Answer:
An angle is 90° if and only if it is a right angle.
Explanation:
The statement is: If an angle is 90°, then it is a right angle.
The converse of this statement would be:
If an angle is a right angle, it is 90°.
Clearly, both the conditional and converse of this statement is true.
Solve the equation 5x + (−2) = 6x + 4 using the algebra tiles. What tiles need to be added to both sides to remove the smaller x-coefficient? What tiles need to be added to both sides to remove the constant from the right side of the equation?
Answer:
a) Adding -5x on both sides of the equation to remove the smaller x-coefficient
b) Adding -4 on both sides will remove the constant from the right side of the equation
Step-by-step explanation:
Given equation:
5x + (−2) = 6x + 4
a) What tiles need to be added to both sides to remove the smaller x-coefficient?
Smaller x-coefficient is 5x to remove the smaller x-coefficient
So, Adding -5x on both sides of the equation to remove the smaller x-coefficient
b) What tiles need to be added to both sides to remove the constant from the right side of the equation?
the constant on right side is 4
Adding -4 on both sides will remove the constant from the right side of the equation
Answer:
What tiles need to be added to both sides to remove the smaller x-coefficient?
✔ 5 negative x-tiles
What tiles need to be added to both sides to remove the constant from the right side of the equation?
✔ 4 negative unit tiles
What is the solution?
✔ x = –6
A soda bottle holds 1.5 liters of soda. How many milliliters does the bottle hold?
Answer:
1.5 = 1,500
Step-by-step explanation:
I actually converted 1.5 to milliliters.
That is how I got 1,500.
The bottle holds 1500 milliliters soda.
How to convert liter to milliliter ?We know that, 1 liter = 1000 milliliters
So, to convert something from liter to milliliter, we have to multiply the given value by 1000.
What is the required value ?Given, the bottle of soda holds 1.5 liters of soda.
So, we have to multiply 1000 with that to get the required value.
∴ 1.5 liters = (1.5 × 1000) milliliters
= 1500 milliliters
The required quantity of soda is 1500 milliliters.
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a^3b^-2c^-1d if a=2 b=4 c=10 d=15 express as a reduced fraction
Answer:
Don't know if this is correct but, I think the answer is 3/4.
Answer:
[tex]\dfrac{3}{4}[/tex]
Step-by-step explanation:
The given expression is
[tex]a^3b^{-2}c^{-1}d[/tex]
We need to find the value of this expression in reduced fraction if a=2 b=4 c=10 d=15.
Substitute a=2 b=4 c=10 d=15 in given expression.
[tex](2)^3(4)^{-2}(10)^{-1}(15)[/tex]
Using the property of exponent, we get
[tex](2)^3\times \left(\dfrac{1}{4^2}\right)\times \left(\dfrac{1}{10}\right)\times (15)[/tex] [tex][\because a^{-n}=\dfrac{1}{a^n}][/tex]
[tex]8\times \left(\dfrac{1}{16}\right)\times \left(\dfrac{1}{10}\right)\times (15)[/tex]
Cancel out common factors.
[tex]1\times \left(\dfrac{1}{2}\right)\times \left(\dfrac{1}{2}\right)\times (3)[/tex]
[tex]\dfrac{3}{4}[/tex]
Hence, the required fraction is 3/4.
What is the domain for the following function?
Y= (x+1)/(x^2+x-6)
A) {x does not equal -1}
B) {x does not equal -3; x does not equal 2}
C) {x does not equal -3}
D) {x does not equal 0}
Answer:
it's B
Step-by-step explanation:
the set of numbers for which a function is defined is called a domain of a function
if a number is not in the domain of a function, then the function is undefined for that number
denominator must not be zero
if we plug -3 then the y
=(-3+1)/(9+-3-6)
=(-2)/9-9
=-2/0
which is undefined for x=-3
now
if we plug 2 we have
(2+1)/(4+2-6)
=3/0
the function is undefined for x=2
so
x≠3, x≠2
The domain of the given function is {x does not equal -3; x does not equal 2}.
Explanation:The domain of a function is the set of all allowable input values. In this case, we need to find the values of x that make the denominator of the function equal to zero, because division by zero is undefined.
To find the domain, we set the denominator equal to zero and solve for x. The denominator is x^2 + x - 6, so we set it equal to zero and factor it: (x+3)(x-2) = 0. Now, we set each factor equal to zero and solve for x: x+3=0, x=-3; x-2=0, x=2.
The domain is the set of all values of x that make the function defined, so the answer is: (B) {x does not equal -3; x does not equal 2}.
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Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <3, 0>, v = <0, -6>
Answer:
They are orthogonal.
Step-by-step explanation:
u = <3, 0> v = <0, -6>
u.v =|u| |v|cosθ
if u.v is 0 this means that cos θ is 0 so θ = 90°
[tex]\theta=cos^{-1}\frac{u.v}{|u|\ |v|}[/tex]
If u.v = 0 then they are orthogonal.
If u.v ≠ 0 then they are neither parallel nor orthogonal
If u.v ≠ 0 and u = kv where k is constant then they are parallel
u.v = 3×0+0×-6
⇒u.v = 0
They are orthogonal.
erika raked 5% more leaves than adam raked. erika raked 357liters of leaves. how many liters of leaves did adam rake?
Erica raked 5% more, so she racked 1.05 times as much.
Divide the amount she racked by the 1.05:
357 / 1.05 = 340
Adam racked 340 liters.
Select the correct answer.
Which expression is equivalent to x + y + x + y + 3(y + 5)?
Answer:
Step-by-step explanation:
Remove the brackets.
x + y + x + y + 3y + 15
Collect the like terms
2x + 5y + 15
This should be your answer.
Answer: 2x + 5y + 15
Write an equation of the line with the given slope and y-ntercept -5,b-4
Answer:
y = - 5x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
here m = - 5 and b = - 4, hence
y = - 5x - 4 ← equation of line
The length of a rectangle is 1 ft more than twice the width, and the area of the rectangle is 66ft. Find the dimensions of the rectangle
Answer:
12 ft long by 5½ ft wide
Step-by-step explanation:
1. Set up an expression for the area.
Let l = the length of the rectangle
and w = the width. Then
2w = twice the width and
2w + 1 = 1 more than twice the width. Then
l = 2w + 1
The formula for the area of a rectangle is
A = length × width
A = lw
66 = (2w +1)w
66 = 2w² + w
2w² + w - 66 = 0
2. Solve the quadratic for w
2w² + w - 66 = 0
(a) Multiply the first and last terms
2 × (-66) = -132
(b) List all the factors of 132
1 132
2 66
3 42
4 33
6 22
11 12
(c) Find a pair of factors whose product is -132 and whose sum is 1.
After some trial and error, you will choose -11 and +12,
-11 × 12 = -132 and -11 + 12 = 1.
(d) Rewrite w as -11w + 12w
2w² - 11w + 12w - 66 = 0
(e) Factor by grouping
w(2w - 11) + 6(2w - 11) = 0
(w + 6)(2w - 11) = 0
(f) Use the zero product theorem
w + 6 = 0 2w - 11 = 0
w = -6 2w = 11
w = 5½
We reject the negative answer, so w = 5½ ft
3. Calculate l
l = 2w + 1 = 2 × 5½ + 1 = 11 + 1 = 12 ft
The rectangle is 12 ft long and 5½ ft wide.
The dimensions of the rectangle are length = 12 ft and wide = 5½ ft
What is an area of a rectangle?
The area of the triangle is the product f length and breath.
Calculation:-
Let l = the length of the rectangle
w = the width.
According to the question: length l = 2w + 1
The area of a rectangle is
⇒ 66 = (2w +1)w
⇒ 66 = 2w² + w
⇒ 2w² + w - 66 = 0
wide=5.5 ft = 5½ ft
lenght =12 ft
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Write an equation:
The product of a number and 12 is 78
Answer: 12 x X=78
Step-by-step explanation: An equation of this would be 12 x X =78.
In circle A, ∠BAE ≅ ∠DAE.
What is the value of x?
14
17
27
34
Answer:
x=17
Step-by-step explanation:
In circle A, ∠BAE ≅ ∠DAE.
∠BAE = 3x-24
∠DAE = x+10
According to the given condition:
∠BAE ≅ ∠DAE.
3x-24 = x+10
Combine the like terms:
3x-x=10+24
2x=34
Divide both the sides by 2
2x/2 = 34/2
x=17
Therefore the value of x = 17
The correct option is 17....
Answer:
The answer is 17 units on edg
Step-by-step explanation:
Doug can download new songs for $1.19 each. Write an equation to show how many songs he can download for $12.00
12x = 1.19
12+x=1.19
1.19+x=12
1.19x=12
Answer:
1.19x=12
Step-by-step explanation:
The 12 represents his budget and 1.19 is the cost of each song, x is the amount of songs.
Answer: [tex]1.19x=12[/tex]
Step-by-step explanation:
Given : Doug can download new songs for $1.19 each.
Let the number of songs downloaded be x .
Then the total cost of x songs will be :-
[tex]1.19x[/tex]
To find the number of songs he can download for $12.00 , we need to put [tex]1.19x[/tex] equals to 12.
We get, the equation to show how many songs he can download for $12.00 will be
[tex]1.19x=12[/tex]
If y= x+1/2-x , evaluate y given x= 5i .
By substituting x = 5i in to the equation y = x+1/2-x, we find that y = 1/2.
Explanation:To solve for y in the equation y= x+1/2-x given that x= 5i, we simply substitute x with 5i.
So, y = 5i + 1/2 - 5i
The term 5i in the numerator and the denominator cancels out so we are left with: y = 1/2
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Find the solution to the following system of equations using the ADDITION method. 3x + 2y = 7 -3x + 3y = 8
Answer:
x = 1/3 and y = 3
Step-by-step explanation:
It is given the system of equations
3x + 2y = 7 ----(1)
-3x + 3y = 8 ----(2)
To find the solution
Add eq(1) and eq (2) we get,
3x + 2y = 7 ----(1)
-3x + 3y = 8 ----(2)
0 + 5y = 15
y = 15/5 = 3
Substitute the value of y in eq(1)
3x + 2y = 7 ----(1)
3x + 2*3 = 7
3x + 6 = 7
3x = 7 - 6 = 1
x = 1/3
Therefore
x = 1/3 and y = 3
Which relation describes a function?
A) {(0, 0), (0, 2), (2, 0), (2, 2)}
B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}
C) {(2, −1), (2, 1), (3, −1), (3, 1)}
D) {(2, 2), (2, 3), (3, 2), (3, 3)}
Explaine Why you chose your answer.
Answer:
B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}
Step-by-step explanation:
For a relation to be a function, every x value must have only one y value. For a, c, and d, some of the x values have multiple different y values
Answer:
B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}
Step-by-step explanation:
For a function to be valid, each value within the domain of the function must give exactly one value in the range of the function.
That is to say, for a function to be valid, every value of x must give only 1 unique value for y.
So basically if you have one value of x which gives a value for y, and if the same value for x gives you another value of y which is different than the first time, then you do NOT have a function.
With this in mind, we can see that for option B, every unique value for x, gives an equally unique value for y. Hence this is a function.
Lets compare this with option A (for example)
For A, we can see that for (0,0), an input of x=0, gave y=0. But then notice that the next set of coordinates (0,2), an input of x=0 gave y=2!!!! (this contradicts the first set (0,0), hence this is not a function.
you'll see similar contradictions for
option C (2,-1) vs (2,1)
option D (2,2) vs (2,3)
How many meters are in .02 kilometers?
Answer:
the answer is 20 meters
Answer:
20
Step-by-step explanation:
A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. An experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. What is the probability that both of the marbles drawn are blue?
Answer:
9/64
Step-by-step explanation:
The probability that the marble on the first draw is blue is 3/8.
The probability that the marble on the second draw is blue is also 3/8.
So the probability that both are blue is:
3/8 × 3/8 = 9/64 ≈ 14%
The probability that both of the marbles drawn from the bag are blue is 9/64.
What is the probability?
Probability is the chance that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that both of the marbles drawn are blue = fraction of blue marbles²
= 3/8 x 3/8 = 9/64
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A large college wishes to determine the average SAT scores for students who apply from New York. They surveyed 105 students from New York and discovered a mean SAT score of 1519. Which of the statements below represent the parameter and the statistic, respectively, of the survey?
I. The mean SAT score of all students from New York
II. The mean SAT score of 105 students from New York
III. The 105 students who apply to the college from New York
IV. All students who apply to the college from New York
Statements I and IV
Statements II and III
Statements I and II
Statements II and IV
Answer:
Statements I and II
Step-by-step explanation:
In Statistics, parameter is any numerical value that characterizes a population while statistics are numerical values that characterizes a sample from a given population.
Statistics are most often used to estimate the population parameters
For example the sample mean is a statistic and the population mean is a paranmeter
The mean SAT score of all students from New York is the parameter.
The mean SAT score of 105 students from New York is called the statistic.
The correct choice is the third option.
5. Regal Reflective signs make speed limit signs for the state department of transportation. By low these signs must be displayed every 5/8 of a mile. How many signs will be required on a new highway that is 34 3/8 miles long?
1. Identify the vertex and the y-intercept of the graph of the function y=-2(x+ 2)+2.
Answer:
Please let me know if your quadratic is [tex]y=-2(x+2)^2+2[/tex].
And if so your vertex is (-2,2) and your y-intercept is (0,-6)
Step-by-step explanation:
It says vertex so I'm thinking you meant [tex]y=-2(x+2)^2+2[/tex]. Please correct me if I'm wrong.
The vertex form of a quadratic is [tex]y=a(x-h)^2+k[/tex]. It is called that because it tells you the vertex (h,k).
So if you compare the two forms you should see -h=2 while k=2.
-h=2 implies h=-2.
So the vertex is (h,k)=(-2,2).
To find the y-intercept, set x=0 and find y.
[tex]y=-2(0+2)^2+2[/tex]
[tex]y=-2(2)^2+2[/tex]
[tex]y=-2(4)+2[/tex]
[tex]y=-8+2[/tex]
[tex]y=-6[/tex]
So the y-intercept is (0,-6).
Simplify the quadratic term by squaring the (x+1) term.
Answer:
y = -2x^2 -4x +1
Step-by-step explanation:
y-3 = -2 (x+1)^2
Foil (x+1)^2
(x+1)(x+1) = x^2 +x+x+1 = x^2 +2x+1
Substitute this back in
y-3 = -2(x^2 +2x+1)
Distribute
y-3 = -2x^2 -4x -2
Add 3 to each side
y-3+3 = -2x^2 -4x -2+3
y = -2x^2 -4x +1
How do you express 140 degrees in radians? Round to nearest tenth
Answer:
2.4 rad
Step-by-step explanation:
To convert degree measure to radian measure
radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]
Thus for 140°
radian = 140 × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{7\pi }{9}[/tex] ≈ 2.4
Answer:
7π/9
Step-by-step explanation:
Degrees To Radians : × · π/180
Radians To Degrees : × · 180/π
Plug into Equation And Solve: 140π/180
Simplify: 7π/9
which point is the image P
Answer:
(-5,2)
Step-by-step explanation:
It alogns with negative 5 on the X axis, and positive 2 on the Y axis, meaning its written as (-5,2)
Ayanna bought three dozen donuts from Dunkin Donuts. She wants to share these between herself and three friends. How many donuts will each person get? Show work and explain how you got the answer.
Answer:
9
Step-by-step explanation:
Ok... So there are 12 donuts in a dozen. And if she bought 3 dozen, she will have 36 donuts. If she plans to share them with her 3 friends, there will be 4 people total sharing the donuts. Then all you have to do is divide the 36 donuts among the 4 friends. 36/4=9. So they will all get 9 donuts.
3(12)/4=x
36/4=x
9=x
x=9
Which of the following is equivalent to Square root -63
Answer:
[tex]3i \sqrt{7}[/tex]
Step-by-step explanation:
The imaginary unit is [tex]i=\sqrt{-1}[/tex].
Now 63 itself is not a perfect square but 63 does contain a factor that is.
63=9×7 and 9 is a perfect square.
So [tex]\sqrt{-63}=i \sqrt{63}[/tex].
[tex]i \sqrt{63}=i \sqrt{9 \cdot 7}=i \sqrt{9} \sqrt{7}=i(3) \sqrt{7}=3i \sqrt{7}[/tex]
To find the square root of -63, you'll need to consider the concept of imaginary numbers because the square root of a negative number is not a real number. Here's how you can find the equivalent expression:
The square root of -63 can be expressed as √(-63). Since you cannot take the square root of a negative number in the real number system, you would use an imaginary unit, which we designate as "i". The imaginary unit "i" is defined as √(-1).
Now, you can factor -63 into -1 and 63, so the expression becomes:
√(-63) = √(-1 * 63)
This simplifies to:
√(-1) * √(63)
We already established that √(-1) is represented by the imaginary unit "i". So now the expression is:
i * √(63)
The √(63) doesn't simplify neatly into a whole number since 63 is not a perfect square. However, 63 can be factored into 9 and 7, where 9 is a perfect square. Let's do that:
√(63) = √(9 * 7)
√(63) = √(9) * √(7)
√(63) = 3 * √(7)
Therefore, the expression now looks like this:
i * 3 * √(7)
Since multiplication is commutative, you can reorder this:
3 * i * √(7)
Thus, the expression 3 * i * √(7) is equivalent to √(-63). This is because 3 * √(7) is the real number part and "i" indicates that it is an imaginary number due to the original square root of a negative number.
How do I find the value of the unknown variable
6x + 2 + 40 = 90
Let x = the unknown
6x + 42 = 90
6x = 90 - 42
6x = 48
x = 48/6
x = 8
Answer:
x=8
Step-by-step explanation:
We know that 40 + (6x+2) +90 = 180 since the three angles form a straight line
40 + (6x+2) +90 = 180
Combine like terms
132 + 6x = 180
Subtract 132 from each side
132-132 +6x= 180-132
6x = 48
Divide each side by 6
6x/6 = 48/6
x = 8
Square ABCD has side length 4. Determine the
area of the shaded region (use pi as 3).
Answer:
The area of the shaded region is [tex]8\ units^{2}[/tex]
Step-by-step explanation:
step 1
Find the curved area ACD (formed by segment AD, segment DC and the curved segment AC)
we know that
The curved area ACD is equal to the curved area ACB
The curved area ACD is equal to the area of the square minus the area of a quarter of circle
[tex]ACD=b^{2} -\frac{1}{4}\pi b^{2}[/tex]
we have that
[tex]b=4\ units[/tex]
substitute
[tex]ACD=4^{2} -\frac{1}{4}(3)(4)^{2}[/tex]
[tex]ACD=16 -12=4\ units^{2}[/tex]
step 2
Find the area of the shaded region
The area of the shaded region is equal to the area of the square minus two times the curved area ACD
so
[tex]4^{2} -2(4)=16-8=8\ units^{2}[/tex]
Choose the correct sum of the polynomials (2x^3 - 5x - 1) + (4x^3 + 8x + 3)
Answer:
answer is b. 6x3 + 3x + 2
Step-by-step explanation:
If x and p are both greater than zero and 4x^2p^2+xp-33=0, then what is the value of p in terms of x?
A) -3/x
B) -11/4x
C) 3/4x
D) 11/4x
Answer:
11/ (4x)Explanation:
1) Make a change of variable:
u = xp2) The new equation with u is:
4x²p² + xp - 33 = 04(xp)² + xp - 33 = 04u² + u - 33 = 03) Factor the left side of the new equation:
Split u as 12u - 11u ⇒ 4u² + u - 33 = 4u² + 12u -11u - 33Group terms: (4u² + 12u) - (11u + 33)Extract common factor of each group: 4u (u + 3 - 11 (u + 3)Common factor u + 3: (u + 3)(4u - 11).4) Come back to the equation replacing the left side with its factored form and solve:
(u + 3) (4u - 11) = 0Use zero product propery: u + 3 = 0 or 4u - 11 = 0solve each factor: u = - 3 or u = 11/45) Come back to the original substitution:
u = xpIf u = - 3 ⇒ xp = - 3 ⇒ x or p is negative and that is against the condition that x and p are both greater than zero, so this solution is discarded.
Then use the second solution:
u = xp = 11/4Solve for p:
Divide both sides by x: p = 11/(4x), which is the option D) if you write it correctly.HELP me please I need it !!
Answer:
A
Step-by-step explanation:
Using the substitution u = [tex]x^{\frac{1}{2} }[/tex]
noting that ([tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{4}[/tex], then
[tex]x^{\frac{1}{2} }[/tex] + 9[tex]x^{\frac{1}{4} }[/tex] + 20 = 0
Can be rewritten as
u + 9u² + 20 = 0, that is
9u² + u + 20 = 0 ← in standard form