Answer:
A. x = two over three and x = -5
The equation 3x^2 + 13x = 10 can be solved using the quadratic formula. The solutions are given by:
[tex]$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$[/tex]
Substituting the values from the equation (where a = 3, b = 13, and c = -10), we get:
[tex]$$x = \frac{-13 \pm \sqrt{13^2 - 4*3*(-10)}}{2*3}$$[/tex]
This simplifies to:
[tex]$$x = \frac{-13 \pm \sqrt{289}}{6}$$[/tex]
So, the solutions are:
[tex]$$x = \frac{-13 + \sqrt{289}}{6} = \frac{2}{3}$$[/tex]
and
[tex]$$x = \frac{-13 - \sqrt{289}}{6} = -5$$[/tex]
So, the correct answer is A. x = two over three and x = −5.
which of the following functions are graphed below
Answer:
The equation of given graph is f(x)=[x]-6
C is correct
Step-by-step explanation:
We are given a graph and to find the equation of graph.
It is a graph of greatest integer function or floor function.
Parent function of greatest integer function:
[tex]f(x)=[x][/tex]
For x = 0 to x= 1 , f(x)=0
For x =1 to x=2 , f(x)=1
We are given a function,
For x = 0 to x= 1 , f(x)=-6
For x = 1 to x= 2, f(x) = -5
If we shift 6 unit down the parent function. We will get original function.
[tex]f(x)=[x]-6[/tex]
Hence, The equation of given graph is f(x)=[x]-6
The graph shows the distance, y, that a car traveled in x hours:
A graph is shown with x axis title as Time in hours. The title on the y axis is Distance Traveled in miles. The values on the x axis are from 0 to 5 in increments of 1 for each grid line. The values on the y axis are from 0 to175 in increments of 35 for each grid line. A line is shown connecting ordered pairs 1, 35 and 2, 70 and 3, 105 and 4, 140. The title of the graph is Rate of Travel.
What is the rate of change for the relationship represented in the graph?
fraction 1 over 35
fraction 1 over 34
34
35
Answer: 35
Step-by-step explanation:
The rate of change of a graph is given by :-
[tex]k=\dfrac{\text{Change in y avlues}}{\text{Change in x values}}[/tex]
For points : (1, 35) and (2, 70)
The rate of change for the relationship in the graph is given by :-
[tex]k=\dfrac{70-35}{2-1}=35[/tex]
Hence, the rate of change for the relationship represented in the graph = 35.
The rate of change of the relationship shown in the graph is 35 miles per hour.
Linear equationLinear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept.
Let y represent the elevator height after x seconds.
From the graph using points (0, 0) and (4, 140):
m = (140 - 0)/(4 - 0) = 35
The rate of change of the relationship shown in the graph is 35 miles per hour.
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Hiram raises earthworms. In a square of compost 4 ft by 4 ft, he can have 1000 earthworms. How many earthworms can he have if his square of compost has a side length that is 8 times longer?
A. 8000
B. 64,000
C. 256,000
D. 32,000
How much would $120 invested at 86% interest compounded monthly to be worth after 21 years round to the nearest cent
A wooden plank of length x is cut into 8 sections such that each section is at most 2 1/2 meters long. What is the length of the entire plank in meters?
a x ≤ 3.2 meters
b x ≤ 20 meters
c x ≥ 10.5 meters
d x ≥ 20 meters
Answer:
b
Step-by-step explanation:
A pet store has k tanks of fish. Each tank has 30 fish. Using k, write an expression for the total number of fish in the store.
A computer training institute has 625 students that are paying a course fee of $400. Their research shows that for every $20 reduction in the fee, they will attract another 50 students. What fee should the school charge to maximize their revenue?
$275
$380
$320
$325
Answer: it’s D $325
Step-by-step explanation:
the fee the school should charge to maximize their revenue is $325
What are the rigid transformations that will map
△ABC to △DEF?
Translate vertex A to vertex D, and then reflect
△ABC across the line containing AC.
Translate vertex B to vertex D, and then rotate
△ABC around point B to align the sides and angles.
Translate vertex B to vertex D, and then reflect
△ABC across the line containing AC.
Translate vertex A to vertex D, and then rotate
△ABC around point A to align the sides and angles.
Answer:
The answer above is correct! The answer is option D.
Step-by-step explanation:
Hope this helped clarify :D
Translating vertex A to vertex D, and then rotate △ABC around
point A to align the sides and angles will bring about a rigid
transformation.
What is Rigid transformation?This is the transformation which preserves the Euclidean
distance between every pair of points. This could be as a result
of the following:
RotationReflectionTranslation etc.Option D when done will preserve the distance between the
points when vertex A is translated to vertex D as they contain
the same angle with other sides and angles being made to
align.
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find the area of a regular nonagon with a side length of 7 and an apothem of 5
Help^^^^^^^^^^^^^^^^^
Solve the equation by extracting the square roots. when a solution is irrational, list both the exact solution and its approximation rounded to two decimal places.
If f(x)=4^x , which statements are true of g(x)? Check all that apply
The true statements about functions f(x) and g(x) are:
b. g(x) = 4^x - 1d.The function f(x) is translated 1 units down to get the function g(x) How to determine the true statements?The function f(x) is given as:
f(x) = 4^x
From the table of values, we can see that the function g(x) is 1 less than the function f(x).
This means that:
g(x) = f(x) - 1
This can be rewritten as:
g(x) = 4^x - 1
In transformation, it means that the function f(x) is translated 1 units down to get the function g(x)
Hence, the true statements are: b and d
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The following table shows information collected from a survey of students regarding their grade level and transportation they use to arrive at school. What is the probability that a randomly selected eighth grader takes the bus?
If sam walks 650 meters in x minutes then write an algebraic expression which represents the number of minutes it will take sam to walk 1500 meters at the same average rate.
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss. (I needed to fill up this space somehow).
Solve for x.
3:12 = x:16
2 1/4
4
64
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
we have
[tex]\frac{3}{12}=\frac{x}{16}[/tex]
solve for x
Cross multiply
[tex]12*x=3*16\\x=3*16/12\\x=48/12\\x=4[/tex]
A line has no width and extends infinitely far in _____ directions.
D is (8,4) it just got cut off
#3 In the figure below, the measure of Arc AC is 65 degree and if angle abc is equal to 78 degree.
True or false
False, The measure of Arc AC is not 65 degree if angle ABC is equal to 78 degree.
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The statement is,
The measure of Arc AC is 65 degree if angle ABC is equal to 78 degree.
Now,
Since, Sum of Measure of arc AC and angle ABC is equal to 360 degree.
So, In angle ABC is 78 degree.
Then, Measure of arc AC = 360 - 78
= 282 degree.
Thus, The measure of Arc AC is not 65 degree if angle ABC is equal to 78 degree.
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The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 40 + 0.008p^3 and that its demand function is D(p) = 200 - 0.16p^2, where p is the price. Determine the price for which the supply equals the demand.
The table below shows 10 data values:
88
92
94
80
85
90
72
83
93
91
What is the five-number summary for these data?
Minimum = 72, Q1 = 83, median = 89, Q3 = 92, maximum = 94
Minimum = 80, Q1 = 85, median = 89, Q3 = 91, maximum = 93
Minimum = 80, Q1 = 83, median = 90, Q3 = 92, maximum = 93
Minimum = 72, Q1 = 85, median = 90, Q3 = 91, maximum = 94
Find the radius of a circle with an x-intercept of -2 if the circle’s center is (2,3) on a coordinate plane.
5
25
16
9
Radius of the circle is option (1) 5 units
What is radius?A radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.
What is circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center
Center of the circle is (2,3) on a coordinate plane,
Radius of the circle with an x intercept of -2
There for the point is (-2,0)
Distance between the (2,3) and (-2,0) = Radius of the circle
Distance between (2,3) and (-2,0)
D= [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Substitute the values
[tex]D=\sqrt{(-2-2)^{2}+(0-3)^{2} }\\D=\sqrt{16+9} \\D=\sqrt{25}\\ D=5[/tex]
Hence, the radius of the circle is option (1) 5 units
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Jonathan sets a camera on a tripod to film birds in a nest. The camera is 1.8 m off the ground and 16.4 m away from the tree. The angle of elevation from the camera to the bird’s nest is 29°. How far above the ground is the bird’s nest? Round your answer to the nearest tenth of a meter. 7.3 m 9.1 m 10.9 m 14.3 m
The area of a triangle is 92 cm2. the base of the triangle is 8 cm. what is the height of the triangle?
a. 11.5 cm
b. 23 cm
c. 4 cm
d. 46 cm
Answer: b. 23 cm
Step-by-step explanation:
We know that area of a triangle is given by :-
[tex]\text{Area}=\dfrac{1}{2}bh[/tex], where b is the base of triangle and h is the height of the triangle.
Given : The area of a triangle is [tex]92\ cm^2[/tex]
The base of the triangle = 8 cm
Let h be the height of the triangle , then we have
[tex]92=\dfrac{1}{2}(8)h\\\\\Rightarrow\ h=\dfrac{92}{4}\\\\\Rightarrow\ h = 23[/tex]
Hence, the height of the triangle = 23 cm
You make $30,000.00 and your spouse makes $35,000.00. using the 20% range, calculate the least and greatest amount you spend on housing
30,000 x 0.20 = $6,000 least amount
30,000 +35,000 = 65,000
65000 x 0.20 = $13,000 greatest amount
(02.02 LC)
Figure ABCD is rotated by 180 degrees about the origin in the counterclockwise direction to obtain figure A′B′C′D′:
Which statement best compares the lengths of the sides of the two figures?
Length of AB = Length of C′D′
Length of CD = Length of A′B
′ Length of CD = Length of B′C′
Length of AB = Length of A′B′
How do you solve
8(x-1)-2x=-(x+50)
The solution to the equation 8(x-1) - 2x = -(x + 50) is x = -6.
To solve the equation 8(x-1) - 2x = -(x + 50).
First, distribute the 8 to the terms inside the parentheses:
8x - 8 - 2x = -(x + 50)
Simplify the left side of the equation:
6x - 8 = -(x + 50)
Distribute the negative sign to the terms inside the parentheses:
6x - 8 = -x - 50
Isolate the x terms on one side and the constant terms on the other side:
6x + x = -50 + 8
Combine like terms:
7x = -42
Divide both sides of the equation by 7:
7x / 7 = -42 / 7
x = -6
Therefore, the solution to the equation 8(x-1) - 2x = -(x + 50) is x = -6.
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Please Help ASAP!
Will award brainliest!
ratio of AB to DE = 30/6 = 5
do 24/6 = 4
x = 4
Find the midpoint of A and D. Simplify completely.
option 5 is none of these.
A = (1,3)
D= (5,0)
midpoint = (x1+x2)/2 , (y1+y2)/2
5+1=6/2 =3
3+0=3/2 = 3/2
(3,3/2)
Determine the growth factor corresponding to 25% increase.
a.
1.75
c.
25
b.
1.25
d.
0.25
Answer:
Step-by-step explanation:
Alright, lets get started.
The given increase is 25 %.
Which means in terms : [tex]25*\frac{1}{100}[/tex]
That will be equal to : [tex]0.25[/tex]
So, the growth of 0.25 means the complete term will be :
[tex]1+0.25=1.25[/tex]
Hence the growth factor of 25 % will be equal to 1.25 : Answer
Hope it will help :)