[tex]\sqrt{3}x^2+10x+7\sqrt{3}=0\\\\\sqrt3(x^2+\dfrac{10x}{\sqrt{3}}+7)=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+7=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+\dfrac{25}{3}-\dfrac{25}{3} +7=0\\\\(x+\dfrac{5}{\sqrt{3}})^2 = \dfrac{4}{3}\\\\|x+\dfrac{5}{\sqrt{3}}| = \dfrac{2}{\sqrt{3}}\\\\x_1 = \dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = -\dfrac{3}{\sqrt{3}} = -\sqrt{3}\\\\x_2 = -\dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = \dfrac{-7}{\sqrt{3}} = -\dfrac{-7\sqrt{3}}{3}[/tex]
Eric has a bag of 100 marbles. The bag contains 27 red marbles and 42 green marbles, and the rest are blue
marbles.
Eric is interested in the following events.
A: drawing a blue marble
B drawing a red marble
if Eric randomly draws two marbles, without replacing the first one, what is P(AB)?
Enter your answer as a fraction in simplest form. For example. If your answer is which reduces to enter it like
this: 3/4
Answer:
P(AB) = 837/9100
Step-by-step explanation:
The given parameters are;
The number of marbles in the bag = 100 marbles
The number of red marbles = 27
The number of green marbles = 42
The number of blue marbles = 100 - 27 - 42 = 31
The probability, A of drawing a blue marble = 31/100
The probability,B of drawing a red marble after a blue marble has been taken without replacement = 27/91
The probability P(AB) = 31/100× 27/91 = 837/9100
The probability that Eric randomly draws two marbles without replacing the first one where the first one is a blue marble and the second marble is a red marble is 837/9100.
what is 12 ÷ 1 1/5 ?
Answer:
10
Step-by-step explanation:
12 ÷ 1 1/5
Change to an improper fraction
12 ÷ ( 5*1+1)/5
12 ÷ 6/5
Copy dot flip
12 * 5/6
12/6 * 5
2*5
10
Answer:
10
Step-by-step explanation:
12 ÷ 1 1/5
Change into an improper fraction.
12 ÷ 6/5
Reciprocal and it becomes multiplication.
12 × 5/6
60/6
= 10
A Line Segment has the points (1,-2), and (3,-2). What are the new points after its dilated by a scale factor of 3/2 or 1.5?
Answer: (1.5,-3) and (4.5, -3)
Step-by-step explanation:
The dilation rule to dilate a point (x,y) by a scaler factor of k is given by :0
[tex](x,y)\to (kx,ky)[/tex]
Given: A Line Segment has the points (1,-2), and (3,-2).
Scale factor = 1.5
Then, the new points after dilation will be :
[tex](1,-2)\to(1.5\times1,\ 1.5\times-2)=(1.5,\ -3)[/tex]
[tex](3,-2)\to (1.5\times3,1.5\times-2)=(4.5,\ -3)[/tex]
Hence, the new points after its dilated by a scale factor of = (1.5,-3) and (4.5, -3)
A plane started on a flight at 9:30 a.m and arrived at its destination at 1:45pm. The plane used 51 gallons of gas. The number of gallons used per hour was
Will mark Brainlist
Answer:
12 gallons per hour
Step-by-step explanation:
Given the following :
Start time of flight = 9:30 a.m
Arrival time of flight = 1:45p.m
Gallons of gas used during duration of flight = 51 gallons
Number of hours spent during flight:
Arrival time - start time
1:45 pm - 9:30 am = 4hours and 15minutes
4hours 15minutes = 4.25hours
If 4.25hours requires 51 gallons of gas;
Then 1 hour will require ( 51 / 4.25)gallons
= 51 / 4.25
= 12 gallons
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
The correct answer should be D.
ebony is solving a quadratic equation. she wants to find the value of x by taking the square root of both sides of the equation. which equation allows her to do this?
a. x^2 - 8x + 64 = 32
b. x^2 - 144x + 12 = 13
c. x^2 - 6x - 9 = 15
d. x^2 - 4x + 4 = 36
Answer:
D
Step-by-step explanation:
x^2 - 4x + 4 = 36
Take the square root on both sides.
x - 2x + 2 = 6
Answer:
Bottom right on TTM/Imagine Math on the question asked it is d.
Step-by-step explanation:
WILL GIVE BRAINLIEST FOR BEST ANSWER Maya wants to perform an experiment with a spinner labeled A, B, and C. The theoretical probabilities for each section are: P(A) = ½, P(B) = ¼, and P(C) = ¼. Which spinner could she use?
Answer: The answer is spinner B. There are 8 sections on the spinner and 4 of them have letter A, so P(A)= 1/2.
Answer:
spinner B
Step-by-step explanation:
there's 8 sides to the spinner and half of them have A on it.
Solve the equation using the zero-product property. (2x − 8)(7x + 5) = 0 x = –2 or x = 7 x = –4 or x = x = 4 or x = x = 4 or x =
Answer:
x = 4 or x = - [tex]\frac{5}{7}[/tex]
Step-by-step explanation:
Given
(2x - 8)(7x + 5) = 0
Equate each factor to zero and solve for x
2x - 8 = 0 ⇒ 2x = 8 ⇒ x = 4
7x + 5 = 0 ⇒ 7x = - 5 ⇒ x = - [tex]\frac{5}{7}[/tex]
How much does a composition notebook weigh?
Answer:
11.2 ounces
Step-by-step explanation:
Please answer this in two minutes
Answer:
4.5cm
Step-by-step explanation:
Using Sine Rule:
a/sinA = b/sinB = c/sinC
step:
7/sin90 = TU/sin40
TU = 7/sin90 X sin40
TU = 4.4995
TU = 4.5cm
MAKE ME AS THE BRAINLIEST
Resolve into factors.
a)x4-5x2y2+4y4
Answer:
(x - y)(x + y)(x - 2y)(x + 2y)
Step-by-step explanation:
Given
[tex]x^{4}[/tex] - 5x²y² + 4[tex]y^{4}[/tex]
Consider the factors of the coefficient of the [tex]y^{4}[/tex] term (+ 4) which sum to give the coefficient of the x²y² term (+ 5)
The factors are - 1 and - 4 , thus
[tex]x^{4}[/tex] - 5x²y² + 4[tex]y^{4}[/tex]
= (x² - y²)(x² - 4y²)
Both of these factors are differences of squares which factor in general as
a² - b² = (a - b)(a + b) , so
x² - y² = (x - y)(x + y)
x² - 4y²
= x² - (2y)² = (x - 2y)(x + 2y)
Hence
[tex]x^{4}[/tex] - 5x²y² + 4[tex]y^{4}[/tex]
= (x - y)(x + y)(x - 2y)(x + 2y) ← in factor form
A square and a regular heptagon are coplanar and share a common side $\overline{AD}$, as shown. What is the degree measure of exterior angle $BAC$? Express your answer as a common fraction.
Answer:
[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]
Step-by-step explanation:
The interior angle of a regular heptagon = = 900/7° = 128.57°
Therefore, angle DAB = 128.57°
The interior angle of the square = 90°
Therefore, angle DAC = 90°
Therefore, we have
angle DAB+ angle DAC + angle BAC = 360° (sum of angles at a point (A))
Angle BAC = 360° - angle DAB - angle DAC = 360° - 900/7° - 90° = 990/7°
Angle BAC = 141.43°
Expressing 141.43° as a common fraction gives;
[tex]141.43 ^{\circ}= \dfrac{990}{7} ^{\circ}=141\frac{3}{7} ^{\circ}[/tex]
[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]
The degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex]
Given, A square and a regular heptagon are coplanar as shown in below figure attached.
We have find the exterior angle of BAC.
We know that, The formula that gives the interior angle measure for a regular polygon with any number of sides is,
[tex]\frac{180(n-2)}{n}[/tex] where n is the number of sides.
Since the heptagon has 7 no. of sides.
So regular heptagon's interior angle measures,
[tex]\frac{180(7-2)}{7}=128\frac{4}{7}[/tex]
Hence [tex]\angle A[/tex] will be[tex]128\frac{4}{7}[/tex] degrees.
We know that a square's interior angle is 90 degrees and a heptagon's interior angle is 128.57 degrees. We will subtract those from 360 degrees to find angle BAC.
[tex]\angle BAC = 360 - (\angle A + 90)\\[/tex]
[tex]\angle BAC = 360 - (128\frac{4}{7} + 90)\\\angle BAC=141\frac{3}{7} ^\circ[/tex]
Hence the degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex].
For more details on Exterior angle follow the link:
https://brainly.com/question/2125016
Determine the money factor for a lease with an interest rate of 9%
Answer:
0.00375
Step-by-step explanation:
The money factor for a lease is used to determine how much is charged monthly on a lease payment. If the money factor is low, the lease payment is low making it a good transaction but if the money factor is high, the lease payment is also high and this is not desirable. The money factor is given by:
Money factor = Interest rate / 2400
Given an interest rate of 9%, the money factor is calculated as:
Money factor = Interest rate / 2400 = 9% / 2400 = 0.00375
The roots of $7x^2 + x - 5 = 0$ are $a$ and $b.$ Compute $(a - 4)(b - 4).$[tex]The roots of $7x^2 + x - 5 = 0$ are $a$ and $b.$ Compute $(a - 4)(b - 4).$[/tex]
Using the factor theorem, we have
[tex]7x^2+x-5=7(x-a)(x-b)[/tex]
and expanding gives us
[tex]7x^2+x-5=7(x^2-(a+b)x+ab)\implies\begin{cases}ab=-5\\a+b=-1\end{cases}[/tex]
So we have
[tex](a-4)(b-4)=ab-4(a+b)+16=-5-4(-1)+16=\boxed{15}[/tex]
two bags and four hats cost $100 in all. three bags and seven hats cost $164 in all. what is the cost of 1 hat?
Answer:
Bags = 22
Hat = 14
22 x 2 = 44
14 x 4 = 56
So the first part is true
3 x 22 = 66
7 x 14 = 98
So the second part is true
14 is the answer
It's trial and error
Step-by-step explanation:
PLEASEEEEEE HELPPPPP Which of the following is the surface area of the right cylinder below?
The correct answer is D. [tex]72 \pi[/tex] [tex]units^{2}[/tex]
Explanation:
The surface area refers to the sum of the area of all sides in a 3D shape such as a cube or cylinder. Additionally, the formula used to calculate the surface area varies with the shape. In the case of cylinders, the general formula is [tex]A = 2\pi r h + 2\pi r^{2}[/tex]. Moreover in this, the r represents the radius (measure from the center of a circle to any side), while the h represents height. Below, all the process is shown:
[tex]A = 2\pi r h + 2\pi r^{2}[/tex]
[tex]A = 2\pi (8 x 3) + 2\pi 8^{2}[/tex]
[tex]A = 2\pi 24 + 2\pi 64[/tex]
[tex]A = 48\pi + 128\pi[/tex]
[tex]A = 176\pi[/tex]
In this point, you have the answer without solving [tex]\pi[/tex] (3.1416). This makes option A the correct answer.
In the diagram, the measure of angle 8 is 124°, and the measure of angle 2 is 84°. What is the measure of angle 7? 56° 84° 96° 124°
================================================
Explanation:
The information about angle 2 is unnecessary info that your teacher likely put in there as a distraction. All we need is angle 8, which is 124 degrees. Angle 7 adds to this to form a 180 degree straight angle.
(angle 7) + (angle 8) = 180
(angle 7) + 124 = 180
angle 7 = 180 - 124
angle 7 = 56 degrees
Answer:
The measure of angle 7 is 56°.
Step-by-step explanation:
here, angle 8 = 124°
now, angle 8+ angle 7=180° (as the sum of linear pair is 180°)
or, 124°+angle 7=180°
or, angle 7=180°-124°
Therefore, tge measure of angle 7 is 56°.
Hope it helps.
what is the equation of 7/12=blank×1/2
Answer: x = [tex]1\frac{1}{6}[/tex]
Step-by-step explanation:
7/12 = 1/2x
Multiply by 2
14/12=x
x = 1 1/6
Hope it helps <3
Equivalent equation to 19-6(-k+4)=
Answer:
-5+6k
Step-by-step explanation:
19-6(-k+4)=16+6k-24=6k-5
Answer:
6k-5
Step-by-step explanation:
19-6(-k+4)=
19+6k-24=
6k-5
Tucker is painting his pool deck over the weekend. The area of the deck is 76 1 2 square meters. He paints 2 3 of the deck before stopping to eat lunch. How many square meters does Tucker have left to paint after lunch?
Answer:
25 1/2 square meters remaining
Step-by-step explanation:
Total area of the pool deck=76 1/2 square meters
He painted 2/3 of the deck before stopping for lunch
Total painted=2/3 of 76 1/2
=2/3*153/2
=306/6
=51 square meters
Total remaining=Total area - total painted area
=76 1/2 - 51
=153/2 - 51
=153-102/2
=51/2
=25 1/2 square meters remaining
Simplify the expression (4x+22x)/(2x)
Answer:
The answer is 13.
Step-by-step explanation:
here, ( 4x+ 22x)/2x
taking 2x common we get, 2x(2+11)/2x
=13 ..... is answer ( as 2x gets cancelled)
Hope it helps..
PLEASE HELP ME WITH THIS PROBLEM ASAP!!!
Answer:
220 units
Step-by-step explanation:
ER = ET = 33 tangents from same poiint
DE = 59 => DS = DR = 59-33 = 26
DC = 77 => CR =CT = 77-26 = 51
Perimeter
= 2 *( ES + DR + CT )
= 2* (33 + 26 + 51)
= 220
Credit and thanks to ValerieUlbrich. :)
Can someone help me with this please? Question and possible answers down below
Answer: D) CPCTC
Step-by-step explanation:
step 6 proves the triangles are congruent.
step 7 states that if the triangles are congruent, then parts of the triangle are congruent.
Congruent Parts of Congruent Triangles are Congruent (CPCTC)
Find the measure of angle b. Note that the measure of angle b is acute. Round to the nearest degree.
Answer:
60.75
Step-by-step explanation:
sinA sinB
------- = -----
a b
sin(79)/9 = sinB/8
inverse sin B = 0.87
B = 60.75
If mArc N P is 6 more than 5 times the measure of Arc M N , what is mArc N P ?
139°
145°
151°
174°
Answer: the answer is 151
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
In order for a word phrase or sentence to translate to an equation, it must have an equality
statement.
O True
O False
You already know how to use inequalities to
describe domain and range. If an endpoint is
included-shown by a closed dot, such as in the
graph to the right-use <= or >= instead of sor >
to indicate the number is included.
Complete the inequality for the domain.
Answer:
The first one is −4 <= x < 4
This second one is −2 <= y < 5
Which table represents a linear function?
Answer:
5, 10, 15, 20, 25 table.
Step-by-step explanation:
So the top table, for sure has a much more consistent, and or constant variable. That just means that the numbers are continuously being put into the table at the right amount, speed, etc. As it is increasing, your y is constant, and x remains in the appropraite way!
5, 10, 15, 20, 25..
It is very good.
Hope that helped.!
Factor the expression
Answer:
Step-by-step explanation:
Your difference of perfect cubes formula is given as
[tex](a-b)(a^2+ab+b^2)[/tex] and you have already correctly identified a as [tex]5q^2[/tex] and b as [tex]r^2s[/tex]. So we fill in the formula as follows:
[tex](5q^2-r^2s)((5q^2)^2+(5q^2)(r^2s)+(r^2s)^2)[/tex] and we simplify. Remember that
[tex](5q^2)^2=(5)^2*(q^2)^2=25q^4[/tex]. It's important that you remember the rules.
Simplifying then gives us
[tex](5q^2-r^2s)(25q^4+5q^2r^2s+r^4s^2)[/tex]
That's it, so fill it in however you need to on your end. Learn the patterns for the sum and difference of cubes and it will save you a ton of headaches...promise!!
a plane started on a flight at 9:30 a.m and arrived at its destination at 1:45pm. The plane used 51 gallons of gas. The number of gallons used per hour was
Brainlist
Answer:
12 gallons
Step-by-step explanation:
Given the following :
Total amount of gas used by aircraft = 51 gallons
Flight departure time = 9:30 a.m
Arrival time of flight = 1:45p.m
Number of hours traveled by flight:
Arrival time - Departure time
1:45pm - 9:30a.m = 4hrs 15 minutes = [(60*4)+15] minutes = 240 + 15 = 255 minutes
Amount of gallons used per hour :
255 minutes = 51 gallons
I minutes = x
255x = 51 gallons
x = 51 / 255
x = 0.2 gallons
0.2 gallons per minute
1 hour = 60 minutes
Number of gallons per hour = (0.2 * 60) = 12 gallons