The expression (5y+4)*(-2y+6) simplifies to -10y² + 22y + 24 when multiplied out using the distribution method. Note, it's very important to use the correct syntax when writing mathematical expressions, clarity helps avoid mistakes.
Explanation:Your question appears to be asking for the result of multiplying two polynomial expressions. However, your question contains a syntax error. It should properly be written as '(5y+4)*(-2y+6)'.
To find the result, you can use the distribution method also known as the FOIL method(First, Outer, Inner, Last). Let's walk through this step by step.
First: Multiply the first terms in each binomial: 5y*-2y=-10y²
Outer: Multiply the outer terms: 5y*6=30y
Inner: Multiply the inner terms: 4*-2y=-8y
Last: Multiply the last terms: 4*6=24
So we have -10y² + 30y - 8y + 24. Combine like terms to get the final answer: -10y² + 22y + 24.
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Express the given logarithm in terms of common logarithms. Then approximate its value to four decimal places.
log2 11
Answer:
3.4594
Step-by-step explanation:
To change the base of a logarithm
• [tex]log_{b}[/tex] x = [tex]\frac{log_{c}x }{log_{c}b }[/tex]
where c represents the new base
Changing the base from 2 to 10
[tex]log_{2}[/tex] 11 = [tex]\frac{log_{10}11 }{log_{10}2 }[/tex] ≈ 3.4594
What is the sum of the series?
For this case we must find the sum of the given series. For this we must expand the series for each value of k.
[tex](-2 (3) +5) + (- 2 (4) +5) + (- 2 (5) +5) + (- 2 (6) +5) =\\(-6 + 5) + (- 8 + 5) + (- 10 + 5) + (- 12 + 5) =[/tex]
Different signs are subtracted and the sign of the major is placed, while equal signs of sum and the same sign is placed.
[tex]-1-3-5-7 =\\-16[/tex]
The value of the series is -16
ANswer:
-16
Heya!
--------------------
Things to know before we solve:
The "6" at the top means that the the sequence only goes to the 6th term.
k = 3 represents that the sequence starts with the 1st term.
(-2k + 5) represents the rule of the sequence, we can substitute 3, 4, 5, and 6 to solve for the terms of the sequence.
--------------------
Solving for each term:
3rd term:
-2(3) + 5
-6 + 5
-1
4th term:
-2(4) + 5
-8 + 5
-3
5th term:
-2(5) + 5
-10 + 5
-5
6th term:
-2(6) + 5
-12 + 5
-7
--------------------
Simplifying:
Write these terms in expanded form:
(-1) + (-3) + (-5) + (-7)
Find the sum of the series:
(-1) + (-3) + (-5) + (-7) = -16
--------------------
Answer:
The sum of the series is -16
--------------------
Best of Luck!
which equation can be used to solve for b?
Answer:
First option
b = (8) * Tan (30)
Step-by-step explanation:
Tan (B) = Oppo. / Adj.
Tan (B) = AC/BC
Tan (30) = b / 8
b = (8) * Tan (30)
Answer
First option
b = (8) * Tan (30)
PLEASE HELP!
The water tank in the diagram is in the shape of an inverted right circular cone. The radius of its base is 16 feet, and its height is 96 feet. What is the height, in feet, of the water in the tank if the amount of water is 25% of the tank’s capacity?
Answer:
The height of the water is [tex]60.5\ ft[/tex]
Step-by-step explanation:
step 1
Find the volume of the tank
The volume of the inverted right circular cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]r=16\ ft[/tex]
[tex]h=96\ ft[/tex]
substitute
[tex]V=\frac{1}{3}\pi (16)^{2} (96)[/tex]
[tex]V=8,192\pi\ ft^{3}[/tex]
step 2
Find the 25% of the tank’s capacity
[tex]V=(0.25)*8,192\pi=2,048\pi\ ft^{3}[/tex]
step 3
Find the height, of the water in the tank
Let
h ----> the height of the water
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
[tex]\frac{R}{H}=\frac{r}{h}[/tex]
substitute
[tex]\frac{16}{96}=\frac{r}{h}\\ \\r= \frac{h}{6}[/tex]
where
r is the radius of the smaller cone of the figure
h is the height of the smaller cone of the figure
R is the radius of the circular base of tank
H is the height of the tank
we have
[tex]V=2,048\pi\ ft^{3}[/tex] -----> volume of the smaller cone
substitute
[tex]2,048\pi=\frac{1}{3}\pi (\frac{h}{6})^{2}h[/tex]
Simplify
[tex]221,184=h^{3}[/tex]
[tex]h=60.5\ ft[/tex]
a school is running a fundraiser. for every $75 worth of wrapping paper sold, the school receives $20. how much wrapping paper must be sold to reach he fundraising goal of $2,500
Answer:
$9259.26
Step-by-step explanation:
The school receives $20 on $75.
We can calculate the percentage by using the values.
20/75 = 0.27%
The school recieved 0.27% of the payment.
Now we know the target amount and percentage, we can calculate the principal amount here.
Let x dennote the worth on which the school will recieve 2500 dollars. [tex]2500 = x * 0.27\\x = \frac{2500}{0.27}\\ x = 9259.26[/tex]
$9259.26 worth of ribbon has to be sold for the school to get $2500 ..
plz help god blees if you do it all i will give u BRAINLIEST
it's the first one !!! so it's A
Find the distance between the points ( - 16, - 9) and ( - 16, - 18).
notice, the x-coordinate is the same for both points, thus is a vertical line.
Check the picture below.
To find the distance between the points (-16, -9) and (-16, -18), subtract the y-coordinates, which gives us a distance of 9 units.
To find the distance between the points (-16, -9) and (-16, -18), we can use the distance formula for two points in a Cartesian coordinate system. However, because the x-coordinates of the two points are the same, this means that the line connecting these two points is vertical, and we can simply subtract the y-coordinates to find the distance.
The distance formula in a two-dimensional Cartesian coordinate system is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Since the x-coordinates are identical, the formula simplifies to:
d = |y₂ - y₁|
Applying this to the points given:
d = |-18 - (-9)|
d = |-18 + 9|
d = |-9|
Therefore, the distance is 9 units.
Daniel looks at the prices of 5 guitars. The prices are $137, $159, $127, $188 and $680. These prices contain one extreme value ($680). Which measure of center should Daniel use to describe the prices?
A. Median
B. Range
C. Mean
D. Mean absolute deviation
Answer:
A. Median
Step-by-step explanation:
Mean and median both are used to measure the central tendency of a given data while range gives us the spread of the data roughly.
Mean is even affected by a single extreme value in the data while median gives us the central value of data even when there are extreme values.
The given set of five prices has one extreme value which will affect the mean. While median is a better option to measure the central tendency of data.
So Daniel will use median to measure the central tendency to describe the prices..
Step-by-step explanation:
Answer is A. Median by jesse
You ask a friend to think of a
number from four to twelve. What
is the probability that his number
will be 8?
The answer is 1/9 or about 11%.
Answer:8
Step-by-step explanation: it’s right
Factor by grouping: x^3 + 3x^2 - 25x -75 Which of the following is one of the factors?
Answer:
Final factor is [tex](x + 3)(x+5)(x-5)[/tex].
Step-by-step explanation:
Given expression is [tex]x^3 + 3x^2 - 25x -75[/tex]
Now we need to factor that expression [tex]x^3 + 3x^2 - 25x -75[/tex] by grouping. So let's make group of first two terms and group of last two terms.
[tex]x^3 + 3x^2 - 25x -75[/tex]
[tex]=(x^3 + 3x^2)+( - 25x -75)[/tex]
factor each group
[tex]=x^2(x + 3)-25(x +3)[/tex]
[tex]=(x + 3)(x^2-25)[/tex]
[tex]=(x + 3)(x+5)(x-5)[/tex]
Hence final factor is [tex](x + 3)(x+5)(x-5)[/tex].
I got the Same answer
Over a period of 12 weeks, Carlos ran an average of 21 miles per week. How many kilometers is this? Round your answer to the nearest hundredth. (1 km = 0.621 mi.)
405.80
13.04
33.82
156.49
Answer:
405.80
Step-by-step explanation:
So, we know Carlos ran 21 miles per week, for 12 weeks....
That makes 21 mi/wk x 12 weeks = 252 miles.
Then we know each km is 0.621 mile.
So, we divide 252 miles by 0.621 mile/km to get= 405.80 km
Dividing miles by miles/km gives us the unit we want (km).
There was a trap in this question, because if instead of dividing the 252 miles by 0.621 you would have multiplied it, you would have gotten another answer listed... just not the right one. :-)
Winona’s bowling scores for the past nine weeks are 195, 180, 195, 212, 208, 231, 179, 246, and 195. Find the mean, median, and mode. Round to the nearest tenth, if necessary.
Winona's bowling scores have a mean of 204.6, a median and mode both of 195.
To find the mean, median, and mode of Winona's bowling scores, we follow these steps:
Mean: Add all the scores together and divide by the number of scores.Median: Arrange the scores in ascending order and find the middle score.Mode: Identify the score that occurs most frequently.The bowling scores are 195, 180, 195, 212, 208, 231, 179, 246, and 195.
Mean: (195 + 180 + 195 + 212 + 208 + 231 + 179 + 246 + 195) / 9 = 1841 / 9 = 204.6
The mean score is 204.6.
To find the median, we first arrange the scores in ascending order: 179, 180, 195, 195, 195, 208, 212, 231, 246.
The median, or the middle score, is the fifth one since there are an equal number of scores on either side of it, which is 195.
The mode is the number that appears most often, which is also 195.
Therefore, Winona's mean score is 204.6, the median score is 195, and the mode is 195.
What is the 6th term of this sequence? 8,-12,18-27
Answer:
-60.75
Step-by-step explanation:
-12 / 8 = -3/2
18 / -12 = -3/2
-27 / 18 = -3/2
This is a geometric sequence with a common ratio of -3/2.
an = 8 (-3/2)^(n-1)
The sixth term is:
a₆ = 8 (-3/2)^(6-1)
a₆ = 8 (-3/2)^5
a₆ = -60.75
I need to know what is 7 percent of 98800
Answer:6,916
6,916
How to find the number:
The decimal of seven percent is 0.07. Take that times 9880
Line t intersects the line given by y=4x-2 at the point (4,14) to form a right angle. Which is the equation of line t
Answer:
y = -1/4 x + 15.
Step-by-step explanation:
y = 4x - 2 has a slope of 4 ( = the coefficient of x).
The line at right angles to it will therefore of a slope of -1/4.
Using the point-slope form of a line the line t which passes through (4, 14) is found as follows:
y - 14 = -1/4(x - 4)
y = -1/4x + 1 + 14
y = -1/4x + 15
In the triangles, and . Which statement correctly compares the angles? Angle G is congruent to angle P. Angle G is smaller than angle P. Angle G is larger than angle P. Angle G is congruent to angle N.
Answer:
B) Angle G is smaller than angle P.
Step-by-step explanation:
It's logic, the only way the hypotenuse could be shorter is if the angle opposite of it is more acute.
I know that's a mouthful and probably sounds really weird but just trust me.
Would appreciate brainliest, new to brainly! good luck!
The correct option is, (B) Angle G is smaller than angle P.
It's logic, the only way the hypotenuse could be shorter is if the angle opposite of it is more acute.
What is called triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.A triangle is also a polygon.Some real-life examples of triangles include sandwiches, traffic signs, cloth hangers, and a rack in billiards.What is triangle and its types?Triangles are shapes with three sides.There are different names for the types of triangles.A triangle's type depends on the length of its sides and the size of its angles (corners).There are three types of triangle based on the length of the sides: equilateral, isosceles, and scalene.
What is triangle shape?In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices.The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.This property is called angle sum property of triangle.
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Find the sum of the measures of the interior angles of each convex polygon decagon
Answer:
Nvm about those questions the answer is 1440 degrees
Step-by-step explanation:
The volume of a sphere is 3052.08 units cubed what is its diameter?
The diameter of the sphere is approximately 19.82 units.
To calculate the diameter of a sphere given its volume, we'll use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3}\pi r^3 \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume of the sphere,
- [tex]\( \pi \)[/tex] is a mathematical constant (approximately equal to 3.14159),
- [tex]\( r \)[/tex] is the radius of the sphere.
Since we have the volume, we rearrange the formula to solve for the radius:
[tex]\[ r = \sqrt[3]{\frac{3V}{4\pi}} \][/tex]
Substituting the given volume [tex]\( V = 3052.08 \)[/tex], and the value of[tex]\( \pi \)[/tex], we can find the radius:
[tex]\[ r = \sqrt[3]{\frac{3 \times 3052.08}{4 \times 3.14159}} \][/tex]
[tex]\[ r \approx \sqrt[3]{\frac{9156.24}{12.56636}} \][/tex]
[tex]\[ r \approx \sqrt[3]{729.128} \][/tex]
[tex]\[ r \approx 9.85 \][/tex]
Now, to find the diameter, we double the radius:
[tex]\[ \text{Diameter} = 2 \times r \][/tex]
[tex]\[ \text{Diameter} = 2 \times 9.85 \][/tex]
[tex]\[ \text{Diameter} \approx 19.82 \][/tex]
So, the diameter of the sphere is approximately 19.82 units.
To recap, we first found the radius of the sphere using the formula for volume, then we doubled the radius to find the diameter.
Complete question:
The volume of a sphere is 3052.08 units cubed what is its diameter?
17400 invested at a rate of 2.5% compounded annually; 8 years
Answer:
348
Step-by-step explanation:
if f(x) =-x^2+3x+5 and g(x)=x^2+2x, which graph shows the graph of (f+g)(x)?
For this case we have the following functions:
[tex]f (x) = - x ^ 2 + 3x + 5\\g (x) = x ^ 2 + 2x[/tex]
We must find (f + g) (x), by definition we have to:
[tex](f + g) (x) = f (x) + g (x)[/tex]
So:
[tex](f + g) (x) = - x ^ 2 + 3x + 5 + (x ^ 2 + 2x)\\(f + g) (x) = - x ^ 2 + 3x + 5 + x ^ 2 + 2x\\(f + g) (x) = 5x + 5[/tex]
ANswer:
See attached image
Answer:
Step-by-step explanation:
see graph below
The graph below is correct for the linear equation y=-3.
True
False
Answer:
False.
Step-by-step explanation:
The graph that is shown is correct for the equation x= -3. The graph for y= -3 would run vertically, not horizontally.
Answer:
True
Step-by-step explanation:flip it and reverse it its esrever dna ti pilf
Write an equation for the line that passes through (-8.5,11) and (5,-2.5)
Answer:
The equation is y = -x + 2.5
Step-by-step explanation:
* Lets explain how to solve the problem
- The form of the equation of a line is y = mx + c , where m is the slope
of the line and c is the y-intercept
- The y-intercept means the line intersect the y-axis at point (0 , c)
- The slope of the line which passes through points (x1 , y1) , (x2 , y2)
is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
* Lets solve the problem
∵ The line passes through the points (-8.5 , 11) and (5 , -2.5)
- Let point(x1 , y1) = (-8.5 , 11) and point (x2 , y2) = (5 , -2.5)
∴ x1 = -8.5 , x2 = 5 and y1 = 11 , y2 = -2.5
∴ [tex]m=\frac{-2.5-11}{5-(-8.5)}=\frac{-13.5}{5+8.5}=\frac{-13.5}{13.5}=-1[/tex]
∴ The slope of the line is -1
∵ y = mx + c
∴ y = -x + c
- To find c substitute x and y in the equation by the coordinates of
one of the two points
∵ Point (5 , -2.5) lies on the line
∴ x = 5 at y = -2.5
∵ y = -x + c
∴ -2.5 = -(5) + c
∴ -2.5 = -5 + c
- Add 5 to both sides
∴ c = 2.5
∴ y = -x + 2.5
* The equation is y = -x + 2.5
The slope and y-intercept to get y = -x + 2.5.
The slope is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Substituting the given points into the formula, we get m = (-2.5 - 11) / (5 - (-8.5)) = -13.5 / 13.5 = -1.
Next, we use the slope-intercept form of a line, y = mx + b, to find the y-intercept (b). Substituting one of the points and the slope into this equation, for example, (-8.5, 11), gives us 11 = (-1)(-8.5) + b, which simplifies to b = 2.5.
Therefore, the equation of the line is y = -x + 2.5.
COSO ---
(3-
O Example: Find the a
a) u =<4,3% and v= <2,5)
calculator
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35. Determine the values of x that cause the polynomial function to be zero, positive, and negative:
f(x) = (x-7)(3x + 4)(x + 4).
Answer:
• zero: -4, -4/3, 7
• positive: -4 < x < -4/3 . . . or 7 < x
• negative: x < -4 . . . or -4/3 < x < 7
Step-by-step explanation:
Zeros of the function are at x=-4, -4/3, +7. These are the values that make each of the individual factors be zero. For example, x-7=0 when x=7.
The function will be negative for x-values left of an odd number of zeros. It will be positive for x-values left of an even number of zeros (including left of no zeros, which is to say right of all zeros). This is because the sign of the factor giving rise to the zero changes for x-values on either side of that zero. (This is not true for zeros with even multiplicity, as the sign does not change at those.)
i need help im stuck on this
Hello There!
Before getting started, we should remember that the top surface and the bottom surface of any cylinder are congruent to each other.
First, we use the formula pi*radius^2 to find the area of a circle since there is always a circle in a cylinder.
Next, we multiply pi*radius^2 * height because a cylinder has a height too.
HOW TO SOLVE
First, we multiply 3.14 which is equal to pi by 25 because the radius is 5 and in the formula we used, it states radius squared so 3.14 multiplied by 25 and then multiplied by the height of our cylinder which equals 6.
Once we multiply, we get a product of 471.
Our final answer is 471.units^3
The price of a gallon of unleaded gas was $2.83 yesterday. Today, the price rose to $2.88 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
The percentage increase from yesterday's gas price to today's price is 1.8%.
Explanation:To find the percentage increase from yesterday's price to today's price, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100.
The difference between $2.88 and $2.83 is $0.05. Dividing $0.05 by $2.83 gives us 0.0176. Multiplying by 100 gives us 1.76%. Rounding to the nearest tenth of a percent, the percentage increase is 1.8%.
Please help I'm very confused
30 ≥ g [keyword - "no more than"
4 ≤ i [keyword - "at least"]
Which is a solution for this equation? Log base 2 x = 2 - log base 2 (x - 3)
X = 1
X = 2
X = 3
X = 4
X = 5
Answer: Fourth Option
[tex]x =4[/tex]
Step-by-step explanation:
First we write the equation
[tex]log_2(x) = 2- log_2(x-3)[/tex]
Now we use the properties of logarithms to simplify the expression
[tex]log_2(x)+log_2(x-3) = 2[/tex]
The property of the sum of logarithms says that:
[tex]log_a (B) + log_a (D) = log_a (B * D)[/tex]
Then
[tex]log_2[x(x-3)]= 2[/tex]
Now use the property of the inverse of the logarithms
[tex]a ^ {log_a (x)} = x[/tex]
[tex]2^{log_2[(x)(x-3)]}= 2^2[/tex]
[tex](x)(x-3))}= 4[/tex]
[tex]x^2-3x -4=0[/tex]
[tex]x^2-3x -4=(x-4)(x+1)=0[/tex]
Then the solution are
[tex]x= -1[/tex] and [tex]x= 4[/tex]
We take the positive solution because the logarithm of a negative number does not exist
Finally the solution is:
[tex]x =4[/tex]
Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?
x2(x – 9) – 5(x – 9)
x2(x + 9) – 5(x + 9)
x(x2 + 5) – 9(x2 + 5)
x(x2 – 5) – 9(x2 – 5)
Answer:
C
Step-by-step explanation:
x(x2 + 5) – 9(x2 + 5)
= x³ + 5x - 9x² - 45
(try to expand one by one of the answer given)
Answer:
x(x2 + 5) – 9(x2 + 5)
Step-by-step explanation:
Question 30
Find the length of the long leg. Leave answer in simplest radical form.
Help plz
Use SOHCAHTOA. You must use sine or cosine since the hypotenuse is involved, but since you are given both angles, it does not matter which one of them you choose. We'll use sine:
sinx=O/H
sin60=O/14
√3/2=O/14
*Cross multiply*
(14√3)=2O
*Divide both sides by 2*
7√3=O
Hope this helps!!
Answer:
B
Step-by-step explanation:
Since the triangle is right we can use the sine ratio to find TI along with
the exact value of sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{TI}{TR}[/tex] = [tex]\frac{TI}{14}[/tex]
Multiply both sides by 14
TI = 14 × sin60° = 14 ×[tex]\frac{\sqrt{3} }{2}[/tex] = 7[tex]\sqrt{3}[/tex]
kate has 567 cars she put 77 on each table how many cars does she have left
Answer:
well how many tables are there?
Step-by-step explanation: