Explanation:
We would be applying similar triangles theorem.
If you check the image, there is a small triangle and a big triangle
For similar triangles, the ratio of the corresponding sides are equal.
Trianglke AEB is similar to triangle ECB
AD corresponds to AB
ED corresponds to CB
AD/AB = ED/CB
AD = 8 ft,
AB = AD + DB = 8+24 = 32
ED = 5 ft
CB = ?
Please please please help me
The lines l, m, and n are parallel to each other and the value of x is 8.34.
What are parallel lines?Parallel lines are lines that are equidistant from each other and do not meet no matter how far they extend in either direction. Parallel lines form angles when crossed by a transversal and show some significant properties.
Angles that correspond are equal.Angles that are vertically opposite or vertically angled are equal.Interior angles that are opposite each other are equal.On the same side of the transversal, a pair of interior angles are supplementary.For the given question, we can see that lines l ║m ║n.
Therefore, (6x - 2)° = 52° [Vertically opposite angles are equal]
6x = 52 - 2
6x = 50
x = 50/6
x = 8.34
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a smmall rectangular tray measures 16 cm by 18 cm determine the length of the diagonal . round you're answer to the nearest tenth.m
Given the dimension of the rectangle:
16 cm by 18 cm
We have the image of the rectangle below:
To find the length of the diagonal AC, use pythagorean theorem since ACD form a right triangle.
Thus, we have:
[tex]\begin{gathered} AC^2=AD^2+DC^2 \\ \\ AC=\sqrt[]{AD^2+DC^2} \end{gathered}[/tex]Input values into the formula:
[tex]\begin{gathered} AC=\sqrt[]{18^2+16^2} \\ \\ AC=\sqrt[]{324+256} \\ \\ AC=\sqrt[]{580} \\ \\ AC=24.08\approx24.1\text{ cm} \end{gathered}[/tex]Therefore, the length of the diagonal is 24.1 cm
ANSWER:
24.1 cm
The values of events A, B, and C are provided. Compare the probabilityof event A occurring, given that event C occurred to the probability ofEvent B happening, given that event C occurred (Compare P(A/C) toP(BIC)] Which event is more likely?P(A) = 0.45P(B) = 0.30P(C) = 0.25
The conditional probability P(A/C) is given by
[tex]P(A|C)=\frac{P(A\cap C)}{P(C)}[/tex]If event A is independent to event C, we can write
[tex]P(A|C)=\frac{P(A)\cdot P(C)}{P(C)}=P(A)[/tex]Similary, if event B is independent to event C, we get
[tex]P(B|C)=\frac{P(B)\cdot P(C)}{P(C)}=P(B)[/tex]Then, by comparing both results we can see that event A is more likey than event B.
What function best represents the perimeter of the orange boxes? *
The formula used to calculate the perimeter of a rectangle is given to be:
[tex]P=2l+2h[/tex]FIRST BOX
For the first orange box, we have that:
[tex]\begin{gathered} l=x+x=2x \\ h=2 \end{gathered}[/tex]Note that the box is divided into 2 parts.
Therefore, this perimeter is:
[tex]P_1=2(2x)+2(2)=2(2x)+4[/tex]SECOND BOX
For the second orange box, we have that:
[tex]\begin{gathered} l=x+x+x=3x \\ h=2 \end{gathered}[/tex]Note that the box is divided into 3 parts.
Therefore, the perimeter is:
[tex]P_2=2(3x)+2(2)=2(3x)+4[/tex]Using the associative property of multiplication, we have that:
[tex]P_2=3(2x)+4[/tex]Since x = 5, we have:
[tex]\begin{gathered} P_1=2(10)+4 \\ P_2=3(10)+4 \end{gathered}[/tex]where 2 and 3 are the number of divisions of the boxes.
If we represent the number of divisions with x, we have the perimeter's function to be:
[tex]P=10x+4[/tex]ANSWER
The correct option is the THIRD OPTION.
CheckWhich applies the power of a power rule properly to simplify this expression?(7-8)O (78)4 = 7-8) +(-4) = 7-12 =17121O (7-8)4 = 7(+8)+(-4) = 74 =741O (7-3) = 71-8)(-4) = 7-32 =732O 7-8,4 = 7(-8)(-4) = 72IntroDone
We are given the expression below
[tex](7^{-8})^{-4}[/tex]This expression can be solved by using one of the laws of indices which is denoted below:
[tex](a^m)^n=a^{m\times n}[/tex]Using the above the given expression beocmes
[tex]undefined[/tex]Solve the following system of equation using substitution4x + 2y = 10?/1x - y = 13What is the solution for x?
ANSWER
x = 6
EXPLANATION
The substitution method consists on taking one equation to solve for one variable as a function of the other. Then substitute that variable with the expression we find in the other equation and then solve for that other variable.
In this case, we want to solve for x, so we'll take one of the equations and find y as a function of x. For the second equation:
[tex]\begin{gathered} x-y=13 \\ y=x-13 \end{gathered}[/tex]Now we replace y by x - 13 in the first equation:
[tex]4x+2(x-13)=10[/tex]And solve for x:
[tex]\begin{gathered} 4x+2x-2\cdot13=10 \\ 6x-26=10 \\ 6x=10+26 \\ 6x=36 \\ x=\frac{36}{6} \\ x=6 \end{gathered}[/tex]Find the radius of the circle with a circumference of 39 yards. Round your answer to the nearest hundredth of a yard.the radius of the circle is blank yards
Answer:
6.207
Explanation:
The circumference C of the circle is given by
[tex]C=2\pi r[/tex]where r is the radius.
Now we are given that C = 39 yd; therefore,
[tex]39=2\pi r[/tex]dividing both sides by 2pi gives
[tex]\frac{39}{2\pi}=\frac{2\pi r}{2\pi}[/tex][tex]r=\frac{39}{2\pi}[/tex][tex]r=6.207yd[/tex]Hence, the radius of the circle is 6.207 yards.
What is the component form of resultant of 4b⃗ −2aa = (7 , -5)b = ( -4 , 4)
1) Since we have this expression, let's do it in parts.
[tex]\begin{gathered} 4\langle-4,4\rangle-2\langle7,-5\rangle \\ x-component=4(-4)-2(7)=-16-14=-30 \\ y-component=4(4)-2(-5)=16+10=26 \\ \end{gathered}[/tex]Note that since each vector has two components x, and y. The resultant will be the vector:
[tex]\langle-30,26\rangle[/tex]determine the degree of the polynomial[tex] - 65b + {53x}^{3}y[/tex]
Determine the degree of the polynomial
656+ 3x^3 y
Degree of the polynomial = 4 = (3 + 1)
3x^3 grade (3)
y grade (1)
________________
The degree of the polynomial is 4
100 pts RESPOND QUICK PLS! Planes S and R both intersect plane T . Horizontal plane T intersects vertical planes S and R. Planes T and S intersect at line x. Planes T and R intersect and line y. Horizontal line v intersects line x at point B and line y at point A. Line z intersects the lower half of plane S at point C. Point D is on line z but not on a plane. Which statements are true based on the diagram? Select three options. Plane S contains points B and E. The line containing points A and B lies entirely in plane T. Line v intersects lines x and y at the same point. Line z intersects plane S at point C. Planes R and T intersect at line y.
Answer:
The line containing points A and B lies entirely in plane T.
Line z intersects plane S at point C.
Planes R and T intersect at line y.
Step-by-step explanation:
draw a sketch (see picture)
Plane S contains points B and E. - can't be true - there is no point E
The line containing points A and B lies entirely in plane T. - since lines x and y are both on plane T, and points B and A lie on x and y respectively
Line v intersects lines x and y at the same point. - can only be true IF points A and B are the same point
Line z intersects plane S at point C. - given
Planes R and T intersect at line y. - given
Answer:
The line containing points A and B lies entirely in plane T.
Line z intersects plane S at point C.
Planes R and T intersect at line y.
Step-by-step explanation:
Note: The given diagram does not match the description. Please see the attachment for the correct diagram.
Planes
A plane is a flat, two-dimensional surface that extends into infinity.
A plane can be named by the letters naming three non-collinear points in the plane or by an uppercase script letter.
Parallel planes are planes that never intersect. Intersecting planes are not parallel and always intersect along a line.Statement 1
Plane S contains points B and E.
This statement is untrue, since point E is contained in Plane R and point B is contained in Plane S.
Statement 2
The line containing points A and B lies entirely in plane T.
This statement is true.
Statement 3
Line v intersects lines x and y at the same point.
This statement is untrue since lines x and y are on different planes.
Statement 4
Line z intersects plane S at point C.
This statement is true.
Statement 5
Planes R and T intersect at line y.
This statement is true.
A given circle has an approximate area of 78.5 square units. How long is the circles diameter?
Remember that
The area of a circle is equal to
[tex]A=\pi\cdot r^2[/tex]we have
A=78.5 unit2
I will assume pi=3.14
substitute in the formula
[tex]\begin{gathered} 78.5=3.14\cdot r^2 \\ r^2=\frac{78.5}{3.14} \\ r=5\text{ units} \end{gathered}[/tex]the diameter is two times the radius
so
D=2(5)=10 units
therefore
The diameter is 10 unitsthe ordered pair (2,16) is a solution for which equation(s) check all that apply
We have the following:
We must evaluate each equation (x = 2), if the result is 16 it will be a solution
A.
[tex]y=(2\cdot2)^2=4^2=16[/tex]B.
[tex]y=(2+2)^2=(4)^2=16[/tex]C.
[tex]y=2\cdot2^2=2\cdot4=8[/tex]D.
[tex]y=2\cdot2+2=4+2=6[/tex]Therefore, the correct answer is A and B
the graph represent 1, and the equation represents function 2: function 2: y=8x + 12how much more is the rate of function 2 then the rate of change of function 1?answer choices:a.3b.4c.5d.8
as the graph represent a constant function, we have that the rate for function 1 is 0. The rate for the second function is 8. So we get that the the answer is D
-3x + 5y = -155x - 2y = -101. Find the solution2. Write an equation to replace the second equation so that the system will have infinitely many solutions.
Problem
-3x + 5y = -15
5x - 2y = -10
Solution
For this case we can solve x from the first equation and we got:
3x = 5y +15
x= (5y+15)/3
Now we can replace this value into the second equation and we got:
5((5y+15)/3) -2y = -10
25/3y +25 -2y= -10
And solving for y we got:
(25/3 -2)y =-10-25
19/3 y = -35
y= -105/19
And then we can solve for x and we got:
x= (5*(-105/19) +15)/3 = -80/19
(5n+6)(5n-5) distribute property
We have the following:
[tex](5n+6)\cdot(5n-5)[/tex]we apply distribute property:
[tex]25n^2-25n+30n-30=25n^2+5n-30[/tex]Resultant of the distributive property is 25n² + 5n - 30 .
Given,
(5n+6)(5n-5)
Now,
Distributive property in multiplication : a x (b x c) = (axb) x c
Thus apply the property in the given expression,
(5n+6)(5n-5)
= 25n² - 25n + 30n - 30
Solve the terms with variable n,
= 25n² + 5n - 30
Final expression : 25n² + 5n - 30
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collin noticed that various combinations of the nickels and dimes could add uo to $0.75 let x equal the numver of nickles let y equal the number of dimes what is the domain where y is a function of x and the total value is $0.75
Input data
nickles = 5 cents
dimes = 10 cents
x = number of nickles
y = number of dimes
Write an equivalent expression of 4(6x+12), and state the property you used to write it.
Solution
Using the distributive property
4(6x + 12)
[tex]4(6x+12)=4\times6x+4\times12=24x+48[/tex]how do i do this i need answers help please
SOLUTION:
Step 1:
In Question 8, we have that:
The three vertices of Triangle ABC are located in Quadrant III.
The image of Triangle ABC after a reflection in the x-axis in the x-axis is
[tex]\text{Triangle A}^IB^IC^I[/tex]Then, the triangle
[tex]A^IB^IC^I[/tex]is located in II -- OPTION B
9 divided by 2765 that’s what I’m am asking for
Answer: 307.22222222222 ......
Step-by-step explanation: use the bus stop method to help you
1.) A.) Name the 'item' on which point L exists.B.) If ML= 6x - 4, LH = 10x+1 and MH = 29, find the length of ML.
Now for the point A), L is in the middle of M and H, and the interval will be:
[tex](M,H)[/tex]For the second point, We need to put the value of the segments in the draw...
From the draw, we can deduce that:
[tex]ML+LH=MH[/tex]We replace with values:
[tex]\begin{gathered} ML+LH=MH \\ 6x-4+(10x+1)=29 \end{gathered}[/tex]We solve to x:
[tex]\begin{gathered} 6x-4+(10x+1)=29 \\ 6x\text{ -4 +10x +1=29 ; we agroup the values with x} \\ (6x+10x)-4+1=29 \\ 16x-3=29 \\ 16x=29+3 \\ 16x=32 \\ x=\frac{32}{16}=2 \\ x=2 \end{gathered}[/tex]Finally, if the value of x = 2, then whi can replace in:
[tex]\begin{gathered} ML=6x-4 \\ ML=6(2)-4 \\ ML=12-4 \\ ML=8 \end{gathered}[/tex]Your answer of point B) is ML=8.
What is the system of inequalities associated with the following graph?A) {y<−1x {+y>1 B) {y>−1 {x+y≥1 C) {y<−1 {x+y≥1 D) {y < -1 {x + y <1
SOLUTION:
Step 1:
In this question, we are given the following:
What is the system of inequalities associated with the following graph?
Step 2:
The details of the solution are as follows:
CONCLUSION:
The final answer is:
C) {y<−1
{x+y≥1
y=-2xy=x-8how do you do this
Separate
y =- 2xy
-2xy = x - 8
Now solve first equation
and then second equation
PART2
y = -2x
y= -4x + 10
Is solved by , substracting both equations
Then
(y - y) = -2x - ( -4x + 10)
0 = -2x + 4x - 10
10 = 2x
10/2= xx
From a point x = 80 feet in front of a public library, the angles of elevation to the base of the flagpole and the top of the flagpole are = 29.5° and 39° 45', respectively. The flagpole is mounted on the front of the library's roof. Find the height of the flagpole.
Let's draw the scenario to better understand the details.
To be able to determine the height of the flagpole, let's create two different triangles with 29.5° and 39° 45' angle. The two triangles have one common base at 80 Feet, yet have different heights at H+h and H respectively.
Where,
H = Height of the library
h = Height of the flag
The two triangles are proportional at a common base, thus, let's generate this expression using the Law of Sines:
[tex]\frac{H+h}{\sin(39\degree45^{\prime})}\text{ = }\frac{H}{\sin(29.5^{\circ})}[/tex]Let's simplify,
[tex]\frac{H+h}{\sin(39\degree45^{\prime})}\text{ = }\frac{H}{\sin(29.5^{\circ})}\text{ }\rightarrow\text{ (}H+h)(\sin (29.5^{\circ}))\text{ = (H)(}\sin (39\degree45^{\prime}))[/tex][tex]H\sin (29.5^{\circ})\text{ + h}\sin (29.5^{\circ})\text{ = H}\sin (39\degree45^{\prime})\text{ ; but }29.5^{\circ}=29^{\circ}30^{\prime}[/tex][tex]H\sin (29^{\circ}30^{\prime})\text{ + h}\sin (29^{\circ}30^{\prime})\text{ = H}\sin (39\degree45^{\prime})[/tex][tex]\text{h}\sin (29^{\circ}30^{\prime})\text{ = H}\sin (39\degree45^{\prime})\text{ - }H\sin (29^{\circ}30^{\prime})[/tex][tex]\text{ h(}0.4924235601)\text{ = H(0.63943900198) -H}(0.4924235601)[/tex][tex]\text{ h(}0.4924235601)\text{ = H(0.14701544188)}[/tex][tex]undefined[/tex]
Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. Not drawn to scale x= 6.9, y = 5.7 x=8, y = 11.3 x 11.3, y = 8 x = 5.7, y = 6.9
x=11.3 y=8
Explanationhere we have a right triangle, so we can use a trigonometric function to find the missing sides
so
Step 1
a)let
[tex]\begin{gathered} angle=45\text{ \degree} \\ opposite\text{ side=8} \\ adjacent\text{ side=y} \\ hypotenuse=x \end{gathered}[/tex]Step 2
now, fin the missing length
a) y
to find the adjacent side we can use the stan function
[tex]tan\theta=\frac{opposite\text{ side}}{adjacent\text{ side}}[/tex]replace and solve for y( adjacent side)
[tex]\begin{gathered} tan45=\frac{8}{y} \\ y=\frac{8}{tan\text{ 45}}=\frac{8}{1} \\ y=8 \end{gathered}[/tex]b)x (hypotenuse)
to find the hyoptenuse we can use the sin function ,
[tex]\sin\theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]replace and solve for x
[tex]\begin{gathered} sin\text{ 45=}\frac{8}{x} \\ x=\frac{8}{sin\text{ 45}}=11.3 \\ x=11.3 \end{gathered}[/tex]therefore, the answer is
x=11.3 y=8
I hope this helps you
On (07.03) Choose the correct simplification of the expression b5.54. (1 point)
explanation/ Working:
[tex]c^2.c^9=c^2\times c^9=c^{2+9}=c^{11}[/tex]Rule on iindex says when the base is same, you should add the powers
[tex]c^2.c^9=\text{ (c}\times c)\times(c\times c\times c\times c\times c\times c\times c\times c\times c)=c^{11}[/tex]help!!! i’ll mark brainliest!!!
For the given diagram, both the triangles are congruent that is ΔLKM ≅ ΔJKM by using theorem of ASA ( Angle side Angle).
As given in the question,
In the given diagram of the triangles,
Given : ∠LKM ≅ ∠JKM
∠LMK ≅ ∠JMK
To prove : ΔLKM ≅ ΔJKM
∠LKM ≅ ∠JKM ( given )
∠LMK ≅ ∠JMK ( given )
KM ≅ KM ( using reflexive property of congruence )
By applying ASA theorem ( Angle Side Angle )
ΔLKM ≅ ΔJKM
Therefore, for the given diagram, both the triangles are congruent that is ΔLKM ≅ ΔJKM by using theorem of ASA ( Angle side Angle).
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The age of the Earth is inferred from the-A. age of the uranium -235B. age of the Grand CanyonC. age of the Canyon Diablo meteoriteD. age of dinosaurs
The age of the Earth is inferred from the - age of the Canyon Diablo meteorite .
To find : The age of the Earth
Age - Age is defined as the length of time during which a thing or being existed .
a ) the half life of age of uranium-238 , uranium's most abundant and longest-lived isotope is approximately 4.47 billion years ago .
b ) the age of Grand Canyon is 1.8 billion years ago .
c ) The fragment of the Canyon Diablo meteorite determined the elements that formed as radioactive uranium decayed over billions of years.
d ) age of dinosaurs was about 252 million to about 66 million years ago .
Hence , c ) age of the Canyon Diablo meteorite .
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Miss Johnson has a tree in her garden that grows apples in the spring and summer the tree has a diameter of 32 ft from its base what is the circumference of that tree in Miss John's Garden
We know that the circunference of a circle is:
[tex]C=2D[/tex]where D is the diameter so the circunference will be:
[tex]\begin{gathered} C=2\cdot32 \\ C=64 \end{gathered}[/tex]I require assistance on a troubling problem
Given data:
The given table.
The standard expression for the exponential function is,
[tex]y=a(b)^x[/tex]Substitute o for x and 5 for y in the above expression.
[tex]\begin{gathered} 5=a(b)^0 \\ 5=a \end{gathered}[/tex]Substitute 1 for x, 15 for y, and 5 for a in the standard exponential expression.
[tex]\begin{gathered} 15=5(b)^1 \\ b=3 \end{gathered}[/tex]The exponential expression can be written as,
[tex]y=5(3)^x[/tex]Thus, the expression for the exponential function is y=5(3)^x.
A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus sine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?
The springs from the original pogo stick and the toddler's pogo stick length are equal after 1 second and 0.9994 second.
Explanation:The given functions are:
[tex]\begin{gathered} f(\theta)=2\cos \theta+\sqrt[]{3} \\ g(\theta)=1-\sin ^2\theta+\sqrt[]{3} \end{gathered}[/tex]The springs from the original pogo stick and the toddler's pogo stick length are equal when both functions coincide
That is;
[tex]\begin{gathered} f(\theta)=g(\theta) \\ \Rightarrow2\cos \theta+\sqrt[]{3}=1-\sin ^2\theta+\sqrt[]{3} \end{gathered}[/tex]Solving the equation, we have:
[tex]\begin{gathered} 2\cos \theta+\sqrt[]{3}=1-\sin ^2\theta+\sqrt[]{3} \\ Subtract\sqrt[]{3}\text{ from both sides} \\ 2\cos \theta=1-\sin ^2\theta \end{gathered}[/tex]Note the identity below:
[tex]\begin{gathered} \cos ^2\theta+\sin ^2\theta=1 \\ \cos ^2\theta=1-\sin ^2\theta \end{gathered}[/tex]This means
[tex]\begin{gathered} 2\cos \theta=\cos ^2\theta \\ \cos ^2\theta-2\cos \theta=0 \\ \cos \theta(\cos \theta-2)=0 \\ \cos \theta=0 \\ \Rightarrow\theta=\cos ^{-1}(0)=1 \\ \\ OR \\ \cos \theta-2=0 \\ \cos \theta=2 \\ \theta=\cos ^{-1}(2)=0.9994 \end{gathered}[/tex]The springs from the original pogo stick and the toddler's pogo stick length are equal after 1 second and 0.9994 second.