The solution interval for x is x ∈ (-1/4 , ∞)
An inequality shows the relationship of a non-equal comparison between two numbers or mathematical expressions.
Here, we are given two inequalities
x/4 > -1 and -4x - 4 < -3
Let us take the first equation
x/4 > -1
⇒ x > 4(-1)
x > -4
Now, the second equation
-4x - 4 < -3
-4x < -3 + 4
-4x < 1
Now since we are dividing both sides by a negative number, that is 4, the sign of the inequality will be reversed,
x > 1/-4
x > -1/4
Thus, we get x > -4 and x > -1/4
This means that all values of x greater than -1/4 will satisfy.
Thus, x ∈ (-1/4 , ∞)
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Find the solutions of the quadratic equation –9x2 + 49 = 0.
Question 8 options:
A)
x = 9∕7, – 9∕7
B)
x = 3∕7, –7∕3
C)
x = 7∕3, –7∕3
D)
x = 7∕9, –7∕9
The solutions to the quadratic equation, -9x² + 49 = 0, are: C. x = 7∕3, –7∕3.
How to Find the Solutions to a Quadratic Equation?Given the quadratic equation, -9x² + 49 = 0, we can factorize to find the roots (the values of x) as shown below:
-9x² + 49 = 0
-(9x² - 49) = 0
Divide both sides by -1
-(9x² - 49)/-1 = 0/-1
9x² - 49 = 0
9x² - 49 + 49 = 0 + 49
9x² = 49
Divide both sides by 9
9x²/9 = 49/9
x² = 49/9
Take the square root of both sides
√x² = √(49/9)
x = ±7/3
Therefore, the solutions to the quadratic equation, -9x² + 49 = 0, are: C. x = 7∕3, –7∕3.
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help please it's urgent
Answer:
15. x<-2 or x>1
16. -5<=x<=-1
17. -0.5<=x<0.25
18. x<=-1.2 or x>=-0.4
Step-by-step explanation:
Andrea, Dina, and Lindsay invested in a partnership in the ratio of 7:9:14, respectively.
Ten years later, their partnership was worth $1,800,000. Dina decided to move to
Europe and sold her part of the partnership to Andrea.
a. How much did Andrea pay Dina for her share of the partnership? Round to the
nearest dollar.
b. What percent of the business did Andrea own after she bought out Dina? Round to
the nearest tenth of a percent.
c. What was the new ratio of ownership once the business was owned by only Andrea
and Lindsay?
ina
The new ratio of ownership once the business was owned by only Andrea and Lindsay is 8 : 7
a. How much did Andrea pay Dina for her share of the partnership?The ratio is given as:
Andrea : Dina : Lindsay = 7 : 9 : 14
The partnership worth is given as
Worth = $1,800,000
The amount received by Dina is:
Dina = Dina Ratio/Total Ratio * Worth
So, we have
Dina = 9/(7 + 9 + 14) * 1800000
Evaluate
Dina = 540000
Hence, Andrea pays Dina $540,000 for her share of the partnership
What percent of the business did Andrea own after she bought out Dina?Initially, we have:
Andrea : Dina : Lindsay = 7 : 9 : 14
So, the new ratio is
Andrea : Lindsay = (7 + 9) : 14
Evaluate
Andrea : Lindsay = 16 : 14
As a percentage, we have
Andrea = 16/(16 + 14) * 100%
This gives
Andrea = 53.33%
Hence, Andrea owns 53.33% of the business after she bought out Dina
What was the new ratio of ownership once the business was owned by only Andrea and Lindsay?In (b), we have:
Andrea : Lindsay = 16 : 14
Simplify
Andrea : Lindsay = 8 : 7
Hence, the new ratio of ownership once the business was owned by only Andrea and Lindsay is 8 : 7
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solve the quadratic formula simpliest set for y^2-7y-9=0
ALGEBRA 1 HW!! PLEASE HELP I WILL GIVE BRAINLYEST also pls explain what the heck an explicit formula is..
Answer:y=10n+15
Step-by-step explanation:
the peremiter of a parallelogram is 56 meters The width of the parallelogram is 4 meters less than its length find the length and the width of the parallelogram
The length of the parallelogram is 16 m and the width of the parallelogram is 12 m.
We are given that the perimeter of a parallelogram is 56 m.
Let the length of the parallelogram be x meter.
So, we get that the width of the parallelogram will be = x - 4 meter.
We also know that:
Perimeter of parallelogram = 2 ( l + b )
Substituting the values in this, we get that:
56 = 2 ( x + x - 4 )
56 = 2 ( 2 x - 4 )
28 = 2 x - 4
2 x - 4 = 28
2 x = 28 + 4
2 x = 32
x = 16
Length = 16 m
Width = 16 - 4 = 12 m
Therefore, the length of the parallelogram is 16 m and the width of the parallelogram is 12 m.
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In a sample of 10,000 observations from a normal population, how many would you expect to lie beyond three standard deviations of the mean? Group of answer choices About 100 About 127 None of them About 27
Around 27 of the observations are expected to lie beyond this interval.
Given data values of 10000 observations, 0.27 percent of 10000 is 0.27∗10000100=27. 0.27 ∗ 10000 100 = 27.
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.
The numbers in between any two particular provided numbers are referred to as an interval. For instance, the interval containing 0, 5, and all values between 0 and 5 is the set of numbers x satisfying 0 x 5.
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150 is 96 percent of what number
Answer:
Step-by-step explanation:
Comment
Let the unknown number = x
You should try and figure out if x is bigger than 150 or less than 150.
The equation will tell you.
96/100 * x = 150 96/100 = .96 So you will get something larger than 150 for x
Combine
96/100 = 0.96
Equation
.96*x = 150 Divide by 0.946
.96x/.96 = 150/0.96
Answer
x = 156.25
And as predicted, the answer is larger than 150, because you were dividing by a number less than 1
4x-6*x=238
solve for x
Answer:
x=-119
Step-by-step explanation:
[tex]4x-6x=238[/tex]
[tex]-2x=238[/tex]
[tex]\frac{-2x}{-2}=\frac{238}{-2}[/tex]
[tex]x=-119[/tex]
Sam had 233 dollars to spend on 7 books. How much did each book cost ?
Answer:
0
3
3
7
2
3
3
-
0
2
3
-
2
1
2
3
-
2
1
2
Step-by-step explanation:
SOOOOOOOOOO THE ANSWER 33 with the reamder of 2
Choose the numbers that are equivalent to two and seven fifteenths.
fourteen fifteenths, 2.46 repeating where the 6 is repeating, 246.6%
fourteen fifteenths, 2.715, 271.5%
thirty-seven fifteenths, 2.46 repeating where the 6 is repeating, 246.6 repeating percent where the 6 is repeating
thirty-seven fifteenths, 2.715, 271.5%
The numbers that are equivalent to two and seven fifteenths are; thirty-seven fifteenths, 2.46 repeating where the 6 is repeating
How to simplify mixed fractions?
We want to find the numbers that are equivalent to two and seven fifteenths. This fraction is a mixed fraction and can be expressed as;
2⁷/₁₅
Converting this to an improper fraction gives us;
37/15
Now, in the first mixed fraction, we can turn the fraction into decimal like this; 2 + 7/15 = 2 + 0.46666 = 2.466666....
Thus, looking at the given options, the only correct option is;
C: thirty-seven fifteenths, 2.46 repeating where the 6 is repeating
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Evaluate and leave your answer in simplest form
(-4/3) (5/12) (9/10) step-by-step
jack graphs how far he plans ton bike over a 3-day charity ride find the slope of the line
The slope of the line for 3-day charity ride is 30.
What is referred as the slope of the straight line?The slope of a straight line indicates the steepness of its inclination. It is also known as the gradient.
The greater the slope of a line, the steeper it is.The slope of a line remains constant throughout its length, ensuring that the line is straight.A line can be thought of as the hypotenuse of such a right-angled triangle.A slope measurement is calculated by comparing its vertical and horizontal components.The formula for the slope is;
slope = m = Δy/Δx
m = (y₂ - y₁)/(x₂ - x₁)
The given coordinators of the points (taken from Jack's graph are);
(x₁, y₁) = (2, 60)
(x₂, y₂) = (3, 90)
Put the values in the formula;
m = (90 - 60)/(3 - 2)
m = 30
Therefore, the slope of the straight line for the 3-day charity ride is 30.
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One cubic foot holds7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much dose 6 cubic feet of water weigh in Tons
We can use the concept of unitary method to solve the question.The weight of 6 cubic feet of water is 0.19 Ton.
Unitary method helps us in finding the solution to seemingly complicated problems, here we have been given the amount of water that one cubic foot can hold, first we need to find out how much water 6 cubic feet can hold.
1 cubic foot hols 7.48 gallons of water
6 cubic feet holds 7.48x6 gallons of water=44.88 gallons
Next we know how much 1 gallon of water weighs in pounds,we need to find out how much 44.88 gallons of water weigh in pounds first and then convert it to tons.
1 gallon weighs 8.33 pounds
44.88 gallons weighs 8.33x44.88=373.8504 pounds
1 Ton=2000 pounds
373.8504 pounds=[tex]\frac{373.8504}{2000}[/tex]=0.1869 Ton≈0.19 Ton
Thus we can see that 6 cubic feet of water weighs 0.19 Ton, we used unitary method step by step to reach this result.
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The relationship between the 8’s in 0.088
Answer:
It's in the Hundredths place uwu
Given the recursive formula shown, what are the first 4 terms of the sequence?
f(n)=
f(1) = 3
(f(n)=f(n-1)+4 if n>1
OA) 3, 7, 11, 15
B) 4, 7, 10, 13
C) 3, 9, 11, 13
D) 3, 8, 10, 12
Answer:
Option A: 3, 7, 11, 15
Step-by-step explanation:
f(2) = f(1) + 4 = 3 + 4 = 7
f(3) = f(2) + 4 = 7 + 4 = 11
f(4) = f(3) + 4 = 11 + 4 = 15
f(5) = f(4) + 4 = 15 + 4 = 19
Is this argument inductive or deductive?
"Whenever I get off at Valencia rather than McBean, I get to campus faster. So Valencia must be
the faster route to school."
Answer:
Step-by-step explanation:
Indutivo
HELP ME pls. It’s hard im not gonna lie to you all
Answer:
greatest -( 9/36, -21/28, -7 )- smallest
Answer:
9/36
-7
-21/28
Step-by-step explanation:
You actually had them in the correct order
Simplify the expression. (2+1)×42÷2
Answer:
63
Step-by-step explanation:
Simplifying the expression,
→ (2+1) × 42 ÷ 2
→ 3 × 42 ÷ 2
→ 126 ÷ 2 = 63
Hence, the answer is 63.
what number is 5 the square root of
Answer: 25
Step-by-step explanation:
We know this because 5 × 5 = 25
or 5² = 25
and also √25 = 5
Simplify.
√45z +√/20z
Assume that the variable represents a positive real number.
Answer:
=5√5z
Step-by-step explanation:
√45z +√/20z
√3*3*5z + √2*2*5z
= 3√5z+2√5z
=3+2√5z
=5√5z
Suppose you transform a square corn field by increasing one side by 2 units and decreasing the other side by 3 units. If the area of the resulting corn field equals 24, what was the length of the original corn field?
Answer:
8 and 3 are the length and the width
Step-by-step explanation:
3
Can the cube of an integer be a negative number? Explain.
Answer: yes only if the number is negative itself.
Step-by-step explanation: [tex]-3^{3}[/tex] = -27
explanation: -3 x -3 x -3 = 9 x -3 = -27
You want to put a 2 inch thick layer of topsoil for a new 25 ft by 34 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
the answer is d just did it
the area of a sector is 5.024cm2 and the angle is 36°. what's the radius
Answer:
mark me brainlest
Step-by-step explanation:
The area of sector is = pi* r^2*β\360 …. . . .(1
Where
Pi=3.14
r = radius
β= angle=36
So. Put value in equation 1
5.024=3.14 * r^2*36/360
5.024*360/(3.14*36)= r^2
16=r^2
r=4
Please solve this. it is due TODAY. no explain needed.
Pls help show work pamdas
Answer:
Answer is -4
Step-by-step explanation:
To solve this, you want to substitute the values of x and y. So, 2(-3)^2-5(-3)(-2)-(-2)^3 which will give you -4.
True or False:
______1. The number of decimal numbers in the product is based on the number of decimal numbers of the factors.
______2. In multiplying with 0.001, move the decimal point to the right 3 times.
______3. Multiplying decimal is almost the same as multiplying whole numbers.
______4. In 3.41 x 1,000, the product is 3,410.
______5. The product of 16.23 and 17.4 is 282.402.
Answer:
Step-by-step explanation:
Q1: What is the inverse of the statement?
If you have read many books, then you have learned many words.
A) If you have learned many words, then you have read many books.
B) If you have read many books, then you have learned many words.
C) If you haven't learned many words, then you haven't read many books.
D) If you haven't read many books, then you haven't learned many words.
Q2: The given figure is a rectangular prism.
Which edges are parallel to QP¯¯¯¯¯ ?
Select all answers that are correct.
A) TR¯¯¯¯¯ (Maybe this?)
segment T R
B) PH¯¯¯¯¯¯
segment P H
C) QT¯¯¯¯¯
segment Q T
D) JA¯¯¯¯¯ (And this?)
segment J A
Answer: The answer for #2 is JA and TR I took the test:)
Step-by-step explanation:
Q1 option D is the correct answer: The inverse of the statement, If you have read many books, then you have learned many words, is If you haven't read many books, then you haven't learned many words.
Q2 Edges parallel to QP are
option Aoption DWhat is inverse of a statement?The inverse of a statement refers to a statement that has opposite to the original statement to which the inverse is required. For example:
the statement: John is coming
inverse of the statement: John is not coming
How to get parallel edgesThe edge refers to a side of the prism while parallel refers to a property of line that implies that the edges are equally spaced apart and will never intersect.
The diagram for Q2 is attached
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5. Tad needs to measure where the free-
throw line should be in front of his
basketball goal. He knows his feet are
1 1/8 feet long and the free-throw line
should be 15 feet from the backboard.
How many toe-to-toe steps does Tad
need to take to mark off 15 feet?
10.i
A basketball court has symmetry; one half of the court is a mirror image of the other. The entire basketball court ( is 94 feet by 50 feet. On each half-court, painted lines show the free throw lane and circle, as well as the three-point arc, whose distance from the basket varies based on the level of hoops being played.
The borders of the court have their own commonsense names:
Along the length of the court, the borders are the sidelines.
Along the ends, the borders are the endlines, or baselines.
Separating both halves of the court is a midcourt line.
In the very center of the midcourt line is the center circle (12 feet in diameter), where the center toss takes place to begin the game.
The free throw lane is the hub of the action in each half-court. This rectangle is 12 feet wide — 16 feet at the men's pro level. Its length, as measured from the basket to the free throw line, is 15 feet at all levels. An offensive player may not stand inside the lane for more than three seconds unless he or one of his teammates is shooting the ball. After a shot is taken, the count starts over again. A defensive player may remain inside the lane for as long as he desires.
A player fouled by another player sometimes receives free throws, also known as foul shots. She takes these shots (they aren't really "throws") from the free throw line at the end of the lane — 15 feet from the basket. The shots are "free" because a defender does not guard the shooter .The remaining players line up alongside the free throw lane (or behind the shooter) and cannot interfere with the shot. They line up in order, on either side of the lane, of defense-offense-defense-offense. (Up to four players may stand on one side of the lane.) If a player opts not to take a spot (say, for example, the second defensive spot), then a player from the opposing team is permitted to step into that spot. The fans behind the basket usually scream, jump up and down, and wave their hands to try to distract an opposing team's shooter during free throws.
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