Answer: No
Step-by-step explanation: 5/3 is greater than 1 because 1 is the same as 3/3 and 5/3 is greater than 3/3 making 5/3 greater than 1.
The yearbook club is handing out T-shirts to its members. There are 5 blue, 7 green, 9 red, and 4 yellow T-shirts in all. If Jacob is handed a T-shirt, what is the probability that the color is red?
Answer:
well it's 9/25 or 0.36% or (36%) only
Step-by-step explanation:
So you add all the numbers up it would be 25, divide the numerator by the denominator and get 0.36%, i can't remember if you divide .36 by 100 or not but anyway you get 36%.
But I hope i have helped you in anyway.
what i the product ? (2x-1)(x+4)
Answer:
[tex]2x^2+7x-4[/tex]
Answer:
2x² + 7x - 4
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
2x(x + 4) - 1(x + 4) ← distribute both parenthesis
= 2x² + 8x - x - 8 ← collect like terms
= 2x² + 7x - 8
The width and length of a rectangle (in feet)are consecutive odd integers. If the length is increased by 5 feet, the area of the resulting rectangle is 60 square feet. What is the area of the original rectangle?
A. 25 ft^2
B. 30 ft^2
C. 35 ft^2
Answer:
Option C is correct.
Step-by-step explanation:
Let x be the original width
then x+2 will be the length (consecutive odd integer)
if length is increased by 5 feet , length will be: (x+2)+5 = x+7
Area = 60 square ft.
Area = length * width
60 = (x+7) *x
60 = x^2 +7x
Rearranging
x^2 + 7x -60 = 0
Solving quadratic equation to find the value of x
using Quadratic formula
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a=1, b =7, c=-60
[tex]x=\frac{-7\pm\sqrt{(7)^2-4(1)(-60)}}{2(1)}\\x=\frac{-7\pm\sqrt{49+240}}{2}\\x=\frac{-7\pm\sqrt{289}}{2}\\x=\frac{-7\pm17}{2}\\x=5 \,\, and \,\, x = -12\\[/tex]
Since width can be positive so x=5
length of original rectangle = x+2 = 5+2 =7
Area of original rectangle = Length * Width
Area of original rectangle = 5 * 7
Area of original rectangle = 35 ft^2
So, Option C is correct.
Final answer:
The width of the original rectangle is 5 feet, and the length is 7 feet, making the area 35 square feet. We determined this by setting up an equation for the area of the enlarged rectangle and solving for the odd integer width.
Explanation:
We are given that a rectangle has dimensions of consecutive odd integers and if the length is increased by 5 feet, the resulting area is 60 square feet. Let's denote the width as w feet (an odd integer) and the length as w + 2 feet (the next consecutive odd integer), since consecutive odd integers are two units apart.
After increasing the length by 5 feet, the new dimensions are w feet and w + 7 feet. The area can be calculated as the product of these dimensions:
w × (w + 7) = 60
Solving this quadratic equation: w² + 7w = 60
Subtracting 60 from both sides gives: w² + 7w - 60 = 0. Factoring this, we get: (w + 12)(w - 5) = 0
Considering the positive value that fits the condition of being an odd integer, we find that w = 5 feet. This makes the width 5 feet and the length 7 feet (5 + 2) for the original rectangle.
Thus, the area of the original rectangle is 5 feet × 7 feet = 35 square feet.
Therefore, the correct answer is C. 35 ft².
Add, subtract, multiply, or divide the following fractions. Remember to find the LCD first.
1/5+1/7+3/21
lcd 210
1/5=42/210
1/7=30/310
3/21=30/210
42+30+30=102/210
reduced 51/105
The sum of the fractions 1/5, 1/7 and 3/21 is 17/35. This was achieved by finding the least common denominator (LCD), converting the fractions to have the LCD, adding them, and then simplifying the result.
Explanation:To add or subtract fractions, it's essential to find the least common denominator (LCD). The LCD in this case would be the least common multiple (LCM) of 5, 7, and 21, which is 105. Once we have the LCD, we can rewrite the fractions as an equivalent fraction with the LCD as the denominator:
For 1/5, multiply both numerator and denominator by 21, so it becomes 21/105.For 1/7, multiply both numerator and denominator by 15, so it becomes 15/105.For 3/21, multiply both numerator and denominator by 5, so it becomes 15/105.Now all the fractions have the same denominator, and we can combine the numerators: 21/105 + 15/105 + 15/105 = 51/105. However, this can be simplified to 17/35 by dividing both numerator and denominator by 3.
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Walter is helping to make cookies for a basketball tournament. He's made 15 cookies so far. His coach asked him to make at least 20 cookies but no more than 55. Solve the inequality and interpret the solution. 20 ≤ x + 15 ≤ 55 5 ≤ x ≤ 40; Walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40; Walter needs to make less than 5 more cookies or more than 40. 35 ≤ x ≤ 70; Walter needs to make at least 35 more cookies but no more than 70. 35 ≥ x ≥ 70; Walter needs to make less than 35 more cookies or more than 70.
Answer: First Option
Walter needs to make at least 5 more cookies but no more than 40
[tex]5 \leq x \leq 40[/tex]
Step-by-step explanation:
If we call x the number of cookies that Walter needs to make, then we know that the amount of cookies will be:
[tex]x +15[/tex]
Then this amount must be greater than or equal to 20 and must be less than or equal to 55 then.
[tex]x + 15 \geq20[/tex] and [tex]x + 15 \leq55[/tex]
This is:
[tex]20 \leq x + 15 \leq 55[/tex]
We solve the inequality for x.
[tex]20-15 \leq x + 15-15 \leq 55-15\\\\5 \leq x \leq 40[/tex]
Then the amount of cookies that Walter must make must be greater than or equal to 5 and less than or equal to 40
Answer: It is A
Step-by-step explanation:
Levi reads 280 words in 2 minutes how many words can he read in 5 minutes.
Hello There!
WHAT WE KNOW Levi reads 280 words in 2 minutes. We need to find out how many words he can read in 5 minutes
To find out how many words Levi can read in 5 minutes, it will first be easier to find out how many words Levi can read in 1 minute. To find this, we will divide 280 by 2 and that will give us the number of words per minute.
Next, once we divide we will get a quotient of 140.
Finally, we take 140 and multiply it by 5 and we get a product of 700
Therefore, Levi reads 700 words in 5 minutes
Factor this polynomial completely.
x^2-8x+12
Answer:
(x - 2) (x - 6)
Step-by-step explanation:
Factor the following:
x^2 - 8 x + 12
The factors of 12 that sum to -8 are -2 and -6. So, x^2 - 8 x + 12 = (x - 2) (x - 6):
Answer: (x - 2) (x - 6)
The factors of the given polynomial are (x-6) and (x-2).
The given polynomial is x²-8x+12.
The factors are the polynomials which are multiplied to produce the original polynomial.
By splitting middle term method, we get
x²-6x-2x+12
x(x-6)-2(x-6)
(x-6)(x-2)
Therefore, the factors of the given polynomial are (x-6) and (x-2).
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what is the third angle of a right triangle if one of the angles measures 51.
Answer:
39
Step-by-step explanation:
The short answer is 39.
Every triangle has 180 degrees. There are no exceptions to this rule.
Since a triangle has 3 angles, all three together must add up to 180o
A right angle = 90 degrees always.
You are given 51 degrees as your second angle
The third one is x
x + 51 + 90 = 180 Total of three angles must be 180
x + 141 = 180 The left has been added to give 141
x = 180 - 141 Subtract 141 from both sides
x = 39 The third angle = 39
Can someone please help me out with this question?
Answer:
It is just right
Step-by-step explanation:
Kermit's fav = 15 tea bags every 2 liters = 15/2 = 7.5 teabags per liter
Peggy made 90 teabags in 12 liters = 90/12 = 7.5 teabags per leter
Hence peggy used the same teabags per liter than kermit's favorite. It is just right.
edit: calculation error. corrected.
Your answer would be C:Just right.
Because:
2 liters of water = 15 tea bags
15/2 = 7.5 tea bags
Peggy needs to make 12 liters
12 x 7.5 = 90 tea bags
Conclusion:
Peggy's 12-liter batch of iced tea with 90 tea bags is JUST RIGHT.
Hope helps!-Aparri
The steps in writing f(x) = 18x + 3x2 in vertex form are shown, but a value is missing in the last step.
Write the function in standard form.
f(x) = 3x2 + 18x
Factor a out of the first two terms. f(x) = 3(x2 + 6x)
Form a perfect square trinomial.
f(x) = 3(x2 + 6x + 9) – 3(9)
Write the trinomial as a binomial squared. f(x) = 3(x + ______)2 – 27
What is the missing value in the last step?
Answer:
3
Step-by-step explanation:
f(x) = 18x + 3x^2
f(x) = 3x^2+18x
Factor out a 3
= 3(x^2 +6x)
Take the coefficient of x, divide by 2 and then square
6/2 = 3 3^2 =9
Remember the 3 out side 3*9 =27 so we are really adding 27
3(x^2+6x+9) -3*9
The number inside the parentheses added to x is b/2 or 6/2
3(x+3)^2 -27
Answer:
[tex]f(x)=3(x+3)^{2}-27[/tex]
Step-by-step explanation:
In the last step is missing the number 3 which is the second term of the binomial squared expression.
Basically, the complete step is
[tex]f(x)=3(x+3)^{2}-27[/tex]
As you can see, the three inside the parenthesis is the missing part in the last step.
The legs of a right triangle measure 6 meters and 8 meters. What is the length of the hypotonuse.
Using the Pythagorean theorem a^2 + b^2 = c^2, where a and b are the sides and c is the hypotenuse, we can find the length needed.
6^2 + 8^2 = c^2
Simplify:
36 + 64 = c^2
100 =c^2
Take the square root of both sides:
c = √100
c = 10
The hypotenuse is 10 meters.
Conner invests $8600 in two different accounts. The first account paid 7 %, the second account paid 12 % in interest. At the end of the first year he had earned $812 in interest. How much was in each account?
$___ at 7 %
$ ___at 12 %
Answer:
Part 1) The amount invested in the first account at 7% was $4,400
Part 2) The amount invested in the second account at 12% was $4,200
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Let
x------> the amount invested in the first account at 7%
(8,600-x) -----> the amount invested in the second account at 12%
in this problem we have
[tex]t=1\ year\\ P1=\$x\\ P2=\$8,600-x\\ I=\$812\\r1=0.07\\r2=0.12[/tex]
substitute in the formula above
[tex]812=x(0.07*1)+(8,600-x)(0.12*1)[/tex]
[tex]812=0.07x+1,032-0.12x[/tex]
[tex]0.12x-0.07x=1,032-812[/tex]
[tex]0.05x=220[/tex]
[tex]x=\$4,400[/tex]
so
[tex]8,600-x=\$8,600-\$4,400=\$4,200[/tex]
therefore
The amount invested in the first account at 7% was $4,400
The amount invested in the second account at 12% was $4,200
Answer:
$4,400 at 7%
$4,200 at 12%
Step-by-step explanation:
Let the amount invested in 7% be x, so,
amount invested in 12% would be "8600 - x"
We can now write an equation and solve for x:
[tex]0.07(x)+0.12(8600-x)=812\\0.07x+1032-0.12x=812\\-0.05x=-220\\x=\frac{-220}{-0.05}=4400[/tex]
Thus, the amount invested in 12% is 8600 - 4400 = 4200
So,
$4,400 at 7%
$4,200 at 12%
Which table shows a proportional relationship between miles traveled and gas used?
Answer:
table d is the proportional relationship
Step-by-step explanation:
If 2/5 ÷ 7/9= N then N is between?
[tex]\bf \cfrac{2}{5}\div\cfrac{7}{9}=N\implies \cfrac{2}{5}\cdot \cfrac{9}{7}=N\implies \cfrac{18}{35}=N\implies 0.514\approx N \\\\[-0.35em] ~\dotfill\\\\ \boxed{0}\rule[0.35em]{10em}{0.25pt}\stackrel{N}{0.514}\rule[0.35em]{9em}{0.25pt}\boxed{1}[/tex]
Which would be the "best" or quickest first step to solve the system using substitution?
x – 2y = -2
- 3+y=2
Solve (rearrange) the 1st equation for X.
Solve (rearrange) the 1st equation for Y.
Solve (rearrange) the 2nd equation for X.
Solve (rearrange) the 2nd equation for y.
Answer:
4th option
Step-by-step explanation:
Solve and rearrange the second equation for y
y= 2 +3
y =5
The substitute y in first equation to get x
Which angle is an inscribed angle
1
2
3
4
Answer:
∠1
Step-by-step explanation:
we know that
An inscribed angle in a circle is formed by two chords that have a common end point on the circle
The measure of the inscribed angle is half of measure of the intercepted arc
In this problem
∠1 is an inscribed angle
∠2 is an outer angle
∠3 is an interior angle
∠4 is an semi-inscribed angle ( angle formed by a chord and a tangent)
Answer:
1. Tangent ray: a ray that lies on a tangent line and contains the point of tangency;
2. Intercepted arc: an angle intercepts an arc if the endpoints of the arc lie on the sides of the angle and all points of the arc except the endpoints lie in the interior of the angle;
3. Secant ray: a ray that lies on a secant line and contains both points of intersection with the circle; and
4. Inscribed angle: an angle with sides containing the endpoints of an arc and with a vertex that is a point of the arc other than an endpoint of the arc.
The cross products of a proportion are never equal.
True
False
Answer:
false
Step-by-step explanation:
It could be equal because what if the proportions are something like 2/3=3/2
In this case the product of both sides is 6.
B. False
What is a proportion?When I say that the proportion is 2 ratios that are equal to each other, It mean this in the sense of 2 fractions being equal to each other.
How do you write equivalent proportions?Proportions could be written as equivalent fractions and as = ratios. When we can say that the ratios in the proportion are =, we mean that we could multiply and divide 1 ratio by some constant to result in the other.
It can be equal because what if the proportions are something such as
2/3=3/2
In this case the product of both sides is 6.
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Solve for 3X^2-6=10-x^2
Answer: x = 2
Step-by-step explanation:
3x2 - 6 = 10 - x2
+6 +6
3x2 = 16 - x2
+x2 +x2
4x2 = 16
4/4 16/4
x2 = 4
√x2 = √4
x = 2
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Solve the following problems.
a. 2 ft 5 in + 9 in
b. 4 yd 8 in + 6 yd 6 in
c. 29 yd 2 ft 11 in + 55 yd 1 ft 10 in + 13 yd 1 ft 3 in
d. 4,839 sq yd 8 sq ft 139 sq in + 7 sq ft 124 sq in
Answer:
(a) 38 inches (b) 374 inches (c) 3564 inches (d) 6273767 square inches
Step-by-step explanation:
a) 2 ft 5 inches + 9 inches
Convert to inches
1 feet = 12 inches
2 feet = 12 x 2 inches = 24 inches
24 inches + 5 inches + 9 inches = 38 inches
b) 4 yards 8 inches + 6 yards 6 inches
Convert to inches
1 yard = 36 inches
4 yards = 36 x 4 = 144 inches
144 inches + 8 inches = 152 inches
6 yards = 36 x 6 = 216 inches
216 inches + 6 inches = 222 inches
152 inches + 222 inches = 374 inches
c) 29 yard 2 feet 11 inches + 55 yard 1 feet 10 inches + 13 yard 1 feet 3 inches
Convert to inches
29 yard 2 feet 11 inches
1 yard = 36 inches
29 yards = 36 x 29 = 1044 inches
1 feet = 12 inches
2 feet = 12 x 2 = 24 inches
1044 + 24 + 11 = 1079 inches
55 yard 1 feet 10 inches
1 yard = 36 inches
55 yards = 26 x 55 = 1980 inches
1 feet = 12 inches
1980 + 12 + 10 = 2002 inches
13 yard 1 feet 3 inches
1 yard = 36 inches
13 yards = 13 x 36 = 468 inches
1 feet = 12 inches
468 + 12 + 3 = 483 inches
1079 + 2002 + 483 = 3564 inches
d) 4,839 sq yard 8 sq feet 139 sq inches + 7 sq feet 124 sq inches
Convert to square inches
4,839 sq yard 8 sq feet 139 sq inches
1 square yard = 1296 square inches
4839 x 1296 = 6271344 square inches
1 square feet = 144 square inches
8 x 144 = 1152
6271344 + 1152 = 6272635 square inches
7 sq feet 124 sq inches
7 x 144 = 1008
1008 + 124 = 1132 square inches
1132 + 6272635 = 6273767 square inches
!!
Which statement best describes f(x)= -2 sqrt (x-7)+1
Answer:
-6 is not in the domain of f(x) but is in the range of f(x)
Step-by-step explanation:
we have
[tex]f(x)=-2\sqrt{x-7}+1[/tex]
Find the domain of the function
we know that the radicand must be greater than or equal to zero
so
[tex]x-7\geq 0\\ \\x\geq 7[/tex]
The domain is all real numbers greater than or equal to 7
The range is the interval -----> (-∞,1]
[tex]y\leq1[/tex]
All real numbers less than or equal to 1
see the attached figure to better understand the problem
therefore
The statement that best describes the function f(x) is
-6 is not in the domain of f(x) but is in the range of f(x)
Answer:
B is the right choice. -6 is not the domain of f(x) but is in the range of f(x)
A line intersects the point (-11,4)and has a slope of -2. What are the inputs to the point -slope formula?
Answer:
The inputs to this formula are:
The x-coordinate of the point: [tex]x_0 = -11[/tex]; The y-coordinate of the point: [tex]y_0 = 4[/tex]; andThe slope of the line: [tex]m = -2[/tex].The equation of this line in point-slope form will be:
[tex]y - 4 = -2(x +11)[/tex].
Step-by-step explanation:
The general form of a 2D line in its point-slope form is:
[tex]l:\; y - y_0 = m(x - x_0)[/tex].
This form of the equation of a line takes two pieces of information:
The x-y coordinate of a point on the line [tex](x_0, y_0)[/tex], andThe slope (a.k.a. gradient) of that line.For this line, the point [tex](x_0, y_0)[/tex] is [tex](-11, 4)[/tex].
[tex]x_0 = -11[/tex], and[tex]y_0 = 4[/tex].The slope of this line is [tex]-2[/tex]. In other words,
[tex]m = -2[/tex].Apply the point-slope formula for a 2D line:
[tex]l:\; y - 4 = -2 (x - (-11))[/tex].
[tex]l:\; y - 4 = -2 (x +11 )[/tex].
Find the measure of x
Answer:
Step-by-step explanation:
The angle adjacent to the 106 degree angle is 180 degrees - 106 degrees, or 74 degrees. Next, the adjacent angle to the 145 degree angle is 35 degrees; in other words, the two bottom angles of this triangle are 35 degrees and 35 degrees. That means that a 35 degree angle is vertical angle to x, and so x is also 35 degrees.
The sum of the three interior angles is 35 degrees + 74 degrees and
Check the picture below.
let's recall that vertical angles, angles across a junction, are equal, namely the angle across the "x" is also "x".
15 points with explanation
Answer:
The answer is 142°
Step-by-step explanation:
Because 38° and m∠2 are corresponding angles, m∠2 = 38°. Also, m∠2 and m∠5 are supplementary angles, which means the sum of their angles adds up to 180°. We can create the equation 38° + m∠5 = 180°. By subtracting 38° on both sides, we get m∠5 = 142°.
The table represents the multiplication of two binomials. What is the value of A?
The calculated value of the variable A from the table of values is -3x²
How to determine the value of the variable A
From the question, we have the following parameters that can be used in our computation:
The contingency table
The cell A is in the row -x and the column 3x
This means that
A = 3x * -x
When the product is evaluated, we have
A = -3x²
Hence, the value of the variable A is -3x²
write and equation for the line that is parallel to the given line and that thale passes through the given point. y=3/4x-9 (-8 -18)
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{3}{4}[/tex] x - 9 ← is in slope- intercept form
with slope m = [tex]\frac{3}{4}[/tex]
• Parallel lines have equal slopes, hence
y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the parallel line.
To find c substitute (- 8, - 18) into the partial equation
- 18 = - 6 + c ⇒ c = - 18 + 6 = - 12
y = [tex]\frac{3}{4}[/tex] x - 12 ← equation of parallel line
Answer:
Step-by-step explanation:
The equation of a linear function in point-slope form is y – y1 = m(x – x1)
The point is A (x1 , y1)
the slope is : m the line that is parallel to the given line so : m = 3/4
passes through the given point (-8 -18)
so : x1 = - 8 and y1 = -18
an equation is : y +18= 3/4(x +8)
Find the focus for y=x^2+4x-7
ANSWER
[tex](2,-10.75)[/tex]
EXPLANATION
The given function is
[tex]y = {x}^{2} - 4x - 7[/tex]
We rewrite this function to obtain,
[tex](y + 11) = {( x- 2)}^{2} [/tex]
We now compare this function to
[tex](y - k) = 4p {( x- h)}^{2} [/tex]
We have
[tex]4p = 1[/tex]
This implies that,
[tex]p = \frac{1}{4} [/tex]
The vertex is (2,-11).
The focus is
[tex](2,-11+ \frac{1}{4} )[/tex]
[tex](2,- \frac{43}{4} )[/tex]
[tex](2,-10.75)[/tex]
what is the value of the ratio 18:21??
Answer:
18:21 is equivalent to 18/21. When you simplify 18/21, you get 6/7
Answer:
85.714285714286%
Step-by-step explanation:
i hope this helps, if you are looking for the percentage.
What are the solutions to the equation 4x 3 - 5x = |4x|? List your answers in increasing order.
The solutions are x =
,
and
Answer:
-1/2 , 0 , 3/2
Step-by-step explanation:
Given equation is:
[tex]4x^3-5x = |4x|[/tex]
We know that [tex]|x|=a\\The\ solution\ will\ be:\\x=a\ and\ x=-a\\[/tex]
So, from given equation,we will get two solutions:
[tex]4x^3-5x = 4x\\4x^3-5x-4x=0\\4x^3-9x=0\\x(4x^2-9) = 0\\x = 0\\and\\4x^2-9 = 0\\4x^2=9\\x^2 = \frac{9}{4} \\\sqrt{x^2}=\sqrt{\frac{9}{4} }\\[/tex]
x= ±√3/2 , 0
and
[tex]4x^3-5x = -4x\\4x^3-5x+4x=0\\4x^3-x=0\\x(4x^2-1) = 0\\x = 0\\and\\4x^2-1 = 0\\4x^2=1\\x^2 = \frac{1}{4} \\\sqrt{x^2}=\sqrt{\frac{1}{4} }[/tex]
x= ±1/2 , 0
We can check that 1/2 and -3/2 do not satisfy the given equation.
[tex]4x^3-5x = |4x|\\Put\ x=1/2\\4(\frac{1}{2})^3 - 5(\frac{1}{2}) = |4 * \frac{1}{2}|\\ 4 * (\frac{1}{8)} - \frac{5}{2} = |2|\\ -2 = 2\\Put\ x=-\frac{3}{2} \\4(\frac{-3}{2})^3 - 5(\frac{-3}{2}) = |4 * \frac{-3}{2}|\\-6 = 6\\[/tex]
So, 1/2 and -3/2 will not be the part of the solution ..
So, the solutions in increasing order are:
-1/2 , 0 , 3/2 ..
Answer:
[tex]-\frac{1}{2},0,\frac{3}{2}[/tex]
Step-by-step explanation:
We are given that an equation
[tex]4x^3-5x=\mid x\mid[/tex]
We have to find the solution of given equation and arrange the solution in increasing order.
[tex]4x^3-5x=4x[/tex] when x >0
and [tex]4x^3-5x=-4x[/tex] when x < 0
because [tex]\mid x\mid =x when x > 0 [/tex]
=-x when x < 0
[tex]4x^3-5x-4x=0[/tex]
[tex]4x^3-9x=0[/tex]
[tex]x(4x^2-9)=0[/tex]
[tex]x(2x+3)(2x-3)=0[/tex]
Using identity [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]x=0,2x+3=0,2x-3=0[/tex]
[tex]2x=3\implies x=\frac{3}{2}=1.5[/tex]
[tex]2x=-3 \implies x=-\frac{3}{2}=-1.5[/tex]
[tex]4x^3-5x=-4x=0[/tex]
[tex]4x^3-5x+4x=0[/tex]
[tex]4x^3-x=0[/tex]
[tex]x(4x^2-1)=0[/tex]
[tex]x(2x+1)(2x-1)=0[/tex]
[tex]x=0,2x+1=0[/tex]
[tex]2x-1=0[/tex]
[tex]2x-1=0[/tex]
[tex]2x=1 \ilmplies x=\frac{1}{2}=0.5[/tex]
[tex]2x+1=0[/tex]
[tex]2x=-1 \implies x=-\frac{1}{2}=-0.5[/tex]
When we substitute x=[tex]\frac{1}{2}[/tex]
[tex]4(\frac{1}{2})^3-\frac{5}{2}=\frac{1}{2}-\frac{5}{2}=\frac{1-5}{2}=-2[/tex]
[tex]\mid 4(\frac{1}{2})\mid=2[/tex]
[tex]-2\neq 2[/tex]
Hence, [tex]\frac{1}{2}[/tex] is a not solution of given equation.
When substitute [tex]x=\frac{-3}{2}[/tex]
[tex]4(\frac{-3}{2})^3+\frac{15}{2}=\frac{-27}{2}+\frac{15}{2}=\frac{-27+15}{2}=-6[/tex]
[tex]\mid 4(-\frac{3}{2}\mid=6[/tex]
[tex]-6\neq 6[/tex]
Hence, [tex]\frac{-3}{2}[/tex] is not a solution of given equation.
Substitute x=[tex]-\frac{1}{2}[/tex] in the given equation
[tex]4(-\frac{1}{2})^3+\frac{5}{2}=-\frac{1}{2}+\frac{5}{2}=2[/tex]
[tex]\mid 4(-\frac{1}{2})\mid=2[/tex]
[tex]2=2[/tex]
Hence, [tex]-\frac{1}{2}[/tex] is a solution of given equation.
Substitute [tex]x=\frac{3}{2}[/tex] in the given equation
[tex]4(\frac{3}{2})^3-\frac{15}{2}=\frac{27-15}{2}=6[/tex]
[tex]\mid 4(\frac{3}{2})\mid =6[/tex]
[tex]6=6[/tex]
Hence, [tex]\frac{3}{2}[/tex] is a solution of given equation.
Answer:[tex]-\frac{1}{2},0,\frac{3}{2}[/tex]
Convert: 31 ft = _yd__ft
Answer:
10 yards and 1 feet
Answer:
10 yards + 1 ft
Step-by-step explanation:
Conversion :
3 feet = 1 yard
or
30 feet = 10 yards
notice that 31 ft = 30 ft + 1 ft
= 10 yards + 1 ft
what is which the relationship between the volume of a cone and the volume of a cylinder? explain
Answer:
The base of the cone is a circle of radius r. The height of the cone is the length h of the straight line from the cone's tip to the center of its circular base. Both ends of a cylinder are circles, each of radius r. ... For example, the volume of a cube is the area of one side times its height.
Step-by-step explanation:
Hope this helps! Please mark brainliest!
Answer:
The volume of a cone is one-third the volume of a cylinder.
Step-by-step explanation: