graph the following system of inequalities. y ≤ 1 3 x − 2 x < 4
By using an online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.
How to graph a system of inequalities?An inequality is a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Given the following system of inequalities:
y ≤ 1/3x ⇒ y - 1/3x ≤ 0
y - 2x < 4
By using an online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.
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Complete Question:
Graph the following system of inequalities.
y ≤ 1/3x and y - 2x < 4
What is the solution to the equation? 4√x-4 =3
A. -8 B. 16 C. 85 D. no solution
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \sqrt[4]{x - 4} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: x - 4 = (3) {}^{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: x - 4 = 81[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 81 + 4[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 85[/tex]
So, the correct choice is 85
Answer:
Step-by-step explanation:
4√(x-4) = 3
√(x-4) = 3/4
Square both sides:
x - 4 = 9/16
x = 4 + 9/16
x = 4 9/16.
Which is the graph of f(x) = }(4)*2
Answer: D
Step-by-step explanation:
Where the x-intercept is 0.25.
20pts!! ANSWER ASAP!! FIRST ANSWER GETS BRAINLIEST
what is the next letter in the pattern below?
a, b, a, a, b, b, a, a, a, b, b, _,
A. c
B. b
C. d
D. a
Answer:
b
Step-by-step explanation:
I'm quite positive its b hopefully:)!
Answer:
B.b if you follow the formula and chances are very high for it to be b
What is the volume of this rectangular prism?
3/2cm
1/2
4 cm
Answer:
7.62
Step-by-step explanation:
length* width* height = 3/2*1/2*4=7.62 cm
Faith purchased a new car in 1998 for $32,900. the value of the car has been depreciating exponentially at a constant rate. if the value of the car was $19,900 in the year 2003, then what would be the predicted value of the car in the year 2007, to the nearest dollar?
The predicted value of the car in the year 2007 is 13310
Given the purchased value of new car in 1998 is $ 32,900
The value of car was $ 19,900 in the year 2003
We need to find the value of the car in the year 2007
Let the predicted value be x
The exponentially constant rate in 2003
32900*x^5 = $19900 (∵ x^5 = 5 years difference that is 1998 to 2003 )
Now In year 2007
2007 = 32900*x^9
x = 0.9043
The predicted value of the car is 0.09043
But we want the predicted value in 2007
Therefore ,
In 2007 ≈ x = 13310.02
Rounding off to the nearest dollar is $13310
Therefore the predicted value of the car in 2007 is $13310
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Evaluate
I don’t know how to type this out so I have the photo
Answer:
3.959797975
Step-by-step explanation:
1. Find the square root of 98 which is 9.899494937
2. Divide 9.899494937 by 2.5 which is 3.959797975
(sorry if it's wrong, but I think it's correct)
help me please.bnt8349rf8
Answer: No solutions
Step-by-step explanation: there would be no solutions, because these equations have the same slope and different y-intercepts, so they would end up being parallel from each other, and would never intersect or be equivalent.
Answer:
No solution.
Explanation:
Given equations:
(1) y - 4x = -3
(2) y = 4x + 7
Substitute equation 2 into 1
y - 4x = -3
4x + 7 - 4x = -3
7 = -3
As L.H.S ≠ R.H.S, There are no solution.
The lines are parallel and do not intersect each other. Their slope is same.
i dont understand this at all
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What are we solving for?}[/tex]
[tex]\mathsf{56 = w(w + 10) }[/tex]
[tex]\huge\textbf{How are we going to solve for the}\\\\\huge\textbf{equation?}[/tex]
[tex]\mathsf{56 = w(w + 10)}[/tex]
[tex]\mathsf{w(w + 10) = 56}[/tex]
[tex]\mathsf{w(w) + w(10) = 56}[/tex]
[tex]\mathsf{w(w) + 10(w) = 56}[/tex]
[tex]\mathsf{w^2 + 10w = 56}[/tex]
[tex]\huge\textbf{Subtract \boxed{\bf 56} to both sides:}[/tex]
[tex]\mathsf{w^2 + 10w - 56 = 56 - 56}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{w^2 + 10w - 56 = 0}[/tex]
[tex]\huge\textbf{Factor the left side of the equation:}[/tex]
[tex]\mathsf{(w - 4)(w + 14) = 0}[/tex]
[tex]\mathsf{(w - 4)\times(w + 14) = 0}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{w - 4 = 0\ or\ w + 14 = 0}[/tex]
[tex]\mathsf{w = 4\ or \ w = -14}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\mathsf w = 4\ or \ \mathsf w = -14}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Three times got the prize money worth $126,000. the first friend would get three times the amount of the third friend's portion. the third friend would get twice the amount of the second friend's portion. determine the amount that each friend would receive.
128000.
Let the three frithe ends x, y, z x is the first friend y is secmy ond friend
z is third friend
X+y+z=128000
x=4z
z=3y
x=4(3y)=12y put values of x and z in the first equation we got
12y+y+3y=128000
16y=128000
= 128000 - = 8000 16
Put the y value in equation 3 wee got
z=3*8000=24000
Put the z value in equation 2 we got
x=4*24000=96000
8000+24000+96000=128000.
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The steps to derive the quadratic formula are shown below:
Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3 x2 + b over a times x equals negative c over a
Step 4
Provide the next step to derive the quadratic formula.
x squared plus b over a times x minus quantity b over 2 times a all squared equals negative c over a minus quantity b over 2 times a all squared
x squared plus b over a times x plus quantity b over 2 times a all squared equals negative c over a plus quantity b over 2 times a all squared
x squared plus b over a times x minus quantity 2 times a over b all squared equals negative c over a minus quantity 2 times a over b all squared
x squared plus b over a times x plus quantity 2 times a over b all squared equals negative c over a plus quantity 2 times a over b all squared
Answer:
[tex]\huge\boxed{\sf Option \ B}[/tex]
Step-by-step explanation:
Step 3:[tex]\displaystyle x^2+\frac{bx}{a} =\frac{-c}{a}[/tex] --------------------(1)
The next step will be:to find the b² for the expression on the left.How to find b²:Take the expression
[tex]\displaystyle x^2 + \frac{bx}{a}[/tex]
We can also write it as:
[tex]\displaystyle (x)^2 + 2(x)(\frac{b}{2a} )[/tex]
According to the formula [tex]a^2+2ab+b^2[/tex], the b of this expression is [tex]\displaystyle \frac{b}{2a}[/tex]. So,
b² will be:
[tex]\displaystyle =(\frac{b}{2a} )^2\\\\=\frac{b^2}{4a^2}[/tex]
So, we will add [tex]\displaystyle \frac{b^2}{4a^2}[/tex] to both sides in Eq. (1)
For STEP 4, the equation will become:
[tex]\displaystyle x^2+\frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Answer:
Below in bold.
Step-by-step explanation:
The next step is to divide b/a by 2 then square it and add to both sides.
This creates a perfect square quadratic on left side.
So the answer is :
x squared plus b over a times x plus quantity b over 2 times a all squared equals negative c over a plus quantity b over 2 times a all squared
What is the scale factor of dilation
(The smaller triangle is the image the bigger one is the pre image)
Robinsons tapestry all measure 1.5m x 1 m. express the tapestries night to width using round numbers and ratio notation
The ratio of the tapestries' height to breadth is 3:2 when using full integers.
CalculationThe ratio of two numbers is used to indicate proportions.
A/b, for example, is the ratio of a to b.
Given the subsequent sides, it is a tapestry.
Height = 1.5 m
Width = 1 m
So, height : width= 1.5:1
or, the fraction = 1.5/1=15/10= 3/2
or, it can be said 3:2
Since entire numbers are used, the ratio of the tapestries' height to breadth is 3:2.
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I can not factor the denominators on any online calculator so I'm unsure of how to do this. Please help!
Answer: 17/y-5
Step-by-step explanation:
Identify a ray in the following figure. WILL MAKE BRAINLIEST
Answer:
The answer is A
Step-by-step explanation:
Answer:
, a ray is a line with a single endpoint (or point of origin) that extends infinitely in one direction.
Then the answer will the first
please help with these 3 questions
Answer:
1. D) Both b) and c)
2. B) Cosine Law
3. B) Find the measures of angles and sides that we can't physically measure.
Step-by-step explanation:
1. To solve non-right triangles we use Sine Law and Cosine Law.
2. If 3 sides lengths were given and you were asked to find an angle, you would use the Cosine Law.
3.Trigonometry is used in real life to find the measures of angles and sides that we can't physically measure.
If the bottom row as a result of sythetic division is 1 3 0 4 0, then the quotient is which of the following? Select one:
The quotient of the synthetic division is x^3 + 3x^2 + 4
How to determine the quotient?The bottom row of synthetic division given as:
1 3 0 4 0
The last digit represents the remainder, while the other represents the quotient.
So, we have:
Quotient = 1 3 0 4
Introduce the variables
Quotient = 1x^3 + 3x^2 + 0x + 4
Evaluate
Quotient = x^3 + 3x^2 + 4
Hence, the quotient of the synthetic division is x^3 + 3x^2 + 4
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In a right triangle, the length of the hypotenuse is 12 and the measure of one of the angles is 36. What is the length of the other leg
Answer:
Either 9.71 (adjacent to 36°) or 7.05 (opposite 36°)
Step-by-step explanation:
The question doesn't specify which leg is under question. Is it the adacent leg or the opposite leg? I'll assume adjacent.
We can use the acronym
SOHCAHTOA which is a helpful mnemonic for remembering the definitions of the trigonometric functions. For an angle other than the right angle, the following relationships are defined.
SOH: S is sine = Opposite/Hypotenuse
CAH: C is cosine = Adjacent/Hypotenuse
TOA: T is tangent = Opposite/Adjacent
For a side adjacent (A) to the 36° angle, we can use
Cosine = Adjacent/Hypotenuse
Since we know the hypotenuse (12) we can find A:
Cosine(36) = A/12
A = Cosine(36)*12
A = (0.809)*12
Adjacent = 9.71
====================
If the opposite leg is calculated, we would use
Sine= Opposite/Hypotenuse
Sine(36) = Opposite/12
O = (0.5877)*12
Opposite = 7.053
What is the equation of the parabola?
coordinate plane with a parabola facing down with vertex at 0 comma 5, the point 0 comma 3 and a horizontal line going through 0 comma 7
y = −one eighthx² + 5
y = one eighthx² + 5
y = one eighthx² − 5
y = −one eighthx² − 5
Option 2. The equation of the parabola is given as y = one eighthx² + 5
How to read the graphWe have the coordinate plane to be passing through the graph at point C on the y axis. This is used to represent the slope.
Hence the slope is 5
The equation of the line is given as y=x²+C
Hence we can see that there is a rising slope. So the answer is Option 2.
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Which of the following polynomials has a remainder of -7 when divided by x - 2?
ANSWER : -7x + 14
EXPLANATION, to reverse division multiply
i need help with this question, thxs
The item which yield the greatest level of accuracy to the true weight of rock with the least error is bricks.
RockA rock refers to a solid substance formed from the fusion of organic minerals.
Types of rockSedimentary rock: They are firmed from sediments, that is, dead plant and animals, silt etc.Metamorphic rock: They are firmed from previously existing rocks.Igneous rock: They are formed from the pressure of molten magma.Therefore, bricks is the item which yield the greatest level of accuracy to the true weight of rock with the least error.
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2. What is the domain and range of the
graph shown?
-8-64
10-
8-
B
4+
2-
4+
6+
do do t
-10
2 4 6 8 10 12
Answer:
domain: x ≥ 0range: y ≥ 0Step-by-step explanation:
The domain of a function is the set of x-values for which it is defined. The range of a function is the set of y-values the function produces.
DomainThe domain is the horizontal extent of the graph. This graph extends from x=0 toward x→∞. The domain is x ≥ 0. In interval notation, it is written [0, ∞).
RangeThe range is the vertical extent of the graph. This graph extends from y=0 toward y→∞. The range is y ≥ 0. In interval notation, it is written [0, ∞).
4. The polynomial-4.9² +40t +20 represents the distance above the ground of an object thrown straight up from an initial height of 20 meters and with an initial speed of 40 meters per second. How long does it take the object to
reach it's maximum height?
20.000 s
8.636 s
4.082 s
101 6330
The object represented by h(t) = -4.9t² + 40t + 20 would take 4.082 seconds to reach it's maximum height.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
The height (h) is represented by:
h(t) = -4.9t² + 40t + 20
The maximum height is at h'(t) = 0, hence:
h'(t) = -9,8t + 40
-9.8t + 40 = 0
t = 4.082
The object represented by h(t) = -4.9t² + 40t + 20 would take 4.082 seconds to reach it's maximum height.
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What is the expansion of the series
sum from n equals 1 to 4 of 4 to the n plus 1 power
4 + 8 + 12 + 16
4 + 16 + 64 + 256
16 + 64 + 256 + 1,024
16 + 20 + 24 + 28
The expansion of the series is 16 + 64 + 256 + 1024
How to expand the series?The series is given as:
[tex]\sum\limits^4_{n=1} 4^{n+1}[/tex]
When n = 1, we have:
[tex]4^{n+1} = 4^{1+1} = 16[/tex]
[tex]4^{n+1} = 4^{2+1} = 64[/tex]
[tex]4^{n+1} = 4^{3+1} = 256[/tex]
[tex]4^{n+1} = 4^{4+1} = 1024[/tex]
Hence, the expansion of the series is 16 + 64 + 256 + 1024
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Answer:
C). 16 + 64 + 256 + 1,024
Step-by-step explanation:
I took the test and got it right :)
Can you please solve this I need help
Answer:
7k - 7
Step-by-step explanation:
- k - (- 8k + 7) ← distribute parenthesis by - 1
= - k + 8k - 7 ← collect like terms
= 7k - 7
Aster first walks 70m in the direction of 37degree north of east then walks 82m 20 degree south of east ,and finally walks 28m inthe direction of 30 degree west of north ,find displacement and angle from initial point ?
Answer:
Step-by-step explanation:
The displacement is 90.7 meter from initial point.
According to the statement
Aster first walks 70m in the direction of 37 degree north of east
Aster walks 82m 20 degree south of east
Aster finally walks 28m in the direction of 30 degree west of north
We use
β= 37 degree +(30 degree −20 degree) = 47 degree
We can use cosine law to solve for R.
R = ((A)^2 + (B)^2 + 2ABcosβ)^1/2
R = ((70)^2 + (28)^2 + 2*70*28cos47)^1/2
R = (4900 + 784 + 3920*0.682)^1/2
R = (4900 + 784 + 2673.5)^1/2
R = (8357.5)^1/2
R = 90.7 m
So, The displacement is 90.7 meter from initial point.
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Given: ABCD is a rectangle.
Prove: ABCD has congruent diagonals.
Rectangle A B C D is shown.
Identify the steps that complete the proof.
♣ =
♦ =
♠ =
By SAS property, ABC ≅ DCB.
How to prove the deductionsIn this question we have to proof ABCD has congruent diagonal. By SAS property and reflexive property it can be proved as follows:
Given:
ABCD is a rectangle.
Prove:
Diagonal AC ≅ Diagonal BD
From the question,
As we can see that, ABCD is a rectangle, it is also a parallelogram.
Thus, ABCD is a parallelogram, opposite sides of a parallelogram are congruent.
⇒ AB ≅ DC
⇒ BC ≅ BC (Reflexive Property of Congruence)
Hence, ∠ABC and ∠DCB are right angles by the definition of rectangle.
∠ABC ≅ ∠DCB (all right angles are congruent)
Therefore, by SAS property, ABC ≅ DCB.
⇒ segment AC ≅ segment BD
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Answer:
♣ = parallelogram side theorem
♦ = SAS
♠ = CPCTC
(Correct On Edgen)
If n is a whole number, and 0.01 is between 1/n and 1/n+2, what is the value of n?
The value of n is 99
Integers are the set of numbers including all natural numbers and 0. They are part of the real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered whole numbers.
Natural numbers together with zero (0) are referred to as whole numbers. We know that natural numbers refer to the set of counting numbers starting from 1, 2, 3, 4 and so on. Simply put, integers are a set of numbers without fractions, decimals, or even negative integers. It is a collection of positive integers and zero. Or we can say that integers are the set of non-negative integers.
Integers are the set of natural numbers togethe with the number 0. In mathematics, the set of integers is given as {0, 1, 2, 3, ...}, denoted by the symbol W.
W = {0, 1, 2, 3, 4, …}
All natural numbers are integers.
All integers are real numbers.
It is given that If n a whole number, and 0.01 is between 1/n and 1/n+2, then we need to find the value of n.
1/n+2 < 0.01 < 1/n
1/n+2 < 1/100 < 1/n
n< 100 < n +2
Put n = 99, then we get
99 < 100 < 101
Hence the value of n is 99.
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If my mother has 5 boys and my father has 4 girls, what is the probability of one being a boy?
Answer:
5/9
Step-by-step explanation:
4+5=9 and there are 5 boys
A building meets the ground at a right angle. the top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground.
The bottom edge of the window is 8 inches above the ground, computed using the Pythagoras Theorem.
According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse, that is, the side opposite to the right angle is equal to the sum of the square of the legs, that is, the two other sides.
If in a right triangle, c is the hypotenuse, and a and b are the two legs, then by the Pythagoras Theorem, we can write:
a² + b² = c².
In the question, we are informed that a building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground.
We are asked to draw a diagram that represents the situation and find the height of the bottom edge of the window from the ground.
We assume the building to be DB, meeting the ground BC at a right angle. At point C, the ladder meets the ground and meets the bottom edge of the window at point A.
The diagram is attached.
Now, we get a right triangle ABC, right-angled at B.
By Pythagoras' Theorem, we know that:
AB² + BC² = AC²,
or, AB² + 6² = 10²,
or, AB² = 10² - 6² sq. inches,
or, AB² = 100 - 36 sq. inches,
or, AB = √64 inches,
or, AB = 8 inches.
Thus, the bottom edge of the window is 8 inches above the ground, computed using the Pythagoras Theorem.
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The provided question is incomplete. The complete question is:
"A building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground. Draw a diagram that represents this situation. How far up from the ground is the bottom edge of the window?"