Answer:
The translation is right 4 units and up 4 units
Step-by-step explanation:
we know that
The rule of the translation of the point V to V' is equal to
(x,y) ----> (x+4,y+4)
That means ----> The translation is right 4 units and up 4 units
Verify
V(-2,3) -----> V'(-2+4,3+4)
V(-2,3) -----> V'(2,7)
Is correct
The true statement is: The transformation is a vertical translation. (Statement 3)
Let's analyze each statement:
1. The point moves two units up and four units to the right.
- This statement is incorrect. The point moves four units up, not two units up.
2. The transformation rule is (x, y) → (x + 0, y + 4).
- This statement is incorrect. The transformation rule should be (x, y) → (x, y + 4) because the point moves vertically by adding 4 to the y-coordinate.
3. The transformation is a vertical translation.
- This statement is correct. The point moves vertically, changing only the y-coordinate.
4. The image is four units to the right of the pre-image.
- This statement is incorrect. The image is at the same x-coordinate as the pre-image (-2), so it's not four units to the right.
5. The translation can be described as (x, y) → (x - 2, y + 7).
- This statement is incorrect. The translation rule should be (x, y) → (x, y + 4) because the point only moves vertically.
Complete question:A translation moves point V(-2, 3) to V prime (-2, 7). Which of the following statements are true about the translation?
1. The point moves two units up and four units to the right.
2. The transformation rule is (x, y) → (x + 0, y + 4).
3. The transformation is a vertical translation.
4. The image is four units to the right of the pre-image.
5. The translation can be described as (x, y) → (x - 2, y + 7).
RS 3560 becomes RS 4272 in 8 years at S.I. What will be the simple interest on Rs 6480 in 14 years at the same rate of interest?
(Answer with explanation and working)
Answer:
[tex]RS\ 8,748[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
step 1
Find the rate of interest
in this problem we have
[tex]t=8\ years\\ P=RS\ 3,560\\ A=RS\ 4,272\\r=?[/tex]
substitute in the formula above
[tex]4,272=3,560(1+8r)[/tex]
solve for r
[tex]8r=(4,272/3,560)-1[/tex]
[tex]r=[(4,272/3,560)-1]/8[/tex]
[tex]r=0.025[/tex]
convert to percentage
[tex]r=0.025*100=2.5\%[/tex]
step 2
What will be the simple interest on Rs 6480 in 14 years at the same rate of interest?
we have
[tex]t=14\ years\\ P=RS\ 6,480\\ A=?\\r=0.025[/tex]
substitute in the formula above
[tex]A=6,480(1+0.025*14)[/tex]
[tex]A=6,480(1+0.35)[/tex]
[tex]A=RS\ 8,748[/tex]
x + y = 6 x - y = 8 Solve the system of equations.
Answer:
x=7
y=-1
Step-by-step explanation:
When the two equations are solved together, they form simultaneous equations.
x+y=6
x-y=8
Let us use the elimination method. if we add the two equations, we eliminate y.
2x=14
x=7
Let us substitute for the value of x obtained above.
x-y=8
7-y=8
y=7-8
y=-1
A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. What is the population of the
culture 6 days after inoculation?
y= 1,000(1.15) 2,313 bacteria
y= 1,000(1.15)
y= 1,000(1.5)
y= 1,000(1.5)6 11,391 bacteria
Answer:
Option A) y=1000(1.15)^6 2313 bacteria
Step-by-step explanation:
The initial value is 1,000 and the growth factor would be the the 15%.
15% can be rewritten to .15, but you have to have to add 1 for the start to make the equation easier. Thus making the growth factor 1.15
After multiplying 1000(1.15)^6 you will get 2313.06076562 which is simplified to 2,313 bacteria.
Hope this is helpful. :)
The population of the culture 6 days after inoculation is y = 1,000(1.15) 2,313 bacteria.
What is population growth of bacteria?The growth of bacterial cultures is defined as an increase in the number of bacteria in a population rather than in the size of individual cells. The growth of a bacterial population occurs in a geometric or exponential manner: with each division cycle (generation), one cell gives rise to 2 cells, then 4 cells, then 8 cells, then 16, then 32, and so forth.According to the given statement, a growth medium exists inoculated with 1,000 bacteria.
Bacteria grow at a rate of 15% = 0.15
Add 1 to create it easier = 0.15 + 1 = 1.15
We have to estimate the population of the culture 6 days after inoculation.
[tex]= 1000(1.15)^6[/tex]
= 1000(2.313)
= 2313 bacteria
The population of the culture 6 days after inoculation = 2313 bacteria
Therefore the correct answer is y = 1,000(1.15) 2,313 bacteria.
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Find the measure of y in the picture please
Answer: A. 47
Step-by-step explanation: The answer would be 47 degrees because the 47 degree angle has one mark, and so does x and y. This means that these angles are the same.
Perimeter of 40 triangles when the sides are all 1 cm long
Answer: 120 cm.
Step-by-step explanation: Each triangle has 3 sides, and each side is 1 cm. Multiply the number of sides for one triangle by the total number of triangles. 3 x 40=120. The perimeter is 120 cm.
Can someone help me please and thank you
Simplify the imaginary number sqr -75
Answer:
5i[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
and [tex]\sqrt{-1}[/tex] = i
Given
[tex]\sqrt{-75}[/tex]
= [tex]\sqrt{25(3)(-1)}[/tex]
= [tex]\sqrt{25}[/tex] × [tex]\sqrt{3}[/tex] × [tex]\sqrt{-1}[/tex]
= 5 × [tex]\sqrt{3}[/tex] × i
= 5i[tex]\sqrt{3}[/tex]
10,825.643 which digit is in the tenths place
Answer:
the number 6 is in the tenths place.
Hope this helps!
Find the area of a triangle with legs that are: 15 mm, 10 mm, and 20 mm.
Answer:
Area = [tex]\frac{75}{4} \sqrt{15} sq mm[/tex]
Step-by-step explanation:
Here we are given with all the sides of the triangle , and we are asked to find the area of it. we will use Heron's Formula to find the area. The formula is as under
Area [tex]= \sqrt{s\times (s-a) \times (s-b) \times (s-c)}[/tex]
Where [tex]s= \frac{a+b+c}{2}[/tex]
Where a , b and c are the three sides of the triangle
a=15 , b=10 and c=20
Substituting those values in the two formula one by one we get
[tex]s=\frac{15+10+20}{2}[/tex]
[tex]s=\frac{45}{2}[/tex]
now putting this value of s in main formula we get
Area= [tex]\sqrt{s\times (s-a) \times (s-b) \times (s-c)}[/tex]
Area = [tex]\sqrt{\frac{45}{2} \times (\frac{45}{2}-15) \times (\frac{45}{2}-10) \times (\frac{45}{2}-20)}[/tex]
Area = [tex]\sqrt{\frac{45}{2} \times (\frac{45-30}{2}) \times (\frac{45-20}{2}-) \times (\frac{45-40}{2})}[/tex]
Area = [tex]\sqrt{\frac{45}{2} \times (\frac{15}{2}) \times (\frac{25}{2}) \times (\frac{5}{2})}[/tex]
Area = [tex]\sqrt{\frac{45}{2} \times (\frac{15}{2}) \times (\frac{20}{2}-) \times (\frac{5}{2})}[/tex]
Area = [tex]\frac{1}{4} \sqrt{45 \times 15 \times 25 \times 5}[/tex]
Area = [tex]\frac{1}{4} \sqrt{45 \times 15 \times 25 \times 5}[/tex]
Area = [tex]\frac{1}{4} \sqrt{9 \times 5 \times 5 \times 3 \times 25 \times 5}[/tex]
Area = [tex]\frac{3\times 5 \times 5}{4} \sqrt{3 \times5}[/tex]
Area = [tex]\frac{75}{4} \sqrt{15}[/tex]
The area of a triangle with legs that are 15 mm, 10 mm, and 20 mm is [tex]72.618 mm^{2}[/tex]
Further Explanation;Area Area is a measure of how much space is occupied by a given shape. Area of a substance is determined by the type of shape in question.For example;
Area of a rectangle is given by; Length multiplied by width Area of a circle = πr². where r is the radius of a circle, Area of a square = S², Where s is the side of the square.etc.Area of a triangle The area of a triangle is given based on the type of the triangle in question.Right triangle.The area of a right triangle is given by;= 1/2 x base x height
Scalene triangleIt is a triangle that with sides and angles that are not equal.Area of a scalene triangle depends on the features of the triangle given.For example;
Sine FormulaArea of a triangle = 1/2 ab sin θ, when given two sides of the triangle and the angle between themHeron's formulaArea of a triangle = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex] when given all the sides of the triangle. where [tex]s =\frac{(a+b+c)}{2}[/tex]In this case we are given, a = 15 mm, b = 10 mm, c = 20 mm
Therefore, we use the Heron's formula;
Area= [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s =\frac{(a+b+c)}{2}[/tex]
[tex]s= \frac{(15+10+20)}{2} \\s= 22.5[/tex]
Therefore;
Area = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]
= [tex]22.5\sqrt{12.5(12.5-15)(22.5-10)(22.5-20)}[/tex]
=[tex]\sqrt{22.5(7.5)(12.5)(2.5)} \\\sqrt{5273.4375}[/tex]
[tex]= 72.618 mm^{2}[/tex]
Keywords: Area, Area of a triangle, Heron's formula, Sine formula, Scalene triangle.
Learn more about: Perimeter: https://brainly.com/question/12905000 Area: https://brainly.com/question/12905000 Area of a triangle: https://brainly.com/question/4125306Heron's Formula: https://brainly.com/question/10713495Example of a question using Heron's Formula: https://brainly.com/question/10713495
Level: Middle school
Subject; Mathematics
Topic: Area
Sub-topic: Area of a triangle
Write the equation of the line parallel to the
y-axis and 7 units to the left of the y-axis.
PLEASE HELP!
Answer:
x=-7
Step-by-step explanation:
If a line is parallel to the y-axis, then it is vertical because the y-axis is vertical.
A vertical line is in the form of x=a number.
Since the line we are looking for is 7 units to the left of the y-axis, then the line is x=-7. -7 is 7 units left of 0.
7 units right would have been x=7.
Answer:
x = -7Step-by-step explanation:
A line parallel to y-axis is a vertical line.
A vertical line has an equation x = a, where a is any real number.
The line is 7 units to the left of the y-axis. Therefore the equation of this line is x = -7 (look at the picture).
Lindsey has $20 to spend. She needs to buy exactly 2 pillets. She spends the remaining amount buying coss. How many coss does Lindsey purchase?
Lindsey purchased 72 coss.
Let's break down the problem:
1. Lindsey needs to buy exactly 2 pillets, and each pillet costs $1. So, she spends $2 on pillets.
2. She has $20 in total, and she spent $2 on pillets, leaving her with $20 - $2 = $18.
3. She spends the remaining $18 on coss, and 4 coss cost $1.
To find out how many coss she can buy with $18, we divide $18 by the cost of 4 coss:
$18 ÷ $1 = 18 coss × 4 coss/$1 = 72 coss
So, Lindsey purchases D. 72 coss with the remaining $18.
Complete Question:
0.5 pillets = 1 dollar
4 coss = 1 dollar
Lindsey has $20 to spend. She needs to buy exactly 2 pillets. She spends the remaining amount buying coss. How many coss does Lindsey purchase?
A. 4
В. 5
С. 64
D. 72
can someone please help me
Answer:
[tex]\large\boxed{\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt2\cdot\sqrt5\cdot\sqrt7\cdot\sqrt{y^2}\cdot\sqrt{y}}\\\boxed{2\cdot2\cdot y\sqrt{2\cdot5\cdot7\cdot y}}\\\boxed{4y\sqrt{70y}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{c|c}1120&2\\560&2\\280&2\\140&2\\70&2\\35&5\\7&7\\1\end{array}\\\\1,120=2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot7=2^2\cdot2^2\cdot2^2\cdot2\cdot5\cdot7\\\\y^3=y\cdot y\cdot y=y^2\cdot y[/tex]
[tex]\sqrt{1,120y^3}=\sqrt{2^2\cdot2^2\cdot2\cdot5\cdot7\cdot y^2\cdot y}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt2\cdot\sqrt5\cdot\sqrt7\cdot\sqrt{y^2}\cdot\sqrt{y}\\\\\sqrt{1,120y^3}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{y^2}\cdot\sqrt{2\cdot5\cdot7\cdot y}\qquad\text{use}\ \sqrt{a^2}=a\\\\=2\cdot2\cdot y\cdot\sqrt{2\cdot5\cdot7\cdot y}\\\\\sqrt{1,120y^3}=2\cdot2\cdot y\cdot\sqrt{2\cdot5\cdot7\cdot y}=4y\sqrt{70y}[/tex]
URGENT 19 points!!!!! PLEASE HELP!!
Aria is playing a game at the school carnival. There is a box of marbles, and each box has a white, a green, a blue, and an orange marble. There is also a spinner separated into 3 equal sections. How many outcomes are in the sample space for pulling a marble out of the box and spinning the spinner? 7 10 12 14
Answer: 12
Step-by-step explanation: Multiply the chances of getting a marble, 4, and the chances of spinning the spinner, 3.
4 x 3 = 12
There are 12 outcomes.
Answer:12
Step-by-step explanation:
I did the test
In 972.6580 which didgit is in the hundreds place
Answer:
9
Step-by-step explanation:
hundreds tens ones . tenths hundredths thousandths ten thousandths
9 7 2 . 6 5 8 0
The 9 is in the hundreds place
When asked to write an equivalent expression to 5(a+3),Alejandra wrote 5a+8. Is she correct? If not, what is the correct answer?
5a+8
Answer is NOT 5a+8
5(a+3) Multiply the bracket by 5
5(a)+5(3)
5a+15
Correct answer is supposed to be: 5a+15
the area of a rectangular box is 24x³-76x²-28x square units. The width of this box is (12x²+4x) units. Write and simplify an expression for the length of the rectangle. (Please show steps:) NEED ASAP
Answer:
(2x-7) units
Step-by-step explanation:
[tex]\tt length=\cfrac{area}{width}\\\\\\ length=\cfrac{24x^3-76x^2-28x}{12x^2+4x}=\cfrac{4x(6x^2-19x-7)}{4x(3x+1)}=\\\\\\=\cfrac{6x^2+2x-21x-7}{3x+1}=\cfrac{2x(3x+1)-7(3x+1)}{3x+1}=\\\\\\=\cfrac{(3x+1)(2x-7)}{3x+1}=2x-7[/tex]
The length of the rectangle can be found by dividing the area given as (24x³-76x²-28x) by the width given as (12x²+4x). This simplifies to 2x - 7 units which is the expression for the length of this rectangle.
Explanation:In mathematics, to find the length of a rectangle when given the area and the width, you have to divide the area by the width. The area A is given as 24x³-76x²-28x square units, and the width w is given as (12x²+4x) units. Following the formula A = lw, where l is length and w is width, the length can be found by rearranging this formula to l = A/w.
Applying this to the given values: l = (24x³-76x²-28x) / (12x²+4x) simplifies to l = 2x - 7 units. Therefore, the expression for the length of the rectangle is 2x - 7 units.
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how many solutions does the following equation have?3(x+5)=−4x+8
Answer:
1
Step-by-step explanation:
Solve the equation for x:
3(x + 5) = -4x + 8
Distribute.
3x + 15 = -4x + 8
Combine like terms.
3x + 15 = -4x + 8
+4x +4x
7x + 15 = 8
-15 -15
7x = -7
Divide both sides by 7.
x = -1
The following equation has one solution, x = -1.
Answer:
1 solution, x = -1.
Step-by-step explanation:
3(x + 5 )= −4x + 8
3x + 15 = -4x + 8
3x + 4x = 8 - 15
7x = -7
x = -1.
At one farmer’s market, bananas cost $0.80 per pound. At another farmer’s market, bananas are sold in 5-pound bags for $4.50 per bag. Which explains how to find the better buy?
Answer with step-by-step explanation:
We are given that at one farmer’s market, bananas cost $0.80 per pound while at another market, bananas are sold in 5 pound bags for $4.50 per bag.
We are to explain how to find the better buy.
For the first market, the rate of bananas is given per pound but for the other market, the rate is given for a 5 pound bag so we will find the rate of bananas per pound to compare the rates of both markets.
One pound of bananas at 2nd market = 4.50/5 = $0.9
Therefore, getting bananas from the first market at $0.80 per pound is a better buy.
Answer: A
Step-by-step explanation:on My quiz I got it right
sin(5x)sin(3x)
Express the given product as a sum or difference containing only sines or cosines.
[tex]\bf \textit{Product to Sum Identities} \\\\ sin(\alpha)sin(\beta)=\cfrac{1}{2}[cos(\alpha-\beta)\quad -\quad cos(\alpha+\beta)]\qquad \leftarrow \textit{we'll use this one} \\\\\\ cos(\alpha)cos(\beta)=\cfrac{1}{2}[cos(\alpha-\beta)\quad +\quad cos(\alpha+\beta)] \\\\\\ sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)][/tex]
[tex]\bf cos(\alpha)sin(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad -\quad sin(\alpha-\beta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(5x)sin(3x)\implies \cfrac{cos(5x-3x)-cos(5x+3x)}{2}\implies \cfrac{cos(2x)-cos(8x)}{2}[/tex]
Answer:[tex] \frac{1}{2}\left ( cos\left ( 2x\right )-cos\left ( 8x\right )\right )[/tex]
Step-by-step explanation:
Solution
[tex]Sin\left ( 5x\right )Sin\left ( 3x\right )[/tex]
We know
[tex] 2sin\left ( a\right )sin\left ( b\right )=cos\left ( a-b\right )-cos\left ( a+b\right ) [/tex]
Applying formula
[tex]Sin\left ( 5x\right )Sin\left ( 3x\right )=\frac{1}{2}\left ( cos\left ( 5x-3x\right )-cos\left ( 5x+3x\right )\right )[/tex]
=[tex] \frac{1}{2}\left ( cos\left ( 2x\right )-cos\left ( 8x\right )\right ) [/tex]
In the diagram above, which two red lines are skew?
A. GK and EF
B. I and GK
c. FL and Ź
D. FL and CK
The shortest living man on Earth is 21 inches tall. The tallest living woman on Earth is approximately 4 times taller than the shortest man. How tall is the tallest living woman on Earth?
Answer: 84 inches, 7 feet tall.
Step-by-step explanation:
4 x 21 = 84 inches
84/12 = 7 feet ( there are 12 inches in 1 foot)
9(x + 1) = 25 + x
x = 2
x = 3
x = 4
X
11
Answer:
x = 2.
Step-by-step explanation:
9(x + 1) = 25 + x
9x + 9 = 25 + x
Subtract x from both sides:
9x - x + 9 = 25
Subtract 9 from both sides:
9x - x = 25 - 9
8x = 16
x = 16/8 = 2.
Answer:
x = 2
Step-by-step explanation:
Given
9(x + 1) = 25 + x ← distribute parenthesis on left side
9x + 9 = 25 + x ( subtract x from both sides )
8x + 9 = 25 ( subtract 9 from both sides )
8x = 16 ( divide both sides by 8 )
x = 2
Roopesh has $24 dollars to spend on a birthday gift. The store where he is shopping has a sale offering $5 off the regular price, r, of any item. Write an inequality that can be used to determine the regular price of an item in the store that Roopesh can afford. (Assume there is no tax.)
What is the unknown?
Which expression can represent the sale price?
Which comparison could be used?
Which inequality represents the situation?
For this case we have the following data:
Available quantity: $ 24
Regular price: r
Sale price:[tex]r-5[/tex]
If we have that Roopesh can not pay more than $ 24, we can write the following inequality, taking into account that the item is sold in [tex]r-5[/tex]:
[tex]r-5 \leq24[/tex]
Clearing r:
[tex]r \leq24+5\\r \leq29[/tex]
Answer:
What is the unknown?[tex]r \leq29[/tex]
Which expression can represent the sale price?[tex]r-5[/tex]
Which comparison could be used?The sale price decreases $ 5 and so the regular price is obtained.
The inequality is: [tex]r-5 \leq24[/tex]Answer:
answer in pic
A small measuring spoon holds 5 milliliters. How many spoons would 1 liters of liquid fill?
1 MILLIliter, namely one thousandth of a liter, meaning there are 1000 mLs in one liter.
the spoon holds 5 mL, how many are there in 1 liter? namely how many times is 5 in 1000? simply 1000 ÷ 5 = 200.
The number of spoon that will hold 1 litre of liquid is 200 spoons.
MeasurementMeasurement is use to show the amount of something.
The small measuring spoon holds 5 millilitres . Therefore, the number of spoon that can hold 1 litres can be calculated as follows;
Let's convert
1000 ml = 1 l
5 ml = 1 spoon
1000 ml = ?
number of spoon = 1000 / 5
number of spoon = 200
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How many solutions does the following equation have? 60z+50-97z=-37z+49
[tex]\bf 60z+50-97z=-37z+49\implies 50~~\begin{matrix} -37z \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=~~\begin{matrix} -37z \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+49\implies \stackrel{\textit{the what?!}}{50=49}[/tex]
well, clearly 50 ≠ 49.
but, whenever we get a result of this kind, is just a way to say no solutions.
you can look at it this way, is a system of equations, the equations are
y = -37z + 50
y = -37z + 49
now, notice, since both equations are in slope-intercept form, both equations have the same slope of -37, however, the y-intercept differs, meaning both equations are parallel and never touch each other.
since a solution for them is where they intercept and they never do, no solutions.
The given equation will have no solution.
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, 60z+50-97z=-37z+49
On solving, we get,
0 = -1
Which is not possible.
Hence, There is no solution.
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The image below is a triangle drawn inside a circle with center O:
8 inches
5 inches
4 inches
Which of the following expressions shows the area, in square inches, of the circle?
(TT = 3.14)
3.14.42
3.14 . 52
3.14.5
3.14 22
Answer:
area ≈ 24π
Step-by-step explanation:
We have solved this problem two ways:
Using a drawing program that writes the formula of the circumscribing circle, so gives the value of r^2.Using rarely-seen formulas for the area of a triangle and for the area of its circumscribing circle.__
Drawing
A drawing of the figure (below) can help you find the radius of circle O. It is about 4.89 inches, so the area of circle O is about ...
area = πr^2 = π(4.89 in)^2 ≈ 23.9π ≈ 24π . . . .square inches
__
Formulas
There is an interesting relationship between the area of the triangle and the radius of the circumscribing circle:
r = (abc)/(4A) . . . . . where a, b, c are the triangle side lengths, and A is the triangle area
Heron's formula can tell us the area of the triangle from the side lengths:
A = √(s(s-a)(s-b)(s-c)) . . . . where s = (a+b+c)/2
For the given triangle with side lengths 4, 5, and 8 (inches), the area can be found as ...
s = (4+5+8)/2 = 8.5
A = √(8.5·4.5·3.5·0.5) = √66.9375 ≈ 8.1815 . . . square inches
Then the radius of the circle is ...
r = (4·5·8)/(4·8.1815) = 4.889 . . . inches
The area of the circle is then ...
Circle O area = πr^2 = π(4.889 in)^2 = 23.9π in^2
__
The closest answer choice is 3.14×22.
Determine whether the trinomial is a
perfect square. If so, factor it. If not,
explain why.
16. 81n2 + 90n+ 100
Step-by-step explanation:
Use (a+b)²= a²+2ab+b² formula
We can see that a²=81n² (so a=9n) and b²=100 (so b=10) and 2ab = 2*9n*10=180n.
therefore only √(81n²+180n+100) would be perfect square and this - isn't.
Examine the quadratic equation 9x^2+24x+16=0.
A: What is the discriminant of the quadratic equation?
B: Based on the discriminant, which statement about the roots of the quadratic equation is correct?
Select one answer choice for question A, and select one answer choice for question B.
A: 120
A: -120
A: 0
B: There is one real root with a multiplicity of 2.
B: There are two real roots.
B: There are two complex roots
Answer:
The correct answer options are,
A: 0
B: There is one real root with a multiplicity of 2.
Step-by-step explanation:
Discriminant of a quadratic equation ax² + bx + c = 0 is given by,
b² - 4ac
It is given a quadratic equation 9x² + 24x + 16 = 0
To find the discriminant
Here a = 9, b = 24 and c = 16
Discriminant = b² - 4ac
= 24² - (4 * 9 * 16)
= 576 - 576
= 0
The correct options are
A: 0
B: There is one real root with a multiplicity of 2.
The discriminant of the quadratic equation 9x^2+24x+16=0 is 0, which means there is one real root with a multiplicity of 2.
Let's examine the quadratic equation 9x^2+24x+16=0 to find the discriminant and interpret its meaning for the roots of the equation.
A: The discriminant of a quadratic equation in the form ax^2+bx+c=0 is given by the formula b^2-4ac. Substituting the coefficients from our equation (where a=9, b=24, and c=16) into this formula gives us the discriminant:
discriminant = b^2 - 4ac = 24^2 - 4(9)(16) = 576 - 576 = 0.
B: The discriminant tells us about the nature of the roots of the quadratic equation. Since the discriminant is zero, this implies that there is one real root with a multiplicity of 2. Therefore, the quadratic equation has a perfect square factor and the graph of the equation touches the x-axis at one point, indicating that both roots are the same.
What is the height of a triangle with an area of 6.72 square meters and a base of 3.2 meters?
Answer:
4.2 meters.
Step-by-step explanation:
Area = 1/2 * base * height.
6.72 = 1/2 * 3.2 * h
h = 6.72 / 1.6
= 4.2 m.
Answer:
4.2 meters
Step-by-step explanation:
The height of a triangle with an area of 6.72 square meters and a base of 3.2 meters is 4.2 meters.
6.72 = 1/2 * 3.2 * h
Consider the function represented by the table.
For which x is f(x)?=–3
–7
–4
4
5
x I f(x)
-7 I -3
-3 I 5
2 I -4
4 I -8
Answer:
f(-7) = -3Step-by-step explanation:
[tex]\begin{array}{c|c}x&f(x)\\-7&\boxed{-3}\\-3&5\\2&-4\\4&-8\end{array}[/tex]
From the table we have f(-7) = -3
Answer:
f(-7) = -3
Step-by-step explanation: