The lengths of the sides of triangle DEF are DE = 0.75 cm, EF = 1.125 cm, and DF = 1.5 cm.
Explanation:Triangles ABC and DEF are similar, which means their corresponding angles are equal. In similar triangles, the ratio of the lengths of corresponding sides is constant. To find the lengths of the sides of DEF, we can use the ratio of the corresponding sides of ABC and DEF.
Let x be the length of DE in triangle DEF. Since DE corresponds to AB, we have the ratio x/2 = 1.5/4, which simplifies to x = 0.75 cm. Similarly, for EF corresponding to BC, y/3 = 1.5/4, giving y = 1.125 cm. Finally, for DF corresponding to CA, z/4 = 1.5/4, yielding z = 1.5 cm.
Therefore, the lengths of the sides of triangle DEF are DE = 0.75 cm, EF = 1.125 cm, and DF = 1.5 cm. This result is consistent with the idea that in similar triangles, the ratio of corresponding sides remains constant.
The calculation involved setting up and solving simple proportions based on the given lengths of the sides of triangle ABC and using them to find the lengths of the sides of triangle DEF.
A ship's sonar finds that the angle of depression to a ship wrack on the bottom of the oceanis 12.5°. If a point on the ocean floor is 60 meters directly below the ship, how many meters is it from that point on the ocean floor to the wreck?
Answer:
The 13.2 meters from that point on the ocean floor to the wreck.
Step-by-step explanation:
As given
A ship's sonar finds that the angle of depression to a ship wrack on the bottom of the ocean is 12.5°.
If a point on the ocean floor is 60 meters.
Now by using the trigonometric identity.
[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]
As shown in the figure given below.
Perpendicular = CB
Base = AC = 60 meters
[tex]\theta = 12.5^{\circ}[/tex]
Put in the identity
[tex]tan\ 12.5^{\circ} = \frac{CB}{AC}[/tex]
[tex]tan\ 12.5^{\circ} = \frac{CB}{60}[/tex]
[tex]tan\ 12.5^{\circ} = 0.22[/tex]
[tex]tan\ 12.5^{\circ} = 0.22[/tex]
[tex]0.22= \frac{CB}{60}[/tex]
CB = 60 × 0.22
CB = 13.2 meters
Therefore the 13.2 meters from that point on the ocean floor to the wreck.
The distance from the point on the ocean floor directly below the ship to the shipwreck is approximately 13.3 meters.
We will use the tangent function, which relates the angle of depression to the opposite side (the distance from the point directly below the ship to the shipwreck) and the adjacent side (the depth of the ocean at the point directly below the ship).
Given:
The angle of depression [tex]\theta[/tex] is [tex]12.5^o.[/tex]
The depth of the ocean at the point directly below the ship, h, is 60 meters.
We want to find the distance from the point directly below the ship to the shipwreck, which we will call [tex]d.[/tex]
Using the tangent function :
[tex]\[ \tan(\theta)[/tex] = [tex][\frac{\text{opposite}}{\text{adjacent}}][/tex]
[tex]\[ \tan(12.5^o) = \frac{d}{60} \][/tex]
To find d, we rearrange the equation: [tex]\[ d = 60 \times \tan(12.5^o) \][/tex]
Now we calculate the tangent of 12.5 and multiply it by 60:[tex]\[ d = 60 \times \tan(12.5^o) \][/tex]
[tex]\[ d \approx 60 \times 0.22169\][/tex]
[tex]\[ d \approx 13.3014 \][/tex]
Therefore, the distance from the point on the ocean floor directly below the ship to the shipwreck is approximately 13.3 meters.
The diagram of question is:
The perimeter of a rectangle is 26 meters. The difference between the length and the width is 5 meters. Find the width
l - lenght
w - width
l - w = 5 → l = 5 + w
26 m - perimeter
l + l + w + w = 2l + 2w - perimeter
substitute l = 5 + w:
2(5 + w) + 2w = (2)(5) + (2)(w) + 2w = 10 + 2w + 2w = 10 + 4w
The equation:
10 + 4w = 26 subtract 10 from both sides
4w = 16 divide both sides by 4
w = 6
Answer: The width = 6 m.Which of the following ordered pairs represents the solution to the system given below?
x − 4y = 7
5x + 9y = 6
Answer:
The solution to the system would be (3, -1)
Step-by-step explanation:
You can find the solution to this system by using the elimination method. To do that, start by multiplying the top equation by -5 and then adding it through.
-5x + 20y = -35
5x + 9y = 6
-----------------
29y = -29
y = -1
Now that we have the value of y, we can plug it into either equation and find the x value.
x - 4y = 7
x - 4(-1) = 7
x + 4 = 7
x = 3
Final answer:
The solution to the given system of equations is the ordered pair (3, -1).
Explanation:
To find the solution to the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
1. Solve the first equation for x:
x = 7 + 4y
2. Substitute this value of x into the second equation:
5(7 + 4y) + 9y = 6
3. Simplify and solve for y:
35 + 20y + 9y = 6
29y = -29
y = -1
4. Substitute the value of y back into the first equation to find x:
x = 7 + 4(-1)
x = 3
Therefore, the solution to the system is the ordered pair (3, -1).
If $a$, $b$, $c$, and $d$ are replaced by four different digits from $1$ to $9$, inclusive, then what's the largest possible value for $a.Bc + 0.D$ ?
The largest possible value for (a.bc + 0.d) is (10.56).
The largest possible value for (a.bc + 0.d) when (a), (b), (c), and (d) are replaced by four different digits from 1 to 9, inclusive, can be found by selecting the largest digits for (a), (b), and (c), and the smallest digit for (d).
This results in the number (9.86 + 0.7), which equals (10.56).
Therefore, the largest possible value for (a.bc + 0.d) is (10.56).
Complete question:
If a,b,c,d are replaced by four different digits from 1 to 9, inclusive, then what's the largest possible value for a.bc + 0.d ?
How to solve this problem?
Answer:
Can not be determined.
Step-by-step explanation:
We can easily notice that the limit is x tends to infinity, whereas x is not present in the given function, we are given (1 + 1/n). So we can not evaluate the given limit for x as parameter, we must have some function of x to solve this problem.
Hence, option C is correct i.e. the limit can not be determined.
Answer:
cannot be determined
Step-by-step explanation:
If we have, [tex]\lim_{n \to \infty} {1+\frac{1}{n}}[/tex]
We plug in infinity for n directly
1/∞ =0
So when we plug in infinity for n then 1/n becomes 0
[tex]\lim_{n \to \infty} {1+\frac{1}{n}}[/tex]
[tex] {1+\frac{1}{infinity}}[/tex]
1+ 0 = 1
In our problem , limit says x-> ∞
there is no x term inside
[tex]\lim_{x \to \infty} {1+\frac{1}{n}}[/tex]
so we can clearly say limit cannot be determined
One ounce of solution x contains only ingredients a and b in the ratio of 2:3 one ounce of solution y count aims only ingredients a and b in the ratio of 1:2 if solution z is created by mixing solutions x and y in the ration of 3:11 then 2520 ounces of solution z contains how many ounces of a
Answer:
Volume of a in z = 876 ounces
Step-by-step explanation:
For z, the ratio of x and y is 3 : 11
x : y = 3 : 11 , which means in 14 parts of solution z : x will be 3 parts and y will be 11 parts
So, in 2520 ounces solution of z ,
[tex]x=\frac{2520*3}{14}=540\\y=\frac{2520*11}{14}=1980[/tex]
Volume of a in z = { Volume of a in x + Volume of b in x }
Therefore,
[tex]Volume \thinspace of \thinspace a\thinspace in\thinspace x = 540\cdot \frac{2}{5} = 216\\Volume \thinspace of \thinspace b \thinspace in \thinspace x = 1980\cdot \frac{1}{3}=660[/tex]
So, Volume of a in z = 876 ounces
Help me with this please
4.42×10^34 molecules/min
Step-by-step explanation:Multiply the various factors, along with the unit conversion (60 s/min).
... (3.35×10^25 molecules/L) × (2.2×10^7 L/s) × (60 s/min)
... = (3.35×2.2×60)×10^(25+7) molecules/min
... = 442.2×10^32 molecules/min
... ≈ 4.42×10^34 molecules/min
_____
Comment on scientific notation problems
Your scientific or graphing calculator will allow you to enter and display numbers in scientific notation.
A total of 60 60 children signed up for hockey. There were 3 3 boys for every 1 1 girl who signed up. How many of the children who signed up for hockey were girls?
Answer: 15
Step-by-step explanation:
Boys : Girls
3x + 1x = 60
4x = 60
x = 15
Girls (1x) = 1(15) = 15
Answer:
The answer is 15
Y is inversy proportional to x. When y=7 , x=9 A) work out an equation connecting y and x? B) work out the value of y when x=21
Answer:
see explanation
Step-by-step explanation:
since y is inversely proportional to x the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportionality
to find k use the given condition when y = 7, x = 9
k = yx = 7 × 9 = 63
y = [tex]\frac{63}{x}[/tex] ← is the equation connecting them
when x = 21, then
y = [tex]\frac{63}{21}[/tex] = 3
The equation connecting y and x is y = 9 + 3x. When x = 21, y = 72.
Explanation:The equation connecting y and x is given by y = 9 + 3x. In this equation, the constant term, also known as the y-intercept, is 9. The coefficient of x, also known as the slope, is 3. This means that for every increase of 1 in x, y increases by 3.
To calculate the value of y when x = 21, substitute x = 21 into the equation: y = 9 + 3(21) = 9 + 63 = 72. Therefore, when x = 21, y = 72.
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Kyle has 125 marbles. Fifty of these marbles are red and the reat are other colors. What is the ratio of the nunber of red marbles to the total of marbles expressed in simplest terms?
Answer:
The required simplest form is: [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
We have been given Kyle has 125 marbles.
And 50 out of total 125 are red and rest of them are other colours
that means other colour marble are 125-50=75
we need to find ratio of the number of red marbles to the total of marbles
The rat io is: [tex]\frac{50}{125}=\frac{2}{5}[/tex]
The required simplest form is: [tex]\frac{2}{5}[/tex]
Answer:
Step-by-step explanation:
2/5
A pair of shoes usually sells for $62. If the shoes are 40% off, and sales tax is 8%, what is the total price of the shoes, including tax?
Answer:
45.57
Step-by-step explanation:
Final answer:
After applying a 40% discount to the original $62 price of the shoes and adding an 8% sales tax, the total cost of the pair of shoes is $40.18.
Explanation:
The question involves calculating the total price of a pair of shoes after a discount and adding sales tax. To find the discounted price, we take 40% off the original price of $62. To calculate 40% of $62, we multiply 62 by 0.40 (which is 40% as a decimal), giving us $24.80. We subtract this discount from the original price: $62 - $24.80 = $37.20, which is the discounted price of the shoes.
Next, calculate the sales tax on the discounted price by converting the sales tax rate from a percent to a decimal. The sales tax rate is 8%, which as a decimal is 0.08. Multiply the discounted price by the sales tax rate: $37.20 x 0.08 = $2.976, which we round to $2.98.
Finally, add the sales tax to the discounted price to find the total cost: $37.20 + $2.98 = $40.18. Therefore, the total price of the shoes, including tax, is $40.18.
Choose which of the following functions has a domain of all real numbers. Select all that apply. y = x, y = 2x^2 + x - 3, y = 3x - 4, y = 2, y = 3 - x^2.
Answer:
all of the above
Step-by-step explanation:
Every one of these functions is defined for all values of x.
All the provided functions: y = x, y = 2x^2 + x - 3, y = 3x - 4, y = 2, and y = 3 - x^2, have a domain of all real numbers. This means any real value can be input into these functions to get a real output.
Explanation:The domain of a function is the set of all possible input values (usually represented by x) that will give an output value. In this case, we are asked to identify which of the provided functions have a domain of all real numbers. For the functions given: y = x, y = 2x^2 + x - 3, y = 3x - 4, y = 2, and y = 3 - x^2, all of them have a domain of all real numbers. This is because no matter what value of x you choose, these functions will always provide a valid output of y. In other words, you can input any real number into these functions and get a real number out.
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Please help me!!!!!!
Answer: 243, 729
Step-by-step explanation:
1, 3, 9, 27, 81 is a geometric sequence where r = 3
a₁ = 1
a₂ = 1 x 3 = 3
a₃ = 3 x 3 = 9
a₄ = 9 x 3 = 27
a₅ = 27 x 3 = 81
To find the next two terms, multiply the previous term by 3:
a₆ = 81 x 3 = 243
a₇ = 243 x 3 = 729
The winter clothing drive has received donations of 5 coats, 23 pairs of gloves, 19 scarves, and 3 hats so far. Based on this data, what is a reasonable estimate of the probability that the next donation is not a pair of gloves?
Answer: Probability that the next donation is not a pair of gloves is 0.54.
Step-by-step explanation:
Since we have given that
Number of coats = 5
Number of pairs of gloves = 23
Number of scarves = 19
Number of hats = 3
Total number of winter clothing is given by
[tex]5+23+19+3=50[/tex]
Probability that the next donation is not a pair of gloves is given by
Not gloves = 50-23=27
P(not gloves ) is given by
[tex]=\frac{Not\ gloves}{total}\\\\=\frac{27}{50}\\\\=0.54[/tex]
Hence, Probability that the next donation is not a pair of gloves is 0.54.
Answer:
.54
Step-by-step explanation:
I know khan, ok?
i think it is a check my answer?
What function equation is represented by the graph?
f(x)= 4 x +4
f(x)= 4 x +5
f(x)= 3 x +5
f(x)= 3 x +4
Answer:
I am 99% sure the answer is f(x)= 4x + 5
Step-by-step explanation:
That is because the line intercepts y at 5 and every 4 cubes the line hits a corner...
Answer:
F(x)=4x +5
Step-by-step explanation:
At the beginning of the week Fayez writes drown the mileage of his limousine - 2529 At the end of the week the mileage is 2834, Fayez knows he used 75.2 litres of petrol during the week. The handbook states that the limo uses 1 gallon of petrol for every 20 miles. Fayez wants to know if his limousine used 1 gallon of petrol for every 20 miles this week 1 gallon = 4.54 litres Did his limo use 1 gallon of petrol for every 20 miles that week? Explain answer in full Please help!!
Please answer this question! 25 points and brainliest!
Answer:
a -5/2 <=x
Step-by-step explanation:
5(x-2) <= 9x
Distribute the 5
5x -5*2 <= 9x
5x-10 <= 9x
Subtract 5x from each side
5x-5x-10 <= 9x-5x
-10 <= 4x
Divide by 4 on each side
-10/4 <=4x/4
-5/2 <=x
Is the following true or false? the derivative with respect to x of the product of x squared and e raised to the x power equals the product of x times e to the x power and the quantity x plus 2 True False
Answer:
It is true
Step-by-step explanation:
To find the quotient of 8 :- 1/3, multiply 8 by
Answer:
3
Step-by-step explanation:
PLEASE HELP ASAP WILL MARK BRAINLIST
The population of a city is 451,400. The population is expected to decrease at a rate of 3.2% each year.
Which function equation represents the population of the city after t years?
f(t)=451,400(0.968)t
f(t)=451,400(0.032)t
f(t)=451,400(1.032)t
f(t)=451,400(3.2)t
2.The ordered pairs model an exponential function, where j is the function name and e is the input variable.
{(1, 10), (2, 50), (3, 250), (4, 1250)}
What is the function equation in sequence notation?
Enter your answer in the box.
Answer:
f(t) = 451,400(0.968)^t
Step-by-step explanation:
Exponential Decay Function:
y = b (1-r) ^t
where
b is the initial amountr is the rate of changet is timef(t)= 451,400 ( 1 - 0.032) ^t
f(t) = 451,400 (0.968) ^t
Answer:
This was the correct answer, I even provided proof from my own test. Hope this helps!
Step-by-step explanation:
It takes layla 2/5 hour to swim 1/2 mile what is the unit rate of miles that layla can swim per hour
Good Morning!
Distance = rate x time
1/2 mile = R x 2/5 hour
1/2=2/5R
/2/5 /2/5
R=1/2 x 5/2
R=1 1/4
She can swim 1 1/4 per hour.
I hope this helps! :)
Answer:
1 1/4
Step-by-step explanation:
Martha estimated there were 89 marbles in a jar for a contest. The actual number of marbles in the jar was 111. What was the percent error of Martha's estimation?
Answer:
18.91 percent
Step-by-step explanation:
Percent error equation: Difference or Difference/Actual
Actual
The difference is the greater amount minus the smaller.
111 - 89 = 22
The actual is 111.
Now divide 22/111.
22/111 = 0.189 repeating
0.189 repeating = about 18.91 percent
Sammy bought a new car. The depreciation equation is given by f(x) = 30,000(.85)x, where x represents the number of years since the purchase of the car, and f(x) represents the value of the car. By what percent does Sammy's car depreciate each year?
In a depreciation equation, you multiply the value of the car by the percent of depreciation minus 1.
In the given equation you are multiplying the value of the car by (.85)
This means the percent of depreciation would be 1 - 0.85 =0.15 which is 15%
The car depreciates by 15% every year.
Answer:
The car depreciates by 15% every year.
Step-by-step explanation:
35 POINT QUESTION, WILL MARK BRAINLIEST. Which of the following options is a 3rd degree polynomial with exactly 1 real root?
Answer:
A. F(x) = x^3+9x^2+27x+27
Step-by-step explanation:
I am not 100% sure but I think this is right.
I found the root for this equation: x=-3
Hope this helps!
Answer:
The correct option is D.
Step-by-step explanation:
In option A,
The given function is
[tex]F(x)=x^3+9x^2+27x+27[/tex]
[tex]F(x)=x^3+3(3)x^2+3(3^2)x+3^3[/tex]
[tex]F(x)=(x+3)^3[/tex] [tex][\because (a+b)^3=a^3+3a^2b+3ab^2+b^3][/tex]
Equate the function equal to zero, to find the roots.
[tex](x+3)(x-3)(x-3)=0\Rigtharrow x=-3[/tex]
The real root of this function is -3 with multiplicity 3. It means this function has 3 real roots.
In option B,
The given function is
[tex]F(x)=x^3+3x^2-9x-27[/tex]
[tex]F(x)=x^2(x+3)-9(x-3)[/tex]
[tex]F(x)=(x^2-9)(x+3)[/tex]
[tex]F(x)=(x+3)(x-3)(x+3)[/tex] [tex][\because a^2-b^2=(a+b)(a-b)][/tex]
Equate the function equal to zero, to find the roots.
[tex](x+3)(x-3)(x+3)=0\Rigtharrow x=-3,3,-3[/tex]
Therefore, this function has 3 real roots.
In option C,
The given function is
[tex]F(x)=x^3-9x^2+27x-27[/tex]
[tex]F(x)=x^3-3(3)x^2+3(3^2)x-3^3[/tex]
[tex]F(x)=(x-3)^3[/tex] [tex][\because (a-b)^3=a^3-3a^2b+3ab^2-b^3][/tex]
Equate the function equal to zero, to find the roots.
[tex](x-3)(x-3)(x-3)=0\Rigtharrow x=3[/tex]
The real root of this function is 3 with multiplicity 3. It means this function has 3 real roots.
In option D,
[tex]F(x)=x^3+3x^2+9x+27[/tex]
[tex]F(x)=x^2(x+3)+9(x+3)[/tex]
[tex]F(x)=(x+3)(x^2+9)[/tex]
Equate the function equal to zero, to find the roots.
[tex](x+3)(x^2+9)=0[/tex]
[tex]x+3=0\Rightarrow x=-3[/tex]
[tex]x^2+9=0\Rightarrow x^2=-9\Rightarrow x=\pm 3i(Imaginary)[/tex]
The roots of this functions are -3, 3i and -3i. Since this function has exactly one real root, therefore option D is correct.
If JK and LM are congruent and parallel, then JKL and MLK are congruent.
Answer:
Given statement is TRUE.
Step-by-step explanation:
Given that line segment JK and LM are parallel. From picture we see that LK is transversal line.
We know that corresponding angles formed by transversal line are congruent.
Hence ∠JKL = ∠ MLK ...(i)
Now consider triangles JKL and MLK
JK = LM {Given}
∠JKL = ∠ MLK { Using (i) }
KL = KL {common sides}
Hence by SAS property of congruency of triangles, ΔJKL and ΔMLK are congruent.
Hence given statement is TRUE.
Antonio earns $5 an hour for raking leaves. He also has $35 in savings. Which equation shows the amount of money, m, Antonio will have after raking leaves for a number of hours, h?
Answer:
35 + 5h = m
Step-by-step explanation:
In the figure shown, what is the measure of angle x?
150 degrees
110 degrees
105 degrees
100 degrees
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
In ΔABC,
∠A= 30°
∠B=75°
We need to find the value of ∠ACD=x
As we know that "Sum of interior angles is equal to exterior angle":
So, we will have,
[tex]\angle A+\angle B=\angle ACD\\\\30\textdegree+75\textdegree=\angle ACD\\\\105\textdegree=\angle ACD[/tex]
Hence, Third option is correct.
Answer:
The answer is 105 degrees
180-75=105
The male elephant weighs 8,000 pounds wich is the is th same as 4 tons the female weighs 7,000 pounds how many tons does the female weighs
Answer:
3.5 tons
Step-by-step explanation:
A summer camp has 32 campers. A total of 22 of them swim, 20 play softball, and 5 do not swim or play softball. Which values complete the table?
a = 15, b = 10, c = 7, d = 5, e = 12
a = 15, b = 7, c = 5, d = 10, e = 12
a = 14, b = 7, c = 5, d = 12, e = 10
a = 14, b = 12, c = 7, d = 5, e = 10
Answer:
a = 15, b = 7, c = 5, d = 10, e = 12
Step-by-step explanation:
You only need to find d.
22+d=32, d=10
Only one choice has d=10
Don't waste time checking the others.
Answer:
It’s B
Step-by-step explanation:
Find tan θ if sec θ = √26/5 and sin θ < 0.
Answer:
Find tan θ if sec θ = (sqrt26)/5 and sin θ < 0 = tan θ = -1/5
Step-by-step explanation:
cos θ = 5/√26
opposite side = s
s^2 = 26-25 = 1
s = -1
tan θ = -1/5