Answer:
n = 8
Step-by-step explanation:
13n-6 = 98
Solution:
13n = 98+613n = 104n = 104/13n = 8Hence the value of n is 8.
13n - 6 = 98
13n = 98 + 6
13n = 104
n = 104/13
n = 8
What is the equivalent exponential expression for the radical expression below? √3+7
Answer:
09 l
Step-by-step explanation:
p0-9
The equivalent exponential expression for the given radical expression √(3 + 7) is √10.
To convert the given radical expression √(3 + 7) into its equivalent exponential expression. This process involves using exponentiation to represent the radical form.
The given radical expression is √(3 + 7). To find its equivalent exponential expression, we need to express the radical in terms of an exponent.
Recall that a radical expression of the form √(a) is equivalent to raising 'a' to the power of 1/2. In this case, 'a' is the quantity inside the radical, which is 3 + 7. So, we can write:
√(3 + 7) = (3 + 7)^(1/2).
Next, we simplify the expression inside the parentheses:
3 + 7 = 10.
Now, the expression becomes:
(10)^(1/2).
To further simplify, we raise 10 to the power of 1/2. Recall that raising a number to the power of 1/2 is the same as finding the square root of that number. So:
(10)^(1/2) = √10.
Therefore, the equivalent exponential expression for the given radical expression √(3 + 7) is √10.
To summarize, we transformed the radical expression √(3 + 7) into its equivalent exponential expression √10 by using the rule that √(a) is equal to a^(1/2). By raising the expression inside the radical to the power of 1/2, we simplified it and found the square root of 10 as the final result.
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A box has 1 red marble, 1 blue marble, and 4 green marbles of the same shape and size. dan draws a marble randomly from the box, replaces it, and then draws another marble randomly. what is the probability of drawing two green marbles in a row? explain your answer.
[tex]|\Omega|=6^2=36\\|A|=4\cdot3=12\\\\P(A)=\dfrac{12}{36}=\dfrac{1}{3}\approx33.3\%[/tex]
Answer: 1/5
Step-by-step explanation:
There are three kinds of Marbles. (M) marbles
(G) green: 4m
(R) red: 1m
(B) blue: 1m
Dan pulled a green marble out leaving
(G) green: 3m
So, the probability of picking a green marble is 1/5
sorry if I'm wrong/correct me if I'm wrong.
PLEASE HELP I WILL MARK BRAINLEST
#1
Error at sign shift due to -Correct version
[tex]\\ \rm\Rrightarrow (x^3+2x^2-x)-(3x^3-3x^2+2x-4)[/tex]
[tex]\\ \rm\Rrightarrow x^3+2x^2-x-3x^3+3x^2-2x+4[/tex]
[tex]\\ \rm\Rrightarrow x^3+5x^2-3x+4[/tex]
#2
Not multiplied 3x with x[tex]\\ \rm\Rrightarrow (x^2-3x+2)(x+1)[/tex]
[tex]\\ \rm\Rrightarrow x(x^2-3x+2)+x^2-3x+2[/tex]
[tex]\\ \rm\Rrightarrow x^3-3x^2+2x+x^2-3x+2[/tex]
[tex]\\ \rm\Rrightarrow x^3-2x^2-x+2[/tex]
Which best describes the data set? it is nonlinear because the ""total houses built"" column does not increase at a constant additive rate. it is nonlinear because the ""months passed"" column does not increase at a constant additive rate. it is nonlinear because the increase in the ""total houses built"" compared to the increase in the ""months passed"" does not show a constant rate of change. it is linear because the increase in the ""total houses built"" compared to the increase in the ""months passed"" shows a constant rate of change.
Answer :C)It is nonlinear because the increase in the “Total Houses Built” compared to the increase in the “Months Passed” does not show a constant rate of change.
:) hope you have a great day!
[tex]\sqrt{6} /\sqrt{27}[/tex]
[tex]\mathrm{Apply\:the\:laws\:of\:exponents}:\quad \dfrac{\sqrt{a}}{\sqrt{b}}=\sqrt{\dfrac{a}{b }},\:\quad \:a\ge 0,\:b\ge 0[/tex]
[tex]\dfrac{\sqrt{6}}{\sqrt{27}}=\sqrt{\dfrac{6}{27}}[/tex]
[tex]=\sqrt{\dfrac{6}{27}}[/tex]
[tex]\mathrm{ Cancel \ \ \dfrac{6}{27} \ \ \ ; \ \ \dfrac{2}{9} }[/tex]
[tex]=\sqrt{\dfrac{2}{9}}[/tex]
[tex]\mathrm{Apply\:the\:laws\:of\:exponents}:\quad \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b }},\:\quad \:a\ge 0,\:b\ge 0[/tex]
[tex]=\sqrt{\dfrac{2}{9}}[/tex]
[tex]\sqrt{9}=3[/tex]
[tex]=\dfrac{\sqrt{2}}{3} \ \ === > \ \ \ Answer[/tex]
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
A sequence of numbers begins with 12 and progresses geometrically. Each number is the previous number divided by 2.
Which value can be used as the common ratio in an explicit formula that represents the sequence?
One-half
2
6
12
The common ratio of the given Geometric progression is one-half.
Let a be first term and r common ratio of the Geometric progression.
The Geometric sequence is the form a,ar,ar^2, ...
Given that the sequence begins with 12, i.e a = 12
and also given that the sequence are in Geometric Progression.
By dividing the preceeding number by 2, we get the successive number
Then the Geometric sequence is 12, 12×1/2, 12×1/4, 12×1/8, 12×1/16 ...
= 12, 6, 3, 3/2, 3/4, ...
Common ratio = Second term / First term
= 6/12
=1/2
Therefore, the common ratio of the given geometric progression is one-half.
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Answer:
its a
Step-by-step explanation:
¿Cuáles son las soluciones x1 y x2 de la ecuación x2 − 5x − 6 = 0?
Answer:
x1 = 4 y x2= 2
Step-by-step explanation:
escuchame
x2 - 5x -6 = 0
(4)^2 - 5(2) - 6 = 0
16 - 10 - 6 = 0
6 - 6 = 0
de nade :)
Which equation completes the system that is satisfied by the solution (1, 1)?
02x+y = 2
O4x - 2y = 2
02x - 2y = 2
Ox+y = 4
Answer: B. 4x-2y=2
Step-by-step explanation:
We will work this out one by one. Plug in the x and y values of the solution to the equations and you will see which one is true or false.
A. [tex]2(1)+y(1)=2\\2+1\neq 2[/tex] B. [tex]4(1)-2(1)=2\\4-2=2[/tex]
C. [tex]2(1)-2(1)=2\\2-2\neq 2[/tex] D. [tex]x(1)+y(1)=4\\1+1\neq 4[/tex]
With this information, we see that B is the correct answer.
I hope this helped!! Pls mark brainliest!! :))
The depreciation method that does not initially use the residual value in depreciation calculations is the.
An asset loses value over time as a result of use, damage, or obsolescence.
What is depreciation?An asset loses value over time as a result of use, damage, or obsolescence. Depreciation is the measurement for this decline.
The depreciation method that does not initially use the residual value in depreciation calculations is the depreciating balance.
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hi! The work I have is solving linear equations with fractions, i only have practice exercises so they should probably be a bit simple, shown work would be appreciated <3
Just 4 questions
1) y / 3 + 6 = -3 / 2
2) -2 / 3 r - 3 = 3
3) 2 / 3 - 2x = x
4) 7x / 2 + -5 / 2 = 9/2
I’ll add a photo of the problems in a simple format
The value of the variables are y = -45/2, r = -9, x = 2/9 and x = 2
How to solve the variables?(1) y/3 + 6 = -3/2
Multiply through by 3
y + 18 = -9/2
Subtract 18 from both sides
y = -18 - 9/2
Take LCM
y = (-18 * 2 - 9)/2
Evaluate
y = -45/2
(2) -2r/3 - 3 = 3
Multiply through by 3
-2r - 9 = 9
Add 9 to both sides
-2r = 18
Divide by 2
r = -9
(3) 2/3 - 2x = x
Multiply through by 3
2 - 6x = 3x
Add 6x to both sides
2 = 9x
Divide by 9
x = 2/9
(4) 7x/2 + -5/2 = 9/2
Multiply through by 2
7x - 5 = 9
Add 5 to both sides
7x = 14
Divide by 7
x = 2
Hence, the value of the variables are y = -45/2, r = -9, x = 2/9 and x = 2
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The least common denominator of 5/6, 2/3, and 3/5 is:
Answer:
30
Step-by-step explanation:
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Answer:
m∠5 + m∠6 =180°m∠2 + m∠3 = m∠6m∠2 + m∠3 + m∠5 = 180°Step-by-step explanation:
m∠5 + m∠6 = 180° - This is true because the exterior angle and interior angle form a linear pair, and are thus supplementary.
m∠2 + m∠3 = m∠6 - This is true by the exterior angle theorem.
m∠2 + m∠3 + m∠5 = 180° - This is true because the interior angles of a triangle add to 180 degrees.
The three right options are:
m∠5 ₊ m∠6 = 180° which represents a linear pair.
∠2 ₊ ∠3 = ∠6 showing the exterior angle property of triangle.
m∠2 m∠3 m∠5 = 180° as the sum-triangle
sum-triangleproperty.
Given,
the interior angles of the triangle are 2,3,5
the exterior angle at ∠2 is ∠1.
the exterior angle at ∠3 is ∠4.
the exterior angle at ∠5 is ∠6.
Now, take into account a triangle with external angles as ∠1 , ∠4 and ∠6.
Apply the exterior angle property of a triangle.
The sum of the opposing internal angles determines the outer angle of a triangle.
For exterior ∠1 we get
∠1 = ∠5 ₊ ∠3
Similarly, for exterior ∠4 we get
∠4 = ∠5 ₊ ∠2
Then for exterior ∠6 we get
∠6 = ∠2 ₊ ∠3
∴ through the exterior angle property we get the correct option as
m∠6 = m∠2 ₊ m∠3
Now we know the sum-triangle property that sum of the angles in triangle is equal to 180°
∴ m∠2 ₊ m∠3 ₊ m∠5 = 180°
We know the linear pair property i.e, If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.,
∴ m∠5 ₊ m∠6 = 180°
Hence we get the statements which match the diagram are:
m∠5 ₊ m∠6 = 180°
m∠2 ₊ m∠3 ₊ m∠5 = 180°
m∠6 = m∠2 ₊ m∠3
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Pls help. !!!!!!!!!!!!!!!!!! (Give steps if you can)
Answer:
[tex]144 cm^{2}[/tex]
Step-by-step explanation:
Step 1: Find the true length of each side
We know that the perimeter is 56cm and the ratio of AD:AB:DC:BC is 5:12:6:5. It is safe to assume that this ratio is the simplified version, which means that if we multiply each of these numbers by a scale factor of [tex]x[/tex], then we get the true length of each side, so we would get [tex]5x, 12x, 6x, 5x[/tex] for the sides. We also know that when we add these numbers, we get the perimeter, which is 56. So, we can create the equation [tex]5x + 12x + 6x + 5x = 56[/tex]. Then, solve the equation for x, which would be 2, and go back and multiply each number with 2 to get the following:
AD = 5*2 = 10cm, AB = 12*2 = 24cm, DC = 6*2 = 12cm, BC = 5*2 = 10cm
Step 2: Calculate the Height
Now we know the lengths of each side, lets take a look at the formula for the area of a trapezium: [tex]\frac{base_{1} + base_2}{2}*height[/tex]. So, the next step would be to calculate the height. We can draw the height by drawing a line straight down from the vertex D and another straight down from the vertex C. These lines are both the height, and will be the exact same length. We can calculate that the height is 8 because AB is 24 cm, but the length from the height at vertex D to the height at vertex C is 12 cm, so that means that the base of each triangle is 12/2 = 6 cm. Then we can use Pythagorean theorem to figure out that the height is 8cm.
Step 3: Calculate the Area
Lastly, we can calculate the area. The formula is [tex]\frac{base_{1} + base_2}{2}*height[/tex]. In this case, the numbers would be [tex]\frac{12 + 24}{2} * 8 = 144cm^{2}[/tex]
I know this is a lot, so let me know if you have any questions!
PLEASE HURRY WILL GIVE POINTS AND BRAINLYEST TO FIRST RIGHT!!!
Answer:
(0, 4) and (-1, 0)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=2x^2+6x+4\\y=-4x^2+4\end{cases}[/tex]
Solve by substitution
Substitute the first equation into the second:
[tex]\implies 2x^2+6x+4=-4x^2+4[/tex]
Add 4x² to both sides:
[tex]\implies 2x^2+6x+4+4x^2=-4x^2+4+4x^2[/tex]
[tex]\implies 6x^2+6x+4=4[/tex]
Subtract 4 from both sides:
[tex]\implies 6x^2+6x+4-4=4-4[/tex]
[tex]\implies 6x^2+6x=0[/tex]
Factor out 6x from the left side:
[tex]\implies 6x(x+1)=0[/tex]
Therefore:
[tex]\implies 6x=0 \implies x=0[/tex]
[tex]\implies x+1=0 \implies x=-1[/tex]
To find the y-coordinates of the found x-values, substitute the found values of x into one of the equations:
[tex]x=0 \implies -4(0)^2+4=4 \implies (0,4)[/tex]
[tex]x=-1\implies -4(-1)^2+4=0\implies (-1,0)[/tex]
Therefore, the solutions to the system of equations are:
(0, 4) and (-1, 0)
Answer:
Solutions:
a) x = 0, y = 4 ⇒ (0, 4)
b) x = -1, y = 0 ⇒ (-1, 0)
Step-by-step explanation:
Given system of equations:
a) y = 2x² + 6x + 4
b) y = -4x² + 4
1. Substitute the value of y in the second equation into the first equation:
⇒ -4x² + 4 = 2x² + 6x + 4
2. Solve for x:
⇒ -4x² + 4 = 2x² + 6x + 4 [subtract 4 from both sides]
⇒ -4x² + 4 - 4 = 2x² + 6x + 4 - 4
⇒ -4x² = 2x² + 6x [subtract 2x² from both sides]
⇒ -4x² - 2x² = 2x² - 2x² + 6x
⇒ -6x² = 6x [subtract 6x from both sides]
⇒ -6x² - 6x = 6x - 6x
⇒ -6x² - 6x = 0 [factor out -6x from the equation]
⇒ -6x(x + 1) = 0
Two cases:
a)
⇒ -6x = 0 [divide both sides by -6]
⇒ -6x ÷ -6 = 0 ÷ -6
⇒ x = 0
b)
⇒ x + 1 = 0 [subtract 1 from both sides]
⇒ x + 1 - 1 = 0 - 1
⇒ x = -1
3. Find the value of y by substituting the found x values into one of the given equations:
a) x = 0:
⇒ y = -4x² + 4
⇒ y = -4(0)² + 4
⇒ y = -4(0) + 4
⇒ y = = 0 + 4
⇒ y = 4
coordinate: (0, 4)
b) x = -1:
⇒ y = -4x² + 4
⇒ y = -4(-1)² + 4
⇒ y = -4(1) + 4
⇒ y = -4 + 4
⇒ y = 0
coordinate: (-1, 0)
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Think About a Plan Write an indirect proof.
Proof
Given: 41 42
Prove:
p
• What assumption should be the first step of your proof?
. In the figure, what type of angle pair do 21 and 22 form?
1) Either [tex]\ell \parallel p[/tex] or [tex]\ell[/tex] ∦ [tex]p[/tex] (only two possibilities)
2) Assume [tex]\ell \parallel p[/tex] (one of two possibilities)
3) [tex]\angle 1 \cong \angle 2[/tex] (if two parallel lines are cut by a transversal, the corresponding angles are congruent)
4) But [tex]\angle 1[/tex] is not congruent to [tex]\angle 2[/tex] (given)
5) So [tex]\ell[/tex] ∦ [tex]p[/tex] (only other possibility)
Sin (5x-28) = cos (3x - 50)
By using trigonometric identities we can solve the trigonometric equation Sin (5x-28) = cos (3x - 50) for x.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
The question is incomplete.
The complete question is:
Solve for X given that sin(5X - 28)° = cos(3X - 50)°.
We have given:
sin(5X - 28)° = cos(3X - 50)°.
[tex]\rm \sin \left(5x-28\right)=\sin \left(\dfrac{\pi }{2}-\left(3x-50\right)\right)[/tex]
[tex]\rm \left5x-28\right= \left\dfrac{\pi }{2}-\left(3x-50\right)\right[/tex]
[tex]\rm x=\dfrac{4\pi n+156+\pi }{16}[/tex] (n = 0, 1, 2, ...)
[tex]\rm x=\dfrac{\pi +4\pi n-44}{4}[/tex]
Thus, by using trigonometric identities we can solve the trigonometric equation Sin (5x-28) = cos (3x - 50) for x.
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A water sample shows 0.033 grams of some trace element for every cubic centimeter of water. Marques uses a container in the shape of a right cylinder with a diameter of 13.2 cm and a height of 19.7 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Marques collected? Round your answer to the nearest tenth.
Answer:
89.0 grams of trace element
Step-by-step explanation:
Step 1Find the volume of the sample container.
Given:
Container is a right cylinder with d = 13.2 cm and h = 19.7 cmVolume formula:
V = πr²h = πd²h/4Substitute to get:
V = π(13.2)²(19.7)/4 = 2695.9 cm³ (rounded)Step 2Find the volume of the trace element, using the given proportion:
2695.9*0.033 = 89.0 grams (rounded)It costs $20 a day to rent a car and $30 for a full tank of gas. If Stacy fills up the tank 3 times and has the car rented for 14 days, how much does she owe?
Answer:
$20 × 14 days = $280
&30 × 3 = $90
&280 + $90 = $370
Answer:
For car she owes=
$20 x 14 = $280
For tank she owes=
$30 x 3 = $90
Therfore in total she owes,
$280 + $90 = $370
A packet of low fat vegetable soup has a mass of 70.5 g. find the mass of 50 such packets
Answer:
300.25
Step-by-step explanation:
The mass of 1 packet of low fat vegetable soup is 70.5g, the mass of 50 packets is 300.25g(70.5x50).
The mass of 50 low-fat vegetable soups has a mass equal to 300.25 g.
Given : The mass of 1 packet of low-fat vegetable soup is 70.5g
To find: The mass of 50 such packets
Concept: In mathematics, a product is the result of multiplication, or an expression that identifies factors to be multiplied. For example, 30 is the product of 6 and 5
The mass of 50 such packets is 70.5x50 i.e., mass of 1 pkt* number of packets given which is given to be 70.5 and 50 respectively
= 300.25 g.
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Which of the following points is NOT visible if the viewing window of a graphing utility is set at:
Xmin : 6
Xmaz: 6
Ymin : —6
Ymaz : 6
The points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible the answers are D, E, and H.
What is graphing utility?A graphing calculator is a portable computer that can plot graphs, solve multiple equations at once, and carry out other variable-related activities.
We have points shown in the coordinate plane.
As the window of a graphing utility is set at:
X(min) : -6
X(max): 6
Y(min) : -6
Y(max) : 6
The points out of 6 will not be visible.
We can draw a square as shown in the attached picture.
The points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible.
Thus, the points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible the answers are D, E, and H.
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PLEASE HELPPPP
one gym membership charges $10 a month with a sign-up fee of $45. Another gym does not charge patrons a sign-up fee but costs $25 a month. at what month is the total cost of both memberships the same?
Answer:
3 MonthsStep-by-step explanation:
Please give me Brainliest!
If an employer reduces the working week from 40 hours to 35 hours, with no
loss of weedy pay, calculate the percentage increase in the hourly rate of pay.
Answer:
14.285714285714 %
Step-by-step explanation:
suppose the weekly payment is of x dollars
Then
Previous payment : $(x/40) per hour
New payment : $(x/35) per hour
Then
The percentage increase in the hourly rate of pay is :
[tex]=\frac{\frac{x}{35} -\frac{x}{40} }{\frac{x}{40} } \times100[/tex]
[tex]=\frac{\frac{5x}{1400} }{\frac{x}{40} } \times100[/tex]
[tex]=\frac{5x}{1400} \times \frac{40}{x} \times100[/tex]
[tex]=\frac{200}{1400} \times100[/tex]
[tex]=\frac{1}{7} \times100[/tex]
[tex]=14.285714285714[/tex]
I need help answering these questions for geometry :)
1. What happens to the measure of the interior angles as the number of sides of the polygon increases? Explain your answer.
2.What happens to the measure of the exterior angles as the number of sides of the polygon increases? Explain your answer.
4. Explain what happens to the total sum of interior angles as the number of sides in the polygon changes.
5. Explain what happens to the total sum of exterior angles as the number of sides in the polygon changes.
The answers to the question have been written below
The changes to a polygon1. If the number of sides of the polygon should increase then the measure of the interior angle would increase by 180.
2. A regular polygon has the sum of its external angles as 360. This is solved as 360/n = 0
Hence the value of the exterior would move towards 0 as its sides increases.
4. As the total sum of the of the polygon changes, it would tend towards infinity.
5. The total sum of the exterior angles as the number of sides changes would tends towards 360 degrees.
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Find the nth term of this number sequence
1, 7, 13, 19, ...
Answer:
now we have to follow up with the formula n² - n¹
which is 7-1= 6
n³-n²
which is 13-7=6
so therefore the nth term=6
On a coordinate plane, a right triangle has points A (negative 5, negative 6), B (negative 5, negative 2), C (negative 2, negative 2). Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line? a rise of 6 and a run of 8 a rise of 8 and a run of 6 a rise of 6 and a run of 5 a rise of 5 and a run of 6
The rise and run that would give us a similar right triangle on the same given line is: B. a rise of 8 and a run of 6.
What is the Rise and Run of Points on the Same Line?The rise/run of any two points on the same line are have the same slope value.
Given the coordinates:
A(-5, -6)B(-5, -2)The rise of triangle ABC = change in y = 4 units
The run of triangle ABC = change in x = 3 units
Rise/run = 4/3
Therefore, a rise of 8 and a run of 6 would give us: 8/6 = 4/3.
This will give us a triangle similar to triangle ABC.
Therefore, the answer is: B. a rise of 8 and a run of 6.
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Which formulas could you use to find the volume of a right circular
cone?
OA) V = B-h where B = I-w
OB) V=B-h where B=1r'
OC) V=B-h where B = Tr
OD) V=B-h where B=1-w
Answer:
The formula for the volume of a cone is V=1/3hπr².
please help I need so much help right now I feel like crying
Answer:
ok the first point there is (-4;-3)
the second point is(0;-6)
Answer the following
The set A satisfying the given inequality is A = (-[tex]\infty[/tex], -10].
What are some properties of an inequality relation?Following are some facts which are true for an inequality relation:
Equal numbers can be added or subtracted from both sides of an inequality without affecting the inequality sign.The Inequality sign is unchanged if both sides are multiplied or divided by a positive number, but when multiplied or divided by a negative number the inequality sign is reversed.[tex]\frac{5x-2}{8} - \frac{3x-5}{10} &\ge& x+y\\\\\Rightarrow\;\; \frac{13}{40}x + \frac{1}{4}&\ge& x+y\\\\\Rightarrow\;\;\;\;\;\; -\frac{27}{40}x &\ge & y - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\;\; -x &\ge & \frac{40}{27}\left( y-\frac{1}{4} \right).\hspace{1cm}(1)[/tex]
Since y ∈ B, -2 ≤ y ≤ 7. So,
[tex]\;\;\;\;\;\;\;\,-2 - \frac{1}{4}\; \le\; y - \frac{1}{4} \;\le\; 7 - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\; -\frac{9}{4}\; \le\; y - \frac{1}{4} \;\le\; \frac{27}{4}\\\\\Rightarrow\;\;\; -\frac{9}{4}\cdot \frac{40}{27} \;\le\; \frac{40}{27} \left( y-\frac{1}{4} \right) \;\le \;\frac{27}{4}\cdot \frac{40}{27}\\\\\Rightarrow\;\;\;\;\;\;\;\; -\frac{10}{3} \;\le\; \frac{40}{27}\left( y - \frac{1}{4} \right)\; \le\; 10.[/tex]
The set {-x | inequality (1) holds ∀ y ∈ B} is [10, [tex]\infty[/tex]) i.e.
10 ≤ -x ≤ [tex]\infty[/tex].
Multiplying -1 throughout gives
-10 ≥ x ≥ -[tex]\infty[/tex].
x, thus, lies in the range A = (-[tex]\mathbf{\infty}[/tex], -10}.
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QuestionFind the set A such that for x ∈ A
[tex]\frac{5x - 2}{8} - \frac{3x - 5}{10} \ge x + y[/tex]
∀y ∈ B = {y ∈ R | -2 ≤ y ≤ 7}.
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Question 10 of 10
Which of the following are necessary when proving that the diagonals of a
rectangle are congruent? Check all that apply.
A. Corresponding parts of similar triangles are similar.
B. Corresponding parts of congruent triangles are congruent.
C. Opposite sides are congruent.
D. Opposite sides are perpendicular.
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Answer:
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