The dimensions of the deck would be increased by 1 feet.
How much should he increase each dimension?Area of a rectangle = length x width
Initial area of the deck = 3 x 8 = 24 feet²
Area of the deck when it is increased = (1 + 0.50) x 24 = 36 feet²
Length of the deck after it is increased = 3 + x
Width of the deck after it is increased = 8+ x
Area of the new deck : (3 + x) + (8 + x) = 36
24 + 3x + 8x + x² = 36
x² + 8x + 3x + 24 - 36 = 0
x² + 11x - 12 = 0
The solutions of the quadratic equation are -1 and 12
-1 + x = 0
x = 1
or
12 + x = 0
x = -12
Thus, the dimension of the deck would be increase by 1 feet.
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Solve u² = -121, where u is a real number. Simplify your answer as much as possible.
Simplifying the answer
What is Real number ?
The value of a continuous quantity that can represent a distance along a line is a real number. René Descartes first used the word "real" in this meaning in the 17th century when he made a distinction between the real and imaginary roots of polynomials.
Solve : u² = -121
putting square root on both side
√u² = √ (-121)
u = (-11)
u = 11i
Since, there is no real square root of -121
If i is the imaginary unit then i = -1 and we find that
11i is square root of -121
Hence, the simplify answer for u² = -121 is 11i
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Write an equation that represents the line.
Use exact numbers.
Answer:
y = -2x -3
Step-by-step explanation:
To write an equation we need two points that the line cuts through.
we then use the formula: Gradient = Rise/Run
the points chosen are (0,-3) and (1,-5)
Gradient = (-5--3)/(1-0)
= -2
to write the equation we need one known point, gradient and one unknown point say (x,y).
we therefore use the formula for gradient/slope
G = Rise/Run
-2 = y+3/x-0
-2x = y + 3
y = -2x -3
Answer:
y = - 2x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (1, - 5) ← 2 points on the line
m = [tex]\frac{-5-(-3)}{1-0}[/tex] = [tex]\frac{-5+3}{1}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2
the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = - 2x - 3 ← equation of line
PLOT THE POINTS FOR BRAINLIST HELPPPP
The graph of the linear equation 4x - y = 8, with two points on the line is shown in the image attached below.
How to Graph a Linear Equation?If we know the slope, m, of the linear equation, which is the rise of the line over the run of the line, and also know the y-intercept value, b, we can graph a linear equation such that the slope of the line would be the value of m, and the point where the line intercepts the y-axis would be the value of b in the linear equation that is represented as y = mx + b.
Given the linear equation, 4x - y = 8, we can rewrite this in slope-intercept form as y = mx + b:
4x - y = 8
-y = -4x + 8 [subtraction property of equality]
y = 4x - 8 [division property of equality]
The slope, m, is 4, while the graph of the linear equation must intercept the y-axis at y = -8, because the y-intercept of the linear equation is b = -8.
Thus, the graph of 4x - y = 8 is shown below.
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The range of F(x) = 7.4* is all positive real numbers.
The range of F(x) = 7.4* is all positive real numbers is true
What is Range ?
When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.
Currently, the function is
f(x) = 7 x 4^x
Suppose,
y = f(x) = 7 x 4^x.
=> y = 7 x 4^x
Hence,
lny = ln (7 x 4^x).
We obtain using the logarithm equation
Hence,
ln y = ln7 + ln 4^x.
= ln y = ln7 + x ln4 .
Hence,
y equals e^(ln7 + x ln4).
=> y = e^ln7.e^(xln4) (xln4)
Using the exponential formula, we obtain
=> y = 7xln4
Consequently, y=f(x)=7.x.ln4
To determine function f's value (x)
7.x.ln7 = 0
As a result, For all possible values of x (x€R). To date,
=> 7x ≥ 0
=> 7xln4 ≥ 0
Therefore interval notation will be (0,∞)
Notation for set builders:
{y|y>0}
The graph will be plotted as follows if all the values of x (x€R) are used:
Hence, it is true that the range of f(x)=7*4x is all positive real integers.
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Suppose you work for a packaging company and are designing a box that has a rectangular bottom with a perimeter of 36cm. The box must be 4 cm high. What dimension give the maximum value. V = l*w*h
I'll give you all 65 points that I have if you tell me how to do it because I want to understand the topic. thank you
Width of the box is the dimension which gives the gives maximum value.
Width of the box = 9 cm
Length of the box = 9 cm
Given,
The perimeter of the rectangular bottom of the box = 36 cm
The height of the box = 4 cm
We have to find the dimension which gives maximum value.
Volume = lwh
Perimeter = 2(l + w)
36 = 2l + 2w
l = (36 - 2w)/2
l = 18 - w
Now,
Volume = length × width × height
V = (18 - w) × w × 4
V = 72w - 4w²
Lets find w by using w = -b/2a
That is,
w = -72/2(-4) = -72/-8 = 9
That is,
Width of the box is 9 cm and it is the dimension which gives the maximum value.
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Write 3/10 + 7/100 as a single fraction using decimal notation pllllllllssss need it In a minute its urgent
Hello!
Here are both solutions to your equation.
Fraction Form:
[tex]\frac{37}{100}[/tex]
OR
Decimal Form:
[tex]0.37[/tex]
Hope this helps!
find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (enter your answers using interval notation. if an answer does not exist, enter dne.)
We need to take the derivative, which is:
[tex]f'(x) = 10x + 2[/tex]
and see where it is positive (increasing) and negative (decreasing). We see that [tex]f'(x) = 0 at x = -1/5, f'(x) < 0 for x < -1/5, and f'(x) > 0 for x > -1/5[/tex]. Therefore, we have
f(x) increasing: (-1/5, ∞)
f(x) decreasing: (-∞, -1/5)
Mrs. McKinnon was making t-shirts. One of the designs had the instructions to make points at the following locations and then draw lines to connect the points in order: A(-5, 5); B (-5, 1); C(2,1); and D (2, 5).
Use graph paper to plot the points.
Connect them in order: A to B, B to C, C to D, and then D back to A. What shape is created?
Answer:
It's basically a quadrilateral, it has no name for it.
Step-by-step explanation:
start off by graphing the points
the number in the front is the x axis and the number after is the y axis
Ex: (-4,3) = (X,Y)/ X is horizontal going left to right & Y is vertical going up and down.
Given the figure below, find the values of x and z.
zº
X
(15x + 35).
100°
Find Z pleasee
ANSWER: x = 3
z = 100
Congruent triangle
Please answers the following question…
The picture is attached below
Use the figure to find the measures of the numbered angles.
Applying the angle relationships, the measures of the numbered angles are:
m∠1 = 145°
m∠2 = 145°
m∠3 = 35°
m∠4 = 35°
m∠5 = 145°
m∠6 = 145°
m∠7 = 35°
How to Find the Measures of Angles Using Angle Relationships?The position of angles when a transversal intersects parallel lines determines the type of angle relationships that exist between the angles, and also their measure.
Based on angle relationships, the angle measures in the image are solved as follows:
m∠1 = 180 - 35 [linear pair angle relationship]
m∠1 = 145°
m∠2 = m∠1 [vertical angles]
m∠2 = 145°
m∠3 = 35° [vertical angles]
m∠4 = 35° [corresponding angles]
m∠5 = m∠2 [alternate interior angles]
m∠5 = 145°
m∠6 = m∠5 [vertical angles]
m∠6 = 145°
m∠7 = m∠4 [vertical angles]
m∠7 = 35°
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A political campaign manager negotiated radio & television time for a candidate’s political announcements. The budget is limited to $48,000 on the announcements. Each 60-second radio spot cost $200, whereas 30 seconds of television time costs $600. The manager wants at least 45 radio spots, but no more than 90 and at least 20 television spots. Is the following system of inequalities correct?
200 r +600 t ≤ 48000
45≤ r ≤ 90
t ≥ 20
Yes, the system of inequalities listed to the represent the wants of the campaign manager are correct
What is inequalities?This refers to the term in mathematics that uses some expressions to typify statements.
The following are the statements in inequalities
less than <greater than >less than or equal to ≤greater than or equal to ≥Considering the question here:
r = each 60-second radio spot
t = 30 seconds of television time
The budget is limited to $48,000 means less than or equal to
The manager wants at least 45 radio spots, but no more than 90
means radio spots from 45 to 90 hence 45≤ r ≤ 90
at least 20 means television spots of 20 and above hence t ≥ 20
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help need help i give 26 pointes
According to the given line, the points are L and M and the segment is LM.
Lines:
The line is defined as the one-dimensional figure, which has length but no width. It is made of a set of points which is extended in opposite directions infinitely.
Given,
Here we have the diagram.
Through the given diagram we have to identify the points and segments from it.
We know that, the points refers the is a dimensionless shape, since it represents a dot only, whereas a line is a one-dimensional shape.
Based on this definition , we have two points that L and M in the given diagram.
Next one we have to identify from the graph is segment,
Segment means the part of the line that connects two points.
So, LM is the segment of the line.
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A 10 inch-candle burns at a linear rate. It measures 9 inches two hours after it was lit. Which equation can be used to find the length of the candle, y, in inches after x hours it was lit?
1. y = 10 - 0.5x
2. y = 10 - 4.5x
3. y = 10 - 9x
4. y = 10 - 2x
Answer:
1. y = 10 - 0.5xStep-by-step explanation:
Find the burning rate of candle per hour:
(10 - 9)/2 = 1/2 = 0.5 inThe rate is the slope of the linear function and the initial length of the candle is the y-intercept:
m = - 0.5,b = 10.The equation is:
y = -0.5x + 10 ory = 10 - 0.5xCorrect choice is the first one.
Solve the equation.
3x^2 + 12 = 0
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 2i [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 3 {x}^{2} + 12 = 0[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 3{x}^{2} = - 12[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: {x}^{2} = - \frac{12}{3} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: x {}^{2} = - 4 [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 4} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ (- 1)(4)} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 1} \sdot \sqrt{4} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: x = i \sdot2[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: x = 2i[/tex]
[ i represents iota, i² = -1, (complex number) ]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
[tex]x=2i[/tex]
Step-by-step explanation:
Given equation:
[tex]3x^2+12=0[/tex]
Factor 3 from the left side of the equation:
[tex]\implies 3(x^2+4)=0[/tex]
Divide both sides of the equation by 3:
[tex]\implies\dfrac{3(x^2+4)}{3}=\dfrac{0}{3}[/tex]
[tex]\implies x^2+4=0[/tex]
Subtract 4 from both sides:
[tex]\implies x^2+4-4=0-4[/tex]
[tex]\implies x^2=-4[/tex]
Square root both sides:
[tex]\implies \sqrt{x^2}=\sqrt{-4}[/tex]
[tex]\implies x^2=\sqrt{-4}[/tex]
Rewrite -4 as 2² · -1:
[tex]\implies x=\sqrt{2^2 \cdot-1}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies x=\sqrt{2^2}\sqrt{-1}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]
[tex]\implies x=2\sqrt{-1}[/tex]
[tex]\textsf{Since $\sqrt{-1}=i$}[/tex]
[tex]\implies x=2i[/tex]
Imaginary numbers
Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter i.
An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].
Which value represents |12|? A. -12 B. -6 C. 6 D. 12
Answer: 12
Step-by-step explanation: Because the absolut value of something will always be positive.
Answer:
The value for |12| is D. 12
Given m/n find the value of x
Answer:
x = 49°
Step-by-step explanation:
x = 49°
since m and n are parallel to each other
with T an oblique vector
forming a Z shape
to make this true
PLSSS HELP I’LL GIVE BRAINIEST
IM ALSO NOT VERY GOOD AT MATH
The speed of light is approximately 1.86 x 10^5 miles per second.
The time it takes for a beam of light to travel from the Sun to Earth is found by dividing the distance between the Sun and Earth by the speed of light. Find the amount of time it takes for a beam of light from the Sun to reach Earth. Show all work and express your answer in minutes.
• Explain or show how to use the numbers in scientific notation to calculate the difference in the distance from Jupiter to the Sun and the distance from Mars to the Sun. Then find
the differences and express your answer in scientific notation.
• Explain or show how to find the number of miles light will travel in 1/2 minute.
THANK YOU IF YOU HELPP <3
Answer:
Step-by-step explanation:
Find the amount of time it takes for a beam of light from the Sun to reach Earth.
Rewrite this sentence
The brick old red depressing building was filled with students
Answer: Students filled the brick old red depressing building.
Step-by-step explanation:
Two numbers add up to $23$ and their difference is $27$. How far apart are the two numbers
Answer:
27
Step-by-step explanation:
x + y = 23
x - y = 27
(x + y) + (x - y) = 23 + 27
2x = 50
x = 25
y = - 2
How to find distance:
|25 -(-2)| = |27| = 27
Answer:-4+27
Step-by-step explanation:
The graphs of two functions are shown. Which statements accurately compare the functions in the graph? Select two options. Neither function has a maximum value. The functions share a y-intercept of –1. The functions share an x-intercept of 1. Both functions have a range of all real numbers. Both functions have a domain of all real numbers.
The correct options are that the functions share a y intercept of -1 and both functions have a range of all real numbers.
A function may be defined as the expression in which for one input variable x there is only one output variable y. The input variable is known as independent variable and output variable is known as dependent variable. Real number may be defined as the set of numbers that has integers, rational numbers, and natural numbers. Here, from the graph we can see that both the functions meet on the y-axis at a point (0, -1). Thus, both these functions share a y intercept of -1. Now, both the functions have a certain value of y for a given value of x. Hence, both functions have a range of all real numbers.
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Answer:b n d
Step-by-step explanation:
its so so so hard heplp !!
need help on this question
Answer: x = 20
Step-by-step explanation:
The angles are corresponding angles so they are equivalent to each other. To solve for x, we set them equal and then solve for x.
65 = 3x + 5
60 = 3x
x = 20
Answer:
the other person has it right- it's x =20
Rewrite as a simplified fraction.
3.8333333333333=?
Answer:
38333333333333/10000000000000
Step-by-step explanation:
An architect has designed two tunnels. Tunnel A is modeled by x2 + y2 + 30x + 56 = 0, and tunnel B is modeled by x2 – 30x + 16y – 95 = 0, where all measurements are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels.
Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work.
Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work.
Part C: Determine the maximum height of each tunnel. Is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your work.
The tunnel A will be damaged and truck can pass through tunnel B.
Given that, tunnel A is modeled by x² + y² + 30x + 56 = 0, and tunnel B is modeled by x² – 30x + 16y – 95 = 0.
What is the standard form of parabola equation?The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y²= = 4ax.
Part A: x²+y²+30x+56=0
Add 15² on both the sides of a equation
That is, x²+30x+15²+y²=-56+15²
⇒ (x+15)²+y²=169
⇒ (x+15)²+y²=13²
Divide 13² on both the sides of the equation
⇒ (x+15)²/13² + y²/13² =1
Part B:
x²-30x+16y-95=0
Now, x²-30x+16y=95
Add 15² on both the sides of a equation
That is, x²-30x+15²+16y=95+15²
⇒ (x-15)²=320-16y
⇒ (x-15)²=16(20-y)
Part C:
Maximum height:
A: 13 feet
B: 20 feet
Width = 8 feet
A: x+15=8/2=4 y=12.37<13.5
B: x-15=8/2=4 y=19>13.5
Hence, the tunnel A will be damaged and truck can pass through tunnel B.
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Answer the 2 question in the photo for EASY points ( 20 points )
Answer:
the answer is 29
Victoria is older than Tyee. Their ages are consecutive even integers. Find Victoria's
age if the product of their ages is 80.
The ages of Victoria and tyee are 72 and 74.
What are linear equations?A linear equation is an algebraic equation of the form y=mx+b that only contains a constant and a first-order (linear) component, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where y and x are the variables. Ax+By=C is the accepted form for two-variable linear equations. Finding both intercepts of an equation in this form is rather simple (x and y). If an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is said to be linear. The point-slope form, standard form, and slope-intercept form are the three primary types of linear equations.
As given
ages are consecutive even integers
Victoria > Tyee
So
Victoria's age = x
Tyee's age = x + 2
x(x + 2) = 80
= x² + 2x - 80
= x² + 8x - 10x - 80
Hence , the ages are 72 and 74.
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Suppose a state has license plates that display seven characters.
a) How many different 7 character plates are possible if only the digits 0-9 are used?
Answer:License plate numbers in certain state consists of seven characters: The first character is digit (0 through 9) The next four characters are capital letters (A through Z) and the last two characters are digits. Therefore; license plate number in this state can be any string - of the form: Digit-Letter-Letter-Letter-Letter-Digit-Digit How many license plate numbers are possible if no digit appears more than once?
Step-by-step explanation: i don't know rm
Which arrangement shows −5 1/2 , −5 , −6.4 , and −26/4 in order from least to greatest?
<3 thx
Answer:
-6.4, -5 1/2, -5, and -2 6/4.
Step-by-step explanation:
Arranging these negative values in order from least to greatest may be tricky if you are not familiar with your integer rules and operations. However, if you seem to understand, even a little, this way may be helpful to you.
All you need to know is this. positive and negative are opposites. Thus, if, for example, +2 is greater than +1 in positives, then -2 is less than -1 in negatives. So, in other words, think about it this way when you see a negative number, but you are used to positive numbers, just assume that the biggest number on the positive side is the smallest number on the negative side.
Therefore, if we were to use this method, we would result in -6.4, -5 1/2, -5, and -2 6/4. Since it would be the opposite in positives.
Find a cubic model for the set of values. (-2,-7)(-1,0)(0,1)(1,2)(2,9)
The required cubic model would be y = 1 + x³ for the given set of values.
What is the cubic model?The cubic model function takes the form:
y = a + bx + cx² + dx³,
where a, b, c, and d are real integers that represent the cubic regression model's coefficients As you can see, we simulate how the value of y changes as x changes.
x₁ = -2, y₁ = -7
x₂ = -1, y₂ = 0
x₃ = 0, y₃ = 1
x₄ = 1, y₄ = 2
x₅ = 2, y₅ = 9
Computing the values in the regression models to get the values of coefficients to which the graph has attached.
y = a + bx + cx² + dx³
Fitted coefficients:
a = 1
b = 0
c = 0
d = 1
Cubic model:
y = 1 + x³
Hence, the required cubic model would be y = 1 + x³ for the given set of values.
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