Which pairs of triangles can be shown to be congruent using rigid motions?
Select Congruent or Not Congruent for each pair of triangles.
Answers
Answer:
Congruent; Not Congruent; Congruent; Not Congruent; Not Congruent; Congruent
Step-by-step explanation:
We will use the distance formula to find the length of each segment:
[tex]AB=\sqrt{(-4--3)^2+(4-2)^2}=\sqrt{(-1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5}\\\\BC=\sqrt{(-3--1)^2+(4-1)^2}=\sqrt{(-2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}\\\\AC=\sqrt{(2-1)^2+(-4--1)^2}=\sqrt{(1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}[/tex]
In order for ABC to be congruent to DEF, AB must be congruent to DE, BC must be congruent to EF, and AC must be congruent to DF:
[tex]DE=\sqrt{(4-3)^2+(-2--4)^2}=\sqrt{(1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5}\\\\EF=\sqrt{(3-1)^2+(-4--1)^2}=\sqrt{(2)^2+(-3)^2}=\sqrt{4+9}=\sqrt{13}\\\\DF=\sqrt{(4-1)^2+(-2--1)^2}=\sqrt{(3)^2+(-1)^2}=\sqrt{9+1}=\sqrt{10}[/tex]
Since AB is congruent to DE, BC is congruent to EF and AC is congruent to DF, the two triangles are congruent.
In order for ABC to be congruent to JKL, AB must be congruent to JK, BC must be congruent to KL, and AC must be congruent to JL. We know the measurements of AB, BC and AC;
[tex]JK=\sqrt{(-4--2)^2+(-1--3)^2}=\sqrt{(-2)^2+(2)^2}=\sqrt{4+4}=\sqrt{8}\\\\KL=\sqrt{(-2--1)^2+(-3-0)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}\\\\JL=\sqrt{(-1--4)^2+(0--1)^2}=\sqrt{(3)^2+(1)^2}=\sqrt{9+1}=\sqrt{10}[/tex]
While AC is congruent to JL, the other two corresponding pairs of sides are not congruent. Therefore the triangles are not congruent.
In order for ABC to be congruent to QRS, AB must be congruent to QR, BC must be congruent to RS, and AC must be congruent to QS. We know the measurements of AB, BC and AC;
[tex]QR=\sqrt{(3-4)^2+(3-1)^2}=\sqrt{(-1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5}\\\\RS=\sqrt{(3-1)^2+(3-0)^2}=\sqrt{(2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}\\\\QS=\sqrt{(4-1)^2+(1-0)^2}=\sqrt{(3)^2+(1)^2}=\sqrt{9+1}=\sqrt{10}[/tex]
Since AB is congruent to QR, BC is congruent to RS, and AC is congruent to QS, this means that the two triangles are congruent.
Since ABC is congruent to DEF, and ABC is not congruent to JKL, this means that triangle DEF is not congruent to triangle JKL.
Since ABC is congruent to QRS, and QRS is not congruent to JKL, this means that triangle QRS is not congruent to JKL.
Since ABC is congruent to DEF and ABC is congruent to QRS, this means that DEF is congruent to QRS by the transitive property.
Related Questions
A cardboard box has a square base and an open top. the four sides are made of wood that costs 2 dollars per square foot, while the base is made of aluminum that costs 25 dollars per square foot. if the volume of the box is to be 50 cubic feet, what is its minimum possible cost?
Answers
Answer:
$300
Step-by-step explanation:
Let x represent the side length of the square base in feet. Then the height of each side is ...
... h = (50 ft³)/(x ft)² = (50/x²) ft
The cost of the sides of the box is then ...
... (4 sides) × (x ft)(50/x² ft)/side × $2/ft² = $400/x
The cost of the bottom is ...
... (x ft)² × $25/ft² = $25x²
So, the total dollar cost is
... C = 400/x + 25x²
This will be a minimum where its derivative with respect to x is zero.
... 0 = -400/x² +50x
... 400/50 = 8 = x³ . . . . . add 400/x²; multiply by x²/50
... x = ∛8 = 2
For this value of x, the minimum cost is ...
... C = 400/2 + 25·2² = 300
The minimum possible cost is $300.
_____
Comments on the problem
1) Cardboard boxes are usually made of cardboard. They are rarely made of wood and alumninum.
2) The cost of the bottom is half the cost of the sides. When the dimensions are unconstrained, you will find (as here) the cost is shared equally between the bottom and pairs of opposite sides—each being 1/3 the total cost.
Find all the zeros of the equation x^4-6x^2-7x-6=0 Explain please.
Answers
I like to look at a graph of the function to see where the zeros might be. Here, there are x-intercepts at x=-2 and x=3. These can be factored out using synthetic division to find the factorization to be ...
... (x +2)(x -3)(x² +x +1) = 0
By completing the square, using the quadratic formula, or by looking at the graph of it, the complex roots of the quadratic factor can be found to be ...
... x = (-1 ±i√3)/2
_____
The second attachment shows my synthetic division. The first division takes out the root x=3 to give a quotient of x³ +3x² +3x +2. The second division takes out the root -2 to give the quotient of x² +x +1. (You can see that I tried -1 as a root first.)
The graph shows both the quartic and the quadratic factor of it. The latter has a leading coefficient of 1 and a vertex at (-1/2, 3/4), so you know the complex roots are -1/2 ±i√(3/4).
_____
From the beginning
There is only a very complicated formula for the roots of a quartic equation, so these are usually solved by machine or by some form of trial and error (iteration). There are some helps, like Descarte's Rule of Signs, and the Rational Root theorem.
Here, the former looks at the one sign change in the coefficients to tell you there will be 1 positive real root. Changing the sign of the odd-degree terms makes there be 3 sign changes, so there will be 3 or 1 negative real roots. Thus, we're assured at least two real roots, one of each sign.
We can look at the constant term to find the y-intercept to be -6. We can add the coefficients to find the value of the function is -18 for x=1, so the positive real root is larger than 1.
The Rational Root theorem says any rational roots will be factors of 6, the constant term. Choices are 1, 2, 3, 6. We have already eliminated 1 as a possibility, and we consider it unlikely that 6 will be a root. (The 4th power overwhelms the other terms in the function.) We tried 2 and found it doesn't work (this was before we graphed the function). The attached division result shows that 3 is a root, as does the graph.
Once you get down to a quadratic, you can find the remaining roots in the usual way. Because it is so simple to read them from the graph, we decided to graph the quadratic factor.
_____
Comment on terminology
"root" and "zero" are essentially the same thing when the function is equated to zero, as here. The terms refer to the value(s) of x that make the polynomial function evaluate to zero.
To find the zeros of the equation x^4-6x^2-7x-6=0, we can apply the rational root theorem and synthetic division. By trying different factors of the constant term -6, we can determine that one of the roots is x = -2. After dividing the equation by (x + 2), we obtain a quadratic equation x^3 - 2x^2 - 11x + 3 = 0. We can then solve this equation by factoring or using a graphing calculator to find the remaining two roots.
Explanation:To find the zeros of the equation x^4-6x^2-7x-6=0, we can apply the rational root theorem and synthetic division. By trying different factors of the constant term -6, we can determine that one of the roots is x = -2. After dividing the equation by (x + 2), we obtain a quadratic equation x^3 - 2x^2 - 11x + 3 = 0. We can then solve this equation by factoring or using a graphing calculator to find the remaining two roots.
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The total revenue for Fred's Estates LLC is given as the function R(x)=200x−0.4x2, where x is the number of rooms booked. What number of rooms booked produces the maximum revenue?
Answers
The number of rooms booked to produce maximum revenue is required.
The number of rooms booked to produce the maximum revenue is 250.
The revenue function is
[tex]R(x)=200x-0.4x^2[/tex]
Differentiating with respect to x we get
[tex]R'(x)=200-0.8x[/tex]
Equating with zero
[tex]0=200-0.8x\\\Rightarrow x=\dfrac{-200}{-0.8}\\\Rightarrow x=250[/tex]
Double derivative of the function is
[tex]R''(x)=-0.8x[/tex]
Substituting the value of [tex]x=250[/tex]
[tex]R''(250)=-0.8\times 250=-200[/tex]
Since, it is negative the maximum value of x will be 250.
The number of rooms booked to produce the maximum revenue is 250.
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The number of rooms that produces the maximum revenue for Fred's Estates LLC is 250 rooms, calculated using the formula -b/2a, where a and b are the coefficients of the quadratic revenue function.
Explanation:To calculate the maximum revenue for Fred's Estates LLC, we need to find the value of x that maximizes the function [tex]R(x)=200*-0.4x2.[/tex]
The maximum value of a quadratic function can be found using the formula -b/2a, where a and b are the coefficients of x² and x in the function. Here, a=-0.4 and b=200.
Using the formula, [tex]x=-b/2a = -200/(2*(-0.4)) = 250[/tex] rooms. Therefore, booking 250 rooms results in the maximum revenue for Fred's Estates LLC.
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Jim needs to rent a car. A rental company charges $21.00 per day to rent a car and $0.10 driven. for every mile . He will travel 250 miles. . He has $115.00 to spend. Write an inequality that can be used to determine d, the maximum number of days that Jim can re ays that Jim can rent a car
Answers
Answer:
21d +25 ≤ 115
Step-by-step explanation:
Jim's cost will be ...
... 21.00·d + 0.10·250 = 21d +25
He wants his cost not to exceed his budget, so ...
... 21d +25 ≤ 115
_____
The solution is ...
... 21d ≤ 90 . . . . subtract 25
... d ≤ 90/21 ≈ 4.3
so Jim can rent the car a maximum of 4 days.
The inequality that can be used to express this scenario is
115 ≤ 21*d+ 25
Given data
Charges = $21 per day
Cost per driven distance = $0.10
Distance he will travel = 250 miles
Amount her has to spend = $115
Let the maximum number of days Jim can rent a car with $115 be "m"
Hence
Total amount = 21*d+ 0.1*250
Substituting and Simplifying we have
115 ≤ 21*d+ 25
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what is the solution to the equation -0.2(x-20)=4-x
Answers
Answer:
x=0
Step-by-step explanation:
-0.2(x-20)=4-x
The first step is to distribute the -.2
-.2 x -.2 * -20 = 4-x
-.2x +4 = 4-x
Add x to each side
x-.2x +4 = 4-x+x
.8x +4 = 4
Subtract 4 from each side
.8x +4-4 = 4-4
.8x=0
Divide by .8
.8x/.8 = 0/.8
x =0
I WILL MAKE YOU THE BRAINLIEST EASY QUESTION For the visual model below, draw lines dividing each individual section into two equal parts. Then write a fraction representing the revised visual model. Do not reduce or simplify the fraction.
Answers
Answer:
see attached
Step-by-step explanation:
Each of the pie slices can be cut in half different ways. An easy way to do it and to understand it is to draw another cut from the center to the middle of the edge.
The result of cutting these slices is that instead of 8 equal pieces (of which 3 are colored), there will be 16, of which 6 are colored.
The new fraction is 6/16.
What is the point slope form of the line with slope -3/7 that passes through the point (5, 8)?
Answers
ANSWER:
Your answer is the 3rd one: y - 8 = -3/7(x - 5)
ABOUT POINT SLOPE FORM:
y - Y1 = m (x - X1)m is the slopeY1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineABOUT PROBLEM:
-3/7 represents m in the slope intercept form5 represents X18 represents Y1y - Y1 = m (x - X1)
y - 8 = -3/7(x - 5) --- IN POINT SLOPE FORM
Hope this helps you!!! :)
The line with a slope -3/7 and passes through the point (5, 8) has an equation of y - 8 = (-3/7)(x - 5)
The equation of a straight line is given by:
y = mx + b;
where y,x are variables, m is the slope of the line and b is the y intercept.
Since the line has a slope -3/7 and passes through the point (5, 8), the equation of the line is:
[tex]y-y_1=m(x-x_1)\\\\y-8=-\frac{3}{7} (x-5)[/tex]
Hence a line with a slope -3/7 and passes through the point (5, 8) has an equation of y - 8 = (-3/7)(x - 5)
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how many tables will be needed to seat 65 people if each table seats 7 people
Answers
so it's will be 10.
Answer:
10 tables are needed to seat 65 people.
Step-by-step explanation:
Given :
There are total 65 people.
7 people can be seated on each table .
To Find : No. of tables required to seat 65 people.
Solution :
Since 7 people can sit on no. of tables = 1
1 people sit on no. of tables = 1/7
65 people sit on no. of tables
= [tex]\frac{1}{7} *65[/tex]
⇒ [tex]9.28[/tex]
⇒ 9.28 ≈ 10 tables are needed to seat 65 people.
Thus 10 tables are needed to seat 65 people.
jim leaves his house traveling at 200 feet per hour, he wants to travel 400 yards to get to 4:00pm. How many hours does he need to travel? Answer and explain your answer.
I'm giving brainliest for the best answer.
A. 2 hours
B. 4 hours
C. 5 hours
D. 6 hours
Answers
Answer:
D. 6 hours
Step-by-step explanation:
There are 3 ft in 1 yd, so 400 yd = 1200 ft.
At 200 ft/h, Jim's travel time for 1200 ft will be
... time = distance/speed = (1200 ft)/(200 ft/h) = (1200/200) · ft · (h/ft)
... time = 6 h
Which line shows the first error in the solution?
A number divided by 3 is four more than -11. What is the number?
x/ + 4 = -11 (1)
x/3 + 4 -4 = -11 -4 (2)
x/3 = -15 (3)
x/3 x 3 = -15 x 3 (4)
x = -45 (5)
A. Line
B. Line 3
C. Line 4
D. Line 2
Answers
The first line.
Step-by-step explanation:If we let x represent "a number", then "a number divided by 3" is x/3. The denominator is missing on the first line.
Further, this "is 4 more than -11", so is = 4 + (-11). The constant 4 is on the wrong side of the equal sign in line 1.
_____
The solution should be ...
... x/3 = 4 + (-11)
... x = 3·(-7)
... x = -21
___
Check
-21 divided by 3 is -7. That is 4 more than -11.
A farmer wants to build a fence enclosing a rectangular region bordering a river. If the farmer has 500 feet of fencing, find the maximum area that can be enclosed.
Answers
Answer:
31,250 ft²
Step-by-step explanation:
Let x represent the length of fence parallel to the river. Then the ends of the rectangle will have dimesion (500-x)/2, and the total area will be ...
... A = x(500-x)/2
This function describes a parabola with zeros at x=0 and x=500. The vertex (maximum) will be located halfway between these, at x=250.
The maximum size pen has area ...
... A = 250(500 -250)/2 = 31,250 . . . . sq ft
Operations with Complex Numbers
Answers
Answer:
B. -9/4 -4i
Step-by-step explanation:
Collect terms the way you would with any algebraic expression.
= (-3 +2 -3)i + (3/4 -3)
= -4i +(3/4 -12/4)
= -9/4 -4i
The product of the complex numbers [tex]\( (3 - 2i) \)[/tex] and [tex]\( (1 + i) \)[/tex] is [tex]\( 5 - 4i \)[/tex].
To find the product of two complex numbers, we multiply them as we would with binomials, remembering that [tex]\( i^2 = -1 \)[/tex]. Let's perform the multiplication step by step:
Given complex numbers [tex]\( (3 - 2i) \)[/tex] and [tex]\( (1 + i) \)[/tex], we multiply them directly:
[tex]\[(3 - 2i) \cdot (1 + i) = 3 \cdot 1 + 3 \cdot i - 2i \cdot 1 - 2i \cdot i. \][/tex]
Now, we simplify the expression by combining like terms and using the fact that [tex]\( i^2 = -1 \)[/tex]:
[tex]\[ = 3 + 3i - 2i - 2i^2 = 3 + i - 2(-1) = 3 + i + 2. \][/tex]
Finally, we combine the real parts and the imaginary parts:
[tex]\[ = (3 + 2) + i = 5 - 4i. \][/tex]
Therefore, the product of the complex numbers [tex]\( (3 - 2i) \)[/tex] and [tex]\( (1 + i) \)[/tex] is[tex]\( 5 - 4i \)[/tex].
A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. A cylindrical hole cut out of the center has a radius of 6 millimeters.Which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? Check all that apply.
options:
21π(10)2 – 21π(6)2
π(20)2(21) – π(6)2
2,100π – 756π
7,644π
1,344
Answers
The volume of metal is the difference of the overall volume of the cylinder and the volume of the hole in it. The formula for the volume of a cylinder is ...
... V = π·r^2·h . . . . . radius r and height h
For the overall dimensions, the radius is half the diameter, so is 10 mm. The hole is said to have a radius of 6 mm. The overall "height" is 21 mm, so the volume in mm³ will be ...
... V_overall -V_hole = π(10)^2(21) -π(6)^2(21)
... = 21π·10^2 -21π·6^2 . . . . . . . matches the first selection
... = 2100π -756π . . . . . . . . . . . matches the third selection
... = 1344π . . . . . . . . . . . . . . . . doesnt' match any selection
The correct expressions for the volume of metal needed, in cubic millimeters, to make the pipe are,
⇒ 21π(10)² – 21π(6)²
⇒ 2,100π – 756π
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters.
And, A cylindrical hole cut out of the center has a radius of 6 millimeters.
Hence, The formula for the volume of a cylinder is,
V = π·r²·h
Where, radius r and height h.
Now, For the overall dimensions, the radius is half the diameter, so is 10 mm. The hole is said to have a radius of 6 mm. The overall "height" is 21 mm,
so the volume in mm³ will be;
V (overall) -V (hole) = π(10)²(21) -π(6)²(21)
= 21π·10² -21π·6²
= 2100π -756π
= 1344π
Thus, The correct expressions for the volume of metal needed, in cubic millimeters, to make the pipe are,
⇒ 21π(10)² – 21π(6)²
⇒ 2,100π – 756π
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Mrs.Wheeler is looking to make a deposit of $2500 dollars into the savings account
that earns simple interest at a rate of 2.02% per year. How many years will it take for her account to reach $3000 if she does not deposit or withdraw any money.
Answers
9.9 years
Step-by-step explanation:A = P(1 + rt) . . . . account balance after time t at rate r starting with principal P
... 3000 = 2500(1 + 0.0202t) . . . . filling in the given numbers
... 1.2 = 1 + 0.0202t . . . . divide by 2500
... 0.2 = 0.0202t . . . . . . subtract 1
... 0.2/0.0202 = t ≈ 9.901
It will take about 9.9 years for the account balance to reach $3000.
tomas wrote an equation 4/5x-8=. Finish the equation so that the equation will have no solution. Explain how you know.
Answers
Answer:
Right part: [tex]\dfrac{4}{5}x+a,[/tex] where [tex]a\neq -8.[/tex]
Step-by-step explanation:
Linear equation have no solution if it is impossible for the equation to be true no matter what value we assign to the variable x.
The left part of the equation Tomas wrote is
[tex]\dfrac{4}{5}x-8.[/tex]
The right part of the equation should be of the form
[tex]\dfrac{4}{5}x+a,[/tex]
where [tex]a\neq -8.[/tex]
In this case, the equation will take look
[tex]\dfrac{4}{5}x-8=\dfrac{4}{5}x+a,\\ \\-8=a.[/tex]
Since [tex]a\neq -8,[/tex] this equality is always false.
Remark: 1) If a=8, the equation [tex]\dfrac{4}{5}x-8=\dfrac{4}{5}x+a[/tex] is equivalent to the equation
[tex]\dfrac{4}{5}x-8=\dfrac{4}{5}x-8,\\ \\0=0[/tex]
and the lest equation has infinitely many solutions.
2) When coefficient at x differs from [tex]\dfrac{4}{5},[/tex] the equation has unique solution.
300 bears were out of hibernation. after 2 years, the population grew to 381 bears. if the population continues to grow how many bears will there be in 10 years?
Answers
Answer:
561 because if you multiple 300 /8 times the number of the before populaiton u got it right Step-by-step explanation:
(7x^3y^2)(4x^3y^2)
^=exponents
solve in scientific Notation
Answers
(2.8×10¹)x⁶y⁴
Step-by-step explanation:Multiplication can be done in the usual way, then the number converted to scientific notation. Scientific notation does not apply to the variables.
[tex](7x^3y^2)(4x^3y^2)=(7\cdot 4)x^{3+3}y^{2+2}=28x^6y^4\\\\=2.8\cdot 10^1x^6y^4[/tex]
_____
If you write the numbers in scientific notation to start, then do the multiplication, the effect is virtually the same: an adjustment is needed in the product to get it back to scientific notation.
(7)(4) = (7×10⁰)(4×10⁰) = 7·4×10⁰⁺⁰ = 28×10⁰ = 2.8×10¹
Find the values of x and y that satisfies the equation.
5x + 3i = 15 + yi
Answers
Answer:
So the value of x=3 and y =3
Step-by-step explanation:
5x + 3i = 15 + yi
To find out x , set the constant terms equal to each other and solve for x
5x= 15
Divide by 5 on both sides
x= 3
To find out y , set the ';i' terms equal to each other and solve for y
3= y
So the value of x=3 and y =3
Answer: The required value of x is 3 and that of y is 3.
Step-by-step explanation: We are given to find the values of x and y that satisfies the following equation :
[tex]5x+3i=15+yi~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
[tex]a+bi=c+di~~~~~~~~~\Rightarrow a=c,~b=d.[/tex]
That is, the real and parts on both sides of the equation are equal.
From equation (i), we have
[tex]5x+3i=15+yi.[/tex]
Equating the real and imaginary parts on both sides of the above equation, we get
[tex]5x=15\\\\\Rightarrow x=\dfrac{15}{5}\\\\\Rightarrow x=3[/tex]
and
[tex]3=y\\\\\Rightarrow y=3.[/tex]
Thus, the required value of x is 3 and that of y is 3.
In one year, a bird farm sold 375 total chickens. of these, there were 37 more Cornish hens than turkeys. How many Cornish hens and how many turkeys were sold?
Answers
Answer:
206 Cornish hens
169 turkeys
Step-by-step explanation:
Let c represent the number of Cornish hens sold. Then c-37 is the number of turkeys sold. The total sales would be ...
... c + (c-37) = 375
... 2c = 412 . . . . collect terms, add 37
... c = 206 . . . . Cornish hens sold
... (c-37) = 169 . . . turkeys sold
_____
Comment on this type of problem
Note that the solution to this problem is that the larger number (number of cornish hens) is half the sum of the total and the difference: (375+37)/2 = 206. This is the general solution for this type of "sum and difference" problem.
The larger contributor is half the total plus half the difference; the smaller contributor is half the total minus half the difference.
Cornish hens = (1/2)(375 +37) = 206
Turkeys = (1/2)(375 -37) = 169
what is the solution to the system of equations?
Answers
First choice: using the first equation, -3(-3)-4(4)+6=-19 not -1 as listed. False.
Second choice: using the first equation, -3(4)-4(-3)+(-1)=-1 ; using the second equation, 2(4)+(-3)-(-1)=6 not -8 as listed. False.
Third choice: using the first equation, -3(-3)-4(4)+8=-17 not -1 as listed. False.
Fourth choice: using the first equation, -3(3)-4(-4)+-(-6)=-1 ; using the second equation,
2(3)+(-4)-(-6)=8 ; using the third equation, 3+8(-4)-(-6)=23
So the answer should be the fourth choice. Hope this helps! :)
In a trapezoid the lengths of bases are 11 and 18. The lengths of legs are 3 and 7. The extensions of the legs meet at some point. Find the length of segments between this point and the vertices of the greater base.
Answers
Answer:
[tex]AS=18\ units,\ DS=\dfrac{54}{7}\ units.[/tex]
Step-by-step explanation:
Consider trapezoid ABCD with bases BC=11 units and AD=18 units. The lengths of legs are AB=7 units and CD=3 units. Point S is the point of intersection of the extensions of the legs AB and CD.
Let BS=x units and CS=y units.
Consider triangles BSC and ASD. By AAA theorem these triangles are similar (because ∠SAD≅∠SBC, ∠ADS≅∠BCS and ∠S is common).
Then
[tex]\dfrac{BS}{AS}=\dfrac{CS}{DS}=\dfrac{BC}{AD},\\ \\\dfrac{x}{x+7}=\dfrac{y}{y+3}=\dfrac{11}{18}.[/tex]
Therefore,
[tex]\dfrac{x}{x+7}=\dfrac{11}{18},\\ \\18x=11(x+7),\\ \\18x=11x+77,\\ \\7x=77,\\ \\x=11\ units.[/tex]
[tex]\dfrac{y}{y+3}=\dfrac{11}{18},\\ \\18y=11(y+3),\\ \\18y=11y+33,\\ \\7y=33,\\ \\y=\dfrac{33}{7}\ units.[/tex]
The lengths of segments between point S and the vertices of the greater base are
[tex]AS=AB+BS=7+11=18\ units,\ DS=DC+CS=3+\dfrac{33}{7}=\dfrac{54}{7}\ units.[/tex]
Can someone please answer this for me i cant figure it out.
Answers
[tex]\displaystyle x^{\frac{2}{3}}[/tex]
Step-by-step explanation:The rules of exponents tell you ...
... (a^b)(a^c) = a^(b+c) . . . . . . applies inside parentheses
... (a^b)^c = a^(b·c) . . . . . . . . applies to the overall expression
The Order of Operations tells you to evaluate inside parentheses first. Doing that, you have ...
... x^(4/3)·x^(2/3) = x^((4+2)/3) = x^2
Now, you have ...
... (x^2)^(1/3)
and the rule of exponents tells you to multiply the exponents.
... = x^(2·1/3) = x^(2/3)
Answer:
x^(2/3)
Step-by-step explanation:
(x^a.x^b)^c = x^[c*(a+b)]
using the above eqn, u can simplify the given expression to
x^[1/3*(4/3+2/3)]
=x^[1/3*(6/3)]
=x^(2/3)
ans is the 2nd choice
To the nearest whole degree, what angle measure has a tangent of 2.0874?
Answers
[tex] { \tan }^{ - 1} (2.0874)[/tex]
You may need to hit the second button on your calculator to get this function.
Your answer turns up to be 64.402~~~~.
Rounded, the answer is 64 degrees.
Hope this helps!
:)
Derek established his own retirement account 10 years ago. He has discovered that he can obtain a better rate for the next 10 years at 12 percent interest compounded semiannually. Consequently, Derek established a new ordinary annuity account (beginning amount $0.00) and he will contribute $7,000.00 semiannually into the account for the next 10 years. What will be the value of this account at the end of the 10-year period?
$83,652.59 $244,707.61 $257,502.00 $264,501.86
Answers
Answer:
https://brainly.com/question/10687203
Step-by-step explanation:
A customer placed an order with a bakery for cupcakes. the Baker has completed 37.5% of the order after being 81 cupcakes how many cupcakes with a customer order
Answers
Answer:
216 cupcakes
Step-by-step explanation:
81 = 0.375 × order
81/0.375 = order = 216 . . . . . divide by the coefficient of the variable
_____
About percentages
% means /100
37.5% = 37.5/100 = 375/1000 = 0.375
50 POINTS!! A 96-ounce container of juice costs $4.80. At what price should a 128-ounce container be sold in order for the unit rate for both items to be the same? Explain your reasoning.
Answers
Answer:
$6.40 because 32 ounces is the difference 128 and 96 hence 32 is 1/3 of 96 so divide $4.80 by 3 which is $1.60 then add $1.60 + $4.80 =$6.40
Step-by-step explanation:
Explain how to solve the equation: b-7 =12
Answers
Answer:
19
Step-by-step explanation:
b - 7 = 12
b = 7 + 12
b = 19
Hi there! :)
Answer:
b=19
*The answer must have a positive sign.*
Step-by-step explanation:
Lesson: Addition/Subtraction/Multiplication/ and Division property of equalityFirst, you add by 7 from both sides of an equation.
[tex]b-7+7=12+7[/tex]
Then, you add by the numbers from left to right.
[tex]12+7=19[/tex]
Final answer is b=19
I hope this helps you!
Have a nice day! :)
:D
-Charlie
Thank you so much! :)
Lisa completed the table to describe the product of a mystery one-digit factor and each number.
× 1 2 3 4 5
? even even even even even
Part A Give all of the possible numbers that could be Lisa’s mystery one-digit factor.
Part B Explain how you know that you have selected all of the correct possibilities.
Answers
Part A.
We're only told that the product of the mystery factor and the number shown is even. This is true when the number shown is odd as well as even, hence the mystery factor is even.
There are no other conditions on the product that might limit the value of the mystery factor (non-zero, or < 10, for example).
Hence, the mystery factor could be any single-digit even number. In our base-10 number system, there are 5 of them: {0, 2, 4, 6, 8}.
___
Part B.
There are only 5 even single-digit numbers in our base-10 number system, so by choosing 5, I know I have all of them.
Solve the inequality) 3a - 4 < 5 (line under greater or less then) As you solve the problem, do it with numbers instead of the word form, for example, 1+1=2 instead of one plus one equals two.
Answers
a ≤ 3
Step-by-step explanation:Undo what is done to the variable. The variable is multiplied by 3 and 4 is subtracted from that result. To undo these operations, you add 4, then divide by 3.
... 3a ≤ 9 . . . . 4 is added to both sides of the inequality
... a ≤ 3 . . . . . both sides of the inequality are divided by 3
_____
Comment on solving inequalities
These are the same steps you would use to solve the 2-step equation ...
... 3a -4 = 5
The only difference between solving equations and solving inequalities is that when you multiply or divide by a negative number, you reverse the sense of the comparison (> becomes <, and vice versa; ≥ becomes ≤, and vice versa). You can see this if you consider numbers: 2 > 1. Multiplying by -1 gives -2 < -1.
Graph The function f(x) = -(x - 2)^2 +4 Make sure to label the vertex and the intercepts
Answers
See the attachment for a labeled graph.
_____
I find it convenient to use "technology" to draw the graph. A spreadsheet, graphing calculator, or on-line graphing program can do this for you.