If APQR = ASTU, complete each blank below with the appropriate length or measure.
Answers
Answer:
ST = 8 m
SU = 7 m
m∠Q = 75°
m∠S = 59°
m∠R = 46°
m∠U = 46°
Step-by-step explanation:
The given parameter are;
ΔPQR is congruent to ΔSTU
In ΔPQR, m∠P = 59°, PR = 8 m, PQ = 7 m
In ΔSTU, m∠T = 75°
By Side-Angle-Side rule of congruence, and given that m∠P ≠ m∠T, we can have;
m∠S ≅ m∠P, by Congruent Parts of Congruent Triangles are Congruent, CPCTC
ST ≅ PR, SU ≅ PQ, m∠Q ≅ m∠T, m∠U ≅ m∠R
Therefore;
ST = PR = 8 m
ST = 8 m
SU = PQ = 7 m
SU = 7 m
m∠Q = m∠T = 75°
m∠Q = 75°
m∠S = m∠P = 59°
m∠S = 59°
m∠U = m∠R = 180 - (75° + 59°) = 46°
m∠R = 46°
m∠U = 46°.
Related Questions
Describe the pattern in the following sequence and list the next three terms:
4, 8, 16, 32, ...
I’ll mark brainliest! Please help me
Answers
Multiples of 4 after continuing 2 digits skip one multiple and continue;-;
Question 10 The hypotenuse of a right triangle is I m longer than the longer leg. The other leg is 7 m shorter than the longer leg. Determine the lengths of the three sides of the triangle. (3 marks)
Answers
Answer:
5, 12, 13
Step-by-step explanation:
let x be the longer leg then x + 1 is the hypotenuse and x - 7 the shorter leg
Using Pythagoras' identity in the right triangle
x² + (x - 7)² = (x + 1)² ← expand using FOIL
x² + x² - 14x + 49 = x² + 2x + 1
2x² - 14x + 49 = x² + 2x + 1 ( subtract x² + 2x + 1 from both sides )
x² - 16x + 48 = 0 ← in standard form
(x - 4)(x - 12) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x - 12 = 0 ⇒ x = 12
x = 4 , then x - 7 = 4 - 7 = - 3 ← not possible
x = 12, then x - 7 = 12 - 7 = 5 and x + 1 = 12 + 1 = 13
The lengths of the 3 sides are
longer leg = 12 m , shorter leg = 5 m and hypotenuse = 13 m
Which graph represents the function f (x) = StartFraction 2 Over x minus 1 EndFraction + 4?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = negative 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = negative 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.
Answers
Answer:
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4
Step-by-step explanation:
The given function is presented as follows;
[tex]f(x) = \dfrac{2}{x - 1} + 4[/tex]
From the given function, we have;
When x = 1, the denominator of the fraction, [tex]\dfrac{2}{x - 1}[/tex], which is (x - 1) = 0, and the function becomes, [tex]\dfrac{2}{1 - 1} + 4 = \dfrac{2}{0} + 4 = \infty + 4 = \infty[/tex] therefore, the function in undefined at x = 1, and the line x = 1 is a vertical asymptote
Also we have that in the given function, as x increases, the fraction [tex]\dfrac{2}{x - 1}[/tex] tends to 0, therefore as x increases, we have;
[tex]\lim_ {x \to \infty} \dfrac{2}{(x - 1)} \to 0, and \ \dfrac{2}{(x - 1)} + 4 \to 4[/tex]
Therefore, as x increases, f(x) → 4, and 4 is a horizontal asymptote of the function, forming a curve that opens up and to the right in quadrant 1
When -∞ < x < 1, we also have that as x becomes more negative, f(x) → 4. When x = 0, [tex]\dfrac{2}{0 - 1} + 4 = 2[/tex]. When x approaches 1 from the left, f(x) tends to -∞, forming a curve that opens down and to the left
Therefore, the correct option is on a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.
Answer:
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4
Step-by-step explanation:
The given function is presented as follows;
From the given function, we have;
When x = 1, the denominator of the fraction, , which is (x - 1) = 0, and the function becomes, therefore, the function in undefined at x = 1, and the line x = 1 is a vertical asymptote
Also we have that in the given function, as x increases, the fraction tends to 0, therefore as x increases, we have;
Therefore, as x increases, f(x) → 4, and 4 is a horizontal asymptote of the function, forming a curve that opens up and to the right in quadrant 1
When -∞ < x < 1, we also have that as x becomes more negative, f(x) → 4. When x = 0, . When x approaches 1 from the left, f(x) tends to -∞, forming a curve that opens down and to the left
Therefore, the correct option is on a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.
For a line that contains the point (3, 4) and has a slope of 4, please name another point on this line. Show the work you did to find this answer.
Answers
Answer:
y = 4x - 8
Step-by-step explanation:
y = 4x + b
4 = 4(3) + b
4 = 12 + b
-8 = b
ANSWER PLEASE
simplify 2n(n2+2n+3)-3(2n+7) and (-4n2-3n-8)+2(n+9)
Answers
Step-by-step explanation:
> 2n³+4²+6n-6n-21
2n³+4n²-21
> -4n²-3n-8+2n+18
-4n²-3n-8+2n+18
-4n²-n-8+18
-4n²-n+10
hi pls help.you do not have to do all 3. just either one will be ok pls explain as well:) thank you
Answers
Answer:
[tex]{7a^{5}b^{5} c\\[/tex]
Step-by-step explanation:
[tex]\frac{28a^{8}b^{6} c^{3} }{4a^{3}bc^{2} }[/tex]
→ First look at the first term of each expression and see if they can be simplified, and they can
[tex]\frac{7a^{8}b^{6} c^{3} }{a^{3}bc^{2} }[/tex]
→ Now look at the a terms, since a larger one is at the top, you subtract
[tex]\frac{7a^{5}b^{6} c^{3} }{bc^{2} }[/tex]
→ Now simplify the b and c terms
[tex]{7a^{5}b^{5} c[/tex]
please please please answer!! will give brainliest and extra points!
Answers
a) y = x
b) y = 10
c) x = 3
Step-by-step explanation:
a) the line passes through the points (-5, -5) and (1, 1).
Step 1. Identify the slope
M = slope
M = change in y/change in x
Two points: (-5, -5) & (1, 1)
M = (y2 - y1)/(x2 - x1)
where y2 = 1 y1 = -5 x2 = 1 & x1 = -5
M = (1 - -5)/(1 - -5)
Note: Two negative signs together makes addition!
M = 6/6
M = 1
Step 2. Find the y-intercept
The slope is 1 but then we need a y-intercept. To do this we have to take a look when the first y-intercept happened.
Answer: y-intercept undefined so therefore our final answer is y = x
••••••••••••••••••••••••••••••••••••••••••••••••••
b) the line that passes through (-2, 10) and (3, 10).
If we would’ve graphed this, we can see that they’re in line with the y-axis so there wouldn’t be any slope.
Step 1. Find the slope.
M = slope
M = change in y/change in x
Two points: (-2, 10) & (3, 10)
M = (y2 - y1)/(x2 - x1)
M = (10 - 10)/(3 - -2)
M = 0/5
M = 0
Therefore the slope is 0
Step 2. Find the y-intercept
And the y-intercept is 10 obviously so now our answer would be y = 10
•••••••••••••••••••••••••••••••••••••••••••••••••••
c) the line parallel to the y-axis that passes through the point (3, -7)
Equation of line parallel to y-axis is x = k
(3, -7) lies on our required line
-> k = 3
The equation of the required line is x = 3
••••••••••••••••••••••••••••••••••••••••••••••••••
d) & e)
I don’t know the answer to the rest I’m sorry but at least appreciate these 3 answers that I’m giving you
Have a good day!
-Unluckydoom
Please hurry I will mark you brainliest
Question’s Picture included*
Answers
Answer:
when you have 32 pennies the total mass will be 185
monica has $340 in the bank and plans to save $10 per week. is this linear or exponential?
Answers
Answer:
linear. Each week adds another 10 dollars.
Step-by-step explanation:
Total = 340 + 10*w
w is the weekly amount
Suppose 5 weeks pass
Then the total amount in her bank account is
Total = 340 + 10*5
Total = 340 + 50
Total = 390
The equation is Linear.
In a triangle, a segment connecting the midpoints of two sides of the triangle is
called:
Answers
Answer:
A.) Midsegment
Step-by-step explanation:
Trust me bro
(X+3)= 1
(2x+5)=(3n+2)
Answers
Hello!
(x + 3) = 1
x + 3 = 1
x = 1 - 3
x = -2
(2x + 5) = (3n + 2)
[2 × (-2) + 5] = (3n + 2)
(-4 + 5) = (3n + 2)
1 = (3n + 2)
1 = 3n + 2
3n + 2 = 1
3n = 1 - 2
3n = -1
n = -1 : 3
n = -1/3
Good luck! :)
Please help me out with my maths I would really appreciate it
Answers
Answer:
a.
1. The rule in this sequence is (+5) every next pattern
2. 22, 27, 32, 37
3. 42
4. 12 term
5. 67
b.
1. The rule in this sequence is (-3) every next pattern
2. -7, -10, -13, -16
3. -16
4. 13 term
5. -37
Step-by-step explanation:
Answer:
I'm not sure about the answer.
a.
1. The rule in this sequence is (+5) every next pattern
2. 22, 27, 32, 37
3. 42
4. 12 term
5. 67
b.
1. The rule in this sequence is (-3) every next pattern
2. -7, -10, -13, -16
3. -16
4. 13 term
5. -37
Hope this helps you ^^
Can someone help please
Answers
Answer:
[tex]10^{-3}[/tex]
Step-by-step explanation:
Answer:
https://tex.z-dn.net/?f=10%5E%7B-3%7D
Step-by-step explanation:
solve
f(x)=4x5−8x4+8x2−4x
Answers
Given:
The function is:
[tex]f(x)=4x^5-8x^4+8x^2-4x[/tex]
To find:
The roots of the given equation.
Solution:
We have,
[tex]f(x)=4x^5-8x^4+8x^2-4x[/tex]
For roots, [tex]f(x)=0[/tex].
[tex]4x^5-8x^4+8x^2-4x=0[/tex]
[tex]4x(x^4-2x^3+2x-1)=0[/tex]
[tex]4x((x^4-1)+(-2x^3+2x))=0[/tex]
[tex]4x((x^2+1)(x^2-1)-2x(x^2-1))=0[/tex]
On further simplification, we get
[tex]4x(x^2+1-2x)(x^2-1)=0[/tex]
[tex]4x(x-1)^2(x+1)(x-1)=0[/tex]
[tex]4x(x+1)(x-1)^3=0[/tex]
Using zero product property, we get
[tex]4x=0[/tex]
[tex]x=0[/tex]
Similarly,
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
And,
[tex](x-1)^3=0[/tex]
[tex]x=1[/tex]
Therefore, the zeroes of the given function are [tex]-1,0,1[/tex] and the factor form of the given function is [tex]f(x)=4x(x+1)(x-1)^3[/tex].
i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have.(hint: one is the other simplified)
Answers
Answer:
0.05N - 0.1N + 1.7 (in dollars
1.7 - 0.05N (in dollars)
Step-by-step explanation:
Given :
Total number of coins = 17
Number of nickels = N
Number of dimes = 17 - N
1 nickel = 5 cent = $0.05
1 dime = 10 cent = $0.1
The amount of money :
(Value of nickel * number of nickels) + (value of dime * number of dime)
(0.05 * N) + (0.1 * (17-N))
0.05N + 1.7 - 0.1N
0.05N - 0.1N + 1.7
-0.05N + 1.7 = 1.7 - 0.05N
Can anyone help me with this question
Answers
Answer:
60
Step-by-step explanation:
A significant figure means the most important (biggest) number.
As it just wants 1 significant figure, you count 1 to the right and round the 6 up.
Hope this helps :)
Write 1= 2x2 + 5x In standard form.
What is the value of b^2 - 4ac?
Answers
Answer:
2x^2+5x-1=0
ax^-bx+c=0
b^2-4ac = 5^2-4(2)(-1) =33
Which is the graph of y = RootIndex 3 StartRoot x EndRoot?
Answers
Given:
The equation is:
[tex]y=\sqrt[3]{x}[/tex]
To find:
The graph of the given equation.
Solution:
We have,
[tex]y=\sqrt[3]{x}[/tex]
The table of values is:
x y
-8 -2
-1 -1
0 0
1 1
8 8
Plot these points on a coordinate plane and connect them by a free hand curve as shown in the below graph.
Answer:
D
Step-by-step explanation:
edge 2020
Find the equation of the line that is parallel
to the line y = 3x + 9 and passes
through the point (2,1) Write the
equation in slope-intercept form.
Answers
Answer:
y = 3x - 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 9 ← is in slope- intercept form
with slope m = 3
Parallel lines have equal slopes, then
y = 3x + c ← is the partial equation
To find c substitute (2, 1) into the partial equation
1 = 6 + c ⇒ c = 1 - 6 = - 5
y = 3x - 5 ← equation of parallel line
Please Help!!
To find the distance AB across a river, a distance BC of 786 m is laid off on one side of the river. It is found that B = 110.2° and C = 13.5°. Find AB. I don't understand how to do this but I know you need to use the Law of Sines, so please show work.
Answers
Answer:
~ 220.6
Step-by-step explanation:
sine rule : a/sinA =b/sinB = c/sinC
AB/sinC =BC/sinA
A = 180 - 110.2 - 13.5 = 56.3 degrees
AB/sin13.5 = 786/sin56.3
AB = 786sin13.5/sin56.3 = 220.5506
The distance across the river of AB is 220.55 m.
What is Law of Sines?Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.
That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,
a / sin A = b / sin B = c / sin C
Given a triangle ABC.
We have,
∠B = 110.2° and ∠C = 13.5°
We know that the sum of the interior angles of a triangle is 180°.
∠A = 180 - (110.2 + 13.5) = 56.3°
Using the law of sines,
BC / Sin A = AB / Sin C
Substituting the values,
786 / sin (56.3°) = AB / sin (13.5°)
AB = (786 / sin (56.3°)) sin (13.5°)
= 220.55 m
Hence the distance is 220.55 m.
Learn more about Law of Sines here :
https://brainly.com/question/13098194
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How could Brent use a rectangle to model the factors of \large x^2-7x+6?
He could draw a diagram of a rectangle with dimensions x – 4 and x + 3 and then show the area is equivalent to the sum of x2, –4x, 3x, and half of –12.
He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
He could draw a diagram of a rectangle with dimensions x + 7 and x – 1 and then show the area is equivalent to the sum of x2, 7x, –x, and 6.
He could draw a diagram of a rectangle with dimensions x – 3 and x – 4 and then show the area is equivalent to the sum of x2, –3x, –4x, and half of 12.
Answers
Answer:He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
Step-by-step explanation:
He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
He could draw a diagram of a rectangle with dimensions x + 7 and x – 1 and then show the area is equivalent to the sum of x2, 7x, –x, and 6.
He could draw a diagram of a rectangle with dimensions x – 3 and x – 4 and then show the area is equivalent to the sum of x2, –3x, –4x, and half of 12.
The slope (m) and the y-intercept (b) of the line 2x + 3y = 12 is:
Answers
Step-by-step explanation:
[tex]2x + 3y = 12 \\ 3y = - 2x + 12 \\ y = - \frac{2}{3} x + 4[/tex]
slope is -2/3
y intercept is 4
Answer:
The slope is -2/3 and the y intercept is 4
Step-by-step explanation:
2x + 3y = 12
Slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
2x + 3y = 12
Subtract 2x from each side
2x-2x+3y = -2x+12
3y = -2x+12
Divide by 3
3y/3 = -2x/3 +12/3
y = -2/3 x +4
The slope is -2/3 and the y intercept is 4
Find the measure of each angle indicated.
A) 95°
C) 26°
B) 92°
D) 20°
Answers
Answer:
D) 20°
Step-by-step explanation:
Using the triangle sum theorem, you know that every triangle's interior angles add up to 180°. Therefore the bottom triangle's missing angle can be found by giving it the variable x.
57° + 30° + x = 180°
Simplify: 87° + x =180°
x=93°
By the vertical angles theorem, the vertical angle directly across this angle is congruent to this one. Meaning that the top triangle's angle are 67°, 93°, and unknown, which we can assign y. We can use the same method from above here.
67° + 93° + y = 180°
Simplify: 160° + y = 180°
y=20°
Answer:
(C). 26°
Step-by-step explanation:
The area of the regular hexagon is 169.74 ft2. A regular hexagon has an apothem with length 7 feet and an area of 169.74 feet squared. What is the perimeter, rounded to the nearest tenth? 24.2 ft 28.3 ft 48.5 ft 56.8 ft
Answers
Answer: [tex]48.5\ ft[/tex]
Step-by-step explanation:
Given
Area of the regular hexagon is [tex]169.74\ ft^2[/tex]
Length of the apothem is [tex]l=7\ ft[/tex]
Suppose the side of the hexagon is a
Hexagon can be divided into six equal triangles with same area
Area of a single triangle is
[tex]\Rightarrow A_1=\dfrac{1}{2}\times 7\times a\\\\\Rightarrow A_1=3.5a\ ft^2[/tex]
Area of hexagon will be equal to area of 6 equal area triangles
[tex]\Rightarrow 6A_1=169.74\\\Rightarrow 6\times 3.5a=169.74\\\Rightarrow a=8.08\ ft[/tex]
Perimeter of the hexagon is
[tex]\Rightarrow P=6a\\\Rightarrow P=6\times 8.08\\\Rightarrow P=48.49\approx 48.5\ ft[/tex]
Thus, the perimeter of the hexagon is [tex]48.5\ ft[/tex]
Answer:
C
Step-by-step explanation:
edge 2021
Please hurry I will mark you brainliest
Answers
Answer:
The sum of interior angle is 360°
Select all the points that are on the graph of the line y = −1/4 x + 3.
a. (0, -1/4)
b. (0, 3)
c. (1, 11/4)
d. (1, 3)
e. (1, 13/4)
f. (3, 0)
Answers
The points on the graph ( b , c )
I hope I helped you ^_^
) Con robot của bạn An được lập trình có thể đi thẳng, quay trái hoặc sang phải một góc 900. Trong cuộc thi "Phát động tài năng ", con robot của bạn An xuất phát từ điểm A đi thẳng 4m, rồi quay sang trái đi thẳng 3m, sau đó quay sang phải rồi đi thẳng 4m, rồi tiếp tục quay sang trái đi thẳng 3m đến B. Hãy tính khoảng cách AB .
Answers
Step-by-step explanation:
chắc là nó như này à :>♡♡♡
the ordered pairs model an exponential function, where w is the function name and t is the input variable.
{(1, 60), (2, 240), (3, 960), (4, 3840)}
what is the function equation in sequence notation?
wt = ____
Answers
Answer:
w = 15 (4^t)
Step-by-step explanation:
Let w be what the function is equal to
Let t be the input variable
equation :
w = k a^t
Plug in any two of the points to solve for k and a
for example, let's take (1, 60) and (2, 240):
60 = k * a^1
k = 60 / a
240 = k a^2
Substituting:
240 = 60/a (a^2)
a = 4
k = 15
The function is
w = 15 (4^t)
quadratics formula 4x^2+3x-1=0
Answers
Answer: X = 1/4 or X = -1
Step-by-step explanation:
4x2+3x−1=0
(4x−1)(x+1)=0
4x−1=0 or x+1=0
4x=1 or x=-1
Now divide 4 from both sides
like this 4x/4=1/4
now cancel out two 4's so the answer will be x=1/4
The two cones below are similar. What is the value of x?
Cone 1
Height = 10
Radius = 3
Cone 2
Height = 3
Radius = x
A. 0.3
B. 0.9
C. 0.09
D. 0.18
Answers
Answer:
If they are similar, the ratio of 10/3 should be the same as the 3/x
then solve
10/3 = 3/x
cross multiply
10x=8
x = 9/10
so C. is the right answer
The missing value in the smaller cone is 0.9 units.
What is similarity?Similarity in math is a concept that relates to the shape and size of figures. Two figures are similar if they have the same shape, but not necessarily the same size.
Given that, two similar cones, we need to find the value of x in the smaller cone,
Since, the cones are similar, then according to the definition of similarity,
we know that the dimensions will be in equal proportion,
Let the dimensions of the big cone be H (height) and R (radius) and that of smaller cone be h (height) and r (radius)
So,
H / R = h / r
10 / 3 = 3 / x
x = 9/10
x = 0.9
Hence, the missing value in the smaller cone is 0.9 units.
Learn more about similarity, click;
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