Answer: Angle I is congruent to angle L
Step-by-step explanation:
Did da test
To prove ΔGHI and ΔJKL are similar following statements must be true,
i) angle I and angle L are congruent.
ii) angle G and angle J are congruent
iii) sides of the triangles are in proportion
⇒[tex]\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}[/tex][tex]\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}[/tex]
What are similar triangles?"Two or more triangles are similar if and only if the corresponding angle measures same and their corresponding side lengths are in proportion.."
What is dilation?"It is a geometric transformation where there is a change in the size of an object without changing its shape.""The size of the object changes on the basis scale factor."For given example,
ΔGHI is dilated to form new ΔJKL.
Also, angle H is congruent to angle K.
To prove ΔGHI and ΔJKL are similar.
i) angle I and angle L are congruent.
ii) angle G and angle J are congruent
iii) sides of the triangles are in proportion
⇒[tex]\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}[/tex]
Therefore, to prove ΔGHI and ΔJKL are similar following statements must be true,
i) angle I and angle L are congruent.
ii) angle G and angle J are congruent
iii) sides of the triangles are in proportion
⇒[tex]\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}[/tex]
Learn more about the similar triangles here:
https://brainly.com/question/25882965
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The measure of an angle is 29º. What is the measure of its complementary angle?
help? please?
9514 1404 393
Answer:
61°
Step-by-step explanation:
An angle and its complement total 90°. Your angle of interest is ...
90° -29° = 61° . . . complementary angle to 29°
If a force of 50 pounds is directed 30° from the horizontal, what vector represents this force?
Answer:
[tex]F_x=43.30\ N[/tex]
Step-by-step explanation:
Given that,
Force, F = 50 pounds
It is directed at 30° from the horizontal.
The force will be given by :
[tex]F_x=F\cos\theta\\\\=50\times \cos(30)\\\\=43.30\ N[/tex]
So, the required force is 43.30 N.
(-2)⁰+(-2)¹+(-2)²+-2)³
Answer:
-15
Step-by-step explanation:
-2 to the power 0 = -1
-2 to the power 1 = -2
-2² = -4
-2³ = -8
-1 + -2 + -4 + -8 = -15
A path 5m wide is to be built along the border and inside a square garden of side 90m. Find the cost of cementing the path at the rate of Rs.10 per meter square.Required to answer. Single choice.
Answer:
Total cost of cementing the path = Rs. 17,000.
Step-by-step explanation:
Let the square garden be PQRS
Let the region inside the garden (PQRS) be KLMN.
Given the following data;
Length of sides of PQRS = 90m
Width of path = 5m
Cost = Rs. 10 per m²
Area of PQRS = 90 * 90
Area of PQRS = 8100m²
To find the area of KLMN;
KL = KN = 90 - (5 + 5)
KL = KN = 90 - 10
KL = KN = 80m
Area of KLMN = KL * KN
Substituting into the equation, we have;
Area of KLMN = 80 * 80
Area of KLMN = 6400 m²
Area of path = Area of PQRS - Area of KLMN
Area of path = 8100 - 6400
Area of path = 1700 m²
Total cost of cementing the path = Area of path * Cost
Total cost of cementing the path = 1700 * 10
Total cost of cementing the path = Rs. 17,000
If ABCD is an isosceles trapezoid what is the value of X?
61. Often it is necessary to rearrange an equation so that one variable is expressed in terms of others. For example, the equation D = 3t expresses D in terms of t. To express t in terms of D, divide both sides of this equation by 3 to obtain D/3 = t.
(a) Solve the equation C = 2πr for r in terms of C.
(b) Solve the equation p = 2w + 2h for w in terms of p and h.
(c) Solve the equation 3x − 2y = 6 for y in terms of x.
Search entries or author
Answer:
after it is necessary to rearrange and equations for that one variable is expressed in terms de in term of tea to express it in terms of d we need to solve the equation c is equal to fir for our in terms of c solve the equation p is equal to 2 w plus two hours for w in terms of p and h
Answer:
after it is necessary to rearrange and equations for that one variable is expressed in terms de in term of tea to express it in terms of d we need to solve the equation c is equal to fir for our in terms of c solve the equation p is equal to 2 w plus two hours for w in terms of p and h
ive just joined into a class from remote to now hybrid. we are doing how to find out if an ordered pair is a solution to the linear equation. i am so lost. please help.
Answer:
Step-by-step explanation:
You'll be given an equation that contains an x and a y.
You'll also be given an ordered pair. Plug the ordered pair into the equation and see if the equation is true.
For example:
Is (0,4) a solution to the equation 2x+3y = 15 ?
Plug the coordinates of (0,4) into the equation:
2·0 + 3·4 = 15
This simplifies to 12 = 15, which is obviously false, so (0,4) is not a solution to the equation.
6.
5.7 + 2(w + 1) = 2w + 9
- 8(4 + 9r) = 7(- 2 – 11r)
-
Answer:
0
Step-by-step explanation:
are given:
\displaystyle \frac{\sin^2(x)-\sin(x)-2}{\sin(x)-2}
sin(x)−2
sin
2
(x)−sin(x)−2
To make it simpler and more clear, we can let u = sin(x). So:
\displaystyle \frac{u^2-u-2}{u-2}
u−2
u
2
−u−2
Now, it becomes obvious that we can factor, which produces:
\displaystyle =\frac{(u-2)(u+1)}{u-2}=
u−2
(u−2)(u+1)
Cancel:
=u+1=u+1
And substituting back:
=\sin(x)+1=sin(x)+1
Hence, our answer is A.
11 + 5 + 52 x 12 – 10 =
(11 + 5) + 52 x (12 - 10) =
Which of the following could be the lengths of the sides of a 30-60-90 triangle?
Answer: D. 15 square root with 3 inside
Step-by-step explanation:
Just try it
Answer:
c
Step-by-step explanation:
How would the area of a triangle be affected if the base and height are dilated by 1/2
Answer:
The area would reduce to 1/4 the original area
Step-by-step explanation:
The area of a triangle = (1/2)(base)(height) or bh/2
If the triangle base and height were to reduce by one-half, the formula would change to:
Area = (1/2)(1/2 base)(1/2 height) or bh/8. Which is a reduction by 1/4
A 6 foot man measured his shadow at13 feet 9 inches. Then he measured the
shadow of a flagpole at 125 feet. How tall is the flagpole?(Round to the
nearest tenth)
Answer:
The flagpole is 54.5 inches tall.
Step-by-step explanation:
We solve this question using proportions, by rule of three.
Each feet has 12 inches. So
A 6 foot man measured his shadow at13 feet 9 inches.
So when the real height is of 6 feet, the shadow is of 13 feet + (9/12) feet = 13.75 feet.
When the shadow is of 125 feet, the height is x. So
6 feet - 13.75 feet
x feet - 125 feet
Applying cross multiplication
[tex]13.75x = 6*125[/tex]
[tex]x = \frac{6*125}{13.75}[/tex]
[tex]x = 54.5[/tex]
The flagpole is 54.5 inches tall.
Sketch the graph of each function. Then State the domain, range and increasing, decreasing intervals. Part 1
Problem 15
Answers:
Graph: Shown belowDomain: [3, infinity) Range: [2, infinity)Increasing interval: [2, infinity)Decreasing interval: NoneEach interval is interval notation.
----------------------------------
Explanation:
To get the graph, you can plug in various x values to find their paired y values, then draw a curve through those points. You can only plug in x values that are 3 or larger, as I'll mention later in the next paragraph. A quicker way to get the graph is to use technology. I used GeoGebra to generate the graphs below.
To get the domain, we need to ensure that the stuff under the square root is never negative. So we need to make the x-3 to be 0 or larger. Solving [tex]x-3 \ge 0[/tex] leads to [tex]x \ge 3[/tex] showing that 3 is the smallest value we can plug in. The domain is the interval from 3 to positive infinity. We can write that as [tex]3 \le x < \infty[/tex] which condenses to the interval notation [3, infinity). Note how the square bracket is used to include the endpoint.
The range can be determined from the graph. The lowest point is when y = 2, so the range consists of y outputs that are 2 or larger. We write the interval notation [2, infinity) to mean [tex]2 \le y < \infty[/tex]
The graph also helps us see where the curve is increasing or decreasing. In this case, the curve goes uphill as we move from left to right. Therefore, the graph is increasing over its entire domain. We write the domain as the answer here. Because the function increases over the entire domain, there's no room for the function to decrease.
===========================================================
Problem 16
Answers:
Graph: Shown belowDomain: [-1, infinity) Range: [-3, infinity)Increasing interval: [-1, infinity)Decreasing interval: None----------------------------------
Explanation:
We follow the same idea as the previous problem.
This time we want the x+1 under the square root to be 0 or larger, so [tex]x+1 \ge 0[/tex] solves to [tex]x \ge -1[/tex] telling us the smallest input allowed. The value of x can be this or larger.
Since this is an increasing function throughout the domain (similar to the previous problem), this means that the smallest domain value corresponds exactly to the smallest range value. Plugging in x = -1 leads to y = -3 which is the smallest possible output. As x gets bigger, so does y. The graph shows that the lowest point occurs when y = -3 to visually confirm this.
The increasing interval is over the entire domain, so we just write the domain again for the increasing interval. This means we write "none" for the decreasing interval.
Side note: The graphs are shown together on the same xy coordinate axis, but for your hw problem, you'll have the graphs on their own separate grid.
Help!! I’ll give u Brainly!
Answer:
(-4,-2)
Step-by-step explanation:
Point f is on x -4, which is in the first slot and y -2 which is your second slot
i really need help!!
Answer:
#8. 2
#9. 7
#10. 2
#11. 2
#12. 0
#13. -4
#14. 17
#15. 1
Answer:#8=2
#9=-11
#10=8
#11=2
#12=0
#14=17
#15=1
Step-by-step explanation: #8-13 (Subtract the numbers using a number line, than add the numbers using a integer chips, after that calculate the sum of the differences) #14-15( normal solving stepping for integers(recommend using a T1-84 Calculator)
Two consecutive positive integers have a product of 6 what are the integers
separate the answer with a comma
Answer:
2,3
Step-by-step explanation:
2 and 3 are consecutive numbers, and when you multiply them, you get 6.
Hope this helps.
Have a nice day.
How to write and graph at least 10 on a number line?
Answer:
x <= 10
<= means less or equal to
Step-by-step explanation:
At least means less or equal to
What da answer I’d does not say
Could anyone Help?
Please
Answer:
a.2^(a+b+c)
b.2^(a+b+a-b)=2^(2a)or 4^a
c.2^(a+b+c)/2^(a+b)=2^(a+b+c-a-b)=2^c
Let T: Rn → Rn be an invertible linear transformation, and let S and U be functions from Rn into Rn such that
S(T(x)) = x and U (T(x)) = x for all x in R^n
Show that
U(v)= S(v) for all v in R^n
Required:
Compute S(v) and U(v).
Answer:
Follows are the solution to this question:
Step-by-step explanation:
[tex]T: 1 \ R^n \to 1 \ R^n[/tex] is invertible lines transformation
[tex]S[T(x)]=x \ and \ V[T(x)]=x \\\\t'x \ \varepsilon\ 1 R^n\\\\[/tex]
T is invertiable linear transformation means that is
[tex]T(x) =A x \\\\ where \\\\ A= n \times n \ \ matrix[/tex]
and [tex]\ det(A) \neq 0 \ \ that \ is \ \ A^{-1} \ \ exists[/tex]
Let
[tex]V \varepsilon\ a\ R^{n} \ consider \ \ u= A^{-1} v \varepsilon 1 R^n\\\\T(u)= A(A^{-1} v)=(A \ A^{-1}) \\\\ v= I_{n \times n} \cdot v = v[/tex]
so,
[tex]s[T(u)]=v[T(u)]\\\\s(v)=v(v) \ \ \forall \ \ v \ \ \varepsilon \ \ 1 R^n[/tex]
Let $f(x) = 4x - 7$, $g(x) = (x + 1)^2$, and $s(x) = f(x) + g(x)$. What is $s(3)$?
s(3)=4(3)-7+(3+1)^2
s(3)=12-7+16
s(3)=21
Answer:
21
Step-by-step explanation:
We find that s(x) = 4x - 7 + (x + 1)^2. Expanding, we get s(x) = x^2 + 6x - 6. Plugging in x = 3, we have s(3) = 3^2 + 6 x 3 - 6 = 21.
Alternatively, we can compute that f(3) = 5 and g(3) = 16, so s(3) = f(3) + g(3) = 21.
An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in firecontrol by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently.
Required:
a. What is the probability that all of the sprinklers will operate correctly in a fire?
b. What is the probability that at least 7 of the sprinklers will operate correctly in a fire?
c. What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.98?
Answer:
0.028 ; 0.649 ; 4
Step-by-step explanation:
P(correctly activation), p = 0.7
Number of sprinklers, n = 10
q = 1 - p = 1 - 0.7 = 0.3
Using the binomial probability relation :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
Probability that all sprinklers activate correctly;
P(x = 10) = 10C10 * 0.7^10 * 0.3^0
P(x = 10) = 1 * 0.0282475249 * 1
P(x = 10) = 0.028
Probability that atleast 7 will operate correctly :
P(x ≥ 7) = p(x = 7) + p(x = 8) + p(x = 9) + p(x = 10)
P(x ≥ 7) = 0.267 + 0.233 + 0.121 + 0.028
P(x ≥ 7) = 0.649
3.)
Probability of atleast 1 operates :
P(x ≥ 1) = 0.98
1 - probability of 0 operates
1 - p(x =0)
P(x = 0) = nC0 * 0.7^0 * 0.3^n = 0.02
Recall :
nC0 = 1 ;
1 - p(x = 0)
P(x = 0) = 1 * 1 * 0.3^n = 0.02
0.3^n = 0.02 - - - (1)
0.3^3.24 = 0.02 - - - (2)
Comparing (1) and (2)
n = 3.24
Since, n cannot be a fraction ;
Then n is rounded to the next whole number = 4
x (power1)+ 10 and x(power0)+10, when x =10
Answer:
20
11
Step-by-step explanation:
10^1+10 steps:
10^1+10
Calculate 10 to the power of 1 and get 10.
10+10
Add 10 and 10 to get 20.
20
10^0+10 steps:
10^0 +10
Calculate 10 to the power of 0 and get 1.
1+10
Add 1 and 10 to get 11.
11
Which equation is true when x = 6 a. 7x = 35 b. (8+3)x = 28 c. 3x – x + 2 = 14 d. 6x + 3x =225
Answer:
c
Step-by-step explanation:
3X-x+2=14
3*6-6+2=14
14=14
plz make me brainliest
The result of multiplying a number by 3 and subtracting 5 is the
same as doubling the number and adding 9. What is the number?
Answer:
n = 14
Step-by-step explanation:
let 'n' = the number
3n - 5 = 2n + 9
n - 5 = 9
n = 14
Answer:
14
Step-by-step explanation:
We have to replace the unknown quantity with "x" and work with it.
The result of multiplying a number by 3 and substracting 5
3x - 5
Is the same as
3x-5= (__)
Doubling the number and adding 9
3x- 5= 2x+9
Then we solve it like any equation
3x - 5 = 2x + 9
3x - 2x = 9 + 5
x = 14
Hope it was helpful ;)
In a computer class, a group of 4 girls shared a computer and printer to print their math projects. The total time to print the project was 1/2 hour. Each girl needed the same amount of time to print her project. What part of an hour did it take each of the 4 girls to print her project?
Answer:
30
Step-by-step explanation:
cause i said so
I need help!!! 10points!!!
I need the slope of this and to come up with an equation for it!! THANK U
Answer:
y = 37/5x + 9
Step-by-step explanation:
The points are not plotted on a single straight line, so I will find the general slope using the first and last point on the graph.
(5, 46) & (10, 83)
slope-intercept form: (y₂ - y₁) / (x₂ - x₁)
(83 - 46) / (10 - 5)
Simplify.
(37)/(5)
Your slope is 37/5.
y = 37/5x + b
To find b, plug in a point to x and y.
46 = 37/5(5) + b
46 = 37 + b
b = 9
Your equation is: y = 37/5x + 9
Check by plugging in the other point.
83 = 37/5(10) + 9
83 = 74 + 9
83 = 83
Your equation is correct.
Hope this helps!
What is the square root
Answer:
the square root is 2.2
Answer:
2.2
Step-by-step explanation:
make me brainestly
the guy who did the second answer wants beef
Yuri thinks 3/4 is a root of the following function.
q(x)=6x^3+19x^2-15x-28
Explain to Yuri why 3/4 cannot be a root.
Answer:
Since [tex]q(\frac{3}{4}) \neq 0[/tex], 3/4 cannot be a root of q(x).
Step-by-step explanation:
Root of a function:
If [tex]x^{\ast}[/tex] is a root of a function f(x), we have that [tex]f(x^{\ast}) = 0[/tex].
In this question.
We have to find [tex]q(\frac{3}{4})[/tex]. So
[tex]q(\frac{3}{4}) = 6(\frac{3}{4})^3 + 19(\frac{3}{4})^2 - 15(\frac{3}{4}) - 28[/tex]
[tex]q(\frac{3}{4}) = \frac{162}{64} + \frac{171}{16} - \frac{45}{4} - 28[/tex]
[tex]q(\frac{3}{4}) = \frac{162}{64} + \frac{684}{64} - \frac{720}{64} - \frac{1792}{64}[/tex]
[tex]q(\frac{3}{4}) \neq 0[/tex]
Since [tex]q(\frac{3}{4}) \neq 0[/tex], 3/4 cannot be a root of q(x).
HELP WILL GIVE BRAINLIST
Answer:
471 square feet
Step-by-step explanation:
150
x3.14
471