Answer:
two real roots
Step-by-step explanation:
x^2 + 7x – 6 = 0
We can use the discriminant
This is in the form ax^2 +bx+c=0
b^2 -4ac
If b^2 -4ac> 0 there are 2 real roots
If b^2 -4ac = 0 there is one real root
If b^2 -4ac <0 there are two complex roots
7^2 -4(1)*(-6)
49 +24
73
Since 73 > 0 there are two real roots
Answer:
The graph of the equation intersects the x-axis at two points. Therefore, it has two solutions.
Step-by-step explanation:
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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Let f(x) = 2x − 5 and g(x) = 7x − 3. What is (f(g(x))
Answer:
14x-11
Step-by-step explanation:
f(x) = 2x − 5
g(x) = 7x − 3
(f(g(x))=
Substitute g(x) into f(x) for every x
f(g(x) = 2 (g(x) -5
=2 (7x-3) -5
Distribute
=14x-6 -5
=14x-11
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
In the event of delinquency, the Buyer may divide any payment not received into not more than three equal installments to be included on the next consecutive monthly payments. Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”
According to the contract, which of the following is not a responsibility of the buyer?
a.
Pay the monthly payment on time.
b.
Notify the bank if a payment is going to be late.
c.
Pay an additional $75.00 with a payment made after the 15th day of the month it was due.
d.
Notify the bank of his or her intent to split a late payment into three partial payments.
Answer:
Option B
Step-by-step explanation:
Given:
As per the contract "Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”
So,buyer needs to only notify the bank about the monthly payments in case of delinquency and not about if payment is going to be late or not.
Option B is correct
Notify the bank if a payment is going to be late !
The buyer is not responsible for paying an additional $75.00 for payments made after the 15th of the month it was due; this is not specified in the contract's provided clauses.
According to the contract, the responsibility that is not a part of the buyer's obligations is option (c): Pay an additional $75.00 with a payment made after the 15th day of the month it was due. The contract stipulates that the buyer should pay the monthly payment on time (a), notify the bank if a payment is going to be late (b), and notify the bank of his or her intent to split a late payment into three partial payments (d) in the event of delinquency. However, there is no mention within the provided excerpt of the contract that indicates an additional fee of $75.00 is imposed for late payments. It is important for individuals facing financial difficulties, such as inability to make timely payments, to communicate effectively with their lenders to find potential solutions and avoid the repercussions of default.
Do you guys know the answer for number 2
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
SUPER EASY WILL GIVE BRAINLEIST IF DONE BEFORE 10 P.M. PLS HURRY. IF U HAVE TIME PLS HELP ME ON OTHER QUESTIONS THANK YOU
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
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:
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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Points A and B have opposite x-coordinates but the same y-coordinates. How many units away are each of the points from the y-axis?
Answer:
2
Step-by-step explanation:
i got it right on the quiz
Points with opposite x-coordinates and the same y-coordinate are symmetrically placed with respect to the y-axis. Their distance from the y-axis is the absolute value of their x-coordinate.
If points A and B have opposite x-coordinates but the same y-coordinates, we can deduce that they are positioned symmetrically with respect to the y-axis. The distance of each point from the y-axis is equal to the absolute value of their x-coordinate. This is because the y-axis serves as a reference line where the x-coordinate is zero.
For example, if point A has coordinates (-5, 3) and point B has coordinates (5, 3), then both points are 5 units away from the y-axis. The only difference between their positions is the direction relative to the y-axis; point A is on the left side and B is on the right side.
So, the general rule is that no matter the y-coordinate, the distance of a point from the y-axis is simply the absolute value of its x-coordinate.
solve the right triangle given that A=30 degrees, C=90 degrees and a =15
Answer:
B = 60°; c = 30; b = 25.98
Step-by-step explanation:
1. Calculate ∠B
∠A + ∠B + ∠C =180°
30° + ∠B + 90° = 180°
∠B + 120° = 180°
∠B = 60°
2. Calculate c
sinA = a/c
sin30° = 15/c
½ = 15/c
c = 2 × 15 = 30
3 .Calculate b
sinB = b/c
sin60° = b/30
√3/2 = b/30
b = (30√3)/2 = 15√3 = 25.98
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.
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
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.
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.
NEED HELP ASAP, WILL GIFT 60 COINS AND MARK BRAINLIEST
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
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
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.
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].
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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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]
What is the Gfc of 3p^4 and 4p
For this case we have by definition, the GFC of two numbers is given by the largest factor that divides both numbers without leaving residue.
We have the following expression:
[tex]3p ^ 4[/tex] and [tex]4p[/tex]
So, we look for the factors of 3 and 4:
3: 1.3
4: 1, 2, 4
Thus, the GFC of both numbers is "1".
The GFC of both expressions is: [tex]1p = p[/tex]
Answer:
p
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!
The rectangle below has an area of x^2-25 square meters and a length of x+5.
What expression represents the width of the rectangle?
Answer:
(x-5)
Step-by-step explanation:
factor the equation and the sign is x-5 because the equation has to be negative at the 25.
The width of the rectangle is found by dividing the area by the length, which simplifies to x - 5.
Explanation:The area of a rectangle is given by the product of its length and width. Given the area is x² - 25 and the length is x + 5, you can find the width by dividing the area by the length.
So, the width = area / length = (x² - 25) / (x + 5).
Factoring the numerator gives us (x + 5) (x - 5), therefore, the width = [(x + 5) (x - 5)] / (x + 5). As you can see, (x + 5) is a common factor in the numerator and denominator so we can cancel them out.
The resulting expression for the width is x - 5.
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Figure ABCD has vertices A(-2,3), B(4,3), C(4,-2), and D(-2,0). What is the area of figure ABCD
Answer:
24 units
Step-by-step explanation:
As we can see in the attached picture. The area will be given by the sum of the area of the rectangle and the area of the triangle in the bottom.
The rectangle has a base of 6 units and a height of 3 units. Therefore:
A1 = bh = 6*3 = 18 units.
The triangle has a base of 6 units and a height of 2 units. Therefore:
A2 = (1/2)bh = (6*2)/ 2 = 6 units
Then, the total area is:
A = A1 + A2 = 6 + 18 = 24 units
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
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.
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!
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 ..