Answers
Factored Form is (x+4)(x+2)
Expanded Form is x^2+6x+8
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Explanation:
The factored form is simply a matter of reading off the values from the given image. There isn't much work to show here.
Along the left side we have x and 4 so x+4 is one of the factors. Along the bottom we have x and 2, so x+2 is another factor
The two factors are (x+4) and (x+2) so that's why the factored form is (x+4)(x+2)
-------------------------------
Let's expand out the factored form
The overall rectangle is broken up into four parts. I'll label the four smaller rectangles as...
Rectangle A in the upper left corner (this rectangle is x by x)
Rectangle B in the upper right corner (this rectangle is 2 by x)
Rectangle C in the lower left corner (this rectangle is x by 4)
Rectangle D in the lower right corner (this rectangle is 2 by 4)
The idea is that adding the areas of rectangles A through D leads us to the overall area for this largest rectangle.
Area of Rectangle A = (length)*(width) = x*x = x^2
Area of Rectangle B = (length)*(width) = 2*x = 2x
Area of Rectangle C = (length)*(width) = x*4 = 4x
Area of Rectangle D = (length)*(width) = 2*4 = 8
Notice we have the like terms 2x and 4x (areas of rectangle C and D respectively). They combine to 2x+4x = 6x
So after adding all the individual areas and combining like terms, we arrive at the fully expanded form of x^2+6x+8
Related Questions
Find the equation of line passing through (-7,-9) and parallel to the 8x-9y+2=0
Answers
8x - 9y + 2 = 0
9y = 8x + 2
y = [tex] \frac{8}{9}x + \frac{2}{9} [/tex]
Since the equation of this line is parallel to the one to be found, both have the same slopes: [tex] \frac{8}{9} [/tex]
Coordinates : ( - 7 , - 9 )
y - ( -9 ) = [tex] \frac{8}{9} [/tex] ( x - ( -7 ) )
y + 9 = [tex] \frac{8}{9}x + \frac{56}{9} [/tex]
y = [tex] \frac{8}{9}x + \frac{56}{9} - 9 [/tex]
y = [tex] \frac{8}{9}x - \frac{25}{9} [/tex]
The expression square root of 576/64 in simplest form is
Answers
I see you have doubts, so I will explain each step.
Step 1: simpliy 576 / 64. In this case when you divide 576 by 64 you get 9 that is a whole number, so that is its simplest form.
Step 2: Calculate the square root of 9, which is 3.
If you use a simple calculator you will obtain that, but the square root of 9 is a calculation that you should know by yourself.
Remember that the square root a number N is the number that multiplied by itself results in the number N. For example the squere root of 4 is 2, because 2 times 2 is 4. So, the square root of 9 is 3 because 3 times 3 is 9.
It will be very helpful for you to learn the 12 first squares because with that you will be able to tell the square roots of the most elemental numbers:
1^2 = 1 => √1 = 1
2^2 = 4 => √4 = 2
3^2 = 9 => √9 = 3
4^2 = 16 => √16 = 4
5^2 = 25 => 25 = 5
6^2 = 36 => √36 = 6
7^2 = 49 => √49 = 7
8^2 = 64 => √64 = 8
9^2 = 81 => √81 = 9
10^2 = 100 => √100 = 10
11^2 = 121 => √121 = 11
12^2 = 144 => √144 = 12
Answer:
Just did it
The answer is 3
Step-by-step explanation:
PLEASE HELP ME QUICK PLEASE!!!!!!
10 PTS ILL GIVE BRAINLIEST IF U ANSWER CORRECTLY
THX
Answers
Only constraint 1 would be met if 6 vanilla cups and 18 chocolate cups were purchased
Rob and john share money in a ratio of 9:4. How much of the £39000 does john get ?
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Last month, the seventh grade and eighth grade math classes at Moore Middle School collected canned goods for the local food shelter. The dot plots below show the number of canned goods collected by the classes.
The mean absolute deviation for each grade level is 1.6. The difference between the mean number of canned goods collected by each grade level is how many times the mean absolute deviation?
A. 5
B. 4
C. 3
D. 6
Answers
Mean of 7th grade class is:
420/20=21
Mean of 8th grade class:
325/25=13
21-13=8
To find how many times , divide 8 by 1.6.
8/1.6= 5 times
The difference of the means is 5 times the MAD (mean absolute deviation).
Suppose a sheet of 100 stamps is 0.77 millimeters thick. If a stack of sheets contains 100,000 stamps, how many millimeters thick is the stack? Write the answer in scientific notation.
7.7 × 104 mm
0.77 × 103 mm
7.7 × 102 mm
77.0 × 101 mm
Answers
To find the thickness of the stack, multiply the thickness of a single sheet by the number of sheets. So, 0.77 mm times 1,000 equals 770 mm. In scientific notation, this is 7.7 × 10² mm.
Explanation:To find out how many millimeters thick the stack is, you need to multiply the thickness of a single sheet of stamps by the number of sheets in the stack. In this case, the thickness of a single sheet is 0.77 millimeters, and there are 1,000 sheets in the stack (since 100,000 stamps divided by 100 stamps per sheet is 1,000).
To represent the thickness of the stack in scientific notation, you would multiply the thickness of a single sheet (0.77) by the number of sheets in the stack (1,000). Multiplying 0.77 by 1,000 gives you 770. To represent this in scientific notation, you would break it down into a number between 1 and 10 multiplied by a power of 10. So, the thickness of the stack is 7.7 × 10² mm.
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Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection y=x+2 y=−12x+5
Answers
Help a fella out. Explain this to me.
Answers
HELLO
add x with exponent 2 to 5x then you get 6x with exponent 2
(if there one x with out a number it = 1x)
change the exponent like time it by its base so its 6*6=36
answer 36x +6 I think the answer is b or c I'm not very sure
have a wonderful Wednesday
can I get brainlest plz
Solve for x: x^19 − 2x^18 + 7x^17 − 12x^6 + 6x^15 = 0
A) 0,1, +/-6i
B) -1,0, +/-√6i
C)-1, 0, +/-6i
D) 0,1, +/-√6i
Answers
x¹⁹ -2x¹⁸ +7x¹⁷ -12x¹⁶ +6x¹⁵ = 0
x¹⁵(x -1)²(x² +6) = 0
x = 0, 1, ±(√6)i . . . . . . . selection D is appropriate
I Really Need Help With This Problem, Please
Listed in the Item Bank are key terms and expressions, each of which is associated with one of the columns. Some terms may display additional information when you click on them. Drag and drop each item into the correct column. The order does not matter.
Answers
1 and 8 are alternate exterior
2 and 6 are corresponding
2 and 7 are alternate exterior
3 and 5 are alternate interior
3 and 6 are consecutive interior
3 and 8 are corresponding
4 and 5 are consecutive interior
4 and 6 are alternate interior
4 and 7 are corresponding
Corresponding angles : 1 & 5 , 2 & 6 , 4 & 7 , 3 & 8 .
Alternate interior angles : 4 & 6 , 3 & 5
Alternate exterior angles : 1 &8 , 2 & 7
Consecutive interior angles : 4 & 5, 3 & 6
Step-by-step explanation:The corresponding angles are the angles that are in the same position made by a line cutting through two or more other lines.The alternate interior angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal. The alternate exterior angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal. The consecutive interior angles are the pair of angles which are formed on one side of the transversal when two lines are intersected by transversal line .By using the above definitions,
Corresponding angles : 1 & 5 , 2 & 6 , 4 & 7 , 3 & 8 .
Alternate interior angles : 4 & 6 , 3 & 5
Alternate exterior angles : 1 &8 , 2 & 7
Consecutive interior angles : 4 & 5, 3 & 6
MEDAL!!!@#$%
7. According to the plate tectonics model, what layer from Earth's rigid, mobile plates?
A. inner and outer core
B. upper and lower mantle
C. crust only
D. crust and upper mantle <---
i think D is the answer,
Answers
A dress normally sells for $45.95. How much does the dress cost after a 20% discount?
Answers
45.95 x .20 =9.19
45.95 - 9.19 =36.76
The office of student services at a large western state university maintains information on the study habits of its full-time students. their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. the hours studied follows the normal distribution with a standard deviation of six hours. suppose we select a random sample of 144 current students. what is the probability that the mean of this sample is less than 19.25 hours?
Answers
To find the answer for this problem, you first need to find the z-score for a value of 19.25.
The z-score is the number of standard deviations from the mean.
Here is the work for our z-score:
19.25 - 20 = -0.75 / 6 = -0.125
Now, you just have to use a standard normal distribution table and look up the probability for a z-score of -0.125. I used the average of the probability for z-scores of -0.12 and -0.13 to get 45.03%.
There is a 22.66% probability that the mean study time of a random sample of 144 students at the large western state university will be less than 19.25 hours.
Explanation:To solve this problem, we need to use the formula for the z-score, which is (X - μ) / (σ / √n), where X is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.
Here, n=144, μ=20, σ=6 and X=19.25. Substituting these values into the formula, we get z = (19.25 - 20) / (6/√144) = -0.75.
The z-score tells us how many standard deviations the value is away from the mean. A negative z-score indicates that the data point is less than the mean.
To find the probability, we need to look up this z-score in the z-table, which gives the area to the left of the z-score on a standard normal distribution. The value associated with z=-0.75 on the table is approximately 0.2266, or 22.66%.
So, there is a 22.66% probability that the mean study time of a random sample of 144 students will be less than 19.25 hours.
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Suppose the test scores of students in a class are normally distributed with a mean of 92 and a standard deviation of 3.
What is the z-score for a student who scored 86 on a test?
−6
−2
2
6
Answers
Shawn is typing a paper for class. He can type 1 5/12 pages in 1/3 of an hour. How many pages can Shawn type in one hour?
Answers
1 5/12 * 3 = 3(1) + 3(5/12)
= 3 5/4
= 4 1/4 pages
Answer:
i think he is right
What is the value of x in the diagram below?
Answers
The answer will be [tex] \frac{ 18\sqrt{2} }{ \sqrt{3} } [/tex] .
Now how is that, there is a rule for the right angled triangle which says:
cosθ = [tex] \frac{adjacent side}{hypotenuse} [/tex] so, if we applied this rule on the lower triangle we can say: cos30°= [tex] \frac{9}{hypotenuse} [/tex] and therefore the hypotenuse = [tex] \frac{9}{cos30} [/tex] = [tex] \frac{18}{ \sqrt{3} } [/tex] .
now in the upper triangle we will apply the same rule so,
cos45°=[tex] \frac{adjacent side}{hypotenuse} [/tex]
and the adjacent side in the upper triangle is [tex] \frac{18}{ \sqrt{3} } [/tex] and the hypotenuse is x.
so cos45°=[tex] \frac{( \frac{18}{ \sqrt{3} } )}{x} [/tex] and then we can say
x=[tex] \frac{ \frac{18}{ \sqrt{3} } }{cos45} [/tex] = [tex] \frac{ 18\sqrt{2} }{ \sqrt{3} } [/tex] .
Answer: B
Step-by-step explanation: EDGE 2022
15.5 ft + 1.25 ft + 13.5 ft=
Answers
What is the y-intercept of the line perpendicular to y= -5/2x + 4/5 including point (-3,-1) ?
Answers
On this case they give you the equation of a line and a point, and is asked to find the y-intercept of the line that is perpendicular to the given one, and that passes through the given point.
The slope of the given line is -5/2, which means that the slope of a line perpendicular to this one, needs to be 2/5. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.
y=mx+b Substitute the values of the given point and the slope
-1=-3(2/5)+b Combine like terms
-1=-6/5+b Add 6/5 in both sides to isolate b
1/5=b
The equation of the line perpendicular to y=-5/2x+4/5 and that passes through the point (-3,-1) is y=2/5x+1/5, and the y-intercept is 1/5 or 0.2.
Please help asap. Super appreciated! <3
Answers
50 POINTS PLZZZZZ HELP NOW I NEED FULL EXPLANATION AND RIGHT ANSWERS
IF the area of the frame was 64inches², what would be 2 possible sets of dimensions that could be used to make a frame with that area?
Answers
We know that the area of the frame is 64 inches^2. Let's list the factors of 64. They are:
1, 2, 4, 8, 16, 32, and 64.
There are many possible sets of dimensions.
The dimensions could be 1 in × 64 in, 2 in × 32 in, 4 in × 16 in, or 8 in × 8 in.
If the frame is shaped like a rectangle, then the first three sets of dimensions would be possible.
If it is a square, then the last (8 × 8) are possible.
The function rule for this graph is y =__ x +__
Answers
It is -1/2x + 2...she just didnt add the negative sign
The equation of line will be -
y = [tex]-\frac{1}{2} x[/tex] + 2
We have a graph as shown in the figure.
We have to find out the equation of this straight line in the graph.
What is the general form of the equation of a Straight line?The general form of a equation of a straight line is -
y = mx + c
where -
m - slope of line
c - the y - intercept
We have -
The y intercept of the straight line as = (0, 2)
The x intercept of the straight line as = (4, 0)
The slope of the line will be m = [tex]\frac{2 - 0}{0 - 4}[/tex] = - [tex]\frac{1}{2}[/tex]
The y-intercept is at (0, 2) , therefore the value of c = 2.
Substituting the values in the general equation of line we get -
y = mx + c
y = [tex]-\frac{1}{2} x[/tex] + 2
Hence, the equation of line will be -
y = [tex]-\frac{1}{2} x[/tex] + 2
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The ancient Babylonians developed a method for calculating nonperfect squares by 1700 BCE. Complete the statements to demonstrate how to use this method to find the approximate value of . In order to determine , let G1 = 2, a number whose square is close to 5. 5 ÷ G1 = , which is not equal to G1, so further action is necessary. Average 2 and G1 to find G2 = 2.25. 5 ÷ G2 ≈ (rounded to the nearest thousandth), which is not equal to G2, so further action is necessary. Average 2.25 and G2 to find G3 = 2.236. 5 ÷ G3 ≈ (rounded to the nearest thousandth), which is equal to G3. That means is approximately 2.236.
Answers
5 ÷ G1 = 2.5
5 ÷ G2 = 2.222
5 ÷ G3 = 2.236
That means √5 is approximately 2.236.
Using the Babylonian method, [tex]\( \sqrt{5} = 2.236}[/tex]. This method involves iteratively averaging and recalculating until the calculated value stabilizes to the desired accuracy.
To demonstrate the Babylonian method for finding the approximate value of [tex]\( \sqrt{5} \)[/tex]
A. In order to determine [tex]\( \sqrt{5} \)[/tex], let [tex]\( G_1 = 2 \)[/tex], a number whose square is close to [tex]5.[/tex]
B. Calculate [tex]\( \frac{5}{G_1} = \frac{5}{2} = 2.5 \)[/tex], which is not equal to [tex]\( G_1 \)[/tex], so further action is necessary. Average [tex]\( 2 \)[/tex] and [tex]\( G_1 \)[/tex] to find [tex]\( G_2 = \frac{2 + 2}{2} = 2.25 \). \( \frac{5}{G_2} = \frac{5}{2.25} = 2.222 \)[/tex], which is not equal to [tex]\( G_2 \)[/tex], so further action is necessary.
C. Average [tex]\( 2.25 \)[/tex] and [tex]\( G_2 \)[/tex] to find [tex]\( G_3 = \frac{2.25 + 2.222}{2} = 2.236 \). \( \frac{5}{G_3} = \frac{5}{2.236} = 2.237 \)[/tex], which is equal to [tex]\( G_3 \)[/tex]. That means [tex]\( \sqrt{5} \)[/tex] is approximately [tex]\( 2.236 \).[/tex]
The complete Question is
The ancient Babylonians developed a method for calculating nonperfect squares by 1700 BCE. Complete the statements to demonstrate how to use this method to find the approximate value of .
A. In order to determine , let G1 = 2, a number whose square is close to 5.
B. 5 ÷ G1 = , which is not equal to G1, so further action is necessary. Average 2 and G1 to find G2 = 2.25. 5 ÷ G2 ≈ (rounded to the nearest thousandth), which is not equal to G2, so further action is necessary.
C. Average 2.25 and G2 to find G3 = 2.236. 5 ÷ G3 ≈ (rounded to the nearest thousandth), which is equal to G3. That means is approximately 2.236.
Chen has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Chen's Jumble has 4 classical songs,3 rock songs,and 2 rap songs on it.Chen is going to listen to 360 songs.What is the best prediction for the number of classical songs that Chen will listen to?
Answers
32 = 4m + 8 solve each equation
Answers
32= 4m+8
Subtract 8 on both sides.
24=4m
Divide 4 on both sides.
m=6
I hope this helps!
~kaikers
Subtract 8 from each side.
4m + 8 (-8) = 32 - 8.
Solve.
4m = 24.
Divide each side by 4.
m = 6.
Hope it helps! :)
1. What is the vertex of the parabola?
A. (-1,0) B. (0, -3) C. (1, -4) D. (3, 0)
2. Which of the following has a graph that is wider than the graph of y=3x^2+2?
A. Y=3X^2+3
B. Y=0.5X^2+1
C. Y=-4X^2-1
D.Y=4X^2+1
3. Which graph represents the unction y=-2x^2-5?
4. What is the order, form narrowest to widest graph, of the quadratic functions f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2
A. f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2
B. f(x)-2x^2, f(x)=-10x^2, f(x)=0.5x^2
C. f(x)=0.5x^2, f(x)=2x^2, f(x)=-10x^2
D. f(x)=0.5X62, f(x)=-10x^2, f(x)=2x^2
Answers
#2
Choice B is wider than the graph of y = 3x^2 + 2. In a quadratic function like this, the value in front of the x^2 controls the width. Any positive number smaller than 3 would be wider.
#4
Choice A has the correct order. Again, the value in front of the x^2 controls how wide or narrow the graph is. First, take the absolute value of each value. Then, place them in order from greatest to least. The greater the number the narrower the graph.
Answer:
1. what is the vertex of the parabola?
C : ( 1, -4 )
2. Which of the following has a graph that is wider than the graph of y=3x^2+2?
B : Y=0.5X^2+1
3. Which graph represents the unction y=-2x^2-5?
D : choose the graph that has the smaller curve and arrows facing down
4. What is the order, form narrowest to widest graph, of the quadratic functions f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2
A : f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2
Step-by-step explanation:
these are the correct answers for 2022
i finished the quick check UwU
simplest form of the expression
3sqrt750+3sqrt2058-3sqrt48
can someone explain
Answers
750 = 2·3·5²
2058 = 2·3·7³
48 = 2⁴·3
Then, enlight all the exponents multiple of 2 (which is the index of the root):
3·√(2·3·5²) + 3·√(2·3·7²·7) + 3·√(2⁴·3)
At this point, you can take outside the square root everything that has an even number, and doing so you have to halve the exponent; you'll get:
3·5·√(2·3) + 3·7·√(2·3·7) + 3·2²·√3
You can now multiply:
15√6 + 21√42 + 12√3
which is the simplest form of your expression.
BRAINLIESTTT ASAP!! :)
How do you know if a parabola has a maximum or a minimum?
Answers
Determine the measures of the angles of triangle DEF if the measures are in the ratio 1:1:16
Answers
and then we give the ratio of 1, one of those pieces, the other ratio of 1, the same, and the ratio of 16, sixteen of those pieces.
[tex]\bf 1:1:16\qquad \cfrac{180}{1+1+16}\implies \cfrac{180}{18}\implies 10\quad \qquad \stackrel{1}{10}~:~\stackrel{1}{10}~:~\stackrel{16}{160}[/tex]
Final answer:
The angles of triangle DEF with the ratio 1:1:16 are 10 degrees, 10 degrees, and 160 degrees, using the property that the sum of interior angles in a triangle is 180 degrees.
Explanation:
To determine the measures of the angles of triangle DEF with the ratio 1:1:16, we utilize the property that the sum of the interior angles of any triangle is always 180 degrees. We can represent the measures of the angles as follows: let the first angle be x, the second angle be x, and the third angle be 16x. Since the sum of angles in a triangle is 180 degrees, we can write the equation:
x + x + 16x = 180
Simplifying the left side of the equation, we get:
18x = 180
Dividing both sides by 18 gives us:
x = 10
Therefore, the measures of the angles are 10 degrees, 10 degrees, and 160 degrees.
Corollary: At least two angles of a triangle are acute. In this case, the two angles with the ratio 1:1 are both acute since they measure 10 degrees each, which is less than 90 degrees.
Use a property of equality to solve this equation: 4.5x = 18 (never mind i figured out the answer.)
Answers
[tex]4.5x=18[/tex]
[tex] \frac{4.5x}{4.5} = \frac{18}{4.5} [/tex]
[tex]x= \frac{18}{4.5} [/tex]
[tex]x=4[/tex]
The solution to the equation 4.5x = 18 is x = 4.
We have,
To solve the equation 4.5x = 18, we can use the property of equality which states that if two quantities are equal, then multiplying or dividing both sides by the same non-zero number will still yield an equal equation.
In this case,
We want to isolate x, so we need to get rid of the coefficient 4.5.
To do this, we can divide both sides of the equation by 4.5:
(4.5x) / 4.5 = 18 / 4.5
Simplifying, we have:
x = 4
Therefore,
The solution to the equation 4.5x = 18 is x = 4.
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How do you write an absolute value equation!? Pls help! 20 points.