Answer:
(4,0)
Step-by-step explanation:
Plug them into see:
Check (4,0)
In order for the lines to intersect at (4,0) it must be on both lines.
2(4)+0=8 is true because it is saying 8=8
4+0=4 is true because 4=4
So (4,0) is a intersection point.
Check (0,4)
2(0)+4=8 is not true because it is saying 4=8
0+4=4 is true so it's on this line while not on the other line.
So (0,4) is not an interestion point for the mentioned lines.
Well all points can't be on the line since (0,4) is not on both lines but just one of them.
We could have solve this out instead plugging in but the problem gave us the option here with the choices.
The system of linear equations given intersects at the point (4, 0), and since these equations represent distinct lines, they only intersect at this single point.
The question involves solving a system of linear equations to find the point of intersection. The system given is:
2x + y = 8x + y = 4Let's solve the equations step by step:
Subtract the second equation from the first to eliminate y, getting 2x - x + y - y = 8 - 4, which simplifies to x = 4.Substitute x = 4 into the second equation: 4 + y = 4, solving for y, which gives y = 0.Therefore, the lines intersect at the point (4, 0).
To determine whether the lines intersect at all points on a line, note that these equations represent distinct lines with different slopes, meaning they only intersect at one point, facing the choice given, (4, 0) is correct.
which of the following statements best describes the graph of x + y equals 4
Answer:
Step-by-step explanation:
the graph of x + y = 4 is the line passes by the point A(2,2) and the slope -1
because 2+2 =4 and y = -x +4
What is the sum of the geometric series?
–122
–2
40
54
The sum of the first six terms of the geometric series will be -364. Hence, option (B) will be correct.
What is geometric series?A geometric series is a series in which the division of any consecutive two terms will be the same.
For example 3, 6, 12, 24 here if you divide 6 by 3 then it gives you 2, and if you divide 12 by 6 then also it gives you 2, and so on.
here, we have,
Given up series is 2, – 6, 18, – 54
The common ratio of this GP is -3 by that
The remaining elements of this gp will be 162, -486
So the sum will be 2 - 6 + 18 - 54 + 162 - 486 = -364 so it will the summation of the given gp.
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Identify the discontinuity and zero of the function f(x)= 4x/x^2-16
Answer:
Step-by-step explanation:
ANSWER
Point if discontinuity:
{x}= \pm3
Zero of the function is
x = 0
EXPLANATION
The given rational function is:
f(x) = \frac{3x}{ {x}^{2} - 9}
This function is not continous when
{x}^{2} - 9 = 0
{x}= \pm \sqrt{9}
{x}= \pm3
The function is zero when,
3x = 0
x = 0
Answer:
x = 0 is the zero of this function and at x = ±4 function is discontinuous.
Step-by-step explanation:
The given function is [tex]f(x) = \frac{4x}{x^{2}-16}[/tex]
For this function we have to find the discontinuity and zeros of this function.
For zeros of the function [tex]0 = \frac{4x}{x^{2}-16}[/tex]
so zero of the function is x = 0
For x² - 16 = 0 this function not defined therefore, x = ± 4 function will be discontinuous.
Finally, x = 0 is the zero of this function and at x = ±4 function is discontinuous.
The lines graphed below are parallel. The slope of the red line is 2/5What is
the slope of the green line?
Answer:
D
Step-by-step explanation:
for the 2 lines to be parallel, they have to have the same slope
4 bananas and 3 peaches cost $10. We can represent this information as 4x +3y = $10. The x represents the cost of bananas and the y represents the cost of peaches.
a) Find an equation for 1 banana and 2 peaches cost $5
b) With the two equations, use a matrix method on your calculator to determine the cost of a banana and the cost of a peach.
Answer:
a x+2y =5
b x=1 y=2
Step-by-step explanation:
4x+3y = 10
So the cost of 1 banana is x and the cost of 1 peach is y
a) we want the cost of 1 banana and 2 peaches
1x+2y
That is equal to 5 dollars
1x+2y =5
x+2y =5
b
The matrixes are
1 2 x 5
* =
4 3 y 10
Using my calculator, x=1 y=2
Which of the following systems of linear inequalities is represented by the
solution graphed below?
Answer:
Option D is correct.
Step-by-step explanation:
Option D is correct.
y < 2 and y >= x
Because the dotted line shows that y < 2 and y >=x is shown is represented by diagonal line.
Option: D is the correct answer.
D. y<2 and y≥x
Step-by-step explanation:The graph of the system of linear inequalities are two lines:
1)
The first is a solid line which passes through (0,0) , (1,1)
i.e. the equation of the line is: y=x
and the inequality will be a inequality with a equality sign ( since the line is solid ) and the shaded region is above the line .
Hence, the inequality is: y≥x
2)
The second line is a dotted line.
This means that the inequality is strict.
Also, the line is a horizontal line parallel to the x-axis and the line pass through (0,2) and the shaded region is below the line.
Hence, the inequality is given by:
y<2
The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth. 10.2 inches 24.0 inches 28.2 inches 30.0 inches
Answer:
10.2 inches
Step-by-step explanation:
Ok let's assume we don't know the larger (the c value).
So this means using [tex]a^2+b^2=c^2[/tex] we have:
[tex]12^2+15^2=c^2[/tex]
[tex]144+225=c^2[/tex]
[tex]369=c^2[/tex]
Square both sides:
[tex]c=\sqrt{369} \aprox 19.2[/tex
Now assume we know the larger is 15 (this means c=15 now), then we have
[tex]a^2+12^2=15^2[/tex]
[tex]a^2+144=225[/tex]
Subtract 144 on both sides:
[tex]a^2=225-144[/tex]
Simplify:
[tex]a^2=81[/tex]
Square root both sides:
[tex]a=9[/tex]
The difference between 19.2 and 9 is 19.2-9=10.2.
Answer:
Option 1 - 10.2 inches.
Step-by-step explanation:
Given : The lengths of two sides of a right triangle are 12 inches and 15 inches.
To find : What is the difference between the two possible lengths of the third side of the triangle?
Solution :
Since, It is a right angle triangle so we apply Pythagoras theorem,
[tex]C^2=A^2+B^2[/tex]
Where, C is the hypotenuse the longer side of the triangle
A is the perpendicular
B is the base
There will be two cases,
1) Assume that C=15 inches and B = 12 inches
Substitute the value in the formula,
[tex]15^2=A^2+12^2[/tex]
[tex]225=A^2+144[/tex]
[tex]A^2=225-144[/tex]
[tex]A^2=81[/tex]
[tex]A=\sqrt{81}[/tex]
[tex]A=9[/tex]
Assume that A=15 inches and B = 12 inches
Substitute the value in the formula,
[tex]C^2=15^2+12^2[/tex]
[tex]C^2=225+144[/tex]
[tex]C^2=369[/tex]
[tex]C=\sqrt{369}[/tex]
[tex]C=19.2[/tex]
Therefore, The possible length of the third side of the triangle is
[tex]L=C-A[/tex]
[tex]L=19.2-9[/tex]
[tex]L=10.2[/tex]
Therefore, The difference between the two possible lengths of the third side of the triangle is 10.2 inches.
So, Option 1 is correct.
Determine the number of x-intercepts that appear on a graph of each function. f(x)= (x-6)^2(x+2)^2
Answer:
Two x-intercepts x = -2 and x = 6Step-by-step explanation:
[tex]f(x)=(x-6)^2(x+2)^2\to y=(x-6)^2(x+2)^2[/tex]
x-intercepts are for y = 0.
Put y = 0 to the equation:
[tex](x-6)^2(x+2)^2=0\iff(x-6)^2=0\ \vee\ (x+2)^2=0\\\\(x-6)^2=0\iff x-6=0\qquad\text{add 6 to both sides}\\\\x=6\\\\(x+2)^2=0\iff x+2=0\qquad\text{subtract 2 from both sides}\\x=-2[/tex]
Answer:
the awnser is 2
Step-by-step explanation:
10=6^2+a^2 what is a
Answer:
[tex]a=\pm i\sqrt{26}}[/tex]
Step-by-step explanation:
[tex]6^2+a^2=10\\\\36+a^2=10\qquad\text{subtract 36 from both sides}\\\\a^2=-26<0\\\\\bold{NO\ REAL\ SOLUTIONS}\\\\\text{In the set of complex numbers:}\\\\i=\sqrt{-1}\\\\a^2=-26\to a=\pm\sqrt{-26}\\\\a=\pm\sqrt{(-1)(26)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\a=\pm\sqrt{-1}\cdot\sqrt{26}\\\\a=\pm i\sqrt{26}[/tex]
8. What is the solution to the equation 2x + 8 - 6 = 4. Show your worn.
Answer:x=1
Step-by-step explanation: 2x+8-6=4
2x+2=4
2x=2
x=1
Answer:
[tex]x = 1[/tex].
Step-by-step explanation:
Apply the associative property of addition to rewrite the left-hand side of the equation.
The two addition operators on the left-hand side are typically evaluated from left to right.
[tex](2x + 8) - 6 = 4[/tex].
However, by the associative property of addition, the second addition can be evaluated before the first:
[tex]2x + (8 - 6) = 4[/tex].
[tex]2x + 2 = 4[/tex].
Move all terms with the unknown ([tex]x[/tex] in this case) to one side of the equation and move all numbers to the other side. For example, add [tex]-2[/tex] to both side of this equation will move the number [tex]2[/tex] to the right-hand side.
[tex]2x +2 -2 = 4 - 2[/tex].
[tex]2x = 2[/tex].
Multiply both sides of the equation by [tex]1/2[/tex] to find the value of [tex]x[/tex].
[tex]x = 1[/tex].
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Answer:
Symbol Words Open dot or closed dot
> greater than open dot
[tex] \ge [/tex] greater than closed dot
or equal to
< less than open dot
[tex] \le [/tex] less than closed dot
or equal to
What are the domain and range of the absolute value parent function?
Answer:
The domain is all real numbers and the range is non-negative real numbers
(y ≥ 0) ⇒ answer B
Step-by-step explanation:
* Lets revise the parent function of the absolute value
- The absolute value or modulus |x| of a real number x is the
non-negative value of x
- The absolute value of a number means the magnitude of the number
without regard to its sign
- The parent function of the absolute value is f(x) = IxI
∵ The domain of the function is all the values of x which make the
function defined
∵ In the function f(x) = IxI, x can be any number
∴ The domain of the f(x) is any real number
∴ The domain is (-∞ , ∞) or {x : x ∈ R}
∵ The range is the set of values of y that corresponding with the
domain
∵ f(x) = IxI is non-negative value
∴ f(x) ≥ 0
∵ f(x) = y
∴ y ≥ 0
∴ The range is the set of real numbers greater than or equal zero
∴ The range is [0 , ∞) or {y : y ≥ 0}
* The true statement is: The domain is all real numbers and the range is
non-negative real numbers (y ≥ 0)
Use the grouping method to factor 2x^3+6x^2-7x-21
Answer:
[x + 3][2x² - 7]
Step-by-step explanation:
Start out by doing this: [2x³ + 6x² ] - [7x - 21]
↑ ⤻ ↑
GCF: 2x² GCF: -7
Do as so: 2x²[x + 3] -7[x + 3]
You see, one factor is already found [x + 3]. You only use it ONCE. Now, the other factor comes from your two Greatest Common Factors from both groups [2x² - 7]. Together, you end up with the above answer. That arrow under the negative tells you that it is attached to the 3 [distribution of the negative].
Well, I am joyous to assist you anytime.
If y= x^2+3x+5, evaluate y given x= 2+i .
The value of y from the given equation with x=2+i is y= 7(i+2).
The given equation is y= x²+3x+5.
We need to evaluate y from the given equation for x= 2+i.
What are complex numbers?A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part Im(z). Also, ib is called an imaginary number.
The alphabet i is referred to as the iota and is helpful to represent the imaginary part of the complex number. Further the iota(i) is very helpful to find the square root of negative numbers.
Now, put x= 2+i in y= x²+3x+5 and simplify.
That is, (2+i)²+3(2+i)+5
=4+i²+4i+6+3i+5
=15-1+7i
=7i+14
=7(i+2)
Therefore, the value of y from the given equation with x=2+i is y= 7(i+2).
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Select the correct answer.
Which transformation will always map a parallelogram onto itself?
a 90° rotation about its center
A.
B.
a reflection across one of its diagonals
c.
a 180° rotation about its center
D.
a reflection across a line joining the midpoints of opposite
Answer:
The answer is c.
This is because when it rotates a 180 degrees around its center it maps a parallelogram on to itself.
True or False? Def is a right triangle.
Answer:
Step-by-step explanation:
We can determine if the triangle is a right triangle by using the Pythagorean theorem
a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse
25^2 + 27^2 = 48^2
625+729=2304
1354 ≠2304
This is not true, so this is not a right triangle
Answer:
FALSE - this is not a right triangle.Step-by-step explanation:
If a ≤ b < c are a length of sides of a right triangle, then
a² + b² = c²
We have a = 25, b = 27 and c = 48.
Substitute:
25² + 27² = 48²
625 + 729 = 2304
1354 = 2304 FALSE
A delivery truck company just bought a new delivery truck...
Answer:
A) 760 ft³
Step-by-step explanation:
The surface area of the figure has to be calculated.
Step 1: Divide the figure
The figure is divided into the following parts to calculate the volume.
Part 1: Box without ledge
Formula for volume of rectangle = length x width x height
Volume = 14.3 x 7.8 x 6.6
Volume = 736.164 ft³
Part 2: Box with ledge-we will only calculate height and width since the length has already been included in part 1 therefore including it again would result in double counting and give the wrong answer.
Volume = height x width
Volume = 2.7 x 7.8
Volume = 21.06 ft³
Step 2: Add both volumes to find the total volume
Volume part 1 + Volume part 2 = 736.164 ft³ + 21.06 ft³
= 757.224 ft³ rounded off to nearest tenth = 760 ft³
Therefore, answer A is correct.
!!
The slope of the line passing through the points (-1, 5) and (3,5) is
Answer:
the slope = 0Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-1, 5) and (3, 5). Substitute:
[tex]m=\dfrac{5-5}{3-(-1)}=\dfrac{0}{4}=0[/tex]
It's a horizontal line y = 5.
Find the value of C in a triangle where a = 6, b = 8, and c = 12.
Answer: 117°
Step-by-step explanation:
Use the Law of Cosines:
c² = a² + b² - 2ab · cos C
12² = 6² + 8² - 2(6)(8)(cos C)
144 = 36 + 64 - 96 cos C
144 = 100 - 96 cos C
44 = -96 cos C
[tex]-\dfrac{44}{96}=cosC\\\\\\cos^{-1}\bigg(-\dfrac{44}{96}\bigg)=C[/tex]
117° = C
In the diagram of circle O, what is the measure of ∠ABC if m(arc)AC= 234 and the measure of little arc AC=126
Answer:
54
Step-by-step explanation:
234-126 = 108
108/2 = 54
Different types of parallelograms have distinguishing traits. Compare and contrast the rectangle, rhombus, and square based upon the characteristics of their angles. Which one(s) have angles whose sum is 360°? Which one(s) have both pairs of opposite angles that are congruent? Which one(s) have four right angles?
Step-by-step explanation:
Rectangles, rhombuses, and squares all have angles that add up to 360°.
Rectangles, rhombuses, and squares all have opposite angles that are congruent.
Rectangles and squares have four right angles.
the square has 4 right angles, the rectangle has both pairs of opposite angles that are congruent, and the rhombus has angles where the sum is 360 degrees.
Your class started at 12:17 PM and ended at 12:49 PM. What angle did the minute hand of a watch sweep through during the class?
A. 186
B. 192
C. 180
D. 168
Answer:
192
Step-by-step explanation:
12:49 - 12:17 = 32min
if 60min = 360°
32min = ?
32×360
60
=192°
Answer:
B. 192 degrees
Step-by-step explanation:
First, calculate how many degrees a minute equals.
The minute hand rotates 360 degrees every 60 minutes.
Thus, one minute is equivalent to dividing 360 degrees by 60 minutes, that is 360/60 = 6 degrees per minute.
Now, we subtract the minutes from the two hours given,
12:49 PM - 12.17 PM = 32 minutes
Finally, we calculate the angle traveled by the minute hand by multiplying 6 degrees by 32 minutes, that is
Angle = 6 * 32 = 192 degrees.
I hope this helps!
what is 362 equal to 126 substracted from r?
Answer:
488 = r
Step-by-step explanation:
362 = -126 + r
126 +126
----------------
488 = r
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the degree of the polynomial 3x^3+0x^4+8
(A) 4
(B) 1
(C) 3
(D) 2
Answer:
(C) 3
Step-by-step explanation:
Let us define the degree of polynomial first
"The degree of a polynomial is the highest power of the variable in the given expression"
Now,
Given expression is:
3x^3+0x^4+8
The highest degree from first observation seems to be 4 but the term with exponent 4 is being multiplied with zero so the degree is then 3 ..
Therefore the correct answer is C. 3 ..
evaluate expression for given value 7x=8 WHEN X=2
Final answer:
The expression 7x = 8 evaluated with x = 2 results in 14, not 8. There was a misunderstanding in the question as it was not asking for a solution to the equation but rather an evaluation of the expression with a given value of x.
Explanation:
The question asks us to evaluate the expression 7x = 8 when x = 2. However, there seems to be a misunderstanding in the way the question is framed. Normally, an expression such as 7x = 8 would be an equation we solve to find the value of x. But since we are given that x = 2, it appears the task is to substitute this value into the expression 7x and see if it equals 8. Let's clarify and solve accordingly.
First, substitute x = 2 into the expression 7x:
7 * 2 = 14
Therefore, when we substitute x = 2 into the expression 7x, we get 14, not 8. It seems there was confusion in the question regarding what was being asked. If the task was to solve 7x = 8, then x would not equal 2 since 7*2 = 14. However, the original instruction was misunderstood, and the correct task was to substitute x = 2 into the expression and evaluate it, which we did correctly.
f(x) = 2x^2 what is f(3)
Answer:
18 since f(3)=18
Step-by-step explanation:
f(x)=2x^2 is give as our function. To find f(3) we need to replace x with 3.
f(3)=2(3)^2 (Replaced x with 3.)
f(3)=2(9) (Did 3^2 which was 3*3=9)
f(3)=18 (Did 2(9) which was 18)
[tex]f(3)=2\cdot 3^2=18[/tex]
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A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 6t, where t represents time in minutes and p represents how far the paint is spreading.
The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2.
Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points)
Part B: How large is the area of spilled paint after 8 minutes? You may use 3.14 to approximate π in this problem. (4 points)
Answer:
A:A(6t)=πp^2
B: about 7234.56
Step-by-step explanation:
First find A[p(t)], Since this is a composite function so whenever you see p(t), you replace it with 6t, that is the value of p(t).
This is a simplified version of the area of the circle as a function of time A(6t)=πp^2
To find how large the area of paint spilled plug in 8 for t because t represents time.
A(48)≈3.14(48)^2
A(48)≈3.14*2304
A(48)≈7234.56
Final answer:
To find the area of spilled paint over time, we replace the time-dependent spread 'p(t)' in the area function 'A(p) = πp²' with '6t'. This results in the equation 'A[p(t)] = 36πt²'. After 8 minutes, the area is approximately 7233.76 square units when using 3.14 for π.
Explanation:
To solve for the area of the circle of spilled paint as a function of time, we need to use the given functions. We are given p(t) = 6t, which represents how far the paint spreads over time in minutes. The area of the circular pattern is given by A(p) = πp².
Part A
To find A[p(t)], we substitute the expression for p(t) into the equation for A(p):
A[p(t)] = π(6t)²
= π(36t²)
= 36πt²
Part B
After 8 minutes, the area of spilled paint can be calculated by substituting t=8 into the function A[p(t)]:
A[p(8)] = 36π(8)²
= 36π(64)
= 2304π
≈ 2304(3.14)
≈ 7233.76 square units
Consider reflections of AJKL.
What line of reflection maps point K to point Kat (-5,2)?
What line of reflection maps point L to point L'at
(-2,3)?
its y-axis for the first answer and the other one its, y=-x
The line of reflection which maps the point K to K' and L to L' is Y axis.
What is Line of Reflection?Reflection is the transformation where the image is flipped.
Line of reflection is the line for which a figure has a mirror image over that line.
Given a triangle JKL.
Let the coordinate of the triangle be J(4, 5), K(5, 2) and L(2, 3).
When a coordinate (x, y) is reflected over the X axis, then the coordinates changes to (x, -y).
When a coordinate (x, y) is reflected over the Y axis, then the coordinates changes to (-x, y).
Here,
K(5, 2) changes to K'(-5, 2).
Here x coordinate changes sign.
So the line of reflection is Y axis.
Similarly, the line of reflection for the other transformation is also Y axis.
Hence the line of reflection is Y axis.
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Complete the table for the given rule y=2x
Answer:
18, 5, 2
Step-by-step explanation:
its pretty much X times 2 to find Y and to find X with Y you must divide Y by 2
Answer:
18, 5, and 2
Step-by-step explanation:
#1 Plug in 9 for x
y = 2(9)
y = 18
#2 Plug in 10 for y
10 = 2x
Divide by 2 on Both sides
5 = x or x = 5
#3 Plug in 1 for x
y = 2(1)
y = 2
Hope this helps!
Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books. One-third of Jason's collection and Nathan's entire collection add up to 31 books.
There are 21 books Jason's have and 24 books Nathan's have.
Given
Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books.
One-third of Jason's collection and Nathan's entire collection add up to 31 books.
Let the number of collection of books Jason's be x.
And the number of collection of books Nathan's be y.
Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books.
[tex]\rm 6x+\dfrac{1}{3} y=134\\\\\dfrac{18x+y}{3} =134\\\\ 18x+y = 134\times 3\\\\18x+y=402[/tex]
One-third of Jason's collection and Nathan's entire collection add up to 31 books.
[tex]\rm \dfrac{1}{3}x+y=31\\\\\dfrac{x+3y}{3} =31\\\\x+3y=31\times 3\\\\x+3y=93[/tex]
On solving both the equations;
From equation 1;
[tex]\rm 18x+y=402\\\\y = 402-18x[/tex]
Substitute the value of y in equation 2
[tex]\rm x+3y=93\\\\x+ 3(402-18x)=93\\\\x+1206 -54x=93\\\\-53x = 93-1206\\\\-53x =-1113\\\\x = \dfrac{-1113}{-53}\\\\x=21[/tex]
Substitute the value of x in equation 2
[tex]\rm x+3y=93\\\\21+3y=93\\\\3y=93-21\\\\ 3y =72\\\\ y = \dfrac{72}{3} \\\\ y=24[/tex]
Hence, there are 21 books Jason's have and 24 books Nathan's have.
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