Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]6x^2-8x+k=0\\\\\text{We compute the discriminant.}\\\\\Delta = b^2-4ac=8^2-4*6*k=8*8-8*3*k=8*(8-3k)[/tex]
And the we know that if the discriminant is
***** [tex]\Delta[/tex] < 0, meaning 8-3k<0, meaning
[tex]\boxed{k>\dfrac{8}{3}}[/tex]
then, there is no real solution.
***** [tex]\Delta = 0[/tex], meaning
[tex]\boxed{k=\dfrac{8}{3}}[/tex]
There is 1 solution.
***** [tex]\Delta[/tex] > 0, meaning
[tex]\boxed{k<\dfrac{8}{3}}[/tex]
There are 2 solutions.
Thank you
PS: To give more details...
[tex]8-3k=0\\\\\text{Add 3k}\\\\8=3k\\\\\text{Divide by 3}\\\\k=\dfrac{8}{3}[/tex]
Nimisha wants to draw a wheel like the one shown. Each shaded part of the wheel should be one-third of each unshaded part. What should be the degree measure of the angle formed at the center by each shaded part?
Answer:
Each shade has a 22.5 degree angle from the middle
Each unshaded has a 67.5 degree angle from the middle.
Step-by-step explanation:
You can solve this by making each unshaded part equal to x and each shaded part equal 1/3x it is a circle so it has to equal 360 so you end up with:
x + 1/3x + x + 1/3x + x + 1/3x + x + 1/3x = 360
Combine Like terms:
16/3x = 360
Multiply both sides by the opposite:
(3/16) (16/3x) = (360) (3/16)
x=135/2 or x=67.5
Then you can plug 67.5 in for x:
1/3x ---> 1/3(67.5) = 22.5
Susan Johnson earns a yearly salary of $83,280. a. How much would Susan be paid if she were
paid monthly? b. How much would she be paid if she were paid bi-weekly?
In a naval engagement, one-third of the fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-seventh of the surviving ships were lost in a storm after the battle. Finally, the twenty-four remaining ships sailed home. How many ships were in the fleet before the engagement?
Answer:
60 ships.
Step-by-step explanation:
Let the total number of ships in the naval fleet be represented by x
One-third of the fleet was captured = 1/3x
One-sixth was sunk = 1/6x
Two ships were destroyed by fire = 2
Let surviving ships be represented by y
One-seventh of the surviving ships were lost in a storm after the battle = 1/7y
Finally, the twenty-four remaining ships sailed home
The 24 remaining ships that sailed home =
y - 1/7y = 6/7y of the surviving fleet sailed home.
Hence
24 = 6/7y
24 = 6y/7
24 × 7/ 6
y = 168/6
y = 28
Therefore, total number of ships that survived is 28.
Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4
Total number of ships in the fleet(x) =
x = 1/3x + 1/6x + 2 + 28
Collect like terms
x - (1/3x + 1/6x) = 30
x - (1/2x) = 30
1/2x = 30
x = 30 ÷ 1/2
x = 30 × 2
x = 60
Therefore, ships that were in the fleet before the engagement were 60 ships.
What is the value of w? inscribed angles (Image down below)
Answer:
w = 100°
Step-by-step explanation:
Opposite angles in an inscribed quadrilateral in a circle are supplementary.
Therefore, [tex] w + 80 = 180 [/tex]
Subtract 80 from both sides
[tex] w + 80 - 80 = 180 - 80 [/tex]
[tex] w = 100 [/tex]
The value of w = 100°
A gallon of paint covers 400 square feet. How many square feet will 2 3/8 gallons of paint cover. How do you solve this problem.
Answers
(A) 950 sq ft
(B) 986 sq ft
(C) 1,040 sq ft
(D) 1,068 sq ft
Answer:
Hey there!
1 gallon=400 square feet
2 3/8 gallon= 400 (2 3/8) square feet
2 3/8 gallon= 950 square feet.
Let me know if this helps :)
Let f (x) = |2). Write a function g whose graph is a vertical shrink by a factor of
followed by a translation 2 units up of the graph of f.
Answer:
This is poorly written, so i will answer it as it was:
"Let f (x) = |2). Write a function g(x) whose graph is a vertical shrink by a factor of A, followed by a translation 2 units up of the graph of f."
I don't really know what you do mean by I2), so i will answer it in a general way.
First, we do a vertical shrink of factor A.
A must be a number smaller than one and larger than zero., then if g(x) is a vertical shrink of factor A of the graph of f(x), we have that:
g(x) = A*f(x)
As 0 < A < 1
We will have that the graph of g(x) is a vertical compression of the graph of f(x)
Now we do a vertical shift of 2 units up.
A general vertical shift of N units up is written as:
g(x) = f(x) + N
Where N is a positive number.
So in our case, we have:
g(x) = A*f(x) + 2.
Where you will need to replace the values of A and f(x) depending on what the actual question says,
If you're good at exact values of trig ratios pea shell me with 13a
It is an equilateral triangle so its angles are equal 60°. From the definition, we know that:
[tex]\sin60^\circ=\dfrac{h}{4}[/tex]
and
[tex]\sin60^\circ=\dfrac{\sqrt{3}}{2}[/tex]
so
[tex]\dfrac{\sqrt{3}}{2}=\dfrac{h}{4}\quad \Big|\cdot4\\\\\\h=\dfrac{4\cdot\sqrt{3}}{2}\\\\\boxed{h=2\sqrt{3}}\\[/tex]
Answer:
h = √12
Step-by-step explanation:
use the Pythagorean
h² = 4² - 2²
h² = 16 - 4
h = √12
PLEASE help me solve this question! No nonsense answers please!
Answer:
[tex]\boxed{\sf Option \ 1}[/tex]
Step-by-step explanation:
The profit is revenue (R ) - costs (C ).
Subtract the expression of costs (C ) from revenue (R ).
[tex]10x-0.01x^2-(2x+100)[/tex]
Distribute negative sign.
[tex]10x-0.01x^2-2x-100[/tex]
Combine like terms.
[tex]8x-0.01x^2-100[/tex]
The first option has a positive 100, which is wrong.
The rest options are right, when we expand brackets the result is same.
Find the constant of proportionality (r) in the equation y = r x
Answer:
r = 11Step-by-step explanation:
y = r x
r is the constant of proportionality
To find r pick any values of x and y provided and substitute it into the above formula and solve for r.
That's
using
x = 2
y = 22
We have
22 = 2r
Divide both sides by 2
r = 11Therefore the constant of proportionality is 11
Hope this helps you
Helppppp!!!! Thank you
Greetings from Brasil...
In a triangle the sum of the internal angles is 180 °.... Thus,
Ô = 180 - 30
Ô = 60
The desired area is the area of the rectangle triangle, minus the area of the circular sector whose angle 60
A1 = area of the rectangle triangle
TG B = OA/AB
AB = OA / TG B
AB = 6 / TG 30
AB = 6√3
A1 = (AB . OA)/2
A1 = (6√3 . 6)/2
A1 = 18√3A2 = area of the circular sector
(rule of 3)
º area
360 ------------ πR²
60 ------------ X
X = 60πR²/360
X = 6π
So,
A2 = 6πThen the area shaded is:
A = A1 - A2
A = 18√3 - 6πSolve: 5x2 + 25x = 0
Answer:
x = -0.4
x = -(2/5)
Answer:
x = ± √5
Step-by-step explanation:
Please indicate exponentiation by using the symbol " ^ ":
5x^2 + 25x = 0
Divide all three terms by 5. We get:
x^2 + 5 = 0, or x^2 = -5
Then x = ± √5
use the formula S = 40,000 (1.06)t to calculate your salary after 4 years. Round your answer to the nearest dollar.
a. $42,400
b. $44,944
c. $47,641
d. $50,499
Answer:
d. $50,499
Step-by-step explanation:
Given:
S = 40,000 (1.06)^t
Where,
t=4 years
S=40,000(1.06)^4
=40,000(1.26247696)
=50,499.0784
To the nearest dollar
S=$50,499
The answer is d. $50,499
Determine what type(s) of angles are described by the following angle measures. Angle of 35 degrees.
Answer:
Acute.
Step-by-step explanation:
An angle of measure between 0 and 90 degrees is an acute angle.
Write the equation of a circle with a center at (12, 6) and a radius of 6.
Answer:
(x-12)² + (y-6)² = 36 (Option C)
Step-by-step explanation:
use circle formula
(x-h)² + (y-k)²= r²
h= 12 and k= 6 and r= 6
(x-12)² + (y-6)² = 6²
6 squared = 36 (6·6)
(x-12)² + (y-6)² = 36
Two stores sell the same computer for the same original price. Store A advertises that the computer is on sale for 25% off the original price. Store B advertises that it is reducing the computer’s price by $180. When Brittany compares the sale prices of the computer in both stores, she concludes that the sale prices are equal. Let p represent the computer’s original price. Which equation models this situation?
Answer:
p= 25/100 = 180/x
Step-by-step explanation:
In order to find the computer's original price, you must use the equation p= 25/100 = 180/x and solve for x.
Answer:
0.75p=p-180
Step-by-step explanation:
0.75p=p-180 is your answer
PLEASE help me with this question!!! REALLY URGENT!
Answer:
The third table is the correct answer
Step-by-step explanation:
Here in this question, we are concerned with determine which of the tables correctly represents what an exponential function is.
An exponential function is a function of the form;
y = x^n
where the independent variable x in this case is raised to a certain exponent so as to give the results on the dependent variable axis (y-axis)
In the table, we can see that we have 2 segments, one that contains digits 1,2 and so on while the other contains purely the powers of 10.
Now, let’s set up an exponential outlook;
y = 10^x
So we have;
1 = 10^0
10 = 10^1
1/10 = 10^-1
1000 = 10^3
1/100 = 10^-2
We can clearly see here that we have an increase in the value of y, depending on the value of the exponent.
However it is only this table that responds to this successive correctness as the other tables in the answer do have a point where they fail.
For example;
10^-2 is not 10 which makes the fourth table wrong
10^4 is not 100 which makes the first table wrong
we have same error on second table too
The quotient of x^2+x-6/x^2-6x+5*x^2+2x-3/x^2-7x+10 has ___ in the numerator and ______ in the denominator.
Answer:
So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.
Step-by-step explanation:
[tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex]
Factorizing the expressions we have
[tex]\frac{x^{2} + 3x -2x - 6}{x^{2} -x - 5x + 5} X \frac{x^{2} + 3x - x - 3}{x^{2} -2x -5x + 10}[/tex]
[tex]\frac{x(x + 3)- 2(x + 3)}{x(x -1) - 5(x - 1)} X \frac{x(x + 3) - 1(x + 3)}{x(x - 2) - 5(x - 2)}[/tex]
[tex]\frac{(x + 3)(x - 2)}{(x - 5)(x - 1)}X\frac{(x + 3)(x - 1)}{(x - 2)(x - 5)}[/tex]
Cancelling out the like factors, (x -1) and (x - 2), we have
[tex]\frac{(x + 3)(x + 3)}{(x - 5)(x - 5)}[/tex]
= [tex]\frac{(x + 3)^{2} }{(x + 5)^{2} }[/tex]
So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.
Micha is playing a game with five cards numbered 1 through 5. He will place the cards in a bag and draw one card at random three times, replacing the card each time. To win a prize, he must draw the number 5 all three times. What is the probability he will draw the number 5 all three times?
Answer: 0.008
Step-by-step explanation:
We have 3 experiments.
Each experiment is exactly the same: "Drawing the card with the number 5, out of a bag with five cards".
in a random selection all the cards have exactly the same probability of being drawn, so the probability of drawing the 5, is equal to the quotient between the number of cards with the 5 (only one) and the total number of cards in the bag (5) then the probability is:
p = 1/5.
And we want this event to happen 3 consecutive times, then the total probability is equal to the product of the probabilities for each event:
P = (1/5)*(1/5)*(1/5) = 1/125 = 0.008
In circle O, AC and BD are diameters. Circle O is shown. Line segments B D and A C are diameters. A radius is drawn to cut angle C O C into 2 equal angle measures of x. Angles A O C and B O C also have angle measure x. What is mArc A B?
Answer:
120
Step-by-step explanation:
Got it right on the assigment
Answer:
c. 120
Step-by-step explanation:
Which one of these relations are functions ?
Please helpppp fast
Answer:
the 4th and 6th one
Step-by-step explanation:
A function is when there are x- and y-values but each x value has only 1 y-value
Simple: If the x-value is repeated its not a function
Answer:
Step-by-step explanation:
1,2,3
What is the square root of 48? what is the square root of 1/49 ? what is the square root of 4/100 ?
Answer:
Step-by-step explanation:
√48 = √(3*16) = 4√3
√1
√(1/49) = ------- = 1/7
√49
√4
√(4/100) = --------------- = ±2/10 =
√100
In 5 hours a small plane can travel downwind for 4000 kilometers
or upward 3000 kilometers. Find the speed of this plane with no wind and the speed of the wind current.
write as an equation
Answer:
the speed of the plane with no wind is 700 km/h and the speed of the wind is 100 km/h
Step-by-step explanation:
Let V be the speed of the plane and v the speed of the wind. Down current, they are in opposite directions, and the plane travels a a distance of 4000 km in 5 hours,so
5(V - v) = 4000
V - v = 800 (1)
For upwind movement, since the plane travels 3000 km in 5 hours, so
5(V + v) = 3000
V + v = 600 (2)
adding equations (1) and (2), we have
V - v = 800
+
V + v = 600
2V = 1400
V = 1400/2 = 700 km/h
subtracting equations (2) from (1), we have
V - v = 800
-
V + v = 600
-2v = 200
v = -200/2 = -100 km/h
So, the speed of the plane with no wind is 700 km/h and the speed of the wind is 100 km/h
What are the solutions to the equation (2x – 5)(3x – 1) = 0? x = or x = 3 x = x = 5 or x = 1
Answer:
x = 5/2 x=1/3
Step-by-step explanation:
(2x – 5)(3x – 1) = 0
Using the zero product property
2x-5 =0 3x-1 =0
2x=5 3x =1
x = 5/2 x=1/3
Answer:
C on edg 2021
Step-by-step explanation:
Estimate. Then determine the area. Please please please, need help!
Estimate:
2.3 rounds down to 2
So after multiplying by 2, the area is estimated to be 4 cm squared.
Actual Area:
2.3 x 2 = 4.6
The actual area of the shape is 4.6 cm squared.
Hope this helped!
Answer:
4.6
Step-by-step explanation:
Which of the following shows the correct solution steps and solution to 7x-4= -18?
Answer:
x = -2
Step-by-step explanation:
To solve for x always get x on one side
First add 4 on each side, 4 + 7x - 4 = -18 + 4
Next subtract 18 from 4, making it -14 7x = -14
Now divide 7 on each side, x = -2
How do I find DG. A. 3 B. -7 c. 16 d. 13
Answer:
x = -7
Step-by-step explanation:
DE + EF + FG = DG
2x+17 + 8+2 = x+20
Combine like terms
2x+ 27 = x+20
Subtract x from each side
2x+27-x = x+20-x
x+27 = 20
Subtract 27 from each side
x+27-27 = 20-27
x = -7
Sophie is making a copy of an angle. The original angle will be labeled G and the new angle will be labeled B. She has just finished using a compass, with the point on G, to draw an arc that intersects both rays of angle G. Which of the following should she do next
Answer:
The next step is;
Label the two intersection points
Step-by-step explanation:
To make a copy of an angle, the steps are;
1) Draw the rays of the original angle passing through the point B
2) Open the compass slightly and place the compass point on the vertices G where the two rays meet to draw an arc that intersect both rays
3) Label the point of intersection of both rays points C and D
4) With the compass still opened to the same width, move the compass to the point B on the line the angle is to be copied and draw a similar arc intersecting the ray at J
5) Open the compass to the width of C and D on the original angle and place the compass at point J to mark the arc on the copied angle location at M
6) Draw a line from B passing through M to complete the second ay of the copied angle.
what is the image (-9,-2) after a reflection over the x-axis ?
Answer:
(-9,2)
Step-by-step explanation:
The rule for reflecting over the x axis is
(x,y)→(x,−y)
(-9, -2) becomes ( -9, - -2) = (-9,2)
Answer:
(-9,2)
Step-by-step explanation:
It will be -9,2 because when you reflect across x axis you change the y axis not the x axis because if you imagine it it works like that
A baker sold apples pies for $10 and blueberry pies for$14. One Saturday they sold a total of 39 pies and collected a total of$458. How many apples pies did they sell and how many blueberry pies did they sell
The total number of apple pies is 22 and the total number of blueberry pies is 17.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that baker sold apples pies for $10 and blueberry pies for$14. One Saturday they sold a total of 39 pies and collected a total of $458.
Asumme the total number of apple pies be 'x' and the total number of blueberry pies be 'y'.
The linear equation that represents the total number of pies is:
x + y = 39
x = 39- y --- (1)
The linear equation that represents the total amount collected is:
10x + 14y = 458--- (2)
Substitute the value of 'x' in equation (2).
10(39- y) + 14y = 458
y = 17
Then Substitute the value of 'y' in the equation (1).
x = 39 - 17
x = 22
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ5
Solve the equation. Do not put "x = "in your answer, just type the number.
Ex: -8 3x - 5 = 13*
Answer:
6
Step-by-step explanation:
3x - 5 = 13
3x = 18 (Add 5 to both sides; 13 + 5 = 18)
x = 6 (Divide both sides by 3; 18 / 3 = 6)
