Answer:
The rule which best represents the dilation that was applied to Triangle ABC to create A’B’C’ will be:
(x, y) → (1/2x, 1/2y)
Step-by-step explanation:
Given the vertices of a triangle
A(-2, -4)B(2, -4)C(0, 2)After the dilation, the vertices of an image triangle be
A' (-1, -2)B '(1, -2)C' (0, 1)If we closely observe, we can notice that the image triangle vertices A'B'C' are half of the original triangle ABC.
i.e. (x, y) → (1/2x, 1/2y)
verification
A(-2, -4) → A'(-2/2, -4/2) = A'(-1, -2)
B(2, -4) → B'(2/2, -4/2) = B'(1, -2)
C(0, 2) → C'(0/2, 2/2) = C'(0, 1)
Thus, it is verified and we conclude that the rule which best represents the dilation that was applied to Triangle ABC to create A’B’C’ will be:
(x, y) → (1/2x, 1/2y)Find two integers whose sum is -8 and product is -48
-12 * 4= 48 and -12+4= -8
Consider the system y=ax+b and y=cx+d. State the conditions on the constants a, b, c, and d for which the system below has...
A. Exactly 1 solution.
B. No solutions
C. Infinitely
The following cases for the solutions of a system of linear equations are listed below:
The system has infinite solutions when a = k · c and b = k · d. The system of linear equations has no solutions for a = c. The system has only one solution if and only if a ≠ k · c and b ≠ k · d.How to infer the nature of the dependent constants in a system of linear equations
In this problem we find the case of a system of linear equations with two variables, of which we must determine the nature of its dependent constants for the following three cases:
The system has one solution.The system has no solutions.The system has infinite solutions.The implicit form of this system is shown below:
a · x - y = - b (1)
c · x - y = - d (2)
According to the linear algebra, a system of linear equations has no solutions if the determinant of the matrix of dependent coefficients is equal to zero. Then, by Cramer's law we find that:
a - c = 0
a = c
Therefore, the system of linear equations has no solutions for a = c.
Also by linear algebra, we know that the two linear equations have infinite solutions if and only if both equations are multiples of each other, then:
a · x - y + b = k · (c · x - y + d)
a · x - y + b = (k · c) · x - k · y + (k · d)
The system has infinite solutions when a = k · c and b = k · d.
Then, the system has only one solution if and only if a ≠ k · c and b ≠ k · d.
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helpppppppppppppppppppppppppp
The answer is: 8m=152
how many lines of symmetry does this have? 5?
Answer:
3
Step-by-step explanation:
I think ttttttttttttttttttttt
The circumference of the great wheel was twelve thousand and forty-one thousand inches. The cricumference of the lesser wheel was only one thousand twenty-one and two hundred-thousand inches. How much lager was the great wheel?
Answer:
The larger wheel is 10979.04098 more than the smaller wheel.
Step-by-step explanation:
Given that,
The circumference of the great wheel was twelve thousand and forty-one thousandth inches.
C = 12000.041 inches
The circumference of the lesser wheel was only one thousand twenty-one and two hundred-thousand inches.
C' = 1021.00002 inches
We need to find how much larger was the great wheel. To find it, take the difference of C and C'.
C-C' = 12000.041 inches - 1021.00002 inches
= 10979.04098 inches
Hence, the larger wheel is 10979.04098 more than the smaller wheel.
Which of the following inequalities matches the graph?
graph of an inequality with a solid vertical line through the point (negative 7, 0) and shading to the left of the line
Answer:
d
Step-by-step explanation:
5 =5v^+^
Susan and Kelvin each receive $100
$
100
as a gift.
Part A
Susan buys a movie ticket for $12.50
$
12.50
and 3
3
buckets of popcorn that cost $14.20
$
14.20
each with her $100
$
100
. Which statement is true?
Answer:
c
Step-by-step explanation:
small word problem! 30 POINTS
8.9 - 1.4x + 6.5x + 3.4
PLEASE HELP
Answer: is 10
Step-by-step explanation:input :
Changes made to your input should not affect the solution:
(1): "3.4" was replaced by "(34/10)". 4 more similar replacement(s)
STEP
1
:
17
Simplify ——
5
Equation at the end of step
1
:
89 14 65 17
((——-(——•x))+(——•x))+——
10 10 10 5
STEP
2
:
13
Simplify ——
2
Equation at the end of step
2
:
89 14 13 17
((——-(——•x))+(——•x))+——
10 10 2 5
STEP
3
:
7
Simplify —
5
What is the range of fx) = 3^x
A. All positive real numbers
B. All real numbers greater than 3
C. All real numbers
D. All real numbers greater than or equal to 3
Answer:
d brainest plz
Step-by-step explanation:
the discriminant of a quadratic equation is the value b2 – 4ac. what is the value of the discriminant of 0
Cannot determine the nature of roots.
The Nature of roots simply means the category in which the roots are falling upon. The roots may be imaginary, real, unequal or equal. If the discriminate is negative, the roots will be imaginary.
The nature of roots of quadratic equations (in the form ax^2 + bx +c=0) we need to calculate the discriminant, which is b^2 - 4 a c. When discriminant is greater than zero, the roots are unequal and real. When discriminant is equal to zero, the roots are equal and real.
The Discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the original polynomial.
Given that ,
b2 – 4ac
first we arrange terms in descending order -4ac + 2b
then find discriminant of quadratic equation :Δ = 4
Identify a, b, c through co-efficient:
a = 0
b= -4c
c = 2b
Substitute the value of a, b, c and calculate discriminant
([tex]b^{2} -[/tex] 4ac)
Δ = [tex]16c^{2}[/tex] determine number of solutions with discriminant:
Can't determine the nature of roots.
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What equation makes the line go through the following points.
(11, -3) and (7, 9)
Answer:
y = -3x + 30
Step-by-step explanation:
First, find the slope using the slope formula:
m = (y2 - y1) / (x2 - x1)
m = (9 - (-3)) / (7 - 11)
m = -12/4
m = -3
Next, find the y-intercept by substituding one of the two points into what the equation is so far:
y = -3x + b
(7, 9)
9 = -3(7) + b
9 = -21 + b
30 = b
Now you have the full equation:
y = -3x + 30
Explain why xyz is similar to lmz
Answer:
Because they both have 65 degree angles and are both triangles
Step-by-step explanation:
Answer:
because they have the same bottom degrees
Step-by-step explanation:
plss tell me the ans
Answer:
I dont know if this is right but I think its 125/343
Zeke read z books over the summer. Michelle read twice as many books over the summer as Zeke. Tay read 3 more books over the summer than Zeke. Which expression represents the total number of books read over the summer by Zeke, Michelle and Tay?
Answer: 4z + 3
Step-by-step explanation:
Number of books read by Zeke = z
Michelle read twice as many book as Zeke. This will be: = 2 × z = 2z
Tay read 3 more books than Zeke. This will be: = z + 3
The expression that represents the total number of books read over the summer by Zeke, Michelle and Tay would be the addition of the books read by each person. This will be:
= z + 2z + z + 3
= 4z + 3
Cristina picked out a new tennis racket that was priced at $35.00. She has saved $40.00 to cover the tax. If there is an 8% tax, then how much will she pay for the tennis racket and the tax
Answer:
37.8
Step-by-step explanation:
(b) Factorise fully 2 a²b + 6ab2
Answer:
2ab(a+3b)Step-by-step explanation:
[tex]2 {a}^{2} b + 6a {b}^{2} [/tex]
Factor out common term : 2ab
[tex] 2 {a}^{2}b \div 2a = a \\ 6a {b}^{2} \div 2ab = 3b \\ 2ab(a + 3b)[/tex]
[tex]2a^2b+6ab^2[/tex]
Perhaps, you mean 6ab² (If not please remind me.)
Factoring the polynomials can be done by pulling out the terms that can be divided by that terms.
For example, [tex]2x^2+4[/tex] We can divide the whole polynomial by 2. Thus, we factor 2 out of the polynomial as we get [tex]2(x^2+2)[/tex] -- Factoring is like dividing, but instead - we pull them out.
Now let's get back to the question.
Notice that the polynomial can be divided by 2, a and b.
So we pull 2, a and b out of the polynomial and divide them.
[tex]\frac{2a^2b+6ab^2}{2ab}\\a+3b[/tex]
When dividing, we should get a + 3b.
Then we pull out 2ab outside the bracket.
[tex]2ab(a+3b)[/tex]
Thus, the answer is 2ab(a+3b)
Which inequality is shown in the graph?
Solve for r: -6+4r=2(r-4)
A) -1
B) 1
C) -12
D) 12
Answer:
r = -1
Step-by-step explanation:
-6 + 4r = 2(r - 4)
-6 + 4r = 2r - 8
+6 +6
4r = 2r - 2
-2r -2r
2r = -2
/2 /2
r = -1
hope this helps
Find the length of side X
Answer:
C
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the 2 other sides, that is
x² + 6² = 17²
x² + 36 = 289 ( subtract 36 from both sides )
x² = 253 ( take the square root of both sides )
x = [tex]\sqrt{253}[/tex] → C
What do we use to replace for an unknown number?
A) A variable
B) A number
C) An Operation
D) An equal sign
Answer:
A. A variable
Step-by-step explanation:
A 20 foot ladder is leaning up against the side of a house. The construction worker who put it there followed the directions on the ladder's specifications which said to make sure the ladder was at least 8 feet away from the base of the wall to ensure safety. Say we want to re-word the directions and specify the angle of elevation of the ladder instead. What could the directions say about the angle of elevation?
Answer:
Keep the ladder at a 66 degree angle of elevation at most.
Step-by-step explanation:
Hypotenuse is 20 feet
Adjacent side is 8 feet
We use inverse cosine to find the angle
arccos(8/20) = 66.4 deg
solve the system by substitution
y=5x
y=9x+8
show ur work
will give brainliest!
Answer:
x = -2
y = -10
( -2, -10)
Step-by-step explanation:
set them equal
5x = 9x + 8
subtract 9x
-4x = 8
divide by -4
x = -2
plug in x
y = 5(-2)
y = -10
Pls help! Be honest pls be honest......
Answer:
ur x intership is (4) and ur y intership is (1)
Step-by-step explanation: its where the dots are or are u doing an equation?
if f(x)=x^2+6 and g(x)=-2x, what is the value of f(g(4))-g(f(4))
2y + 7x = -5
5y - 7x = 12
x =
y =
Answer:
x = - 1, y = 1
Step-by-step explanation:
Given the 2 equations
2y + 7x = - 5 → (1)
5y - 7x = 12 → (2)
Adding the2 equations term by term will eliminate the term in x, that is
7y = 7 ( divide both sides by 7 )
y = 1
Substitute y = 1 into either of the 2 equationsand solve for x
Substituting into (1)
2(1) + 7x = - 5
2 + 7x = - 5 ( subtract 2 from both sides )
7x = - 7 ( divide both sides by 7 )
x = - 1
solution is x = - 1, y = 1
Elizabeth is making lemonade. She uses a box of mix to make of a gallon. How much mix will she need to make one gallon?
Answer:
she will need one box to make one gallon. If the question is correct, she will ned one box.
Step-by-step explanation:
Point G lies between points F and H on Line segment F H.
A line contains points F, G, H. The space between F and G is 4 x. The space between G and H is 2 x.
If the length of FH is 18 units, what is the value of x?
Answer:
We get the value of x: x = 3
Step-by-step explanation:
Point G lies between points F and H on Line segment F H.
Space between F and G = 4x
Space between G and H = 2x
Length of FH = 18
We need to find value of x.
As point G lies between point F and H, sum of FG and GH will give FH, we can write
[tex]FG + GH = FH[/tex]
Putting values to make equation
[tex]4x + 2x = 18[/tex]
Now, solving the equation we can find value of x
[tex]4x + 2x = 18 \\6x=18\\x=\frac{18}{6}\\x=3[/tex]
So, we get the value of x: x = 3
Answer:
dlfkv
Step-by-step explanation:
Which table represents y as a function of x
Answer:
B
Step-by-step explanation:
Only one in which x is not more than one number matching y in function.
The table 4 represent the function.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
The function should have distinct input with corresponding output.
If there are 2 same input vales then it not said to be a function.
So, according the definition the table 4 represent the function because the table 1, 2 and 3 have repeated input value,
Hence, the table 4 represent the function.
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Tony has 3/4 pound of candy. He wants to make small bags that are 1/8 pound each. How many bags can he make? Show all steps.
Answer: 6 bags
Step-by-step explanation:
We will divide the total amount [3/4 pounds] by the amount per bag [1/8 pound] to find how many bags he can make.
After writing the problem, we will use "Keep, change, flip" (Keep the first fraction, change to multiplication, flip the second fraction).
[tex]\displaystyle \frac{3}{4}\ \text{pounds} \div \frac{1}{8} \ \text{pounds}[/tex]
[tex]\displaystyle \frac{3}{4}\ \text{pounds} * \frac{8}{1} \ \text{pounds}[/tex]
[tex]\displaystyle \frac{3*8\ \text{pounds}}{4*1\ \text{pounds}}\[/tex]
[tex]\displaystyle \frac{24}{4}\[/tex]
6 bags