Answer:
The discriminant is 0.
Step-by-step explanation:
Since, the discriminant of a quadratic equation [tex]ax^2+bx+c=0[/tex] is,
[tex]D=b^2-4ac[/tex]
Here, the given equation is,
[tex]4x^2+16x+16=0[/tex]
By comparing,
a = 4, b = 16 and c = 16,
Hence, the discriminant of the given equation is,
[tex]16^2-4\times 4\times 16[/tex]
[tex]=256 - 256[/tex]
[tex]=0[/tex]
Create a log expression, using the laws of logs, that simplifies to 7^x = 64.
This makes no sense to me! Help!
What are the log laws?
To create a log expression that simplifies to 7^x = 64, we need to use the logarithmic and exponential laws.
Explanation:To create a log expression that simplifies to 7^x = 64, we need to use the logarithmic and exponential laws.
First, we can rewrite the exponential equation as a logarithmic equation, which is x = log7(64).Next, we can use the logarithmic property that states logb(ax) = x * logb(a). Applying this property, we have x = log7(26) = 6 * log7(2).Therefore, the log expression that simplifies to 7^x = 64 is x = 6 * log7(2).
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Which term describes the dotted line in the quadrilateral?
A. vertex
B. side
C. diagonal
D. angle ...?
An equation of the line tangent to y=sinx+2cosx at (pi/2, 1) is
A. 2x-y=pi-1 B. 2x+y=pi+1 C. 2x-2y=2-pi D. 4x+2y=2-pi I got A
The following set of coordinates represents which figure?
(3, -5), (5, -2), (10, -4), (8, -7)
A. parallelogram
B. rectangle
C. trapezoid
D. square
...?
Answer:
Option A is correct.
Step-by-step explanation:
Given:
Coordinates of the figure are ( 3 , -5 ) , ( 5 , -2 ) , ( 10 , 4 ) and ( 8 , -7 )
To find: Shape of the figure.
First we plot the given coordinates of the point on the graph then see which shape we obtained.
Graphing these points we get attached graph.
Clearly from graph it is a parallelogram because opposite sides are equal and parallel.
It is not a rectangle as clearly from graph angles at vertex are not right angle.
Therefore, Option A is correct.
To identify the geometric figure that the coordinates represent, plot the points, determine the slopes and lengths of the sides, and verify the properties of the geometric figures such as parallel sides and right angles.
Explanation:The student has provided the coordinates of a figure and asks which geometric figure they represent. To determine the figure, we need to consider the characteristics of the points given.
The coordinates provided are (3, -5), (5, -2), (10, -4), and (8, -7). By plotting these points on a Cartesian plane and connecting them in order, we could identify the figure based on the slopes of the sides and the lengths of the segments, which indicate parallel and perpendicular lines.
We need to calculate the distances between consecutive points and the slopes of the lines to confirm whether opposite sides are equal and parallel (a characteristic of a parallelogram) and whether all angles are right angles (a characteristic of a rectangle). These calculations can confirm the identity of the figure.
Three dentists wanted to compare the ages of their patients. They each calculated their patients’ mean age and the mean absolute deviation of their ages. They displayed the results in a table.
Which statements are true?
Choose exactly two answers that are correct.
DentistMean patient ageMAD
Appiah439.7
Cantwell2913.9
Singh4114.1
A. Dr. Appiah’s patients’ ages vary more than do Dr. Cantwell’s patients’ ages.
B. Dr. Appiah’s patients’ ages vary less than do Dr. Singh’s patients’ ages.
C. Dr. Cantwell’s patients’ ages and Dr. Singh’s patients’ ages vary about the same amount.
You are dividing two square roots, and the radicand in the denominator does not divide into the radicand in the numerator. Explain what you need to do.
Reg sells cars. he makes a base salary of $25,000, plus $1500 per car he sells. the function that models this situation is s = 1500x 25000. after working at the car dealership for 2 years, he gets a raise. he now makes $1700 per car he sells. what is the new function that models this situation?
The table shows the result of a restaurant survey.
Meals Service Good Service poor Total
Lunch 49 39 88
Dinner 19 15 34
Total 68 54 122
Find the probability the service was poor, given that the meal was dinner.
Solve the inequality 2x - 3 < x 2 ≤ 3x 5. show your work
Answer:
-3/2 ≤ x < 5
Step-by-step explanation:
2x - 3 < x + 2 ≤ 3x+5
Solve the inequality separately
2x-3 <x+2 and x+2≤ 3x+5
LEts solve one by one
2x-3 <x+2
Subtract x from both sides
x -3 < 2
add 3 on both sides
x< 5
x+2≤ 3x+5
Subtract 3x from both sides
-2x + 2 ≤ 5
Subtract 2 from both sides
-2x ≤ 3
Divide both sides by -2
x ≥ -3/2
we got x>= -3/2 and x<5
so x lies between -3/2 and 5
-3/2 ≤ x < 5
The solution to the given inequality is -3/2 ≤ x < 5.
To solve the given inequality: 2x - 3 < x + 2 ≤ 3x + 5, we can break it down into two separate inequalities and solve them individually.
2x - 3 < x + 2:
Subtracting x from both sides:
2x - x - 3 < x - x + 2
x - 3 < 2
Adding 3 to both sides:
x - 3 + 3 < 2 + 3
x < 5
Now x + 2 ≤ 3x + 5:
Subtracting x from both sides:
x - x + 2 ≤ 3x - x + 5
2 ≤ 2x + 5
Subtracting 5 from both sides:
2 - 5 ≤ 2x + 5 - 5
-3 ≤ 2x
Dividing both sides by 2:
-3/2 ≤ x
Combining the results from both inequalities:
-3/2 ≤ x < 5
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195 s; minutes
a. 4.5 min
b. 3 min
c. 3.25 min
d. 2.5 min
Solve -23.7 + d = -48.57.
-4.62
-46.2
-24.87
-72.27
Answer:-24.87 is the correct answer, i checked it!
Step-by-step explanation:
PLEASE HELP ME IM TRYING TO GET THIS DONE AND NOBODY IS HELPING ME Triangle ABC below is reflected over the y-axis.
a What are the coordinates of the reflected triangle
b Describe in words what happened to the x coordinates and the y coordinates of the original triangles vertices as a result of this reflection
Marta walked at 3.9 miles per hour for 0.72 hours. How far did she walk?
Find the possible value or values of z in the quadratic equation z2 – 4z + 4 = 0. A. z = 2√ 2 + 2, z = −√ 2 + 2 B. z = 2 C. z =√ 2 + 2, z = −√ 2 + 2 D. z = 10, z = 6
Answer:
z=2
Step-by-step explanation:
im not going to explain it because the other person explained it but i will just show you a trick, might not always work but for the equation z^2 -4z+4=0 if you try putting 2 in for z it will be true 0=0... (2)^2 -4(2) +4= 0
is (4,2) a solution to the system y-x=2 and -3x -2y= -8
How do i describe the shape of the graph of each cubic function by determining the end behavior and number of turning points?
for ex. y=3x^3-x-3 ...?
A plumber charges a $45 fee to make a house call and then $25 for each hour of labor. The plumber uses an equation in the form y=mx +b to determine the amount to charge each customer. What is the value of m in the equation?
Answer:
Let x represents the number of hours of labor and y represents the total charges.
Since, in the given situation,
The total charges = A fixed charge for house call + Extra charge per hours,
Fixed charge for house call = $ 45,
Extra charges for every hour = $ 25,
⇒ Extra charge for x hours = 25 x,
Thus, the total charges for x hours,
y = 45 + 25 x
Which is the required equation that will use to determine the amount to charge each customer.
By comparing this equation with y = mx + c,
m = 25
On average, sloths spend 16.5 hours per day sleeping. what percent of the day do sloths spend sleeping? round your answer to the nearest percent.
4.2(3.9r – 5.9s) 7.9s – 9.53r
Answer:
D
Step-by-step explanation:
i just did the quiz
what is 40% in fraction form
To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100. In this case, 40% can be written as the ratio 40 to 100 or [tex]\frac{40}{100}[/tex]. Notice however that [tex]\frac{40}{100}[/tex] is not in lowest terms so we need to divide the numerator and the denominator by 20 which gives us [tex]\frac{2}{5}[/tex].
Rotating a triangle by 50 degrees will change the measures of the exterior angles by _________.
A. -50 degrees
B. 50 degrees
C. 0 degrees
PLEASE HELP AND BRAINLYEST ANSWER TO CORRECT ANSWER
A woman at a point A on the shore of a circular lake with radius r=4 wants to arrive at the point C diametrically opposite A on the other side of the lake in the shortest possible time. She can walk at the rate of 10mph and row a boat at 5mph. What is the shortest amount of time it would take her to reach point C?
I'm not sure where to start... :(
The shortest possible time for the woman to reach the point diametrically opposite on the other side of the lake is 0.8 hours, regardless if she chooses to walk around the lake or row across it.
Explanation:The subject of this problem is about distance and speed, and involves optimizing the total travel time. The woman has two main options: to walk around the lake or to row across it. The diameter of the lake is 2r=8, if she walked, it would take her 8/10=0.8 hours to reach point C.
However, if she rows straight across the lake, the distance is the radius of the lake, which is 4 miles. The time taken to row across the lake is therefore 4/5=0.8 hours.
So, both options take the exact same time of 0.8 hours. Therefore, the shortest amount of time it would take for her to reach point C is 0.8 hours whether she chooses to walk around the lake or row across it.
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The shortest amount of time it would take for the woman to reach point C is [tex]2[/tex] hours.
1. Walking from A to B:
- Distance [tex]\( AB = 4 \)[/tex] miles
- Walking speed = 10 mph
- Time [tex]\( \text{Time}_{\text{walk}} = \frac{4}{10} = 0.4 \) hours[/tex]
2. Rowing from B to C:
- Distance [tex]\( BC = 8 \)[/tex] miles (since [tex]\( AC = 8 \)[/tex] miles and [tex]\( AC = 8 \)[/tex] miles)
- Rowing speed = 5 mph
- Time [tex]\( \text{Time}_{\text{row}} = \frac{8}{5} = 1.6 \) hours[/tex]
3. Total time:
[tex]\( \text{Total time} = \text{Time}_{\text{walk}} + \text{Time}_{\text{row}} = 0.4 + 1.6 = 2 hours[/tex]
Therefore, the shortest amount of time it would take for the woman to reach point C is [tex]2[/tex] hours.
What number is 0.77% of 900?
Which of the following is the inverse function of y = 3x + 1?
x = 3y + 1
y = (1/3)x + 1/3
y = (x – 1)/3
y = x/3 - 1
Answer:
Option C is the correct answer : [tex]y=\frac{(x-1)}{3}[/tex]
Step-by-step explanation:
[tex]y=3x+1[/tex]
For finding the inverse of this function, we will interchange x and y, then solve for y.
[tex]3y=x-1[/tex]
[tex]y=\frac{x-1}{3}[/tex]
Hence, option C is the correct answer : [tex]y=\frac{(x-1)}{3}[/tex]
4 (x+5)=3 (x-2)-2 (x+2)
Which is the graph of linear inequality x-2y>-12 help!
Answer:
The below attached graph shows the given inequality.
Step-by-step explanation:
Here, the given inequality,
x - 2y > -12
Since, related equation of the inequality,
x - 2y = -12
Which is a line passes through (-12, 0) and (0, 6)
Also, '>' represents dotted line,
So, join these two points by dotted line in the coordinate plan,
Now,
0 - 2(0) > -12 (True)
i.e. shade the region of the line that contains origin.
By the above explanation we will get the graph of given inequality ( shown below )
The product of 8 and the sum of 4 and a number is 112. What is the number?
Which equation could be used to solve for the number?
Baby jacobs birth weight was 10 pounds one week after being born his weight was 9 pounds what was the percent of decrease in jacobs weight
solve the equation. Check for extraneous solutions.
[tex]2|7-7x|=2x+4 [/tex]
Answer: The answer is [tex]\dfrac{5}{8},~\dfrac{3}{2}[/tex] and no extraneous solution.
Step-by-step explanation: The given equation is
[tex]2|7-7x|=2x+4.[/tex]
We are given to solve this equation and also find its extraneous solution.
The solution is as follows:
[tex]2|7-7x|=2x+4\\\\\Rightarrow |7-7x|=x+2\\\\\Rightarrow 7-7x=x+2,~~~~~-7+7x=x+2\\\\\Rightarrow 8x=5,~~~~~~~~~~~~~~~~\Rightarrow 6x=9\\\\\\\Rightarrow x=\dfrac{5}{8},~~~~~~~~~~~~~~~~~\Rightarrow x=\dfrac{3}{2}.[/tex]
now, for [tex]x=\dfrac{5}{8}[/tex], we have
[tex]L.H.S.=2|7-7\times \dfrac{5}{8}|=\dfrac{21}{4},\\\\R.H.S.=2\times\dfrac{5}{8}+4=\dfrac{21}{4}.[/tex]
So, this solution is not extraneous.
For [tex]x=\dfrac{3}{2}[/tex], we have
[tex]L.H.S.=2|7-7\times \dfrac{3}{2}|=7,\\\\R.H.S.=2\times\dfrac{3}{2}+4=7.[/tex]
So, this solution is also not extraneous.
Hence, the solution is [tex]\dfrac{5}{8},~\dfrac{3}{2}[tex] and there is no extraneous solution.