x = 2t
y = t + 5, -2 ≤ t ≤ 3
Can you please graph this
Answers
Answer:
See attachment
Step-by-step explanation:
The given parametric equations are;
[tex]x=2t[/tex] and [tex]y=t+5[/tex], [tex]-2\le t\le 3[/tex].
We can graph this by plotting some few points within the given range or eliminate the parameter to identify the type of curve.
Plotting points;
When [tex]t=-2[/tex],
[tex]x=2(-2)=4[/tex] and [tex]y=-2+5=3[/tex]
This gives the point (-4,3).
When [tex]t=0[/tex]
[tex]x=2(0)=0[/tex] and [tex]y=0+5=5[/tex]
This gives the point (0,5).
When [tex]t=3[/tex]
[tex]x=2(3)=6[/tex] and [tex]y=3+5=8[/tex]
This gives the point (6,8).
We plot these points and draw a straight line through them.
Eliminating the parameter.
[tex]x=2t[/tex]
[tex]y=t+5[/tex]
Make t the subject in the second equation;
[tex]t=y-5[/tex]
Substitute into the first equation;
[tex]x=2(y-5)[/tex]
This implies that;
[tex]x=2y-10[/tex]
[tex]y=\frac{1}{2}x+5[/tex]
This is an equation of a straight line with slope [tex]\frac{1}{2}[/tex] and y-intercept 5 on the interval
[tex]-4\le x \le 6[/tex]
Answer:
The answer is in attachment
Step-by-step explanation:
First step finde a function t(x) ⇒ t=x/2;
Now we need to finde the limits of that function:
if t=-2 ⇒ x=-4 and t=3 ⇒ x=6. That means -4≤x≤6
Now replace on y(t) ⇒ y(x)= x/2+5, 4≤x≤6
Related Questions
Determine whether the ffunction X/(x^2-1) is odd even or neither
Answers
equation is:
[tex] f(x) = \frac{x}{ {x}^{2} - 1 } [/tex]
so if its even f(-x) should be equal to f(x)
that means
[tex]f( - x) = \frac{ - x}{ {( - x)}^{2} - 1} \\ \\ f( - x) = - \frac{ x}{ {x}^{2} - 1} [/tex]
so f(x) is not equal to f(-x) so its not even
If its odd than f(-x) should be equal to -f(x)
[tex] - f(x) = - ( \frac{ x}{ { x}^{2} - 1 } ) \\ - f(x) = - \frac{ x}{ {x}^{2} - 1 } [/tex]
so as we can see f(-x)= - f(x)
so the function is odd
Ans:function is odd and not even
By replacing x with -x in the given function X/(x^2-1), we find that it doesn't fulfill the criteria for even or odd functions. Therefore, the function is neither odd nor even.
Explanation:To determine whether the function X/(x^2-1) is odd, even or neither, you can plug in -x into the function and simplify. For a function to be considered even, f(x) should be equal to f(-x). For a function to be considered odd, f(-x) should be equal to -f(x).
For the given function X/(x^2-1), after replacing x with -x, we get -X/((-x)^2 - 1) which simplifies to -X/(x^2 - 1). Since f(-x) is not equal to f(x) or -f(x), the function is neither odd nor even.
Generally, an even function is symmetrical around the y-axis. That is, if you fold the graph of the function over the y-axis, both halves align. On the other hand, an odd function is symmetric about the origin. That is when the graph is rotated 180 degrees about the origin, the graph remains unchanged.
Learn more about Even and Odd Functions here:https://brainly.com/question/14302660
#SPJ12
Can someone please help me with this?
Answers
Step-by-step explanation:
3) adjacent angles add up to 180°
4)substitution property of equality
5) subtraction property of equality
A rectangular prism has a volume of 189cm^3. The height of the prism is 3cm. What are the dimensions of the base
Answers
Answer:
l = 9 cm
b = 7 cm
h = 3 cm
Step-by-step explanation:
Formula:-
Volume of cuboid = lbh
l - Length of cuboid
b - breadth of cuboid
h - Height of cuboid
To find the dimensions of prism
Here prism is like a cuboid.
Volume of prism = 189 cm^3
Height h = 3 cm
Volume = lbg
189 = l * b* 3
l * b = 189/3 = 63 = 9 * 7
Therefore l and b may be 9 and 7
Betsy is buying topsoil for the flower bed shown below.
One bag of topsoil covers 20 square meters.
How many bags of topsoil does Betsy need to cover her flower bed?
A 2 bags
B 3 bags
C 4 bags
D 5 bags
Answers
Answer:
Option B. 3 bags
Step-by-step explanation:
step 1
Find the area of the flower bed
The area of the flower bed is the area of a triangle
A=(1/2)bh=(1/2)(20)(6)=60 m^2
step 2
Divide the area by 20 square meters to find the number of bags of topsoil
(60)/(20)=3 bags
Answer:
B. 3 Bags
Step-by-step explanation:
Let’s say we want to find the size of a deer population. Suppose that we capture 80 deer, tag them, and release them back into the forest. After some time has passed—allowing the marked deer to thoroughly mix with the rest of the population—we come back and capture another 100 deer. Out of these deer, we find that 20 are already marked. Using this information, what can you estimate the deer population to be?
A. 1,000
B. 400
C. 200
D. 800
E. 600
Answers
Answer:
400
Step-by-step explanation:
20/100 = 80/x
Cross multiply and divide
100 X 80 = 8000 / 20 = 400
The total deer population in the forest will be 400. Then the correct option is B.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
Suppose we need to track down the size of a deer populace. Assume that we catch 80 deer, label them, and deliver them back into the timberland. After some time has elapsed - permitting the noticeable deer to completely blend in with the remainder of the populace - we return and catch another 100 deer. Out of these deer, we observe that 20 are as of now checked.
Then the ratio of the number of tag deer to the total deer will be constant. Then the equation is given as,
20 / 100 = 80 / x
x = 80 × (100/20)
x = 400
The total deer population in the forest will be 400. Then the correct option is B.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ2
The radius of a circle is 9. Using π, which equation expresses the ratio of the circumference of the circle to the circle's diameter?
Answers
Answer:
[tex]\large\boxed{\dfrac{C}{d}=\pi}[/tex]
Step-by-step explanation:
We have the radius r = 9.
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
The diameter d = 2r.
The ratio of the circumference of the circle to the circle's diameter:
[tex]\dfrac{C}{d}=\dfrac{2\pi r}{2r}=\pi[/tex]
H20(l) > h20(g) calculate H rxn
Answers
H20 (liquid)- H20(gas)
The Enthalpy change for the above process can be written as:
ΔH=ΔHgas−ΔHliquid
and let us assume the claim in the question is right i.e
ΔHgas>ΔHliquid
Find the area of the arrow above
Answers
Answer:
1200
Step-by-step explanation:
Aa=At+As
As=L•h
=20(30)
As=600
At=½(b)h b=10+10+20=40
=½(40)30
At=600
Aa=600+600
Aa=1200
The area of an arrow is the sum of the area of the triangle and the area of the rectangle. Then the area of the arrow is 1,200 square inches.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Given
The dimension of the arrow is shown in the figure.
The area of an arrow is the sum of the area of the triangle and the area of the rectangle.
The area of the triangle will be
[tex]\rm Area \ of \ triangle = \dfrac{1}{2} 40 * 30\\\\Area \ of \ triangle = 600[/tex]
The area of the rectangle will be
[tex]\rm Area \ of \ rectangle= } 20* 30\\\\Area \ of \ rectangle = 600[/tex]
Then the area of an arrow will be
[tex]\rm Area \ of \ arrow= 600 + 600\\\\Area \ of \ arrow = 1200[/tex]
Thus, the area of the arrow is 1,200 square inches.
More about the geometry link is given below.
https://brainly.com/question/7558603
Which mathematical terms originated from the Arabic mathematician al-Khwarizmi
Answers
Final answer:
Algebra and algorithm are mathematical terms originating from al-Khwarizmi, a prominent Arab mathematician.
Explanation:
Algebra and algorithm are two mathematical terms that originated from the Arabic mathematician al-Khwarizmi. Al-Khwarizmi's work in the ninth-century book 'ilm al-jabr wa'l-muqabala laid the foundation for these terms and significantly influenced the field of mathematics.
Which congruency statement is true?
Answers
bc = fg
the letters should correspond with each other
(b is in the middle of abc and f is in the middle efg; c & g are both at the end)
The side lengths of triangle ABC are 3,4, and 5 which set of ordered pairs from a triangle that is congruent to triangle ABC?
Answers
The answer is A.)(-3,1) , (-3,5) , (0,5)
Hope this helps! :)
HELP!!!!!!! Choose the graph that matches the following system of equations:
4x + 2y = −2
x − 3y = 24
Answers
Answer:
The answer in the attached figure
Step-by-step explanation:
we have
[tex]4x + 2y = -2[/tex] -----> equation A
[tex]x-3y=24[/tex] -----> equation B
Isolate the variable x in the equation B
[tex]x=3y+24[/tex] ----> substitute in the equation A and solve for y
[tex]4(3y+24) + 2y = -2[/tex]
[tex]12y+96+ 2y = -2[/tex]
[tex]14y = -2-96[/tex]
[tex]14y = -98[/tex]
[tex]y = -7[/tex]
Find the value of x
[tex]x=3(-7)+24=3[/tex]
The solution of the system of equations is the point (3,-7)
What is the quotient?
Answers
Answer: FIRST OPTION
Step-by-step explanation:
According the quotient of powers property, when you have the division of two powers with the same base, then you must subtract the exponents.
Therefore, keeping the property above on mind, you have that the quotient is the shown below:
[tex]\frac{(-7)^2}{(-7)^{-1}}=(-7)^{(2-(-1))}=(-7)^{(2+1)}=(-7)^3=-343[/tex]
Quick pls!!
ABC is reflected over l and then over m. Which could be the image of a rotation of ABC?
A) ABC
B) XYZ
C) QRS
D) None of the above
Answers
Answer:
Option B
Step-by-step explanation:
The Triangle given is ΔABC.
It is reflected over l mirror so it will form a image like ΔQRS.
Again the triangle is reflected over mirror m so it will form a image like ΔXYZ.
A line has a rise of 3 and a run of 12. Find the slope of the line. Type a numerical answer in the space provided. If necessary, use the / key to represent a fraction bar.
Answers
Because the formula is rise over run, it would be 3/12, and simplified is 1/4.
What is the value of y in the equation y − 7 = 21? (4 points)
Select one:
a. 7
b. 17
c. 21
d. 28
Answers
Answer:
D. 21
Step-by-step explanation:
28-21=7
28-7=21
28-21=7
So that’s your answer
find missing term.x/x2-4x+4-x/x2-3x+2= ?/(x-2)2(x-1)
Answers
Answer:
-3x
Step-by-step explanation:
x x
----------------- - --------------------
x^2 -4x + 4 x^2-3x+2
x x
= ---------------- - --------------------
(x -2)^2 (x - 2)(x - 1)
x (x-1) - x(x +2)
= ----------------------------
(x -2)^2 (x - 1)
x^2 -x -x^2 - 2x
= --------------------------
(x -2)^2 (x - 1)
-3x
= -----------------------
(x -2)^2 (x - 1)
Therefore; the missing term is -3x
Find the surface area of the prism
Answers
Answer:
80
Step-by-step explanation:
times it all
Answer:
68 in^2
Step-by-step explanation:
Bottom and Top
base of parallelogram = 4*4 = 16
Since there are two of them, the area = 2 * 16 = 32
left and right faces
I think you have to assume this is a rectangle. We do not know the height for a parallelogram.
Area = l*w
Area = 4 * 2.5
Area = 10 in^2
But there are two of them.
Area = 2* 10 = 20 in^2
Front and back faces
The area is the area of a parallelogram
Area = b * h
Area = 2 * 4
Area = 8 in^2
But there are 2 of them
The area for 2 is 8*2 = 16 in^2
Total Area
Total Area = 16 + 20 + 32
Total Area = 68 in^2
Tony’s credit card statement says that he must pay a minimum payment of 15% or $20 whichever is greater. How much will he pay if his new balance is $138.90
Answers
Answer: $20.84
Step-by-step explanation: In order to calculate Tony’s minimum payment you need to calculate how much 15% is of his balance.
138.90 x .15 = $20.84, which is 15% of his balance.
The minimum payment is the greater of 15% or $20, so his minimum payment will be $20.84.
The answer is $188.90. If I am wrong, please correct me.
PLEASE HELP!!!!!!
Find the number of ways in which 9 people can be divided into 2 groups: the first group has 5 people and the second group has 4 people.
Answers
2. group 1: 6 people group 2: 3 people
3. group 1: 3 people group 2: 6 people
4. group 1: 2 people group 2: 7 people
5. group 1: 7 people group 2: 2 people
6. group 1: 8 people group 2: 1 person
7. group 1: 1 person group 2: 8 people
8. group 1: 9 people group 2; 0 people
9. group 1 : no people group 2: 9 people
Which function is quadratic function?
Answers
To be a quadratic equation, the first number has to be rasied by the power of 2.
The answer would be c(x) = -8x^2 + 3x-5
Answer:
The correct option isC(x) -8x² + 3x - 5
Step-by-step explanation:
Quadratic function is a function that can be written as in the form of f(x) = ax² + bx + c, where a ≠ 0.
In a quadratic function, the greatest power of the variable is 2.
So, there is only one function from provided options which has greatest power is 2.
Hence, the correct option is C(x) -8x² + 3x - 5
A pizza company makes pizza in three different sizes: small, medium, and large. There are four popular toppings: pepperoni, sausage, green pepper, and mushroom. How many different kinds of pizza with one topping are available?
Answers
Hey there!
The correct answer should be 12
Since there are 3 different pizza sizes & 4 different toppings, all we have to is multiply 3 by 4 (number of pizza sizes multiplied by the number of toppings)
3 * 4 = 12
Here is the work:
1. Small with pepperoni
2. Medium with pepperoni
3. Large with pepperoni
4. Small with sausage
5. Medium with sausage
6. Large with sausage
7. Small with green pepper
8. Medium with green pepper
9. Large with green pepper
10. Small with mushroom
11. Medium with mushroom
12. Large with mushroom
As you can see, there are 12 options
Hope this helps you!
God bless ❤️
xXxGolferGirlxXx
The equation shows the relationship between x and y: y = −7x + 9 What is the slope of the equation?
A. −7
B. −2
C.7
D. 9
Answers
Answer:
A (-7)
Step-by-step explanation:
compare y = −7x + 9 to the slope-intercept form of the equation of a straight line: y = mx + b.
Here -7 corresponds to the slope, m, and 9 corresponds to the y-intercept, b.
The slope of the line represented by y = −7x + 9 is thus A (-7).
Final answer:
The slope of the equation 'y = -7x + 9' is represented by the coefficient of x, which is -7. Thus, the slope of the line is -7.
Explanation:
The equation given is y = -7x + 9. In this equation, -7 is the coefficient of x, and according to the slope-intercept form of a linear equation, which is y = mx + b, the coefficient m represents the slope of the line. Therefore, the slope of the equation y = -7x + 9 is -7.
To confirm, consider that the slope is the amount by which y changes for a unit change in x. So if you were to plot this line, for every one unit increase in x, y would decrease by 7 units, indicating a negative slope. This is consistent with the negative sign in front of the 7 in the equation. Hence, the correct answer is A. -7.
i need help ASAP!!!!! PLEASE
Answers
Subtract 4 from both sides
6x =48
X=8
Is F(x)= X^2(X^2+9)(X^3+2X) even or odd
Answers
Answer:
The function is odd.
Step-by-step explanation:
A function is even if the graph of the function is symmetric with respect to the y-axis. A function is odd if the graph of the function is symmetric with respect to the origin. To find if the function is even or odd, we're going to graph the function using DESMOS.
As you can see in the attached picture, the function is symmetric with respect to the origin. Therefore, the function is odd.
What is the length,width,and height
Answers
Answer:
5 cubic units
Step-by-step explanation:
If each cube represents 1 cubic unit, then the volume will be the number of cubes to make the figure. When you count, there are 5 cubic units. The volume is 5.
students ages 10-17 were survey about their eating habits during breakfast.
Answers
Answer:
The percentage of students who eat breakfast given that they are int the 10-13 age bracket is 74%
Step-by-step explanation:
Just took it on algebra nation
The true statement is that, "the percentage of students who eat breakfast given that they are int the 10-13 age bracket is 74%".
What is a survey?A survey is a review that is constructed in the form of questions to which the participants are required to respond honestly. The review is often targeted at obtaining vital ionformation that could be used for decision making.
Looking at the table, the true statement is that, "the percentage of students who eat breakfast given that they are int the 10-13 age bracket is 74%".
Learn more about survey:https://brainly.com/question/17373064
#SPJ2
What is the slope of a line that is perpendicular to the line x=-3?
A.-3
B.0
C.1/3
D.undefined
Answers
Answer:
B. 0
Step-by-step explanation:
The line x = -3 is vertical, thus undefined, because there is no y in the equation. The slope that is perpendicular to an undefined one is 0.
x = 3 is a vertical line.
A line perpendicular to x = 3 is a horizontal line.
A horizontal line has slope = 0.
General formula for a straight line
The general formula for a straight line is ‘y=mx+c'.
But in the equation ‘x = -3’, ‘y' isn't present meaning that the line is independent of ‘y' which is true for a line parallel to the ‘y-axis'. This case can be compared to a generic equation ‘x=a' where a is the distance of the parallel line (to y-axis') from the origin.
This line represents a parallel line to the y-axis which is 3 units left side from the origin.
Now about calculating the slope, we can use the formula ‘m = tan ϴ’
where ‘m' is the slope and ‘ϴ’ is the angle of the line with the X-axis.
Here the value of ϴ is 90° as it is parallel to the y-axis. So the line perpendicular to it will surely have ϴ=0°. Which will be parallel to the
x-axis.
Another method of explaining this can be, for ϴ=90°, m=tan(90),
so m= infinity. if the slope of the line parallel to it is ’n', the relation between the slope of two perpendicular lines is ‘[tex]m*n=-1[/tex]’. Putting the value of ‘m=infinity' we get ‘n=0’.
Now for getting n=0 the angle must be O° as tan(0°)=0 which is nothing but a line parallel to the x-axis.
Therefore, the correct answer is option B.0.
To learn more about the general formula for a straight line
https://brainly.com/question/24325206
#SPJ2
Find the area of a 8-gon with radius length 6. Round to a whole number.
Answers
Answer:
Area = 102
Step-by-step explanation:
Length 1 side of the octagon.
The formula for the side of an octagon (given the radius of 6) is
s^2 = 2*R^2(1 - cos(45) )
s^2 = 2*6^2(1 - sqrt(2)/2)
s^2 = 72 ( 1 - 0.707)
s^2 = 72*0.2929
s^2 = 21.09
s = sqrt(21.09)
s = 4.5922
===============
Height of one triangle =
H = R * cos(22.5)
H = 6 * 0.9329
H = 5.5433
===============
Area of 1 triangle
Area = 1/2 * s * h
Area = 1/2 * 4.5922*5.4433
Area = 12.7279
Area of 8 triangles
Area of 8 triangles = 1 triangle * 8
Area of 8 triangles = 101.82
Rounded that comes to 102
Comment
I'm sure you can find a formula for this on the internet, but it this is the way the formula works and if you break it down step by step, you can see how the formula works.
The dimensions of a bathroom floor are 25 inches by 45 inches what is the floors area in square inches
Answers
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷To find the area you need to multiply length and width.
45*25 = 1125 square inches for the area
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
DOGE
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷ To find the area of the floor, you need to multiply the length and the width.
Width:25 inches
Length:45 inches
Multiply: 45*25=1125
Final answer:
1125 square inches
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
TROLLER