Pls answer question thx
Answer:
x = 36.9°
Step-by-step explanation:
We need to find out what sides of the triangle we have, so we can find the formula for the missing angle, x.
We have been given the opposite and hypotenuse so we are using sine
SOH, CAH, TOA
sin (x) = opp ÷ hyp
Substitute in the values
sin (x) = 9 ÷ 15
Simplify
sin (x) = 0.6
Rearrange to find x
x = sin^-1(0.6) - Type this into your calculator
sin^-1 is the inverse or opposite of sinx = 36.8698... ≈ 36.9°
If two acute angles of a right angled triangle are in the ratio 1:2, Find them.
Answer:
30°,60°,90°
Step-by-step explanation:
Let :-
Ratio = 1x : 2xAs we know :-
Sum of all angles = 180°So that ,
x + 2x + 90 = 180 3x = 90 x = 90/3 x = 30Angles ,
90° x = 30° 2x = 60°Answer:
Let the angles be x and 2x.
We know that the sum of all interior angles of a triangle is 180°.
Therefore,
x+2x+90 = 1803x+90 = 1803x = 180-90x = 90/3x = 30Angles,
90°x = 30°2x = 2×30 = 60°show that P(x)=x³-6x²+11x-6 is divisible by x-1.
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Hello haohaoxNienie!
[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
Show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
[tex] \huge \boxed{\mathfrak{Explanation} \downarrow}[/tex]
To show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1, we must divide the polynomial by x - 1. If we get the remainder as 0, then we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
__________________
So, let's do the division (steps in the attached picture).
__________________
We got the remainder as 0. So, yes p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
__________________
More steps :-x² - 5x + 6
= (x - 3) (x - 2) [use the splitting the middle term method].
So, the zeroes are,
(x - 3)
x - 3 = 0
x = 3 ⇨ 1st zero.
(x - 2)
x - 2 = 0
x = 2 ⇨ 2nd zero.
Now, use the values of x on the equation. If we get 0 as the solution of the equation then we can prove that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
p(x) = x³ - 6x² + 11x - 6
p(3) = 3³ - 6(3)² + 11 (3) - 6
p(3) = 27 - 54 + 33 - 6
p(3) = 0.
p(x) = x³ - 6x² + 11x - 6
p(2) = 2³ - 6(2)² + 11 (2) - 6
p(2) = 8 - 24 + 22 - 6
p(2) = 0
Since we got the solutions as 0 we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
__________________
Hope it'll help you!
ℓu¢αzz ッ
60% of all bald eagles survived their first flight. If 25 randomly selected bald eagles are observed, what is the probability that at least 15 of them will survive their first flight.
a) Use the binomial distribution to approximate the probability.
Answer:
[tex]100%[/tex][tex]\%[/tex]
28. Katrina buys a 64-ft roll of fencing to
make a rectangular play area for her dogs.
Use 2(1 + w) = 64 to write a function for the
length, given the width. Graph the function.
What is a reasonable domain for the situation?
Explain.
Answer:
Step-by-step explanation:
The reasonable domain for the function 2 ( l + w ) = 64 is:
5, 10, 15, 20, and 25
The graph of the function 2 ( l + w ) = 64 is given below.
What is a function?A function is defined as a relation between a set of inputs having one output each.
We have,
A function of the perimeter of a rectangle:
2 ( l + w ) = 64
Here,
l = length and w = width
We need to find the value of length and width such that the perimeter of the rectangle is 64.
Now,
2 ( l + w ) = 64
l + w = 32
This means the combined measure of length and width must give us 32.
We need to write as a function for length where width is given.
We can assume the width to be: 5, 10, 15, 20, and 25.
Now,
l + 5 = 32
l = 27
l + 10 = 32
l = 22
l + 15 = 32
l = 17
l + 20 = 32
l = 12
l + 25 = 32
l = 7
We consider,
Width = 5, 10, 15, 20, and 25 to be the domain.
Length = 27, 22, 17, 12, and 7 to be the range.
We consider width values as the x-axis and length values as the y-axis.
The graph is given below.
Thus the reasonable domain for the situation given above is:
5, 10, 15, 20, and 25
The graph of the function 2 ( l + w ) = 64 is given below.
Learn more about functions here:
https://brainly.com/question/28135761
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5. The two figures are scaled copies of each other.
a. What is the
scale factor that
takes Figure 1
to Figure 2?
e
P
ס
R
С
A
A
b. What is the
scale factor that
takes Figure 2.
to Figure 1?
D
Figure 1
Figure 2
S
The quadrilaterals are similar and are related by a scale factor, taken from
a specific location, that maps the points on one figure to the other.
a. The scale factor that takes Figure 1 to Figure 2, is 3
b. The scale factor that takes Figure 2 to Figure 1 is [tex]\dfrac{1}{3}[/tex]
Reasons:
From the question, we have that Figure 1 is a scaled copy of Figure 2, therefore;
Let ABCD represent Figure 1, we have;
ABCD ~ PQRS
Length of [tex]\overline{AD}[/tex] = √(2² + 3²) = √(13)
Length of [tex]\overline{PS}[/tex] = √(6² + 9²) = √(117) = √(9 × 13) = 3·√(13)
Therefore;
a. The scale factor that takes Figure 1 to Figure 2, SF₁₂, is therefore;
[tex]SF_{12} = \mathbf{\dfrac{\overline{PS}}{\overline{AD}}}[/tex]
Which gives;
[tex]SF_{12} = \dfrac{3 \cdot \sqrt{13} }{\sqrt{13} } = 3[/tex]
The scale factor that takes Figure 1 to Figure 2, SF₁₂ = 3
(3 times the lengths of Figure 1 gives the lengths on Figure 2)
b. The scale factor that takes Figure 2 to Figure 1, SF₂₁, is given as follows;
[tex]SF_{21} = \mathbf{\dfrac{\overline{AD}}{\overline{PS}}}[/tex]
Which give;
[tex]SF_{21} = \dfrac{\sqrt{13} }{3 \cdot \sqrt{13} } = \mathbf{\dfrac{1}{3}}[/tex]
The scale factor that takes Figure 2 to Figure 1, SF₂₁ is [tex]\underline{\dfrac{1}{3}}[/tex]
Learn more here:
https://brainly.com/question/17207164
Help me please Asap
Answer:
it is the last one {-4, -1, 0, 1, 2}
Step-by-step explanation:
46.6 is what percent of 67?
Answer:
46.6 is 69.5522% of 67
Step-by-step explanation:
brainliest plz
In the given figure ABCD is a tripepizeum with AB||CD. If AO = x-1, CO = BO = x+1 and CD = x+4. Find the value of x.
[tex]\longmapsto[/tex]The value of "x" is 5.
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
A trapezium ABCD in which AB || CD such that
AO = x - 1CO = BO = x + 1OD = x + 4Now,
[tex]\rm In \: \triangle \: AOB \: and \: \triangle \: COD[/tex]
[tex]\rm \: \angle \: AOB \: and \: \angle \: COD \: \: \{vertically \: opposite \: angles \}[/tex]
[tex]\rm \: \angle \:ABO \: and \: \angle \: CDO \: \: \{alternate \: interior \: angles \}[/tex]
[tex]\bf \: \triangle \: AOB \: \sim \: \triangle \: COD \: \: \: \{AA \: similarity \}[/tex]
[tex]\bf\longmapsto\:\dfrac{AO}{CO} = \dfrac{BO}{DO} [/tex]
[tex]\rm \longmapsto\:\dfrac{x - 1}{x + 1} = \dfrac{x + 1}{x + 4} [/tex]
[tex]\rm \longmapsto\:(x - 1)(x + 4) = {(x + 1)}^{2} [/tex]
[tex]\rm \longmapsto\: {x}^{2} - x + 4x - 4 = {x}^{2} + 1 + 2x[/tex]
[tex]\rm \longmapsto\: 3x - 4 = 1 + 2x[/tex]
[tex]\rm \longmapsto\: 3x - 2x= 1 +4[/tex]
[tex]\bf\longmapsto \:x = 5[/tex]
Ayuda por favor, no quiero reprovar
When negative five is subtracted from a number the result is 10.
Find the number.
O 15
O -5
O -15
O 5
.............................
Answer:
D. 5
Step-by-step explanation:
Ok, so the number is represented by n.
n-(-5)=10.
Negative Times Negative makes Positive. The equation is now:
n+5=10
Subtract 5 from both sides.
n=5
Belinda is thinking about buying a house for $286,000. The table below shows the projected value of two different houses for three years:
Number of years 1 2 3
House 1 (value in dollars) 294,580 303,417.40 312,519.92
House 2 (value in dollars) 295,000 304,000 313,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)
Part C: Belinda wants to purchase a house that would have the greatest value in 25 years. Will there be any significant difference in the value of either house after 25 years? Explain your answer, and show the value of each house after 25 years. (4 points)
Answer: Part C: House 1 at 25 is at
$598820.5 (rounded to the
nearest cent) and House 2 is at
$511000. House 1 has a higher
value. I hope that helps
ABCD is a rectangle and AC and BD are its diagonals. If AC = 10 cm, then BD is?
A. 10 cm
B. 5 cm
C. 15 cm
Or D. 20 cm
Lemme know, take ur timeee
Answer:
A. 10 cm
Step-by-step explanation:
In a right angled triangle, a² + b² = c² where c is the diagonal or hypotenuse. If you split a rectangle diagonally into two right angle triangles, the a and b of both triangles would be the same length. Therefore, the c or diagonals would also be the same length - 10 cm.
Hope this helps!
which number is bigger 5.72 or 4.75?
Answer:
5.72
Step-by-step explanation:
Answer:
5.72 is bigger then 4.75
Step-by-step explanation:
What is the value of x in this equation? Enter your answer in the box.
(2.4 × 103) × (3 × 10x) = 7.2 × 109
Answer:
17.92
Step-by-step explanation:
there years ago Ava lent her sister $400 to buy some clothes. today Ava's sister pay her loan in full with $454. what simple annual interest rate did she pay?
Answer:
4.5% per year
Use the GCF and the Distributive Property to find the sum.
42+66
Write each number as a product using the GCF as a factor, and apply the Distributive Property.
42+66=??
Answer:
40 plus (2)42 plus 6x11
Step-by-step explanation:
Multiply
please help me find " What does the rate of change indicate about the context?"
Answer:
Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable. ... Subtract one and multiply the resulting number by 100 to give it a percentage representation.
PLEASE HELP 20 points!
Find the value of x and y
Answer:
x=14.y=12
Step-by-step explanation:
Given that
R
=
9
x
+
8
y
Find
x
when
y
=
3
and
R
=
5
Give your answer as an improper fraction in its simplest form.
Answer:
X = 19/9
Step-by-step explanation:
R = 9x + 8y
R = 5, Y = 3
5 = 9x + 8(3)
9x = 8(3) - 5
9x = 19
x = 19/9
Mr. Ramirez purchased 50 concert tickets for a total of $575. The concert tickets cost $15 for adults and $10 for children under the age of 12.
Write and solve a system of equations to represent the given scenario. Use the variables "a" for adults and "c" for children.
What is the slope of the following line?
A. 1/3
B. - 1/3
C. 3
D. - 3
Answer:
A
Step-by-step explanation:
Points of origin are (-3,0) and (0,1). Now we determine if it is a positive slope, it is as it goes up not down. It goes up 1 unit and over to the right 3 units, making the slope 1/3.
In the triangle below, suppose that mZL=(x+3)°, mZ M=(5x-7)°, and m N= (2x).
Find the degree measure of each angle in the triangle.
N
(2x)
mL =
日。
х
M
(5x - 7).
m M =
•
•
mZN =
(x + 3)°
Answer:
GivenTriangle ABC is right angled at A.
[tex]m\angle B=(5x+7)^∠B=(5x+7)∘[/tex]
[tex]m\angleC=(4x+29)^∠C=(4x+29) [/tex]
To find:
The degree measure of each angle in the triangle.
Solution:According to the given information,
[tex]m\angleA=90^\circm∠A=90[/tex]
[tex]m\angleB=(5x+7)^\circm∠B=(5x+7) [/tex]
[tex]m\angleC=(4x+29)^\circm∠C=(4x+29) ∘[/tex]
Now,
[tex]m\angleA+m\angleB+m\angleC=180^\circm∠A+m∠B+m∠C=180 ∘[/tex]
(Angle sum property)
[tex]90^\circ+(5x+7)^\circ+(4x+29)^\circ=180^\circ90∘+(5x+7)∘+(4x+29) ∘ =180[/tex]∘
[tex](9x+126)^\circ=180^\circ(9x+126)∘ =180∘[/tex]
9x+126=1809x+126=180
9x=180-1269x=180−126
9x=549x=54
Divide both sides by 9.
[tex] \sf{x=\dfrac{54}{9}x=954}[/tex]
x=6x=6
Now,
[tex]m\angle A=90^\circm∠A=90
∘[/tex]
[tex]m\angleB=(5(6)+7)^\circm∠B=(5(6)+7) [/tex]
∘
[tex]m\angle B=37^\circm∠B=37[/tex]
∘
[tex]m\angleC=(4(6)+29)^\circm∠C=(4(6)+29)[/tex]
∘
[tex]m\angle C=53^\circum \: ∠C=53[/tex]
Therefore,
The measures of ∠A, ∠B, ∠C are 90°, 37°, 53° respectively.
Answer:
26°, 108°, 46°Step-by-step explanation:
Assumed the given is:
ΔLMN with angle measures of (x + 3), (5x - 7) and 2x.We need to find the angle measures in degrees.
We know the sum of interior angles is 180:
x + 3 + 5x - 7 + 2x = 1808x - 4 = 1808x = 184x = 184/8x = 23Find the angle measures:
m∠L = x + 3 = 23 + 3 = 26m∠M = 5x - 7 = 5*23 - 7 = 108m∠N = 2x = 2*23 = 46Sienna, Rhys, and Micah are all reading the same book for school. Sienna has read 40% as far as Rhys has, and Rhys has read 40% as far as Micah has. If Sienna has read 60 pages, how many pages has Micah read?
Based on the fact that Sienna has read 60 pages, we can infer that Micha has read 375 pages of the book.
Sienna has read 40% of what Rhys has read and that corresponds to 60 pages. The number of pages read by Rhys is therefore:
= Number of pages / Percentage read
= 60 / 40%
= 150 pages
The 150 pages read by Rhys is 40% of what Micah has read. Micah has therefore read:
= 150 / 40%
= 375 pages
In conclusion, Micah has read 375 pages.
Find out more at https://brainly.com/question/2807698.
I really need help finding the solution!!
Answer:
-0.5 is not a solution
2 is a solution
Step-by-step explanation:
To check if something is a solution of the equation, you need to substitute the value in place of the variable
15 + 2y = -12 - 4y
15 + 2(-0.5) = -12 - 4(-0.5)
15 - 1 = -12 + 2
14 ≠ -10 ∴ -0.5 is not a solution
5 - 2(3x + 5) = 3 - 10x
5 - 2[3(2) + 5] = 3 - 10(2)
5 - 2(6 + 5) = 3 - 10(2)
5 - 12 - 10 = 3 - 120
-17 = -17 ∴ 2 is a solution
Holly is displaying a postcard collection on a bulletin board that is 35 3/4 inches wide. Each postcard is 5 7/8 inches wide. Holly estimates that the number of postcards she can display in each row is 7. Is this the best estimate Explain
100 POINTS AND BRAINLIEST
Answer:
Yes.
Step-by-step explanation:
By looking at the numbers of 35 3/4 inches and 5 7/8 inches, you already know that 35 ÷ 5 is 7. Holly might need extra space in between the postcards, which is perfect since she has the leftover fractions, that equal more than 1.
-kiniwih426
Length of board=35 3/4=143/4in
Length of postcard=5 7/8=47/8in
Total postcards
. [tex]\\ \sf\longmapsto \dfrac{143}{8}\div \dfrac{47}{8}[/tex]
[tex]\\ \sf\longmapsto \dfrac{143}{8}\times \dfrac{8}{47}[/tex]
[tex]\\ \sf\longmapsto \dfrac{143}{47}[/tex]
[tex]\\ \sf\longmapsto 3(Approx)[/tex]
No not best estimated option
Please could I have some help with this question? Thanks
Answer: 270
Step-by-step explanation:
1) Find DE
1 : 6
17 : x
Cross multiply
x = 17 * 6
x = 102
DE = 102
2) Compare the two triangles
1st (ABC)
side = 45
base = 17
2nd (ADE)
side = x
base = 102
[tex]\frac{x}{45} = \frac{102}{17}[/tex]
Cross multiply
17x = 102 x 45
17x = 4590
x = 4590/17
x = 270
AD = 270
overy
A line intersects the points
(8,-10) and (9,4).
What is the slope of the line in
simplest form?
Answer:
m = 14
Step-by-step explanation:
The entered points belong to an increasing, linear function.
This is 8th-grade math please help
