Answer:
AB is A
BC is B
AC is D
Step-by-step explanation:
To find the length of each side, use the formula for the distance between coordinate pairs.
We can find the distance using the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AB
We then substitute (-3,6) as [tex](x_1,y_1)[/tex] and (2,1) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(2--3)^2+(1-6)^2} \\d=\sqrt{(2+3)^2+(-5)^2} \\d=\sqrt{25+25}\\d=\sqrt{50}[/tex]
BC
We then substitute (2,1) as [tex](x_1,y_1)[/tex] and (9,5) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(9-2)^2+(5-1)^2} \\d=\sqrt{(-7)^2+(4)^2} \\d=\sqrt{49+16}\\d=\sqrt{65}[/tex]
AC
We then substitute (-3,6) as [tex](x_1,y_1)[/tex] and (9,5) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(9--3)^2+(5-6)^2} \\d=\sqrt{(12)^2+(-1)^2} \\d=\sqrt{144+1}\\d=\sqrt{145}[/tex]
a school has 18 classes with 35 students in each class in order to reduce the class size 30 how much new classes much must be formed
Answer: 3 classes
If we removed 5 students from each of the classrooms, we would be able to keep the 18 classes and give them exactly 30 students. However, we would also have the leftover students to put into classrooms.
If there are 18 classrooms with 5 extra students from each, we can use 18*5 to find how many total students we have.
18 * 5 = 90.
If each class size is 30, we need to divide 90 by 30 to find how many classes we need.
90 / 30 = 3 classes
Therefore, to reduce the class size to 30 students per class, 3 new classes must be formed.
To reduce the class size from 35 students to 30 students in a school with 18 classes, we need to calculate the total number of students and then determine how many new classes are needed.
1. **Total number of students:**
[tex]\[ \text{Total students} = 18 \text{ classes} \times 35 \text{ students/class} = 630 \text{ students} \][/tex]
2. **Number of classes required with 30 students per class:**
[tex]\[ \text{Required classes} = \frac{630 \text{ students}}{30 \text{ students/class}} = 21 \text{ classes} \][/tex]
3. **New classes to be formed:**
[tex]\[ \text{New classes} = \text{Required classes} - \text{Current classes} = 21 - 18 = 3 \text{ classes} \][/tex]
In the diagram below P is circumscribed about quadrilateral ABCD. What is the value of x?
Answer:
(A) [tex]x=60^{\circ}[/tex]
Step-by-step explanation:
Given: It is given that the circle P is circumscribed about quadrilateral ABCD and ∠BCD=120°.
To find: The value of x
Solution: It is given that the circle P is circumscribed about quadrilateral ABCD and ∠BCD=120°.
Now, we know that the sum of opposite angles in a cyclic quadrilateral is 180°, therefore
[tex]{\angle}BAD+{\angle}BCD=180^{\circ}[/tex]
substituting the given values, we get
[tex]x+120^{\circ}=180^{\circ}[/tex]
[tex]x=60^{\circ}[/tex]
Thus, the value of x is 60°.
Hence, option A is correct.
Answer: 60
Step-by-step explanation:
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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For what values of t can 3(x^2) + tx + 8 be written as the product of two binomials and what are the pairs of binomials?
Final answer:
Explanation of values of t for which the given expression can be factored into binomials.t = 0; pairs of binomials: (x) and (3x + 8)
t = 1; pairs of binomials: (x + 1) and (3x + 8)
t = 2; pairs of binomials: (x + 2) and (3x + 4)
Explanation:
Values of t for which 3(x²) + tx + 8 can be factored into binomials: To factor this expression, we need to identify values of t that allow the expression to be split into two binomials that, when multiplied, give the original expression.
t = 0; pairs of binomials: (x) and (3x + 8)
t = 1; pairs of binomials: (x + 1) and (3x + 8)
t = 2; pairs of binomials: (x + 2) and (3x + 4)
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]
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.
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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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]
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
* 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:
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.
Which of the following describes the expression 4 divided by (5x1/2)?
Answer:
8/11
Step-by-step explanation:
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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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.
Help me with this question
Answer:
A
Step-by-step explanation:
This is an even polynomial because both ends end up. This means the degree of the polynomial is even. This means b and c are not solutions since their degrees are odd.
To determine between A and D look at the x-intercepts. The x-intercepts of a polynomial graph have a special relationship with its equation. The x-intercepts are the solutions or roots of the factors. This means that when each factor is set equal to 0 and solved, its solution is an x-intercept. Here the x-intercepts are x = -1, 0,3. This means the factors are x(x+1)(x-3).
Notice at x = -1, the function touches but does not cross? This means the factor has an even exponent on it.
So the expression is likely x(x+1)^2 (x-3).
Since only one factor has an exponent, the answer is A.
78.2 times 10 to the fourth power in standard form
you would move the decimal to the right four times giving you 782000
what is minus root 6, minus root six
➷ It would be [tex]-2\sqrt{6}[/tex]
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Which of the following statements best describes the location of −(−4) on a number line?
It is 4 units to the left of 0.
It is 4 units to the right of 4.
It is 4 units to the left of 4.
It is 4 units to the right of 0.
Answer:
Step-by-step explanation:
Two negatives make a positive, so -(-4) = +4. On a number line, -(-4) would be located 4 units to the right of 0.
The statement "It is 4 units to the right of 0" best describes the location of −(−4) on a number line.
When you have a double negative like −(−4), it becomes positive, so −(−4) is equal to 4, and it is 4 units to the right of 0 on the number line.
The statement "It is 4 units to the right of 0" accurately describes the location of −(−4) on a number line. When dealing with a double negative like −(−4),
it effectively becomes a positive value. In this case, −(−4) simplifies to 4. Therefore, the point −(−4) is located at the position corresponding to the number 4 units to the right of the origin, which is represented by 0 on the number line.
Moving to the right on the number line means increasing the numerical value, so, as a result, −(−4) is found 4 units to the right of 0.
This concept highlights the fundamental principle that negating a negative value results in a positive value, and the position of that positive value is to the right of the origin on the number line.
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an obtuse angles measure is
Answer:
between 90° and 180°
Step-by-step explanation:
Rewrite the number in scientific notation. 0.000000000045 = 4.5 × 10
Answer:
4.5 * 10^-11
Step-by-step explanation:
the reason why is there is 11 zeros in front of the 45
hope this helps :)
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]
Can anybody help me please
Answer:
Not entirely positive of about the answers, but all of the values would equal 15
First Y = 5
First X = 15
Second X = -3
Answer:
x / y
0/5
15/0
-3/6
Step-by-step explanation:
HURRY PLEASE!!!!! Triangle RST is translated 2 units left and then reflected over the y-axis.
I cant post the pictures but the points are on s(-4,4) t(-1,4) r(-1,1)
Which transformations of RST will result in the same image? Check all that apply.
a reflection over the y-axis and then a translation 2 units right
a 180 rotation about the origin, then a translation 2 units right, and then a reflection
over the x-axis
a reflection over the y-axis and then a translation 2 units left
a 180 rotation about the origin, then a translation 2 units left, and then a reflection over the x-axis
a reflection over the x-axis and then a translation 2 units right
a reflection over the x-axis and then a translation 2 units left
Answer:
The correct options are 1 and 2.
Step-by-step explanation:
The vertices of triangle are S(-4,4), T(-1,4), R(-1,1).
If triangle translated 2 units left,
[tex](x,y)\rightarrow (x-2,y)[/tex]
and then reflected over the y-axis,
[tex](x-2,y)\rightarrow (-x+2,y)[/tex]
The relation between image and preimage is
[tex](x,y)\rightarrow (-x+2,y)[/tex] ..... (1)
The vertices of image are
[tex]S(-4,4)\rightarrow S'(6,4)[/tex]
[tex]T(-1,4)\rightarrow T'(3,4)[/tex]
[tex]R(-1,1)\rightarrow R'(3,1)[/tex]
Therefore the vertices of image are S'(6,4),T'(3,4), R'(3,1).
1. A reflection over the y-axis and then a translation 2 units right is defined as
[tex](x,y)\rightarrow (-x+2,y)[/tex]
It is equivalent to relation 1, therefore option 1 is correct.
2. A 180 rotation about the origin, then a translation 2 units right, and then a reflection over the x-axis is defined as
[tex](x,y)\rightarrow (-x+2,y)[/tex]
It is equivalent to relation 1, therefore option 2 is correct.
3. A reflection over the y-axis and then a translation 2 units left is defined as
[tex](x,y)\rightarrow (-x-2,y)[/tex]
It is not equivalent to relation 1, therefore option 3 is incorrect.
4. A 180 rotation about the origin, then a translation 2 units left, and then a reflection over the x-axis is defined as
[tex](x,y)\rightarrow (-x-2,y)[/tex]
It is not equivalent to relation 1, therefore option 4 is incorrect.
5. A reflection over the x-axis and then a translation 2 units right is defined as
[tex](x,y)\rightarrow (x+2,-y)[/tex]
It is not equivalent to relation 1, therefore option 5 is incorrect.
6. A reflection over the x-axis and then a translation 2 units left is defined as
[tex](x,y)\rightarrow (x+2,-y)[/tex]
It is not equivalent to relation 1, therefore option 6 is incorrect.
Therefore the correct options are 1 and 2.
Answer:
1 and 2 are the correct answers.
Step-by-step explanation:
Find slope of line perpendicular to given line x=3
perpendicular means negative reciprocal so it would be -1/3
Answer:
slope = 0
Step-by-step explanation:
x = 3 is a vertical line parallel to the y- axis with undefined slope.
A line perpendicular to x = 3 is a horizontal line parallel to the x- axis with a slope of zero.
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]
What does the line y= 5x-13y=7 look like horizontal vertical slanted right upwards slanted right downward
Answer:
The line y = 5x - 13, looks slanted right upwards
Step-by-step explanation:
To easily solve this question, we use a graphing tool, or a calculator to plot the graph.
Please see image below.
From looking at the graph, we know that the function is slanted right upwards.
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
Which function is represented by the graph?
a). f(x)=-2x+6
b). f(x)2x+6
c). f(x)1/2x +6
d). f(x)=-1/2x +6
Answer:
d). f(x)=-1/2x +6 (see attachment)
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.
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