Answers
Answer:
The length of z is [tex]3\sqrt{3}[/tex] unit
Step-by-step explanation:
First Label the diagram as shown in the attachment:
In right [tex]\triangle ABC[/tex];
first find the value of y:
Use Pythagoras theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides.
In [tex]\triangle ABC[/tex]
length of AB =6 unit , length of BC =y unit and the length of AC = 3+9 =12 unit
Now, using Pythagoras theorem to get the value of y;
[tex]AB^2+BC^2=AC^2[/tex]
[tex]6^2+y^2=12^2[/tex] or
[tex]36+y^2=144[/tex] or
[tex]y^2=144-36[/tex]=108 or
[tex]y=\sqrt{108}[/tex]
on simplify we get, [tex]y=6\sqrt{3}[/tex] unit
Therefore, the length of BC is [tex]6\sqrt{3}[/tex] unit.
now, in [tex]\triangle BDC[/tex]
using Pythagoras theorem to find the value of z;
[tex]BD^2+CD^2=BC^2[/tex]
Putting the values of BD = z units , BC = [tex]6\sqrt{3}[/tex] unit and DC = 9 units we have,
[tex]z^2+9^2=(6\sqrt{3})^2[/tex] or
[tex]z^2+81=108[/tex] or
Simplify:
[tex]z^2=27[/tex] or
[tex]z=\sqrt{27} = 3 \sqrt{3}[/tex]
Therefore, the value of length z is [tex]3\sqrt{3}[/tex] unit
Related Questions
helppppppppppppppppppppppp
Answers
1. Vertex (1,2), Point (2,-5)
2. Vertex (-3,6), Point (1,-2)
3. Vertex (0,5), Point (1,-2)
4. Vertex (1/4, -3/2), Point (1.3)
Answers
he difficulty of graphing a quadratic function varies depending on the form you find it in. We'll start things off relatively easily.
f(x) = a(x – h)2 + k
No, we're not lying to you; that is a quadratic function. Go ahead, multiply it out.
f(x) = ax2 + (-2ah)x + (ah2 + k)
The h and k are constants, so (-2ah) and (ah2 + k) are also constants, which we could call, say, b and c. See, you can trust us, it's totally quadratic.
When you have a parabola written out like f(x) = a(x – h)2 + k, it's in vertex form. With vertex form, you have several pieces of important information thrown at you right away. When you first meet someone, your first impression tends to stick with you. It's the same with this equation.
The sign of a tells you if the parabola opens up or down. If a is positive, it opens up. If a is being a Negative Nancy, the parabola opens down. You also know that the vertex of the parabola is at the point (h, k). Be careful with the sign of h, though.
At a store, customers are randomly selected to participate in a survey. On Friday, there were 500 customers at the store. Out of all those people, 90 were selected to participate in the survey. On Saturday, the store manager expects 700 customers in the store. If the probability of being selected to participate in the survey on Saturday is the same as it was on Friday, how many customers will be selected to participate in the survey on on Saturday?
Answers
90/500 = .18
This means that 18% of the customers were selected for the survey.
If the probability is the same on Saturday, then we can multiply the expected customers by our .18
700 x .18 = 126
126 should be selected for the survey on Saturday.
Six times a number decreased by 10 is eight
Answers
6n - 10 = 8
Six times a number decreased by 10 is 8
Your equation is
6x - 10 = 8
Now solve for x
6x - 10 = 8
Add 10 to each side
6x - 10 + 10 = 8 + 10
6x = 18
Divide each side by 6
6x ÷ 6 = 18 ÷ 6
x = 3
I Will Mark it the brainiest
A bouncy ball is dropped such that the height of its first bounce is 3.5 feet and each successive bounce is 75% of the previous bounce's height. What would be the height of the 9th bounce of the ball? Round to the nearest tenth (if necessary).
Answers
y = A * (b) ^ x
Where,
A: initial height
b: decrease rate of initial height
x: number of bounces.
We have then:
y = 3.5 * (0.75) ^ x
For the ninth bounce:
y = 3.5 * (0.75) ^ x
y = 0.26
Answer:
The height of the 9th bounce of the ball is:
y = 0.26 feet.
The highest point in Africa is Mount Kilimanjaro in Tanzania, with an altitude of 5895 meters above sea level. The lowest point on the continent is Lake Assal in Djibouti. It is 155 meters below sea level. FInd the difference between the altitudes.
Answers
To find the difference between the two values, you just have to subtract them.
Our problem is: 5895 - (-155)
To do this, we change it to 5895 + 155 = 6050
We change it because we are subtract a negative number and subtracting a negative number is the same thing as adding it.
Answer:
6050 meters
Step-by-step explanation:
The difference between the altitudes will be the distance from the highest point of kilimanjaroto the lowest point on lake assai.
This distance will be the distance from the highest point of kilimanjaro to the sea level (5895m) plus the distance from the sea level to the lowest point on lake assai (155m, this distances wont be negative because it is taken as a distance from a point of reference not as a value below 0). Like this:
[tex]5895m+155m=6050m[/tex]
What’s is the value of the digit 5 in the number 57,634?
5,000
1,000
50,000
10,000
Answers
(5)7,,634= The 5 would equal the ten thousands because first, once the number would have it's (first) comma, this would be in the thousands. And also, this number has (2) numbers in it's thousands, and not just 1. But if it were to have 3, this would be another story, and from this, it would clearly explain to be your (option (b)).
Which of the following sets of whole numbers represents all the even three-digit numbers with a 6 in the hundreds place and 3 in the tens place? 361; 363; 365; 367; 369 630; 632; 634; 636; 638 360; 633; 635; 637; 639
Answers
630, 632, 634, 636, and 638 :)
In a given amount of time , Nijah drove twice as far as Jared. Altogether they drove 135 miles. Find the number of miles driven by Nijah
Answers
3x = 135
x = 135 /3
x = 45
Nijah = 2*45 = 90 miles
Is (a-3) a factor of (a^3-6a^2+29)?
Answers
f(3) = 8 - 6*9 + 29
f(3) = 8 - 54 + 29
f(3) = - 17
As further "proof", here is the graph. Notice that the graph cuts the x axis around -2 , 2.5 and 4.2 (These are rough guesses). The factors are
(a+2)(a - 2.5)(a - 4.2)
The points (15, 10), (25, 20), (30, 22), (40, 32), (55, 53), (60, 55) represent the time, x, it takes 6 people to travel y miles. The scatterplot below represents the situation.
(Graph Below)
A. 32 miles
B. 42 miles
C. 48 miles
D. 54 miles
Answers
Answer:IT IS B
Step-by-step explanation:
I GOT A 100 ON MY TEST YOUR WELCOME :D
2.
How can you tell when a quadratic equation has two identical, rational solutions? (1 point)
when the radicand is negative
when b in the quadratic formula is greater than the radicand
when the radicand equals zero
when the radicand is not a perfect square,
Answers
ax² + bx + c = 0
are given by:
x₁₂ = [- b +- √(b²-4ac) ] / 2a
You have three cases:
1) the radicand is positive: you then have two dinstinct soutions, one with the root added to (-b) and then divided by 2a, and the other one with the root subtracted to (-b) and then divided by 2a.
2) the radicand is negative: you then have no solutions, because the root can't be performed. This case means that the given polynomial is never equal to zero.
3) the radicand is equal to zero: you then have the same value for both the solutions, which is -b/(2a).
Therefore your answer should be: C) when the radicand is equals to zero.
(Please help, urgent).
What is the value of r?
Round your final answer to the nearest whole number.
Answers
[tex] Heya \: ! \: \\ \\ We \: know \: that \\ \\ \: \sin( \alpha ) = \frac{perpendicular}{hypotenuse} \\ \\ \sin(67.4) = \frac{12}{r} \\ \\ \\ also \: , \\ \\ \sin(67.4) = 0.9231 \\ \\ comparing \: both \: ,\\ \\ \frac{12}{r} = 0.9231 \\ \\ r = \frac{12}{0.9231} \\ \\ r = 13 \: \: \: \: \: ans.[/tex]
Can someone please explain how to find this answer? thanks
Answers
.. 5x -2y = 5(-2) -2(3) = -16
Then solve for y.
.. 2y = 5x +16 . . . add 2y+16; then divide by 2 for the next equation
.. y = (5/2)x +8 . . . . . . . corresponds to selection (B)
[tex]\bf 5x-2y=-12\implies 5x+12=2y\implies \cfrac{5x+12}{2}=y \\\\\\ \cfrac{5x}{2}+\cfrac{12}{2}=y\implies \stackrel{slope}{\cfrac{5}{2}}x+6=y[/tex]
so, notice, from the slope-intercept form, it happens that the slope is 5/2, well, the line will have the same slope.
so we're looking for the equation of a line whose slope is 5/2 and runs through -2,3
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1\\ &&(~ -2 &,& 3~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{5}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-3=\cfrac{5}{2}[x-(-2)] \\\\\\ y-3=\cfrac{5}{2}(x+2)\implies y-3=\cfrac{5}{2}x+5\implies y=\cfrac{5}{2}x+8[/tex]
Which best describes the relationship between the successive terms in the sequence shown?
9, –1, –11, –21, …
a)The common difference is –10.
b)The common difference is 10.
c)The common ratio is –9.
d)The common ratio is 9.
I believe i understand it but have to ask it would be the common difference is -10 bevause you would take -1-9 and get -10?,
Answers
Jenny has saved $3,800 over the last 12 months. She saved either $250 or $350 a month. During the 12 month period, how many times did Jenny save $250 for the month? A) 3 B) 4 C) 5
Answers
Here is your answer:
The proper answer to the question is option A "3".
Here is how:
There is only two options 250 and 350 and there is 12 months which means there can only be three for both.
Your answer is A.
If you need anymore help feel free to ask me!
Hope this helps!
Answer:
the answer is actually 4
Step-by-step explanation:
brainliest for best answer
Answers
Answer:
Step-by-step explanation:
________
Good evening ,
_______________
-4x+3y=-12
-2x+3y=-18
This system is the same as
y = (4/3)x - 4
y = (2/3)x - 6
We note that the two coefficients 4/3 and 2/3 are positives
So the right answer is C (graph 2).
___
:)
Find the greatest common factor : 25p^2q^3, 15p^2q^2 and 35pq^4
Answers
Answer:
The greatest common factor is [tex]5pq^2[/tex].
Step-by-step explanation:
The given expressions are [tex]25p^2q^3[/tex], [tex]15p^2q^2[/tex] and [tex]35pq^4[/tex].
Greatest common factor of two numbers is the greatest number that divides both numbers completely.
Find factors of each expression.
[tex]25p^2q^3=5\times 5\times p\times p\times q\times q\times q[/tex]
[tex]15p^2q^2=3\times 5\times p\times p\times q\times q[/tex]
[tex]35pq^4=5\times 7\times p\times q\times q\times q\times q[/tex]
The common factors are 5,p,q and q. So, the greatest common factor of given expressions is
[tex]G.C.F.=5\times p\times q\times q[/tex]
[tex]G.C.F.=5pq^2[/tex]
Therefore the greatest common factor is [tex]5pq^2[/tex].
the equation Y= -16t2 + 120 can be used to represent the fruit's height above the ground, where t represents time, in seconds, after she threw the apple. How long did it take the apple to hit the ground? Round your answer to the neares hundreth.
Answers
Let y = 0
Solve for t.
0 = -16t^2 + 120
-120 = -16t^2
-120/-16 = t^2
7.5 = t^2
sqrt{7.5} = sqrt{t^2}
2.7386127875 = t
We now round to the nearest hundredths, which means to 2 decimal places.
Answer: t = 2.74 seconds
Estimate 92.49 - 63.854 by first rounding each number to the nearest whole number.
Answers
____
Actual difference is 28.636.
Jesse wants to write a function to represent the graph. He says that the period of the graph is triple that of sin x and that the equation of the graph is f(x)=3sin x. Why is he incorrect?
a. The period of the graph is twice that of sin x.
b. The frequency of the graph is triple that of sin x.
c. The equation of the graph should be f(x)=sin x/3.
d. The equation of the graph should be f(x)=3sin x.
Answers
Answer C
the value of sin(pi/2) =1
the value of sin(pi) = 0
according to the graph sin(3pi/2) = 1 and sin(3pi) =0
so the correct equation for the graph must be f(x) = sin(x/3)
Jesse is incorrect, because the equation of the graph should be [tex]f(x) = \sin(\frac{x}{3})[/tex]
From the question, we understand that the period is 3 times sin x.
The above claim is wrong.
Given that, the period (B) is 3.
i.e B = 3
The function is represented as:
[tex]f(x) = \sin(\frac{2\pi}{B})[/tex]
So, we have:
[tex]f(x) = \sin(\frac{2\pi}{3})[/tex]
Represent [tex]2\pi[/tex] with x
[tex]f(x) = \sin(\frac{x}{3})[/tex]
Hence, the equation of the graph should be [tex]f(x) = \sin(\frac{x}{3})[/tex]
Read more about sine functions at:
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PLEASE HELP ME OUT PLEASE!!
EXPLAIN IT PLEASE SO I CAN UNDERSTAND IT BETTER
THX
Answers
Factor completely x^2 − 36.
(x + 6)(x − 6)
(x + 6)(x + 6)
(x − 6)(x − 6)
Prime
Answers
[tex](First \ step) \\ \\ Factoring: (x2-36) \\ \\ \boxed{ A^2 - B^2 \ can \ be \ factored \ into \ (A+B) * (A-B)} \\ \\\ \left[\begin{array}{ccc}Proof : (A+B) * (A-B) = \\ A2 - AB + BA - B2 = \\ A2 - AB + AB - B2 = \\ A2 - B2\end{array}\right] \\ \\ \\ Factorization is : (x + 6) * (x - 6) \\ \\ \boxed{FINAL \ ANSWER} \\ \\ \boxed{\boxed{ (x + 6) * (x - 6)}}[/tex]
Your correct answer would be (option a) the first option.
I hope this helps you!
You have decided to buy a new car, but you are concerned about the value of the car depreciating over time. You do some research on the model you are looking at and obtain the following information:
Suggested retail price - $18,790
Depreciation per year - $1385 (It is assumed that this value is constant.)
The following table represents the value of the car after n years of ownership.
Answers
3125 = 3200*(d)^3
3125/3200 = d^3
3-root (3125/3200) = d
d = 0.992125657...
1 - d = 0.007874...
Therefore it depreciates at about 0.8% monthly
To find the depreciation 6 months from now, or 9 months from the beginning:
v = 3200 (d)^9
= 2980.232239...
So after 9 months the car would be about $2980.23
Answer: D on edge
Step-by-step explanation:
Patrick compared the slope of the function g(x) = -2x - 8 to the slope of the linear function shown in the table below. Let m = the slope of g(x) and n = the slope of h(x).
Which statement is true? Choose all that apply.
A. m < n
B. m > n
C. m = n
D. both slopes have the same sign.
E. both slopes have different signs.
Answers
The function f(x) is defined as follows:
f(x)= 3x+1 if x is less than or equal to 0
2x^2 if 0
4 if c is greater than or equal to 2
determine the following values of the function
f(-3)= __
f(2)= ___
Answers
[tex]f(x)=3x+1[/tex]
[tex]f(-3)=3(-3)+1[/tex]
[tex]f(-3)=-9+1[/tex]
[tex]f(-3)=-8[/tex]
Similarly, when you are evaluating the function at 2, you are saying that [tex]x=2[/tex]. Since [tex]2 \geq 2[/tex], we are going to use our second rule to evaluate our function:
[tex]f(x)=2 x^{2} [/tex]
[tex]f(2)=2(2^{2} )[/tex]
[tex]f(2)=2(4)[/tex]
[tex]f(2)=8[/tex]
We can conclude that [tex]f(-3)=-8[/tex] and [tex]f(2)=8[/tex].
To determine the values of the function f(x) at specific points, we need to look at the different cases given in the definition of f(x).
Explanation:To determine the values of the function f(x) at specific points, we need to look at the different cases given in the definition of f(x).
If x is less than or equal to 0, then f(x) = 3x + 1. So, f(-3) = 3(-3) + 1 = -8.If x is greater than 0 and less than 2, then f(x) = 2x^2. So, f(2) = 2(2^2) = 8.If x is greater than or equal to 2, then f(x) = 4. So, f(2) = 4.Therefore, f(-3) = -8 and f(2) = 4.
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What is the second term when 3+2x^2-3x^4+x3
Answers
I can explain if you want.
I need to write these description into the new function but I keep getting the wrong thing -.-
1.The function f(x)=(1/2)^x is translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5
2.The function f(x)=ln x is translated 3 units left, horizontally compressed by a factor of 1/4 and translated 0.5 units down.
3. The function f(x)=e^x is horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right.
Answers
.. translation right by k units: f(x) ⇒ f(x-k)
.. translation up by k units: f(x) ⇒ f(x) +k
.. horizontal stretch by a factor of k: f(x) ⇒ f(x/k) . . . . same as compressed by 1/k
.. vertical stretch by a factor of k: f(x) ⇒ k*f(x)
.. reflection across the x-axis: f(x) ⇒ -f(x)
.. reflection across the y-axis: f(x) ⇒ f(-x)
The sequence in which these are done is important.
1. f(x) = (1/2)^x
.. translated 4 units right: f(x) = (1/2)^(x -4)
.. reflected across the x-axis: f(x) = -(1/2)^(x -4)
.. vertically stretched by a factor of 1.5: f(x = -1.5(1/2)^(x -4)
2. f(x) = ln(x)
.. translated 3 units left: f(x) = ln(x +3)
.. horizontally compressed by a factor of 1/4: f(x) = ln(x/4 +3)
.. translated down 0.5 units: f(x) = -0.5 +ln(x/4 +3)
3. f(x) = e^x
.. horizontally stretched by a factor of 3: f(x) = e^(x/3)
.. reflected across the y-axis: f(x) = e^(-x/3)
.. translated 1 unit right: f(x) = e^(-(x -1)/3)
The transformed equations for each of your base functions according to given changes are f(x) = -1.5*(1/2)ˣ⁻⁴, f(x) = ln(4×(x+3))-0.5, and f(x)=e⁻³×(x-1) respectively.
Explanation:1. The transformed function for your first one, namely f(x)= (1/2)ˣ, after being translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5 would be f(x) = -1.5×(1/2)⁽ˣ⁻⁴⁾.
2. Your second function, f(x) = ln(x), after being translated 3 units left, horizontally compressed by a factor of 1/4, and translated 0.5 units down becomes:
f(x) = ln(4×(x+3))-0.5.
3. Your final function, f(x)=e^x, when it's horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right, would transform into: f(x)=e⁻³×(x-1).
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Jovan bought a bond with a face value of 15,000 and a coupon rate of 8.5%. The bond will mature in 15 years. How much interest will he receive semiannually
Answers
19,125
Explanation
The value of bond has an interest of 8.5% annually. Monthly it will be 8.5/2%=4.25%
The initial value of bond is 15,000.
The formula for calculating the interest is;
Interest=PRT
Where p is the money deposited, R is the interest rate and T is the period.
Since the interest semiannually for 15 years, the interest period is (15×2) = 30.
Interest=15,000×0.045×30
=19,125.
What is the median of the data set?
42 55 27 31 17 24 65 47 39 18
A. 21
B. 35
C. 17
D. 24
Answers
Y᷉᷈o᷉᷈u᷉᷈ p᷉᷈l᷉᷈a᷉᷈c᷉᷈e᷉᷈ t᷉᷈h᷉᷈e᷉᷈m᷉᷈ i᷉᷈n᷉᷈ n᷉᷈u᷉᷈m᷉᷈e᷉᷈r᷉᷈i᷉᷈c᷉᷈a᷉᷈l᷉᷈ o᷉᷈r᷉᷈d᷉᷈e᷉᷈r᷉᷈
T᷉᷈h᷉᷈e᷉᷈n᷉᷈ f᷉᷈i᷉᷈n᷉᷈d᷉᷈ t᷉᷈h᷉᷈e᷉᷈ m᷉᷈i᷉᷈d᷉᷈d᷉᷈l᷉᷈e᷉᷈ n᷉᷈u᷉᷈m᷉᷈b᷉᷈e᷉᷈r᷉᷈