A linear equation has the form:
[tex]y=mx+b[/tex]Let's find a linear equation using the table, and let's check if it satisfy all the points:
[tex]\begin{gathered} x=0,y=-1 \\ -1=b \\ ------ \\ x=1,y=1 \\ 1=m+b \\ 1=m-1 \\ m=2 \end{gathered}[/tex]so:
[tex]y=2x-1[/tex]Let's check the other points:
[tex]\begin{gathered} x=-3 \\ y=2(-3)-1=-6-1=-7_{\text{ }}True \\ ------ \\ x=-2 \\ y=2(-2)-1=-4-1=-5_{\text{ }}True \\ ------ \\ x=-1 \\ y=2(-1)-1=-2-1=-3_{\text{ }}True \end{gathered}[/tex]Therefore, we can conclude it is a linear function.
how many solutions does 2(x+4)=4(x+2)
lets solve the equation!
[tex]\begin{gathered} 2(x+4)=4(x+2) \\ x+4=\frac{4}{2}(x+2) \\ x+4=2(x+2) \\ x+4=2x+4 \\ 4-4=2x-x \\ x=0 \\ \\ \text{Thus there is only ONE solution, and it is x=0} \end{gathered}[/tex]The diagram shows a field.
66 m
140m
102 m
Work out the area of the field.
4
Answer:
The area of the field will be 60504 Sq. m
Step by Step calculation:
Area of the cuboidal field
A cuboid is a three-dimensional figure bounded by six rectangular planes that have different lengths, widths, and heights. If you look around and see a box, brick, or anything in the shape of a rectangle, it might be a cuboid. A cuboid ([tex]3[/tex]-dimensional) can be seen as composed of rectangles ([tex]2[/tex]-dimensional) of different dimensions when viewed from either end
Total area of block = lh + lh + lb+ lb+ hb+ hb=[tex]2[/tex](lb+bh+hl).......(1)
where l means length h means height and b means the breadth of the cuboid
Put the value of length, breadth, and height in (1)
We get TSA of field as= 2(66*140+140*102+102*66 ) = 60504 m^2
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I need the answer right now please someone help.Use the figure below to complete the following problem.Given:R, S, T are midpoints of AC, AB, and CB. AB||RTRCTC
From the diagram provided, line AB is parallel to line RT
AB | | RT
find the unit price of 16 oz of candy with sells for $4.82
The price of 16 oz candy is $4.82.
Determine the unit price of candy.
[tex]\begin{gathered} s=\frac{4.82}{16} \\ =0.30125 \end{gathered}[/tex]4.) Rotate 90° counterclockwise about the origin.Original NewCoordinates: Coordinates:A: (___) A: ()YAON+COB:(_)B': ()2D2CC: (-)C':(___)D: (___)D:(__)
The Solution:
Rule:
When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
The original coordinates of the given points are as follows:
[tex]\begin{gathered} A(-4,3)_{} \\ B(2,3) \\ C(2,-1) \\ D(-4,-1) \end{gathered}[/tex]So, the new coordinates of the given points are below:
[tex]A^{\prime}(-3,-4)[/tex][tex]B^{\prime}(-3,2)[/tex][tex]C^{\prime}(1,2)[/tex][tex]D^{\prime}(1,-4)[/tex]helpp pleasee List the domain of the following function.(0,1),(9,0), (2,7),(4,3)
Problem
Solution
For this case we want to determine the domain from the following relation:
(0,1), (9,0), (2,7), (4,3)
And if we see the first cooridnate for all the points we have the domain and then the answer we have:
0,2,4,9
thanks for the help!!!
The value of expression cos(A + B) is equivalent to 0.9902.
What is the relation between sinФ and cosФ?The relation between sinФ and cosФ is as follows -
sin²Ф + cos²Ф = 1
Given is sin(A) = -11/61 and sin(B) = 9/41
We have -
sin(A) = -11/61
sin(B) = 9/41
Evaluating the expression -
cos(A + B)
We can write -
cos(A + B) = cos[A] cos[B] - sin[A] sin[B]
Now, we know -
sin²Ф + cos²Ф = 1
cos²A = 1 - sin²A = 1 - 0.033 = 0.97
cos A = 0.98
cos²B = 1 - sin²B = 1 - 0.04 = 0.95
cos B = 0.97
Using the values -
cos(A + B) = cos[A] cos[B] - sin[A] sin[B]
cos(A + B) = 0.98 x 0.97 + 0.18 x 0.22
cos(A + B) = 0.9902
Therefore, the value of expression cos(A + B) is equivalent to 0.9902.
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I keep getting the wrong answer for some reason, help please
In order to find the measure of angle A we have the next equation. Remember that the sum of the interior angles of a triangle is 180°
[tex](3x-6)+(8x+4)+(180-130)=180[/tex]Then we sum like terms
[tex]11x+48=180[/tex]Then we isolate the x
[tex]11x=180-48[/tex][tex]11x=132[/tex][tex]x=\frac{132}{11}[/tex][tex]x=12[/tex]For angle A
angle A= 3x-6=3(12)-6=30°
angle A=30°
Miles per gallon of a vehicle is a random variable with a uniform distribution from 23 to 47. The probability that a random vehicle gets between 28 and 36 miles per gallon is?
The probability that a random vehicle gets between 28 and 36 miles per gallon is 0.3333.
What's probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Given that,
a = 23
b = 47
P(c < x < d) = (d - c) / (b - a)
P(28 < x < 36) = (36 - 28) / (47 - 23) = 0.3333
Probability = 0.3333
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A line passes through the point (-3, -9) and has a slope of -2.
Write an equation in slope-intercept form for this line.
The drama club is selling tickets to their play to raise money for the show's expenses.Each student ticket sells for $5 and each adult ticket sells for $7.50. The auditoriumcan hold at most 125 people. The drama club must make no less than $790 fromticket sales to cover the show's costs. If 73 adult tickets were sold, determine allpossible values for the number of student tickets that the drama club must sell inorder to meet the show's expenses. Your answer should be a comma separated list ofvalues. If there are no possible solutions, submit an empty answer.
Let
x ------> number of student tickets that the drama club must sell
so
we have
[tex]x+73\leq125[/tex][tex]\begin{gathered} x\leq125-73 \\ x\leq52 \end{gathered}[/tex]and
[tex]5x+7.50\cdot73\ge790[/tex][tex]\begin{gathered} 5x\ge790-547.5 \\ 5x\ge242.5 \\ x\ge48.5 \end{gathered}[/tex]the values of x lie on the interval [48.5,52]
therefore
all possible values for the number of student tickets are on the interval
[49,52]
Integers greater than or equal to 49 and less than or equal to 52possibles values are 49,50,51,52Solve the triangle. (Do not round until the final answer. Round angles to the nearest degree and side lengths to the nearest tenth of a unit.)C=___∠A=___∠B=___
Explanation
to solve this we need to use the cosine law
Law of cosines says
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos (A) \\ b^2=a^2+c^2-2ac\cdot\cos (B) \\ c^2=a^2+b^2-2ab\cdot\cos (C) \end{gathered}[/tex]then
Step 1
find c
Let
[tex]\begin{gathered} b=8 \\ a=5 \\ \angle C=67 \end{gathered}[/tex]now, let's find c
[tex]\begin{gathered} c^2=a^2+b^2-2bc\cdot\cos (C) \\ \text{replace} \\ c^2=5^2+8^2-2\cdot5\cdot8\cdot\cos (67) \\ c^2=25+64-31.25849028 \\ c^2=57.74 \\ \text{square root in both sides} \\ \sqrt{c^2}=\sqrt{57.74} \\ c=7.598 \\ \text{rounded} \\ c=7.6 \end{gathered}[/tex]Step 2
now,let's find the angle A
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos (A) \\ replace \\ 5^2=8^2+7.6^2-2\cdot8\cdot7.6\cdot\cos (A) \\ 25=64+57.76-121.6\text{ cos(A)} \\ 25=121.76-121.6(\cos A) \\ \text{subtract 121.76 in both sides} \\ 25-121.76=121.76-121.6(\cos A)-121.76 \\ -96.76=-121.6(\cos A) \\ \text{divide both sides by -121.6} \\ \frac{-96.76}{-121.6}=\frac{-121.6(\cos A)}{-121.6} \\ 0.795=\cos \text{ (A)} \\ Inverse\text{ cosine} \\ \cos ^{-1}(0.795)=\cos ^{-1}(\cos \text{ (A))} \\ 37.276=\text{ A} \\ \text{rounded} \\ A=37\~\text{ =A} \end{gathered}[/tex]Step 3
Finally,let's find angle B
we can use the formula as we did in step 2 to find angle A, but also we can use this fact:
the sum of the internal angles in a triangle equals 180 ,so
[tex]\angle A+\angle B+\angle C=180[/tex]replace and solve for angle C
[tex]\begin{gathered} \angle A+\angle B+\angle C=180 \\ 37+\angle B+67=180 \\ 104+\angle B=180 \\ \text{subtract 104 in both sides} \\ 104+\angle B-104=180-104 \\ \angle B=76 \end{gathered}[/tex]the baseball stadium the price for popcorn is $16.20 for 6 bags. If youwanted to buy 5 bags of popcorn, how much would it cost?
It is given that the cost of 6 bags of popcorn is $16.20
So the cost of 1 bag is:
[tex]\frac{16.20}{6}=2.7\text{ dollars}[/tex]So the cost of 5 bags at $2.70 per bag is:
[tex]2.7\times5=13.5\text{ dollars}[/tex]So the cost of 5 bags of popcorn is $13.5.
Solve the equation below.
3(x−9)−6=16x−72
3x-27-6=16x-72
3x-33=16x-72
3x-16x= -72+33
-13x=39
x= -3
Solve the equation: 3x - 6 = 2(x - 2)no solution0all real numbers0.752
Problem
Solve the equation: 3x - 6 = 2(x - 2)
Solution
For this case we can do the following:
3x -6= 2x -4
And now we can subtract in both sides 2x and we got:
3x- 2x = 6-4
x = 2
And the final solution for this case would be x=2
heyyyy i need help with jumber 2
We are asked to determine whether the given two polygons are similar or not.
Recall that the two polygons are said to be similar if the ratio of their corresponding sides is equal.
The corresponding sides of the two polygons are
side 3 = side 6
side 4 = side 8
side 5.5 = side 11
Let us check if they are in the same ratio
[tex]\begin{gathered} \frac{3}{6}=\frac{4}{8}=\frac{5.5}{11} \\ \frac{1}{2}=\frac{1}{2}=\frac{1}{2} \end{gathered}[/tex]As you can see, the ratio of the corresponding sides is equal.
Therefore, the given pair of polygons is similar.
Find the area and perimeter of the following rectangle guru angad education
1.
[tex]A=l\times w=11\times8=88\operatorname{cm}\text{ }[/tex][tex]P=2l+2w=2(11)+2(8)=22+16=38\text{ cm}[/tex]2.
[tex]\begin{gathered} A=11\times11=121 \\ P=2(11)+2(11)=22+22=44 \end{gathered}[/tex]3.
[tex]\begin{gathered} A=8\times6=48 \\ P=2(8)+2(6)=16+12=28 \end{gathered}[/tex]4.
[tex]\begin{gathered} A=7\times2=14 \\ P=2(7)+2(2)=14+4=18 \end{gathered}[/tex]5.
[tex]\begin{gathered} 35=7\times w \\ \frac{35}{7}=\frac{7w}{7} \\ w=5 \\ P=2(7)+2(5)=14+10=24\text{ units} \end{gathered}[/tex][tex]\begin{gathered} 25=l\times5 \\ \frac{25}{5}=\frac{5l}{5} \\ l=5 \\ P=2(5)+2(5)=10+10=20\text{ units} \end{gathered}[/tex]6.
[tex]P=11+18+9+3+3+8+5+7=64[/tex]all you need is in the photo please don't put the step by step ANSWER FAST
The given expression is
[tex]3x^2+12x-15=0[/tex]First, we factor our the number 3.
[tex]3(x^2+4x-5)=0[/tex]Then,
[tex]x^2+4x-5=0[/tex]Now, we look for two numbers whose product is 5, and whose difference is 4, those numbers are 5 and 1.
[tex](x+5)(x-1)=0[/tex]Hence, the solutions are x = -5 and x = 1.a rectangle measures 12 inches by 20 inches. what size squares can tile the rectangle completely? choose all that apply
Therefore, supplying 4X4 square tiles can tile the rectangle completely with the help of the HCF concept.
What is HCF?
The greatest number that totally divides two numbers is known as the Highest Common Factor (HCF).
HCF for 12 and 20 is equal to 4. Factors of 12 & 20 = 1, 2, 3, 4, 6, and, respectively, 1, 2, 4, 5, 10, 20. In this case, 4 is the biggest number that can be found in the factors for 12 and 20.
We interpret the study released as the component of the product factors in order to determine the HCF by listing common factors in prime factorization.
Consequently, 12 and 20 can be written as;
12 equals 2 × 2 × 3
20 equals 2 × 2 × 5
2 and 2 are frequent prime factors for 12 and 20.
Therefore,
HCF (12, 20) equals 2 × 2 = 4
Therefore, supplying 4X4 square tiles can tile the rectangle completely with the help of the HCF concept.
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Will picks a Marble random puts it back and then picks another Marble at random are these 2 events depended or independent
When Will puts back the marble, the number of marbles in the sample space has not changed. This is similar to having a replacement marble. The event therefore, is independent.
a parabola can be drawn given a focus of (4, -7) and a directrix of y=-1
The equation of parabola is -12(y + 4) = (x-4)² with vertex(4, -7) and Latus rectum 12.
What is Parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
Any point on the parabola is equidistant from the focus an directrix.
Distance of a point (x,y) from y=-1 is (y+1)
Distance of a point (x,y) from (4,-7) say L, then
L² = (x - 4)² + (y+7)²
since, L = y + 1
(y + 1)² = (x - 4)² + (y+7)²
y² + 1 + 2y = (x - 4)² + y² + 49 + 14y
-12y - 48 = (x-4)²
-12(y + 4) = (x-4)²
Therefore, The equation of parabola is -12(y + 4) = (x-4)² with vertex(4, -7) and Latus rectum 12.
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Classify each angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. <1 and <3 <3 and <7 <8 and <10<4 and <14<6 and <14<2 and <3
EXPLANATION:
To make a correct classification we must do the following:
First we must know the following terms:
-Corresponding angles:
They are on the same side of the parallels and on the same side of the transversal.
For example: <1 <3 ; <6 and <14
-Alternate interior:
They are found within the parallel lines and on the opposite sides to the transversal
For example: <3 and <7 ; <8 and <10
-Alternate Exterior:
they lie outside the parallel lines and on the opposite sides to the transversal.
For example: <4 and <14
-Consecutive interior angles:
They are the pairs of angles on one side of the transversal that are between the lines.
For example: <2 and <3
(05.01)Neil has been running a tutoring business since 2005. He charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount. The table shows what Neil charged each customer for two given years of his business:YearAnnual Tutoring Fee2005$12002008$1350A. What is the rate of change and initial value for Neil’s business? How do you know?B. Write an equation in slope-intercept form to represent the fees that Neil charges each year.
Solution:
Given that, the initial year (2005), the tutoring fee is $1200. Three years later (2008), the tutoring fee is $1350.
Thus, the rate of change, m, is;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ x_1=0,y_1=1200,x_2=3,y_2=1350 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{1350-1200}{3-0} \\ \\ m=\frac{150}{3} \\ \\ m=50 \end{gathered}[/tex]Then, the rate of change for Neil's business is 50 and the initial value is $1200.
(b) The slope-intercept form is written as;
[tex]\begin{gathered} y=mx+b \\ \\ \text{ Where }m\text{ is the rate of change, }b\text{ is the initial value;} \\ y\text{ is the annnua tutoring fee,}x=year \end{gathered}[/tex]ANSWER:
[tex]y(x)=50x+1200[/tex]A circle has a radius of 4 in find the length s of the arc
The rule of the length of an arc is
[tex]s=r\theta[/tex]r is the radius of the circle
Cita is the central angle subtended by this arc in radian measure
Since the radius of the circle is 4 inches, then
[tex]r=4[/tex]Since the measure of the central angle is 1.9 radian, then
[tex]\theta=1.9[/tex]Substitute them in the rule above
[tex]\begin{gathered} s=4\times1.9 \\ s=7.6\text{ inches} \end{gathered}[/tex]The length of the arc is 7.6 inches
Work out the value of (-8)2
Answer:
-16
Step-by-step explanation:
2x(-8)=16
Hey there!
Assuming you meant:
(-8)^2
= (-8)(-8)
= 64
Therefore, your answer should be:
64
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
What is the solution to this equation?4x - 6 + 2x = 18OA. x = 6OB. X= 4OC. X = 2OD. x = 12
In order to solve this equation, we can do the following steps:
[tex]\begin{gathered} 4x-6+2x=18\\ \\ 6x-6=18\\ \\ 6x=18+6\\ \\ 6x=24\\ \\ x=\frac{24}{6}\\ \\ x=4 \end{gathered}[/tex]Therefore the correct option is B.
Show your work (no explanation just the answer and how you got it) DUE TODAY
The solutions to the absolute value equations are given as follows:
1. k = -8 or k = 8.
2. x = -7 or x = 7.
3. a = -10 or a = 6.
4. a = -2.5 or a = 2.5.
5. m = -4 or m = 22.
6. x = -4 or x = 6.8.
7. x = -16 or x = 9.
8. a = -2.4 or a = 1.2.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.|x| = -x, x < 0.This means that there are two possible solutions for the equation |x| = a, which are:
x = a or x = -a.
Item 1The equation is:
|k| = 8.
Applying the definition of the absolute value function, we have that the possible solutions are:
k = -8 or k = 8.
Item 2The equation is:
|x| = 7.
Applying the definition of the absolute value function, we have that the possible solutions are:
x = -7 or x = 7.
Item 3The equation is:
|a + 2| = 8.
The possible solutions are that the inside term can be equals to either -8 or 8, hence:
a + 2 = -8 -> a = -10.a + 2 = 8 -> a = 6.Item 4The equation is:
|8a|/10 = 2
In standard format, the equation is:
|8a| = 20
Then the solutions are:
8a = -20 -> a = -20/8 = -2.5.8a = 20 -> a = 20/8 = 2.5.Item 5The possible solutions are:
-m + 9 = -13 -> m = 22.-m + 9 = 13 -> m = -4.Item 6The possible solutions are:
7 - 5x = -27 -> 5x = 34 -> x = 6.8.7 - 5x = 27 -> 5x = -20 -> x = -4.Item 7Applying cross multiplication, the expression is:
|2x + 7| = 25
The possible solutions are:
2x + 7 = -25 -> 2x = -32 -> x = -16.2x + 7 = 25 -> 2x = 18 -> x = 9.Item 8Applying cross multiplication, the expression is:
|-3 -5a| = 9.
The possible solutions are:
-3 - 5a = -9 -> 5a = 6 -> a = 1.2.-3 - 5a = 9 -> 5a = -12 -> a = -2.4.More can be learned about absolute value equations at https://brainly.com/question/5012769
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Given f(x)
= 3x + 1, solve for x when
f(x) = 7.
Answer:
Answer:
x=2
Step-by-step explanation:
7=3x+1
6=3x
2=x
Hopes this help please mark brainliest
Graph the inequality on the numberlineA + 5/3 > 1/2
Okay, here we have this:
Let's solve first A + 5/3 > 1/2:
[tex]\begin{gathered} A+\frac{5}{3}>\frac{1}{2} \\ A>-\frac{7}{6} \end{gathered}[/tex]So, according with this we obtain the following in the number line:
A hot air balloon descended 3240 feet in an hour. Find the change in altitude per minute?
Unit analysis is a tool that we can use to convert units. It involves multiplying the original number by a fraction to cancel out units.
Solving the QuestionWe're given:
[tex]\dfrac{3240\hspace{4}feet}{hour}[/tex]
We also know that:
[tex]\dfrac{hour}{60\hspace{4}minutes}[/tex]
Multiply the two to cancel out the hour:
[tex]\dfrac{3240\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{3240\hspace{4}feet}{60 minutes}[/tex]
Simplify:
[tex]=\dfrac{54\hspace{4}feet}{minute}[/tex]
Answer[tex]\dfrac{54\hspace{4}feet}{minute}[/tex]
