The solutions for the given quadratic equation are:
[tex]x = 8 \pm i[/tex]
How to find the solutions of the quadratic equation?
Here we have the quadratic equation:
[tex]x^2 = 16x - 65[/tex]
We can rewrite it as:
[tex]x^2 - 16x + 65 = 0[/tex]
Using Bhaskara's formulas, we get:
[tex]x = \frac{-(-16) \pm \sqrt{(-16)^2 - 4*65} }{2} \\\\x = \frac{16 \pm \sqrt{(-4)} }{2}[/tex]
Now, remember that:
[tex]\sqrt{-1} = i[/tex]
Then we can rewrite:
[tex]x = \frac{16 \pm \sqrt{-1} *\sqrt{4} }{2}\\\\x = 8 \pm i[/tex]
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I am studying geometry this summer but can’t solve this question what would be the correct answer
Answer: F
Step-by-step explanation:
Bisectors of an angle split the angle in half which you can visually see from the image. So, the answer is F.
Find the polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity.
The polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity is x⁴ - 4x³ + 5x²- 4x + 4 = 0. This can be obtained by finding factors and multiplying them.
What is the required polynomial ?
Given that zeroes, 2 of multiplicity 2, and i of single multiplicity, that is, (x - 2), (x - i) and (x + i) are the factors of the polynomial.
Thus the polynomial can be written as
(x - 2)²(x - i)(x + i) = 0 ((x - 2) is squared as multiplicity is 2)
(x² - 4x + 4)(x²-i²) = 0
(x² - 4x + 4)(x²+1) = 0
x⁴ - 4x³ + 4x² + x² - 4x + 4 = 0
⇒ x⁴ - 4x³ + 5x²- 4x + 4 = 0
Hence the polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity is x⁴ - 4x³ + 5x²- 4x + 4 = 0.
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A number line goes from negative 5 to positive 5. Point D is at negative 4 and point E is at positive 5. A line is drawn from point D to point E.
What is the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio?
Negative one-eleventh
One-eleventh
Two-fifteenths
Fifteen-halves
Directed numbers are numbers that have either a positive or negative sign, which can be shown on a number line. Therefore, point F is Fifteen-halves of line segment DE.
A number line is a system that can show the positions of positive or negative numbers. It has its ends ranging from negative infinity to positive infinity. Thus any directed number can be located on the line.
Directed numbers are numbers with either a negative or positive sign, which shows their direction with respect to the number line.
In the given question, the distance between points D and E is 9 units. So that dividing 9 units in the ratio of 5 to 6, we have;
[tex]\frac{5}{6}[/tex] x 9 = [tex]\frac{45}{6}[/tex]
= [tex]\frac{15}{2}[/tex]
Therefore, the location of point F, which partitions the directed line segment from d to E into a 5:6 ratio is [tex]\frac{15}{2}[/tex]. Thus the answer is Fifteen-halves.
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Answer:
1/11
Step-by-step explanation:
Got it right on assignment
the sum of seven odd consecutive is 217. Find the middle number
Answer:
x + x+1 + x+2 + x+3 + x+4 + x+5 + x+6 =217
7x+21=217
7x=196
x=28
Middle Number will be:
x+3
28+3
=31
Therefore, the middle number is 31.
Step-by-step explanation:
Answer:
31
Step-by-step explanation:
Let's put this into equation form.
n + (n + 1) + (n+2) + (n+3) + (n+4) + (n + 5) + (n+6) = 217
Each number is increasingly getting farther away from n (the first number) by 1.
If we simplify, by adding all of the numbers and the n's. We get:
7n + 21 = 217
Let's subtract 21 from both sides to start the process of isolating x.
7n = 196
Now we can divide both sides by 7, to isolate x.
n = 28.
That looks like the answer, but it is not. Remember n is the first number, we want the middle, which out of 7 is the 4th number.
The 4th number is equal to (n+3) or (28 + 3)
The 4th number is 31.
Let's check if this is correct.
28 + 29 + 30 + 31 + 32 + 33 + 34 = 217.
The problem is complete.
The root rafter of a house has been raised to a height of 18 yards at the ridge. Half of the length of the run measures 14 yards. Find the length of the rafter.
The length of the rafter as detailed in the question is approximately; 22.80 yards
How to use Pythagoras theorem?
The formula for Pythagoras theorem is;
a² + b² = c²
where;
a and b are adjacent and opposite sides of the triangle formed
c is the hypotenuse
Now, a rafter is a sloped member of a roof structure. Thus, if the rafter is raised to a height of 18 yeards, it means that is the vertical height of the top of the rafter to the bottom of the kingpost.
Now, if half the length run is 14 yards, it means that half of the tie beams is 14 yards. Thus, from the base of the rafter to the center of the tie beams is 14 yards. Thus, we will use Pythagoras theorem to find the length of the rafter.
c = √(14² + 18²)
c = √520
c = 22.80 yards
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how do i find the slope of the line containing ordered paid? A(2,-5), B(-2,6)
The slope of the given containing ordered paid A(2,-5) and B(-2,6) is -11/4.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the given containing ordered paid A(2,-5) and B(-2,6) is:
Slope = 6+5/-2-2 = 11/-4
Hence, the slope of the given containing ordered paid A(2,-5) and B(-2,6) is -11/4.
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Out of 54 jelly beans, two were found to be defective. What is the experimental probability a jelly bean is defective?
26/27
1/27
2/27
24/27
Answer:
1/27
Step-by-step explanation:
To find the probability of a defective jelly bean
P(defective) = number defective/ total
=2/54
= 1/27
For each of the following a) identify the inverse function needed to solve for the indicated angle and b) solve for the angle (round to the nearest tenth of a degree).
The angle is the cosine inverse function because base over hypotenuse. Then the angle will be 37°.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The triangle with base of 4 units and hypotenuse of 5 units.
We know that the angle is given by the cosine inverse function because base over hypotenuse. Then we have
⇒ cos⁻¹ (4/5)
Then the angle will be
⇒ 36.869 ≈ 37°
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Please help me. Due today. Please show work so I can get it correct!!!!
Based on the inscribed angle theorem, the value of x is: 126°.
What is the Inscribed Angle Theorem?The inscribed angle theorem states that, the measure of inscribed angle (63 degrees) equals half of the measure of central angle (x).
Thus, we would have:
63 = 1/2(x)
2(63) = x
126 = x
x = 126°
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At a weather station in the Artic the temperature was recorded as -23° C.
Two hours later it had fallen by 11° C.
(i) What was the new temperature?
()Four hours after the first readings the temperature was -45° C.
By how much had the temperature fallen in four hours.
Answer:
(i) -34° C.
(ii) The temperature had fallen by 11° C.
Step-by-step explanation:
(i) As it's a negative number its like we are adding it so 23 + 11 = 34 and as it is a negative number it would be -23 - 11 = -34 which makes it -34° C.
(ii) We know that the temperature now is -45° C, we need to find out how much the temperature had fallen in the 4 hours which had passed. So what we do is essentially add it considering its a negative number so we add -34 by 11 which equals -45. We do this so we can find out how much the temperature had dropped within the 4 hours and as we know that we needed to add 11 to the previous temperature (-34° C) it means that the temperature has dropped by 11° C.
What is the measure of z?
Z
X
y
4
9
z = [ ? ]VI
Answer:
z= [ 5] VI
that is my answer
According to the data in the figure, find the value of x and y.
Answer:
This is a educated guess, but x is 80 and y is 100.
Step-by-step explanation:
My logic here is that the triangles are the same because of all the congruent lines and stuff. But from there, you know that both the right and the left side are 40 degrees. You know the total degree of a triangle is 180 so 180 - 40 - 40 is 100. So the final angle is 100. If you look at x, its on the outside, but on a line. If you can imagine a circle, its half, so its a 180 degrees total. Then its 180 = x + 100. So x is 80. And then by that same logic its y = 100.
Can someone help.
Triangle not drawn to scale
Given: m = 53°, a = 18, and c = 14. Find me to the
nearest whole number.
Answer:
m∠C = 38° (nearest whole number).
Step-by-step explanation:
To find the missing angle, use the Sine Rule.
Sine Rule (for angles)
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
where:
A, B and C are the anglesa, b and c are the sides opposite the anglesGiven:
A = 53°a = 18c = 14To find m∠C, substitute the given values into the formula and solve for C:
[tex]\implies \sf \dfrac{\sin 53^{\circ}}{18}=\dfrac{\sin C}{14}[/tex]
[tex]\implies \sf \sin C= \dfrac{14 \sin 53^{\circ}}{18}[/tex]
[tex]\implies \sf C= \sin^{-1} \left( \dfrac{14 \sin 53^{\circ}}{18}\right)[/tex]
[tex]\implies \sf C= 38.40096301...^{\circ}[/tex]
Therefore, m∠C = 38° (nearest whole number).
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Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is impossible?.
Suppose that a probability is approximated to be zero based on empirical results, this does not mean that the event is impossible.
What is probability?The likelihood that an event will occur is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
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Of the houses in Lucia's neighborhood, 1/10 are teal and another 7/10 are red. What
fraction of the houses are either teal or red?
(D) Write your answer as a fraction or as a whole or mixed number.
Answer:
the answer is 8/10
Step-by-step explanation:
The reason is that both of the denominators are the same so that you can add the two numerators and then get the answer.
Please help for 50 points with solution
Answer:
(d) 60°
Step-by-step explanation:
Theorems
Interior angles of a triangle sum to 180°Angles on a straight line sum to 180°Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
⇒ (a + 20) + (a + 10) = (a + 90)
⇒ a + 20 + a + 10 = a + 90
⇒ 2a + 30 = a + 90
⇒ 2a + 30 - a = a + 90 - a
⇒ a + 30 = 90
⇒ a + 30 - 30 = 90 - 30
⇒ a = 60
Answer:
a = 60
Step-by-step explanation:
→ Find the sum of all the angles
2a + 30 + 90 - a = 180
→ Collect the a terms
a + 120 = 180
→ Find a
a = 60
Use slope-intercept form to write the equation of a line that has a slope of −3 and passes through the point (1, −5).
y=
x=
m=
Answer:
y=-3x-2
Step-by-step explanation:
The slope-intercept form is y=mx+b
where m is slope and b is y-intercept.
Substitute m=-3 and point (x,y)=(1,-5) into the equation:
-5=-3(1)+b
-5=-3+b
b=-5-(-3)=-5+3=-2
Therefore, the required equation:
y=-3x-2
what are the possible numbers of positive, negative, and complex zeros of f(x)=-3x^4+5x^3-x^2+8x+4
Answer:
There could be 0, 2, or 4 complex solutions
Step-by-step explanation:
The Fundamental Theorem of Algebra states that any polynomial with n degree will have n solutions So since the degree of the polynomial you provided has a degree of 4, that means there are 4 possible solutions. This question specifically asks for complex zeroes. Complex zeroes come in conjugate pairs, so that means if you have one complex zero, there is another complex zero which is it's conjugate. For this reason, there can only be an even number of complex zeroes. And since there's 4 possible solutions, There could be 0, 2, or 4 complex solutions
How many x-intercepts does the graph of y=2x^2-4x+2 have?
A.0
B.1
C.2
Answer:
B. 1
Step-by-step explanation:
Please see attachment.
Hope this helps!
If not, I am sorry.
Select the correct answer. Consider the following system of equations. Use this graph of the system to approximate its solution. A diagonal curve rises through (negative 5, 1) through (6, 6). A diagonal curve declines through (negative 6, 5) through (7, negative 6) on the x y coordinate plane. A. B. C. D.
The approximate solution to the given system of equations, considering the graph, is given as follows:
D. [tex]\left(-\frac{13}{4}, \frac{5}{2}\right)[/tex].
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
On a graph, the solution of a system of equations is given by the intersection between the curves. In this graph, the intersection of the two curves happen close to x = -3.25, y = 2.5, hence the solution is approximated by:
D. [tex]\left(-\frac{13}{4}, \frac{5}{2}\right)[/tex]
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Answer:
d
Step-by-step explanation:
A student received test grades of 83, 90, and 88. What was her grade on a fourth test if the average for the four tests is 84
Her grade on a fourth test is 75.
The average of e for the four tests is 84.
By substituting the given data in the equation, we get
Let the fourth test marks be x
83 + 90 + 88 + x / 4 = 84
261 + x / 4 = 84
261 + x = 336
x = 336 - 261
x = 75
An average may be described as the sum of all numbers divided by means of the whole quantity of values.
A mean can be defined as an average of the set of values in a sample of data. In different words, a median is also called the mathematics mean.
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if you apply to college as a freshman in 2023, and they accept you, when you start going to college?
Answer: Likely May through August 2023
Step-by-step explanation: It really depends on the college.
Why is partitioning a directed line segment into a ratio of 1:3 not the same as finding One-third the length of the directed line segment?
The ratio given is part to whole, but fractions compare part to part.
The ratio given is part to part. The total number of parts in the whole is 3 – 1 = 2.
The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
The ratio given is part to whole, but the associated fraction is One-third.
The reason why partitioning and fractioning are different is because; The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
Why is partitioning different from fractioning?It follows from the task content that a close analysis of the statement of ratios; 1:3 implies that the whole is divided into four parts; 1+3 = 4.
On the contrary, one-third simply means 1 out of 3 equal parts of the line.
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Answer: OPTION C
Step-by-step explanation:
Calculate: 6666666x666666/1+2+3+4+5+6+5+4+3+2+1- 777777x777777/1+2+3+4+5+6+7+6+5+4+3+2+1
Answer: 3.8395025e+12
Lol
3839502493910
Step-by-step explanation:
you will multiple the 6 and the 7 digits and the other digits
isabella and aiden get a reward of $119 in the ratio of 4 3, what fraction of the total reward does isabella get
Using proportions, considering the given ratio, Isabella gets [tex]\frac{4}{7}[/tex] of the total reward.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The ratio of Isabella and Aiden is 4:3, which means that out of 4 + 3 = 7 items, Isabella gets 4 and Aiden gets 3, hence the fraction is given by:
[tex]\frac{4}{7}[/tex].
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A frog with bionic legs leaps from a stump with an initial velocity of 64 ft/sec. It
is determined that the height of the frog as a function of time can by modeled
by h (t) = -16t² +64t + 3. How many seconds will it take for the frog to
land on the ground?
Considering the given quadratic function, it is found that it will take 4.05 seconds for the frog to land on the ground.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
The height after t seconds is given by:
h(t) = -16t² + 64t + 3.
it hits the ground when h(t) = 0, hence:
-16t² + 64t + 3 = 0
16t² - 64t - 3 = 0.
The coefficients are a = 16, b = -64, c = -3, hence:
[tex]\Delta = (-64)^2 - 4(16)(-3) = 4288[/tex][tex]t_1 = \frac{64 + \sqrt{4288}}{32} = 4.05[/tex][tex]t_2 = \frac{64 - \sqrt{4288}}{32} = -0.05[/tex]Time has to be positive, hence the frog lands on the ground after 4.05 seconds.
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A squared garden has area 1764m2. Find its length and perimeter?
Answer:
length = 42 mperimeter = 168 mStep-by-step explanation:
A squared garden has area 1764m2. Find its length and perimeter?
Area = l²
inverse formulal = √Area
length√1764 = 42 m
Perimeter l × 442 * 4 = 168 m
Answer:
length=42m
perimeter=168m
Step-by-step explanation:
Area=L^2
L^2=1764
L=√1764
L=42m
Perimeter=42+42+42+42 which equals to 168m
(LOOK AT IMAGE)
A robot can be programmed to draw any regular polygon.
The instructions seen in the example below are used to draw a regular 10- sided polygon with side lengths of 3 cm.
By changing the numbers in the program below, write down the simplest set of instructions needed to make the robot draw a regular 12-sided polygon with side lengths of 5 cm.
Repeat the following 12 times:
> Move forward 5 cm
> Turn clockwise 30°
Want to know how I found this out? Well, let me tell you.
First, they gave us the information that a 12-sided polygon is to be modeled with side lengths 5 cm. So, that basically gives us our first step. That was easy!
Well, now this is a bit harder. How many degrees do we move? There're so many possibilities! Well, not quite.
According to the Polygon Exterior Angle-Sum Property, the exterior angles of any polygon is always 360 degrees. So, we just divide 360 by how many sides there are in the polygon.
There are 12 sides in this polygon, so, [tex]\frac{360}{12}[/tex] is equal to 30 degrees per side. Well, now we have the second step! We're all done. Congratulations!
Mario is having a pizza party on Saturday night. He ordered 8 pizzas. if the average person eats 1/3 of a pizza, how many persons will 8 pizzas serve?
Answer:
24 people
Step-by-step explanation:
I pizza will feed 3 people
There are 8 pizza's
8 x 3 = 24
Determine the equation of the parabola shown in the diagram in vertex form. (check picture below)
The equation of the parabola is y - 1 = (2/3) * (x - 3)².
What is equation of the parabola ?The general equation of a parabola is: y-k = a(x-h)²
(h, k) - Coordinates of the vertex.
a - Vertex constant
Here:
(h, k) = (3, 1) and (x, y) = (0, 7).
So,
7 - 1 = C · (0 - 3)²
6 = 9 · C
C = 2/3
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