 2)}^{2} + 4(x + 2) - 5 = 0[/tex]
let (x + 2) = y
So equation will be
[tex] \sf {y}^{2} + 4y - 5 = 0[/tex]
Further it becomes quadratic equation
we will solve it by breaking middle term method
[tex] \sf \implies {y}^{2} + 5y - y - 5 = 0 \\ \\ \sf \implies y(y + 5) - 1(y + 5) = 0 \\ \\ \sf \implies (y + 5)(y - 1) = 0[/tex]
Now put the value of y
[tex] \sf \implies (x + 2 + 5)(x + 2 - 1) = 0 \\ \\ \sf \implies (x + 7)(x + 1) = 0[/tex]
(x + 7) =0⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(x + 1) = 0
x = -7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ x = -1
What is plagiarism?
A. Using reliable sources in your paper
B. Letting the reader know where you got your information from
C. Providing constructive criticism.
D. Using another person's ideas or writing without citing them.
Answer: D. Using another person's ideas or writing without citing them.
Step-by-step explanation: Plagiarism is the use of someones work and claiming it as their own without giving them credit
help pls!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
y = -3x - 1
hope this helps!
. Carl bought one book for $3.95 and a second book for $4.95. What is his total cost? $9.90 $9.00 $8.90 $7.90
The Cost of Carl's first item is 3.95. The Cost of his second item is 4.95. To find the total amount we need to add these two numbers together.
3 plus 4 is 7
95 cents plus 95 cents is 1.90
7+1.90 is 8.90
The total cost is $8.90
Hope this helps!
Determine the equation of the line that has an x-intercept of 6 and passes through the point (6,4)
Draw a line representing “rise” and line representing the “run of the line state the slope of the line .state the slope of the line in the simplest form.
Answer:
slope 4/5
Step-by-step explanation:
The attachment shows the rise in green (4 grid squares), and the run in red (5 grid squares). The slope is the ratio rise/run.
__
The slope is rise/run = 4/5.
same here, i rlly need help
Answer:
Area = 50.125 cm^2
Perimeter = 26 + 15 = 41 cm
Step-by-step explanation:
Area Rectangle = 6 * 7 = 42 cm^2
Area Triangle = 1/2 * (9.5 - 7) * 6.5
Area Triangle = 1/2 * (2.5) * 6.5 = 8.125 cm^2
Total Area = 42 + 8.125 = 50.125 cm^2
Perimeter Rectangle = 6 + 7 + 6 + 7 = 26 cm
Perimeter or Triangle = 2.5 + 6.5 + 6 = 15 cm
Total Perimeter = 26 + 15 = 41 cm
7. AB = AC. AMON is a ____
Justify your answer.
Answer: Cyclic quadrilateral
Step-by-step explanation:
Since angles OMB and ONC are right angles, it follows that AMO and ANO are also right angles. Thus, there is a pair of opposite angles that are supplementary, and thus AMON is a cyclic quadrilateral.
the diagram represents a rectangular garden of length 14 m and width 10 m
The flower bed is a triangle and the vegetable patch is a trapezium
the rest of the garden is lawn
Answer:
The area of the lawn is 68 [tex]m^2[/tex].
Step-by-step explanation:
Area of lawn = Area of garden - (Area of triangle + Area of trapezium)
Area of garden = length x width
= 14 x 10
= 140 [tex]m^2[/tex]
Area of triangle = [tex]\frac{1}{2}[/tex] x base x height
= [tex]\frac{1}{2}[/tex] x 3 x 8
= 12 [tex]m^2[/tex]
Area of trapezium = [tex]\frac{1}{2}[/tex] (a + b) h
= [tex]\frac{1}{2}[/tex](5 + 7) 10
= 60 [tex]m^2[/tex]
So that;
Area of lawn = 140 - (12 + 60)
= 140 - 72
= 68
The area of the lawn is 68 [tex]m^2[/tex].
Use the drop-down menus to complete each statement about the functions f and g.
Note: Exponential functions are of the form f(x) = abx.
The function f is (linear, exponential, neither)
.
Consecutive (differences, quotients)
are (constant, nonconstant )
.
The function g is (options are same for the rest)
.
Consecutive
are
.
The function f(x) is the linear and the function g(x) is the exponential. Then the equations are f(x) = 6x and g(x) = 3(2)ˣ.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The functions f(x) and g(x).
The table is shown below.
Let the function f(x) be the linear function and the function g(x) be the exponential. Then we have
Then the function f(x) will be
f(x) = mx + c
Then we have
12 = 2m + c
6 = m + c
Then we have
m = 6 and c = 0
Then the equation will be
f(x) = 6x
Then the function g(x) will be
g(x) = abˣ
Then we have
48 = ab⁴
24 = ab³
We have
a = 3 and b = 2
Then the function g(x) will be
g(x) = 3(2)ˣ
More about the function link is given below.
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solve for BC without working out the size of angle A
Answer:
BC = 6 units
Given following:
AC = 4 unitstan(A) = 3/2Solve for BC:
Formula:
[tex]\rightarrow \sf tan(A) =\dfrac{opposite}{adjacent}[/tex]
insert values and make them proportional
[tex]\rightarrow \sf tan(A) =\dfrac{BC}{AC} = \dfrac{3}{2} = \dfrac{6}{4}[/tex]
So, BC is 6 units.
Answer:
1) BC = 6
2) B = 33.7° (nearest tenth)
3) [tex]\sf AB=2\sqrt{13}[/tex]
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Question 1Given:
Angle = ASide opposite angle = BCSide adjacent angle = AC = 4Substituting the values into the tan ratio:
[tex]\implies \sf \tan A=\dfrac{BC}{AC}=\dfrac{BC}{4}[/tex]
Given:
[tex]\sf \tan A=\dfrac{3}{2}[/tex]
Therefore:
[tex]\implies \tan \sf A = \tan \sf A[/tex]
[tex]\implies \sf \dfrac{BC}{4}=\dfrac{3}{2}[/tex]
[tex]\implies \sf BC=\dfrac{4 \cdot 3}{2}=6[/tex]
Question 2Given:
Angle = BSide opposite angle = AC = 4Side adjacent angle = BC = 6Substituting the values into the tan ratio and solving for B:
[tex]\implies \sf \tan B=\dfrac{AC}{BC}[/tex]
[tex]\implies \sf \tan B=\dfrac{4}{6}[/tex]
[tex]\implies \sf B=\tan ^{-1}\left(\dfrac{4}{6}\right)[/tex]
[tex]\implies \sf B=33.69006753...^{\circ}[/tex]
[tex]\implies \sf B=33.7^{\circ}\:(nearest\:tenth)[/tex]
Question 3Pythagoras’ Theorem
[tex]a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = AC = 4b = BC = 6c = ABSubstituting the values into the formula and solving for AB:
[tex]\implies \sf AC^2+BC^2=AB^2[/tex]
[tex]\implies \sf 4^2+6^2=AB^2[/tex]
[tex]\implies \sf 16+36=AB^2[/tex]
[tex]\implies \sf AB^2=52[/tex]
[tex]\implies \sf AB=\sqrt{52}[/tex]
[tex]\implies \sf AB=2\sqrt{13}[/tex]
The point P = (-15/4, y) lies on the unit circle shown below. What is the value of
y in simplest form?
Considering the equation of the circle graphed on this problem, the value of y is given by:
[tex]y = -\frac{1}{4}[/tex]
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this problem, the circle is centered at the origin, with radius 1, hence the equation is given by:
[tex]x^2 + y^2 = 1[/tex]
Hence, when [tex]x = -\frac{\sqrt{15}}{4}[/tex], the values of y are given by:
[tex]y^2 = 1 - x^2[/tex]
[tex]y^2 = 1 - \frac{15}{16}[/tex]
[tex]y^2 = \frac{1}{16}[/tex]
Looking at the graph, we want the negative value of y, hence:
[tex]y = -\sqrt{\frac{1}{16}}[/tex]
[tex]y = -\frac{1}{4}[/tex]
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Answer: its positive 1/4
Step-by-step explanation: got the question right
Find AUB and AnB for set A and B
Answer:
Option C is the correct answer
Step-by-step explanation:
A= {-4, -6, 6, 4} (Given)B = {-8, -4, -5, -6, 0} (Given)[tex]A \cup B = \{-4, -6,\: 6, \:4, -8, -5, \:0\}[/tex][tex]A\cap B= \{-4, -6\}[/tex]Given that x = 2u + v, y = u/v and z = e^(xy) find dz/du and dz/dv using the chain rule.
Answer:
[tex]\displaystyle \boxed{ \frac{dz}{du} = \frac{e^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 4u + v \Bigg] }[/tex]
[tex]\displaystyle \boxed{ \frac{dz}{dv} = \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 1 - \frac{2u + v}{v} \Bigg] }[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Multivariable Calculus
Partial Derivatives
Partial Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{dw}{dt} = \frac{\partial w}{\partial x} \frac{\partial x}{\partial t} + \frac{\partial w}{\partial y} \frac{\partial y}{\partial t} + \frac{\partial w}{\partial z} \frac{\partial z}{\partial t}[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle x = 2u + v[/tex]
[tex]\displaystyle y = \frac{u}{v}[/tex]
[tex]\displaystyle z = e^{xy}[/tex]
Step 2: Find Derivatives
[tex]\displaystyle \frac{dz}{du}[/tex]:
[Derivative] Rewrite [Partial Derivative Rule - Chain Rule]:We can find the partial derivatives by differentiating using basic differentiation rules found under "Calculus":
[tex]\displaystyle\begin{aligned}\frac{\partial z}{\partial x} & = ye^{xy} \\\frac{\partial x}{\partial u} & = 2 \\\frac{\partial z}{\partial y} & = xe^{xy} \\\frac{\partial y}{\partial u} & = \frac{1}{v} \\\end{aligned}[/tex]
Substituting in our partial derivatives and our variables x and y, we can obtain a final derivative:
[tex]\displaystyle\begin{aligned}\frac{dz}{du} & = 2ye^{xy} + \frac{xe^{xy}}{v} \\& = \frac{2ue^\big{\frac{u(2u + v)}{v}}}{v} + \frac{(2u + v)e^\big{\frac{u(2u + v)}{v}}}{v} \\& = \boxed{ \frac{e^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 4u + v \Bigg] }\end{aligned}[/tex]
∴ we have found the derivative of z with respect to u.
[tex]\displaystyle \frac{dz}{dv}[/tex]:
[Derivative] Rewrite [Partial Derivative Rule - Chain Rule]:We can find the partial derivatives by using the same method(s):
[tex]\displaystyle\begin{aligned}\frac{\partial z}{\partial x} & = ye^{xy} \\\frac{\partial x}{\partial v} & = 1 \\ \frac{\partial z}{\partial y} & = xe^{xy} \\\frac{\partial x}{\partial v} & = \frac{-u}{v^2} \\ \end{aligned}[/tex]
Substituting in our partial derivatives and our variables x and y, we can obtain a final derivative:
[tex]\displaystyle\begin{aligned}\frac{dz}{dv} & = ye^{xy} + \frac{-uxe^{xy}}{v^2} \\& = \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} + \frac{-u(2u + v)e^\big{\frac{u(2u + v)}{v}}}{v^2} \\& = \boxed{ \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 1 - \frac{2u + v}{v} \Bigg] }\end{aligned}[/tex]
∴ we have found the derivative of z with respect to v.
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Topic: Multivariable Calculus
Unit: Partial Derivatives and Applications
quadrilateral has angles that measure 90°, 46°, and 120°.
What is the measure of the fourth angle
Answer:
the measure of the fourth angle is 104 degrees
Step-by-step explanation:
Answer:
Fourth angle = 104º
Step-by-step explanation:
Angles in a quadrilateral add to 360º so:
90 + 46 + 120 + fourth angle = 360º
90 + 166 + fourth angle = 360º
256 + fourth angle = 360
fourth angle = 104º
. A reception hall holds 96 people. If the hall
is filled with 3/4th of the maximum
capacity at a wedding reception, how
many people are at the reception?
A. 48
B. 36
C. 24
D. 72
Answer:
D.72
Step-by-step explanation:
first you have to divide 96 and 4 than it will equal 24 than you multiple by 3 and so 24×3=72
If f(x) = 3x+2, find f(f¹(14))
Answer:
f(f¹(14)) = 134
Step-by-step explanation:
Given :
f(x) = 3x + 2Find the value of f(14) :
f(14) = 3(14) + 2f(14) = 42 + 2f(14) = 44Therefore, f(f¹(14)) = f(44).
Solving :
f(44) = 3(44) + 2f(44) = 132 + 2f(f¹(14)) = 134A marble is 2 centimeters long. A rock is 75% longer than the marble. How long is the rock?
Answer:
3.5 centimeters
Step-by-step explanation:
75% of 2 cm = .75 x 2 = 1.5 cm
2 cm + 1.5 cm = 3.5 cm
NEED HELP ASAP - Which
represents the inverse of the function f(x) = 4x?
h(x) = x + 4
• h(x) =x-4
h(x) = =3/4x
O h(x) = 1/4
Answer:
O h(x)=1/4
Step-by-step explanation:
anyone understands this?
Answer:
See below
Step-by-step explanation:
Not sure what they are looking for here....unless there is more info
[tex]\sqrt[14]{y}[/tex] = [tex]y^{1/14}[/tex] perhaps?
Oliver completed his project in no more than twice the amount of time it took Karissa to complete her project. Oliver spent 4 and one-fourth hours on his project. If k represents the amount of time that it took Karissa to complete her project, which inequality can be used to represent the situation?
4 and one-fourth less-than 2 k
4 and one-fourth less-than-or-equal-to 2 k
4 and one-fourth greater-than 2 k
4 and one-fourth greater-than-or-equal-to 2 k
Answer:
4 and one-fourth less-than or equal-to 2k
Step-by-step explanation:
4 and one-fourth is no more than 2k
i.e,4 and one-fourth can be equal or less than 2k
pls mark brainliest:)
What is the area of this rectangle?
18 m
9 m
14 sq m
16 sq m
Answer:
14
A = base × height = 2 × 7 = 14
Answer:14
Step-by-step explanation:
suppose the mean height in inches of all 9th grade students at one high school is estimated. The population standard deviation is 4 inches. The heights of 10 randomly selected students are 66, 61, 67, 61, 75, 71, 70, 61, 61, and 74
A mean is an arithmetic average of a set of observations. The height of the 9th-grade students will be 66.7±4 inches.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
Given the height of the 10 selected students is {66, 61, 67, 61, 75, 71, 70, 61, 61, and 74}, also, the standard deviation of the 9th-grade students is 4 inches. Therefore, The mean height in inches of the selected students is,
Mean = (66+61+67+61+75+71+70+61+64)/10 = 66.7inches
Therefore, the height of the 9th-grade students will be 66.7±4 inches.
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Researchers found a fertilizer treatment to have a mean plant height of 76 in. and a standard deviation of 3 in. Find the height of a plant treated with this fertilizer that has a z-score of 0.25. Round to the nearest tenth.
Answer:
milk because ur dad left the milk
Step-by-step explanation:
ur mum bc she is a pro statue
Can someone answer theese 3 questions i will give brainliest
Answer:
#3
A
#2
D
#1
B
Hope this helps
Answer:
1.) 10/16 = 5/8
2.) 14/16 = 2 7/8
3.) 6/16 = 1 3/8
Step-by-step explanation:
Just count the lines.
Tom would like to stock groceries for his shop. The wholesaler where he buys his stock sells sugar in packets of 10 per carton, flour in packets of 6 per carton and rice in packets of 5 per carton. How many cartons of each item should Tom buy so that there are equal number of packets of sugar, flour and rice.
Answer: Sugar = 3 cartons, Flour = 5 cartons, Rice = 6 cartons
Step-by-step explanation:
Sugar = 10 packets/carton
Flour = 6 packets/carton
Rice = 5 packets/carton
10, 20 30... sugar
6, 12, 18, 24, 30... flour
5, 10, 15, 20, 25, 30... rice
30/10 = 3 cartons of sugar
30/6 = 5 cartons of flour
30/5 = 6 cartons of rice
For all the number of packets to be equal.
Enter the number that belongs in the green box.
Answer:
The answer is x = 10.
Step-by-step explanation:
Two options:
1. Looking at the image it looks like a parallelogram. So, most side lengths are equal to each other or are the same.
2. We can use the Pythagorean Theorem to solve for x.
Solve the quadratic equation by using either a numeric or a graphic approach. x squared minus 16 x minus 64 = 0 a. x = -11.1 or x = -12.4 c. x = 16.3 or x = -2.9 b. x = 19.3 or x = -3.3 d. x = 1.3 or x = -3.4
Answer:
B.
Step-by-step explanation:
[tex]x^2 - 16x - 64 = 0[/tex]
[tex](x-8)^2 = 128[/tex]
[tex]x = 8 + \sqrt{128}[/tex]
or
[tex]x=8-\sqrt{128}[/tex]
so x = 19.3
or x = 3.3
The radius of the circle above is 39 mm. What is the circumference of the circle? Use 7 = 3.14.
Circumference = 2017
A. 244.92 mm
B. 9,551.88 mm
C. 122.46 mm
D. 4,775.9400000000 mm
Answer:
244.92 or A
Step-by-step explanation:
r=39, so we can then find the diameter.
39*2= 78 (the diameter)
c=(pi)(d)
c=3.14*78
c= 244.92
A submarine starts 15 meters above sea level and travels 95 meters below sea level. How far did the submarine travel? *
The height attained by the submarine in the sea will be 80 meters.
What is the height?
Height is a vertical distance travelled by any object. Here the submarine is going down in the sea from 15 meters to 95 meters below the sea.
So the height attained by the submarine will be:-
H= 95-15
H= 80 meters.
Therefore the height attained by the submarine in the sea will be 80 meters.
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