Solve these problems using the berry method. Please show me the work! (291-298)
Answers
So, you start with a factorization that looks like
.. (ax + __)*(ax + __)
with the blanks to be filled by the numbers you determine in the second step.
Finally, you divide this product by "a" in an appropriate way. Often, that will mean you factor "a" from one of the binomials.
291) 5c^2 +13c +6
.. form to fill: (5c + __)*(5c + __)
We're looking for factors of 5*6 = 30 that add to 13.
.. 30 = 1*30 = 2*15 = 3*10 = 5*6 . . . . . . sums of factors are 31, 17, 13, 11.
The numbers we want are 3 and 10. Putting these into the form gives
.. (5c +3)*(5c +10)
.. = 5(5c +3)(c +2)
The factorization we want is
.. 5c^2 +13c +6 = (5c +3)(c +2)
294) 4d^2 +8d -21
.. 4*-21 = -84 = 84*-1 = 42*-2 = 28*-3 = 21*-4 = 14*-6 = 12* -7
.. These factor pairs have sums 83, 40, 25, 17, 8, 5, so our numbers are 14, -6.
.. (4d +14)(4d -6) . . . . form with numbers filled in
.. = 2(2d +7)*2(2d -3) . . . . . remove a factor of 4 by removing a factor of 2 from each binomial
.. = 4(2d +7)(2d -3)
The factorization we want is
.. 4d^2 +8d -21 = (2d +7)(2d -3)
297) 3g^2 -16g -12
.. 3*-12 = -36 = -36*1 = -18*2 = -12*3 = -9*4 = -6*6
.. These factor pairs have sums -35, -16, -9, -5, 0, so the numbers we want are -18 and 2.
The Berry Method form now looks like
.. (3g -18)(3g +2)
.. = 3(g -6)(3g +2)
The factorization we want is
.. 3g^2 -16g -12 = (g -6)(3g +2)
Related Questions
This floor has a grape juice stain. Tyler wants to cover the stain with the green carpet. Perform a series of two or more transformations to cover the stain. You must use at least two of the following types of transformation: reflection, rotation, translation, dilation.
Answers
in mrs marshall's classroom 6/7 of the students play sports. of the students who play sports, 4/5 also play an instrument. if there are 35 students in her class how many play sports and an instrument?
Answers
If the equation y = x + 4 is changed to y = x - 2, how will the graph of the equation change?
A) The original graph will shift 2 units down.
B) The original graph will shift 6 units down.
C) The original graph will shift 6 units to the left.
D) The original graph will shift 2 units to the left.
Answers
Answer:
The original graph will shift 6 units down.
Step-by-step explanation:
Given : If the equation y = x + 4 is changed to y = x - 2.
To find : How will the graph of the equation change.
Solution : We have given
Original graph equation : y = x + 4.
Transformed equation : y = x -2.
y = x + 4 →→ y = x - 2.
If we subtract the 6 from 4 it become - 2
We can see x + 4 -6 = x -2 .
So , y = x +4 -6 →→ y = x - 2.
By the transformation rule : f(x) →→ f(x) - k it mean graph shifted down by k units.
Then the original graph will shift 6 units down.
Therefore, The original graph will shift 6 units down.
John is constructing a triangle with two sides 5 cm and 7 cm and the included angle is 70°. First, John draws a 5 cm segment on his paper. He is not sure how to construct the 70° angle. What should he do?
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John could also construct a segment 13.74 cm long at the end of his segment that is perpendicular to the one he has. The angle formed between the other end of his 5 cm segment and the end of the 13.74 cm segment will be 70°.
Another choice John has is to draw an arc from each end of his 5 cm segment that has a radius of 7.3 cm. The point where these intersect over the middle of his segment will form an angle of 70° when a segment is drawn from there to the end of his 5 cm segment.
Alex has 11 apples. He needs 5 apples to make 1 pie. If he has to make 5 pies how many more apples does he need
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during the 8-month shrimping season in the Gulf mexico, 325 shrimpers caught 4,913,977 pounds of shrimp and sold the shrimp $2 per pound. if that money was split evenly between each of the shrimpers, how much money would each receive? (round your answer to the nearest dollar) and show ur work plzzzzzz
Answers
Find the $ total sold. Multiply total pounds by $2 sale price per pound.
=4,913,977 pounds * $2 a pound
=$9,827,954 total sold
STEP 2:
Divide the total sold above by the 325 shrimpers.
=$9,827,954 ÷ 325
=$30,239.858
Rounded to nearest dollar:
Each of the 325 shrimpers will take home $30,240.
Hope this helps! :)
Picking a blue shirt from a drawer with 8 blue shirts and 2 white shirts.
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You got ten shirts 8 are blue 2 are white.
So you have an 80% chance of grabbing blue and 20% of white.
And 8:2 ratio
The probability of picking a blue shirt from the drawer is 4/5 or 0.8
The probability of picking a blue shirt from a drawer with 8 blue shirts and 2 white shirts can be calculated as follows:
Probability of picking a blue shirt = Number of blue shirts / Total number of shirts
Probability of picking a blue shirt = 8 / (8 + 2)
Probability of picking a blue shirt = 8/10
Probability of picking a blue shirt = 4/5
Therefore, the probability of picking a blue shirt from the drawer is 4/5 or 0.8.
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a rock band has 5 members, and 2/5 of the members play string instruments. Also, 0.4 of the members sing. does the band have the same number of string instrument players as singers?
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If 5 pounds of broccoli cost is $12 then how much will 7 pounds of broccoli cost?
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7 pounds costs $16.4 I think
12 / 5 = 2.4
One pound of broccoli costs $2.40, SO. To find how much 7 pounds would cost we multiply 7 by 2.4.
7 x 2.4 = 16.8
So, 7 pounds of broccoli costs $16.80
Which are equivalent ratios to 4:9?
Check all that are true.
9:28
20:45
12:27
4:24
8:18
Answers
Final answer:
The equivalent ratios to 4:9 are 20:45, 12:27, and 8:18 because they all simplify proportionally to 4:9.
Explanation:
To determine which of the given ratios are equivalent to 4:9, we need to have ratios that can be simplified to 4:9 or for which 4:9 can be scaled up proportionally. We check each given ratio by either simplifying it or finding a common multiplier that would lead us back to 4:9.
9:28 is not equivalent because it does not simplify to 4:9 or scale from 4:9.20:45 simplifies to 4:9 when both numbers are divided by 5.12:27 simplifies to 4:9 when both numbers are divided by 3.4:24 is not equivalent because it simplifies to 1:6, not 4:9.8:18 simplifies to 4:9 when both numbers are divided by 2.Therefore, 20:45, 12:27, and 8:18 are equivalent ratios to 4:9.
23=30-g;6,7,8 what is the solution
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30-7=23
7=g
Solve the equaton backwards to get the answer
Emma wrote the expression 2(3w-6) to represent the amount of money that Juan spent.Is she correct?Explain
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Total money earned by Juan = 3w-6
Now Juan saved 1/3 of the money.
So money Juan spent will be 2/3 of what he earned.
Money Juan spent :
[tex] \frac{2}{3} (3w-6) [/tex]
Simplifying we get :
2w-4
Emma wrote the expression as 2(3w-6) which is not equal to 2w-4.
So we can say that the expression found by Emma was incorrect .
PPPPPPPPPPllllllllllllleeeeaaaaassssssssseeeeeee Helpppppppppppppppppp!!!!!! Will Give Brainliest !!!!!!!!!!
Principal Jenkins has a portion of the basketball court that needs to be repaved. This portion of the court has been split into three sections. Use the drawing of the damaged section below to complete the statements that follow.
The area of section 1 is_________ square feet, the area of section 2 is________
square feet, and the area of section 3 is_____________ square feet.
The area of the basketball court that needs to be repaved is
square feet.
Answers
section 2 = 4 x 10 = 40 ft
section 3= 2 x 3 = 6 ft
(05.05)Jacob and Kerrie are trying to figure out how long they can live off their $84,670 savings if they spend $370 each month. They have each created an equation. Jacob’s Equation Kerrie’s Equation y = 84,670 + (370x) y = 84,670 − (370x) Which person has the correct equation to model this linear relationship?
Answers
Answer:
kerries because they are spending money not gaining and it will be B
Step-by-step explanation:
Select the points you need to calculate the average rate of change from the beginning of the slide to when the slide has covered a horizontal distance of 15 feet.
A (0, 80)
B (5, 40)
C (10, 20)
D (15, 10)
Answers
Answer: The correct options are A and D.
Explanation:
If we want to find the average rate of change from the beginning of the slide to when the slide has covered a horizontal distance of 15 feet, the we have to find the initial point and point where horizontal distance is 15 feet.
In the given graph x axis represents the horizontal distance and y axis represents the height of the slide.
From the figure it is crealy noticed that the coordinates of the points are (0,80), (5,40), (10,20), (15,10) and (20,5).
Since at the initial point the horizontal distance is 0, so the coordinates of initial point is (0,80).
The coordinates of the point where horizontal distance is 15, are (15,10).
Therefore to find the slope or average rate of from the beginning of the slide to when the slide has covered a horizontal distance of 15 feet the required points are (0,80)and (15,10). So option A and D are correct.
Answer:
A and D
Step-by-step explanation:
Just took it. Edg 2020. Hope this helps :)
Find the slope of a ski run that descends 15 feet for every horizontal change of 24 feet. *Make sure to look at the sign of the slope and include in your answer. Positive or negative? Please help me quick
Answers
slope means rises over run. and with the facts that we know, it gives us m=-15/24
Answer:
15/24 i think'
Step-by-step explanation:
How can you determine if a piece-wise relation is a function?
Answers
Imagine you are drawing lines parallel to the y axis, if any of your lines touches the graph twice, the graph does not represent a function. otherwise, it does.
Create an expression that is equivalent to 8 x 24z
Answers
Volunteer has 12 pounds of birdseed to put in bird feeders in all of the city parks. There are 3/1/4 cups of birdseed in a pound and each bird feeder holds about 3/4 cup of birdseed. How many birdfeeders can the volunteer fill completely
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Find total number of cups of seed in 12 pounds.
1 pound= 3 1/4 cups
=3 1/4 cups * 12 pounds
=39 cups
STEP 2:
Find number of feeders that can be filled with 39 cups of seed.
1 feeder= 3/4 cups of seed
= 39 cups ÷ 3/4 cup of seed
Multiply by the reciprocal
= (39*4)/3
=156/3
=52 feeders can be filled
Hope this helps! :)
10:10 - 6:20 =
WITH REGROUPING
Answers
6:20 + 40 = 7:00
10:10 - 2:40 = 7:00
2:40 is the answer.
20 POINTS, PLZ HELP!
The circumference of a circular tabletop is 72 π inches. What is the area, in square inches, of the tabletop?
144π
5185 π
1296 π
36π
WILL MARK BRANLIEST 20 POINTS!
Answers
] The circumference=72π, this the radius will be found as follows:
C=2πr
therefore radius r will be:
2πr=72ππ
r=(72ππ)/(2π)
r=36
hence:
Area=πr²=π(36)²=1296π
Name the angle that is supplementary to < COB 1. AOF 2.COD 3.BOF 4.DOC
Answers
and when you add the two angles together, they shall equal 180°.
Hope this will help
To find the angle supplementary to <COB, we must look for an angle that adds up to 180 degrees with <COB. Assuming <COD is adjacent and forms a straight line with <COB, option 2. COD would be the supplementary angle.
The subject of this question is Mathematics, and it requires an understanding of angle relationships, particularly supplementary angles. Supplementary angles are two angles whose measures add up to 180 degrees.
Based on the given theorems and proofs, we must assume that the angles are situated such that finding the angle supplementary to <COB involves identifying an angle that, when combined with <COB, equals 180 degrees.
Given the options provided:
1. AOF2. COD3. BOF4. DOCThe correct answer to find the angle supplementary to <COB is 2. COD, assuming that <COB and <COD are adjacent angles forming a straight line.
This is a picture of a cube and the net for the cube. What is the surface area of this cube. Enter your answer in the box.
___ ft^2
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16 x 16 = 256
There are 6 sides of a square. We then multiply this by the number of sides:
256 x 6 = 1536
Answer : 1536 ft squared
The value of the surface area of this cube is,
⇒ 1536 feet²
What is mean by Cuboid?A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.
Given that;
One side of a cube = 16 feet
We know that;
the surface area of this cube is,
⇒ 6 × (side)²
Here, Side = 16 feet
Thus, The value of the surface area of this cube is,
⇒ 6 × (side)²
⇒ 6 × (16)²
⇒ 6 × 256
⇒ 1536 feet²
Thus, The value of the surface area of this cube is,
⇒ 1536 feet²
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Find the angles of the rhombus if the ratio of the angles formed by the diagonals and the sides is 4:5.
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Answer: The angles are 100 degrees, and 80 degrees.
Here's an explanation:
It says that the ratio of the angles are 4:5. In a rhombus, the opposite angles are equal to each other. So, the it would be (4*2)+(5*2) = 360 degrees, since the ratio symbolizes the angle measurements. So, if you calculate that, then 18 units is 360 degrees. 4 units is 80 degrees, and 5 units is 100 degrees.
A rhombus is a quadrilateral. The angles of the rhombus are 80°, 100°, 80°, and 100°.
What is a rhombus?A rhombus is a quadrilateral such that the pair of opposite sides of the quadrilateral are parallel, and all the sides of the quadrilateral are equal.
As we know that if the ratio of the angles formed by the diagonals and the sides is 4:5, then the ratio of the angles of the rhombus is also 4:5. Also, the pair of opposite angles of a rhombus are equal to each other. Therefore, the angles of the rhombus are 4x, 5x, 4x, and 5x.
Now, as the sum of adjacent angles of a rhombus is 180. Therefore, we can write the sum as,
[tex]4x+5x=180\\\\ 9x=180\\\\x=20[/tex]
Further, the measure of the angles can be written as,
[tex]4x = 4(20) =80^o\\\\5x = 5(20) =100^o\\\\4x = 4(20) =80^o\\\\5x = 5(20) =100^o\\[/tex]
Hence, the angles of the rhombus are 80°, 100°, 80°, and 100°.
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What fraction of students prefer Mt Rushmore over Grand Canyon ? Write in simplest form ?
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To find "What fraction of students prefer Mt Rushmore over Grand Canyon ?", we need to take away Grand Canyon [tex] (\frac{8}{28} ) [/tex] from Mt Rushmore [tex] (\frac{14}{28} ) [/tex]
[tex] \frac{14}{28} - \frac{8}{28}\\\\ When \; we \; have\; like\; fractions\; with\; same\; denominator,\; we \; should\; combine \; numerator \\ \\ \frac{14-8}{28} \\ \\ \frac{6}{28} [/tex]
[tex] Divide \; numerator\; and \; denominator\; by \; common\; factor\; 2\\ \\ \frac{6 \div2 }{28 \div 2} = \frac{3}{14} [/tex]
Conclusion:
6/28 fraction of students prefer Mt Rushmore over Grand Canyon.
3/14 is the simplest form of above fraction.
A boy flying a kite lets out 150 feet of string that makes an angle of 64 degrees w/ the ground if the stringforms a straight line how high is the kite above the ground
Answers
The height of the kite above the ground is approximately 134.82 feet.
To find the height of the kite above the ground, we can use trigonometry. The string of the kite forms a right triangle with the height of the kite as the vertical side and the length of the string as the hypotenuse. We can use the sine function to find the height. sine(64°) = height/150. Rearranging the equation, we get height = 150 * sine(64°).
Using a calculator, we find that sine(64°) ≈ 0.8988. Therefore, height ≈ 150 * 0.8988 ≈ 134.82 feet.
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WILL GIVE THE BRAINLIEST!!!
PLEASE HELP!!!
The graph shows the payh of a rider on a ride ate the amusement park.
What does the x-coordinate of the vertex represent?
Answers
This should get you a hundred on the 4.11 quiz. :)
Martha tries to exercise at least 30 minutes eac day write an inequality to represent the number of minutes Martha exercises each day
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t ≥ 30
Cassandra ordered sandwich platters for a party. There were 6 different kinds of sandwiches with 5 of each kind on a platter. Cassandra ordered 5 platters in all. Part A. What is the total number of sandwiches Cassandra ordered? Explain in detail.
Part B. Each platter was shared equally by 10 guests. Cassandra says each guest will get 15 sandwiches. Is Cassandra Correct ? Explain. How many sandwiches will each guest get?
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Determine which of the following situations requires the distributive property in order to simplify the expression. Select all situations that apply.
x(2y)
9(x ∙ y)
9(x + y)
(7 ∙ a)(b)
(7 - a)(b)
(2 ∙ x) ∙ y
*(OML PLEASE HELP ME ON THIS IT'S DRIVING ME NUTS!)*
Answers
(7 - a )(b)
9(x ∙ y), the distributive property is not used because (x ∙ y) = xy which means that only one term can be multiplied by the term outside the parenthesis.
(7 ∙ a)(b), the distributive property is not used because (7 ∙ a) = 7a which means that only one term can be multiplied by the term outside the parenthesis.