Learning Task 4. Solve the problem by applying the sum and product of roots
of quadratic equations.
The perimeter of a rectangular metal plate is 36 dm and its area is 80
dm². Find its dimensions. (Relate the measures to the sum and product of a
quadratic equation.)
The perimeter of a rectangle is twice the sum of its length and width while
its area is the product of its length and width. Such that,
Perimeter = 2(L+w) and Area = L•w.
Answers
Answer:
Thus, the dimensions of the metal plate are 10 dm and 8 dm.
Step-by-step explanation:
For a quadratic equation:
[tex]x^2+bx+c=0[/tex]
The sum of the roots is -b and the product is c. Note the leading coefficient is 1.
We know the perimeter of the rectangular metal plate is 36 dm and its area is 80 dm^2. Being L and W its dimensions, then:
P=2(L+W)=36
A=L.W=80
Note both formulas are closely related to the roots of the quadratic equation, we only need to adjust the data for the perimeter to be exactly the sum of L+W and not double of it.
Thus we use the semi perimeter instead as P/2=L+W=18
The quadratic equation is, then:
[tex]x^2-18x+80=0[/tex]
Factoring by finding two numbers that add up to 18 and have a product of 80:
[tex](x-10)(x-8)=0[/tex]
The solutions to the equation are:
x=10, x=8
Thus, the dimensions of the metal plate are 10 dm and 8 dm.
Related Questions
Which student’s first step was incorrect, and why?
Answers
Answer:
Todas las sustancias esenciales para el funcionamiento del organismo se obtienen a partir de los alimentos?Hurry will mark!!! María determined that these expressions are equivalent expressions using the values of x = 3 and x=7. Which
statements are true? Check all that apply.
5+3x-2 and x + 2(x+1)+1
The expressions are only equivalent when evaluated with odd values.
The expressions are only equivalent for x = 3 and X= 7.
The expressions should have been evaluated with one odd value and one even value.
The expressions have equivalent values when X = 6.
When x=0, the first expression has a value of 3 and the second expression has a value of 4.
The expressions have equivalent values for any value of x.
When x= 10, both expressions have a value of 33.
Answers
Answer: D, F, G / 4, 6, 7
Step-by-step explanation:
We have the following equations:
5 + 3x - 2 and x + 2(x+1) + 1
Before checking the statements. Let's solve the syste of equations:
5 + 3x - 2 = x + 2(x+1) + 1
5 + 3x - 2 = x + 2x+2 + 1
3x + 3 = 3x + 3
Both equations are equivalent. Now, let's judge the statements:
1. The expressions are only equivalent when evaluated with odd values.
Given that the both expression are the same, the expressions are equivalent for ALL values.
Therefore, the statement IS FALSE ❌
2. The expressions are only equivalent for x=3 and x=7.
Given that the both expression are the same, the expressions are equivalent for ALL values, not only x=3 and x=7.
Therefore, the statement IS FALSE ❌
3. The expressions should have been evaluated with one odd value and one even value.
If two expressions are equivalent, they should be equivalent for ALL values. Sometimes, evaluating just one odd and one even value isn't enough. That's why the best approach is to solve the system of equations.
Therefore, the statement IS FALSE ❌
4. The expressions have equivalent values when x=6.
Given that the both expression are the same, the expressions are equivalent for x=6 (And all the real values too).
Therefore, the statement IS TRUE ✅
5. When x=0, the first expression has a value of 3 and the second expression has a value of 4.
Given that BOTH expressions are equvalent, they have the same value when x=0, which is 3.
Therefore, the statement IS FALSE ❌
6. The expressions have equivalent values for any value of x.
Given that the both expression are the same, the expressions are equivalent for ALL values of x.
Therefore, the statement IS TRUE ✅
7. When x=10, both expressions have a value of 33
Given that the both expression are the same, the expressions are equivalent for ALL values of x. That's why when x=0, both expressions have a value of 33.
Therefore, the statement IS TRUE ✅
Find the distance between (1, 0) and (9, 15).
Answers
Answer:
[tex]\mathrm{Distance\:between\:}\left(1,\:0\right)\mathrm{\:and\:}\left(9,\:15\right)=\:17[/tex]
Step-by-step explanation:
Given the points
(1, 0)(9, 15)[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]\mathrm{The\:distance\:between\:}\left(1,\:0\right)\mathrm{\:and\:}\left(9,\:15\right)\mathrm{\:is\:}[/tex]
[tex]=\sqrt{\left(9-1\right)^2+\left(15-0\right)^2}[/tex]
[tex]=\sqrt{8^2+\left(15-0\right)^2}[/tex]
[tex]=\sqrt{8^2+15^2}[/tex]
[tex]=\sqrt{64+225}[/tex]
[tex]=\sqrt{289}[/tex]
[tex]=\sqrt{17^2}[/tex]
[tex]=17[/tex] ∵ [tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a[/tex]
Therefore,
[tex]\mathrm{Distance\:between\:}\left(1,\:0\right)\mathrm{\:and\:}\left(9,\:15\right)=\:17[/tex]
Which two consecutive integers does the square root of 200 fall between
Answers
Answer:
14 and 15
Step-by-step explanation:
Cindy says she found a shortcut for doing multiplication problems.When she multiplies 3 x 24 she says,"3 x 4 is 12 ones or 1 ten and 2 ones. Then there's just 2 tens left in 24 ,so add it up, and you get 3 tens and 2 ones .Do you think Cindy shortcut works explain your thinking
Answers
Answer:
Of course it doesn't work, 3 x 24 = 72, not 32 (3 tens and 2 ones)
Step-by-step explanation:
This method is similar to decomposition, but it doesn't work. The problem is that she is mixing multiplication, division and addition all together without any sense at all. The way decomposition works is as follows.
Examples of decomposition:
first you can multiply 3 x 4 = 12
then 3 x 20 = 60
add them and you get 72
for example: 6 x 122
6 x 2 = 12
6 x 20 = 120
6 x 100 = 600
add them together = 732
another example: 9 x 356
9 x 6 = 54
9 x 50 = 450
9 x 300 = 2700
add them to get 3,204
please hurry!
Part A: Determine the average rate of change over the interval [B, C] .
O 6
O 24
O 96
O 384
Part B: Determine the average rate of change over the interval [D, E] .
O 6
O 24
O 96
O 384
Part C: The average rate of change is
O larger over the interval [D,E] than [B,C].
O smaller over the interval [D,E] than [B,C].
O the same over the interval [D,E] than [B,C].
Answers
Answer:
Part A: 24
Part b: 384
Part c: larger over the interval
Step-by-step explanation:
A walk in interview 12% of Candidates can be selected and 28% of Canada can be put on hold for the next hiring date if 75 candidates are interviewed about how many are expected to be rejected
Answers
Answer:
45 candidates are expected to be rejected
Step-by-step explanation:
Here, we want to calculate the number of candidates to be rejected
The number of candidates to be rejected can be calculated from;
100% - (28% + 12%) = 60%
So 60% of the 75 interviewed are to be rejected
Thus, we have
60/100 * 75
= 45
The number of candidate expected to be rejected is 45 if the 12% of candidates can be selected and 28% of Canada can be put on hold for the next hiring date.
What is percentage?It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
We have:
A walk in interview 12% of Candidates can be selected and 28% of Canada can be put on hold for the next hiring date if 75 candidates are interviewed.
Let's suppose total candidate is 100%
So,
= 100 - (12+28)
= 60%
Number of candidate expected to be rejected:
= 60% of 75
= (60×75)/100
= 45
Thus, the number of candidate expected to be rejected is 45 if the 12% of candidates can be selected and 28% of Canada can be put on hold for the next hiring date.
Learn more about the percentage here:
brainly.com/question/8011401
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1)) Is 6.618 an irrational number?
yes
no
Submit
Answers
Answer:
No
Step-by-step explanation:
An irrational number cannot be represented in the form a/b while a and b are integers and b isn't zero. We can write this number in this form:
6618/1000.
Since we can, it isn't irrational, it is actually rational
Hope this helps!
Answer:
Rational
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
So, the answer to this question would be no. This number is not irrational.
In the diagram below, quadrilateral PQRS is a rectangle. Diagonal PR splits the rectangle into triangles PQR and RSP.
Based on the assumption that quadrilateral PQRS is
a rectangle, determine whether each statement below is true or false. Select True or False for each statement.
TRUE or FALSE
1.) Triangles POR and RSP are congruent because they satisfy the side-side-sido (SSS) triangle congruence criterion.
2.)Triangles POR and RSP are congruent because they satisfy the side-anglo-sido (SAS) triangle congruence criterion
3.)Triangles POR and RSP are congruent because there is a rotation that carries one triangle onto the other.
4.)Triangles POR and RSP are congruent because there is a translation that carries one triangle onto the other
Answers
Answer:
False
True
True
False
Step-by-step explanation:
Answer:true true true false
Step-by-step explanation: did it in class
let's see who can answer this;)
Answers
Answer:
0.88, 8.08, 8.80
2.4, 2.49, 3.71, 3.87, 4.92
Step-by-step explanation:
By logic.
Or mathematically speaking, if x is greater than y, means that x-y > 0.
What is the slope of a line parallel to the line whose equation is 6x + 9y = 216.
Fully reduce your answer.
Answers
Answer:
Solve the equation so it is in the y=mx+b form.
Step 1. 6x+9y = 216
Step 2. 9y = -6x+216
Step 3. y = -6/9x+24
Step 4. Simplify/Reduce to get y = -2/3x+24
Since it is Parallel then the slope is the same so the slope is -2/3x.
The slope of line parallel to line with equation → 6x + 9y = 216 is
m = -2/3.
What are Parallel lines?
Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.
Given is a line which is parallel to a line whose equation is 6x + 9y = 216.
We know that the general equation of straight line is -
y = mx + c ... Eq [ 1 ]
where 'm' represents the slope of the line.
The equation of line given -
6x + 9y = 216.
Rearranging it -
9y = - 6x + 216
y = (-6/9)x + (216/9)
y = (-2/3)x + 24 ... Eq [ 2 ]
Comparing Eq[2] with Eq[1], we get -
m = -2/3
Therefore, the slope of the line with equation → 6x + 9y = 216 is -2/3.
Two parallel lines have same slope. Hence, the slope of line parallel to
line with equation → 6x + 9y = 216 is -2/3
Therefore, the slope of line parallel to line with equation →
6x + 9y = 216 is -2/3.
To solve more questions on Straight lines, visit the link below-
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Determine the area of squre ABCD with AB=3cm
Answers
Answer:
The area of the square is 2.25cm
Step-by-step explanation:
Here's what we know:
-Each letter represent a side
-A square is made up of 4 congruent sides
-To find the area of a square you need 2 sides
-We have 2 sides (A and B)
Now we can solve:
If 3cm is the length of A and B together, then we can determine that separately The sides are 1.5cm. We can then multiply 1.5 by itself to get 2.25cm.
Hope this helps :)
write the equation of this line
Answers
Answer:
Y = -3/2x + 5
Step-by-step explanation:
Slope (rise/run) is -3/2 and the y - intercept is 5.
Hope this helps. Pls give brainliest.
Which ratio is equivalent to 3;9?
Answers
Answer:
sorry if its incorrect
Step-by-step explanation:
I think its 18:54
9:27
1:3
I hope this helps
If the coordinates of the vertices of two triangles are given, it is possible to check SSS similarity for these triangles.
true or false
Answers
Answer:
I think so it is false
Hope it helps you
A number minus 6. Help me plz (translating Expressions)
Answers
Answer:
x - 6
Step-by-step explanation:
If i am driving 45 miles per from my house to my job. My job is 35 minutes from my house. It is 9:30 i have to be there by 10:00 on the dot so how much should i increase the speed?
Answers
Usual speed is given by :
[tex]s = \dfrac{45\times 60}{35} \ mph\\\\s=77.14 \ mph[/tex]
Now, we want to reach job exactly at 10 : 00 .
So, time taken is , t = 10:00 - 09:30
t = 30 minutes = 0.5 hours .
New speed is :
[tex]s'= \dfrac{45}{0.5} = 90 \ mph[/tex]
Therefore, increase in speed is ( 90 - 77.14 ) = 12.86 mph.
Hence, this is the required solution.
3.
Stacey has a part-time job.
She earns £8 an hour.
She wants to buy a new smartphone costing £220.
How many hours does she need to work to earn enough to buy it?
Answers
Answer:
28 hours
Step-by-step explanation:
Divide the total cost of the new smartphone by how much Stacey earns per hour.
220 / 8 = 27.5
Round the quotient up to the nearest whole number to get your answer. We do this because Stacey would not get paid for only working part of an hour.
28
Figure PQRS is a parallelogram. The expressions represent the measures of the angles in degrees. Parallelogram P Q R S is shown. Angle Q is (20 + 2 x) degrees and angle R is (6x) degrees. What is the value of x?
Answers
Answer:
20°
Step-by-step explanation:
the sum of the angles gives 180°
20+2x+6x=180
20+8x=180°
8x=180-20
x=160°÷8°
x=20°
thank you!
Answer:
c) 20
Step-by-step explanation:
on edge 2021 || pls mark brainliest
The accompanying graph shows the revenue from sales of summer sandals. a) At what price will the company receive the maximum amount of revenue? 40+ 45- 35+ Revenue(1005) b) What is the meaning of the increasing region? 20- 18+ 10+ sh c) What is the meaning of the decreasing region? -10 -5+ 10 20 30 40 50 60 70 80 90 11 Selling Price(8) d) What happens to sales if the item is priced at over $85? The cost of carrying this sandal in the store is shown by the linear relation in this graphical model. The intersection points of the graphs show the points where the revenue equals the cost of carrying the item. This is called the breakeven point. Where the revenue graph appears above the cost graph, the store will make a profit. What is the lowest and highest 45+ price the manager can place on the sandals and still make a 40+ profit? 301 Revenue 1005 20+ 15+ 10+ 5+ -10 -5+ 10 20 30 40 30 60 70 80 90 L Seling Price($)
Answers
!!!!really need help!!!!Polygon ABCDEF is rotated 90°, reflected across the line y = -x, and then translated up
3 units and to the left 2 units to produce the image polygon A'B'C'D'EF'. What are the
coordinates of D' ?
Answers
Answer:
D'(-4, 1)
Step-by-step explanation:
Polygon ABCDEF is transformed by number of steps given in the question.
We have to find the coordinates of point D'.
Coordinates of point D → (2, -2)
Step - 1,
Polygon rotated 90° counterclockwise about the origin,
Rule for this rotation,
(x, y) → (-y, x)
Coordinates of image E after rotation,
D(2, -2) → E(2, 2)
Step - 2,
Point E then reflected across the line y = -x,
Rule for the reflection,
(x, y) → (-y, -x)
Image of E after reflection will be,
E(2, 2) → F(-2, -2)
Step -3,
Then point F was translated up by 3 units and 2 units left,
Rule for the translation,
(x, y) → (x -2, y + 3)
Image of F will be point D',
F(-2, -2) → D'(-4, 1)
(x-790°
(x-45)
Solve for x.
Answers
Answer:
107
Step-by-step explanation:
(x - 79)° + (x - 45)° = 90°
2x - 124 = 90
2x = 214
x = 107
Given that
R
=
6
x
+
5
y
Find
y
when
x
=
7
and
R
=
18
Answers
Answer:
[tex]\frac{24}{5}[/tex]
Step-by-step explanation:
Answer:
y = - 24/5
Step-by-step explanation:
Write an algebraic equation: Three-fifths of a number increased by seven is twenty-two.
Answers
Answer:
hmm, let me think some more
Step-by-step explanation:
3. Milo's dog weighs 18.25 pounds. Kristen's dog weighs 2.5 pounds less than Milo's dog. How much does Kristen's dog weigh? (A) 13.25 pounds B 15.75 pounds © 16.75 pounds D 20.75 pounds
Answers
Answer:
(B). 15.75
Step-by-step explanation:
If Kristens dog weighs 2.5 pounds less, then you just have to subrtact 2.5 from 18.25
The answer is B. 15.75 pounds. Kristen's dog weighs 2.5 pounds less than Milo's dog which is 18.25. So, all you have to do is subtract 2.5 from 18.25. 18.25 - 2.5 = 15.75.
Solve for the missing variable
(5, 4) & (2, c) slope is equal to 1/2
Please answer fast
Answers
Answer:
c = [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula and equate to [tex]\frac{1}{2}[/tex]
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (2, c)
m = [tex]\frac{c-4}{2-5}[/tex] = [tex]\frac{c-4}{-3}[/tex] , then
[tex]\frac{c-4}{-3}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2(c - 4) = - 3
2c - 8 = - 3 ( add 8 to both sides )
2c = 5 ( divide both sides by 2 )
c = [tex]\frac{5}{2}[/tex]
Cherries cost $5 for 2 pounds and $7.50 for 3 pounds.
What is the cost per pound?
b. Is it constant?
c. If you were to graph this situation, would you put weight or cost on the x-axis? Which one would you put on the y-axis?
d. Plot the two points described.
e. How much would 5 pounds of cherries cost? What did you do to solve this problem?
Answers
Answer:
Cherries cost $2.50 per pound
Yes, it is constant.
Weight would go on the x-axis and the cost would go on the y-axis.
The two points are (2, 5) and (3, 7.5)
5 pounds of cherries would cost $12.50. To solve the problem I multiplied the 5 pounds by 2.5, the cost per pound to find the cost.
Step-by-step explanation:
$5 for 2 pounds and $7.50 for 3 pounds can be turned into the points (2, 5) and (3, 7.5).
To find the cost per pound, input the two points into the slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{7.5-5}{3-2}[/tex]
Solve:
7.5 - 5 = 2.5
3 - 2 = 1
[tex]\frac{2.5}{1}[/tex] = 2.5
The cost of cherries per pound is $2.50. This is our slope.
The equation that represents the cost of cherries for x amount of pounds is:
y = 2.5x
To find how much 5 pounds of cherries would cost, replace x with 5 in the equation:
y = 2.5(5)
y = 12.5
5 pounds of cherries would cost $12.50.
I hope this helps :)
Rewrite in simplest terms: -(2c + 8) + 8c
Answers
Answer:
[tex]6c-8[/tex]
Step-by-step explanation:
We have:
[tex]-(2c+8)+8c=[/tex]
[tex]-2c-8+8c=\\[/tex]
[tex]6c - 8[/tex]
How much fencing is needed to enclose a rectangular garden that measures 65 feet by 17 feet
Answers
Answer:
164
Step-by-step explanation:
65+65=130
17+17=34
130+34=164
Answer:
You will need 164 feet of fencing.
Step-by-step explanation:
Add up 17+17+65+65 or follow along to the perimeter formula to get your answer of 164 feet.
You pay $144 for 12 pounds of mangoes. How much does it cost for 1 pound?
Answers
Answer:
$12
Step-by-step explanation:
$144 = 12 mangoes
Divide both sides by 12
$12 = 1 mango