we have the following:
[tex]\begin{gathered} 6Write the equation in point slope and slope intercept form of a line that passes through the given point and has given slope m.(5,-6);m=-1
Given:
A line passes through the point,
[tex](x_1,y_1)=(5,-6)[/tex]The slope of the line is m = -1.
The objective is to find the equation of the line in point-slope and slope-intercept form.
Explanation:
To find equation in point-slope form:
The general formula of point-slope form is,
[tex]y-y_1=m(x-x_1)\text{ . . . . . . ..(1)}[/tex]On plugging the given values in equation (1),
[tex]\begin{gathered} y-(-6)=-1(x-5) \\ y+6=-x+5\text{ . . . . . .(2)} \end{gathered}[/tex]To find the equation in slope-intercept form,
The general formula of slope-intercept form is,
[tex]y=mx+b\text{ . . . . (3)}[/tex]On further solving the equation (2),
[tex]\begin{gathered} y+6=-x+5 \\ y=-x+5-6 \\ y=-x-1 \end{gathered}[/tex]Hence,
The equation of the line in point-slope form is y+6 = -x+5.
The equation of the line in slope-intercept form is y = -x-1.
given AD is congruent to AC and AB is congruent to AE, which could be used to prove?
Answer
Option B is correct.
SAS | 2 sides and the angle between them in one triangle are congruent to the 2 sides and the angle between them in the other triangle, then the triangles are congruent.
Explanation
We have been told that the two triangles have two sets of sides that are congruent to each other.
And we can see that the angle between those congruent sides for the two triangles is exactly the same for the two triangles.
So, it is easy to see that thes two triangles have 2 sides that are congruent and the angle between these two respective sides are also congruent.
Hope this Helps!!!
A rectangular field of corn is averaging 125 bu/acre. The field measures 1080 yd by 924 yd. How many bushels of corn will there be?
Based on the dimensions of the rectangular field, and the corn per acre, the number of bushels of corn can be found to be 25,772 bushels
How to find the number of bushels of corn?First, find the area of the rectangular field:
= 1,080 x 924
= 997,920 yard²
Then convert this to acres with a single acre being 4,840 yards²:
= 997,920 / 4,840 square yards per acre
= 206.18 acres
The number of bushels of corn that can be grown is:
= 206.18 x 125 bushel per acre
= 25,772 bushels
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The area of a semicircle is 0.5652 square inches. What is the semicircle's diameter? Use 3.14 for a inches Submit can you explain
Given :
The area of semicircle is given as 0.5652 sq.inches.
To find:
The diameter of semicircle which is denoted as d.
Explanation:
The area of semicircle is given as
[tex]A=\frac{\pi r^2}{2}[/tex]The relation between radius and diameter is
[tex]d=2r[/tex]Now substitute the given area in the area of semicircle formula.
[tex]0.5652=\frac{3.14\times r^2}{2}[/tex][tex]r=\sqrt[]{\frac{2\times0.5652}{3.14}}=\sqrt[]{0.36}[/tex][tex]r=0.6in[/tex]The semicircle diameter is determined as
[tex]d=2r\Rightarrow2\times0.6=1.2in[/tex]Answer:
Hence the diameter of semicircle is determined as 1.2 in.
What is an equation of the line that passes through the point (-4,-6)(−4,−6) and is perpendicular to the line 4x+5y=25?
HELP PLEASE ANWER AS SOON AS POSSIBLE ALSO PLEASE GIVE A STEP BY STEP EXPLANATION PLEASE!!
Given that f(x)=x2-4/3, f(a)=7, and f(11)=b, a+b can only be a multiple of prime numbers is 5
This calculator for finding the prime factors and the factor tree of an integer is available for use.
How is a prime factor discovered?
The simplest method for determining a number's prime factors is to keep dividing the starting number by prime factors until the result equals 1. When we divide the number 30 by its prime factors, we obtain 30/2 = 15, 15/3 = 5, and 5/5 = 1. We received the balance, thus it cannot be factored any further.
Example: 36 can be written as the product of two prime factors, 22 and 32. The prime factorization of 36 is stated to equal the equation 22 32.
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10)BONUSKelll walks into science class and they have 6 hershey kisses and 6 reese cups on a scale that reads82.4 ounces. She wants some chocolate so she eats 2 hersey kisses and 1 reese cup and now thescale reads 63.8 ounces.a) Define your variables and set up a system of equations.
Leah, this is the solution:
Variables:
Let x to represent the weight of one Hershey kiss
Let y to represent the weight of one Reese cup
System of equations:
6x + 6y = 82.4
4x + 5y = 63.8
______________
Let's multiply the second equation by - 3/2, therefore:
6x + 6y = 82.4
-6x - 15y/2 = -95.7
________________
-15/2 + 6 = -3/2
_________________
-3y/2 = -13.3
Dividing by -3/2 at both sides:
-3y/2 / -3/2 = -13.3 / -3/2
y = 8.87
______________
Replacing y in the first equation and solving for x:
6x + 6 * 8.87 = 82.4
6x + 53.22 = 82.4
Subtracting 53.22 at both sides:
6x +53.22 - 53.22= 82.4 - 53.22
6x = 29.18
Dividing by 6 at both sides:
6x/6 = 29.18/6
x = 4.86
_________________
In conclusion, one Hershey kiss weights 4.86 ounces and one Reese cup weights 8.87 ounces.
i Which equation, when solved, results in a different value of x than the other three?' 7 3 4 37 X=-20 3 119-8-2014
You have the first equation:
[tex]-\frac{7}{8}x-\frac{3}{4}=20[/tex]Let's analize the others equation.
You can see that the second equation is just like the first one, but it was multiplied by -1:
[tex]\begin{gathered} (-1)(-\frac{7}{8}x-\frac{3}{4})=(20)(-1) \\ \frac{7}{8}x+\frac{3}{4}=-20 \\ \frac{3}{4}+\frac{7}{8}x=-20 \end{gathered}[/tex]So the value of "x" of the first one and the second one will be the same.
The third equation is:
[tex]-7(\frac{1}{8})x-\frac{3}{4}=20[/tex]If you simplify it, you get:
[tex]-\frac{7}{8}x-\frac{3}{4}=20[/tex]So you can notice that the three equations are the same, therefore the result of the third one will be the same too.
You can identify that even simplifying the last equation, it is not the same equation, then you will obtain a different value of "x" than the other three.
Therefore,the answer is the Last option.
K
Determine whether the statement is true or false, and explain why.
The derivative value f'(a) equals the slope of the tangent line to the graph of y=f(x) at x = a.
Choose the correct answer below.
OA. The statement is true because f'(x) is a function of x.
B. The statement is false because f(a) gives the instantaneous rate of change of f' at x = a.
OC. The statement is true because f'(a) gives the instantaneous rate of change of fat x = a.
OD. The statement is false because f'(a) gives the average rate of change of f from a to x.
Answer: C. The statement is true because f'(a) gives the instantaneous rate of change of fat x = a.
If there are 3 possible outcomes for event A, 5 possible outcomes for event B, and 2 possible outcomes for event C, how many possible outcomes are there for event A & event B & event C? Note that these three events are independent of each other. The outcome of one event does not impact the outcome of the other events.
Possible outcomes for events A and events B and events C which are independent of each other is equal to 3/100.
As given in the question,
Total number of outcomes = 10
Possible outcomes of event A =3
P(A) =3/10
Possible outcome of event B =5
P(B) =5/10
Possible outcome of event C =2
P(C)=2/10
A, B, C are independent of each other
P(A∩B∩C) = P(A) × P(B) × P(C)
= (3/10) × (5/10) × (2/10)
= 3/100
Therefore, possible outcomes for events A and events B and events C which are independent of each other is equal to 3/100.
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Elisa has 24 black and white photographs and 72 photographs that are in color. She is arranging the photographs in an album and wants to contain the same combination of color and black and white photographs. What is the greatest number of pages elisa can fill with photographs
Which of the following functions has an amplitude of 3 and a phase shift of pi over 2 question mark
Remember that f(x) = A f(Bx-C) +D
Where |A| is the Amplitude and C/B is the phase Shift
Options
A, B C all have amplitudes of |3| so we have just eliminated D with the amplitude
We need a phase shift of C/B = pi/2
A has Pi/2
B has -Pi/2
C has pi/2 /2 = pi/4
Choice A -3 cos ( 2x-pi) +4 has a magnitude of 3 and and phase shift of pi/2
In Exercises 25–26, the domain of each piecewise function is (-⬁,⬁). a. Graph each function. b. Use the graph to determine the function’s range.
We have to graph this piecewise function.
It will be two horizontal lines that change when x = -1: to the left it will be y = 5, as x ≤ 1, and to the right, it will be y = -3.
We can see it graphed as:
b) The range is the set of values that f(x) takes for the domain for which it is defined.
We can see that f(x) only takes two values: y = -3 and y = 5, so the set {-3,5} is the range of f(x).
Answer:
a) Graph
b) Range = {-3, 5}
If m ll n, which statement is true? 3 1 5 2. 4 6 O A.
∠1 and ∠2 have equal measures because they are corresponding angles
Please helpMe if your good with mathI appreciate it thank u!
Let x be the number of tshirt sold.
A/q,
[tex]\begin{gathered} 5x+40=125 \\ \Rightarrow5x=85 \\ \Rightarrow x=17 \end{gathered}[/tex]Thus the number of tshirt sold is 17.
A figure is made up of a triangle and a square. The square andthe triangle have the same base of 9 inches. The triangle has aheight of 7 inches, what is the total area of the figure?
To solve the exercise, it is helpful first to draw the situation that the statement describes:
The total area of the figure will be
[tex]A_{\text{total}}=A_{\text{square}}+A_{\text{triangle}}[/tex]Then, we can calculate the area of the square using the following formula:
[tex]\begin{gathered} A_{\text{square}}=s\cdot s \\ \text{ Where s is one side of the square} \end{gathered}[/tex]So, we have:
[tex]\begin{gathered} s=9in \\ A_{\text{square}}=s\cdot s \\ A_{\text{square}}=9in\cdot9in \\ \boldsymbol{A}_{\boldsymbol{square}}\boldsymbol{=81in}^{\boldsymbol{2}} \end{gathered}[/tex]Now, we can calculate the area of the triangle using the following formula:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{b\cdot h}{2} \\ \text{ Where b is the base and} \\ h\text{ is the height of the triangle} \end{gathered}[/tex]So, we have:
[tex]\begin{gathered} b=9in \\ h=7in \\ A_{\text{triangle}}=\frac{b\cdot h}{2} \\ A_{\text{triangle}}=\frac{9in\cdot7in}{2} \\ A_{\text{triangle}}=\frac{63in^2}{2} \\ \boldsymbol{A}_{\boldsymbol{triangle}}\boldsymbol{=31.5in}^{\boldsymbol{2}} \end{gathered}[/tex]Finally, we calculate the total area of the figure
[tex]\begin{gathered} A_{\text{total}}=A_{\text{square}}+A_{\text{triangle}} \\ A_{\text{total}}=81in^2+31.5in^2 \\ \boldsymbol{A}_{\boldsymbol{total}}\boldsymbol{=112.5in}^{\boldsymbol{2}} \end{gathered}[/tex]Therefore, the total area of the figure is 112.5 square inches, and the correct answer is option C.
Find the oth term of the geometric sequence 5,--25, 125,
Given the geometric progression below
[tex]5,-25,125,\ldots[/tex]The nth term of a geometric progression is given below
[tex]T_n=ar^{n-1},\begin{cases}a=\text{first term} \\ r=\text{common ratio}\end{cases}[/tex]From the geometric progression, we can deduce the following
[tex]\begin{gathered} T_1=a=5 \\ T_2=ar=-25 \\ T_3=ar^2=125 \end{gathered}[/tex]To find the value of r, we will take ratios of two consecutive terms
[tex]\begin{gathered} \frac{T_2}{T_1}=\frac{ar}{a}=\frac{-25}{5} \\ \Rightarrow r=-5 \end{gathered}[/tex]To find the 9th term of the geometric, we will have that;
[tex]\begin{gathered} T_9=ar^8=5\times(-5)^8=5\times390625 \\ =1953125 \end{gathered}[/tex]Hence, the 9th term of the geometric progression is 1953125
please helpppppp i dont get it
The subtraction of the mixed fractions and presenting the result in simplest form gives;
[tex] \displaystyle{9 \frac{2}{5} - 4 \frac{4}{5} = 14 \frac{1}{5}} [/tex]
What is are mixed fractions?A mixed fraction is one that has both a quotient part as a whole number, the remainder, as the numerator of the fraction part, and the divisor as the denominator of the fraction part.
The equation involves the subtraction of mixed fractions, which are expressed as follows;
[tex] \displaystyle{9 \frac{2}{5} - 4 \frac{4}{5} } = [/tex]
To subtract the mixed fractions, the mixed fraction can first be rearranged into improper fractions as follows;
[tex] \displaystyle{ \frac{5 \times 9 + 2}{5} - \frac{5 \times 4 + 4}{5} = \frac{47}{5} + \frac{24}{5} }[/tex]
[tex] \displaystyle{ \frac{47}{5} + \frac{24}{5} = \frac{71}{5} }[/tex]
The result of the addition of the improper fraction which is also an improper fraction can be rearranged into partial fractions again as follows;
71 = 5 × 14 + 1
Which gives;
[tex] \displaystyle{ \frac{71}{5} = 14 \frac{1}{5} }[/tex]
Therefore;
[tex] \displaystyle{9 \frac{2}{5} - 4 \frac{4}{5} = 14 \frac{1}{5}} [/tex]
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Kaylee read 1 book in 4 months. What was her rate of reading, in books per month? Give your answer as a whole number or a FRACTION in simplest form.On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
If Kaylee read 1 book in 4 months, this means that in 1 month, she read 1/4 of the book. We can see this in the following figure:
Is my answer correct help me please
Rewrite the expression in lowest terms.
4x²-12x +9
________
4x2-9
A. -12 x
B. 4x-3
2x-3
C. 2x+3
2x-3
D. 2x-3
2x+3
answer is D
no real explanation its just math
Point (7, 2) is translated up 2 units and left 5 units. Where is the new point located?(12, 4)(9, -3)(2,0)(2, 4)
The new point is located at (2,4)
Here, we want to get the result of a translation
2 units up simply mean, we are adding 2 to the y-axis value
5 units left mean we are subtracting 5 from the x-axis value
We can represent the translation as;
[tex]\begin{gathered} (x,y)\rightarrow\text{ (x-5 , y+2)} \\ =\text{ (7-5,2+2) = (2,4)} \end{gathered}[/tex]Look at this set of ordered pairs: (-8, 19) (11, 1) (0, 15. Is this relation a function?
Answer:
Yes, the set of ordered pairs is a function.
Explanation:
To test whether a given set of ordered pairs represents a function, we have to make sure that it satisfies the definition.
By definition, a function cannot have two outputs for one input. For example, the set of ordered pairs (3, 10 ) and (4, 5) represents a function whereas (3, 10) and (3, 13) does not.
With this in mind, looking at the given set we see that every input gives a unique output; therefore, the set represents a function.
Which problems can be solved using the equation 3 X 6 = |? Circle all the correct answers. A Cleo has 3 times as many bananas as Arianna has. Cleo has 6 bananas. A How many bananas does Arianna have? B Dylan has 6 oranges. Jane has 3 times as many oranges as Dylan. В How many oranges does Jane have? C Liam has 3 cherries. Brian has 6 times as many cherries as Liam. How many cherries does Brian have? D Tina has 3 more peaches than Charlie. Charlie has 6 peaches. How many peaches does Tina have? E Jaclyn has 6 times as many grapes as Kaitlyn. Kaitlyn has 3 grapes. How many grapes does Jaclyn have?
A. Cleo (C) has 3 times as many bananas as Arianna (A) has. Cleo has 6 bananas. How many bananas does Arianna have? Equation:
[tex]\begin{gathered} 3A=C \\ \\ C=6 \\ \\ 3A=6 \\ \\ ?=\frac{6}{3} \end{gathered}[/tex]It doesn't correspond to the given equation
_______________
B. Dylan (D) has 6 oranges. Jane (J) has 3 times as many oranges as Dylan. How many oranges does Jane have? Equation:
[tex]\begin{gathered} D=6 \\ J=3D \\ \\ J=3\times D \\ \\ \text{?}=3\times6 \end{gathered}[/tex]It correspond to the given equation
___________
C. Liam (L) has 3 cherries. Brian (B) has 6 times as many cherries as Liam. How many cherries does Brian have? Equation:
[tex]\begin{gathered} L=3 \\ B=6L \\ \\ \text{?}=6\times3 \end{gathered}[/tex]It correspond to the given equation
_______________
Tina (T) has 3 more peaches than Charlie (C). Charlie has 6 peaches. How many peaches does Tina have? Equation:
[tex]\begin{gathered} T=3+C \\ C=6 \\ \\ T=3+6 \\ \\ \text{?}=3+6 \end{gathered}[/tex]It doesn't correspond to the given equation
___________________
E. Jaclyn (J) has 6 times as many grapes as Kaitlyn (K). Kaitlyn has 3 grapes. How many grapes does Jaclyn have? Equation:
[tex]\begin{gathered} J=6K \\ K=3 \\ \\ J=6\times3 \\ \\ \text{?}=6\times3 \end{gathered}[/tex]It correspond to the given equation
____________
Answer: B, C and EGraph for a 3rd degree polynomial function whose graph crosses the horizontal axis more than one
Given the 3° degree function:
[tex]x^3-4x+2[/tex]Graph:
A buoy oscillates in simple harmonic motion as waves go past. At a given time it is noted that the buoy moves a total of 3.9 feet from its low point to its high point, and that it returns to its high point every 16 seconds
Concept
What is a simple harmonic motion ?Repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side. The time interval of each complete vibration is the same
a) y= 1.95ftcos(π/2)
b) v(t)= -0.76sin(π/5t)
Part aSince the buoy oscillates in simple harmonic motion the equation to model this is given by: y= A cos(ωt+θ)
For this case from the info given we know that:
2A= 3.9 , A= 3.9/2= 1.95ft
It returns to its high point every 16 seconds. That means period = 16 , and the angular frequency can be founded like this:
ω=2π/16
= π/8
Assuming that the value for the phase is (θ=0°) our model equation is given by
y= 1.95ftcos(π/2)
Part bFrom definition we can obtain the velocity with the derivate of the position function and if w calculate the derivate we got this,
dy/dt= v(t)= -1.95ft(π/8)sin(π/8t)
v(t)= -0.76sin(π/8t)
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Dave jogs 8 feet per second. Give each rate in miles per hour.
Answer:
Step-by-step explanation:
first find seconds in an hour
60(seconds in a minute) *60(minutes in an hour) = 3600 seconds in an hour
then multiply 8 by 3600 to see how many feet per hour
28,800
we need miles so there are 5280 feet in a mile
28800/5280 is 5.45454545 or 5.455 miles per hour
find the simple interest earned, to the nearest cent, for each principal interest rate, and time.
Answer:
$8.40
Explanation:
From the given statement:
Principal = $840
Time = 6 Months
Rate = 2%
Note that Time must be in Years, therefore:
Time = 6 Months = 6/12 = 0.5 Years
[tex]\begin{gathered} \text{Simple Interest }=P\times R\times T \\ =840\times2\%\times0.5 \\ =840\times0.02\times0.5 \\ =\$8.40 \end{gathered}[/tex]The simple interest earned is $8.40
mr dudzic has above ground swimming pool thatbis a circular cylinder. the diameter of the pool is 25 ft. and the height isb4.5 ft. in order to open he needs to shock it with chlorine. if one gallon of liquid chlorin treats 3000 gallons of water, how many full gallons will he need to buy. (1 foot^3=7.48 gallons)
The volume of the cylinder is
[tex]V=\pi\text{ }\times r^2\times h[/tex]The diameter of the cylinder is 25 feet, then
The radius of it = 1/2 x diameter
[tex]r=\frac{1}{2}\times25=12.5ft[/tex]Since the height is 4.5 ft
Substitute them in the rule above
[tex]\begin{gathered} V=3.14\times(12.5)^2\times4.5 \\ V=2207.8125ft^3 \end{gathered}[/tex]Now we will change the cubic feet to gallons
[tex]\because1ft^3=7.48\text{ gallons}[/tex]Then multiply the volume by 7.48 to find the number of gallons
[tex]7.48\times2207.8125=16514.4375gallons[/tex]Now let us divide the number of gallons by 3000 to find how many gallons of liquid chlorin he needs to buy
[tex]\frac{16514.4375}{3000}=5.5048125[/tex]Then he has to buy 6 full gallons
question: determine whether the function is one-to-one. If it is sketch the graph of its inverse.i already found out it is a one-to-one, i just don't know how to graph its inverse
The inverse function of f(x) = y is f(y) = x
This means, switch the coordinates of the points of the graph
If we choose a point on the given graph like (5, 3) it will be (3, 5) in the inverse function
Also, point (-5, -3) it will be (-3, -5) in the inverse function
You can plot them with point (0, 0) and draw the curve
Let me try to show it
It will be like that
