Answer:
A
Step-by-step explanation:
A trinomial can be factored into two binomials, when the discriminant of the trinomial is greater than or equal to 0.
The discriminant for trinomial [tex]ax^2+bx+c[/tex] is he expression [tex]D=b^2-4ac.[/tex]
Check all options:
A.
[tex]D=3^2-4\cdot 1\cdot 2=9-8=1,[/tex]
then
[tex]x_{1,2}=\dfrac{-b\pm\sqrt{D}}{2a}=\dfrac{-3\pm\sqrt{1}}{2}=-2,\ -1.[/tex]
Thus,
[tex]x^2+3x+2=(x-x_1)(x-x_2)=(x-(-2))(x-(-1))=(x+2)(x+1).[/tex]
B.
[tex]D=4^2-4\cdot 1\cdot 5=16-20=-4<0,[/tex]
so this trinomial cannot be factored.
C.
[tex]D=5^2-4\cdot 1\cdot 7=25-28=-3<0,[/tex]
so this trinomial cannot be factored.
D.
[tex]D=6^2-4\cdot 1\cdot 10=36-40=-4<0,[/tex]
so this trinomial cannot be factored.
This table shows the size in acres of four parks.
What is the median of the sizes of the four parks?
A. 27 acres
B. 30 acres
C. 34 acres
D. 49 acres
I think it would be B.30 here's why i think it would be 30 because it wants to know what the median. and i know that 49 and 27 is not it (i think) and 34 is not it so my answer is 30 PLEASE CORRECT ME IF I AM WRONG.
Answer: 30 acres
Step-by-step explanation: I got a 100% on my quiz!
if ||M and M6 = 4X - 15 and m7 = x + 30 then m 6 =
Answer:
15Step-by-step explanation:
∠6 and ∠7 are Alternate Interior Angles.
The lines l and m are parallel, therefore ∠6 and ∠7 are congruent.
m∠6 = m∠7 → 4x - 15 = x + 30 add 15 to both sides
4x = x + 45 subract x from both sides
3x = 45 divide both sides by 3
x = 15
Answer:
[tex]\angle 6 =45^{\circ}[/tex]
Step-by-step explanation:
We are given that l || m
[tex]\angle 6 = 4x-15[/tex]
[tex]\angle 7 = x+30[/tex]
Since l || m
So, [tex]\angle 6 = \angle 7[/tex] (Alternate interior angles are equal )
So, [tex]4x-15 = x+30[/tex]
[tex]3x= 45[/tex]
[tex]x= 15[/tex]
[tex]\angle 6 = 4x-15=4(15)-15 = 45^{\circ}[/tex]
So, [tex]\angle 6 =45^{\circ}[/tex]
Translate "the product of z,x, and y"
into a mathematical expression
The mathematical expression for "the product of z, x, and y" can be represented as [tex]\( z \times x \times y \)[/tex].
The mathematical expression for "the product of z, x, and y" can be represented as [tex]\( z \times x \times y \)[/tex]. In this expression, the symbol [tex]\( \times \)[/tex] denotes multiplication, and the three variables [tex]\( z \), \( x \), and \( y \)[/tex] are multiplied together to obtain their product.
This expression succinctly captures the idea of multiplying these three variables. In mathematical terms, a product refers to the result of multiplying two or more numbers or variables.
Therefore, [tex]\( z \times x \times y \)[/tex] represents the outcome of multiplying the values represented by the variables [tex]\( z \), \( x \), and \( y \)[/tex].
This expression provides a clear and concise way to articulate the mathematical concept of the product of three variables.
The product of ( z ), ( x ), and ( y ) is: ( zxy ).
To translate the phrase "the product of ( z ), ( x ), and ( y )" into a mathematical expression, follow these steps:
1. Identify the Variables:
The variables involved in the expression are ( z ), ( x ), and ( y ).
2. Understand the Operation:
The term "product" indicates multiplication.
3. Write the Expression:
To express the product of ( z ), ( x ), and ( y ) mathematically, you simply multiply these variables together.
1. Start with the First Two Variables:
Multiply ( z ) and ( x ) together.
[tex]\[ z \times x \][/tex]
2.Include the Third Variable:
Now, multiply the result from the first step by ( y ).
[tex]\[ (z \times x) \times y \][/tex]
3. Simplify the Expression:
In multiplication, the order in which you multiply numbers does not matter due to the commutative property of multiplication. Therefore, we can drop the parentheses.
[tex]\[ z \times x \times y \][/tex]
Final ExpressionThe mathematical expression for "the product of ( z ), ( x ), and ( y )" is:
[tex]\[z \cdot x \cdot y\][/tex]
or simply:
[tex]\[zxy\][/tex]
This is the complete mathematical translation of the given phrase.
Geometry! Please help!
Answer:
X=3
Y=9
Step-by-step explanation:
X is equal to the 3 and multipy 3 by its self to get Y=9
A photograph is 6 in x4 in. If you make a copy of the photograph with double the length and width, what is the area of the copy?
The area of the copy would be 36 in x16in
The area of the copy of the photograph, with doubled dimensions of 12 inches by 8 inches, is 96 square inches, which is four times the area of the original photograph.
To find the area of a copy of a photograph with dimensions that are double the original, you first find the new dimensions. Since the original photograph is 6 inches by 4 inches, doubling both the length and the width gives us dimensions of 12 inches by 8 inches for the copy.
The area of a rectangle is found by multiplying the length by the width. Therefore, the area of the copied photograph is 12 inches x 8 inches, which equals 96 square inches. This is four times the area of the original photograph since the scale factor for both the length and the width is 2, and the area scales with the square of the scale factor (22).
In conclusion, the area of the copied photograph is 96 square inches. This calculation demonstrates that when you change the linear dimensions of a figure by a scale factor, the area changes by the square of that scale factor.
Which net represents the figure?
Answer:
Last net.Step-by-step explanation:
All sides of the figure are triangles. Therefore, the last net represents this figure.
Answer:
It is the Last Net!
Step-by-step explanation:
I learned this in Class and on the lessons. Thankyou have a great day!
Plz help !!!!!!!!!!!
Answer:
the first one
Step-by-step explanation:
the 36 and the 5 stay in the same places
the x with the negative 4 exponent moves to the bottom and combines with x squared so that makes x to the 6th power on the bottom.
The y and x move to the top to combine with what is there.
Answer: [tex]\bold{a)\quad \dfrac{36y^5z^2}{5x^6}}[/tex]
Step-by-step explanation:
[tex]\dfrac{36x^{-4}y^2z^0}{5x^2y^{-3}z^{-2}}\\\\\\=\dfrac{36x^{-4+4}y^{2+3}z^{0+2}}{5x^{2+4}y^{-3+3}z^{-2+2}}\\\\\\=\dfrac{36x^{0}y^5z^2}{5x^6y^{0}z^{0}}\\\\\\=\dfrac{36y^5z^2}{5x^6}[/tex]
Write an equation of each line that passes through the following points in slope-intercept form:
A (8, –1) and B (–4, 17)
Answer:
[tex]\large\boxed{y=-\dfrac{3}{2}x+11}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the point A(8, -1) and B(-4, 17). Substitute:
[tex]m=\dfrac{17-(-1)}{-4-8}=\dfrac{18}{-12}=-\dfrac{3}{2}[/tex]
The equation of a line:
[tex]y=-\dfrac{3}{2}x+b[/tex]
Put the coordinates of the point A(8, -1) to the equation of a line:
[tex]-1=-\dfrac{3}{2}(8)+b[/tex]
[tex]-1=-3(4)+b[/tex]
[tex]-1=-12+b[/tex] add 12 to both sides
[tex]11=b\to b=11[/tex]
Finally we have the equation of a line in a slope-intercept form:
[tex]y=-\dfrac{3}{2}x+11[/tex]
find the size of angle acb
The answer is a 74 degree angle. This is a simple one to remember.
20 POINTS
Please help
Divide total miles by miles per gallon:
1200 / 30 = 40 gallons of gas are needed.
Multiply gallons by price per gallon:
40 x 3.85 = $154 total for gas.
Now add the total for gas to the rental cost:
154 + 99 = $253 total cost
What are two lines in the same plane that intersect at right angles?
Answer: perpendicular
Step-by-step explanation: perpendicular lines are lines that intersect at right angles.
Answer: Perpendicular lines intersect so much so that they create 4 90 degree angles around them.
write standard form of line that is parallel to 2x + 3y= 4 and passes through the point (1, -4)
Answer:
2x + 3y = -10
Step-by-step explanation:
First convert the line into slope intercept form to find the slope of the line.
2x + 3y = 4
3y = 4 - 2x
y = -2/3x + 4/3
The slope of the line is -2/3. Parallel lines have the same slope so the slope for a line through the point (1,-4) will be -2/3. Substitute m = -2/3 and (1,-4) into the point slope of a line.
[tex]y --4 = -\frac{2}{3}(x-1)\\y + 4 = -\frac{2}{3}(x -1)[/tex]
Now convert the line into standard form by using the distributive property.
[tex]y + 4 = -\frac{2}{3}(x -1)\\y + 4 = -\frac{2}{3}x + \frac{2}{3}\\3y + 12 = -2x + 2\\2x + 3y + 12 = 2\\2x + 3y = -10[/tex]
Eli chooses two shirts from a group of five to pack for a weekend trip. Let each shirt be represented by A, B, C, D, and E. Which statements about the situation are true? Check all that apply. The combination of AB and BA are the same. Each shirt can be paired with any one of other the remaining shirts. There are twenty possible ways to choose the group of shirts. He has five choices for the first shirt and five choices for the second shirt. If he chooses shirt B, there are four possible outcomes for choosing the second shirt.
Answer:
the answer is a b and e
Step-by-step explanation:
i jus took the assignment
Answer:
A,B,E
Step-by-step explanation:
passed the assignment
Simplify this expression. 35 ÷ 33 A. 27 B. 9 C. 6 D. 3
Hello, this is a bet tough so follow the steps!
First we need to set up long division.
__
33|35
If we calculate 33 divided by 35 we get 1 with a remainder of 2.
Our work:
1
__
33|35
-33
_____
2
So therefore we get 1 with a remainder of 2.
Enjoy your day!
Answer: The correct option is (B) 9.
Step-by-step explanation: We are given to simplify the following expression :
[tex]E=3^5\div 3^3.[/tex]
We will be using the following property of exponents :
[tex]\dfrac{x^a}{x^b}=x^{a-b}.[/tex]
Therefore, the simplification of the given expression is as follows :
[tex]E\\\\=3^5\div 3^3\\\\\\=\dfrac{3^5}{3^3}\\\\\\=3^{5-3}\\\\=3^2\\\\\=9.[/tex]
Thus, the required simplified answer is 9.
Option (B) is CORRECT.
A yogurt company charges 72 cents for a 6 ounces container of yogurt. How much does it charge for an 8 ounce container?
Answer:
96¢
Step-by-step explanation:
We need to find out how much they charge per ounce so
0.72 divided by 6 = 0.12
so it's 12¢ They charge 12¢ an ounce
0.12 x 8 = 96
96¢ for 8 ounces
Hope this helps! Please mark as brainliest! Thanks!
What is the value of ln e^4
Answer:
[tex]\large\boxed{\ln e^4=4}[/tex]
Step-by-step explanation:
[tex]Use\\\\\log_ab^n=n\log_ab\\\\\log_aa=1\\\\\ln a=\log_e a\to\ln e=1\\====================================\\\\\ln e^4=4\ln e=4(1)=4[/tex]
4 is the value of the given logarithmic function.
The natural logarithm (ln) and the exponential function [tex](e^x)[/tex] are inverse operations of each other. Therefore, [tex]ln(e^x)[/tex] will cancel out and leave us with just x.
In this case,[tex]ln(e^4)[/tex] simplifies to just 4:
[tex]ln(e^4) = 4[/tex]
So, the value of [tex]ln(e^4)[/tex] is 4.
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round 4.2894 to two decimals
Answer:
4.29
Step-by-step explanation:
Answer:
Step-by-step explanation:
We want to round 4.732 to 2 decimal places, it will either round to 4.73 or 4.74. 4.732 rounded to 2 decimal places would be 4.73 (because it is the nearest number to 2 decimal places). 4.737 rounded to 2 decimal places would be 4.74
an obtuse angles measure is
Answer:
between 90° and 180°
Step-by-step explanation:
7 1/2 divided by 1 9/10 simplified
Answer:
[tex]\large\boxed{3\dfrac{18}{19}}[/tex]
Step-by-step explanation:
[tex]\text{First step:}\\\text{Convert the mixed number to the improper fractions:}\\\\7\dfrac{1}{2}=\dfrac{(7)(2)+1}{2}=\dfrac{15}{2}\\\\1\dfrac{9}{10}=\dfrac{(1)(10)+9}{10}=\dfrac{19}{10}\\\\7\dfrac{1}{2}:1\dfrac{9}{10}=\dfrac{15}{2}:\dfrac{19}{10}\\\\\text{Dividing by a fraction is the same as multiplying by the inverse of a fraction}\\\\=\dfrac{15}{2}\cdot\dfrac{10}{19}=\dfrac{15}{2\!\!\!\!\diagup_1}\cdot\dfrac{10\!\!\!\!\diagup^5}{19}=\dfrac{15}{1}\cdot\dfrac{5}{19}=\dfrac{75}{19}=3\dfrac{18}{19}[/tex]
First, convert the mixed fractions into improper fractions. Then, turn the division problem into a multiplication problem by utilizing the concept of reciprocal. This gives us 75/19, or about 3.95 in decimal.
We first need to convert the mixed fractions into improper fractions. To do this, we multiply the whole number by the denominator of the fractional part and then add the numerator, placing this sum over the original denominator. This makes 7 1/2 into 15/2 and 1 9/10 into 19/10. The division problem 7 1/2 divided by 1 9/10 simplifies to 15/2 divided by 19/10.
Next, we remember that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is obtained by swapping the numerator and denominator. So, we change our division problem into a multiplication problem, transforming 15/2 divided by 19/10 into 15/2 * 10/19.
After multiplying these fractions, we get 150/38, which simplifies to 75/19, which is approximately 3.95 when converted to decimal.
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Which of the following describes the expression 4 divided by (5x1/2)?
Answer:
8/11
Step-by-step explanation:
solve the following problems. remember, its easiest to solve the questions in the paranthesis first.
4 ÷ (5+12)
(3+6) + 17
(3+4) + (5÷6)
Problem 1:
Simplify 5+12+to 17.
4÷17
4 divided by 17 is 0.235294.
Problem 2.
Simplify 3+6+ to 9.
9 + 17 = 26.
Problem 3.
Change 3 + 4 to 7.
7+5÷6
Simplify 5 divided by 6 to 0.833333.
7 + 0.833333.
You simplify that to get 7.833333.
Have an amazing day and thanks for using Brainly.
drag each term to the correct location on the expression. each term can be used more than once, but not all terms will be used.
Consider the expression shown.
Factor the expression completely.
Answer:
Answer:
4(x-3)(x+6)
Step-by-step explanation:
We factor out the 4 first since all numbers are divisible by 4. That leaves us with x^2+3x-18.
Then we factor this to get (x-3)(x+6).
So the factored form of the equation is 4(x-3)(x+6)
Step-by-step explanation:
The factors of the equation 4x²+12x -72 will be 4(x-3)(x+6).
What is a quadratic equation?A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Factor out the 4 first since all numbers are divisible by 4. That leaves us with x² +3x -18.
4( x² +3x -18 ) = 4 ( x² + 6x - 3x -18 )
= 4 ( x(x+6) -3 (x + 6)
= 4 ( x + 6 ) ( x - 3 )
Hence, the factors are 4 ( x + 6 ) ( x - 3 ).
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Which is the product 2y/y-3 x 4y-12/2y+6
Answer:
The answer is [tex]\frac{4y}{y+3}[/tex] ⇒ the 4th answer
Step-by-step explanation:
* Lets talk about the product of two fraction
- If we have two fraction a/b and c/d, the product of them
will be ac/bd
- The there is any simplify can do between numerator and
denominator we must to make it
Ex: 2a²/5b × 15b/4a, we can simplify 2a² with 4a at first and
simplify 15b with 5b and then put the answer
∵ 2a²/4a = a/2 ⇒ 2 ÷ 4 = 1/2 and a² ÷ a = a
∵ 15b/5b = 3 ⇒ 15 ÷ 5 = 3 and b ÷ b = 1
∴ 2a²/5b × 15b/4a = a/1 × 3/2 = 3a/2
* Now lets solve the problem
∵ [tex]\frac{2y}{y-3}*\frac{4y-12}{2y+6}[/tex]
- We can simplify the second fraction at first
∵ [tex]\frac{4y-12}{2y+6}=\frac{4(y-3)}{2(y+3}=\frac{2(y-3)}{y+3}[/tex]
- At first we took 4 as a common factor from 4y - 12 ⇒ 4(y - 3)
and then simplify 4 with 2 in the denominator
- we can cancel the term x - 3 in the numerator of the second
fraction with the same term in the denominator of the first fraction
∴ [tex]\frac{2y}{1}*\frac{2(1)}{y+3}=\frac{4y}{y+3}[/tex]
* The answer is [tex]\frac{4y}{y+3}[/tex]
* A turtle and a snail start moving towards each other when they are 200 feet apart. The turtle is running at a speed of T feet per minute, and the snail is moving at a speed of S feet per minute. How soon will they meet?
Answer:
S+T
Step-by-step explanation:
What is the value of x in simplest radical form?
Answer:
x=37
Step-by-step explanation:
Since this is a right triangle, we can use Pythagorean theorem
a^2 +b^2 =c^2
12^2 +35^2 = x^2
144+1225= x^2
1369 = x^2
Take the square root
sqrt(1369) = sqrt(x^2)
37 = x
Answer:
x = 37
Step-by-step explanation:
Two leg lengths (35 and 12) are given, and the hypotenuse length is to be found. The Pythagorean Theorem links, these three quantities and enables us to find x quickly and easily:
35² + 12² = x² → 1225 + 144 = 1369 → x² = 1369
Find x by taking the square root of both sides:
√(x²) = ±√1369 → x = ± 37.
Because length is always +, omit x = -37 and keep x = +37.
PLEASE HURRY!!!
The graph of g(x) is a reflection and translation of f(x) = 3 √x. Which equation represents g(x)?
Answer:
it’s d
Step-by-step explanation:
just took the test
The graph represents the equation g(x) = -∛(x - 1).
Option D is the correct answer.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
f(x) = ∛x
Reflection over the x-axis.
f(x) = -∛x
And,
Translated one unit to the left.
g(x) = -∛(x - 1)
The graph of g(x) = -∛(x - 1) is shown on the given graph.
Thus,
The graph represents the equation g(x) = -∛(x - 1).
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a number is four times larger than the square of half the number
Answer:
Step-by-step explanation:
Let the number = x
Read carefully the sentence part beginning with 4 times larger
4* something
4 times larger than the square of 1/2 the number
4 * (x/2)^2
4*(x/2)^2 = x
4*x^2/4 = x
x^2 = x be very careful how you handle this. It looks like 0 might be an answer, but it isn't. If you divide x on both sides and you allow 0, you will get 0 / 0 and that is undefined. You must exclude that possibility with some sort of statement.
x cannot be 0.
x^2/x= x/x
x = 1
Kermit's favorite iced tea is made with 15 tea bags in every 2 liters of water. Peggy made a 12 liter batch of iced tea with 90 tea bags.
What will Kermit think of Peggy's iced tea?
(Choice A)
A
It is too strong.
(Choice B)
B
It is too weak.
(Choice C)
C
It is just right.
Answer:
Choice C.
Step-by-step explanation:
Kermit likes :
15 tea bags
every 2 liters
Peggy:
90 tea bags
12 liters
You would simplify it by dividing 90 by 15, equaling 6. And 12 divided by 2, also equaling 6. Which would mean they are equal and Peggy's tea is exactly like Kermit's favorite iced tea.
Answer: The correct choice is
Choice (C) It is just right.
Step-by-step explanation: Given that Kermit's favorite iced tea is made with 15 tea bags in every 2 liters of water and Peggy made a 12 liter batch of iced tea with 90 tea bags.
We are to select the correct choice that describes the thinking of Kermit about Peggy's Iced tea.
The ratio of quantity of water and number of tea bags in Kermit's favorite iced tea is given by
[tex]R_k=2:15.[/tex]
And the ratio quantity of water and number of tea bags in Peggy's iced tea is given by
[tex]R_p=12:90=\dfrac{12}{90}=\dfrac{2}{15}=2:15.[/tex]
Since the ratio of water and number of tea bags in Peggy's iced tea is same as that in Kermit's favorite iced tea, so
Kermit will think that Peggy's iced tea is just right.
Choice (C) is CORRECT.
A square and a rectangle have the same perimeter. The square has a side length of 8x units. The rectangle has a length of (5x+8) units and a width of 14 units. What will the perimeter of both the rectangle and the square
Answer:
The perimeter of both figures is equal to [tex]64\ units[/tex]
Step-by-step explanation:
step 1
we know that
The perimeter of a square is equal to
[tex]P=4b[/tex]
where
b is the side length of the square
we have
[tex]b=8x\ units[/tex]
substitute
[tex]P=4(8x)=32x\ units[/tex]
step 2
we know that
The perimeter of a rectangle is equal to
[tex]P=2(L+W)[/tex]
we have
[tex]L=(5x+8)\ units[/tex]
[tex]W=(14)\ units[/tex]
substitute
[tex]P=2(5x+8+14)=10x+44\ units[/tex]
step 3
Equate both perimeters and solve for x
[tex]10x+44=32x[/tex]
[tex]32x-10x=44[/tex]
[tex]22x=44[/tex]
[tex]x=2\ units[/tex]
step 4
Find the perimeter of both
square
[tex]P=32x=32(2)=64\ units[/tex]
rectangle
[tex]P=10x+44=10(2)+44=64\ units[/tex]
Find the surface area of a water tower
Answer:
SA = 3,140 ft³Step-by-step explanation:
We have:
h = 40 ft
2r = 20 ft → r = 10 ft
Substitute to the formula of a Surface Area of a cylinder:
[tex]SA=2\pi r^2+2\pi rh[/tex]
[tex]SA=2\pi(10^2)+2\pi(10)(40)=2\pi(100)+2\pi(400)\\\\=200\pi+800\pi=1,000\pi\ ft^3\\\\\pi\approx3.14\to SA\approx1,000(3.14)=3,140\ ft^3[/tex]