the solution to the inequality is x < -12.5.
Solution in set notation:
{x | x < -12.5}
Solution in interval notation:
(-∞, -12.5) (read as "negative infinity to -12.5")
what is inequality ?In Algebra, inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol.
The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa.
If the relationship between two algebraic expressions is defined using the inequality symbols, then it is called literal inequalities.
Let's solve the inequality step by step.
Given inequality:
-x/5 + 2 > x/5 + 7
Step 1: Add x/5 to both sides of the inequality to eliminate the x/5 term on the right-hand side:
-x/5 + x/5 + 2 > x/5 + x/5 + 7
This simplifies to:
2 > 2x/5 + 7
Step 2: Subtract 2 from both sides of the inequality to eliminate the constant term on the left-hand side:
2 - 2 > 2x/5 + 7 - 2
This simplifies to:
0 > 2x/5 + 5
Step 3: Multiply both sides of the inequality by 5 to eliminate the fraction:
0 * 5 > 5 * (2x/5 + 5)
This simplifies to:
0 > 2x + 25
Step 4: Divide both sides of the inequality by 2 to isolate x:
0/2 > (2x + 25)/2
This simplifies to:
0 > x + 12.5
Step 5: Subtract 12.5 from both sides of the inequality to isolate x:
0 - 12.5 > x + 12.5 - 12.5
This simplifies to:
-12.5 > x
So, the solution to the inequality is x < -12.5.
Solution in set notation:
{x | x < -12.5}
Solution in interval notation:
(-∞, -12.5) (read as "negative infinity to -12.5")
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Sophie drove 189 miles in 7 hours. If she continued at the same rate, how long would
it take to travel 216 miles?
Answer:
8 hours
Step-by-step explanation:
if 189 miles= 7 hours. what about 216 miles.you cross multiply
Evan is building a fort for his pet Bearded Dragon. He uses a total of 300
pieces of tile to build the fort. The ratio of blue tiles to red tiles is 1:2. How
many blue tiles did Evan use to build the fort?*
Answer:
100
Step-by-step explanation:
blue = 1
red = 2
(blue) 100
(red) 200
Graph Linear equation y= -2x + 1/3
The graph of the function y = -2x + 1/3 is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
y = -2x + 1/3
The above function is a linear function that has been transformed as follows
Vertically stretched by a factor of -2Shifted up by 1/3 unitsNext, we plot the graph using a graphing tool by taking not of the above transformations rules
The graph of the function is added as an attachment
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Tom is going to build a fence around his garden which is a rectangle measuring by He will first put in posts which will be 4 m apart. If the posts cost $3.40 each, what will be the total cost for all the posts?
Answer:
13.6
Step-by-step explanation:
4 × 3.40 = 13.6
I hope I have helped
1. Select all equations that have two solutions.
A.x² = 16
B. 4x² = 0
C. x² = -16
D. 3x + 2 = 14
Ex² - 1 = 24
F) (x + 8) (x - 8) = 0
BOWLING The cost for Nobu to go bowling is $4 per game plus an additional flat fee of $3.50 for the rental of bowling shoes. The cost can be modeled by the function f(x)=4x+3.5, where x represents the number of games bowled. Describe the graph of g(x) as it relates to f(x) if Nobu does not rent bowling shoes.
g(x) = , 1 of 3.
Select Choice
, which is the translation of f(x) , 2 of 3.
Select Choice
units , 3 of 3.
Select Choice
The graph of g(x) = 4x, is the translation of f(x) by subtracting 3.5 units, 2 of 3.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
The cost can be modeled by the function f(x)=4x+3.5, where x represents the number of games bowled.
As per the given question, the required solution would be as:
g(x) = 4x , is the translation of f(x) by subtracting 3.5 units, 2 of 3.
The graph of g(x) would be identical to the graph of f(x), but shifted 3.5 units downward, 3 of 3.
This is because the flat fee for the rental of bowling shoes is not present in the function g(x), so the y-intercept of the graph would be at (0,-3.5) instead of (0,0) in f(x) function.
The slope and the shape of the function will remain the same.
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What is the distance from home to library?
Check the picture below.
\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~5 - 2~~)^2 + (~~7 - 1~~)^2} \implies d=\sqrt{( 3 )^2 + ( 6 )^2} \\\\\\ d=\sqrt{ 9 + 36 } \implies d=\sqrt{ 45 }\implies d\approx 6.7\)
Select the correct answer. What is this expression in simplified form? √32×5√2
the square root of 32 multiplied by 5 to square root of 2
\( \sqrt{32 \times 5 \sqrt{2} } \)
I'm not sure but I think it's the right answer.
15.0424123723
Answer:
15.04
Step-by-step explanation:
need help with this problem
Answer:
area=28cm^2
Step-by-step explanation:
4×5=20
20÷2=10 area of the bigger triangle
4×2=8
8÷2=4 area of the smaller triangle
10+10=20 for area of the the 2 bigger triangles
4+4=8 for the area of the 2 smaller triangles
area of kite= 20+8= 28
A puzzle has 1080 pieces. How many pieces are 80% of the puzzle?
Answer:
864
Step-by-step explanation:
80/100 simplified is 4/5
so you do 4/5 of 1080
which is 1080 divided by 5 that is 216
and then 216 x 4 which is 864
Identify the correct weight to the nearest 1/8 pound, then reduce the fraction if possible.
A. 2 12/16 = 2 3/4 Ib
B. 2 2/8 = 2 1/4 Ib
C. 2 14/16 = 2 7/8 Ib
D. 2 1/2 Ib
The measured weight is (2 + 3/4) lb, so the correct option is A.
How to read the measure?
First, we can see that the needle is between the 2lb and 3lb mark, so we know that we have a measure between these two values.
Now, let's count the number of small lines between the needle and the 2lb mark. There are 12 marks (the 12th is below the needle). Then the measure will be:
(2 + 12/16) lb.
Now we want to simplify the fraction. If we divide both numerator and denominator by 4, we get:
12/16 = 3/4
Then the weight is:
(2 + 3/4) lb
Then the correct option is A.
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Answer: Now, let's count the number of small lines between the needle and the 2lb mark. There are 12 marks (the 12th is below the needle). Then the measure will be:
(2 + 12/16) lb.
Now we want to simplify the fraction. If we divide both numerator and denominator by 4, we get:
12/16 = 3/4
Then the weight is:
(2 + 3/4) lb
Then the correct option is A.
Step-by-step explanation:
find the future value of each deposit if the account pays (a) simple interest (b) interest compounded annually round to the nearest cent as needed
Answer:
Given that;
The account has $900 at 6% for 3 years.
a) For simple interest
The future value will be;
\(\begin{gathered} F=P+I \\ F=P+\text{Prt} \\ F=P(1+rt) \\ P=\text{ \$900} \\ r=0.06 \\ t=3 \\ F=\text{ \$900(1+0.06(3))} \\ F=\text{ \$900(1+0.18)} \\ F=\text{ \$900(1.18)} \\ F=\text{ \$1,062} \end{gathered}\)Therefore, the future value is;
\(\text{ \$1,062}\)b) For compound interest.
The future value will be;
\(\begin{gathered} F=P(1+\frac{r}{n})^{nt} \\ P=\text{ \$900} \\ r=0.06 \\ n=1 \\ t=3 \\ F=\text{ \$900(1+}\frac{0.06}{1})^{1(3)} \\ F=900(1.06)^3 \\ F=\text{ \$1,071.91} \end{gathered}\)Therefore, the future value will be;
\(F=\text{ \$1,071.91}\)Mandy is trying to subtract 9 - 10, and she has asked you for help. How would you explain the process of solving the problem to Mandy, using an number line?
Which algebraic expression is a polynomial
World War II began in the year 1939.
Let x represent any year. Write an inequality in terms
of x and 1939 that is true only for values of x that
represent years before the start of World War II. PLS ANSWER ILL GIVE U 5 STARS
Answer:
x < 1939
Step-by-step explanation:
If we want years before 1939, then x must be less than 1939. From this we can make the inequality: x < 1939. It shows that x must be anything less than 1939.
Given: mAngleTRV = 60° mAngleTRS = (4x)° Prove: x = 30 3 lines are shown. A line with points T, R, W intersects with a line with points V, R, S at point R. A line extends from point R to point Z between angle V R W. Angle V R T is 60 degrees and angle T, R, S is (4 x) degrees. What is the missing reason in step 3?
Answer:
the answer is angle addition postulate
Step-by-step explanation:
Given the proof for x = 30, the missing reason in step 3 is: angle addition postulate
What is Angle Addition Postulate?Angle addition postulate states that if D is the interior of ∠ABC, therefore, the sum of the smaller angles equals the sum of the larger angle, which is: m∠ABD + m∠DBC = m∠ABC.
The given diagram as shown in the image attached below alongside the proof of x = 30.
T is the interior of straight angle ∠VRS.
m∠VRS = 180° (straight line angle)
Therefore, based on the angle addition postulate, m∠TRS + m∠TRV = 180°.
Thus, given the proof for x = 30, the missing reason in step 3 is: angle addition postulateLearn more about angle addition postulate on:
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Question 3 of 10
Which statement is not correct?
A. A 100° angle is an obtuse angle.
B. A 175° angle is a reflex angle.
C. The terminal side of a 225° angle is in quadrant III.
D. An 85° angle is an acute angle.
SUBMIT
From the above explanation, the option B statement is not correct.
From the given options we need to identify which statement is not correct.
What is an obtuse angle?An obtuse angle is any angle greater than 90° and less than 180°.
From option A:
100° angle is an obtuse angle, because which is greater than 90° and less than 180°.
From option B:
175° angle is a reflex angle because it is greater than 180° and less than 360°.
From option C:
Less than 90° lies in I quadrant, more than 90° and less than 180° lies in II quadrant and more than 180° and less than 270° lies in III quadrant.
From option D:
An 85° angle is an acute angle because it is greater than 0° and less than 90°.
From the above explanation, the option B statement is not correct.
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Find X and round to the nearest tenth.
The side length x of the triangle rounded to the nearest tenth is 31.3.
What is the numerical value of x?The figure in the image is a right triangle.
Angle θ = 38°Adjacent to angle θ = 40Opposite to angle θ = xTo determine the value of x, use trigonometric ratio.
Tangent = Opposite / Adjacent
tan( 38° ) = x / 40
Solve for x
x = tan( 38° ) × 40
x = 0.781285 × 40
x = 31.3
Therefore, the value of x is 31.3.
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What is the formula to find the area of a circle?
Answer:
A= \(\pi\)r²
Step-by-step explanation:
the area of a circle
4. A bus drives 1 mile west and 4 miles north. Sketch the path of the bus and find the straight line distance and angle from the bus's location to its starting point. (Hint: Use Tan¹ to find the angle whose Tangent is 4/1)
The distance of the straight line is √17 miles and the angle formed is
75.96°.
We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, A bus drives 1 mile west and 4 miles north.
Let, The distance the bus travels along the west be adjacent and the distance traveled in the north be the height.
So, By Pythagoras' theorem,
The straight line distance = √(1² + 4²).
= √(1 + 16) miles.
= √17 miles.
Now, We know tan = opposite/adjacent.
tan = 4/1.
tan⁻¹(4/1) = Ф.
Ф = 75.96°.
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how do you
Evaluate 11/6 - 2/8
Answer:
1 7/12
Step-by-step explanation:
an=26-6n find the 5th term in the sequence
5th term of the sequence is -4
To find the 5th term in the sequence, we need to substitute n = 5 into the expression given
\(a_5\) = 26- 6( 5)
\(a_5\) = 26- 30
\(a_5\) = -4
The formula given, an = 26- 6n, represents an computation sequence with a common difference of-6.
This means that each term in the sequence is attained by obtain 6 from the former term.
It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the matching value of n.
In this case, we were asked to find the 5th term, so we substituted n = 5 into the formula to get a5 = -4.
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how is 1/14x42=3 can someone? explain
Answer:
This is why \(\frac{1}{14}\) x 42 = 3
Step-by-step explanation:
\(\frac{1}{14}\) x 42 can also be written as \(\frac{1}{14}\) x \(\frac{42}{1}\)
we can reduce diagonally by 7 so \(\frac{1}{14}\) x \(\frac{42}{1}\) = \(\frac{1}{2}\) x \(\frac{6}{1}\)
now we multiply across \(\frac{1}{2}\) x \(\frac{6}{1}\) = \(\frac{6}{2}\)
6 divided by two or \(\frac{6}{2}\) = \(\frac{3}{1}\) or 3
i’m so confused ahhhhh
Answer:
91.................
A plane flying with a constant speed of 360 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30°. At what rate (in km/h) is the distance from the plane to the radar station increasing a minute later? (Round your answer to the nearest whole number.)
The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).
To solve this problem, we can use the concepts of trigonometry and related rates.
Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.
Given:
The plane is flying with a constant speed of 360 km/h.
The plane passes over the radar station at an altitude of 1 km.
The plane is climbing at an angle of 30°.
We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.
We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:
sin(30°) = 1/D.
To find dD/dt, we can differentiate both sides of this equation with respect to time:
cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.
Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:
cos(30°) * 0 = -1/D^2 * dD/dt.
We can substitute the known values:
cos(30°) = √3/2,
D = 1 km.
Therefore, we have:
√3/2 * 0 = -1/(1^2) * dD/dt.
Simplifying further:
0 = -1 * dD/dt.
This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.
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whatre the values of x and y
By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).
What are the values of two variables associated with two angles from a right triangle?
In this system we have a geometrical system formed by two right triangles with a common hypotenuse. Right triangles are triangles where one of its internal angles are right angles and the sum of the measures of the internal angles within a triangle equals 180°. Then, this geometrical system can be modelled by using the following linear equations:
(x + 20) + 90 + 30 = 180 (1)
20 + 90 + (y + 30) = 180 (2)
By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).
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Would this expression:
\((x^{2} -16)^{2}\)
be classified as a difference of squares? Or a perfect square trinomial?
Why?
The given expression is a perfect square trinomial.
How to classify the given expression?
Here we have the expression:
\((x^2 - 16)^2\)
Notice that we can rewrite it as:
\((x^2 - 4^2)^2\)
Then we can see that inside the parenthesis we have a difference of squares, but it is squared, so if we define:
\(x^2 = a\\4^2 = b\)
We will have:
\((a - b)^2 = a^2 + -2ab + b^2 = (x^2)^2 - 2*(4^2)*(x^2) + (4^2)^2\)
Which is in fact, a perfect square trinomial.
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n is an odd number.
Which statements are true?
You must get them all correct to get any marks.
A: n²-1 is odd
E: n(n-2) is odd F: (n-2)² is odd
B: n(n-1) is odd C: (n-1)² is odd
D: n² + 2 is odci
Answer:
True:
D.
E.
F
Step-by-step explanation:
First, you should know that the square of any odd number is also odd.
The easiest way to go about this is to plug in an odd number for n. Lets use 3:
Plug 3 into A:
\(3^{2} -1=9-1=8\)
Plug 3 into B:
\(3(3-1)=9-3 = 6\)
Plug 3 into C:
\((3-2)^{2} = 2^{2} = 4\)
Plug 3 into D:
\(3^{2} +2 = 9+2=11\)
Plug 3 into E:
\(3(3-2) = 9-6 = 3\)
Plug 3 into F:
\((3-2)^{2}=1^{2} =1\)
From 180 books to 150 books
What's the rest?You only said, From 180 books to 150 books sooo you gotta put the rest or nobody will answer it.
A jar of peanut butter contains 50 tablespoons of peanut butter.
How many sandwiches can you make from the jar of peanut butter, assuming you have plenty of bread and jelly?
A. 25 sandwiches
B. 9 sandwiches
C. 10 sandwiches
D. 50 sandwiches
Answer:
the correct answer is A. 25 sandwiches.
Step-by-step explanation:
Assuming you have plenty of bread and jelly, you can make 25 sandwiches from the jar of peanut butter.
Each sandwich typically requires 2 tablespoons of peanut butter, one slice of bread with peanut butter and one slice of bread with jelly.
So, if you have 50 tablespoons of peanut butter, you can make 25 sandwiches with it, because 50 / 2 = 25.
Therefore, the correct answer is A. 25 sandwiches.
Answer: 25
Step-by-step explanation:
We have 50 tablespoons of peanut butter and we know that it requires 2 tablespoons to make a single sandwich. In order to find how many sandwiches we can make with our 50 tablespoons, we would have to do 50 divided by 2.
2+2...=50