Answer:
[tex]x=-72[/tex]
Step-by-step explanation:
The given equation is [tex]\sqrt[3]{x+8}=-4[/tex].
We cube both sides of this equation to obtain;
[tex](\sqrt[3]{x+8})^3=(-4)^3[/tex].
This implies that;
[tex](x+8)=-64[/tex]
We group similar terms to obtain;
[tex]x=-64-8[/tex]
We simplify the right hand side of the equation to obtain;
[tex]x=-72[/tex]
Therefore x=-72 is the solution of the given equation.
The equation 3 √x + 8 = -4 has no solution. The square root term, when isolated, shows a contradiction since the square root of a non-negative number multiplied by a positive constant cannot be negative.
Explanation:The solution to the equation 3 √x + 8 = -4 involves finding the value of x for which the equation holds true. Given that √4 can be both 2 and -2, we explore the possibility of squaring both sides of an equation to solve for x. However, in this case, since the square root of a number cannot be negative and the original equation involves a square root on the left side, this hints at no solution being possible because the left side (involving the square root) will always be non-negative, and cannot equal a negative number.
Nevertheless, let's attempt to formally solve the equation. Isolating the square root term by subtracting 8 from both sides results in 3 √x = -12. At this point, we encounter a contradiction: the left side represents a non-negative value (since it's 3 times the square root of x), but the right side is negative. This confirms there are no real solutions to the equation because the square root of a non-negative number (x) cannot result in a negative value when multiplied by a positive constant (3).
It costs 3 tickets to play a game at the fair. If you spent 21tickets on the game, which equation could you use to solve for the number of games, g?
A) 21g=3
B) 21·3=g
C) g/3=21
D) 3g=21
➷ The correct option would be D. 3g = 21
As it is 3 tickets per game, the total number of tickets would be 3 multiplied by the number of games
This equation could then be rearranged to find the number of games.
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Answer:
The answer is D.
Step-by-step explanation:
It costs 3 tickets to play a game at the fair.
So the number of games, g = total number of tickets / 3,
g = 21 / 3
3g = 21
The answer is D.
What is the y-intercept in the equation y=4x-3?
➷ Equations come in the form y = mx + c
'c' is the y intercept
In this equation, the y intercept is -3
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The y-intercept of the given equation y = 4x-3 is -3.
What is y-intercept?The y-coordinate of a point where a line, curve, or surface intersects the y-axis is called y-intercept.
According to the given question.
We have an equation y = 4x -3.
To find the y-intercept substitute x = 0 in the above equation y = 4x -3.
[tex]\implies y = 4x -3\\\implies y = 4(0) - 3\\\implies y = -3[/tex]
Hence, the y-intercept of the given equation y = 4x-3 is -3.
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what is long and yellow and never rings worksheet
Answer:
A banana my dude.
Step-by-step explanation:
The answer to the riddle 'what is long and yellow and never rings' is likely a banana, as this is an example of the type of playful thinking and language interpretation often encouraged in English exercises.
Explanation:
The question "what is long and yellow and never rings" might be referring to a type of riddle or a joke commonly found in English language or creative thinking exercises. Since it mentions something that is long and yellow but never rings, a possible answer could be a banana. This is because a banana is indeed long and yellow, yet it certainly cannot ring like a telephone or bell could. Such tasks are designed to engage students in out-of-the-box thinking and interpreting language in a playful manner.
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Please help me and please don't answer if you're not a 100% sure!
The answer choices are
A. 93
B. 31
C. 69
D. 300
Answer:
A
Step-by-step explanation:
We obviously can take out D and B, as roses are 31% while carnations are 19%. Since roses have a larger percentage, it obviously can't be less than carnations but 300 is beyond the logical answer. This leaves us with 69 or 93. 19% is 57, so a 12 percent rise will not equal an increase of only 12 flowers. Therefore, without even any calculations, I can confidently tell you that your answer is A.
over the weekend statton and Taylor drove to Montana to go hunting. now they're preparing to go home. Tyler needs gas for his jeep, which gets 30 miles per gallon for gas mileage. When he stops at the gas station, he already has 8 gallons of gas in his tank. he buys more gas for $1.50 per gallon
If Tyler spends $16.50 on gas, what is the total distance the boys could travel? round, if necessary, the nearest tenth.
Answer:
Step-by-step explanation:
Givens
His tank contains 8 gallons
He spends 16.50 on gas
A gallon of gas costs 1.50 dollars
Millage = 30 mpg
Find the gas added.
Total gas (in gallons) added = amount spent / cost per gallon
Total gas (in gallons) added = 16.50 / 1.50
Total gas (in gallons) added = 11 gallons.
Find the total number of gallons in his tank.
Total = what was there + What he bought.
Total = 8 + 11
Total = 19 gallons.
Find the distance he can travel
Total distance = gallons * miles / gallon
Total distance = 19 * 30
Total distance = 570 miles.
Tyler and Statton could potentially travel a total distance of 570 miles with the amount of gas they have.
Explanation:The question is asking for the total distance that the boys could travel on the bought gas. Tyler bought $16.50 worth of gas at $1.50 per gallon, which means he bought 11 gallons ($16.50/$1.50). Tyler initially had 8 gallons of gas in his tank. Therefore, he now has a total of 8 + 11 = 19 gallons of gas. His Jeep gets 30 miles for every gallon of gas. Therefore, the total distance they can travel is 19 gallons * 30 miles/gallon = 570 miles.
So, "Tyler and Statton could potentially travel 570 miles with the gas in the tank".
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a teacher read part of a book to class. The graph shows the number of pages read by the teacher over the next several days. Find and interpret the rate of change and the initial value.
The rate of change on a graph represents how fast or slow the changes are happening, while the initial value is the starting point. To find these on a graph, you determine the slope of the line for the rate of change, and look at the intercept on the y-axis for the initial value. These values give us insights into the reading pace and starting point of the teacher.
Explanation:The rate of change in a graph represents the slope of the line. It tells us how the quantity being measured changes over time. If the graph is a straight line, the rate of change is constant, but if the line is curved, the rate of change varies.
To find the rate of change, you need to select two points on the graph and find the difference in the page numbers divided by the difference in the corresponding time points. That is (pages end - pages start) / (time end - time start).
The initial value is the point where the teacher started reading the book. This point is seen as the intercept on the y-axis of the graph.
The interpretation of these values would be that the rate of change tells us how quickly the teacher is reading the book, and the initial value tells us at what page number the teacher started reading.
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Initial value: The teacher initially read 150 pages. Rate of change: The teacher read 100 pages per day. The graph shows that the teacher is reading at a consistent pace and is making good progress on the book.
The initial value of the graph is the y-intercept, which is 100 pages. This means that the teacher had already read 100 pages before the graph starts.
The rate of change of the graph is the slope, which is calculated as (change in y) / (change in x). In this case, the slope is (750 - 100) / (5 - 1) = 130 pages/day.
This means that the teacher is reading 130 pages per day.
Interpretation:
The teacher is reading at a rate of 130 pages per day. This means that each day, the teacher is reading 130 more pages than the previous day.
The initial value of 100 pages means that the teacher had already read a significant portion of the book before the graph starts. It is possible that the teacher was reading ahead, or that the teacher was reading a chapter book to the class and had already finished the first chapter.
Overall, the graph shows that the teacher is reading at a consistent pace and is making good progress on the book.
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An 8-in wide photo has been reduced to a 5-inch wide by 7-inch tall photo. how tall was the original?
Answer:
Step-by-step explanation:
jajajajajajajajajajajajajaja
11.2
Work out the base of a square with area, A = 4cm2.
Answer:
each side of the square is 2cm
To find the base of a square with an area of 4 cm², we take the square root of the area. The base of the square is 2 cm because the square root of 4 is 2.
To work out the base of a square with an area of 4 cm², we note that a square's area is calculated by multiplying one of its sides by itself, which is represented as side length² or a². Given that a square's area is 4 cm², we set up the equation a² = 4 cm². Solving for a, we take the square root of both sides of the equation. The side length a is thus 2 cm, since the square root of 4 is 2. Therefore, the base of the square is 2 cm.
They are the same because the central angle measure is the same. The arc lengths are proportional: . The arc lengths are proportional: . The arc lengths are proportional:
Is this an answer? I don’t think this is a question buddy
confused someone help
Answer:
y = -5x - 21
Step-by-step explanation:
Given in the question,
equation of a parallel line
y = -5x + 6
point through which it passes
(-4,-1)
Step1
Find the gradient of the equation given, as it is parallel so it will have same gradient
equation of straight line
y = mx + c
where m is gradient
c is y intercept
y = -5x + 6
m =-5
Step2
Find y-intercept
-1 = -5(-4) + c
-1 = 20 + c
c = -20 - 1
c = -21
Step3
form the equation
y = -5x - 21
Answer:
[tex]y=-5x-21[/tex]
Step-by-step explanation:
The given line has equation;
[tex]y=-5x+6[/tex]
This line is in the form [tex]y=mx+c[/tex], where [tex]m=-5[/tex]
[tex](x_1,y_1)=(-4,-1)[/tex]
The required equation can be found using the formula;
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the given point and slope to get,
[tex]y+1=-5(x+4)[/tex]
Expand
[tex]y=-5x-20-1[/tex]
[tex]y=-5x-21[/tex]
Find the area of A triangle with a base length of six units and a height of seven units
Answer:
A = 21
Step-by-step explanation:
Hello
The triangle area is= (base*height)/2, so
A = (6*7)/2
A = 42/2
A = 21
Remember that a trinagle is the area of half square =D
Best regards
Jerry is driving at a steady speed on an inter-state highway. 2.5 hours after he starts, he notes that he has driven 150 miles. After 5.5 hours, he notes that he has covered 330 miles.
Jerry is driving at a steady speed on an inter-state highway. 2.5 hours after he starts, he notes that he has driven 150 miles. After 5.5 hours, he notes that he has covered 330 miles.
Which graph shows how his distance covered varies with time?
A)B)C)D)
Answer:
graph a
Step-by-step explanation:
you have to look at the numbers carefully and that was the only graph that showed everything
Answer:
Step-by-step explanation:
Jerry is driving at a steady speed on an highway.
After 2.5 hours he has driven = 150 miles.
speed = [tex]\frac{150}{2.5}[/tex] = 60 miles/hour
then after 5.5 hours he has covered 330 miles.
speed = [tex]\frac{330}{5.5}[/tex] = 60 miles/hour
Total time he has driven = 2.5 + 5.5 = 8 hours
total distance he covered = 150 + 330 = 480 miles.
Therefore, after 2.5 hours he covered 150 miles and after 8 hours he covered 480 miles with an steady speed of 60 miles/hour.
Graph A shows his constant speed and his distance covered varies with time.
Which set of three numbers could be the side lengths of a triangle
Answer:
C
Step-by-step explanation:
if you add 2 sides of a triangle the other must be smaller and if you subtract 2 sides the other must be greater
Answer with explanation:
For, set of three numbers to be sides of triangle, the sum of two should be greater than third.
→1.
3, 3,8
3 +3 is not greater than 8.So, it can't be sides of triangle.
→2.
5,5,14
5+5 is not greater than 14.So, it can't be sides of triangle.
→3.
3,3,2
3+3>2
3+2>3
Sum of two sides is greater than third, so it can be sides of triangle.
→4.
5,5,10
5+5 is not greater than 10.So, it can't be sides of triangle.
Option: C→3,3,2
Which statement must be true about the diagram?
Point K is a midpoint of .
mJKN = mJKM
Ray KM is an angle bisector of NKL.
JK = KL
Answer:
Find out the true statement of the diagram.
To proof
The statement true about the diagram is
Ray KM is an angle bisector of ∠NKL
REASON
KM ia an angle bisector of ∠NKL.
angle bisector is a line which divide the an angle in two equal parts.
As shown in the diagram
KM divided the angle ∠ NKL
and also in the diagram
∠LKM =61°
∠MKN = 61°
that means KM divided ∠NKL in two equal angle
thus
Ray KM is an angle bisector of ∠NKL
Hence proved
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Step-by-step explanation:
Answer:
Ray KM is an angle bisector of NKL.
Step-by-step explanation:
edge 2022
Simplify the expression. (X^3)^-5
➷ When exponents are separated with parenthesis, multiply them together:
3 x -5 = -15
The simplified expression would be X^-15
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Answer: x^15
have a great day
PLEASE HELP ME!!!!! THIS IS DUE IN LIKE 10 MINS!!! PLEASE DO IT QUICKLY!!! I WILL BE MARKING BRAINLIEST!!
(The answers you can chose from are in the screen shot)
All sides are equall
Answer:
side a is less then a sum of the other two
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. If you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side.
how do i factor 8g^2-10g-12
Answer:
(4g+3)(g-2)
Step-by-step explanation:
well they all have a common factor of 2
so divide all of it by two 2[(4g^2-5g-6)]
then factory that to get (4g+3)(g-2)
Hopefully this helps you :)
Wes and Tom are buying rare coins for $9,500 and investing money in the ratio of 3 to 2. How much will each man invest?
Answer:
one spent $3,800 and the other spent $5,700
Step-by-step explanation:
first add the 3 and 2 so you get 5 then divide 9,500 into 5 which is 1900 then multiply that by 2 which is 3800 now we know one man spent $3800 then we do the same thing with 3 so we take 1900 and multiply it by three which is $5700
your answer is that one man spent $3,800 and the other spent $5,700
The equation h=-16t^2 , HELP! ID APPRECIATE IT!
Answer:
37.52 feet
Step-by-step explanation:
Given in the question the equation
h = -16t² + 47t + 3
where h is height in feet
t is time in minutes
a = -16
b = 47
c = 3
To find the maximum height of the football
If a, the coefficient of the x² term, is positive, then the parabola opens upward. If a is negative, then the parabola opens downward. In this case it is -16 which is negative so it open downward.The value of -b/2a tells you the x value of the vertex of the curve at which it is maximumPlug this value in the equation to find h, maximum height.t = -b / 2a
= -47 / 2(-16)
= 1.47 sec
h = -16(1.47)² + 47(1.47) + 3
= 37.52 feet
Tomato paste is sold in a cylindrical can. The can has a radius of 1.5 inches and a height of 4.8 inches. What is the volume of the can?
Answer:
33.912 in
Step-by-step explanation:
find the area of the circle first by: multiplying 1.5squared X 3.14= 7.065
the multiply it by the height (4.8) = 33.912
The volume of the cylindrical can is 33.9292 cubic inches.
What is volume of a cylinder ?The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. The volume is given by the formula -
V = π * [tex]r^{2}[/tex] * h
where V = volume of cylinder, r = radius and h = vertical height
How to calculate the volume of the given cylinder ?It is said that the cylindrical can has a radius of 1.5 inches and a height of 4.8 inches.
Thus we have r = 1.5 inches and h = 4.8 inches .
⇒ Volume (V) = π * 1.5 * 1.5 * 4.8 cubic inches
∴ V = 33.9292 cubic inches .
Therefore, the volume of the cylindrical can is 33.9292 cubic inches.
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What is the value of z?
Answer options: 140, 25, 35, 70
Answer:
I think its 70
Step-by-step explanatio
Hope this helps!
Answer:
A. 140
Step-by-step explanation:
We have been given an image of a circle. We are asked to find the value of z.
Upon looking at our given circle we can see that z is the intercepted arc to the inscribed angle that measures 70 degrees.
We know that measure of intercepted arc of a circle in two times the measure of inscribed angle.
Using inscribed angle theorem we can set an equation as:
[tex]z^{\circ}=2\times 70^{\circ}[/tex]
[tex]z^{\circ}=140^{\circ}[/tex]
Therefore, the value of z is 140 and option A is the correct choice.
Tony rode his bicycle 3 7/10 miles to school. What is this distance written as a decimal?
Answer:
The distance written as a decimal is 3.7
To write 3 7/10 miles as a decimal, multiply the whole number by the denominator and add the numerator, then write the result over the denominator. Simplify the fraction if possible.
Explanation:To write the distance in decimal form, we need to convert the mixed number to a decimal. The given distance is 3 7/10 miles. To do this, we multiply the whole number, 3, by the denominator, 10, and add the numerator, 7. So, 3 multiplied by 10 plus 7 equals 37. Then, we write 37 over the denominator 10, giving us 37/10. Finally, we can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which in this case is 1. Dividing 37 by 1 gives us 37, and dividing 10 by 1 gives us 10. Therefore, the distance of 3 7/10 miles can be written as the decimal 3.7 miles.
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PLEASE HELP!!!!! EXPLAIN!!!!
Sam conducted a survey to find out the favorite weekend activity of the students in his middle school. He asked 20 of his classmates. He found out that the favorite weekend activity of his middle school is playing video games because 75% of the students he surveyed liked to play video games. Explain why Sam’s sample may not be valid. Provide 2 or 3 sentences of explanation with facts to support your answer. How could Sam improve his survey to be more representative of his school?
Answer:
So, Sam only asked 20 people in his entire middle school. That is a very small fraction of the amount of kids attending that school. He cannot say that video games is 75% of the entire school's favorite weekend activity if he only asked 20 people. To get a better, more valid result, he should ask around 100+ kids.
Step-by-step explanation:
WILL BE MARK BRAINL 2(2x+32)+2/5(4x+4)
= 28/5x + 328/5
is the answer. work is on attached piece of paper
Answer:
4
(
7
x
+
82
)
5
Step-by-step explanation:
which is the next term in the number pattern
1/12, 4/15, 9/18, 16/21,
a)24/25
b)19/24
c)25/24
d)19/25
ONLY RIGHT ANSWERS PLEASE :)
Factor & Finding Zeros
x^{2} -x-6=0
Answer:
x = 3, -2
Step-by-step explanation:
To help us factor, we can split the middle term up into the sum of the terms -3x and 2x:
[tex]x^2+(-3x)+2x-6=0[/tex]
From there, we can factor out an x from the first two term and a 2 from the last two to obtain the equation
[tex]x(x-3)+2(x-3)=0[/tex]
Factoring out an (x - 3) from each term gives us the equation
[tex](x-3)(x+2)=0[/tex]
At this point, we can divide by either x - 3 or x + 2 to obtain the two equations
[tex]x-3=0[/tex] and [tex]x+2=0[/tex]
Solving both for x gives us the solutions x = 3 and x = -2. We can verify these by substituting them back into the original equation:
[tex]3^2-3-6=0\\9-3-6=0\\6-6=0\\0=0[/tex]
[tex](-2)^2-(-2)-6 = 0\\4+2-6=0\\6-6=0\\0=0[/tex]
What all is required when graphing a function? Check all that apply.
Slope
Y-intercept
X-intercept
The equation
Calculator
Axis of symmetry
Vertex
Answer:
A line: slope, y-intercept from the equation
A quadratic: vertex or axis of symmetry from the equation
Step-by-step explanation:
When graphing a line, you need the y-intercept and slope. This can be found by using the equation.
When graphing a parabola or quadratic, you need the vertex or axis of symmetry. This can also be found from the equation.
Which number line best shows how to solve −4 − (−6)?
Answer:
the answer is A
Step-by-step explanation:
because two negatives turn to a positive
Answer:
A
Step-by-step explanation:
It is a rule that two negatives make a positive. Also, it is the only one with the correct format on the number line.
Evaluate C(7, 3). 4 35 70
Answer:
option B
35
Step-by-step explanation:
Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.
Formula to calculate combination
nCr = n! / r! * (n - r)!
We are given C(7,3)
here n = 7
r = 3
So plug values in the formula7C3 = 7! / 3! * (7 - 3)!
= (7x6x5x4x3x2) / (3x2)(4x3x2)
= (7x6x5) / (3x2)
= 210 / 6
= 35
Final answer:
The value of C(7, 3), which is the number of combinations of 7 items taken 3 at a time, is 35. The calculation uses the combinations formula C(n, k) = n! / (k! * (n - k)!), simplifying the factorials and the result is determined.
Explanation:
To evaluate C(7, 3), we need to calculate the number of combinations of 7 items taken 3 at a time. The formula for a combination is given as:
C(n, k) = n! / (k! * (n - k)!)
Here, n represents the total number of items and k represents the number of items to choose. Let's plug in the values to calculate this:
C(7, 3) =[tex]7! / (3! * (7 - 3)!) = 7! / (3! * 4!)[/tex] = (7 x 6 x 5 x 4 x 3 x 2 x 1) / ((3 x 2 x 1) * (4 x 3 x 2 x 1))
After canceling the matching factorial terms, we get:
C(7, 3) = (7 x 6 x 5) / (3 x 2 x 1) = 210 / 6 = 35
Therefore, the value of C(7, 3) is 35.
Add 5/6 + 3/4 + 2/3 simplify the answer write it as a mixed number if possible
Answer: 27/12 or 2 3/12
Step-by-step explanation: First off we would need to find a common denominator, so all the fractions could be added together easily, and we could use a denominator of 12 because 6 times 2 equals 12, 4 times 3 equals 12, and 3 times 4 equals 12. So 5/6 would become 10/12, 3/4 would become 9/12, and 2/3 would become 8/12. So adding them all together would give you a sum of 27/12 or 2 3/12. Hope this helped!