Given:
x varies directly with y, and x=6 when y=8
Required:
We need to find the value of x when y =18.
Explanation:
if x varies directly as y the equation of variation is expressed as follows.
[tex]y=kx[/tex]Substitute x =6 and y =8 in the equation to find teh value of k.
[tex]8=k(6)[/tex]Divide both sides by 6.
[tex]\frac{8}{6}=\frac{k(6)}{6}[/tex][tex]\frac{4}{3}=k[/tex]We get k =4/3.
The equation is
[tex]y=\frac{4}{3}x[/tex]Substitute y =18 in the equation to find the value of x.
[tex]18=\frac{4}{3}x[/tex]Divide both sides by 3/4.
[tex]18\times\frac{3}{4}=\frac{4}{3}x\times\frac{3}{4}[/tex][tex]13.5=x[/tex]We get x =13.5
Final answer:
[tex]x=13.5\text{ when y =18.}[/tex]
Lines AB and CD at E. If m∠AEC=x^2+3x and m∠BED=6x+4 ,find m∠CEB.
Explanation
Step 1
when two lines intersect, vertical angles that are equal are formed.Also two angles are Supplementary when they add up to 180 degrees
then
[tex]\begin{gathered} m\measuredangle\text{AEC =}m\measuredangle BED \\ \text{replacing} \\ x^2+3x=6x+4 \end{gathered}[/tex]and
[tex]m\measuredangle\text{AEC}+\text{ m}\measuredangle CEB=180[/tex]Step 2
solve for x,
[tex]\begin{gathered} x^2+3x=6x+4 \\ x^2+3x-6x=+4 \\ x^2+3x-6x-4=0 \\ x^2-3x-4=0 \\ \text{factorize} \\ (x-4)(x+1)=0 \\ it\text{ means} \\ x-4=0 \\ x=4 \\ or \\ x+1=0 \\ x=-1 \end{gathered}[/tex]we just take the positive number, because we are searching for an angle ( angles and distance are always positives)
then
[tex]x=4[/tex]Step 3
replace the value of x in the angle AEC
[tex]\begin{gathered} m\measuredangle AEC=x^2+3x \\ m\measuredangle AEC=4^2+3\cdot4 \\ m\measuredangle AEC=16+12 \\ m\measuredangle AEC=28 \\ \end{gathered}[/tex]replace the value of AEC in equation (2) to find CEB
[tex]\begin{gathered} m\measuredangle\text{AEC}+\text{ m}\measuredangle CEB=180 \\ 28+m\measuredangle CEB=180 \\ \text{subtract 28 in both sides} \\ 28+m\measuredangle CEB-28=180-28 \\ m\measuredangle CEB=152 \end{gathered}[/tex]I hope this helps you.
Instructions: Given the coordinate points of the preimage, use the transformation given to provide the points of the image. V(-5,-2) W(-2,1) X(-3,-3) Rotation: 90º about the origin v' W'( X'(3 -3 > Check
The rotation is 90 degree about the origin. The rule can be express below
[tex](x,y)\rightarrow(y,-x)[/tex]Therefore,
[tex]\begin{gathered} V(-5,-2)\rightarrow V^{\prime}^{}(-2,5) \\ W(-2,1)\rightarrow W^{\prime}(1,2) \\ X(-3,-3)\rightarrow X^{\prime}(-3,3) \end{gathered}[/tex]Note this is a clockwise 90 degree rotation.
3/8 / 1/4 as a model
The given expression :
[tex]\frac{3}{8}\div\frac{1}{4}[/tex]Simplify :
Write an equation of the line that passes through a pair of points: 5 4 37 2 1+ 4 -3 -2 -1 1 -3 a. y = x + 3 b. y = x - 3 C. y = -x + 2 d. y = -x-2 Please select the best answer from the choicon
From the given, it shows two points that pass through the given graph. These points are:
Point A : x1, y1 = 4, 1
Point B : x2, y2 = 5, 2
We will be using these points in generating the equation of the line.
Step 1: Let's determine the slope m of the line.
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{\text{ 2 - 1}}{\text{ 5 - 4}}\text{ = }\frac{1}{1}\text{ = 1}[/tex]Step 2: Let's determine the y-intercept b. Substitute x,y = 4, 1 and m = 1 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ 1 = (1)(4) + b}[/tex][tex]\text{ 1 = 4 + b}[/tex][tex]\text{ 1 - 4 = b}[/tex][tex]\text{ -3 = b}[/tex]Step 3: Let's complete the equation. Substitute m = 1 and b = -3 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (1)x + (-3)}[/tex][tex]\text{ y = x - 3}[/tex]Therefore, the equation of the line is y = x - 3.
The answer is letter B.
What is the least common multiple of 3,4,and 8
Answer:the least common multiple of 3, 4, 8 is 48
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
Use the graph to answer the questionWhat is the average rate of change of f(x) between P and Q?
The average rate of change of a function over a interval [a,b] is given by:
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]Where, in this case:
[tex]\begin{gathered} a=1 \\ b=2 \\ f(a)=0 \\ f(b)=3 \\ so: \\ r=\frac{3-0}{2-1}=\frac{3}{1}=3 \end{gathered}[/tex]Answer:
D. 3
Simplify: 8z + 5y + 6z + Зу * O 14z + 8y 13y + 9z O 22y 22z
Answer:
14z + 8y
Explanation:
Given the equation 8z + 5y + 6z + Зу
first is to collect the like terms;
8z + 5y + 6z + Зу
= (8z + 6z) + (5y + 3y)
= 14z + 8y
Hence the simplified form is 14z + 8y
Select ALL the correct answers.Consider the geometric sequence below.Select all functions that define the given sequence-4, -6, -9, -27/2, -81/2
Given:
The geometric series
-4, -6, -9, -27/2, -81/2
Required:
Choose the correct option.
Explanation:
The given series is:
-4, -6, -9, -27/2, -81/2
The nth term of the geometric series is given by the formula:
[tex]a_n=ar^{n-1}[/tex]Where a = first term and r = common ratio
From the given series
a = -4
[tex]\begin{gathered} r=\frac{-6}{-4} \\ r=\frac{3}{2} \end{gathered}[/tex]Thus the nth term is:
[tex]f(n)=-4(\frac{3}{2})^{n-1}\text{ where n =2,3,4,.....}[/tex]Final Answer:
[tex][/tex]A rectangular window is 48 in long and 24 in wide.Christine would like to buy a screen for the window. Thecost of the screen is based on the number of squarefeet the screen is. Use the facts to find the area of thewindow In square feet.Conversion facts for length1 foot (ft) = 12 inches (in)1 yard (yd) = 3 feet (ft)1 yard (yd) = 36 Inches (in)x 6 ?
we have that
1 ft=12 in
so
L=48 in
Convert to ft
48 in=48/12=4 ft
W=24 in
24 in=24/12=2 ft
therefore
the area is (4*2=8 ft2)
I answered a few of these already. Am I right? What are the others? Thank you.
Answer:
Step-by-step explanation:
1. Number 1 is correct.
2. Number 2 is base angles.
3. Number 3 is correct.
4. Number 4 is vertical angles.
5. Number 5 is alternate interior angles.
6. Number 6 is corresponding parts.
7. Number 7 is correct.
8. Number 8 is vertex angles.
9. Number 9 is reflexive property.
10. Number 10 is correct.
Good luck! I hope you give me brainliest!
I need this answered from my prep guide, I will include the picture of the answer options
SOLUTION
(a) The vertex of the parabola
[tex]\begin{gathered} (y+1)^2=12(x-3) \\ so,\text{ } \\ 12(x-3)=(y+1)^2 \end{gathered}[/tex]Now,
[tex]\begin{gathered} 4p\mleft(x-h\mright)=\mleft(y-k\mright)^2 \\ \mathrm{\: is\: the\: standard\: equation\: for\: a\: right-left\: facing\: parabola\: with\: vertex\: at}\: \: \\ \mleft(h,\: k\mright),\: \\ \mathrm{and\: a\: focal\: length\: }\: |p| \end{gathered}[/tex]From the initial equation we have
[tex]\begin{gathered} 12(x-3)=(y+1)^2 \\ 4\times3(x-3)=(y-(-1)^2) \\ \text{comparing to }4p(x-h)=(y-k)^2 \\ \text{vertex (h, k) = (-3, -1)} \end{gathered}[/tex]Therefore, the vertex of the parabola is (-3, -1)
(b) The parabola opens at?
Let us see the graph of the parabola
From the image, we can see that the Parabola opens right
(c) The focus
This can be determined using the formula
[tex]\begin{gathered} (h+p,-1) \\ \text{note from above that h = 3 and p = 3} \\ \text{the focus becomes } \\ (3+3,-1) \\ (6,-1) \end{gathered}[/tex]Now, the focus has coordinates (6, -1). Looking at the graph, we can see that from the point x = 6, the focus is 3 units away from the vertex.
(d) The directrix is read from point x = 0.
So, reading from x = 0, from the graph we can see that directrix is 6 units away from thr focus
From our explanation above, we can see that
(e) The focus is the point (6, -1)
(f) And the directrix is
[tex]x=0[/tex]I have this practice question from my ACT prep guide, THE SUBJECT IS PRE CALC!! MEANING ITS HARD AND COMPLEX. Below will be the questions to this problem ( includes 5 questions )1. What is the balance of Albert’s $2000 after 10 years? 2. What is the balance of Marie’s $2000 after 10 years? 3. What is the balance of Han’s $2000 after 10 years?4. What is the balance of Max’s $2000 after 10 years? And lastly, 5. Who is $10,000 richer at the end of the competition?
Albert
Compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where:
A: final amount
P: principal
r: annual interest rate, as a decimal
t: time in years
n: number of times interest applied per year
Substituting with P = $1000, r = 0.012 (= 1.2/100), n = 12 (interest is compounded monthly), t = 10 years, we get:
[tex]\begin{gathered} A=1000(1+\frac{0.012}{12})^{12\cdot10} \\ A=1000(1.001)^{120} \\ A=1127.43\text{ \$} \end{gathered}[/tex]If $500 lost 2%, then it keeps 98% of its original value, that is,
$500x98% = $490
Continuous compound formula:
[tex]A=Pe^{rt}[/tex]where the variables have the same meaning as before.
Substituting with P = $500, r = 0.008 ( = 0.8/100), and t = 10 years, we get:
[tex]\begin{gathered} A=500\cdot e^{0.008\cdot10} \\ A=541.64\text{ \$} \end{gathered}[/tex]The balance of Albert’s $2000 after 10 years is:
$1127.43 + $490 + $541.64 = $2159.07
Marie
Substituting in the compound interest formula with P = $1500, r = 0.014 (= 1.4/100), n = 4 (interest is compounded quartely), t = 10 years, we get:
I need help with this practice problem solving It is trigonometry At the bottom of the picture is the answer options, one answer per box.
First, remember how does the graph of the function f(x) = tan(x) look:
For the inverse of a function to exist, the function has to be an injective function.
A function is injective if it passes the horizontal line test.
Since the function f(x) = tan(x) is periodic and its period is equal to π, its domain must be restricted to an interval of length π in order to pass the horizontal line test.
If we keep the piece of the graph that passes through the origin, we must restrict the domain of the tangent function to the interval (-π/2,π/2) for the function to be injective, and thus for the inverse of the function to be defined.
Therefore, in both cases the answer is:
[tex](-\frac{\pi}{2},\frac{\pi}{2})[/tex]d. 12/1312. Use the unit circle to find cos ( 7 )a.S S/-b.o. 1/2d. -1/2
Step 1
Write the trigonometric expression
[tex]cos(\frac{7\pi}{6})[/tex]Step 2:
Step 3
[tex]cos(\frac{7\pi}{6})\text{ = -cos\lparen}\frac{\pi}{6}\text{\rparen= -cos30}\degree\text{ = -}\frac{\sqrt{3}}{2}[/tex]Final answer
[tex]-\frac{\sqrt{3}}{2}[/tex]Write an equation that best describes the pattern in the table. 12 | 14 | 17 | 19 | 22 6 | 8 | 11 11 | 13 | 16 y у
We need two ordered pairs of the table
(12,6)=(x1,y1)
(14,8)=(x2,y2)
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{8-6}{14-12}=\frac{2}{2}=1[/tex]the equation is
[tex]\begin{gathered} y-6=1(x-12) \\ y=x-12+6 \\ y=x-6 \end{gathered}[/tex]the equation is
y=x-6
Point O is the center of a regular hexagon. Find the image of C given the counter clock-wiserotation of r (120,0)ABFC сEDОЕOFОАOD
ANSWER:
A.
STEP-BY-STEP EXPLANATION:
Because a full turn is a total of 360°, since there are 6 sides, each side represents 60° (360°/6).
They tell us that point C. is rotated counterclockwise 120°.
Therefore, it would be to rotate two sides in that sense counterclockwise, since 120°/60° = 2
If we look closely, the artist who meets these characteristics is A.
What is the solution to the equation k - 4 3/4 = 8 1/4?k = 4 1\2k = 12k = 13k = 4
Answer:
Explanation:
The given equation is
k - 4 3/4 = 8 1/4
The fist step is to convert the mixed number to improper fractions.
4 3/4 = 19/4
8 1/4 = 33/4
Thus, the expression becomes
k - 19/4 = 33/4
Adding 19/4 to both sides, we have
k - 19/4 + 19/4= 33/4 + 19/4
k = 52/4
k = 13
valuate the expression when x = 10. Show your work, and explain each step you take 5x = 152.Evaluate the expression when b = 5 and h = 6. Show your work and explain each step you take 1/2b*h
In the first part, we have the followed expression:
[tex]5x\text{ - 15}[/tex]Wants to know the value of it when x=10, so we just need to substitute the value in the expression, wich gives us:
[tex]5\times(10)\text{ - 15, wich give us the expression: 50 - 15 = 35}[/tex]In the second part, we have the expression:
[tex]\frac{1}{2}b\times h[/tex]And we want to know the value of it when b=5 and h=6, so lets substitute those values in our expression:
[tex]\frac{1}{2}(5)\times(6),\text{ wich gives us, }\frac{1}{2}30\text{ = }\frac{30}{2}\text{ = 15}[/tex]Write the equation in slope-intercept form and then graph the equation that passes through (5, -7) and is parallel to to y = −4x + 3
The slope-intercept form is:
[tex]y=mx+b[/tex]Where m is the slope and b is the intercept.
For two lines to be parallel they have to have the same slope. So a line parallel to
[tex]y=-4x+3[/tex]Has m = -4. So until now we have this equation:
[tex]y=-4x+b[/tex]To find the intercept b we use the given point (5,-7). We just have to replace these values of x and y into the equation above and solve for b:
[tex]\begin{gathered} -7=-4\cdot5+b \\ -7+20=b \\ 13=b \end{gathered}[/tex]So there we have the complete equation of the asked line:
[tex]y=-4x+13[/tex]And the graph is:
of what theorem is theorem 21 the converse?theorem21:if the opposite sides of a quadrilateral are equal then the figure is a parallelogram
Theorem 1:
Opposite Sides Theorem Converse: If both pairs of opposite sides of a quadrilateral are congruent, then the figure is a parallelogram.
What is the missing length? y 16 km area = 144 km y = kilometers
Area = length x width
Area = 144km^2
length = 16km
width = y
144 = 16 x y
y = 144/6 = 26 km
y = 24km
I don’t really need an explanation I just need the answers if you could help me out that would be nice
A' = (3, -1)
B' = (0 -3)
C' = (2, -4)
Explanation:Given:
A = (1, -3)
B = (3, 0)
C = (4, -2)
First we will apply the 90 degrees counterclockwise rotation:
interchange x and y, then negate the new x value
[tex]\begin{gathered} (x,\text{ y) }\rightarrow\text{ (-y, x)} \\ A\text{ becomes: (-(-3), 1) = (3, 1)} \\ B\text{ becomes: (-0, 3) = (0, 3)} \\ C\text{ becomes: (-(-2), }4\text{) = (2, 4)} \end{gathered}[/tex]Next we will apply reflection over the x axis:
negate y coordinate while keeping x coordinate constant
[tex]\begin{gathered} (x,\text{ y) }\rightarrow(x,\text{ -y)} \\ (3,\text{ 1) becomes (3 -1)} \\ A^{\prime}\text{ = (3, -1)} \\ \\ (0,\text{ 3) becomes (0, -3)} \\ B^{\prime}\text{ = (0, -3)} \\ \\ (2,\text{ 4) becomes (2, -4)} \\ C^{\prime}\text{ = (2, -4)} \end{gathered}[/tex]What is the area of the figure? Round to the nearest tenth if necessary. Include units in your answer.
We can think of a hexagon in the next way:
This is, a shape made of 6 smaller triangles. So, we only need to calculate the area of one of those triangles and multiply it by 6
There is something interesting, each of the angles of every one of the triangles is 60°, those are equilateral triangles. So, let's focus on one triangle:
Notice that the blue line is the height of the triangle, that's what we need to find it's are using the formula:
[tex]A(triangle)=\frac{hb}{2}[/tex]So, to calculate the height we use the Pythagoras Theorem
[tex]H^2-O^2=b^2\Rightarrow(20\operatorname{cm})^2-10\operatorname{cm}=b^2\Rightarrow b^2=300\operatorname{cm}\Rightarrow b=10\sqrt[]{3}[/tex]Finally, the area of one of the triangles is:
[tex]A(triangle)=\frac{1}{2}(20cm)(10\sqrt[]{3}cm)=173.2cm^2[/tex]And, by multiplying the previous result by 6, we get the area
[tex]A(hexagon)=6\cdot A(triangle)=6(173.2cm^2)=1039.2\operatorname{cm}[/tex]Rewrite the following expression in exponential form. log, 0.04 = -2 O A. - 25 = 0.04 O B. 5-2=0.04 O c. 50.04 = -2 O D. 0.04 -² = 5 5 SUE PREVIOUS
Answer:
B
What is the term-to-term rule for the following sequences? Solve (A)A) 1,2,3,4,5,6,7,8,…B) 4,9,14,19,24,29,…C) 32,30,28,26,24,22,…D) 6,13,20,27,34,41,…E) 3,6,12,24,48,96,…F) 36,30,24,18,12,6,…G) -13,-11,-9,-7,-5,…H) 48,45,42,39,36,…I) 1,7,49,343,2401,…
A) Given:
The sequence is,
[tex]1,2,3,4,5,6,7,8,…[/tex]To find: The term-to-term rule
Since the given sequence has the common differnce 1.
So, it is of the arithmetic sequence.
Therefore, let us take
[tex]a_1=1[/tex]Then the second term will be,
[tex]\begin{gathered} a_2=a_1+1 \\ =1+1 \\ =2 \end{gathered}[/tex]The third term will be,
[tex]\begin{gathered} a_3=a_2+1 \\ =2+1 \\ =3 \end{gathered}[/tex]And so on.
So, the term to term rule must be,
[tex]a_n=a_{n-1}+1[/tex]Final answer: The term to term rule is,
[tex]a_{n}=a_{n-1}+1[/tex]Question 2 of 15, Step 1CorrectThe value of a machine, V, at the end of years is given by V = C(1 - 1), where is the original cost of the machine and r is the rate of depreciation. A machine thatoriginally cost $19,600 is now valued at $15,528. How old is the machine if r = 0.12? Round your answer to two decimal places.
If C = $19600, V = $ 15528 and r = 0.12, we have:
[tex]\begin{gathered} 15528=19600(1-0.12)^t \\ 15528=19600\cdot0.88^t \\ \frac{15528}{19600}=0.88^t \\ \frac{1941}{2450}=0.88^t \\ log(\frac{1,941}{2,450})=log(0.88^t) \\ log(\frac{1,941}{2,450})=t\cdot log(0.88^) \\ t=\frac{log(\frac{1,941}{2,450})}{log(0.88^)} \\ t=\frac{-0.101}{-0.056} \\ t\approx1.82\text{ years} \end{gathered}[/tex]Solve the y system of inequalities by choosing the correct graph.y> 3y< |x-2|
The solution graph of the system of inequalities : y> 3 and y< |x-2| is attached below.
The given inequalities are:
y>3 and y< |x-2|
Now we will solve y< |x-2|
applying absolute value we get
x - 2 < -y or x - 2 > y
Now we will solve the two equations graphically.
Using the graph we can clearly see that the red part represents the inequality y< | x - 2 | while the blue part denotes the inequality y > 3
Hence the solution of the two inequalities will be the region shaded by both the graphs.
Any monotonically increasing function can, by definition , be applied both for sides of just an inequality without distorting their relationship as long as both expressions fall inside the scope of the function. If a monotonically falling function are applied to both sides of an inequality, the inequality relation might be reversed.
To learn more about inequality visit:
https://brainly.com/question/20383699
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The pilot in a plane is cruising at 4 miles sees a tree. The angle of elevation from the base of the tree to the plane is 40°.
We have to find x.
We can use the trigonometric relations to find the value of x.
We know that, for a right triangle, the sine of an angle is equal to the quotient between the opposite side and the hypotenuse.
In this case, the opposite side of the angle is the height of the plane (4 mi) and the hypotenuse is x, so we can write:
[tex]\begin{gathered} \cos (40\degree)=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{4}{x} \\ x=\frac{4}{\cos (40\degree)}\approx\frac{4}{0.766}\approx5.22 \end{gathered}[/tex]Answer: the value of x is approximately 5.22 miles.
-11b+7=40 how do we solve for b?
We want to find the unknown value b in the following equation
-11b + 7 = 40
Since both sides are the same we can substract 7 both sides and it will be true
-11b + 7 - 7 = 40 - 7
-11b + 0 = 33
-11b = 33
We want to have just b in one side of the equation, we can divide both sides by -11, since they are equal:
-11b = 33
[tex]\begin{gathered} \frac{-11b}{-11}=\frac{33}{-11} \\ 1\cdot b=-3 \\ b=-3 \end{gathered}[/tex]Answer: b = -3Sarah spends of her monthly take-home pay on rent, food, and clothing. If she earns $1,830 in take-home pay each month, how much does she spend on rent, food, and clothing? A$610 B $915 C $990 D $1,220 E $2,745
We have that Sarah spends 2/3 of $1,830 in rent food and clothing
In order to find the money she spends, we just have to divide $1,830 in 3 and multiply the result by 2:
[tex]\begin{gathered} \frac{1830}{3}=610 \\ 610\cdot2=1220 \end{gathered}[/tex]Answer - D. $1,220