Which theorem can be used to prove ABC ~ EDC ?
Answer: SAS
Step-by-step explanation:
Since [tex]\frac{BC}{CD}=\frac{AC}{CE}=\frac{1}{2}[/tex], and [tex]\angle ACB \cong \angle DCE[/tex] because they are vertical angles, the triangles are similar by SAS
can someone please help mee
Answer:
[tex]f(z) = z^2-3z+2[/tex]
[tex]f(x+1) = x^2-x[/tex]
[tex]f(\sqrt{2}+1) = 2-\sqrt{2}[/tex]
Step-by-step explanation:
[tex]f(x+1) = x^2+2x+1-3x-3+2[/tex]
[tex]f(\sqrt{2}+1) = 2+2\sqrt{2}+1-3\sqrt{2}-3+2[/tex]
What are the zeroes of the function? Round to the nearest hundredth. 0 2.05 8.33 14.61
The zeros of the given quadratic functions are x₁ = -2.05 and x₂ = 14.61
The complete question is given below:-
Y=-6x²+100x-180 What are the zeroes of the function? Round to the nearest hundredth.
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
Use the quadratic formula to solve it:
Y= -6x² +100x -180
a= -6
b= 100
c= -180
x =[tex]\dfrac{ -b \pm \sqrt{(b^2 - 4ac)} }{ 2a}[/tex]
x =[tex]\dfrac{-100 \pm \sqrt {(10,000 -4*-6*-180)}}{ -12}[/tex]
x1 =[tex]\dfrac{ (-100 + 75.3658 )} { -12}[/tex]
x1 = 24.6342 / -12
x1 = -2.05285
x2 =[tex]\dfrac{ (-100 - 75.3658 )} { -12}[/tex]
x2 = (- 175.3658 ) / -12
x 2 = 14.6138
Therefore the zeros of the given quadratic functions are x₁ = -2.05 and x₂ = 14.61
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Answer:
D.. last one
If soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.
Step-by-step explanation:
Find the longer and shorter lengths and hypotenuses
Answer:
Short leg: 9 in
Long leg: 40 in
Hypotenuse: 41 in
Step-by-step explanation:
This problem involves the Pythagorean Theorem, solving a system of equations, and solving a quadratic equation.
The Pythagorean Theorem applies because the question states this is a right triangle. That is one equation.
Two more equations come from descriptive relationships between various sides of the triangle.
Solving the system is done here with the Substitution Method, and solving the quadratic equation is done with factoring and the zero product property. Other methods could be used, but there is a character limit, so we can't dive into every way to solve this.
The Pythagorean TheoremPythagorean Theorem: [tex]a^2+b^2=c^2[/tex] where "c" is the hypotenuse of the right triangle.
"c" must be hypotenuse.
It doesn't matter which of the two legs' lengths is used for "a" & "b". However, because of other parts of the question, we'll need to know which one is which.
The question refers back multiple times to one specific leg (the short one). So, when we refer back to that leg in our equations, we need to make sure we're using the same leg each time.
Keeping track of which leg is which
Let's use "a" for the smaller leg, and "b" for the longer leg.
"c", as always, is the hypotenuse.
Setting up the relationships between the sidesNext, the question gives two statements relating the side lengths of the triangle to each other.
For the first statement, "the length of the longer leg of a right triangle" (that's "b") "...is 13 inches more than three times the length of the shorter leg ("a").
Translating the first sentence into math:
"the length of the longer leg of a right triangle" means "b""...is..." means "=""...13 inches more than..." means " +13 " (start with what's coming next, and then do the adding)"...three times..." means " 3* ""... the length of the shorter leg." means "a".[tex]b=3a+13[/tex]
Similarly from the second statement, we get: [tex]c=3a+14[/tex]
Combining this with the Pythagorean Theorem, we have a system of 3 equations, and 3 unknowns.
[tex]b=3a+13[/tex]
[tex]c=3a+14[/tex]
[tex]a^2+b^2=c^2[/tex]
Solving a system of equationsTo solve a system of equations, there are two main methods:
The substitution methodThe elimination methodEither method can be used, but the substitution method is the most intuitive.
Substitution method
To solve a system with the substitution method, isolate variable in an equation, written in terms of the other variables, and substitute them in to try to get a single equation with a single unknown.
Looking at our system, the first two equations already have "b" and "c" isolated in terms of "a". If we substitute both of these into the third equation, we'll have a single equation in terms of a, and can attempt to solve it.
[tex]b=3a+13[/tex]
[tex]c=3a+14[/tex]
[tex]a^2+b^2=c^2[/tex]
Substituting...
[tex]a^2+(3a+13)^2=(3a+14)^2[/tex]
Rewrite the square binomials as a product...
[tex]a^2+(3a+13)(3a+13)=(3a+14)(3a+14)[/tex]
Apply FOIL (a combination of the distributive property, the commutative properties of multiplication, and combining like terms)...
[tex]a^2+(9a^2+39a+39a+169)=(9a^2+42a+42a+196)\\a^2+(9a^2+78a+169)=(9a^2+84a+196)\\[/tex]
Observe that the equation is a degree-2 polynomial (polynomial with highest power of 2; aka quadratic). Move all terms to one side to get the equation equal to zero in preparation for solving:
[tex]a^2+(9a^2+78a+169)=(9a^2+84a+196)\\a^2+9a^2+78a+169-(9a^2+84a+196)=0\\a^2-6a-27=0\\[/tex]
There are a few ways to solve this, including the quadratic formula. However, factoring the polynomial and using the zero product property is quite efficient here:
Factoring to solve a Quadratic
Since the leading coefficient is 1, we can use the shortcut and find factors of -27 that add to make -6.
-27 has factor pairs of:
1 and -273 and -99 and -327 and -13 and -9 add to make -6, so factoring the polynomial is
[tex]a^2-6a-27=0\\(a+3)(a-9)=0[/tex]
Applying the zero product property...
[tex](a+3)=0[/tex] or [tex](a-9)=0[/tex]
So a=-3 or a=9. Given that this represents a length in a triangle, we discard the negative solution. So a=9.
Finding the other two unknowns
To finish up, substitute the "a" back into the two equations for "b" and "c".
[tex]b=3a+13\\b=3(9)+13\\b=27+13\\b=40[/tex]
[tex]c=3a+14\\c=3(9)+14\\c=27+14\\c=41[/tex]
The original problem set up our measurements in inches, so all three values are measured in inches.
Remember which length was which
"a": short leg
"b": longer leg
"c": hypotenuse
Short leg: 9 in
Long leg: 40 in
Hypotenuse: 41 in.
A rectangle has a side length of three and two sevenths centimeters and a side width of 4 centimeters. What is the area of the rectangle?ten and six sevenths cm2
thirteen and one seventh cm2
thirteen and five sevenths cm2
fifteen and one seventh cm2
The area of the rectangle is thirteen and one seventh cm2
What is the area of the rectangle?A rectangle is a four-sided object that has two widths and two lengths. The sum of angles in a rectangle is 360 degrees.
Area of a rectangle = length x width
3 2/7 x 4
23/7 x 4 = 92 / 7 = 13 1/7 cm²
We conclude that the area of the rectangle is (13 + 1/7) cm²
How to get the area of the rectangle?
For a rectangle of length L and width W, the area is:
A = L*W
Here we know that:
L = (3 + 2/7)cm
W = 4cm
Then the area is:
A = (3 + 2/7)cm*4cm = (12 + 8/7)cm² = (13 + 1/7) cm²
We conclude that the area of the rectangle is (13 + 1/7) cm²
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The perimeter of a triangle is 73 inches if two sides are of equal length and the third side is 7 inches longer than the others find the length of three sides
Answer:
22,22,29 in
Step-by-step explanation:
x + x + x+7 = 73
3x = 66
x = 22 then lengths = 22, 22, 29 in
Make d the subject of the formula h=d/3+2
Bella wants to know how long her dog is. She measure its body and finds that it is 54 cm long. Then she measures the tail and find it is 34 cm long. How long is Bella's dog from body to tail?
Answer:
88 cm
Step-by-step explanation:
body to tail = length of body + length of tail
body to tail = 54 cm + 34 cm
body to tail = 88 cm
PLEASE HELP
In a softball diamond, each of the bases, including home plate, are equidistant from each other. Although the name implies differently, a softball diamond is in the shape of a square. Given that the distance between the bases is unknown, determine an expression for the straight line distance between first and third bases.
So far I know that the equation is
x² + x² = c²
But i dont know how to simplify that
The expression for the distance from the 1st base to the 3rd base in terms of side length will be c=x√2
Given that the softball diamond is square in shape.
Let the side of the square i.e. distance between consecutive bases is x
The distance from the 1st base to the 3rd base creates the hypotenuse of a right triangle, where each side is equal to x i.e. x is the side length of the square formed by the baseball diamond.
Using the Pythagorean theorem we have:
x² +x²= c²,
where c is the distance from the 1st base to the 3rd base.
Combining similar terms gives us
2x²=c²
Taking the square root of both sides we have
√2x²= √c²
⇒x√2=c
⇒c=x√2
This is the expression for the distance from the 1st base to the 3rd base in terms of side length.
Therefore the expression for the distance from the 1st base to the 3rd base in terms of side length will be c=x√2.
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simplify 12 + 15 ÷ 3 × 6 – 4
find arc length
x=t^(3)-2t
y=t^(2)-3
Answer:
Step-by-step explanation:
What is the slope of the line shown below (3,-2) (2,4)?
A. -2
B. -1/2
C. 1/2
D. 2
Answer:
D. 2
Step-by-step explanation:
rise / run = slope
rise = 2
run = 1
2/1 = 2
slope = 2
Answer:
2 (Answer D)
Step-by-step explanation:
The green line has a positive slope, so we can immediately reject Answers A and B.
A line with a slope of +2 rises steeply as we move from left to right, whereas a line with slope +1/2 rises much less steeply. Also, it's quite clear, visually, that the slope of the given line is greater than 1. Thus, the slope of the given line is +2 (Answer D).
A paint mix uses red and white paintin a ratio of 1:12.
a) How much white paint will be needed to mix with 1.4
litres of red paint ?
b) Ifatotalof15.5litresofpaintismixed,calculate
the amount of white paint and the amount of red paint used. Give your answers to the nearest 0.1 litre.
Answer:
(a).16.8 litres
(b).red-1.2 litres
white-14.3 litres
A 7 x 8 array is 7 rows of ____
Answer:
8
Step-by-step explanation:
It's 7 rows of 8 items
A woman passed gas silently. I said "it stinks", and she said "I apologize. Excuse me". Why did she say both of those things?
Answer:
one possible way was because she knew what she did and started playing innocent
2x+3y=9 -2x+2y=6 The y cordinate
Answer:
y = 3
Step-by-step explanation:
2x + 3y = 9
-2x + 2y = 6
We have to add these two equations which gives us 5y = 15. Now, if you divide by 5 on both sides you get y = 3.
What is the domain of the linear parent function?
Answer:
The parent function of linear functions is y=x and it passes through the origin.The domain and range of all linear functions are all real numbers.
Step-by-step explanation:
solve the compound inequality -5<4x+3<=8
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a< b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
We are given
-5 < 4x+3 ≤ 8
⇒ (add -3 to all sides to get ) -5+(-3) < 4x+3+(-3) ≤8+(-3)
⇒-8 < 4x ≤ 5
⇒[tex]\frac{-8}{4} < x \leq \frac{5}{4}[/tex]
⇒-2<x<5/4
Hence, the solution is -2<x<5/4.
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I need all of these please
Answer:
second answer is 120
firsr answer is 25
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:f(4)= -1 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
If a point point (x , y) satifys a function, then it can be written as :
[tex]\qquad \tt \rightarrow \: f(x) = y[/tex]
Here, point (x , y) is replaced by (4 , -1)
[tex]\qquad \tt \rightarrow \: f(4) = - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
What are the solutions to the quadratic equation below?
x²-2x-168 =0
Answer:
x= 14, –12
Step-by-step explanation:
The given question might make you believe that it's difficult due to it's frightening digit (168) but in fact in you use the following methods, it's going to be a pieces of cake.
the delta formula:
Δ=b²–4ac===> (–2)²–4(1)(–168)=676
[tex]x 1 = \frac{ - ( - 2) + \sqrt{676} }{2} = 14 [/tex]
[tex]x2 = \frac{ - ( - 2) - \sqrt{676} }{2} = - 12[/tex]
well this can be on of the methods and the other one is
The full square formula:
[tex]x ^{2} - 2x - 168 = 0 \\ {x}^{2} - 2x = 168[/tex]
[/tex]
now what you need to do is to put this on both side of the equation (½b)²=1
[tex] {x}^{2} - 2x + 1 = 168 + 1 \\ {(x - 1)}^{2} = 169 \\ x - 1 = 13 = = > x = 14 \\ x - 1 = - 13 = = = > x = - 12[/tex]
write a quadratic function in standard form with zeros -5 and 0
Answer:
(x^2+5x)
Step-by-step explanation:
An airplane is flying at an altitude of 26,843 feet. The plane descends (goes down) 1,284 feet. Then the plane ascends (goes up) another 5,832 feet.
Let a represent the altitude of the plane.
Which equation could be used to find the final altitude of the plane?
A. a = 26,843 + 1,284 + 5,832
B. a=26,843+1,284−5,832
C. a=26,843−1,284+5,832
D. a=26,843−1,284−5,832
Answer:
Hi
The answer is C
Step-by-step explanation:
Because it descend means goes down so it's minus and after that it ascends means goes up so it's plus so the answer will be -
26,843-1,284+5832
Gertrude has a life insurance policy that will pay her family $97,000 per year I she dies. If interest rates are at 1.4% when the insurance company has to pay, what is the amount of the lump sum that the insurance company must put into a bank account? A. $692,857,142.90 B. $6,928,571.43 c. $692,857.14 D. $69,285,714.29
The amount of the lump sum that the insurance company must put into a bank account is $6,928,571.43 option (B) is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
Gertrude has a life insurance policy that will pay her family $97,000 per year.
If interest rates are at 1.4% when the insurance company has to pay
r = 1.4%
or
r = 0.014
The amount of the lump sum that the insurance company must put into a bank account:
= 97,000/0.014
= 6928571.429 ≈ $6,928,571.43
Thus, the amount of the lump sum that the insurance company must put into a bank account is $6,928,571.43 option (B) is correct.
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Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 20 13 7 40
Female 9 2 8 19
Total 29 15 15 59
If one student is chosen at random,
Find the probability that the student got an A.
20
29
29
59
20
59
The grades and gender is 29/59
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given:
A B C Total
Male 20 13 7 40
Female 9 2 8 19
Total 29 15 15 59
Total candidates who have A grade = 20+9 = 29
So, the probability that the student got an A
= 29/59
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NEED HELP!!!!!!!!!!!!!!!!!!!!!!
Answer:
The third answer
Step-by-step explanation:
if p is equivalent to q then q must be equivalent to p. I’m not 100% sure but that’s my best guess. I hope this helps :)
24. Demography A city has a population of 71,500. Ten years ago the population
was 32,500. What percent of the population 10 years ago is the population now?
Use the proportion method.
Answer:
45.5%
Step-by-step explanation:
The increase in population was 45.5%
Which is the graph of f(x) = √x?
Look at the attached image.
Suppose line g is the line with the equation y = x. Given A (7,-3) , B (6,3), and C (-2,-7), what are the coordinates of the vertices of a’b’c’ for the reflection
Answer: A'(-3, 7), B'(3, 6), C'(-7, -2)
Step-by-step explanation:
Reflecting over y = x maps (x,y) onto (y,x).
In what table does y vary directly with x?
Answer:
The phrase “ y varies directly as x” or “ y is directly proportional to x” means that as x gets bigger, so does y, and as x gets smaller, so does y. That concept can be translated in two ways. for some constant k. The k is called the constant of proportionality. Therefore a chance of probability is a binary table.
Step-by-step explanation:
