Answer:
Step-by-step explanation:
First pull out the common factor of ab
ab(8a^3 + (1/125)b^3)
This is basically the sum of cubes. The linear factor is
(2a + 1/5 b)
The other factor is these two factors squared and their multiplicand subtracted.
(2a^2 - 2/5 ab + 1/25b^2)
Now put all this together and you get
ab(2a + 1/5 b)((2a^2 - 2/5 ab + 1/25b^2)
What is the volume of the pyramid?
A solid right pyramid has a square base. The length of the
base edge is 4 cm and the height of the pyramid is 3 cm.
Answer: 16 cm^2.
Step-by-step explanation: The volume of a pyramid is equal to one-third the product of the area of the base and the height:
[tex]V=\frac{1}{3}A*h[/tex]
In this case, the base is a square, so its area is:
A=L^2 where "L" is the lenght of the base edge
So the volume would be:
[tex]V=\frac{1}{3}L^{2} *h[/tex]
[tex]V=\frac{1}{3}4^{2} *3[/tex]
V=16*3/3
[tex]V=16cm^{2}[/tex]
Suppose an elevator is 400 feet above the ground. It descends at a steady rate.
After 15 seconds, it is 250 feet above the ground.
Write a linear function for the height of the elevator as a function of time.
Answer:
The answer is....
Step-by-step explanation:
y= -10x+400
Follow below steps:
The student's question involves writing a linear function for the height of an elevator as a function of time, given that the elevator descends from 400 feet to 250 feet in 15 seconds.
First, let's find the rate of descent by calculating the change in height over the change in time. This gives us (250 feet - 400 feet) / (15 seconds) = -10 feet per second. The negative sign indicates a downward movement.
Now, we can construct the linear function for height h(t), where t is the time in seconds. The initial height is 400 feet, so the y-intercept of our linear equation is 400. With a slope of -10, the function takes the form:
h(t) = -10t + 400
This function represents the height of the elevator after t seconds.
Interest rate is 4.25%, the time is 3 1/4 years, simple interest is $330. What is the principal?
Answer:
$2389.14
Step-by-step explanation:
The equation is I = PRT
330= (0.0425)(3.25)P
P=2389.14
Answer:
$2389.14.
Step-by-step explanation:
Use the formula
I = PRT/100 where I = interest , P is the principle, t = time and R = the rate.
330 = P * 4.25 * 3.25 / 100
33000 = P * 13.8125
P = 33,000 / 13.8125
P = $2389.14.
1 and 3/4 + 2 and 3/8
Hello There!
1[tex]\frac{3}{4}[/tex] + 2[tex]\frac{3}{8}[/tex] = 4[tex]\frac{1}{8}[/tex]
First, when we are trying to find the sum of a mixed number, I always add the natural numbers first meaning that the numbers before the fraction so I would add 1 and 2 together so we get a sum of 3 and now we are left with just a plain fraction.
Next, I find the least common denominator which is the smallest number that can be a common denominator for a set of fractions. Our lowest common denominator is 8 because [tex]\frac{3}{4}[/tex] = [tex]\frac{6}{8}[/tex].
Then, we add our fractions with the denominator of 8 together and get a sum of 9/8 which we can turn into a mixed number because the numerator is bigger than our denominator.
Our mixed number turns into 1 and 1/8 and we add 4 to it because that was the sum of our natural numbers and get a sum of 4 and 1/8
ANSWER 4 1/8
The values in the table represent an exponential function. What is the common ratio of the associated geometric sequence?
Answer:
D. 3Step-by-step explanation:
[tex]a_1,\ a_2,\ a_3,\ ...,\ a_n-\text{geometric series}\\\\r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...=\dfrac{a_n}{a_{n-1}}-\text{common ratio}\\\\\text{From the table we have:}\\\\a_1=7,\ a_2=21,\ a_3=63,\ a_4=189,\ a_5=567\\\\\text{Check the common ratio:}\\\\\dfrac{21}{7}=3\\\\\dfrac{63}{21}=3\\\\\dfrac{189}{63}=3\\\\\dfrac{567}{189}=3\\\\\bold{CORRECT}[/tex]
a pair of shoes is on sale for 30% off . the original price is p. which expression can be used to find the price of shoes after the dicount?
Answer:
.30p
Step-by-step explanation:
Simplify the expression 3/2 (5/3) -1 1/4 + 1/2
Answer:
7/4, 1.25 or 1 3/4
Step-by-step explanation:
Answer:
Exact form 7/4
Decimal form 1.75
Mixed Number 1 3/4
Step-by-step explanation:
(4x^2y^3+2xy^2-2y)-(-7x^2y^3+6xy^2-2y)
Answer:
x y^2 (11 x y - 4)
Step-by-step explanation:
Simplify the following:
4 x^2 y^3 + 2 x y^2 - 2 y - (-7 x^2 y^3 + 6 x y^2 - 2 y)
Factor y out of -7 x^2 y^3 + 6 x y^2 - 2 y:
4 x^2 y^3 + 2 x y^2 - 2 y - y (-7 x^2 y^2 + 6 x y - 2)
-y (-2 + 6 x y - 7 x^2 y^2) = 2 y - 6 x y^2 + 7 x^2 y^3:
4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3
Grouping like terms, 4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3 = (4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y):
(4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y)
x^2 y^3 4 + x^2 y^3 7 = 11 x^2 y^3:
11 x^2 y^3 + (2 x y^2 - 6 x y^2) + (2 y - 2 y)
x y^2 2 + x y^2 (-6) = -4 x y^2:
11 x^2 y^3 + -4 x y^2 + (2 y - 2 y)
2 y - 2 y = 0:
11 x^2 y^3 - 4 x y^2
Factor x y^2 out of 11 x^2 y^3 - 4 x y^2:
Answer: x y^2 (11 x y - 4)
Answer: xy2 • (11xy - 4)
Step-by-step explanation:
4 x^2 y^3 + 2 x y^2 - 2 y - (-7 x^2 y^3 + 6 x y^2 - 2 y)
Factor y out of -7 x^2 y^3 + 6 x y^2 - 2 y:
4 x^2 y^3 + 2 x y^2 - 2 y - y (-7 x^2 y^2 + 6 x y - 2)
-y (-2 + 6 x y - 7 x^2 y^2) = 2 y - 6 x y^2 + 7 x^2 y^3:
4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3
Grouping like terms, 4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3 = (4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y):
(4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y)
x^2 y^3 4 + x^2 y^3 7 = 11 x^2 y^3:
11 x^2 y^3 + (2 x y^2 - 6 x y^2) + (2 y - 2 y)
x y^2 2 + x y^2 (-6) = -4 x y^2:
11 x^2 y^3 + -4 x y^2 + (2 y - 2 y)
2 y - 2 y = 0:
11 x^2 y^3 - 4 x y^2
Factor x y^2 out of 11 x^2 y^3 - 4 x y^2:
Answer: x y^2 (11 x y - 4)
In parallelogram ABCD, AB=7cm and the perimeter of ABCD is 30cm. What is the length of AD?
Answer:
8cm
Step-by-step explanation:
Ab=7cm
Since opposite sides are equal
Cd=7cm
7cm + 7cm = 14cm
Perimeter equals 30cm
:.30cm - 14cm =16cm (bc+ad)
Since both bc and ad are equal,
16cm/2=8cm
:.ad=8cm
Final answer:
In a parallelogram, opposite sides are equal, so by using the given perimeter of 30 cm and one side of 7 cm, we find the length of the adjacent side AD to be 8 cm.
Explanation:
In the given problem with parallelogram ABCD, we know AB = 7 cm and the perimeter is 30 cm. In a parallelogram, opposite sides are equal in length, so if AB = 7 cm, then CD also equals 7 cm. The perimeter P of a parallelogram is the sum of all its sides:
P = AB + BC + CD + DA
Given P = 30 cm and AB = CD = 7 cm, we can find the length of AD (which is also equal to BC) using the formula:
P = 2(AB + AD)
30 = 2(7 + AD)
30 = 14 + 2(AD)
30 - 14 = 2(AD)
16 = 2(AD)
AD = 16 / 2 = 8 cm
Therefore, the length of AD is 8 cm.
I NEED HELP NOW!!!! I'LL MARK YOU BRAINLIEST IF YOU ANSWER!!!!!
Answer:
0, 5, 7, 11, ...
Step-by-step explanation:
1^2 = 1; 1 - 1 = 0; 0 is divisible by 6
5^2 = 25; 25 - 1 = 24; 24 is divisible by 6
7^2 = 49; 49 - 1 = 48; 48 is divisible by 6
11^2 = 121; 121 - 1 = 120; 120 is divisible by 6
the sum of three consecutive natural numbers is 156 find the number which is the multiple of 13 out of these numbers
Answer:
52 is the multiple of 13
Step-by-step explanation:
3x+3=156
3x=153
x=52
Answer:
52 is the multiple of 13 out of 51 , 52, 53 numbers.
Step-by-step explanation:
Given: Sum of three consecutive integers 156
To find: Three consecutive integers .
Solution: We have given that
Let first consecutive number x ,
Second consecutive number= x+1
Third number = x+2
According to question :
Sum of three consecutive number
x + x+1 +x+2 = 156 .
Combine like term
3x+3 = 156
On subtracting by 3 both side
3x + 3 -3 = 156 - 3
3x = 153
On dividing by 3
x = 51.
X+1 = 51+1
x+1 = 52.
x +3 = 51+2 = 53.
We can see second number 52 is multiple of 13.
Therefore, 52 is the multiple of 13 out of 51 , 52, 53 numbers.
How do you do this question down below?
Answer:
y = 3m - 6
Step-by-step explanation:
y = mx + b
b is the point where the line cuts the y axis.
That happens at (0,-6)
So far what you have on this equation is
y = mx - 6
You could use the point that cuts the x axis to find m.
y = 0
x = 2
0 = m*2 - 6 Add 6 to both sides
6 = m*2 - 6 + 6
6 = 2*m Divide by 2
6/2 = 2m/2 Do the division
3 = m
Answer
y = 3m - 6
find the length of AB leave your answer in terms of pi help please
[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =\textit{angle in}\\ \qquad \textit{degrees}\\ \cline{1-1} r=6\\ \theta =30 \end{cases}\implies s=\cfrac{\pi (30)(6)}{180}\implies s=\pi[/tex]
Given: -x > 4. Choose the solution set.
Final answer:
The solution to the inequality -x > 4 is all real numbers less than -4, which can be expressed as the interval (-∞, -4). This is found by dividing both sides by -1 and reversing the inequality to x < -4.
Explanation:
When considering the inequality -x > 4, we are trying to find the set of all values for the variable x that make the inequality true. The solution to such an inequality requires inverse operations and understanding the rules for inequalities, especially the rule that multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol.
Step by step, let's solve the given inequality:
Divide both sides of the inequality by -1 to isolate x. It is important to remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality, so our inequality becomes x < -4 after this step.Now that we have x isolated, we can interpret the solution set. The values of x that satisfy this inequality are all real numbers less than -4. Therefore, the solution set can be written in interval notation as (-∞, -4).This means that any number lower than -4 will be a valid solution for the inequality -x > 4. It's also valuable to visualize this set on a number line, where everything to the left of -4 (but not including -4 itself) is part of the solution set.
Which is a solution to the equation?
(х-2)(х + 5) = 18?
[tex]\bf (x-2)(x+5)=18\implies \stackrel{\mathbb{F~O~I~L}}{x^2+3x-10}=18\implies x^2+3x-28=0 \\\\\\ (x-4)(x+7)=0\implies x= \begin{cases} 4\\ -7 \end{cases}[/tex]
What are the x- and y-intercepts for the equation "2x + 3y = 6"?
(2,0) & (3,0)
(0, 2) & (3, 0)
(0,3) & (2,0)
(0,3) & (0,2)
Answer:
(0,2) & (3,0)
Step-by-step explanation:
Given the equation [tex]2x+3y=6[/tex]:
Step 1:
To find the y-intercept, you want to set the x value to zero. This will allow you to solve for y, and find where the equation intercepts why on the 0 line:
[tex]2(0)+3y=6 \\ 0+3y=6\\ 3y=6\\ y=\frac{6}{3} \\ y = 2[/tex]
So, at x=0, y=2. or (0,2)
Step 2:
Set y = 0 and solve for x:
[tex]2x+3(0)=6\\ 2x+0=6\\ 2x=6\\ x=\frac{6}{2}\\ x=3[/tex]
so at y=0, x=3. which is the same as saying: when x=3, y=0, or (3,0)
If f(x) = 3x + 10 and g(x) = 2x– 4, find (f+ g)(x).
Answer:
5x+6
Step-by-step explanation:
f(x) = 3x + 10
g(x) = 2x– 4
(f+ g)(x) = 3x+10 + 2x-4
Combine like terms
= 5x+6
Answer:
5x + 6
Step-by-step explanation:
(f+ g)(x) = 3x + 10 + 2x– 4
= 5x + 6
A triangle in the coordinate plane has coordinates of (2,3), (-4,-5), and (-2, 4). It is translated 3 units down. What are its new coordinates?
A) (5,3), (-1,-5), (1,4)
B) (2,6), (-4,-2), (-2, 7)
C) (2,0), (-4,-8), (-2, 1)
D) (-1,3), (-7,-5), (-5,4)
Answer: C) (2,0), (-4,-8), (-2, 1)
Step-by-step explanation:
The translation rule for translating a point (x,y) by k units down :-
[tex](x,y)\rightarrow(x,y-h)[/tex]
Given : A triangle in the coordinate plane has coordinates of (2,3), (-4,-5), and (-2, 4). It is translated 3 units down.
Then, its new coordinates will be :
[tex](2,3)\rightarrow(2,3-3)=(2,0)[/tex]
[tex](-4,-5)\rightarrow(-4,-5-3)=(-4,-8)[/tex]
[tex](-2, 4)\rightarrow(-2,4-3)=(-2,1)[/tex]
Hence, the new coordinates = (2,0), (-4,-8), (-2, 1)
What is the value of x?
50°
100
А. 50°
Ов. 150°
Ос. 100°
Op. 30°
Answer:
The answer is 30
Step-by-step explanation:
BC the inside of a triangle equals 180
Consider the following equation
Select the equation that has the same solution as the given equation.
Answer:
Option C [tex](3/2)p-5+(9/4)p=7-(5/4)p[/tex]
Step-by-step explanation:
we have that
The given equation is
[tex]-16p+37=49-21p[/tex]
Solve for p
Group terms that contain the same variable
[tex]-16p+21p=49-37[/tex]
Combine like terms
[tex]5p=12[/tex]
[tex]p=12/5[/tex]
[tex]p=2.4[/tex]
we know that
If a equation has the same solution as the given equation, then the solution of the given equation must satisfy the equation
Verify each case
case A) we have
[tex]2+1.25p=-3.75p+10[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex]2+1.25(2.4)=-3.75(2.4)+10[/tex]
[tex]5=1[/tex] ----> is not true
therefore
The equation does not have the same solution as the given equation
case B) we have
[tex]-55+12p=5p+16[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex]-55+12(2.4)=5(2.4)+16[/tex]
[tex]-26.2=28[/tex] ----> is not true
therefore
The equation does not have the same solution as the given equation
case C) we have
[tex](3/2)p-5+(9/4)p=7-(5/4)p[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex](3/2)(2.4)-5+(9/4)(2.4)=7-(5/4)(2.4)[/tex]
[tex]4=4[/tex] ----> is true
therefore
The equation has the same solution as the given equation
case D) we have
[tex]-14+6p=-9-6p[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex]-14+6(2.4)=-9-6(2.4)[/tex]
[tex]0.4=-5.4[/tex] ----> is not true
therefore
The equation does not have the same solution as the given equation
Help me out again Please
At a point on the ground 60 Ft
from the base of a tree, the distance
to the top of the tree is 4 ft more
than 2 times the height of the tree.
Find the height of the tree in ft.
The height of the tree is 32 feet.
Step-by-step explanation:
Let the height of the tree be x.
Connect the top of the tree, the point on the ground, and the bottom of the tree to form a right triangle.
Use Pythagorean theorem to solve for x.
(4+2x)^2 = x^2 + 60^2
x = 32
The height of the tree is 4 feet.
Explanation:To find the height of the tree, we can set up a right triangle with the tree height as one leg, the distance from the base of the tree as the other leg, and the distance to the top of the tree as the hypotenuse. Let's call the tree height x. From the given information, we can write the equation:
x = 2x + 4
Simplifying this equation, we get:
x = 4
Therefore, the height of the tree is 4 feet.
Learn more about Geometry here:https://brainly.com/question/31408211
#SPJ3
If an airplane flies at an average speed of 7.5 miles per minute, in 1 1/2 hours it will have flown?
Answer:
675 miles
Step-by-step explanation:
7.5*90 (for the 1 1/2 hour)
Answer:
1 1/2= 90 minutes
90 minutes/7.5 miles per minute
Multiply
90/7.5
= 675 miles in 1 1/2
Hope this helped :)
Hamid ha gained weight, he now weighs 88kg which is 10% higher than the normal, what i Hamid normal weight?
Answer:
80 kg is Hamid's normal weight
Step-by-step explanation:
The following equation will help you to find the answer:
(1.10)x = 88
Answer:79.2kg
Step-by-step explanation:
10%of 88kg is 8.8. Subtract 8.8 from 88 and the answer is 79.2.
what is the distance between (1,4) and (4,0) ?
Answer:
5 units
Step-by-step explanation:
To calculate the distance (d) use the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (4, 0)
d = [tex]\sqrt{(4-1)^2+(0-4)^2}[/tex]
= [tex]\sqrt{3^2+(-4)^2}[/tex]
= [tex]\sqrt{9+16}[/tex] = [tex]\sqrt{25}[/tex] = 5
4x(3x-7)-19x^2 simplify the expression below
Answer:
opening the bracket, the expression becomes
12x^2-28-19x^2
collect like terms
12x2-19x^2-28
-7x^2-28
-7(x^2+4)
write y+1=-2x-3 in standard form
Answer:
2y=-5x
Step-by-step explanation:
First you mark your terms, which means to basically put the equation in order.
Then you add, for instance, first you'll add y and 1, you'll have 2y because y means one. Then, you'll have -2 minus 3 and you'll get -5 then you carry on the variables to the solutions.
Answer:
2y=-5x
hope this helps :3
Question 1
The number of laptop computers sold each month for one year was
recorded by an electronics store. The results were 14, 15, 15, 30, 29, 5, 9, 15,
21, 21, 26, and 15. Calculate the median number of laptop computers sold
per month.
The median number of laptop computers sold per month is 15, calculated by arranging the sales data in ascending order and averaging the two middle values in the even-numbered dataset.
Explanation:The median of laptop computers sold per month can be calculated by first arranging the given numbers in ascending order and then finding the middle value. If there is an even number of observations, the median is the average of the two middle numbers.
Arrange the sales numbers in ascending order: 5, 9, 14, 15, 15, 15, 15, 21, 21, 26, 29, 30.Since there are 12 months, we have an even number of observations, so we take the average of the 6th and 7th values which are both 15.The median number of laptop computers sold per month is 15.The roots of the equation 2×^2 + 3x -4=0 are a and b.
find the values of
a^2ß^2
Answer:
hello : a²b² =4
Step-by-step explanation:
2ײ + 3x - 4=0
The roots of this equation exist because (2)(-4)<0
note : a'x²+b'x +c' =0.......The roots of this equation : a and b
a×b = c'/a' a' =2 and b'=3 and c' = - 4
in this exercice ; a²b² = (ab)² = (c'/a')² = (-4/2)² = (-2)² =4
Answer:
4
Step-by-step explanation:
given a quadratic equation in standard form
y = ax² + bx + c = 0 : a ≠ 0
with roots α and β, then
the sum of the roots α + β = - [tex]\frac{b}{a}[/tex] and
the product of the roots αβ = [tex]\frac{c}{a}[/tex]
2x² + 3x - 4 = 0 ← is in standard form
with a = 2, b = 3 and c = - 4
αβ = [tex]\frac{-4}{2}[/tex] = - 2, hence
α²β² = (αβ)² = (- 2)² = 4
6 x j = 42 ??????? Help
Answer:
j = 7
Step-by-step explanation:
flip the equation around: instead of using multiplication you use division to find out what j is.
1st step: 42 divided by 6 is 7
2nd step: (check your answer): 7 times 6 does equal 42, therefore j = 7 is correct.
Answer:
[tex]\huge \boxed{J=7}[/tex]
Step-by-step explanation:
Switch sides.
[tex]\displaystyle6j=42[/tex]
Divide by 6 from both sides.
[tex]\displaystyle \frac{6j}{6}=\frac{42}{6}[/tex]
Simplify, to find the answer.
[tex]\displaystyle 42\div6=7[/tex]
[tex]\huge \boxed{j=7}[/tex], which is our answer.