For direct variation, an increase or decrease in one variable leads to a proportional increase or decrease in the other variable
Given that y varies directly with x, we would introduce a constant of proportionality, k
The expresion becomes
y = kx
For x = 2 and y = 5,
5 = 2k
k = 5/2 = 2.5
The direct variation equation is
y = 2.5x
Find an angle e in the interval [0°, 90°) that satisfies each statement. Give answer to the nearest TENTH of a degree. a) sin= 0.3697 degrees b) cos= 0.7265 degrees degrees c) sec= 2.3232 degrees d) csc= 1.1234
first at all, we are gonna solve this using inverse trigonometric functions
like this:
[tex]\begin{gathered} \sin \alpha\text{ = x} \\ \alpha\text{ = }\sin ^{-1}x \end{gathered}[/tex]for the first case:
a)
[tex]\begin{gathered} \sin \alpha\text{ = }0.3697 \\ \alpha=\sin ^{-1}(0.3697) \\ \alpha=21.697\ldots \\ \alpha\cong20 \end{gathered}[/tex]b)
[tex]\begin{gathered} \cos \alpha\text{ = }0.7265 \\ \alpha=\cos ^{-1}(0.7265) \\ \alpha=43.406\ldots \\ \alpha\cong40 \end{gathered}[/tex]c)
In this case, we are going to use the following trigonometric identity:
[tex]\begin{gathered} \sec \alpha=\frac{1}{\cos \alpha} \\ \end{gathered}[/tex]later,
[tex]\begin{gathered} \sec \alpha=2.3232 \\ \frac{1}{\cos \alpha}=2.3232 \\ \cos \alpha=\frac{1}{2.3232} \\ \alpha=\cos ^{-1}(\frac{1}{2.3232}) \\ \alpha=64.504\ldots \\ \alpha\cong60 \end{gathered}[/tex]d)
In this case, we are going to use the following trigonometric identity:
[tex]\begin{gathered} csc\alpha=\frac{1}{sin\alpha} \\ \end{gathered}[/tex]later,
[tex]\begin{gathered} \csc \alpha=1.1234 \\ \frac{1}{sin\alpha}=1.1234 \\ \sin \alpha=\frac{1}{1.1234} \\ \alpha=\sin ^{-1}(\frac{1}{1.1234}) \\ \alpha=62.892\ldots \\ \alpha\cong60 \end{gathered}[/tex]finally, those are your answers.
X-2y=5 and 2x+3y=10
Hello!
Let's set up some things:
[tex]x-2y=5[/tex] <-- equation 1
[tex]2x+3y = 10[/tex] <-- equation 2
________________
(equation 1) multiplied by 2
[tex]2x - 4y=10[/tex] <-- equation 3
________________
(equation 2) - (equation 3)
7y = 0
y = 0 <-- equation 4
________________
(equation 4)'s value of y into (equation 1)
[tex]x-2(0) = 5\\x = 5[/tex]
Thus x = 5 and y = 0
Hope that helps!
An irrigation canal is 10 kilometers long and 2 meters deep. It is 4 meters wide at the 2 meters wide at the bottom. How many cubic meters of earth were excavated to make the canal?
The cross section of the canal will form a trapezoid. First, find the area of the cross section. The area of a trapezoid is defined as
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{a+b}{2}h \\ \\ \text{Given} \\ h=2\text{ meters (2 meters deep)} \\ a=4\text{ meters (4 meters wide)} \\ b=2\text{ meters (2 meters wide at the bottom)} \end{gathered}[/tex]Substitute the following values and we get the area
[tex]\begin{gathered} A=\frac{a+b}{2}h \\ A=\frac{4+2}{2}(2) \\ A=\frac{6}{2}(2) \\ A=6\text{ m}^2 \end{gathered}[/tex]Now that we have the area of the cross section, multiply it to the length of the irrigation canal.
[tex]\begin{gathered} \text{Before multiplying, all units must be the same, convert km to meters} \\ 10\operatorname{km}\rightarrow10,000\text{ meters} \\ 6\text{ m}^2\times10000\text{ meters} \\ \Longrightarrow60000\text{ m}^3 \end{gathered}[/tex]Therefore, they have to excavate 60,000 cubic meters of earth to make the canal.
Which property is shown -2x1/-2=1
Answer: The answer is Multiplicative Inverse.
Step-by-step explanation: I hope this helps.
HELP
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Apply the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, a^2 + b^2 = c^2 where c is the hypotenuse.
a^2 + b^2 = c^2
8^2 + 5^2 = c^2
64 + 25 = c^2
89 = c^2
√89 = √c^2
c = √89
For each table, determine whether it shows a direct variation.If it does, write its direct variation equation.Not direct variationNot direct varlationXхyу41N1Direct variationEquation:51.2542Direct variationEquation:I78.75105The
For the right table , y/x = constant = k = 0.5
The value of a in y = ax²+bx+c and the vertex of the parabola are given. How many x-intercepts does the parabola have? Explain how you arrived at this number.a=1; vertex at (2,0)The parabola has x-intercept(s), because the parabola opensand the vertex isthe x-axis.
Given: The value of 'a' in y = ax²+bx+c is a=2 and vertex is at (2,0).
Required: To find the x-intercepts.
Explanation: The x-coordinate of the vertex is 2. Also, we know that x-coordinate is given by
[tex]x=-\frac{b}{2a}[/tex]Hence, putting the value of x=2 and a=1 we get
[tex]\begin{gathered} 2=-\frac{b}{2(1)} \\ b=-4 \end{gathered}[/tex]Now putting y=0, x=2, a=1, and b=-4 in eq of parabola we get
[tex]\begin{gathered} 0=2^2-4(2)+c \\ c=4 \end{gathered}[/tex]Now the equation of the parabola is,
[tex]y=x^2-4x+4[/tex]Now to find x-intercepts put y=0 i.e.,
[tex]\begin{gathered} x^2-4x+4=0 \\ (x-2)^2=0 \\ x=2,2 \end{gathered}[/tex]Hence there is only one x-intercept at (2,0). The opening of the parabola can be seen in the graph below-
Final Answer: The parabola has one x-intercept because the parabola opens upward and the vertex is on the x-axis.
Part 1: Factorial!2. Explain the steps that you took to calculate it on your calculator.
Given:
a factorial 14! is given
Find:
we have to evaluate the given factorial
Explanation:
we know, the factorial 14! is calculated as following
14! = 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
14! = 87178291200
or
14! = 8.71783E10
Is w = 12 a solution to the inequality below?
Answer:
No
Step-by-step explanation:
No, it is not a solution. You can find this answer by plugging in 12 for 2 for w.
0>12-132/12
132/12=11
12-11=1
0>1
0 is not greater than 1, so the answer is no.
If one mini Hershey bar weighs 0.3 ounces how many mini candy bars would you have to eat to eat the same amount as a regular size Hershey bar that weighs 1.55 ounces?
when trying to find the probability of rolling a number four on a number cube with the number 1 through 6 how many desired outcomes are there
ANSWER
One desired outcome
EXPLANATION
We are trying to roll the number 4 on a number cube with numbers 1 through 6.
Since we are only trying to get one outcome/result from the experiment (4), there is only one desired outcome.
The answer is 1.
can somebody please help me with this question
What is the value of (-3)-4?
Answer:
-7
Step-by-step explanation:
-3-4=-7
:]
Answer:
-7
Step-by-step explanation:
180/9 as a whole number
Answer:
20
Step-by-step explanation:
180 ÷ 9 = 20
Find the value of x and the length of ST
x = 13
The length of ST is 78
Explanation:ST and SR are tangents
From the diagram
ST = 9x - 39
SR = 6x
Note that:
Two tangents drawn from the same point external to a circle are equal
That is, ST = SR
9x - 39 = 6x
9x - 6x = 39
3x = 39
x = 39/3
x = 13
ST = 9x - 39
Suubstitute x = 13
ST = 9(13) - 39
ST = 117 - 39
ST = 78
Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]A. 28.53 units²B. 26.47 units²C. 27.28 units²D. 33.08 units²
Answer
A. 28.53 units²
Explanation
Finding the area of irregular quadrilateral ABCD, we divide the given figure into shapes (two triangles) as shown below:
Then, we find the area of the two triangles.
Triangle ABD:
[tex]\begin{gathered} Area=\sqrt{s(s-a)(s-b)(s-c)} \\ \\ s=\frac{a+b+c}{2}=\frac{2.89+8.59+8.6}{2}=\frac{20.08}{2}=10.04 \\ \\ Area\text{ }of\text{ }triangle\text{ }ABD=\sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)} \\ \\ Area\text{ }of\text{ }triangle\text{ }ABD=\sqrt{10.04(7.15)(1.45)(1.44)} \\ \\ Area\text{ }of\text{ }triangle\text{ }ABD=\sqrt{149.889} \\ \\ Area\text{ }of\text{ }triangle\text{ }ABD=12.24\text{ }unit^2 \end{gathered}[/tex]Triangle ADC:
[tex]\begin{gathered} Area=\sqrt{s(s-a)(s-b)(s-c)} \\ \\ s=\frac{a+b+c}{2}=\frac{4.3+7.58+8.6}{2}=\frac{20.48}{2}=10.24 \\ \\ Area\text{ }of\text{ }triangle\text{ }ADC=\sqrt{10.24(10.24-4.3)(10.24-7.58)(10.24-8.6)} \\ \\ Area\text{ }of\text{ }triangle\text{ }ADC=\sqrt{10.24(5.94)(2.66)(1.64)} \\ \\ Area\text{ }of\text{ }triangle\text{ }ADC=\sqrt{265.346} \\ \\ Area\text{ }of\text{ }triangle\text{ }ADC=16.29\text{ }unit^2 \end{gathered}[/tex]Therefore, the area of the quadrilateral ABCD = the Sum of the two triangles
The area of the quadrilateral ABCD = 12.24 units² + 16.29 units² = 28.53 units²
At many bakeries, there are deals that if you buy twelve donuts, you get a thirteenth one at a discount. Sometimes "13" items is called a baker's dozen. I One store is advertising: Donuts! $1.05 individually, or $13 per baker's dozen. They want to program their cash register to be able to show the exact price for any number of donuts. You will help them by producing a data table, a graph and an algorithm. You will: 1. Fill in and expand the data table 2. Make a scatter plot to show the pattern visually. This means to plot an (x,y) point for every row in the data table. For example the first point can be (1, 1.05) 3. Develop an algorithm to find the cost for any number of donuts. Note: An algorithm is like a set of instructions to solve a problem. They are useful for telling computers or people exactly how to do something. For example, here is an algorithm that finds 15% of a number: Step 1: take any number, callit N.
Table
Number of donuts Price
1 $1.05
2 $ 2.1
3 $3.15
4 $4.2
5 $5.25
6 $6.3
10 $10.5
slope = (10.5 - 1.05) / 10 - 1
= 9.45 / 9
= 1.05
Equation
y - 10.5 = 1.05 (x - 10)
y = 1.05x - 10.5 + 10.5
y = 1.05x
For 40 donuts
y = 1.05(40)
y = $42
Enter the corredeach column.4. Madam Malkin owns Madam Malkin's Robes for AllOcassions which is a clothing store. She has abudget of $6000 to restock 200 clothing items.She can buy Hogwarts shirts for $12 each, Robes for$24 each, and Quidditch shirts for $36 each. If shewants to have twice as many Quidditch shirts asRobes, how many of each type of shirt should shebuy?11)223HOW MANY QUIDDITCH SHIRTS DID MADAMMALKIN BUY?445
Let's define some notation first:
H= number of Hogwarts, R= number of robes, Q= number of Quidditch
We can set up the following equation for the total of clothing items:
[tex]H+R+Q=200[/tex]We also know that Q= 2R so we have:
[tex]H+3R=200[/tex]Now we can create an equation for the amount of money and we have:
[tex]12H+24R+36Q=6000[/tex][tex]12H+96R=6000[/tex]Now we can replace H=200-3R and we got:
[tex]12(200-3R)+96R=6000[/tex]And solving for R we got:
[tex]60R=3600[/tex][tex]R=\frac{3600}{60}=60[/tex]And then Q would be:
[tex]Q=2R=120[/tex]A police car traveling south toward Sioux Falls, Iowa, at 160 km/h pursues a truck traveling east away from Sioux Falls at
140 km/h.
At time t = 0, the police car is 60 km north and the truck is 50 km east of Sioux Falls.
Calculate the rate at which the distance between the vehicles is changing at t = 10 minutes.
(Use decimal notation. Give your answer to three decimal places.)
Using the Pythagorean Theorem, the rate at which the distance between the vehicles is changing at t = 10 minutes is of -20 km/hour.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the equation given below:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In the context of this problem, the distances of the cars from Sioux Falls, considering the initial distances and the velocities, are given as follows:
Police: P(t) = 60 - 160t.Truck: T(t) = 50 + 140t.The distance after t hours is the hypotenuse of a right triangle in which the legs are the functions, hence:
D²(t) = P²(t) + T²(t).
Hence the rate of change of the distance after t hours is:
2D'(t) = 2P'(t) + 2T'(t)
Simplifying by 2:
D'(t) = P'(t) + T'(t).
Applying the exponent rules, the derivatives are given as follows:
P'(t) = -160.T'(t) = 140.Hence the constant rate is:
D'(t) = -160 + 140 = -20 km/hour.
Meaning that the police car is getting 20 km closer to the truck each hour.
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54 is the product of 3 and Janelle's age
Can a table with same input and output be a function like in the picture:
Yes, because each value of x still corresponds to only one value of y.
Evaluate (2 +40) : 2 when z = 8 answer A 8 B 5C 6D 48
1) Let's solve the equation given the condition
[tex]\frac{\mleft(x+40\mright)}{2^3}\Rightarrow\frac{(8+40)}{8}\Rightarrow\frac{48}{8}=6[/tex]After plugging into the equation, all that's left is to solve it with the PEMDA order of operation.
2) So the answer is C
Need help please. ASAP
(2y - 1)/ -3 = -5 , prove y = 8: Hence proved
5n - 42 = 12n, prove n = -6: Hence proved
2x + 30 = -4(5x -2), prove x = -1 : Hence proved
18x - 2(3x + 1) = 5x -16, prove x = -2 : Hence proved
What is Algebra?
One of the many different mathematical disciplines is algebra. Algebra, a common thread that runs through nearly all of mathematics, is the study of mathematical symbols and the rules for using them in formulas.
1) (2y - 1)/ -3 = -5
Solving for y
(2y - 1)/ -3 = -5
multiply both side with -3
(2y - 1) x (-3)/(-3) = (-5)(-3)
2y - 1 = 15
adding 1 both side
2y - 1 + 1 = 15 + 1
2y = 16
dividing 2 both side
2y / 2 = 16 / 2
y = 8
Hence Proved
2) 5n - 42 = 12n
Solving for n
5n - 42 = 12n
adding 42 both side
5n - 42 + 42 = 12n + 42
5n = 12n + 42
adding -12n both side
5n - 12n = 12n - 12n + 42
-7n = 42
dividing -7 both side
-7n/-7 = 42/ -7
n = -6
Hence proved
3) 2x + 30 = -4(5x -2)
solving for x
first simplify -4(5x -2)
2x + 30 = -20x + 8
adding 20x both side
2x + 20x + 30 = -20x + 20x + 8
22x + 30 = 8
adding -30 both side
22x + 30 - 30 = 8 - 30
22x = -22
dividing 22 both side
22x / 22 = -22/22
x = -1
Hence proved
4) 18x - 2(3x + 1) = 5x -16
solving for x
first simplify - 2(3x + 1)
18x - 6x - 2 = 5x - 16
adding -5x both side
18x - 5x - 6x - 2 = 5x - 5x - 16
13x - 6x - 2 = -16
7x - 2 = -16
adding 2 both side
7x - 2 + 2 = -16 + 2
7x = -14
dividing 7 both side
7x/ 7 = -14 / 7
x = -2
Hence proved
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Please help with this question pl
The missing reason 6 of the two column proof that m∠Z = 65° is; Substitution
How to carry out two column proof?The two column proof is as follows;
Statement 1: XYZ is a triangle
Reason 1; Given
Statement 2: m∠x + m∠y + m∠z = 180°
Reason 2: Postulate
Statement 3: m∠y = 50°
Reason 3: Given
Statement 4: ∠X ≅ ∠Z
Reason 4: Given
Statement 5: m∠X = m∠Z
Reason 5: Congruency
Statement 6: m∠Z + m∠Z = 180°
Reason6: Substitution
Statement 7: m∠Z + m∠Z = 130°
Reason 7: ?
Statement 8: 2(m∠Z) = 130°
Reason 8: Algebra
Statement 9: m∠Z = 65°
Reason 9: Division property of equality
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Angle 1,7,3 and 5 all those angles has the same equivalent to the angle 5 angle 2 is supplementary to angle 1 so angle 2 is 30 degrees because 150+ 30 is 180 degrees and we use the same thing that I did in the first step that if angle number to is 30 angle 8,4 and 6 is going to be 30
Given:-
To find all angle values.
So from the given image. we get,
[tex]\begin{gathered} \angle5+\angle4=180 \\ \angle7+\angle4=180 \\ \angle7+\angle6=180 \\ \angle6+\angle5=180 \end{gathered}[/tex]Also,
[tex]\begin{gathered} \angle1=\angle7 \\ \angle2=\angle4 \\ \angle8=\angle6 \\ \angle3=\angle5 \end{gathered}[/tex]So now we know angle 5 is 150 degrees. so we get,
[tex]\begin{gathered} \angle5+\angle4=180 \\ 150+\angle4=180 \\ \angle4=180-150 \\ \angle4=30 \end{gathered}[/tex]So angle 4 is 30 degree.
Also,
[tex]\begin{gathered} \angle7+\angle4=180 \\ \angle7+30=180 \\ \angle7=150 \end{gathered}[/tex]So angle 7 is 150 degree.
Also,
[tex]\begin{gathered} \angle6+\angle5=180 \\ \angle6+150=180 \\ \angle6=30 \end{gathered}[/tex]So angle 6 is 30 degree.
So now we equate the values. so we get,
[tex]undefined[/tex]Please find it if needed.-The Area of a Rectangle-The Area of a Triangle-The Area of a Square-Or The Area of a Circleand find the area of the composite figure (andplease put the areas separate)FIND THE AREA OF THE SHADED REGION
First find the area of the rectangle
A = l*w = 9*16 = 144
The unshaded area is a trapezoid
A = 1/2 ( b1+b2) *h = 1/2 ( 5+11) * 4 = 1/2 (16) * 4 =32
The area of the shaded region is
rectangle - trapezoid
144-32
112cm^2
Answer:
112cm²
Step-by-step explanation:
First, let us find the area of the rectangle.
Area = length × width
Area = 16 cm × 9 cm
Area = 144 cm²
Now, let us find the area of the trapezium.
Area = 1/2 ( Sum of the parallel sides ) × height
Area = 1/2 × ( 11 + 5 ) × 4
Area = 1/2 × 16 × 4
Area = 32 cm²
Area of the shaded region.
To find the area of the shaded region, subtract the area of the rectangle from the area of the trapezium.
Area = 144cm² - 32cm²
Area = 112cm²
what is the product of 24.154 and 0.18
Answer:
4.34772
4.3 with the correct amount of sig figs but you don't really have to worry about that unless you've talked about it in class
Step-by-step explanation:
the product of two numbers is the result of those two numbers being multiplied. So, 24.154 * 0.18 = 4.34772
Carina has a piece of wire that is 301cm long . She bends the wire to make 6 shapes of the same perimeter . She has 97cm of wire left . What is the perimeter of each shape ?
Answer:
34
Step-by-step explanation:
301 - 97 = 204
204 / 6 = 34
Write an equation in point-slope form for the line that passes through the given points.
(-4,7). (6.3)
Answer:
[tex]y=-\frac{2}{5}x+5.4[/tex]
Step-by-step explanation:
Step 1: plot points
Step 2: find the RISE/RUN (-4/10 or -2/5)
Step 3: find where it intersects the y axis (5.4)
y=mx+b where x and y are varables, m is the slope, and b is the y-int
[tex]y=-\frac{2}{5}x+5.4[/tex]
Hope that helps
help me with the last question pleaseeeeeeeeeeeeeee
Answer:
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.