Answer:
D. 48 in.^2
Step-by-step explanation:
Sides DE and AB are corresponding, and the triangles are similar.
linear scale factor = k = AB/DE = 12/60 = 1/5
area square factor = k^2 = (1/5)^2 = 1/25
area of ABC = area of DEF * area scale factor = 1200 sq in * 1/25
area of ABC = 48 sq in
Answer: D. 48 in.^2
The average age of 15 students is 16 years. If teacher’s age is included the average increases
by 1. Find teacher’s age
31
because 15 +16 :31
[tex]. = y1 = \times [/tex]
These figures are similar the area of one is give. Find the area of the other
Answer:
80 in²
Step-by-step explanation:
8/10 = x/100
x = 80
The quadratic 3x^2-24x+72 can be written in the form a(x+b)^2+c, where a, b, and c are constants. What is a+b+c?
Answer:
7
Step-by-step explanation:
Quadratic Equation: 3x² - 24x + 72
The form we are to convert the equation to:
3x² - 24x + 72
a(x + b)² + 72
3(x² - 8x + 24)
Step 1
Make the Quadratic equation (x² - 8x) in the bracket factorisable using completing the square method
3( x² - 8x +(- 8/2)²) + 24
3( x² - 8x + 16 = -24 + 16
3( x² - 8x + 16 + 8 = 0)
3( x² - 8x + 16) + 8
3( x² - 4x + 4x + 16) + 8
3( x(x - 4) -4(x - 4) + 8
3((x - 4)(x - 4) )+ 8
3( (x - 4)² + 8
Using this form
a(x + b)² + c
a = 3
b = -4
c = 8
We were asked to add up constants a, b, c
Therefore,
3 +(-4) + 8
= 7
What is the first step to circumscribe a circle around a triangle? a Find the diameter b Find the angle bisectors c Find the perpendicular bisectors d Draw the circle
Answer:
Step 1-Construct the perpendicular bisector of one side of the triangle.
Step 2-Construct the angle bisector of another side of the triangle.
Explanation:
A circumscribed circle is the circle that passes through all three vertices of the triangle. The center of the circumscribed circle is the circumcenter of the triangle, the point where the perpendicular bisectors of the sides meet
i cant see the answers anyone else has the problem
Answer: im having the same problem
Step-by-step explanation:
A triangle has three sides of the following side lengths: 7, 10, and x^2. What are all of the positive integer values of x such that the triangle exists? Separate your answers using commas and express them in increasing order.
Answer:
x = {2,3,4} (if x can only be positive whole numbers)
Step-by-step explanation:
For a triangle exists, the side lengths of the triangle must be such that the sum of the two shorter sides must be greater than the third side.
This also is equivalent to any two sides must have a sum greater than the third side.
So
7+10 > x^2, => x^2 < 17 => x < sqrt(17) (maximum)
7+x^2 > 10, => x^2 >3 => x > sqrt(3)
Therefore
sqrt(3) < x < sqrt(17)
If x must be an integer,
2< x < 4, or x = {2,3,4}
ABC is a triangle in which DE ∥BC. Find ∠A
Answer:
∠A = 35°
Step-by-step explanation:
From the question above,
Sum of Angles on a straight line = 180°
180° = ∠BDE + ∠ADE
∠BDE = 105°
∠ADE = 180° - 105°
∠ADE = 75°
To find Angle ∠EBC and ∠DEB are alternate angles, this means that they are equal to each other
Hence, ∠EBC = ∠DEB
30° = 30°
Sum of Angles on a straight line = 180°
180° = ∠DEB + ∠BEC + ∠DEA
180° = 30° + 80° + ∠DEA
∠DEA = 180° -(30+ 80)°
∠DEA = 180° - 110°
∠DEA = 70°
It is important to note that the sum of Angles in a triangle = 180°
180° = ∠ADE + ∠DEA + ∠A
∠ADE = 75°
∠DEA = 70°
180° = 75° + 70° + ∠A
∠A = 180° - (75° + 70°)
∠A = 180° - 145°
∠A = 35°
Find the length of the unknown side. Round your answer to the nearest whole number.
7 m
7 m
07 meters
09 meters
10 meters
12 meters
Answer:
10 meters
Step-by-step explanation:
From your question, it seems we are dealing with a triangle and we are given the two legs of the triangle.
The given dimensions are:
7 meters and 7 meters.
Required:
Here, we are required to find the third side of the triangle which is the hypotenus.
Using Pythagoras theorem:
a² + b² = c²
Where a = 7 & b = 7
Thus, we have:
7² + 7² = c²
c² = 49 + 49
c² = 98
Take the root of both sides
√c² = √98
c = √98
c = 9.899
c ≈ 10 meters
Therefore the length of the unknown side is approximately 10 meters
Examine the diagram of circle C. Points A, B, and Q are on circle C. Given that m∠ACB=52∘, what is the arc length of AQB⌢?
Hey there! :)
Answer:
Third choice: 13π/15 in.
Step-by-step explanation:
Begin by finding the circumference of the entire circle. Use the formula
C = 2rπ to solve:
C = 2(3)π
C = 6π.
Next, we can set up a proportion to find the arc length of AQB:
[tex]\frac{6\pi }{360}= \frac{x}{52}[/tex]
Cross multiply:
52 · 6π = 360 · x
312π = 360x
Divide both sides by 360:
312π/360 = 360x/360
x = 13π/15 in.
Answer:
The answer is 77n/15 inches :)
Step-by-step explanation:
Use the screen shot to find the x
Answer:
69
Step-by-step explanation:
A triangle has a 180 degree angle so you do 180-111=69
Answer: x=24
Step-by-step explanation:
lets say 94 is ∠ a
41 is ∠ b
___ ∠ c
111∠ d
x ∠ e
so with that you will figure out that ∠ c is to find X
108-94-41= 45
so ∠ c is 45
now you can ∠a ∠ b∠ c
with that yo take
108-111-45=24
So X=24
HELP ASAPPP ITS TIMED
Given that sin thata= 21/29, what is the value of cos thata, for 0°<thata<90°?
a- sqrt 20/29
b -20/29
c 20/20
d sqrt 20/29
Answer:
The value of cos theta for 0° < theta < 90° will be 20 / 29
Step-by-step explanation:
To solve this problem we can express three trig functions as ratios involving the sides of a right-angle triangle, the adjacent side, the opposite side and the hypotenuse. In this case sin θ = a / c, such that a = 21 and c = 29.
By Pythagorean Theorem,
[tex]b = \sqrt{c^2-a^2} = \sqrt{29^2-21^2} = \sqrt{841-441} = \sqrt{400} = 20[/tex]
Therefore cos θ = b / c = 20 / 29. This is the cosine ration of the adjacent side over the hypotenuse.
What is the constant of proportionality in the equation y = 2.51?
constant of proportionality
Answer:
The constant of proportionality (k) equals the total price (y) divided by the number of cans (x).
Step-by-step explanation:
might help
Hey, can anyone help me out plz?
Answer:
Hey there!
That would be the SAS postulate.
This states that one angle is congruent and between two congruent sides.
Hope this helps :)
What the correct answer fast
Answer:
[tex] s = 5.8 [/tex]
Step-by-step Explanation:
Given:
∆RST,
m < T = 17°
t = RS = 5
m < S = 20°
s = RT = ?
Apply the Law of Sines to find s
[tex] \frac{s}{sin(S)} = \frac{t}{sin(T)} [/tex]
[tex] \frac{s}{sin(20)} = \frac{5}{sin(17)} [/tex]
Multiply both sides by sin(20) to make s the subject of formula.
[tex] \frac{s}{sin(20)}*sin(20) = \frac{5}{sin(17)}*sin(20) [/tex]
[tex] s = \frac{5*sin(20)}{sin(17)} [/tex]
[tex] s = 5.8 [/tex] (to nearest tenth)
Shawn and Dorian rented bikes from two different rental shops. The prices in dollars, y, of renting bikes from the two different shops for x hours is shown. Shop Shawn used: y = 10 + 3.5x Shop Dorian used: y = 6x If Shawn and Dorian each rented bikes for the same number of hours and each paid the same price, how much did each pay for the rental? $ What is the y-value in the solution to this system of linear equations? 4x + 5y = −12 -2x + 3y = −16 −4 −2 2 5
Answer:
They both rented the bikes for 4 hours and paid $ 24.
Answer:$24
Step-by-step explanation:
i have tried everything At Central Online High School, 45100 of the students have a dog, 30100 of the students have a cat, and 18100 of the students have both a dog and a cat. What is the probability that students who have a cat also have a dog?
Work Shown:
Let's say this school has 100 people total. We know that 30 of the people have a cat since 30/100 is the fractional portion of cat owners. Similarly, 18 have both a cat and a dog.
The probability of selecting someone who has both pets, given we know they are a cat owner, is 18/30 = 3/5
To reduce the fraction, divide both parts by the GCF 6.
Note: we don't use 45/100 because we know that whoever selected wasn't solely a dog owner.
Answer:
at the rate of 100000.
u t cute
Which relation is a function?
The relation { (3,4), (-3, 8), (6,8) } is a function.
====================================================
Explanation:
Choice A can be ruled out because we have x = -3 repeat itself for different y values. For any x input, there must be exactly one y output. This is assuming the x value is in the domain of course.
Choice C can be ruled out for similar reasoning. This time x = 3 repeats.
Choice D is the same story, but we go back to x = -3 showing up twice.
Choice B is the only thing left. Each x value is unique or only written one time. This graph passes the vertical line test. The other graphs fail the vertical line test (it is possible to draw a vertical line through more than one point).
Multiply using distributive property.
(2x-5)(4x2-3x+1)
PLEASE HELP!!! ASAP!!!
Answer:
33x-6x(square)-45
Step-by-step explanation:
(2x-5)(9-3x)
= 2x(9-3x) + -5(9-3x)
= 18x-6x(square) - 45+15x
= 33x-6x(square)-45
Answer:
8x^3 - 26x^2 + 17x - 5.
Step-by-step explanation:
(2x - 5)(4x^2 - 3x + 1)
= (2x * 4x^2) + (-5 * 4x^2) + (2x * -3x) + (-5 * -3x) + (2x * 1) + (-5 * 1)
= 8x^3 + (-20x^2) + (-6x^2) + 15x + 2x - 5
= 8x^3 - 26x^2 + 17x - 5.
Hope this helps!
URGENT PLEASE HELP
1. Use the rules of divisibility to check which of the following
numbers are multiples of (are divisible by) 2,3,4,5,6, 8, 9 and 10
a) 552
b) 315
c) 620
d) 426
Which transformation(s) can map ABCD onto AWXY?
rotation only
reflection only
O translation, then rotation
O translation, then reflection
Answer:
Translation, then rotation.Step-by-step explanation:
If you translate the triangle BCD in such a way that vertex B maps onto vertex W, you'll realize that with rotation, you'll map the whole BCD triangle onto triangle WXY.
On the other hand, reflections can't be used here, because the sides of both triangles are not in opposite positions.
Therefore, the right answer is the third choice.
Sequences as Functions: Practice
Save and Exit
Question 8 of 8
Consider the geometric sequence below.
2, 12, 72, 432, ...
Select the explicit function which defines the sequence.
f(n) = 6.3(m – 1)
0 0
f(n) = 6.2(1 - 1)
f(1) = 3.2(0 - 1)
O f(x) = 2.6(n - 1)
Submit
Reset
points Q and R are midpoints of the sides of triangle ABC. Triangle A B C is cut by line segment Q R. Point Q is the midpoint of side A B and point R is the midpoint of side A C. The lengths of A Q and Q B are 4 p, the length of Q R is 2 p + 3, and the length of C B is 6 p minus 4. The lengths of A R and R C are congruent. What is AQ? 10 units 14 units 20 units 32 units
Answer:
AQ = 20 units
Step-by-step explanation:
I tried figuring in the pic below..
Similar triangles are triangles whose corresponding measures are proportional. All of their corresponding angles are also congruent. There are theorems and postulates that prove triangle similarity. Usually they requrie at least three parts of each triangle. The symbol for similarity is ~.
We have two triangles in the figure. ΔAQR and ΔABC. We will prove first that they are similar.
Answer:
20
Step-by-step explanation:
RQ is 1/2 of CB, so 2(2p+3)=6p-4. This would make p=5. Then, 5*4=20.
(also it is right on edgenuity)
What is function?write one example
A function is a relation between sets defined by a formation law. Examples:
[tex]F(x)=0[/tex]
[tex]F(x) =x[/tex]
[tex]F(x) = ax+b[/tex]
Instructions: Find FS if BS=16.
Answer:
48
Step-by-step explanation:
FB:BS=2:1
[tex]\frac{FB}{BS} =\frac{2}{1} \\add~1~to~both~sides\\\frac{FB}{BS} +1=\frac{2}{1} +1=3\\\frac{FB+BS}{BS} =3\\\frac{FS}{BS} =3\\FS=3 \times~BS\\FS=3 \times~16=48[/tex]
Answer:
48
Step-by-step explanation:
5. Use long division:
a. 483 ÷ 15
b. 907÷12
Answer:
Please look at the picture attached to see the long division.
a. 32 remainder 3
b. 75 remainder 7
Step-by-step explanation:
Answer:
Hey! The answer to your question will be below.
Step-by-step explanation:
Part A would be 32 R 3
And Part B would be 75 R 7
If you want to see how I got this by long division, below I attached a picture which shows how you would do the long division!
Hope this helps! :)
⭐️Have a wonderful day!⭐️
Which of the following equations have no solutions?
Choose all answers that apply:
-602 + 32 = –60r – 32
-60.X + 32 = 32.r – 60
-60r = 32 — 322 – 60
-602 + 32 = -60r - 60
Answer:
-60.X + 32 = 32.r – 60
Because we only have one equation for 2 unknowns.
Step-by-step explanation:
All the equations have solution for r but the one that has 2 unknowns (r and X).
That is because we only have one equation and 2 unknowns.
Then, we only can express one unknown in function of the other and have an indeterminate solution.
Write the equation of the conic section satisfying the given conditions. focus at the pole, e = 3/4, horizontal directrix 2 units above the pole
Answer:
The equation in the polar form is;
[tex]r = \dfrac{6}{4 + 3 \cdot sin(\theta)}[/tex]
Step-by-step explanation:
e = 3/4 > 1, we have an hyperbola
The polar equation of a conic is of the form;
For vertical directrix
[tex]r = \dfrac{k \cdot e}{1\pm e \cdot cos (\theta)}[/tex]
For horizontal directrix
[tex]r = \dfrac{k \cdot e}{1\pm e \cdot sin(\theta)}[/tex]
Where;
k = Distance from the focus to the directrix = 2
We have;
[tex]r = \dfrac{2 \cdot \dfrac{3}{4} }{1 + \dfrac{3}{4} \cdot sin(\theta)}[/tex]
[tex]r = \dfrac{\dfrac{3}{2} }{1 + \dfrac{3}{4} \cdot sin(\theta)}[/tex]
Which gives the equation in the polar form as follows;
[tex]r = \dfrac{6}{4 + 3 \cdot sin(\theta)}[/tex].
factor the equation x2-2x-15=0
Answer:
(x + 3)(x - 5)
Step-by-step explanation:
Well to factor x^2-2x-15,
we need to find 2 numbers that multiply to get -15 and add to get -2.
3*-5 = -15
3x + -5x = -2x
x*x = x^2
Factored (x + 3)(x - 5)
Hope this helps :)
Answer:
(x - 5)(x + 3)
Step-by-step explanation:
Step 1- Find 2 number that multiplies to be -15, but also add to be -2
This would be -5 and 3
-5 * 3 = -15
-5 + 3 = -2
Step 2- write the equation
The equation can be written 2 different ways
1st way- (x - 5)(x + 3)
2nd way- (x + 3)(x - 5)
Katie has 8 black marbles, 12 clear marbles, and 14 blue marbles in a bag. If she picks one at random, what is the probability that she will pick a black marble? (Enter your answer as a fraction in its reduced form.) a 4/17 b 7/34 c 6/17 d 12/34
Answer:
a 4/17
Step-by-step explanation:
if you add them all up, you get 34. 8 out of 34 reduced is 4/17
Answer:
4/17
Step-by-step explanation:
8 black marbles, 12 clear marbles, and 14 blue marbles = 34 marbles
P( black) = number of black/ total
= 8/34
=4/17
how do you solve this y= 6x - 3 y= -3 i need to graph so if you can show how to graph it also
Answer:
:)
Step-by-step explanation:
y=6x-3
y=-3
-3=6x-3
-3=6x-3
+3 +3
=6x
Answer:
Step-by-step explanation:
y=6x-3
y=-3
6x-3=-3
6x=-3+3
6x=0,
x=0
y=-3
so solution is point (0,-3)