Given the equilateral triangle ABC; AE, BD, & CF are altitude intersecting at point G. How many right triangles are in the diagram?
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Solution
Given the equilateral triangle ABC;
The following are the numbers of right triangles:
[tex]\begin{gathered} CFB \\ CFA \\ CEA \\ AEB \\ CDB \\ BDA \\ FHD \\ FHE \\ DJE \\ DJF \\ EID \\ EIF \end{gathered}[/tex]There are 12 right triangles in the diagram.
Related Questions
Geometry MAFS.912.G-C0.3.9 11. Peach Street and Cherry Street are parallel. Apple Street intersects them as shown in the diagram below. Apple Street 12 RS Peach Street Cherry Street If mZ1 = 2x +36 and m22 = 7x-9, what is m 1? A 9 B. 17 C. 54 D. 70
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therefore,
[tex]m\angle1=2(17)+36=34+36=70[/tex]I need help with this please, thank you very much
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1. translation 1 unit left and 6 units down
[tex]h(x)=6(2^x)-1[/tex]2. Stretch vertically by a factor of 6 and translate 1 unit down
[tex]j(x)=2^{6x}-1[/tex]3. Compress horizontally by a factor of 6 and translate 1 unit down
[tex]k(x)=2^{x+6}+1[/tex]4. Translation 6 units left and 1 unit up
How do you simplify 780(49)
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Tou have the following expression:
780(49)
in order to simplify the previous expression, write 49 as 40 + 9 and apply distributive property:
780(40 + 9) = 780*40 + 780*9 = 3120 + 7020 = 10140
Hence, the answer is 10140
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function. v(t)=25,900(0.86)^t Find the intial value of the car and the value after 13 years. Round your answers to the nearest dollor as necessary.
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To find the initial value of the car replace when t=0
[tex]\begin{gathered} V(0)=25,900(0.86)^0 \\ V(0)=25,900 \end{gathered}[/tex]To find the value after 13 years use t=13
[tex]\begin{gathered} V(13)=25,900(0.86)^{13} \\ V(13)=3645.69\approx3646 \end{gathered}[/tex]hi can we work relationship of x and y pls?
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step 1
Find out the slope
we need two points
looking at the table
we take
(1,3) and (2,4)
m=(4-3)/(2-1)
m=1/1
m=1
step 2
Find out the equation in slope-intercept form
y=mx+b
we have
m=1
point (1,3)
substitute and solve for b
3=(1)(1)+b
3=1+b
b=2
therefore
y=x+2
the answer is the last optioni need help on number 1Find 3 point in the graph
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To graph a linear equation:
1. Find the x-intercept
The x-intercedpt is the point when the line cross the x-axis (when y=0)
[tex]\begin{gathered} 0=-3x-3 \\ 3=-3x \\ \frac{3}{-3}=x \\ \\ x=-1 \end{gathered}[/tex]First point (-1 ,0)
2. Find the y-intercept
The y-intercept is the point when the line cross the y-axis (when x=0)
[tex]\begin{gathered} y=-3(0)-3 \\ y=-3 \end{gathered}[/tex]Second point (0 , -3)
3. Put in the plane the x and y-intercepts and draw a line that pass through these points:
Besides the x- and y-intercepts you can identify point (-2,3)
Find the area of the shaded sector. Leave your answer in terms of pi or round to the nearest 10th
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SOLUTION
The shaded part is a sector.
It is one-fourth the area of the whole circle
Area of a circle is given as
[tex]\begin{gathered} \text{Area of a circle = }\pi r^2 \\ \text{where r = radius and from the diagram, the radius = 5} \end{gathered}[/tex]So, the area of the shaded sector becomes
[tex]\begin{gathered} \text{Area of a sector = }\frac{1}{4}\times area\text{ of a circle } \\ \text{Area of sector = }\frac{1}{4}\times\pi r^2 \\ \text{Area of sector = }\frac{1}{4}\times\pi\times5^2 \\ =\frac{25}{4}\pi \end{gathered}[/tex]Hence, the answer is
[tex]\frac{25}{4}\pi[/tex]A triangle has 2 sides of length 15 and 19 what is the smallest possible whole number length for the 3rd side
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We have a triangle with 2 sides of length 15 and 19.
We have to find the smallest possible whole number length for the 3rd side.
We can draw this as:
The third size is x.
If we reduce h, approaching to 0, x is minimized.
When h is very close to 0 (if h=0, the triangle cease to exist), the value of x can be written as a little bigger than the difference between the largest side (19) and the other side (15).
Then, x is, in the limit h-->0:
[tex]x+15>19\Rightarrow x>19-15=4\Rightarrow x>4[/tex]As x>4, the next whole number is 5.
NOTE: if x=4, the triangle does not exist, as there is no height or 3 angles.
Answer: The smallest whole number length for the 3rd side is 5.
Given two supplementary angles, n and (2n+3). Find the value of n.
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Answer:
n = 59°
Explanation:
Given: Angles n and (2n+3) are supplementary.
Two angles are said to be supplementary if they add up to 180 degrees.
Therefore:
[tex]n+(2n+3)=180\degree[/tex]Solve the equation for n:
[tex]\begin{gathered} n+2n+3=180 \\ 3n+3=180 \\ \text{Subtract 3 from both sides:} \\ 3n+3-3=180-3 \\ 3n=177 \\ \text{Divide both sides by 3} \\ \frac{3n}{3}=\frac{177}{3} \\ n=59\degree \end{gathered}[/tex]The value of n is 59°.
rotate the following ploygon 90 degrees ccw. List the new image coordinates. write the general rule.
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The general rule for a 90° counterclockwise rotation is
[tex](x,y)\rightarrow(-y,x)[/tex]We have to apply this rule to each point on the given table.
[tex]\begin{gathered} A(2,3)\rightarrow A^{\prime}(-3,2) \\ B(5,3)\rightarrow B^{\prime}(-3,5) \\ C(1,5)\rightarrow C^{\prime}(-5,1) \\ D(6,5)\rightarrow D^{\prime}(-5,6) \end{gathered}[/tex]Therefore, the new image coordinates areA'(-3,2)
B'(-3,5)
C'(-5,1)
D'(-5,6)
find the unit rate 12 chocolate bars cost $18 how much for 1
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To find the unit rate we need to divide the the total cost of the bars by the number of bars bought. On this case we have:
[tex]\text{rate}=\frac{18}{12}=1.5\text{ \$ per bars}[/tex]On this case each bar costs $ 1.5
A frequency table of gradəs has five classes (A, B, C, D, F) with frequencies of 4, 10, 17,6, and 2 respectively. Using percentages, what are the relativefrequencies of the five classes?Complete the table.Grade Frequency Relative frequencyА4%B10%с176F2%(Round to two decimal places as needed.)%62
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GRADE FREQUENCY RELATIVE FREQUENCY % RELATIVE FREQUENCY
A 4 4/39 4/39 x 100 = 10.26
B 10 10/39 10/39 x 100 = 25.64
C 17 17/39 17/39 x 100 = 45.59
D 6 6/39 6/39 x 100 = 15.38
F 2 2/39 2/39 x 100 = 51.28
∑F = 39
How do I transform this function by y=f(3x) if this is the original function?
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Let y=f(x) is the original function and y=f(ax) is the new function, where a is a constant.
Then, y=f(ax) is a horizontal stretch or horizontal compression of f(x).
If a>1, then the graph of f(x) is compressed by 1/a.
If 0
The given function is y=f(x).
The new function is y=f(3x). It is of the form y=f(ax).
The constant 3 is greater than 1.
Therefore, the graph of y=f(3x) is the compression of the graph of f(x) by 1/3.
Identify some points on the graph of f(x) in the form (x, y).
(3, 0), (0, 3) and (-3, 0 ) are points on the graph of f(x).
Let (x', y') be a point on the graph of y=f(3x).
The transformation of each of the point on y=f(x) to y=f(3x) can be represented as,
(x, y)-->(x', y')-->(x/3, y).
For points (3, 0), (0, 3) and (-3, 0 ), the transformation can be described by ,
[tex]\begin{gathered} (3,\text{ 0)}\longrightarrow(3,\text{ }3\times0)=(3,\text{ 0)} \\ (0,\text{ 3)}\longrightarrow(0,\text{ 3}\times3\text{)=}(0,\text{ 9)} \\ (-3,0)\longrightarrow(-3,3\times0)=(-3,\text{ 0)} \end{gathered}[/tex]Ping says that subtracting 2- 1 1/3 yields the same result as computing 2-1+ 1/3. Quon disagrees. He thinks its the same result as computing 2-1- 1/3. Is either correct? Explain.
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2 - 1 1/3 is
2 - 4/3 = (6-4)/3 = 2/3
2 - 1 + 1/3 is
1 + 1/3 = 4/3
According to Q
change 0.2 to a fraction
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hello
to convert 0.2 to fraction, we simply find two numbers that when divided, the quotient would be 0.2
[tex]0.2=\frac{2}{10}[/tex]Asuka is planting grass seeds on her new lawn. The dimensions of her lawn are 4 ft by 3 ft. The instructions to plant the grass seeds suggest planting 16 seeds for every squarefoot How many seeds should Asuka use to plant her entire lawn? foot
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Since she can plant 16 seeds per square foot, then
We must find the area of the lawn
Since the lawn is shaped a rectangle of dimensions 4 ft and 3 ft, then
[tex]\begin{gathered} A=L\times W \\ A=4\times3 \\ A=12ft^2 \end{gathered}[/tex]Since 1 square foot = 16 seed, then
12 square feet = 12 x 16 = 192 seeds
She will need 192 seeds to plant the entire lawn
Can you pls help me with this question thank you
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First, identify an expression for the phrase "twice a number v".
The word "twice" means "two times" or "double", and refers to a multiplication by the number 2.
Then, "twice a number v" can be written using algebraic language as 2v.
So, the phrase "twice a number v plus 52" is equivalent to "2v plus 52", which can be expressed in algebraic languaje as 2v+52.
Therefore, the correct choice is option A) 2v+52
i really really need some help to finish this
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The quadratic function given:
[tex]f(x)=2(x-3)(x+7)[/tex]The x-intercept(s) is the x-axis cutting points. It occurs at y = 0. Thus, we substitute '0' into 'f(x)' and solve for the x values.
[tex]\begin{gathered} f(x)=2(x-3)(x+7) \\ 0=2(x-3)(x+7) \\ x-3=0,x=3 \\ \text{and} \\ x+7=0,x=-7 \end{gathered}[/tex]As we can see, there are 2 x-intercepts, at x = 3 and x = -7.
what is the value of F(3) in the function below? F(x)=2^x
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Y=f(x) and find the domain of f(x)Options for range:[0,5) (0,5)[0,5][-2,3](-2,3)
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Answer:
• Domain: (0,5)
,• Range: [-2,3]
Explanation:
Domain
The domain is the set of all the real values x along the x-axis for which there is a point on the given graph.
The graph is open at x=0 and open at x=5.
Therefore, the domain of f(x) is:
[tex]\begin{gathered} Inequality\; Notation\colon0RangeThe range is the set of all the real values y along the y-axis for which there is a point on the given graph.
• The minimum value of y=-2 and the graph is closed at that point.
,• The maximum value of y=3 and the graph is also closed at that point
We represent the range using the notation below:
[tex]\begin{gathered} Inequality\; Notation\colon-2\leqslant y\leqslant3\text{ } \\ Interval\; Notation\colon\lbrack-2,3\rbrack \end{gathered}[/tex]Can you please help me out with a question
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Step 1: Write out the formuar for the lateral area of the shape given
[tex]\text{Area}=\text{ 2}\pi rh[/tex]Step 2: Write out the given data
[tex]\begin{gathered} \pi=3.14 \\ r=\text{radius}=\text{ 2ft} \\ h=\text{height}=4ft \\ \end{gathered}[/tex]Step 3: Substituting and getting the solution
[tex]\begin{gathered} Area=\text{ (2}\times3.14\times2\times4)ft^2 \\ \text{Area}=\text{ 50.24}ft^2 \end{gathered}[/tex]Hence the answer is 50.24ft²
The answer is C
ADBA. 9°B. 10°C. 81°D. 91°99⁰CABCD is a quadrilateral. If mZC = (x²)°, find mZC..
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Since ABCD is a quadrilateral, the sum of internal angles is equal to 360°.
Using this property, let's find the measure of angle C:
[tex]\begin{gathered} A+B+C+D=360°\\ \\ 90+99+C+90=360\\ \\ C+279=360\\ \\ C=360-279\\ \\ C=81° \end{gathered}[/tex]The measure of angle C is 81°, therefore the correct option is C.
1) if b is a root of a polynomial equation then (x-b) is a ______of the polynomial2). polynomial equation y=x^2+x-6 root=2 ,factor=__
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If b is a root of a polynomial equation then (x - b) is a FACTOR of the Polynomial
Question 2
polynomial y = x^2 + x + 6
If root = 2
Then the factor is iven by
(x - 2)
Write an equation in point-stope form for the line through the two points. Then change it toslope intercept form, Rewrite the equation in standard form.10. (1, 2) and (3, 12) 11. (6, 2) and (-2,-2) 12. (4,1) and (1.4)
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10. (1, 2) and (3, 12)
x₁ = 1 y₁= 2
x₂ = 3 y₂=12
Using the formula;
m = y₂ - y₁ / x₂ - x₁
= 12 - 2 / 3- 1
= 10 / 2
= 5
y = mx + b
substitute x = 1 y=2 m = 5 in the above and then solve for b
2 = 5(1) + b
2 = 5 + b
2- 5 = b
-3 = b
b = -3
substitute m = 5 and b = -3 in y=mx + b
y = 5x - 3
(6, 2 ) and ( -2, -2)
x₁= 6 y₁= 2 x₂= -2 y₂=-2
m = y₂ - y₁ / x₂ - x₁
m = -2 -2 / -2 -6
= -4 / -8
= 4/8
= 1/2
x = 6 y = 2 m = 1/2
substitute in y = mx + b and then solve for b
2 = 5(1/2) + b
2 - 5/2 = b
4 - 5 / 2 = b
-1 /2 = b
substitute m= - 1/2 and b = -1/2 into y=mx + b
y = -(1/2)x - 1/2
12. (4,1) and (1.4)
x₁= 4 y₁= 1 x₂= 1 y₂= 4
m = y₂ - y₁ / x₂ - x₁
= 4-1 / 1-4
= 3/ -3
= - 1
substitute m = -1 x =4 y= 1
y = mx + b
1 = -1(4) + b
1 = -4 + b
1+4 = b
5 = b
b = 5
substitute m = -1 b=5 into y=mx+b
y= -x + 5
Spin Company has $52,000 in its Cash account, $20,000 in its Inventory account, and $12,000 in its Notes Payable (short-term) account. If Spin's only other account is Common Stock, what is the balance of that account?
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Assuming the other account is Common Stock, The balance of that account is: $60,000.
What is the account balance?Account balance can be defined as the amount that is left after substracting or deducting the liabilities from the assets.
Using this formula to determine or find the amount that will be the balance in the account
Account balance = ( Cash account+ Inventory account ) - Notes Payable (short-term) account
Where:
Cash account = $52,000
Inventory account = $20,000
Notes Payable (short-term) account = $12,000
Let plug in the formula so as to find the account balance
Account balance :
Account balance = ($52,000 + $20,000 ) - $12,000
Account balance = $ 72,000 - $12,000
Account balance = $60,000
Therefore we can conclude that the amount of $60,000 is the account balance.
Learn more about account balance here: https://brainly.com/question/2510966
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find the values of x and y if l || m.
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Explanation
Step 1
when a lines intersects a pair of parallel lines , diverse angles are created
All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent,so ( in the image yellow angles are corresponding, so)
[tex]\begin{gathered} (5x+14)=(7x-30) \\ \end{gathered}[/tex]solve for x
[tex]\begin{gathered} (5x+14)=(7x-30) \\ \text{subtrac 5x in both sides} \\ (5x+14)-5x=(7x-30)-5x \\ 14=2x-30 \\ \text{add 30 in both sides} \\ 14+30=2x-30+30 \\ 44=2x \\ \text{divide both sides by 2} \\ \frac{44}{2}=\frac{2x}{2} \\ 22=x \end{gathered}[/tex]Step 2
now, yellow angle and ble angles are supplementary( Two Angles are Supplementary when they add up to 180 degrees),so
[tex]\begin{gathered} (3y+11)+(7x-30)=180 \\ \end{gathered}[/tex]let
x=22
and solve for y
[tex]\begin{gathered} (3y+11)+(7x-30)=180 \\ (3y+11)+(7\cdot22-30)=180 \\ (3y+11)+(7\cdot22-30)=180 \\ 3y+11+124=180 \\ 3y+135=180 \\ \text{subtract 135 in both sides} \\ 3y+135-135=180-135 \\ 3y=45 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{45}{3} \\ y=15 \end{gathered}[/tex]I hope this helps you
Given the definitions of f(x) and g(x) below, find the value of (gof)(9).f(x) = 2 – 14g() = 2?+ 2a + 12
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Answer
(g o f)(9) = 27
Explanation
We are given that
f(x) = x - 14
g(x) = x² + 2x + 12
We are then told to find (g o f)(9)
(g o f)(x) refers to writing g(x), but instead of x, we will replace x by f(x).
That is,
(g o f)(x)
= g(f(x))
= [f(x)]² + 2 [f(x)] + 12
= (x - 14)² + 2 (x - 14) + 12
= x² - 28x + 196 + 2x - 28 + 12
= x² - 26x + 180
So, for (g o f) (9), we will substitute 9 for x
(g o f)(x) = x² - 26x + 180
(g o f)(9) = 9² - 26(9) + 180 = 81 - 234 + 180 = 27
Hope this Helps!!!
i need help finding the bottom layer of the cake
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In a trpezium, the median line is always parallel to the bases. The expression for the length of the median of trapezium is :
[tex]\text{length of mediam=}\frac{Sum\text{ of parallel sides}}{2}[/tex]In the trapezium: NM = ML=LK=PQ=QR=RS
we have : NP = 8, LR =20
Conisder the case of trapezium NPLR, where MQ is the median
From the expression of the length of median:
[tex]\begin{gathered} MQ=\frac{NP+LR}{2} \\ MQ=\frac{8+20}{2} \\ MQ=\frac{28}{2} \\ MQ=14 \end{gathered}[/tex]Now, consider the case of trapezium MQSK, where LR is act as median, MQ= 14, LR =20
From the expression of the length of median
[tex]\begin{gathered} \text{length of median=}\frac{Sum\text{ of parallel sides}}{2} \\ LR=\frac{MQ+KS}{2} \\ 20=\frac{14+KS}{2} \\ 14+KS=40 \\ KS=40-14 \\ KS=26\text{ inches} \end{gathered}[/tex]So, the diameter of the bottom KS is 26 inches
Answer : the diameter of the bottom KS is 26 inches
given this image create a dilation with a scale factor of 2
Answers
the image after a dilation factor can be found using the multiplication of the dilation factor with the coordinates.
[tex]k(x,y)\Rightarrow(kx,ky)[/tex]using this,
[tex]\begin{gathered} A(2\cdot(2,2))\Rightarrow A^{\prime}(4,4) \\ B(2\cdot(6,2))\Rightarrow B^{\prime}(12,4) \\ C(2\cdot(2,5))\Rightarrow C^{\prime}(4,10) \\ \text{Then,} \\ A^{\prime}(4,4) \\ B^{\prime}(12,4) \\ C^{\prime}(4,10) \end{gathered}[/tex]Jody invested $5500 less in an account paying 4% simple interest than she did in an account paying 3% simple interest. At the end of the first year, the total interest from both accounts was 648. Find the amount invested in each account.
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We will have the following:
*First, we construct the expression that is given in the text, that is:
[tex]0.04(x-5500)+0.03x=648[/tex]*Second: We operate:
[tex]\Rightarrow0.04x-220+0.03x=648\Rightarrow0.07x-220=648[/tex][tex]\Rightarrow0.07x=868\Rightarrow x=12400[/tex]So, Jodie invested $12 400 in each account.