Answer:
f(x)= -x²-4x-2
Step-by-step explanation (this way is not the shortest one):
1. for intercept (-2-√2;0): a(-2-√2)²+b(-2-√2)+c=0
for intercept (-2+√2;0): a(-2+√2)²+b(-2+√2)+c=0
for the point (-1;1): a(-1)²+b(-1)+c=1
2. using the three record written above, it is possible to make up the system of equations and calculate 'a', 'b' and 'c':
[tex]\left \{ \begin{array}{ccc}a-b+c=1\\a(-2- \sqrt2)^2+b(-2- \sqrt2)+c=0\\a(-2+ \sqrt2)^2+b(-2+ \sqrt2)+c=0\end{array}[/tex]
[tex]\left \{ \begin{array}{ccc}a=-1\\b=-4 \\c=-2\end{array}[/tex]
3. the required equation is: -x²-4x-2
What is the meaning of the slope of the line in this context?
Answer:
The correct answer is D) The rate in which he burns calories
Step-by-step explanation:
We can tell this because the slope is always the change in y value over the change in x value. Since the y value is calories and the x value is minutes, we get the following.
Calories/minute
Which can also be written as calories per minute, which is a rate.
The graph says about the rate of calorie burned.
What is Cartesian plane?A plane created by the intersection of two perpendicular coordinate axes is referred to as a cartesian plane. The x-axis is the horizontal axis, while the y-axis is the vertical axis. These axes cross at the origin, whose location is specified as (0, 0). Any location on the cartesian plane is shown as (x, y).
Given the graph between calories burned and time in minutes,
X axis shows the time and Y axis shows the calorie burned,
The ratio of the change in y value to the change in x value is the slope. We obtain the following because the y value is calories and the x value is minutes.
Calories/minute
This is a rate and can also be represented as calories per minute.
Hence Option D is best suitable for condition.
Learn more about Cartesian plane;
https://brainly.com/question/28574364
#SPJ2
Which sequence of transformations would change two congruent figures into two similar figures that are no longer congruent ?
A) reflection and rotation
B) translation and dilation
C) reflection and translation
D) translation and reflection
Answer:
B
Step-by-step explanation:
....
The sequence of translation and dilation of transformation would change two congruent figures into two similar figures that are no longer congruent.
Option B is the correct answer
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and size.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
Two congruent figures:
If a translation is applied to the two congruent figures we get the same shape and size.
If we apply a dilation after the translation to the two congruent figures the size of the figures changes.
If translation and dilation are applied to two congruent figures this sequence would change two congruent figures into two similar figures that are no longer congruent.
Thus,
The sequence of translation and dilation of transformation would change two congruent figures into two similar figures that are no longer congruent.
Option B is the correct answer.
Learn more about translation here:
https://brainly.com/question/12463306
#SPJ6
Given the vertices of isosceles trapezoid ABCD: A(2, 0), B(4, 0), C(5, -2), D(1, -2). If the image is reflected over the y-axis, C' = (5, 2) (-5, 2) (-5, -2) (5, -2)
Here is the image https://addenbrooke.owschools.com/media/g_geo_ccss_2016/10/q910l4.gif
Answer:
C' = (-5, -2)
Step-by-step explanation:
Reflection over the y-axis negates the x-coordinate.
C(5, -2) ⇒ C'(-5, -2)
Answer:
The correct option is 3.
Step-by-step explanation:
The vertices of isosceles trapezoid ABCD are A(2, 0), B(4, 0), C(5, -2), D(1, -2).
If a figure reflected over the y-axis, then the relation between coordinates of preimage and image is defined as
[tex](x,y)\rightarrow (-x,y)[/tex]
It is given that ABCD reflected over the y-axis and coordinates of point C are (5,-2), so the coordinates of C' are
[tex]C(5,-2)\rightarrow C'(-5,-2)[/tex]
The coordinates of C' are(-5,-2). Therefore the correct option is 3.
The graph shows the functions f(x), p(x), and g(x):
Part A: What is the solution to the pair of equations represented by g(x) and p(x)? (3 points)
Part B: Write any two solutions for p(x). (3 points)
Part C: What is the solution to the equation g(x) = f(x)? Justify your answer. (4 points)
A solution to a pair of equations is the set of points where their graphs intersect. Points in that set will satisfy both equations, which is what "solution" means.
Here, the graphs of p(x) and f(x) each intersect the graph of g(x) in one place. Hence f(x) = g(x) has one solution, as does p(x) = g(x).
Finding the solution is a matter of reading the coordinates of the point of intersection from the graph.
A. The graphs interesect at x=1, y=-1.
B. Any point on the red line is a solution. We already know one of them from part A. Another is the x-intercept, where y=0. That point is (2, 0).
C. g(x) intersects f(x) at their mutual y-intercept: y = 3. x = 0 at that point.
Which pair of triangles is congruent by ASA? - Please help ASAP. THANKS!
Answer:
it would be c
Step-by-step explanation:
all you have to do is find the picture that maches the stament
asa means angle side angle so therefore c if im correct
Find an equation for the line that passes through the points , −3−3 and , 5−1 .
y +3 = (1/4)(x +3)
Step-by-step explanation:The two-point form of the equation for a line is good for this.
... y -y1 = (y2-y1)/(x2-x1)(x -x1)
Substituting your values, we have ...
... y -(-3) = (-1-(-3))/(5-(-3))(x -(-3))
... y +3 = 2/8(x +3)
Since you ask for "an equation," we can leave it in this form.
... y +3 = (1/4)(x +3)
_____
Or we can rearrange it to slope-intercept form:
... y = (1/4)x -(2 1/4)
or put it in standard form:
... x -4y = 9
TIMED PLEASE HELP What is the approximate degree measure of angle B in the triangle below? A. 16.3 B. 43.8 C. 46.2 D. 73.7
Answer:
The answer is the option D
[tex]73.7\°[/tex]
Step-by-step explanation:
we know that
In the right triangle ABC of the figure
[tex]sin(B)=\frac{AC}{BC}[/tex]
in this problem
[tex]AC=24\ units[/tex] ------> opposite side angle B
[tex]BC=25\ units[/tex] ------> the hypotenuse of the right triangle
substitute the values
[tex]sin(B)=\frac{24}{25}[/tex]
[tex]B=arcsin(\frac{24}{25})=73.7\°[/tex]
what are the x-intercepts of the parabola represented by the equation y = 3x2 + 6x − 10
x ≈ {-3.082, 1.082}
Step-by-step explanation:I find the easiest way to answer such a question (with medium accuracy) is to use a graphing calculator. The graph shown in the attachment gives the answers listed above.
___
From vertex form
The graphing calculator also makes it easy to find the vertex of the parabola. If we divide by 3 so the scale factor is 1, then the y-value of the vertex is -13/3 and the vertex form of the equation can be written ...
... y = (x +1)² -13/3
This has x-intercepts easily found.
... 0 = (x +1)² -13/3 . . . . x-intercepts are where y=0
... (x +1)² = 13/3 . . . . . . . add 13/3
... x +1 = ±√(13/3) . . . . . take the square root
... x = -1 ±√(13/3) . . . . . subtract 1
... x ≈ {-3.0816660, 1.0816660}
_____
Using the quadratic formula
This equation has a=3, b=6, c=-10, so we can put these values into the quadratic formula to find the x-interecepts.
... x = (-b±√(b²-4ac))/(2a)
... x = (-6 ±√(6² -4(3)(-10)))/(2(3))
... x = (-6 ±√156)/6 = -1 ±√(13/3) . . . or . . . -1 ±(√39)/3
put the following values in order from least to greatest 3.
2^0=1
2^-2=1/4
(-2)^2=4
-2^2=-4
-2^2,2^-2,2^0,(-2)^2
Find the measure of the acute angle x. Round your answer to the nearest tenth, if necessary.
29.1
0.01
60.9
0.03
Answer:
60.9
Step-by-step explanation:
Given sin(−θ)= −1/4 and tanθ= 15√15 .
What is the value of cosθ ?
please help me asap!
Answer:
Option b. 30.5
Step-by-step explanation:
Given in the picture is a triangle ABC with sides AB = 22.3 and side BC=24.1
The included angle B = 82 degrees
We have to find the third unknown side AC = b
REcollect the cosine formula for triangles.
[tex]b^{2} =a^{2} +c^{2} -2ac cos B[/tex]
substitute for a and c
We get
[tex]b^2 = 22.3^2+24.1^2-2(22.3)(24.1) cos 82\\=928.587[/tex]
b = square root of 928.587
b =30.47=30.5
Thus we get b = 30.5
**PLEASE HELP WILL GIVE BRAINIEST!**
$16,307.64
Step-by-step explanation:The table value for n=8 quarters (2 years) and 2.00% (8% annual rate divided by 4) is 8.58297. Multiply this by the dollar amount Carlene deposits to get the balance at the end of the period.
... $1900 × 8.58297 ≈ $16,307.64
Marvin Company has a beginning inventory of 12 sets of paints at a cost of $1.50 each. During the year, the store purchased 4 sets at $1.60, 6 sets at $2.20, 6 sets at $2.50, and 10 sets at $3.00. By the end of the year, 25 sets were sold. Calculate (a) the number of paint sets in ending inventory and (b) the cost of ending inventory under the LIFO, FIFO, and weighted-average methods. Round to nearest cent for the weighted average
Answer:
(a) 13
(b) LIFO: $19.60; FIFO: $37.50; Avg: $28.26
Step-by-step explanation:
(a) The starting inventory was 12 sets. Added to that were 4, 6, 6, 10, to make a total of 38 paint sets. 25 were sold, so 13 remained at the end of the year.
(b)
LIFO
Sets purchased at the end of the year are sold first (last-in, first-out). So the sets remaining in inventory are the ones purchased at the beginning of the year. Those 13 sets cost 12@1.50 +1@1.60 = $19.60.
FIFO
Sets purchased first are sold first, so the sets remaining in inventory are the ones purchased last. Those 13 sets cost 10@3.00 +3@2.50 = $37.50.
Avg
The total cost of all inventory purchases was ...
... 12@1.50 +4@1.60 +6@2.20 +6@2.50 +10@3.00
... = 18.00 +6.40 +13.20 +15.00 +30.00 = $82.60
Then the value of the remaining 13 of the 38 items bought is ...
... (13/38)·$82.60 = $28.26.
_____
I find it convenient to let a spreadsheet do the arithmetic.
Q. P
12. 1.5. 18.00
4. 1.6. 6.40
6. 2.2. 13.20
6. 2.5. 15
10. 3. 30
__ __. ___
38. 10.8. 82.6
Sales. 25
Ending inventory 25-38=13. Answer a
B) ending inventory under LIFO
12×1.5=18
1×1.6=1.6
___
19.6 Answer
Ending inventory under FIFO
10×3=30
3×2.5=7.5
___
37.5. Answer
Ending inventory under weighted average
82.6÷38=2.17
2.17× 13=28.21 ...Answer
Hope it helps!
Marta believes that the equation of the line of best fit for the scatterplot below is
Which statement best summarizes why Marta is likely incorrect?
Answer:
Marta’s equation has a positive y-intercept, but the scatterplot suggests a negative y-intercept.
Step-by-step explanation:
https://brainly.com/question/5873063
Sorry if this does not help
Answer:
A
Step-by-step explanation:
For which of these functions does the function value change at a constant rate per unit change in x? Explain.
Answer:
The function r(x) represents a constant rate per unit change in x.
Step-by-step explanation:
This is because when you increase in 2, it goes from 37 to 25, a decrease in 12, then when the x goes from 2 to 3, then it has to drop down by 6, or else it won't be linear. It does. 25-6 is 19. Then it goes from 3 to 5, meaning it has an increase of 2 in x, meaning it has to drop down in 12 to be linear, It does. 19-12 is 7. So it is linear, meaning it has a constant rate per unit change in x.
Consider the following equation. 1000=5(10^2t) which of the following equations can be used to find true value of t. A.log2(1000) B.log2(200)=10t C.log10(1000)=5(2t) D.log10(200)=2t
D. log₁₀(200) = 2t
Step-by-step explanation:Dividing by 5 gives you ...
... 200 = 10^(2t)
Taking the log to the base 10 gives you ...
... log₁₀(200) = 2t . . . . . . matches selection D
Find the diagonal of a square whose sides are 5cm long
Answer:
5√2 cm or 7.1 cm
Step-by-step explanation:
We can use Pythagoras' Theorem:
The square on the diagonal is equal to the sum of the squares of the other two sides.
d² = 5² + 5²
d² = 25 + 25
d² = 50
d = √50
d = √(25×2)
d = 5√2
d≈ 7.1 cm
1. Find the volume for 5 different spheres by randomly choosing different radii.
Using the same radii values, find the volume of 5 cylinders where the height of the cylinder is the same as the diameter of the sphere.
The volume of the sphere is given by :
V=[tex]\frac{4}{3}\pi r^{3}[/tex]
And volume of cylinder is given as :
V=[tex]\pi r^{2}h[/tex]
So, as given to select the radius randomly and the height of the cylinder will be the diameter of the sphere.
The radius are = 3, 5, 8, 10, 12
And height will be = 6, 10, 16, 20, 24
1. Volume of sphere with radius 3 = [tex]\frac{4}{3}*3.14*3*3*3= 113.04[/tex] units
Volume of cylinder with radius 3 and height 6 = [tex]3.14*3*3*6=169.56[/tex] units
2. volume of sphere with radius 5 = 523.60 units
volume of cylinder with height 10 = 785.40 units
3. volume of sphere with radius 8 = 2144.66 units
volume of cylinder with height 16 = 3216.99 units
4. volume of sphere with radius 10 = 4188.79 units
volume of cylinder with height 20 = 6283.19 units
5. volume of sphere with radius 12 = 7238.23 units
volume of cylinder with height 24 = 10857.34 units
Define perpendicular lines.
A. Lines that cut across two or more lines.
B. Two non–coplanar lines that do not intersect.
C. Two coplanar lines that do not intersect.
D. Two coplanar lines that intersect at a 90 degree angle.
Answer:
It is D. Perpendicular lines intersect at a 90 degree angle.
Step-by-step explanation:
If Jose makes 14 of his 20 free throws in a basketball game, what is his free throw shooting percentage? A) 20% B) 30% C) 70% D) 90%
Answer:
C) 70%
Step-by-step explanation:
To find his percentage we take part over total
14/20
We want it over 100, so multiply the top and bottom by 5
14*5
---------
20*5
70/100
Percent means out of 100
so we have 70 percent
70 %
Answer:
c 70%
Step-by-step explanation:
20 into 14 = 70%
Help meeeeeeweeeeeeee
A. y = (-6/5)x +10
Step-by-step explanation:The given line has a negative slope (downward to the right). The only equation offered with a negative slope is the one of selection A.
_____
Complete working
A parallel line will have the same slope. If there are less-obvious choices to select from, you need to know the slope of the given line. That is computed from ...
... slope = (change in y)/(change in x)
The coordinates of two points are given, so we can find the slope as ...
... slope = (-4-2)/(-1-(-6)) = -6/5
There are a number of ways to write the equation of a line, but in slope-intercept form, the slope is the coefficient of x. You will be looking for a choice that has an x-coefficient of -6/5.
The graph shows f(x) and its transformation g(x) . Enter the equation for g(x) in the box. g(x) =
You can see that the graph of [tex] g(x) [/tex] is the graph of [tex] f(x) [/tex] translated one unit to the left.
Horizontal translations are given by the transformation
[tex] f(x) \mapsto f(x+k) [/tex]
If [tex] k>0 [/tex] the function is translated k units to the left, else if [tex] k<0 [/tex] the function is translated k units to the right.
So, in your case, [tex] k=1 [/tex]
And thus you have
[tex] g(x) = f(x+1) = 2^{x+1} [/tex]
Answer:
2^x+1
Step-by-step explanation:
Prove whether or not the point (√21,2) lies on a circle centered at the origin and containing the point (5,0).
check the picture below.
so, we know the radius of this circle is 5 then, namely, the distance from (0,0) to (5,0) is 5.
now, if (√(21) , 2) indeed lies on that circle curve, then the distance from (0,0) to (√(21) , 2) will also be the same radius of 5 units.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{\textit{origin}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad (\stackrel{x_2}{\sqrt{21}}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ r=\sqrt{(\sqrt{21}-0)^2+(2-0)^2}\implies r=\sqrt{(\sqrt{21})^2+2^2} \\\\\\ r=\sqrt{21+4}\implies r=\sqrt{25}\implies r=5~~~~\checkmark[/tex]
Answer:
It does. "Proof" below.
Step-by-step explanation:
In order for the given points to lie on the circle, they must both be the same distance from the origin. The Pythagorean theorem is used to make a "distance formula" for computing the distance between two points.
For a point (x, y), its distance (d) to the origin will be ...
... d = √(x² +y²)
For the reference point that we know is on the circle, this distance (the circle's radius) is ...
... d = √(5² +0²) = √25 = 5
For the point in question, the distance to the origin is ...
... d = √((√21)² +2²) = √(21 +4) = √25 = 5
Both points have the same distance to the origin, 5 units, so a circle (of radius 5) centered there will contain both points.
_____
A graph is not proof, but it can confirm the result.
A tree is 75 inches tall. How tall is it in feet and inches? ft in
Answer:
6ft 3in
Step-by-step explanation:
The height of a tree that is 75 inches tall is approximately 6 feet 3 inches when converted.
Explanation:In this question, we are required to convert the height of a tree from inches to feet and inches. One foot equals twelve inches. Therefore, to convert 75 inches into feet, we divide 75 by 12. This results in a quotient approximately equal to 6.25 ft. However, we want to also express the height in the remaining inches, so we take the decimal portion (0.25) and multiply it by 12 to convert it back to inches, giving us 3 inches. Hence, a tree that is 75 inches tall corresponds to 6 feet 3 inches tall when converted.
Learn more about Unit Conversion here:https://brainly.com/question/19420601
#SPJ3
I do not understand this math question. If someone can help you get 25 points
In degrees: -270°, 90°, 450°.
In radians: -3π/2, π/2, 5π/2.
Step-by-step explanation:The cosine is always zero where the sine is 1. The sine is 1 at an angle of 90°, and every integer number of 360° added (or subtracted) to that. The corresponding point on the unit circle is (0, 1), labeled A in the diagram.
The angle from the x-axis to the positive y-axis can be called any of ...
... 90°
... -270°
... 450°
... 810°
... π/2 radians
... -3π/2 radians
... 5π/2 radians
... 9π/2 radians
You are asked to pick three of these (or some others you may choose) so that you have 3 different names for the angle to this point.
_____
Comment on the second figure
The graphing calculator easily shows places where function values are zero. To show where sin(x) = 1, we rewrite it as sin(x) -1 = 0. Then, the zeros are highlighted. In degrees, the ones shown are -270°, 90°, 450°, 810°. You can see that cos(x) is zero at those same angles.
please help just looking for the answer
Answer: Correct Answer is 4th option , 28
Step-by-step explanation:
We can find the measure of the angle using the tangent.
We know, tangent of an angle = Perpendicular/Base, corresponding to that angle.
So, Tan of angle T = RG / RT
or, Tan of angle T = 8/15
or, angle T = tan inverese of 8/15
or, angle T = 28.07
So, angle T rounded to nearest degree = 28
Hope this helps.
Thank you.
Suppose you can replace one number cube with a nonstandard number cube, where any of the numbers 1 through 6 can appear on multiple faces. How can you arrange the numbers on the nonstandard cube so that the mean of the rolls is the same as that of two standard number cubes, but the standard deviation is as large as possible? What is this value? Explain your thinking
Answer:
Replace 5 and 4 with 6s. Replace 2 and 3 with 1s. Then there will be 3 faces with 6 and 3 faces with 1.
Step-by-step explanation:
In order for the mean to remain unchanged, the sum of opposite faces must remain the same: 7. In order to have the standard deviation as large as possible, the largest and smallest possible numbers need to be used: 6 and 1.
Replacing 4 and 5 with 6s, and replacing 2 and 3 with 1s will accomplish your goal.
A school purchases jars of marbles.
* Each jar contains 500 pieces of marbles.
* Each jar costs $10.
How much does the school have to charge for each piece of marbles to make a profit of $25 per
jar?
a. $0.07
b. $0.10
c. $0.14
d. $0.25
Answer:
a. $0.07
Step-by-step explanation:
Profit = Charge -Cost
We want to make a profit of 25 and the cost is 10
25 = Charge -10
Add 10 to each side
25+10 = Charge -10+10
35 = Charge
We need to charge 35 per jar.
Each jar contains 500 marbles
The cost per marble is Cost/ number of marbles
cost per marbles = $35 / 500
= $.07
Answer:
Option A : $0.07
Step-by-step explanation:
Given :
A school purchases jars of marbles.
Each jar contains 500 pieces of marbles.
Each jar costs $10.
To Find : How much does the school have to charge for each piece of marbles to make a profit of $25 per jar?
Solution :
Cost of one jar is $10
Now, school wants to make profit of $25 on each jar .
using formula : Profit = Charge - cost
⇒$25 = charge - $10
⇒$35 = charge
Thus school should charge one jar of marbles of $35.
Since each jar contains 500 marbles.
So,to calculate cost of each marble when charge of jar is $35.
Cost of 500 marbles is $35
Cost of 1 marble = 35/500 = $0.07
cost of each marble when charge of jar is $35 is $0.07
Hence , the school have to charge $0.07 for each piece of marble to make a profit of $25 per jar.
Option A is correct
What is the x-intercept of the line 6x – 3y = 24?
Answer:
(4,0)
Step-by-step explanation:
insert 0 where the y is located and solve for x
6x – 3y = 24
6x – 3(0) = 24?
6x = 24
6x / 6 = 24 / 6
x = 4
x-intercept = (4, 0)
The x-intercept of the line 6x - 3y = 24 is (4, 0).
Explanation:The x-intercept of a line represents the point where the line intersects the x-axis. To find the x-intercept of the line 6x - 3y = 24, we need to set y = 0 and solve for x.
Substituting y = 0 into the equation, we get 6x - 3(0) = 24. Simplifying this equation gives us 6x = 24, and dividing both sides by 6 gives x = 4.
Therefore, the x-intercept of the line 6x - 3y = 24 is (4, 0).
Learn more about x-intercept here:https://brainly.com/question/14180189
#SPJ3