Answer:
Step-by-step explanation:
The GCF is the common "thing" in each one of the terms in our polynomial. Since 3 doesn't divide evenly out of 10, 3 is not a GCF. But b-squared is common in both. So for part A. the GCF is b-squared.
part B. Factor out the GCF:
[tex]b^2(3b+10)=0[/tex]
For part C. What are the solutions? The solutions are found in the Zero Product Property which states that if the factors of a polynomial, when multiplied together, equal 0, then either one of the factors or both of the factors have to equal 0 because 0 times anything equals 0. That means that
[tex]b^2=0[/tex] and/or 3b + 10 = 0
Solving the first equation:
[tex]b^2=0[/tex] and b = 0.
Solving the second equation:
3b + 10 = 0 and
3b = -10 so
[tex]b=-\frac{10}{3}[/tex]
Plz help me with my math
If the area is 10 square meters than double that is area of a rectangle with height = 5m and base of 4m because height • base should produce 20m^2.
Hope this helps.
Answer: base length = 4 metres
Step-by-step explanation:
A = ½bh
10m² = ½ * b * 5m
10 = 5b/2
Cross multiply
20 = 5b
b = 4m
Adam burns 225 calories per 30 minutes of bicycling how many calories in 10 mins.
Answer:
7.2
Step-by-step explanation:
You divide 225 by 30 and get 7.2
Answer:
c
Step-by-step explanation:
How does this polynomial identity work on numerical relationships?
(y + x) (ax + b)
Let us take 'a' in the place of 'y' so the equation becomes
(y+x) (ax+b)
Step-by-step explanation:
Step 1:
(a + x) (ax + b)
Step 2: Proof
Checking polynomial identity.
(ax+b )(x+a) = FOIL
(ax+b)(x+a)
ax^2+a^2x is the First Term in the FOIL
ax^2 + a^2x + bx + ab
(ax+b)(x+a)+bx+ab is the Second Term in the FOIL
Add both expressions together from First and Second Term
= ax^2 + a^2x + bx + ab
Step 3: Proof
(ax+b)(x+a) = ax^2 + a^2x + bx + ab
Identity is Found .
Trying with numbers now
(ax+b)(x+a) = ax^2 + a^2x + bx + ab
((2*5)+8)(5+2) =(2*5^2)+(2^2*5)+(8*5)+(2*8)
((10)+8)(7) =(2*25)+(4*5)+(40)+(16)
(18)(7) =(50)+(20)+(56)
126 =126
what is an equation in point-slope form of the line that passes through the given point and with the given slope m (-5,1);m=4
Equation for line: y=mx+b where m is the slope and b is the y-intercept
We have the slope. We just need to find the y-intercept. Plug in the point and the slope and solve for b.
y=mx+b
1=4(-5)+b
b=21
Answer: y=4x+21
Rewrite the equation by completing the square. x^2-20x+100 = 0
By completing the square, the equation x²- 20x + 100 = 0, we get, (x-10)²=0
Here, we have,
To rewrite the equation x² - 20x + 100 = 0 by completing the square, we can follow these steps:
Step 1: Move the constant term to the right side of the equation:
x² - 20x = -100.
Step 2: Take half of the coefficient of the x-term (-20/2 = -10) and square it to get (-10)² = 100.
Step 3: Add the result from step 2 to both sides of the equation:
x² - 20x + 100 = -100 + 100.
Simplifying:
x² - 20x + 100 = 0.
Step 4: Factor the left side of the equation. In this case, the left side is a perfect square trinomial:
(x - 10)² = 0.
Therefore, by completing the square, the equation x²- 20x + 100 = 0,
we get, (x-10)²=0
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Final answer:
The equation [tex]x^2 - 20x + 100 = 0[/tex] is already a perfect square and does not need to be completed. However, completing the square involves moving the constant to the other side, squaring half the coefficient of x, and solving for x, which leads us back to the original equation [tex](x - 10)^2 = 0[/tex] and reveals that x = 10.
Explanation:
The equation given is [tex]x^2 - 20x + 100 = 0[/tex]. This equation appears to already be a perfect square, as the constant term (100) is the square of half the coefficient of the x term (which is 10), thus completing the square is actually not needed. However, to illustrate the method of completing the square, let's ignore for a moment that it's already a perfect square and proceed with the steps:
Move the constant term to the right side of the equation: [tex]x^2 - 20x = -100.[/tex]Take half of the coefficient of x, which is -10, and square it, giving us 100.Add this square (100) to both sides of the equation, which yields [tex]x^2 - 20x + 100 = 0[/tex], the same as we started with.Now the left side is a square of (x-10): [tex](x - 10)^2[/tex] = 0.To solve for x, take the square root of both sides, giving us x - 10 = 0, which simplifies to x = 10.We've found that x = 10 is the solution to the equation, which is the same result you would get by recognizing the equation was already a perfect square in its original form.
Which of the following are solutions to 2x2 – 8x - 90? Select all that apply.
Answer:
x=-5, x=9
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]2x^{2} -8x-90[/tex]
equate to zero
[tex]2x^{2} -8x-90=0[/tex]
so
[tex]2=-1\\b=-8\\c=-90[/tex]
substitute in the formula
[tex]x=\frac{-(-8)\pm\sqrt{-8^{2}-4(2)(-90)}} {2(2)}[/tex]
[tex]x=\frac{8\pm\sqrt{784}} {4}[/tex]
[tex]x=\frac{8\pm28} {4}[/tex]
[tex]x=\frac{8+28} {4}=9[/tex]
[tex]x=\frac{8-28} {4}=-5[/tex]
therefore
The solutions are x=-5, x=9
1. Using n, n+1, and n+2 to represent three consecutive integers, write the statement of multiplying three consecutive integers and then adding the middle integer to the result of the multiplication as an expression.
2. Simplify the expression from problem 1 and write the answer in standard form.
3. Show that the answer from problem 2 is equivalent to the cube of the middle integer.
Answer:
1) Expression is
[tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]
2) The standard form of the expression is
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
3) The expression is
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
Where [tex](n+1)^3[/tex] is the cube of the middle integer
Step-by-step explanation:
1) Given three consecutive integers are n. n+1, and n+2
Now multiplying the three consecutive integers
[tex](n)(n+1)(n+2)=(n^2+n)(n+2)[/tex]
[tex]=n^3+2n^2+n^2+2n[/tex]
[tex]=n^3+3n^2+2n[/tex]
Therefore [tex](n)(n+1)(n+2)=n^3+3n^2+2n[/tex]
Now adding the middle integer to the result of the multiplication.
ie, adding (n+1) to the result of the multiplication [tex]n^3+3n^2+2n[/tex]
[tex](n+1)+(n^3+3n^2+2n)=n+1+n^3+3n^2+2n[/tex]
[tex]=3n+1+n^3+3n^2[/tex]
Therefore [tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]
2) Expression is [tex]n^3+3n^2+3n+1[/tex]
Now we simplify the above expression
[tex]n^3+3n^2+3n+1=n^3+3n^2(1)+3(n)(1)^2+1^3[/tex]
[tex]=(n+1)^3[/tex] (by using [tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex] , Here a = n and b=1)
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
3) The expression is
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
Where [tex](n+1)^3[/tex] is the cube of the middle integer.
ie, expression is equivalent to the cube of the middle integer
Is (-5,2), (5,2), (0,-3), (3,-8), (-7,4), (-1,-1) a function
Each point listed is of the form (x,y). The x coordinate is always listed first. We dont have any repeat x values, so this is enough to conclude we have a function.
If you wanted to, you could graph each point given on the same coordinate grid. Note how none of the points stack on top of each other. Or put another way, note how it is impossible to draw a single straight line through more than one point graphed. This graph passes the vertical line test.
A function is where plugging in any x value leads to exactly one y value.
If you had two points like (5,2) and (5,7) then the input x = 5 leads to more than one output y = 2 and y = 7 at the same time, making this example not a function.
if g(x) = 2x - 5 and h(x) = 3x + 7, then g(h(x)) = ?
Answer:
Step-by-step explanation:
g(h(x))=g(3x + 7). Since h(x)=3x + 7
g(h(x))= 2(3x + 7) - 5
g(h(x))= 6x + 14 -5
=6x +9
On a map, the distance from Los Angeles to San Diego is 6.35 cm. the scale is 1cm = 20 miles. What is the actual distance?
Answer:
The actual distance is 127 miles.
Step-by-step explanation:
Given:
On a map, the distance from Los Angeles to San Diego is 6.35 cm.
The scale is 1 cm = 20 miles.
Now, to find the actual distance.
Let the actual distance be [tex]x\ miles.[/tex]
And the distance on map is 6.35 cm.
So, 6.35 cm is equivalent to [tex]x\ miles.[/tex]
And as given on the scale 1 cm is equivalent to 20 miles.
Now, to get the actual distance by using cross multiplication method:
[tex]\frac{6.35}{x} =\frac{1}{20}[/tex]
By using cross multiplication we get:
⇒ [tex]127=x[/tex]
⇒ [tex]x=127\ miles.[/tex]
Therefore, the actual distance is 127 miles.
you want to buy a new phone. The sales prise is $149.The sign says that this is $35 less than the original cost. What is the original cost of the phone?
Answer:
$114
Step-by-step explanation:
Sales price = Original Cost - $35
Sales price - $35 = Original Cost
Substitute in known values
$149 - $35 = Original Cost
$114 = Original Cost
Hope this helps :)
Alan is conducting a survey to find out the type of art preferred by students in the town’s high school. Identify the population of his survey and describe a possible sample of the population.
The other answer is wrong the following is the sample response.
Answer:
Sample Response: The population of Alan's survey is all the students at the town's high school. The sample must be representative of the population. A possible sample would be an equal number of freshman, sophomores, juniors, and seniors.
Step-by-step explanation:
just finished the assignment and this was the sample response.
(please mark brainliest)
Have a great day!
Alan's survey population encompasses all students at the high school with art preferences. A sample could be randomly chosen from students from each grade or art class, reflecting the school's diversity and maintained by a random sampling method for fairness and representation.
Explanation:The population of Alan's survey is all the students at the town’s high school who have preferences for types of art. To conduct his survey, Alan needs to choose a sample, which is a smaller group from the population that can provide reliable information about the entire population's art preferences. An example of a possible sample would be selecting a certain number of students from each grade level or art class to ensure a variety of perspectives. It could also involve stratification by demographic characteristics such as age, gender, socioeconomic status, or ethnicity if these factors are believed to influence art preferences.
An efficient method to create a representative sample could be to use a random sampling technique where each student has an equal chance of being selected. For instance, Alan could use a random number generator to pick students from a list, or he might use a stratified random sampling by first dividing the student body into subgroups (such as by grade or art class) and then randomly selecting students from each subgroup.
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On a bike trip, you traveled 21 miles on
the second day. On the 3rd day, you traveled 3
second day.
e trip, you traveled 21 miles on the first day, and n miles on
y. On the 3rd day, you traveled 5 miles less than on the rest
a. Write an expression for the number of miles traveled in three day
b. Simplify the expression. Explain each step.
c. Find the number of miles traveled in three days when you traveled
19 miles on the second.
Answer:
She traveled 13 23/56 miles on the third day.
Step-by-step explanation:
HOPE THIS HELPED ;3
BRAINLIEST!!
Find the probability that a point chosen at random lies in the shaded region.
Answer:
0.60
Step-by-step explanation:
Again, we have a 10x10 space, which means there are 100 squares.
In this case, there are 60 shaded squares. This gives the probability of [tex]\frac{60}{100}[/tex] which simplifies to 0.60
Answer:
0.60
Step-by-step explanation:
Because there are 100 squares and 60 out of it is shaded if you chose a random point amongst these 100 square the probability of choosing a shaded one is 60/100 which is equal to 0.60.
find the area of the shape shown below
Answer:
6
Step-by-step explanation:
all you have to do is split the shape in half to create a square and a triangle then for the triangle the equation would be 2*2=4 then divide by 2 witch is 2 the do the square witch is 2*2=4 then you add 4+2=6 and i'm only in 7th grade.
Robert has seven more than five times the number of video games that Samuel has. The total number of video games that Robert and Samuel have is 25. How many video games does Robert have?
Answer: Robert has 22 video games.
Step-by-step explanation:
Let be "r" the number of video games that Robert has and "s" the the number of video games that Samuel has.
Set up a system of equations:
[tex]\left \{ {{r=5s+7} \atop {r+s=25}} \right.[/tex]
You can use the substitution method to solve the system:
- You need to substitute the first equation into the second equation and solve for "s":
[tex](5s+7)+s=25\\\\6s=25-7\\\\s=\frac{18}{6}\\\\s=3[/tex]
- Finally you must substitute the value of "s" into the first equation and evaluate:
[tex]r=5(3)+7\\\\r=22[/tex]
Answer:3
Step-by-step explanation:
5x+7=25
So lets subtract 7 from 25 to get 5x alone...
5x=18
5x/5=x
18/5=3.3
You cant have 0.3 of a video game so the answer is 3
80 Point Offer, Help is required on these questions. Highest offer I've given.
Answer:
Answer 1.) f(x)=0x-4
Answer 2.) f(x)=2/3x+4
Answer 3.) i don't really get this one so sorry
Answer 4.) f(x)= -1/5x+2
hope this helped it took me a while to figure out this but looks like the guy ahead of me beat me to it
Step-by-step explanation:
Solve
2w+2(w+3.8)=58
Answer:
w=12.6
Step-by-step explanation:
2w+2(w+3.8)=58
2w+2w+7.6=58
4w+7.6=58
4w=58-7.6
4w=50.4
w=50.4/4
w=12.6
Does anyone know how you work out this bearings question???
The bearing of A from B according to the diagram is 82.86°
Using trigonometric relations ;
Tan B = opposite/ AdjacentB = bearing of A from B
Now we have;
Tan B = 40 /5
Tan B = 8
Take the inverse value of the tangent ;
[tex]B = Tan^{-1} (8) [/tex]
B = 82.86°
Hence, the bearing of A from B is 82.86°
In the equation 3/4y+1/2=3 1/4, the fractional coefficient is what
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Given equation: [tex]\frac{3}{4}y + \frac{1}{2} = 3 \frac{1}{4}[/tex]
In the given equation, [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable.
coefficient is a constant number or quantity multiplied to a variable in an algebric expression. Like in the above equation [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable. We use term variable for y as its value may vary or change. If variable does not have any coefficient in any expression then in that case, we consider 1 as coefficient, for example: [tex]x+4[/tex], here variable have 1 as coefficient.
Hence, the fractional coefficient is [tex]\frac{3}{4}[/tex].
A bag contains 1 blue, 2 green, 3 yellow, and 3 red marbles, as shown.
What is the probability of drawing a red marble out of the bag without looking?
10
CVO
-10
-ICV
The probability of drawing a red marble out of the bag without looking is 1/3.
Explanation:The probability of drawing a red marble out of the bag without looking can be calculated by dividing the number of red marbles by the total number of marbles in the bag. In this case, there are 3 red marbles out of a total of 9 marbles, so the probability is 3/9, which simplifies to 1/3.
What expression will Help me find 4% of 25
57, 59, 64, 72, 76, 77, 77, 78, 85, 87, 88, 88, 88, 92, 94, 96, 98, 100
Find the Median of the data set
Answer:
82
Step-by-step explanation:
Mean of a set of data is simply the average. It's calculated by adding up all the numbers, then divide by how many numbers there are.
57 + 59 + 64 + 72 + 76 + 77 + 77 + 78 + 85 + 87 + 88 + 88 + 88 + 92 + 94 + 96 + 98 + 100 = 1,476
1476/18 = 82
Therefore 82 is the mean of the set of numbers
Answer:
Median = 86
Step-by-step explanation:
the middle of the data set is 85 and 87. to find the median you would do 85+87/2= 172/2 median = 86
what is the differance look at the link
Answer:
The difference is [tex]\frac{3}{4}[/tex] inches.
Step-by-step explanation:
See the attached number line where the worm lengths in inches are plotted.
From the number line plotted in the attached photo, it is clear that the shortest worm has the length of [tex]\frac{3}{4}[/tex] inches and the longest worm has the length of [tex]1\frac{1}{2}[/tex] inches i.e. [tex]\frac{3}{2}[/tex] inches.
Therefore, the difference in length between the shortest and longest worm is [tex](\frac{3}{2} - \frac{3}{4}) = \frac{3}{4}[/tex] inches. (Answer)
A relation is plotted as a linear function on the coordinate plane starting at point A (0, 3) and ending
at point B (2, 7)
What is the rate of change for the linear function and what is its initial value?
Answer:
initial value=2
Step-by-step explanation:
equation of line,
y-[tex]y_1[/tex]=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex][tex](x-x_1)[/tex]..............(1)
put co ordinate (0,3) and (2,7) in the equation (1)
y-3=[tex]\frac{7-3}{2-0}[/tex](x-0)
y-3=2x
y=2x+3
rate of change of linear equation=[tex]\frac{\partial (2x+3)}{\partial x}[/tex]
[tex]\frac{\partial y}{\partial x}[/tex]=2
hence, initial value=2 answer
Demuestra que al utizar agrupaciones de terminos para factorizar el polinomio 6a2,+15a-4a-10 la respuesta es( 2a+5)(3a-2)
Answer:
Step-by-step explanation:
Given ƒ(x) = −12x + 72, find x when ƒ(x) = 24. A) 1 B) 3 C) 4 D) 6
will give brainliest
Answer:
if f(x)=24
24=-12x+72
24-72=-12x
-48=-12x
x=48/12
x=4
so it's (C)
Answer:
x=4; Option C is your answer.
Step-by-step explanation:
Plug in 24:
[tex]f(x)=24\\[/tex]
[tex]24=-12x+72[/tex]
Solve For X:
[tex]-12x+72-72=24-72\\-12x=-48\\\frac{-12x}{-12} =\frac{-48}{-12}\\ x=4[/tex]
Find the sum of the first 56 terms of the following sequence {-8, -1, 6, ...}
A. 10,332
B. 1,344
C. 10,584
Answer:
A
Step-by-step explanation:
Given sequence [tex]-8,\ -1,\ 6,\ ...[/tex]
In this sequence,
[tex]a_1=-8\\ \\a_2=-1\\ \\a_3=6\\ \\...[/tex]
Hence,
[tex]d=a_2-a_1=-1-(-8)=7\\ \\d=a_3-a_2=6-(-1)=7[/tex]
Find 56th term:
[tex]a_{n}=a_1+(n-1)\cdot d\\ \\a_{56}=-8+(56-1)\cdot 7\\ \\a_{56}=-8+385\\ \\a_{56}=377[/tex]
The sum of 56 terms is
[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n\\ \\S_{56}=\dfrac{-8+377}{2}\cdot 56=\dfrac{369}{2}\cdot 56=369\cdot 28=10,332[/tex]
plz hurry!!!! thank you!!!!
Answer:
[tex]m\angle KLM=53.13^o[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of angle KOM
In the triangle KOM
we have
[tex]KO=MO=r=5\ units[/tex]
[tex]KM=8\ units[/tex]
Applying the law of cosines
[tex]8^2=5^2+5^2-2(5)(5)cos(KOM)[/tex]
[tex]64=50-50cos(KOM)[/tex]
[tex]50cos(KOM)=50-64[/tex]
[tex]50cos(KOM)=-14[/tex]
[tex]cos(KOM)=-14/50[/tex]
[tex]m\angle KOM=cos^{-1}(-14/50)[/tex]
[tex]m\angle KOM=106.26^o[/tex]
step 2
Find the measure of the arc KM
we know that
[tex]arc\ KM=m\angle KOM[/tex] ----> by central angle
we have
[tex]m\angle KOM=106.26^o[/tex]
so
[tex]arc\ KM=106.26^o[/tex]
step 3
Find the measure of angle KLM
we know that
The inscribed angle is half that of the arc comprising
[tex]m\angle KLM=\frac{1}{2}[arc\ KM][/tex]
we have
[tex]arc\ KM=106.26^o[/tex]
substitute
[tex]m\angle KLM=\frac{1}{2}[106.26^o][/tex]
[tex]m\angle KLM=53.13^o[/tex]
Higher Order Thinking A mother
manatee, pictured to the right, is three
times as long as her baby manatee.
a. How long is her baby manatee? Write
and solve an equation.
b. If a blue whale is 9 times as long as the
manatee shown, how much longer is
a blue whale than the manatee? Write
and solve equations.
12 feet
The equation for baby manatee is 3x = 12 and length is 4 feet and length of blue whale is 108 feet.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have given:
Length of Mother manatee = 12 feet.
Let's suppose the length of a baby manatee is 'x'.
So the equation can be framed as:
3x = 12
x = 4 feet
The length of blue whale is = 9(length of mother manatee)
The length of blue whale is = 9(12) = 108 feet
Thus, the equation for baby manatee is 3x = 12 and length is 4 feet and length of blue whale is 108 feet.
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