Answer:
12 feet
Step-by-step explanation:
By Pythagoras theorem, a²+b²=c², where c represents the diagonal and a and b represents the other sides of a right angled triangle
As a flag is a rectangle, the two triangles cut would be right angled triangles
Therefore, a²+9²=15²
a²+81=225
a²=144
a=√144
a=12 feet
Final answer:
To calculate the length of the Scottish flag, the Pythagorean theorem is applied. With a diagonal (hypotenuse) of 15 feet and a height of 9 feet, the length is found to be 12 feet.
Explanation:
The question involves calculating the length of the Scottish flag given the length of one diagonal and the flag's height. To find the length of the Scottish flag, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here, we know the length of the diagonal (hypotenuse) is 15 feet and the height (one side) is 9 feet.
Let x be the length of the Scottish flag (the other side of the right-angled triangle). According to the Pythagorean theorem, [tex]x^2 + 9^2 = 15^2.[/tex]
Solving for x, we get:
[tex]x^2 + 81 = 225[/tex][tex]x^2 = 225 - 81[/tex][tex]x^2 = 144[/tex][tex]x = \sqrt144[/tex]x = 12Therefore, the length of the Scottish flag will be 12 feet to the nearest foot.
Find the difference 7/8 - 3/10
Hello
Good Luck
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Classify the following triangle
Answer:
B acute
D equilateral
Step-by-step explanation:
All the sides are equal (line in the middle of each side) = equilateral
All the angles are equal (single line in each angle) = equilangular
That means 180/3 = 60
Each angle is 60 degrees 60 degree angles are acute
Given: AB= 4
AD= 6
What point is in the interior of both circles?
H
A
B
That would be point A. Point A is inside the outer bigger circle AND the smaller inner circle
Hope this helped!
~Just a girl in love with Shawn Mendes
For this case we have that, if we look at the figure, we have two circles. The large circle is of radius AD = 6, while the small circle is of radius AB = 4.
We can see that point A is inside the small circle, since the small circle is inside the large one, so A is inside the two circles.
Answer:
Point A
Factor completely 2x5 + 10x4 - 22x3.
Answer: 2x³(x² + 5x - 11)
Step-by-step explanation:
2x⁵ + 10x⁴ - 22x³
Factor out the GCF (2x³)
2x³(x² + 5x - 11)
Since there are no values whose product is -11 and sum is +5, this cannot be factored further.
-2(7a+4b)-6c=
Simplify
Answer:
Because of the minus sign
2 becomes - 2
The answer is -2
Multiply a and 7
Multiply a and 1
The a just gets copied along.
The answer is a
a
7*a evaluates to 7a
Multiply b and 4
Multiply b and 1
The b just gets copied along.
The answer is b
b
4*b evaluates to 4b
7*a+4*b evaluates to 7a+4b
Multiply -2 by 7a+4b
we multiply -2 by each term in 7a+4b term by term.
This is the distributive property of multiplication.
Multiply -2 and 7a
Multiply 1 and a
The a just gets copied along.
a
-2 × 7a = -14a
Multiply -2 and 4b
Multiply 1 and b
The b just gets copied along.
b
-2 × 4b = -8b
-2*(7*a+4*b) evaluates to -14a-8b
Multiply c and 6
Multiply c and 1
The c just gets copied along.
The answer is c
c
6*c evaluates to 6c
The answer is -14a-8b-6c
-2*(7*a+4*b)-6*c evaluates to -14a-8b-6c
The final answer is
-14a-8b-6c
Step-by-step explanation:
Please mark brainliest and have a great day!
What is the value of K?
Answer:
2
Step-by-step explanation:
m² = 4² + 8²
m² = 16 + 64
m² = 80
l² = k² + 4²
l² = k² + 16
m² + l² = (k + 8)² m² = 80, (b)
80 + k² + 16 = k² + 16k + 64
k² - k² - 16k = 64 - 80 -16
-16k = -32
k = -32/-16
k = 2
Rounded to the nearest tenth, what is the value of x
Answer:
0.6 ft
Step-by-step explanation:
The ratios of corresponding sides are equal, that is
[tex]\frac{2.3}{x}[/tex] = [tex]\frac{16.8}{4.5}[/tex] ( cross- multiply )
16.8x = 10.35 ( divide both sides by 16.8 )
x ≈ 0.6 ft ( to the nearest tenth )
Factor the polynomial 3x4 – 2x2 + 15x2 - 10 by grouping.
Which product is the factored form of the polynomial?
(x2 - 5)(3x2 + 2)
O (22 – 2)(3x2 + 5)
(22 + 5)(3x2 – 2)
0 (372 - 5)(2+2)
Answer:
see explanation
Step-by-step explanation:
Given
3[tex]x^{4}[/tex] - 2x² + 15x² - 10
Factor the first/second and third/fourth terms )
= x²(3x² - 2) + 5(3x² - 2) ← factor out (3x² - 2) from each term
= (3x² - 2)(x² + 5)
Answer: (3x² - 2)(x² + 5)
Step-by-step explanation:
g(x)=x2-16x
b=-16, so =16 = 64
9(x) = (x2 - 16x + 64) - 64
9(x) = (x - 1)2-
Which is the solution the equation 3.5(2h + 4.5)
[tex]\text{Hey there!}[/tex]
[tex]\text{In order for you to solve this equation, you need to DISTRIBUTE!}[/tex]
[tex]\text{The algebraic formula for distribution is: a(b+c) = a(b)+a(c) = ab + ac}[/tex]
[tex]\text{Now, that we have that portion solved, we can answer your question!}[/tex]
[tex]\text{3.5(2h) + 3.5(4.5)}[/tex]
[tex]\text{3.5(2h) = 7h}[/tex]
[tex]\text{3.5(4.5) = 15.75}[/tex]
[tex]\text{= 7h + 15.75}[/tex]
[tex]\boxed{\boxed{\bf{Answer:7h+15.75}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
solution set of 2x + y < 4
Step-by-step explanation:
Subtract
2
x
from both sides of the equation.
y
=
4
−
2
x
x
−
y
=
2
Subtract
x
from both sides of the equation.
y
=
4
−
2
x
−
y
=
2
−
x
Multiply each term in
−
y
=
2
−
x
by
−
1
Tap for more steps...
y
=
4
−
2
x
y
=
−
2
+
x
Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.
(
2
,
0
)
ANSWER
See attachment
EXPLANATION
The given inequality is
[tex]2x + y \: < \: 4[/tex]
To solve we need to graph this inequality.
To do that we graph the corresponding linear equation
[tex]y = - 2x + 4[/tex]
This is a straight line with slope
[tex]m = - 4[/tex]
and y-intercept (0,4)
The graph of this function is to the right of the origin.
The solution set of the corresponding inequality is the half plane that is shaded.
We plot the point (0,0) into the given inequality to determine which half plane must be shaded
[tex]2(0) + 0 \: < \: 4[/tex]
[tex]0 < 2[/tex]
This is true so we shade the lower half plane. The solution set is the lower half plane shaded in the attachment.
Note that the boundary line must be a dashed line because the inequality does not involve equal sign.
A stereo system is being installed in a room with a rectangular floor measuring 14 feet by 9 feet and a 7- foot ceiling. The stereo amplifier is on the floor in one corner of the room. A speaker is at the ceiling in the opposite corner of the room. What is the shortest connection
Answer:
Approximately 24 feet.
Step-by-step explanation:
Refer to the two diagrams attached (created with Geogebra.)
The wire between the speaker and the amplifier shall be routed along the wall. The length of the connection depends on the height of the point P at which the wire turns. Point P is shown in green in both diagrams.
To find the optimal position of that turning point, imagine that the two adjacent walls of the room are unfolded into two rectangles in the same plane (diagram 2.) Consider the claim: the shortest connection shall be a straight line that links the two devices when the two walls are unfolded. This explanation will show why this claim is true using the triangle inequality theorem.
Assume this claim is false: the connection will be even shorter if the wire turns at P', which is a point other than P. The length of the connection is now the sum of the two segments:
the distance between the amplifier and P', and the distance between P' and the speaker.In contrast, if the wire is routed through point P, the length of the connection will simply be
the length of the segment between the amplifier and the speaker.Point P is on the line that connects the amplifier and the speaker in diagram 2. However, P' is a point other than P, meaning that P' is off the line between the speaker and the amplifier. It is thus possible for the following three points to form a triangle:
The amplifier,The speaker, andPoint P'.By the triangle inequality theorem, the sum of any two sides of a triangle is greater than the length of the third side. To make full use of this theorem, consider the length of the three sides in this triangle:
[tex]\left\{\begin{array}{ll}\left.\begin{aligned}&\text{distance between amplifier and P}'\text{.}\\&\text{distance between P}' \text{ and speaker.}\end{aligned}\right\}&\text{Length of the second connection}\\\text{distance between amplifier and speaker}\end{array}\right.[/tex].
The sum of the first two distances shall be greater than the third. In other words, the length of the connection through P' will be greater than the length of the connection through P. This fact contradicts the assumption that the original claim is false. In other words, the claim that P gives the shortest connection is true.
Find the length of the shortest connection using the Pythagorean Theorem. Refer to the second diagram, the connection is the hypotenuse of a right triangle with
a leg of length [tex]14 + 9 = 23[/tex] feet, andanother leg of length [tex]7[/tex] feet.The length of the connection (the hypotenuse) will be:
[tex]\sqrt{23^{2} + 7^{2}}\approx 24[/tex] feet.
which similarity postulate or theorem can be used to verify that the two triangles shown below are similar?
Answer:
B
Step-by-step explanation:
You are given two right triangles PQR and XYZ with PQ=12, PR=6, XY=4, XZ=2. Note that
[tex]\dfrac{PQ}{XY}=\dfrac{12}{4}=3\Rightarrow PQ=3XY\\ \\\dfrac{PR}{XZ}=\dfrac{6}{2}=3\Rightarrow PR=3XZ[/tex]
So, in these triangles:
∠P=∠X=90°;PQ=3XY;PR=3XZ.Hence, by SAS theorem these triangles are similar.
SAS Similarity Theorem states that given two triangles are similar if their two sides are in proportion and their angles adjacent to these sides have the same measure.
I need help please?!!!!):
Answer:
4
Step-by-step explanation:
The mean of a set of data: (n₁ + n₂ + n₃...)/n, where n₁,₂,₃... are numbers in the set, and n is the number of numbers.
Plug in: (1 + 5 + 5 + 7 + 3 + 3 + 4)/7
Add: 28/7
Divide: 4
Answer:
4
Step-by-step explanation:
When finding the mean of a data set you add up all the numbers and divide it my how many numbers there is
1+5+5+7+3+3+4= 28
28 divided by 7 = 4
Mean of the set of data is 4
Hope this helps :)
if it does please mark brainliest :D
- A. Hazle <3
I to the exponent of 65
Answer:
Step-by-step explanation:
A= 1 * 1 = 2
A2 = 1 * (1 * 1)
A2 = 1 * 1
A2 = 1
a3 = 1 * 1 * (1 * 1)
a3 = 1 *1 * 1
a3 = 1 * (1*1)
a3 = 1* 1
a3 = 1
You keep on going in this manner until you hit 1^65 = 1
The only thing you have to accept is that (1 * 1) = 1
i live in a house that 3 metets below sea level go to school 5 meters above sea level how many meters do i go
what is the domain of (g°f)(x)
A.all real numbers except x=-4
B.all real numbers except x=0
C.all real numbers except x=4
D.all real numbers
(1/(x-1))-(3/(x^2+2x-3))
[tex] \frac{1}{x - 1} - \frac{3}{x {}^{2} + 2x - 3 } [/tex]
[tex]
\dfrac{1}{x-1}-\dfrac{3}{x^2+2x-3} \\
\dfrac{1}{x-1}-\dfrac{3}{(x+3)(x-1)} \\
\dfrac{1\cdot(x+3)-3}{(x+3)(x-1)} \\
\dfrac{x+3-3}{(x+3)(x-1)} \\
\dfrac{x}{(x+3)(x-1)}
[/tex]
Hope this helps.
r3t40
How many solutions exist for given equation 12x + 1 = 3(4x + 1
Answer:
no solutions
Step-by-step explanation:
12x + 1 = 3(4x + 1)
Distribute the 3
12x + 1 = 12x + 3
Subtract 12x from each side
12x-12x +1 = 12x-12x+3
1 =3
This is never true, so there are no solutions
Answer:
There are no solution
Step-by-step explanation:
A(B+C)=ab+ac
3(4x+1)=12x+1
12x+1=12x+3
Subtract by 1 both sides of equation.
12x+1-1=12x+3-1
Simplify.
3-1=2
12x=12x+2
Then subtract by 12x both sides of equation.
12x-12=12x+2-12x
Simplify, to find the answer.
0=2
The sides are not equal.
It's should be no solution.
No solution is the correct answer.
5/6 + 1/8 what is it?
Answer:
Step-by-step explanation:
[tex]\frac{5}{6} +\frac{1}{8} = \frac{20}{24} +\frac{3}{24} = \frac{23}{24}[/tex]
Answer:
23/24
Step-by-step explanation:
5/6 = (5×4)/(6×4)=20/24
1/8 = (1×3)/(8×3)=3/24
5/6 + 1/8 = 20/24 + 3/24 =23/24
A milkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate. This table gives the number of shakes of each flavor sold during three shifts on one day. Mango Strawberry Chocolate Shift 1 16 13 29 Shift 2 26 19 45 Shift 3 6 11 0 Total sales were $419 in the first shift, $649 in the second shift, and $96 in the third shift. If you form a linear system representing the data in the table and create a matrix from it, the determinant is 578. What is the price of one chocolate shake?
Step-by-step explanation:
you need to add together all the milkshakes sold and then add together the amount of money made and then divide the two numbers. i think this is right. hope i helped. i think your answer should be around 7 dollars for a milkshake.
The price of one chocolate shake is $9 if the milkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate option (D) is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
A milkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate.
Let x be the price of one mango shake
Let y be the price of one strawberry shake
Let z be the price of one chocolate shake
From the question we can frame three linear equations in three variables:
16x + 13y + 29z = 419
26x + 19y + 45z = 649
6x + 11y + 0z = 96
After solving the above system of equations:
x = $5
y = $6
z = $9
Thus, the price of one chocolate shake is $9 if the milkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate option (D) is correct.
Learn more about the linear equation here:
brainly.com/question/11897796
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Complete the square for 2x2 - 4x = 14.
Answer:
2x^2-4x=14
x^2-2x=7
x^2-2x+1=8
(x-1)^2=8
What is the midpoint of the line segment with the endpoints J(-9,-4) and K(7,8)?
Answer:
Step-by-step explanation:
22
calculate the scale factor for thr dilation. What is AB?
6 units
7.6 units
9.5 units
12 units
Answer:
AB is 6 units
Hope this helps
Step-by-step explanation:
The scale factor of the dilation is: 2.5.
The length of AB is: 6 units.
What is the Scale Factor of a Dilation?The scale factor of a dilation (reduction or enlargement) = dimension of new figure / corresponding dimension of original figure.
The scale factor of the image given = B'C'/BC
Scale factor = 9.5/3.8 = 2.5
To find the length of AB, divide the length of A'B' by the scale factor of the dilation.
AB = 15/2.5
AB = 6 units. (option A)
Learn more about scale factor on:
https://brainly.com/question/2826496
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The radius is 14 and CD = 22. Find EB.
Answer:
14 - [tex]\sqrt{23}[/tex]
Step-by-step explanation:
CD=22 => ED=11
AD=14 (radius). With Pythagorean theorem, [tex]AE^{2}[/tex]=[tex]AD^{2}[/tex]-[tex]ED^{2}[/tex] => AE = [tex]\sqrt{23}[/tex]
EB= AB-AE = 14 - [tex]\sqrt{23}[/tex]
The measure of EB from the expression is 5.34
The given diagram is A circle with the following sides
radius AB = 14
CD = 22
From the diagram, AB = AE + EB
Determine the measure of AE using Pythagoras theorem
AD² =AE² + ED²
14² = AE² + 11²
AE² = 14² - 11²
AE² = 196 - 121
AE² = 75
AE = √75
AE = 8.66
EB = AB - AB
EB = 14 - 8.66
EB = 5.34
Hence the measure of EB from the expression is 5.34
The graph for the equation y=x-4 is shown below.
Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?
A. y - x = -4
B. y - x = -2
C. y - 4 = x
D. y + 4x = 1
Answer:
A. y - x = -4
Step-by-step explanation:
y=x-4
To get infinite equations, the equation must be equal to y=x-4
We will solve each of these for y to see if they are identical
A. y - x = -4
Add x to each side
y-x+x = x-4
y = x-4
This is the same
It will give infinite solutions
B. y - x = -2
y-x+x = x-2
y =x-2
This is not the same.
It is parallel and will give no solutions
C. y - 4 = x
y-4+4 = x+4
y = x+4
This is parallel and will give no solutions
D. y + 4x = 1
y +4x-4x = -4x+1
This will intersect at a point
Answer: The correct answer is c.
Step-by-step explanation:
I just answered the question for school
Choose the function whose graph is given by:
A. y=3sin(x-2)+1
B. y=3cos(x-3)+1
C. y=6sin(x-2)-2
D. y=3sin(x-2)+2
Answer:
A
Step-by-step explanation:
a site called desmos, its a graphing calculator and you should use it :)
The function whose graph is given below is:
A) [tex]y=3\sin (x-2)+1[/tex]
Step-by-step explanation:From the graph that is provided to us we observe that,
when x=2
then f(x)=1
Hence, we will check which function satisfies this point.
B)
[tex]y=3\cos(x-3)+1[/tex]
At x=2 we have:
[tex]y=3\cos (3-2)+1\\\\i.e.\\\\y=3\cos(1)+1\\\\y>1[/tex]
Hence, option: B is incorrect.
C)
[tex]y=6\sin (x-2)-2[/tex]
when x=2 we have:
[tex]y=6\sin (2-2)-2\\\\i.e.\\\\y=6\sin 0-2\\\\i.e.\\\\y=-2\neq 1[/tex]
Hence, option: C is incorrect.
D)
[tex]y=3\sin (x-2)+2[/tex]
when x=2 we have:
[tex]y=3\sin (2-2)+2\\\\i.e.\\\\y=3\sin 0+2\\\\i.e.\\\\y=2\neq 1[/tex]
Hence, option: D is incorrect.
So, we are left with option: A
A)
[tex]y=3\sin (x-2)+1[/tex]
when x=2
we get: y=1
Similarly all the other points are satisfied.
Also, the graph of this function matches the given graph.
Which expression is equivalent to?...
Answer:
B x^9 ∛ y
Step-by-step explanation:
(x^27 y) ^ (1/3)
x^27^(1/3) y^(1/3)
We can distribute the exponent a^b ^c = a^(b*c)
x^(27*1/3) y^(1/3)
x^9 y^(1/3)
What is 510° expressed in radian measure?
Answer: π/180
Step-by-step explanation:
510 Degree (°) =. 8.90118 Radian (rad) Degree : A degree, a degree of arc or arc degree is a measurement of plane angle, on behalf of 1/360 of a full rotation. The symbol for degree is °. It is not an SI unit, however, it is accepted for use with SI. One degree is equal to π/180 radians.
Answer:
17pi/6 rad
Step-by-step explanation:
2 pi radians = 360 degrees
Divide both sides by 2.
pi radians = 180 degrees
From the statement above, you get the conversion factors:
(pi rad)/(180 deg) = (180 deg)/(pi rad) = 1
Both fractions above equal 1. Since multiplying by 1 does not change the number, multiply 510 deg by the fraction above that will cancel out degrees and will leave you with radians.
510 deg * (pi rad)/(180 deg) = 510pi/180 rad = 17pi/6 rad
A pyramid is placed inside a prism as shown. The pyramid has the same base area, B, as the prism but half the height, h,of the prism. Which expression gives the volume of the pyramid
Answer:
[tex]\large\boxed{V_{pyramid}=\dfrac{1}{6}Bh=\dfrac{1}{6}V_{prism}}[/tex]
Step-by-step explanation:
[tex]B-\text{base area}\\h-\text{height of the prism}\\\dfrac{1}{2}h-\text{height of the pyramid}\\\\\text{The formula of a volume of a prism:}\\\\V_{prism}=Bh\\\\\text{The formula of a volume of a pyramid:}\\\\V_{pyramid}=\dfrac{1}{3}Bh\to V_{pyramid}=\dfrac{1}{3}B\left(\dfrac{1}{2}h\right)=\dfrac{1}{6}Bh=\dfrac{1}{6}V_{prism{[/tex]
Answer:
V = 1/6 BH
Step-by-step explanation:
the volume of a pyramid is 1/3 BH , since the pyramid is only half the height of the prism you'll have to multiply 1/3 x 2 = 1/6