Given the point (-4,6).
So, The rule for a rotation by 180° about the origin is (x,y)→(−x,−y). Therefore, the new point is:
(-4,6) --> ( - ( - 4), - (6) ) --> (4, - 6)
Answer: ( 4, - 6 )
The table shows how the number of sit-ups Marla does each day has changed over time. At this rate, how many sit-ups will she do on Day 12? Explain your steps in solving this problem.see image
Maria willdo 61 sit-ups on Day 12
Explanation
the table represents a linear function so, we can find the equation of the function and then evaluate for day 12
the equation of a line is given by:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]so
Step 1
find the slope of the line
the slope of a line is given by.
[tex]\begin{gathered} \text{slope}=\frac{change\text{ in y }}{\text{change in x}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \\ \text{are 2 points from the table } \\ or\text{ 2 coordinates ( from the table)} \end{gathered}[/tex]let
P1(1,17)
P2(4,29)
now, replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{29-17}{4-1}=\frac{12}{3}=4 \\ \text{slope= 4} \end{gathered}[/tex]Step 2
now,find the equation of the line,use the slope-point formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m is the slope} \\ \end{gathered}[/tex]now, replace
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-17=4(x-1) \\ y-17=4x-4 \\ y=4x-4+17 \\ y=4x+13 \end{gathered}[/tex]so,the equation of the lines is
y= 4x+13
Step 3
finally, evaluate for day 12, it is x= 12
so,replace
[tex]\begin{gathered} y=4x+13 \\ y=4(12)+13 \\ y=48+13 \\ y=61 \end{gathered}[/tex]it means Maria will do 61 sit-ups on Day 12
I hope this helps you
The volume of a large tank is 350 ft. It is 65 ft wide and 4 ft high. What is the length of the tank?
The volume of a rectangular prism can be calculated by the formula
[tex]V=l\cdot w\cdot h[/tex]in which l, w and h represent the length, width, and heght respectively.
clear the equation for l
[tex]l=\frac{V}{w\cdot h}[/tex]replace with the data given
[tex]undefined[/tex]By the Remainder Theorem, what can be said about the polynomial function w(x) if w(−5)=3 ?
the remainder must be _________ when w(x) is divided by _________
thanks so much!
well, ding ding ding!! let's recall the remainder's theorem
if some function f(x) has a factor of say x - a, then if we plug the "a" in f(x) what we get is the remainder, that is, the remainder in a division of f(x) by (x-a).
all that mouthful said, well, since we know of w(-5), that means w(x) must have a factor of x - (-5) or namely x + 5.
we also know that w(-5) = 3, well, that means that 3 is the remainder of such division, that is, w(x) ÷ (x + 5), gives us a remainder of 3.
Determine which of the following statements is NOT correct
THe statement that is not correct is the first one
If x decreases by 3 units what is the corresponding change in y ?
We have the equation:
[tex]y=6x-2[/tex]The rate of change in linear functions like this is equal to the slope, which in this case is m = 6.
So, for each unit increase in x, y will increase in 6 units.
[tex]\Delta y=m\cdot\Delta x=6\cdot1=6[/tex]This rate of change is constant for linear functions, so when x decreases by 3 units, we expect y to decrease by 3*6 = 18 units, 3 times the slope. So y will be -18 of the previous value.
[tex]undefined[/tex]Answer: a) 6, b) -18.
is 0.343434343434 rational or irrational, explain how u know
EXPLANATION
The number 0.343434343434 is a periodic number rational because the all the periodic numbers are rational ones.
Find the sales tax.
Sales Tax
Selling Price Rate of Sales Tax Sales Tax
$70.00
3%
?
The sales tax is $.
Answer: $2.10
Step-by-step explanation: 3% of $70 is $2.10.
The total cost would be $72.10
How to calculate percentages:
Divide the number that you want to turn into a percentage by the whole. In this example, you would divide 2 by 5. 2 divided by 5 = 0.4. You would then multiply 0.4 by 100 to get 40, or 40%.
x + y + zX=5 y=3 z=7
1. Find the value of x.
2. Find the value of t.
Answer:
x=15
t=2
Step-by-step explanation:
to find x both of these triangles have the same angle measure and we know 2 of them and the sum of all three angles of a triangle always equal 180 degrees
45+90=135
Now we subtract from 180
180-135=45
45 degrees is what 3x is equal to so to figure out X just set 3x equal to 45
3x=45
/3. /3
x=15
Now to find t the 2 sides in the bottom of the triangle are equivalent so we can set them equal to each other
2t=4
/2. /2
t=2
Hopes this helps please mark brainliest
can you please help me
Answer
The graph of y = -3x + 1 is presented below
Explanation
We are asked to plot the graph of y = -3x + 1
We will use intercepts to obtain two points on the line and connect those two points
y = -3x + 1
when x = 0
y = -3x + 1
y = -3(0) + 1
y = 0 + 1
y = 1
First point on the line is (0, 1)
when y = 0
y = -3x + 1
0 = -3x + 1
3x = 1
Divide both sides by 3
(3x/3) = (1/3)
x = ⅓ = 0.333
Second point on the line is (⅓, 0) or (0.333, 0)
The graph of this question is presented under 'Answer' above.
Hope this Helps!!!
find any points of discontinuity for each rational functiony= 2x^2 + 3 / x^2 + 2
We have the rational function:
[tex]y=\frac{2x^2+3}{x^2+2}[/tex]and we have to find points of discontinuity.
This points happen when the denominator becomes 0, because the function became undefined in those cases.
In this case it would happen when:
[tex]\begin{gathered} x^2+2=0 \\ x^2=-2 \end{gathered}[/tex]As there is no real value for x that makes the square of x be a negative number, we don't have points of discontinuity for this function.
NOTE: x^2+2 has two complex roots and never intercepts the x-axis.
Answer: this function has no points of discontinuity.
Check for asymptotes.
As there are no discontinuities, we don't have vertical asymptotes.
We will check if there are horizontal asymptotes:
[tex]\lim _{x\to\infty}\frac{2x^2+3}{x^2+2}=\frac{\frac{2x^2}{x^2}+\frac{3}{x^2}}{\frac{x^2}{x^2}+\frac{2}{x^2}}=\frac{2+0}{1+0}=2\longrightarrow y=2\text{ is an horizontal asymptote}[/tex]If we repeat for minus infinity (the left extreme of the x-axis), we also get y=2.
Calculate the limitlim x => -4 [tex] \frac{x {}^{2} + 2x - 8}{x {}^{2} + 5x + 4} [/tex]
The limit to be calculated is:
[tex]\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}[/tex]Notice that:
[tex]\begin{gathered} \frac{x^2+2x-8}{x^2+5x+4}=\frac{(x-2)(x+4)}{(x+1)(x+4)} \\ =\frac{(x-2)}{(x+1)},x\ne-4 \end{gathered}[/tex]Remember that, in the limit when x->-4, the value of x approaches to -4, but it never is -4. Thus, we can use the last line of the identity above,
[tex]\begin{gathered} \Rightarrow\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}=\lim _{x\to-4}\frac{(x-2)(x+4)}{(x+1)(x+4)}=\lim _{x\to-4}\frac{(x-2)}{(x+1)}=\frac{(-4-2)}{(-4+1)}=-\frac{6}{-3}=2 \\ \Rightarrow\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}=2 \end{gathered}[/tex]The answer is 2.
S= ut+1/2 at²
U=10 a=-2 t=1/2
The value of the unknown variable, S, is S = 4 3/4
Determining the value of unknown variable in an equationFrom the question, we are to determine the value of the unknown variable in the given equation
From the given information,
The given equation is
S = ut + 1/2at²
Also,
From the given information
u = 10
a = -2
t = 1/2
Substituting the values of u, a, and t into the given equation
S = ut + 1/2at²
S = (10)(1/2) + 1/2(-2)(1/2)²
Simplify
S = 5 + (-1)(1/4)
S = 5 + (-1/4)
S = 5 - 1/4
S = 4 3/4
Hence, the value of S is 4 3/4
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The Voronoi diagram below shows the locations of the four post offices P_{1} , P_{2} P_{3} , and P_{4}in a city.y(km)8P_{3}P2r (km)6P_{1}PKatie's apartment lies inside the shaded circle shown on the diagram.(a) Write down the post office nearest to Katie's apartment.P is located at coordinates (3-6), and the edge between P and P_{i} has the equation y = - 5/3 * x = 16/3(b) Determine the location of PPa is located at coordinates (1.7).3(c) Find the gradient. A. of the edge between P, and P.
Given -
Voronoi diagram:
To Find -
(a) Write down the post office nearest to Katie's apartment.
(b) Determine the location of P4
(c) Find the gradient k. of the edge between P3 and P4
Step-by-Step Explanation -
(a)
We can see from the voronoi diagram that the center of the x-axis where the circle covers is where Katie's apartment is located.
It is located near P4.
So,
P4 is nearest to Katie's apartment.
(b)
The location of P4:
(2, -3)
(c)
[tex]k\text{ = }\frac{Y_2\text{ - Y}_1}{X_2\text{ - X}_1}\text{ = }\frac{7}{50}[/tex]Final Answer -
(a) The post office nearest to Katie's apartment = P4
(b) The location of P4 = (2, -3)
(c) The gradient k of the edge between P3 and P4 = 7/50
In the triangle below, if < C = 62 °, what is the measure of angle B?
In the given triangle ABC
[tex]BA=BC[/tex]Then the triangle is isosceles
In the isosceles triangle, the base angles are equal
Since [tex]m\angle A=m\angle C[/tex]Since m[tex]m\angle A=62^{\circ}[/tex]In any triangle the sum of angles is 180 degrees, then
[tex]m\angle A+m\angle B+m\angle C=180^{\circ}[/tex]Substitute angles A and C by 62
[tex]\begin{gathered} 62+m\angle B+62=180 \\ \\ m\angle B+124=180 \end{gathered}[/tex]Subtract 124 from both sides
[tex]\begin{gathered} m\angle B+124-124=180-124 \\ \\ m\angle B=56^{\circ} \end{gathered}[/tex]The answer is b
If the value of tan θ<0 and sin θ>0 , then the angle θ must lie in which quadrant?
Given:
[tex]\tan \theta<0\text{ and }\sin \theta>0[/tex][tex]\text{ we know that }\tan \theta=\frac{\sin \theta}{\cos \theta}\text{.}[/tex][tex]\text{ Replace tan}\theta=\frac{\sin \theta}{\cos \theta}\text{ in tan}\theta<0\text{ as follows.}[/tex][tex]\frac{\sin \theta}{\cos \theta}<0[/tex][tex]\text{Multiply cos}\theta\text{ on both sides.}[/tex][tex]\frac{\sin\theta}{\cos\theta}\times\cos \theta<0\times\cos \theta[/tex][tex]\sin \theta<0[/tex][tex]\text{But given that sin}\theta>0[/tex]hence sine value should be equal to 0.
[tex]\sin \theta=0[/tex][tex]\theta=\sin ^{-1}0[/tex][tex]\theta=\sin ^{-1}\sin (n\pi)[/tex][tex]\theta=n\pi\text{ where n is integer.}[/tex]evaluate the function found in the previous step at x=-2
Given:
[tex]5x^2+2y=-3x-2y[/tex]To evaluate the function at x=-2, we simplify the given relation first:
[tex]\begin{gathered} 5x^2+2y=-3x-2y \\ \text{Simplify and rearrange} \\ 2y+2y=-3x-5x^2 \\ 4y=-3x^{}-5x^2 \\ y=\frac{-3x^{}-5x^2}{4} \end{gathered}[/tex]We let y=f(x):
[tex]f(x)=\frac{-3x^{}-5x^2}{4}[/tex]Next, we plug in x=-2 into the function:
[tex]\begin{gathered} f(x)=\frac{-3x^{}-5x^2}{4} \\ f(-2)=\frac{-3(-2)-5(-2)^2}{4} \\ \text{Simplify} \\ f(-2)=\frac{-14}{4} \\ f(-2)=-\frac{7}{2} \end{gathered}[/tex]Therefore,
[tex]f(-2)=-\frac{7}{2}[/tex]Rewrite the equation below so that it does not have fractions. 3+ = x= = Do not use decimals in your answer.
First we have to find the least common multiple between the denominators ( 3 and 7). Since they are prime numbers the LCM is : 3*7 = 21
Then, multiply each term of the equation by 21 and simplify
[tex]\begin{gathered} 3\cdot21+21\cdot\frac{2}{3}x=\frac{2}{7}\cdot21 \\ 63+7\cdot2x=2\cdot3 \\ 63+14x=6 \end{gathered}[/tex]The answer is 63 + 14x = 6
Law of Exponents. Simplify each expression. Answers should be written with positive exponents.(-5p^6 times r^-9)^0
Solution:
Given the expression:
[tex](-5p^6\cdot r^{-9})^0[/tex]Simplifying using the law of exponents,
[tex]\begin{gathered} (-5p^6\cdot r^{-9})^0=(-5\times p^{-6}\times r^{-9})^0 \\ \end{gathered}[/tex]but
[tex]a^{-b}=\frac{1}{a^b}[/tex]thus, we have
[tex]\begin{gathered} (-5\times p^{-6}\times r^{-9})^0=(-5\times\frac{1}{p^6}\times\frac{1}{r^9})^0 \\ =(-\frac{5}{p^6r^9})^0 \end{gathered}[/tex]From the zero index law of exponents,
[tex]a^0=1[/tex]This implies that
[tex](-\frac{5}{p^6r^9})^0=1[/tex]Hence, the solution to the expression is 1
If 2/3rd of a trail is 3/4ths of a mile, how long is the whole trail?
Answer:
1 1/2 or 1.5 miles
Step-by-step explanation:
we can multiply 3/4 by 2/3 to see how many miles is in each third of a trail
3/4*2/3=6/12
1/2 of a mile per third of the trail so now we multiply by 3 to get whole trail
1/2 x/3/1=3/2
3/2= 1 1/2
Hopes this helps please mark brainliest
23 The list gives information about the favorite color of each of 22 students.• 6 students chose red.• 2 students chose yellow.• 5 more students chose blue than yellow.• 3 fewer students chose purple than red.• The rest of the students chose green.Which frequency table represents the number of students who chose each color?
ANSWER
Option B
EXPLANATION
We are given the information regarding favorite colors of 22 students.
=> 6 students chose red.
=> 2 students chose yellow.
=> 5 more students chose blue than yellow.
Let the number of students that chose blue be b. This means that:
b = yellow + 5
b = 2 + 5
b = 7 students
7 students chose blue.
=> 3 fewer students chose purple than red.
Let the number of people that chose purple be p. This means that:
p = red - 3
p = 6 - 3
p = 3 students
3 students chose purple.
=> The rest of students chose green.
To find the number of students that chose green, add up the number of students that chose the other colors and subtract from the total number of students.
That is:
22 - (6 + 2 + 7 + 3)
22 - 18
= 4 students
4 students chose green.
Therefore, the correct frequencey table is option B.
Solve fir X in the equation?
First, find the missing angle of the triangle. Remember that the internal angles of a triangle should add up to 180°, then, the missing angle is given by:
[tex]180-64-27=89[/tex]On the other hand, the angle of 89° plus the angle of (97+x)° should add up to 180 since they are adjacent angles on a straight line. Then:
[tex]89+(97+x)=180[/tex]Solve for x:
[tex]\begin{gathered} \Rightarrow89+97+x=180 \\ \Rightarrow186+x=180 \\ \Rightarrow x=180-186 \\ \Rightarrow x=-6 \end{gathered}[/tex]Therefore, the value of x is:
[tex]-6[/tex]Hello!I have (m^3n^5)^1/4 and I do not know how to take the n out since it is n^5/4.Thanks
We are given
[tex](m^3n^5)^{\frac{1}{4}}[/tex]
We want to take n out
Solution
Given
[tex]\begin{gathered} (m^3n^5)^{\frac{1}{4}} \\ (m^3\times n^4\times n)^{\frac{1}{4}} \\ (m^3)^{\frac{1}{4}}\times(n^4)^{\frac{1}{4}}\times(n)^{\frac{1}{4}} \\ (m^3)^{\frac{1}{4}}\times n^{}\times(n)^{\frac{1}{4}} \\ n\times(m^3)^{\frac{1}{4}}^{}\times(n)^{\frac{1}{4}} \\ n(m^3n)^{\frac{1}{4}} \end{gathered}[/tex]Solve the system of two linear inequalities graphically.{x<5<2x - 4Step 1 of 3: Graph the solution set of the first linear inequality.Answer3 KeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. Theregions will be added once the line is drawn.HOANChoose the type of boundary line:O Solid (-)Dashed ---)SEnter two points on the boundary line:10-5ज510JOO5Select the region you wish to be shaded:ОАOB101
From the problem, we have :
[tex]\begin{gathered} x<5 \\ x\ge-4 \end{gathered}[/tex]For the first inequality, x < 5
Since the symbol is "<", the boundary line is dashed line.
The boundary line is at x = 5 which has points (5, 0) and (5, 2)
and the region is to left of x = 5.
The graph will be :
Next is to graph the second inequality, x ≥ -4
Since the symbol is "≥", the boundary line is a solid line
The boundary line is at x = 4 which has points (-4, 0) and (-4, 2)
and the region is to the right.
The graph will be :
The solution to the inequalities is the overlapping region when joined together.
This will be :
The overlapping region is the middle region or region in between the boundary line which is also -4 ≤ x < 5
find the measure of an angle whose supplement is thirteen times its component. Hint: The supplement and complement of an angle are (180-0)⁰ and (90-0)⁰ respectively.
If the angles are suplemental it means that their sum equals 180º
Let A represent one angle and B represent the other
The first one A measures x and B is 13 times greather then B=13x
A+B=180º
x+13x=180º
14x=180º
x=12.85
A= 12.85º
B= 12.85*13= 167.05º
Q4 O center (-1,3), radius = 1 What is the center and radius of the circle, 2 2 r + y + 2x - 6y +9=0 - 9 center (1,-3), radius = 1 center (-1,3), radius = 9 center (1,-3), radius = 3
Step 1: Write out the formula
The equation of a circle given by
[tex](x-a)^2+(y-b)^2=r^2[/tex][tex]\begin{gathered} \text{where} \\ (a,b)\text{ is the center of the circle} \\ r\text{ is the radius of the circle} \end{gathered}[/tex]Step 2: Write out the given equation and rewrite it in the form shown above
[tex]x^2+y^2+2x-6y+9=0[/tex][tex]\begin{gathered} x^2+2x+y^2-6y+9=0 \\ \text{ By completing the square, we have} \\ (x+1)^2-(+1)^2+(y-3)^2-(-3)^2+9=0 \\ \end{gathered}[/tex][tex]\begin{gathered} (x+1)^2+(y-3)^2-1-9+9=0 \\ (x+1)^2+(y-3)^2=1=1^2 \end{gathered}[/tex]By comparing the equation with the formula above, we have
[tex]a=-1,b=3,r=1[/tex]Therefore,
center (-1,3), radius = 1
HELP PLEASE QUICKLYYY
The equivalent expressions are 3a + b + 13a and 16a + b, 20b + 11a - 3b and 11a + 17b and 20b - 5b + 2b and 17b
How to determine the equivalent expressions?From the question, we have the following parameters that can be used in our computation:
3a + b + 13a
Collect the like terms
So, we have
3a + 13a + b
Evaluate
16a + b
Also, we have
20b + 11a - 3b
Collect the like terms
So, we have
11a + 20b - 3b
Evaluate
11a + 17
Lastly, we have
20b - 5b + 2b
Collect the like terms
So, we have
20b - 5b + 2b
Evaluate
17b
Hence, the equivalent expression of 20b - 5b + 2b is 17b
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in the figure shown Sigma MN is parallel to y z what is the length of segment MX
We will solve for MX using similar angles theorem
Let line MX be= y
we have to find the ratio of the small triangle to that of the big triangle
Therefore we will have,
[tex]\begin{gathered} \frac{\text{xcm}}{(x+12)cm}=\frac{3.5\operatorname{cm}}{17.5\operatorname{cm}} \\ \text{when we cross multiply we wil have,} \\ 17.5\times x=3.5(x+12) \\ 17.5x=3.5x+42 \\ by\text{ collecting like terms we wll have} \\ 17.5x-3.5x=42 \\ 14x=42 \end{gathered}[/tex]to get x we divide both sides by the coefficient of x which is 14
[tex]\begin{gathered} \frac{14x}{14}=\frac{42}{14} \\ x=3.0\operatorname{cm} \end{gathered}[/tex]Hence ,
[tex]\vec{MX}=3.0\operatorname{cm}[/tex]Therefore,
The correct option will be OPTION A
Lines from Two Points (Point Slope Form) Write the equation of the line that passes through the points (0,8) and (−1,−4). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
1) The first thing to do is to find out the slope of the line that passes through points (0,8) and (-1,-4). We can do this using the Slope Formula:
[tex]m=\frac{-4-8}{-1-0}=\frac{-12}{-1}=12[/tex]2) Now, we need to find out the linear coefficient "b". Let's pick a point and plug it into the Slope-Intercept Formula with the slope:
[tex]\begin{gathered} y=mx+b \\ 8=12(0)+b \\ b=8 \end{gathered}[/tex]3) Then the answer is:
[tex]y=12x+8[/tex]what is the center and radius for the circle with equation (x-2)^2 + (y-5)^2=49
Solution
For this case we have the following equation given by:
[tex](x-2)^2+(y-5)^2=49[/tex]The general equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]And for this case by direct comparison we have:
[tex]r^2=49[/tex]Then we have:
[tex]r=\sqrt[]{49}=7[/tex]And the center si given by C=(h,k)
From the equation given we have:
[tex]C=(2,5)[/tex]