Triangle ABC
A
B
C
and triangle DEF
D
E
F
are similar. What is the measure of side DF
D
F
?
Answers
Answer:
DF = 15 cm
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{DF}{AC}[/tex] = [tex]\frac{EF}{BC}[/tex] ( substitute values )
[tex]\frac{DF}{9}[/tex] = [tex]\frac{25}{15}[/tex] ( cross- multiply )
15 DF = 9 × 25 = 225 ( divide both sides by 15 )
DF = 15
Answer:
12
Step-by-step explanation:
1. Use the Pythagorean theorem for triangle ABC
a squared (one side of the triangle) + b squared (another side) = c squared (hypotenuse)
so
c squared - b squared = a squared
225 - 81 = 144 ( Find the square root )
which is 12
since Triangle ABC is the same with Triangle DEF then
DF = 12
Related Questions
Jolene invests her savings in two bank accounts, one paying 6 percent and the other paying 10 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 8602 dollars. How much did she invest at each rate?
Answers
The amount she invested at each rate of interest for the simple interest are $39,100 and $78,200.
Given that,
Jolene invests her savings in two bank accounts.
Rate of interest for one account = 6% per year
Rate of interest for the other account = 10% per year
Let x be the principal amount invested in the account yielding 10% interest.
Interest amount = 0.1x
Principal amount in the account of 6% interest = 2x
Interest amount = 0.06 × 2x = 0.12x
Annual interest = $8602
0.1x + 0.12x = 8602
0.22x = 8602
x = $39,100
Amount invested for 10% interest account = $39,100
Amount invested for 6% interest account = 2 × $39,100 = $78,200
Hence the amount invested are $39,100 and $78,200.
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Suppose f(x) =8^3x and g(x) =8^4x which of these function operations are correct select all that apply
Answers
Suppose [tex]f(x) =8^{3x[/tex] and [tex]g(x) =8^{4x[/tex], function operations that are correct include the following:
A. (f + g)(x) = [tex]8^{3x} + 8^{4x}[/tex]
B. (f × g)(x) = [tex]8^{7x}[/tex]
C. (f - g)(x) = [tex]8^{3x} - 8^{4x}[/tex]
What is an exponent?In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:
(f × g)(x) = [tex]8^{3x+ 4x}=8^{7x}[/tex]
(f ÷ g)(x) = [tex]8^{3x- 4x}=8^{-x}[/tex]
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Ted's company has received an order to print 106 pages. Ted's company has 100 machines, each of which can print 104 pages a day.
Ted’s company can print the 106 pages in
10 days
.
In exponent form, this number of days can be represented as
10^1
.
Answers
The number of days required to complete the job in exponent form is 10¹ = 10.
What is the exponent form of the number of days?
The exponent form of the number of days is calculated as follows;
number of pages that can be printed by all machines = n x P
where;
n is the number of machinesP is the pages per machineN = 100 x 104
N = 10400 pages/day
However, the Ted's company needs 10 days to print 106 pages, our equation is formed as follows;
x = log(y)
where;
y is the number of days = 1010ˣ = y
10ˣ = 10
x = 1
so the exponential form = 10¹ = 10
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48 inches by 36 inches what is the square feet
Answers
Answer:
1728 square ft²
Step-by-step explanation:
48x36=1728
Answer:
[tex]\large \boxed{\mathrm{Area}}[/tex] = [tex]\large \boxed{\mathrm{12 \ ft^2}}[/tex]
Steps:
12 inches = 1 foot
48 / 12 = 4 [tex]\meduim \boxed{\mathrm{feet}}[/tex]
36 / 12 = 3 [tex]\large \boxed{\mathrm{feet}}[/tex]
Answer:
3 x 4 = 12 ft²
Using any example of a 2 by 2 matrix;
Show that (A inverse) inverse = A; where A is a 2 by 2 matrix
Answers
The inverse of A is A^-1 (see picture), where A^-1 = (1/(determinant of A))*(adjoint of A). Note that the inverse of A only exists if ad - bc ≠ 0.
So, if ANY example of a 2 by 2 matrix is allowed… we use an example where a = 1, b = 2, c = -3, d = -5. The inverse matrix will have the terms -5, -2, 3, 1. (See photo)
To show that the inverse OF the inverse equals A, follow the same process. And.. yes, (A^-1)^-1 = A. We want to see the identity matrix 1, 0, 0, 1 since A*A^-1 = I (this is an uppercase i).
I’m on my phone so it’s harder to type. Refer to the picture to see my work:
I hope this helps!
Hurry pls Time limit
Tell me the domain and the range
Tell me whether the graph is a function or not
The answer choices are below
Answers
Answer:
its not a function
Step-by-step explanation:
The perimeter of a rectangle is 120 meters and the length is 40 meters longer than the width. Find the dimensions of the rectangle. Let x= the length and y= the width. The corresponding modeling system is {2x+2y=120x−y=40 . Solve the system graphically.
Answers
The dimension of the rectangle is 50 meters by 10 meters
What is the perimeter of a figure?The perimeter of a figure is the sum of all the external sides of the figure
The formula for calculating the perimeter of rectangle [tex]= 2(\text{l}+\text{w})[/tex]
If the length is 40 meters longer than the width, then:
[tex]\text{l} = 40 + \text{w}[/tex]
Substitute
[tex]120 = 2(40+2\text{w})[/tex]
[tex]60 = 40 + 2\text{w}[/tex]
[tex]30 = 20+ \text{w}[/tex]
[tex]\bold{w = 10 \ meters}[/tex]
Since [tex]\text{l} =40 + \text{w}[/tex]
[tex]\text{l} =40 +10[/tex]
[tex]\bold{l=50 \ meters}[/tex]
Hence the dimension of the rectangle is 50 meters by 10 meters
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Sophia wishes to retire at age 65
with $1,600,000
in her retirement account. When she turns 28
, she decides to begin depositing money into an account with an APR of 9%
compounded monthly. What is the monthly deposit that Sophia must make in order to reach her goal? Round your answer to the nearest cent, if necessary
Answers
Answer:
To determine the monthly deposit that Sophia must make in order to reach her retirement goal, we can use the formula for the future value of an annuity:
FV = P * ((1 + r/n)^(nt) - 1) / (r/n)
where:
FV = future value of the annuity (which is Sophia's retirement goal of $1,600,000)
P = monthly deposit
r = annual interest rate (which is 9%)
n = number of times interest is compounded per year (which is 12 for monthly compounding)
t = number of years until retirement (which is 65 - 28 = 37)
Substituting the given values, we get:
1600000 = P * ((1 + 0.09/12)^(12*37) - 1) / (0.09/12)
Simplifying and solving for P, we get:
P = 1600000 * (0.09/12) / ((1 + 0.09/12)^(12*37) - 1)
P ≈ $524.79
Therefore, Sophia must make a monthly deposit of approximately $524.79 in order to reach her retirement goal of $1,600,000.
Step-by-step explanation:
18. What is the slope of the line that passes through
the points
Answers
Check the picture below.
bearing in mind that a vertical line always has that slope.
A researcher started tracking the number of mice in the lab.
Which of the following equations models how many mice there will be in the lab after 10 months?
Select one:
m(10) = 3 + 2(10)
m(10) = 2(3)^10
m(10) - 3(10)^2
m(10) = 3(2)^10
Answers
The correct equation that models how many mice there will be in the lab after 10 months is m(10) = 3 × 2^10.
We have,
From the given data, we can see that the number of mice is being multiplied by 2 every month.
That means the growth is exponential.
We can use the formula for exponential growth:
[tex]m(t) = a \timesr^t[/tex]
where m(t) is the total number of mice after t months, a is the initial number of mice (when t = 0), and r is the common ratio
From the given data, we can see that when t = 0, there are 3 mice.
So, a = 3.
Also, we can see that the common ratio is 2 (i.e., the number of mice is being multiplied by 2 every month).
Now,
The equation that models how many mice there will be in the lab after 10 months is:
m(10) = 3 × 2^10
Simplifying this equation gives:
m(10) = 3 × 1024
m(10) = 3072
Therefore,
The correct equation that models how many mice there will be in the lab after 10 months is m(10) = 3 × 2^10.
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Solve the equation 4m = 28 for m.
A. 3
B. 4
C. 5
D. 7
Answers
Answer:
Dividing both sides by 4, we get:
4m/4 = 28/4
Simplifying, we get:
m = 7
Therefore, the answer is D. 7.
Please help I need this will give 100 points please help
Answers
The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:
-∞ < x < 1 or 1 < x < 6 or 6 < x < 2
Solving Inequality in a given domainGiven the inequality,
f(x²-2) < f(7x-8) over D₁ = (-∞, 2)
We need to find the values of x that satisfy this inequality.
Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.
First, we can find the values of x that make the expressions inside the function equal:
x² - 2 = 7x - 8
Simplifying, we get:
x² - 7x + 6 = 0
Factoring, we get:
(x - 6)(x - 1) = 0
So the values of x that make the expressions inside the function equal are x = 6 and x = 1.
We can use these values to divide the domain (-∞, 2) into three intervals:
-∞ < x < 1, 1 < x < 6, and 6 < x < 2.
We can choose a test point in each interval and evaluate
f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.
Let's choose -1, 3, and 7 as our test points.
When x = -1, we have:
f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)
Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.
When x = 3, we have:
f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)
Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.
When x = 7, we have:
f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)
Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.
Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:
-∞ < x < 1 or 1 < x < 6 or 6 < x < 2
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I can prove that 2=1, where is the error?
X = 1
X+X = 1+X
2x = 1+X
2x = X+1
2X-2 = X+1-2
2x-2 = X-1
2 (x-1)/(x-1) = X-1/X-1
2 times 1 = 1 1-1 / 1-1
2 = 1
I subtracted -2
because thats the # I chose to subtract with.
Answers
The mistake is when you try to divide by X - 1, because you can't divide by zero.
Where is the problem in this procedure?Here we start by defining:
X = 1
The second step makes sense, we are adding the same value in both sides:
X + X = X + 1
2X = X + 1
Now subtract 2 in both sides:
2X - 2 = X + 1 - 2
2X - 2 = X - 1
Here is the mistake, you divide both sides by X - 1
But we already defined that X = 1
Then you are trying to divide by zero, and that opeartion is not defined, that is why you reach a false equation.
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the sum of three numbers is 56. the difference of the larges and smallest is 44 and the sum of the two smaller numbers is 16. what are the numbers?
Answers
The three numbers are -2, 42 and 16 these we obtained by solving the equations
Let the three numbers x, y, and z. We know that:
x + y + z = 56 (Equation 1)
z - x = 44 (Equation 2)
x + y = 16 (Equation 3)
From Equation 3, we can solve for one of the variables in terms of the other:
y = 16 - x
Substituting this into Equation 1, we get:
x + (16 - x) + z = 56
Simplifying this equation, we get:
z = 40 - x (Equation 4)
Substituting Equation 4 into Equation 2, we get:
(40 - x) - x = 44
Simplifying this equation, we get:
40 - 2x = 44
Subtracting 40 from both sides, we get:
-2x = 4
Dividing both sides by -2, we get:
x = -2
z = 40 - (-2) = 42
Finally, using Equation 1, we can solve for y:
-2 + y + 42 = 56
y=16
Hence, the three numbers are -2, 42 and 16
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Claire tried to subtract two polynomials which step did Claire make an error or are there no errors
Answers
If diameter EF bisects BC, what is the angle of intersection?
Answers
Answer:
The angle of the intersection is 90 degrees
Step-by-step explanation:
How I know this is because EF is the diameter, which means that arc EF is equal to 180 degrees. Because we know this that means when it is spilt into two parts, the arc and angle measure has to be 90 degrees.
Another way to do this is to remember that a circle is 360 degrees and the circle is split into 4 parts. So all you have to do is divide 360/4 to get 90. Your answer.
Find the median of the data. $93,81,94,71,89,92,94,99$
Answers
Answer:
92.5
Step-by-step explanation:
First, we need to put the data in order from smallest to largest:
$71, 81, 89, 92, 93, 94, 94, 99$
There are 8 numbers in the data set, which is an even number. To find the median, we need to average the two middle numbers.
The middle two numbers are 92 and 93, so the median is:
$(92+93)/2 = 92.5$
Therefore, the median of the data is 92.5.
Find the surface area of the square pyramid (above) using its net (below)
Answers
Answer:
Step-by-step explanation:
the square base = 5 * 5 = 25
each of the triangular sides = 4*2.5=10
so… 25+(10*4)=25+40=65
Just look at the picture
Answers
Answer:
perimeter = 84 feet
Step-by-step explanation:
using Pythagoras' identity in the right triangle to find a
a² + 35² = 37²
a² + 1225 = 1369 ( subtract 1225 from both sides )
a² = 144 ( take square root of both sides )
a = [tex]\sqrt{144}[/tex] = 12
then
perimeter = 35 + 37 + 12 = 84 feet
(a + 2)/(1 + a + a ^ 2) - (a - 2)/(1 - a + a ^ 2) - (2a ^ 2)/(1 + a ^ 2 + a ^ 4)
Answers
The first term has a denominator of 1 + a + a^2, the second term has a denominator of 1 - a + a^2, and the third term has a denominator of 1 + a^2 + a^4.
To find a common denominator, we need to factor each of the three denominators.
The first denominator can be factored as (a + 1/2)^2 + 3/4.
The second denominator can be factored as (a - 1/2)^2 + 3/4.
The third denominator can be factored as (a^2 - a√2 + 1)(a^2 + a√2 + 1).
Now we can rewrite the expression with a common denominator:
[(a + 2)((a - 1/2)^2 + 3/4) - (a - 2)((a + 1/2)^2 + 3/4) - 2a^2(a^2 - a√2 + 1)(a^2 + a√2 + 1)] / [(a + 1/2)^2 + 3/4][(a - 1/2)^2 + 3/4](a^2 - a√2 + 1)(a^2 + a√2 + 1)]
We can simplify this expression by multiplying out the terms in the numerator and combining like terms. After doing so, we get:
[-4a^4 + 8a^3 - 4a^2 - 4a√2 + 12a - 4√2] / [(a + 1/2)^2 + 3/4][(a - 1/2)^2 + 3/4](a^2 - a√2 + 1)(a^2 + a√2 + 1)]
So the simplified expression is:
(-4a^4 + 8a^3 - 4a^2 - 4a√2 + 12a - 4√2) / [(a + 1/2)^2 + 3/4][(a - 1/2)^2 + 3/4](a^2 - a√2 + 1)(a^2 + a√2 + 1
which ordered pair is a solution to the Equation? 3y = -2x - 4
(1, -2)
(-1, 3)
(3, 4)
(-2, 4)
Answers
The ordered pair that is a solution to the equation 3y = -2x - 4 is given as follows:
(1, -2).
How to obtain the ordered pair?The equation for this problem is defined as follows:
3y = -2x - 4
To verify whether an ordered pair is a solution to the equation, it must make the equation true.
When x = 1 and y = -2, we have that:
3y = 3(-2) = -6.-2x - 4 = -2(1) -4 = -6.Hence the ordered pair (1,-2) is a solution to the equation for this problem.
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Find the missing angle
A
B
C
D
Answers
Answer:
53
Step-by-step explanation:
20+8=28
90-28=62
62-9=53
90 angle!
Let GH be the directed line segment beginning at point G(4,4) and ending at point H(-7,-1). Find the point P on the line segment that partitions the line segment into the segments GP and PH at a ratio of 5:6.
Answers
The coordinates of point P are (-1, 1 8/11).
We have,
G(4, 4) and H(-7, 1)
m :n = 5:6
Using Section formula
x = (mx₂ + nx₁)/ (m+n) and y = (my₂ + ny₁)/ (m+n)
Here, x₁ = 4, y₁ = -7, x₂ = 4 and y₂ = -1
So, x = (5(-7) + 6(4))/ 11 and y = (5(-1) + 6(4))/ 11
x = -35+24/11 and y = -5 + 24/11
x = -11/11 and y = -19/11
x = -1 and y = 1 8/11
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What are the angles of △ABC with side lengths a=12, b=21, and c=14?
Round each angle to the nearest tenth of a degree and use that rounded value to find the remaining angles.
Answers
Answer: the answer is A=33∘, B=107.5∘, and C=39.5∘ is correct or c
Step-by-step explanation:
To find the angles of triangle ABC with side lengths a=12, b=21, and c=14, we can use the Law of Cosines and then apply the Law of Sines to find the remaining angles. Let's denote the angles as A, B, and C respectively.
According to the Law of Cosines:
c^2 = a^2 + b^2 - 2ab * cos(C)
Plugging in the given side lengths:
14^2 = 12^2 + 21^2 - 2 * 12 * 21 * cos(C)
196 = 144 + 441 - 504 * cos(C)
504 * cos(C) = 389
cos(C) = 389 / 504
C = arccos(389 / 504)
Using a calculator to find the approximate value of C, we get C ≈ 43.5°.
If sin 0 = 3/4 and angle 0 is in quadrant I, what is the exact value of tan20 in simplest radical form?
Answers
The exact value of tan2θ in simplest radical form is -21/√7.
What is the value of tan2θ?The value of tan2θ is calculated as follows;
From Pythagorean identity, we know that;
sin² θ + cos² θ = 1
cos² θ is calculated as follows;
(3/4)² + cos² θ = 1
9/16 + cos² θ = 1
cos² θ = 1 - 9/16
cos² θ = 7/16
cos θ = √(7/16)
tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7
Now, we will find tan 2θ;
tan 2θ = 2tan θ / (1 - tan² θ)
tan 2θ = 2(3/√7) / (1 - (3/√7)²)
tan 2θ = (6/√7) / (-2/7)
tan 2θ = -21/√7
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Marco, Garret, and Dino are hiding during a game of hide-and-seek. Their relative locations are shown in the diagram.
What is the distance between Garret and Dino?
Enter your answer in the box. Round your final answer to the nearest yard.
Answers
The distance between Garret and Dino to the nearest yard is: 21 yds
How to find the missing length of the triangle?The Law of Cosines is defined as a numerical formula that expresses the relationship between the side lengths and points of any triangle. It usually expresses that the square of any particular side of a triangle is equal to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.
Numerically, the Law of Cosines can be expressed as:
c² = a² + b² - 2abcos(C),
where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.
Thus, the distance here is expressed as:
d² = 15² + 17² - 2(15 * 17)cos(81)
d = √434.218
d = 20.838 yds
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Does anyone know the answer to this question
Answers
x= 1+ 3i and x= 1-3i
14. Describe a pattern in the numbers.
9, 12, 15, 18, 21, 24
Answers
9+3=12
12+3=15
15+3=18
18+3=21
21+3=24
24+3=27
Verify Euler’s theorem: (, ) =
3
+
3
.
Answers
The mass of a bowling ball is 9ibs and the volume is 135 in³. How many lbs per cubic inch is its density? Round to the nearest hundreth
Answers
Answer:
9 pounds/135 cubic inches
= 1 pound/15 cubic inches
= .07 pounds/cubic inch