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Find the GCF for the pair of numbers. 9,4
The GCF of numbers is the greatest common factor of the numbers.
The numbers are given as: 4 and 9.
Factorize both:
[tex]\mathbf{4 = 1 \times 2 \times 2}[/tex]
[tex]\mathbf{9 = 1 \times 3 \times 3}[/tex]
The common factor between both is 1.
So, we have:
[tex]\mathbf{GCF = 1 }[/tex]
Hence, the GCF of 4 and 9 is 1
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Here's a question ~
p1 and p2 are points on either of the two lines
[tex]y - \sqrt{3} |x| = 2[/tex]
at a distance of 5 units from their point of point of intersection. Find the coordinates of the foot of perpendiculars drawn from p1 , p2 on the bisector of the Angle between the given lines.
Answer:
(0, 5√3/2 + 2)Step-by-step explanation:
Given is the absolute value function.
Observations:
It has a slope of ±√3 and the y- intercept of 2.There is no horizontal shift, so the the y-axis is the line of symmetry.The y-axis is also an angle bisector of the two lines.The foot P₁P₂ is parallel to the x-axis since it's perpendicular to the y- axis.We need to find the coordinates of intersection of the line P₁P₂ with the y- axis (the point Y in the picture).
Consider the triangle AYP₂.
We know AP₂ = 5.
The angle YAP₂ is:
arctan (1/√3) = 30°The distance AY is:
AY = AP₂ cos 30° = 5*√3/2The distance from the x-axis to the point Y is:
5√3/2 + 2, added the y- intercept of the graphed linesThe coordinates of the point Y:
(0, 5√3/2 + 2)_____13. Public opinion polls are only estimates because (A) random digit dialing has replaced person-to-person interviewing. (B) all surveys have a sampling error. (D) samples of fewer than one million people are too small. (E) opinion polls have been deemed ineffective by political candidates.
Answer:
(B) all surveys have a sampling error.
Step-by-step explanation:
Steve leaves the corner of First and Maple on his bicycle and travels an average speed of 9 mi/hr. Two hours later,his brother leaves from First and Maple, following him on a moped traveling 27 mi/hr. How long will it take him to catch up with steve?
Answer:
Two hours later his brother leaves from first and maple and comes after him on a moped travelling 27 mph, His uphill speed was 8 miles per hour slower than his downhill speed.
Step-by-step explanation:
PLEASE HELP 20 points!
3.5m/min = how manny miles/hour
Answer:
[tex]\sf\longmapsto0.13 miles/hour[/tex]
Step-by-step explanation:
Firstly we have to use the formula to find the miles/hour
[tex]\sf\longmapsto \: Formula:Divide \: the \: speed \: value \: by \: 26.822.[/tex]
[tex]\sf\longmapsto \: 3.5 \div 26.822[/tex]
[tex]\sf\longmapsto \: 0.13 miles/hour[/tex]
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]
WILL GIVE BRAILIST TO PERSON WHO ANSWERS CORRECTLY!!
For FHG find the measure of the smallest angle ∠HFG, if m∠GHF = 92° and m∠HGF =72°
Answer:
The Answer is 16
Step-by-step explanation:
The three angles enclosed in a triangle, made by its sides, are called its internal angles. The sum of internal angles of a triangle is
180
o
. Based on its internal angles, a triangle can be classified as acute angled, right angled and obtuse angled.
Your Welcome! :)
The sum of the measure of angle of a triangle = 180° .
Given two angles = 92° and 72°
_________________________
92° + 72° = 164°
180° - 164° = 16° (Ans)
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]
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parallelogram ABCD with vertices A(6,8) B(10,9) C(9,3) and D(5,2): 90 counterclockwise rotation about P(4,1)
A ( , )
B ( , )
C ( , )
D ( , )
Answer:
A(-3 , 3) B(-4 , 7) C(2 , 6) D(3 , 2)
Step-by-step explanation:
Rotation of the parallelogram about the point P(4, 1), is done by taking
point P as the origin, and using relative coordinates for the rotation.
[tex]\underline{A(-3, \, 3)}[/tex][tex]\underline{B(-4, \, 7)}[/tex][tex]\underline{C(2, \, 6)}[/tex][tex]\underline{D(3, \, 2)}[/tex]Reasons:
The given parameters are;
Vertices of the parallelogram ABCD are;
A(6, 8), B(10, 9), C(9, 3) and D(5, 2)
Point about the parallelogram is rotated = P(4, 1)
Angle of rotation = 90°
Direction of rotation = Counterclockwise
90° rotation counterclockwise of (x, y) about the origin gives → (-y, x)
Therefore, we have;
The given points relative to the point P are;
A'(6-4, 8 - 1) = A'(2, 7)
B'(10 - 4, 9 - 1) = B'(6, 8)
C'(9 - 4, 3 - 1) = C'(5, 2)
D'(5 - 4, 2 - 1) = D'(1, 1)
Therefore, we get;
A'(2, 7) [tex]\underrightarrow {R_{180^{\circ}}}[/tex] A''(-7, 2)
B'(6, 8) [tex]\underrightarrow {R_{180^{\circ}}}[/tex] B''(-8, 6)
C'(5, 2) [tex]\underrightarrow {R_{180^{\circ}}}[/tex] C''(-2, 5)
D'(1, 1) [tex]\underrightarrow {R_{180^{\circ}}}[/tex] D''(-1, 1)
Which then gives;
The image location are;
A(-7 + 4, 2 + 1) = A(-3, 3)
B''(-8 + 4, 6 + 1) = B(-4, 7)
C''(-2 + 4, 5 + 1) = C(2, 6)
D''(-1 + 4, 1 + 1) = D(3, 2)
Therefore, we have;
A(-3, 3), B(-4, 7), C(2, 6), and D(3, 2)
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PLEASE HELP!!!!! You are given an isosceles trapezoid ABCD with median XY. Complete the following.
m
The product of four and a number C is decreased by five?
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
HELP PLEASE
Write each number as a logarthm with base 3.
0
1
-2
4
Answer:
See belowStep-by-step explanation:
Let the number is x in each case.
Use the property below:
logₐc = b ⇒ aᵇ = c or vice versaWe have:
[tex]log_3x = 0 -->x = 3^0=1 -->log_31=0[/tex][tex]log_3x = 1 -->x = 3^1=3 -->log_33=1[/tex][tex]log_3x = -2 -->x = 3^{-2}=1/9 -->log_3(1/9)=-2[/tex][tex]log_3x = 4 -->x = 3^4=81 -->log_381=4[/tex]Answer:
[tex]\log_31=0[/tex]
[tex]\log_33=1[/tex]
[tex]\log_3\left(\frac{1}{9}\right)=-2[/tex]
[tex]\log_{3}81=4[/tex]
Step-by-step explanation:
[tex]\textsf{Apply log law}: \quad \log_ax=c \iff x=a^c[/tex]
Therefore:
[tex]\log_3x=0 \implies x=3^0=1[/tex]
[tex]\log_3x=1 \implies x=3^1=3[/tex]
[tex]\log_3x=-2\implies x=3^{-2}=\dfrac{1}{3^2}=\dfrac{1}{9}[/tex]
[tex]\log_3x=4 \implies x=3^4=81[/tex]
Additionally, the logarithm of 1 with any base is always zero:
[tex]\log_a1=0[/tex]
The logarithm of the same number as the base is always 1:
[tex]\log_aa=1[/tex]
46.6 is what percent of 67?
Answer:
46.6 is 69.5522% of 67
Step-by-step explanation:
brainliest plz
Plsss help me with this question!!!
show that P(x)=x³-6x²+11x-6 is divisible by x-1.
HERE IS YOUR ANSWER MATE
HOPE ITS HELPFUL
HAVE A GREAT FUTURE
LOVE FROM INDIA
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
write the equation of the line perpendicular to the given line y - 2 = 1/4 (x+2)
HELP ASAP 100 POINTS!
Functions can be defined using graphs, tables, and ordered pairs. What is the range of a function?
The range is the input.
The range is all numbers.
The range is the output.
The range is any x-value.
Answer:
the range is the set of possible output of values
Step-by-step explanation:
The range is the set of y-values (OUTPUT) that map to the set of x-values (INPUT).
THANK YOU TO WHOEVER DOES THIS <3
Answer:
2436 cubic centimeters
Step-by-step explanation:
11 * 14 = 154
14 * 7 / 2 = 49
154 + 49 = 203
203 * 12 = 2436
Help me please Asap
Answer:
it is the last one {-4, -1, 0, 1, 2}
Step-by-step explanation:
Sienna, 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.
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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]
May I please receive help?
Answer:
Parallel: y=2x+3
Perpendicular= 1/2x+6
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
This is 8th-grade math please help
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:
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.
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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°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.
