Answer: [tex]x= \frac{-1+\sqrt{97} }{8} , \frac{-1-\sqrt{97} }{8}[/tex]
Step-by-step explanation:
Use the Quadratic Formula .. if you use Completing the Square it'll take longer!!
In general, given [tex]ax^{2} +bx+c=0[/tex] , there exists two solutions where:
[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] , [tex]\frac{-b-\sqrt{b^{2} }-4ac}{2a}[/tex]
In this case, a=4 , b=1 and c= -6
[tex]x= \frac{-1+\sqrt{1-4*4*-6} }{2*4}[/tex] , [tex]\frac{-1-\sqrt{1-4*4*-6} }{2*4}[/tex]
Simplify.
[tex]x=\frac{-1+\sqrt{97} }{8}[/tex] , [tex]\frac{-1-\sqrt{97} }{8}[/tex]
Inside triangle ABC point O was drawn such that ∠OAB, ∠OBA, ∠OBC, and ∠OCA are all congruent. It is also true that ∠OAC and ∠OCB congruent. Find the angle measures in triangle ABC.
Answer:
m∠A = 60
m∠B = 60
m∠C = 60
Step-by-step explanation:
Please mark Branilest
6) Name all factors of x3 – 3x2 – 10x.
A. x
B. x + 5
C. x – 5
D. x + 2
E. x – 2
F. 2
G. 5
H. None of the above
its not on edg
Answer:
A. x
C. x – 5
D. x + 2
Step-by-step explanation:
From the question above, we are asked to find the factors of an algebraic expression that is given as:
x³ - 3x² - 10x
We would use the step of factorisation
Step 1
x(x² - 3x- 10)
The first factor of the algebraic expression has been obtained = x
Step 2
We factorise x² - 3x - 10
x² +2x - 5x - 10
(x²+2x) - (5x - 10)
x(x + 2) -5(x + 2)
(x + 2)(x - 5)
Step 3
x³ - 3x² - 10x
x(x² - 3x- 10)
(x)(x + 2)(x - 5)
Therefore, the factors of the algebraic expression are:
(x), (x + 2), (x - 5)
How many dimensions does a plane have?
Ο Α. Two
O B. Zero
O C. One
O D. Three
Answer:
2
Step-by-step explanation:
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far
How many dimensions does a plane have?
● Α. Two
O B. Zero
O C. One
O D. Three
30. The box-and-whisker plot shows the average temperatures in Tucson, Arizona in December. (1 point)
Which statement about the temperatures in Tucson must be true?
About half of the days in December had average temperatures above 60 degrees.
About half of the days in December had average temperatures between 52 and 60 degrees.
The coldest day in December was 52 degrees.
The hottest day in December was 65 degrees.
Answer:
About half of the days in December has average tempetare between 52 and 60 degrees
(SEE THE ATTACHMENT)
Step-by-step explanation:
See the box-and-whisker plot.
Median = 58
1st quartile (which is the median of all value below 58) = 52
2nd quartile (which is the median of all value above 58) = 60
From 1st quartile to median = Almost quarter of the values
From median to 2nd quartile = Almost quarter of the values
From 1st quatile to 2nd quartile = Almost half of the values
So
1st statement is wrong
2nd statement is correct
3rd statement is wrong (Coldest day was 49 degrees)
4rth statement is wrong (Hottest day was 68 degrees)
What are the lines in the picture parallel ?
A. They both lie in the same plane
B. They both travel on forever and ever
C. They are both the same size
D. They are equal width apart, travel in the same direction, and never meet.
Please help me with this
The lines in the picture parallel because they are equal width apart , option (D) is correct.
What are parallel lines?Two straight lines in a plane such that even on getting extend till infinity they do not intersect each other and always at same distance from each other .
In the given picture the red line and black lines appears to have same distance between them .They are parallel not only because they are coplanar as coplanar lines can intersect each other.
Two lines travelling to infinity need not to be parallel always as they can intersect at some point and still travel to infinity.
If two lines of same size are there still they can have different perpendicular distance between them at diff points, they can be slightly tilted towards each other . Therefore they need not be parallel when they are of same size. And given lines are infinite therefore we cannot say that they are of same size also.
If two lines are equal width apart and never meet then it means the distance between them is always same therefore they are parallel,
Therefore, the lines in the picture are parallel because they are equal width apart option (d) is correct.
Also, Learn more about the parallel lines from the given below link:
https://brainly.com/question/19714372
#SPJ5
Colleen is knitting a scarf. For every 45 pieces of blue yarn she uses, she uses 18 pieces of red yard. What equation can be used to represent the proportional relationship between the amount of blue yarn, b, and red yard, r, that Colleen uses when knitting a scarf?
Answer:
The equation that can be used to represent the proportional relationship between the amount of blue yarn, b, and red yarn, r, that Colleen uses when knitting a scarf is:
b = 2.5 ror
b = 5r/2Step-by-step explanation:
In the exercise are given the variables that we must use in the equation: b and r, where b is the amount of blue yarn and r is the amount of the red yarn, now it's just missing the proportion that must be used in the equation, to identify this you only must divide the biggest amount (45) by the smallest amount (18), how I show below:
Proportion = 45/18 = 2.5 or 5/2Having this, you can make the equation taking into account the proportion:
b = 2.5 rThis equation marks that by each piece of blue yarn, are needed 2.5 pieces of red yarn, we can prove the equation replacing the r-value by 18:
b = 2.5 r b = 2.5 (18) b = 45How you can see, replacing the r-value by 18, the value given for red yarn, we obtain the value given for the blue yarn: 45.
Answer:
b = 2.5 r
or
b = 5r/2
A rectangular garden has a length of x + 2 ft. and a width of x + 8 ft. What must x be in order for the garden to have an area of 91 sq. ft.?
Answer:
x=5
Step-by-step explanation:
5+2=7
5+8=13
13*7=91
Answer: 5 ft
Step-by-step explanation:
Our equation can be (x + 8)(x + 2) = 91. Now we solve:
(x + 8)(x + 2) = 91
x^2 + 2x + 8x + 16 = 91 expand
x^2 + 10x + 16 = 91 simplify
x^2 + 10x - 75 = 0 subtract 91 from both sides
(x + 15)(x - 5) = 0 factor
x + 15 = 0 x - 5 = 0
x [tex]\neq \\[/tex] -15 x = 5
x can't equal -15 because you cannot have negative feet, so x = 5 feet
What is the slope of the line shown below?
10
(6,2)
10 (-2,-3)
10
10-
O
A.
olm
O
B.
LOCO
O c.
D.
O
100
Helpppppp
question 3 <><><><><><><><><><><>
Answer: C. none of the above
Step-by-step explanation:
Because you are dealing with a positive and a negative number here, the only way you would be able to get a positive number out of both would be if you squared both of the numbers in parentheses. (grab a calculator and try it if you have one)
(6)^2 and (-6)^2 both give you 36.
And, 6)^3 and (-6)^3 both give you 216.
But, because there are no parentheses in the equation, then the answers would be different, so the correct answer is none of the above.
For the graph, what is a reasonable constraint so that the function is at least 300?
(Graph Below)
A) x ≥ 0
B) −5 ≤ x ≤ 30
C) 0 ≤ x ≤ 25
D) All real numbers
Answer:
C) 0 ≤ x ≤ 25
Step-by-step explanation:
We are supposed to find a reasonable constraint so that the function is at least 300 i.e. the value of x at which f(x) is greater or equal to 300
A)x ≥ 0
Refer the graph
At x = 0
f(x)=300
On increasing the value of x , f(x) increases but at x = 12 it starts decreasing
So, x ≥ 0 can also have f(x)<300
So, Option A is wrong
B)−5 ≤ x ≤ 30
At x = -5
f(x) = 100
So, Option B is wrong since we require f(x) is greater or equal to 300
c)0 ≤ x ≤ 25
At x = 0
f(x)=300
At x = 12 , it starts decreasing
At x = 25
f(x)=300
So, The value of f(x) is at least 300 when 0 ≤ x ≤ 25
D)All real numbers
At x = 30
f(x)=0
But we require f(x) greater or equal to 300
Hence Option C is true
Answer:
C) 0 ≤ x ≤ 25
Its correct! Hope this helps :)
please help me find the volume for this triangular prism
Answer:
140 yd³
Step-by-step explanation:
The volume (V) of the triangular prism is calculated as
V = Ah ( A is the area of the triangular face and h is the depth )
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
= 0.5 × 5 × 8 = 20 yd² , thus
V = 20 × 7 = 140 yd³
In the notation "s(x) = ...," what does "s(x)" represent?
A.
The value of x depends on the value of s(x), since xis a function of s.
OB.
There is not enough information to answer this question.
C.
The value found when sis multiplied by the value x.
D.
The value of s(x) depends on the value of x, since s is a function of x.
Answer:
C
Step-by-step explanation:
I think
What's the largest eight-digit base 2 integer? Express your answer in base 10.
Answer:
[tex]11111111_{2} =255_{10}[/tex]
Step-by-step explanation:
The largest eight-digit base 2 integer is 11111111.
[tex]\begin{array}{rcr}1\times 2^{7} & = & 128\\1\times 2^{6} & = & 64\\1\times 2^{5} & = & 32\\1\times 2^{4} & = & 16\\1\times 2^{3} & = & 8\\1\times 2^{2} & = & 4\\1\times 2^{1} & = & 2\\1\times 2^{0} & = & 1\\\mathbf{11111111_{2}} & = & \mathbf{255_{10}}\\\end{array}[/tex]
Answer:1111111
Step-by-step explanation:
The largest eight-digit base 2 integer is 11111111
Evaluate 3x for x = −2, x = 1, and x = 3. Question 18 options: A) 1∕3, 0, 9 B) 1∕9, 3, 27 C) 9, 3, 27 D) 1∕9, 9, 27
Answer:
D
Step-by-step explanation:
Took it on Ed but it might be different
Answer:
D
Step-by-step explanation:
I did the math :)
If f(x) = 5x, what is y(x)?
Answer:
Step-by-step explanation:
y(x) and f(x) are similar in meaning; they both state that the dependent variable is a function of the independent variable x.
f(x) = 5x = y(x).
Which took place in 1853?
O The US made the Gadsden Purchase.
The US received payment from Mexico for Texas.
Mexico won the Mexican-American War.
Mexico paid the US for the Mexican Cession.
Answer:
The answer is a
Step-by-step explanation:
I hoped i helped
M is directly proportional to r3
When r = 4, M = 160
a) Work out the value of M when r = 2.
Answer:
M = 20
Step-by-step explanation:
Given that M is directly proportional to r³ then the equation relating them is
M = kr³ ← k is the constant of proportion
To find k use the condition when r = 4, M = 160, that is
160 = k × 4³ = 64k (divide both sides by 64 )
2.5 = k
M = 2.5r³ ← equation of proportion
When r = 2, then
M = 2.5 × 2³ = 2.5 × 8 = 20
Answer:
M<varies>r³
M=kr³(k= constant)
when M=160,r=4
160=k(4)³
160=64k
k=2.5
therefore,M=2.5r³
when r=2
M=2.5r³
M=2.5(2)³
M=2.5(8)
M=20
Which is the graph of y=[x]-2?
Please help me i dont understand this is 15 points
Answer:
2. y =13x + 143
Step-by-step explanation:
plug in numbers in your calculator; go to stat → edit,then again to stat → calculate →linear reg→ enter and get a and b, round the numbers
a = 13 , b = 143
The fabric for Isabella’s new dress is sold by the yard. The pattern for the dress requires 8 feet of fabric. How many yards of fabric does Isabella need to purchase if 1 yard is equal to 3 feet?
1 third yard
2 2 over 3 yards
6 yards
24 yards
Answer:
2 2/3 yd
Step-by-step explanation:
Let's convert from feet to yards. See how the feet cancel, because feet is in the denominator and the numerator?
8 ft x 1 yd/3 ft = 8/3 yd
As a mixed number:
8/3 = 2 2/3 yd of fabric
If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, then which statement would be true?
The figure must be an isosceles trapezoid because it has 2 congruent base angles.
The figure must be a rectangle because all rectangles have exactly 2 lines of symmetry.
The figure could be a rhombus because the 2 lines of symmetry bisect the angles.
The figure could be a square because the diagonals of a square bisect the right angles.
Answer:
the figure could be a rhombus because the 2 lines of symmetry bisect the angles
Step-by-step explanation:
Option C is correct. , if a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, the figure could be a rhombus because the 2 lines of symmetry bisect the angles.
Quadrilaterals are figures with four sides and angles. Examples of quadrilateral include:
RectangleSquarerhombusA line of symmetry is a line that divides a shape such that they become mirror images of each other.
Hence, if a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, from the options, the figure could be a rhombus because the 2 lines of symmetry bisect the angles (divides the angles equally).
Learn more here: https://brainly.com/question/19670823
Explain how you can use the inscribed angle theorem to justify its second corollary, that an angle inscribed in a semicircle is a right angle
Step-by-step explanation:
Explanation:
An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define what we call an intercepted arc on the circle. The intercepted arc might be thought of as the part of the circle which is "inside" the inscribed angle. (See the pink part of the circle in the picture above.)
A central angle is any angle whose vertex is located at the center of a circle. A central angle necessarily passes through two points on the circle, which in turn divide the circle into two arcs: a major arc and a minor arc. The minor arc is the smaller of the two arcs, while the major arc is the bigger. We define the arc angle to be the measure of the central angle which intercepts it.
The Inscribed Angle Conjecture I gives the relationship between the measures of an inscribed angle and the intercepted arc angle. It says that the measure of the intercepted arc is twice that of the inscribed angle.
The precise statements of the conjectures are given below. Each conjecture has a linked Sketch Pad demonstration to illustrate its truth (proof by Geometer's Sketch Pad!). The linked activities sheet also include directions for further "hands on" investigations involving these conjectures, as well as geometric problems which utilize their results.
The precise statement of the conjectures:
Conjecture (Inscribed Angles Conjecture I ): In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc..

Corollary (Inscribed Angles Conjecture II ): In a circle, two inscribed angles with the same intercepted arc are congruent.

Proof: The measure of each inscribed angle is exactly half the measure of its intercepted arc. Since they have the same intercepted arc, they have the same measure.
Corollary (Inscribed Angles Conjecture III ): Any angle inscribed in a semi-circle is a right angle.

Proof: The intercepted arc for an angle inscribed in a semi-circle is 180 degrees. Therefore the measure of the angle must be half of 180, or 90 degrees. In other words, the angle is a right angle.
PLEASE HELP ME! I BEG YOU! ILL EVEN GIVE BRAINLIEST!! HELP ASAP!!!
Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By = C.
(-6,3), (-7, - 7)
Answer:
-10x + y = 63
Step-by-step explanation:
Let's find the slope of this line. Going from (-7, -7) to (-6, 3), the "run" is +1 (this is the increase in x) and the "rise" is -10 (y increases by 10). Thus, the slope, m, is m = rise / run = 10 / 1 = 10.
Using the point-slope version of the equation of a straight line, we get
y + 7 = 10(x + 7)
Performing the multiplication results in
y + 7 = 10x + 70.
Rearranging these terms in the form Ax + By = C, we get:
-10x + y = 63
Check this by substituting -6 for x and 3 for y:
-10(-6) + 3 = 63 This is TRUE
Answer plz!
Which choices are equivalent to the expression below? Check all that apply.
The right options are:
Option AOption COption Eplease see the attached picture
Hope it helps
Good luck on your assignment
4x (2x® - 7x2 + x)
O 8x4 - 28x3+4x2
o 16x - 7x2 +4x
o 8x4 - 7x2 + x
o 16x4 - 3x3+4x2
Answer:
8x^4 - 28x^3 + 4x^2.
Step-by-step explanation:
4x(2x^3 - 7x^2 + x)
= 4 * 2x^3 + 4x*-7x^2 + 4x*x
= 8x^4 - 28x^3 + 4x^2.
Answer:
8[tex]x^{4}[/tex]-28x³+4x²
Step-by-step explanation:
4x(2x³-7x²+x)=
8[tex]x^{4}[/tex]-28x³+4x²
2x³ × 4x = 8[tex]x^{4}[/tex]
7x² × 4x = 28x³
x × 4x = 4x²
9x - 3y = -42 and -9x + 8y =22
Answer:
(-5 1/9, -4)
Step-by-step explanation:
Add the equations
5y=-20
y=-4
-9x+8(-4)=22
-9x-32=22
-9x=46
x= - 5 1/9
Which expression is equivalent to 3x + 6y?
Answer:
3x+6y =0
-6y
3x=-6y
x=-2y
Step-by-step explanation:
Three kids play tennis at the same tennis courts. Mark plays every fourth day, David plays every seventh day and Bryan plays every sixth day. All of them were at the tennis court on Wednesday, July 18th. What will be the next day, when all three of them will be at the court together?
Answer:
Wednesday (9 weeks later) = 10th October.
Step-by-step explanation:
We label the days with the initials of the names.
M= 4
D = 7
B = 6
LCM of 6 +7 = 42
LCM of 6+7 + 4 = 84
We find 84 is the amount of days we need to add on to july 18th
We first find the weeks 84/7 = 9 weeks.
As Wednesday July 18th is exclusive it would be 84 days after this event.
18+ 84 = 102 days.
31 days in july = 31
31 days in Aug = 31
30 days in Sept = 30
= 92
102-92 = 10
We now know date is Wednesday 10th October
We can check 84 days = 9 weeks
13 days in July makes 31st july
31 days in Aug makes 31st Aug
30 days in Sept makes 30th Sept
= 74 days + 10 days = 84
10th October is the checked date and we know it is also a Wednesday as Wednesday had stayed exclusive and prove that there are 7 days in the week to account x 9, to account for an exact 9 weeks later duration.
Answer:
Wednesday, October 10
Step-by-step explanation:
David play every 7 days, so since the first day is a Wednesday, David plays every Wednesday. We need to find the smallest common multiple of 4 and 6 that is also a multiple of 7. Since 4 * 3 = 12 and 6 * 2 = 12, we see that all multiples of 12 are also multiples of 4. We list the multiples of 12:
12, 24, 36, 48, 60, 72, 84, 96, ...
The smallest multiple of 12 that is a multiple of 7 is 84.
The first day all of them play together after July 18th is 84 days later.
84/7 = 12
We look in a calendar, and we see that exactly 12 weeks after July 18 is Wednesday, October 10.
Answer: Wednesday, October 10.
If the acute angle made by two intersecting lines l and m is 51° and image ABCD is reflected across the line l followed by a reflection across line m, then find the angle through which ABCD is rotated. Question 10 options: A) 25.5° B) 102° C) 26° D) 51°
Answer:
B) 102°
Step-by-step explanation:
Reflection is an example of transformation in which a given image is flipped over a reference line which changes the orientation of the figure, but not its length and shape. A rotational transformation is formed by two reflections.
In the given question, image ABCD is reflected over lines I, then m at an angle of 51° to each other. Since rotation is twice the acute angle with respect to the center of rotation, therefore ABCD rotates through an angle of 102°.
