Answers
Answer:
[tex]\large\boxed{c.\ \triangle CDE\sim\triangle FGH}[/tex]
Step-by-step explanation:
[tex]\text{Calculate the maeasure of the angle}\ E:\\\\180^o-(60^o+53^o)=180^o-113^o=67^o\\\\\angle C\cong\angle F\\\\\angle E\cong\angle H\\\\\angle D\cong\angle G\\\\\text{Therefore:}\\\\\triangle CDE\sim\triangle FGH[/tex]
Answer: The correct option is
(c) [tex]\triangle CDE\sim \triangle FGH.[/tex]
Step-by-step explanation: We are given to write a similarity statement for the triangles shown in the figure.
In the given triangles, we have
m∠C = 60°, m∠D = 53°, m∠F = 60° and m∠H = 67°.
Fist, we have to fin d the measures of angles E and G.
From angle sum property of a triangles, we can write
[tex]m\angle C+m\angle D+m\angle E=180^\circ\\\\\Rightarrow 60^\circ+53^\circ+m\angle E=180^\circ\\\\\Rightarrow 113^\circ+m\angle E=180^\circ\\\\\Rightarrow m\angle E=180^\circ-113^\circ\\\\\Rightarrow m\angle E=67^\circ.[/tex]
Similarly, we have
[tex]m\angle F+m\angle G+m\angle H=180^\circ\\\\\Rightarrow 60^\circ+m\angle G+67^\circ=180^\circ\\\\\Rightarrow 127^\circ+m\angle G=180^\circ\\\\\Rightarrow m\angle G=180^\circ-127^\circ\\\\\Rightarrow m\angle G=53^\circ.[/tex]
So, we get
m∠C = m∠F,
m∠D = m∠G
and
m∠E = m∠H.
Therefore, by angle-angle-angle similarity postulate. we get
[tex]\triangle CDE\sim \triangle FGH.[/tex]
Thus, option (c) is CORRECT.
Related Questions
The function g(x) = 3x2 − 12x + 7 written in vertex form is g(x) = 3(x − 2)2 − 5. What is the vertex of g(x)?
Answers
ANSWER
The vertex of g(x) is (2,-5).
EXPLANATION
The given function is:
[tex]g(x) = 3 {x}^{2} - 12x + 7[/tex]
The vertex form of this function is:
[tex]g(x) = 3 {(x - 2)}^{2} -5[/tex]
This is of the form
[tex]g(x) = a {(x - h)}^{2} + k[/tex]
where (h,k) is the vertex.
When we to
[tex]g(x) = 3 {(x - 2)}^{2} -5[/tex]
h=2 and k=-5
The vertex of the parabola is (2,-5).
The equation for the circle is:
x²+y²+14x+10y−7=0 .
What is the center of the circle?
Answers
Answer:
(-7,-5)
Step-by-step explanation:
Converting the circle into the form (x-h)^2+(y-k)^2=r^2, we get
x^2+14x+49+y^2+10y+25=7+25+49
So we get
(X+7)^2+(y+5)^2=81
So the center of the circle is (-7,-5)
Answer:
centre = (- 7, - 5)
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Arrange the equation by placing the x and y terms together
x² + 14x + y² + 10y - 7 = 0 ( add 7 to both sides )
x² + 14x + y² + 10y = 7
Use the method of completing the square
add (half the coefficient of the x/y term)² to both sides
x² + 2(7)x + 7² + y² + 2(5)y + 5² = 7 + 7² + 5²
(x + 7)² + (y + 5)² = 7 + 49 + 25 = 81 ← in standard form
with (h, k) = (- 7, - 5) ← centre of circle
Math
Need to find volume
Fractions
Answers
V= length x width height.
5/3 x 1/4 x 3/2
15 /24 or 5/8
Jolene invests her savings in two bank accounts, one paying 6 percent and the other paying 9 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 7266 dollars. How much did she invest at each rate?
Amount invested at 6 percent interest is $
Amount invested at 9 percent interest is $
Answers
Answer:
Amount invested at 6 percent interest is $69,200
Amount invested at 9 percent interest is $34,600
Step-by-step explanation:
Let the amount invested (or principal) at 6 percent interest be $2x
The principal(P) (amount invested) at 9 percent interest will be $x
Amount(A) = P(1 + rt)
Time(t) = one year = 1
Amount at 6% interest = 2x(1 + 0.06) = $2.12x
Interest accumulated = Amount - Principal = $2.12x - $2x = $0.12x
Amount at 9% interest = x(1 + 0.09) = $1.09x
Interest accumulated = Amount - Principal = $1.09x - $x = $0.09x
Total interest = $7,266
So, $0.12x + $0.09x = $7,266
$0.21x = $7,266
x = [tex]\frac{7,266}{0.21}[/tex] = $34,600
The principal (amount invested) at 9 percent interest rate is $34,600
The principal (amount invested) at 6 percent interest rate is 2 × $34,600 = $69,200
ILL MARK YOU AS BRAINLIEST, RATE YOU A 5, AND THANK YOU! 70 POINTS!
what is the surface area of this rectangular prism? i-ready
Answers
Answer:
290 in²Step-by-step explanation:
From the net:
S.A. = 2(25 in²) + 4(60 in²) = 50 in² + 240 in² = 290 in²
From the model:
The formula of a Surface Area of a rectangular prism:
S.A. = 2(lw + lh + wh)
l - length
w - width
h - height
We have l = 5 in, w = 5 in, and h = 12 in. Substitute:
S.A. = 2(5 · 5 + 5 · 12 + 5 · 12) = 2(25 + 60 + 60) = 2(145) = 290 in²
Answer: 290 in.^2
Step-by-step explanation: Just did on iready. Hope i helped! (:
Given: ΔXYZ
AB is a midsegment parallel to XY. The slope of AB is
2
3
.
What is the slope of XY?
A) 0
B) -
2
3
C)
2
3
D) undefined
Answers
Answer:
C) 2/3Step-by-step explanation:
If AB is parallel to XY, then they have the same slope.
If the slope of AB is 2/3, then the slope of XY is 2/3 too.
which equation could generate the curve in the graph below?
Answers
the answer is c
hope this would help you
Answer:
[tex]y=-2x^2 -16x -28[/tex]
Step-by-step explanation:
We are given with the graph of a parabola
[tex]y=-2x^2 + 3x -5[/tex]
a=-2, b=3 and c=-5
Discriminant = [tex]b^2-4ac= 3^2 -4(-2)(-5)= 9-40= -31[/tex]
Discriminant is negative so x intercepts are imaginary.
In the graph we have two x intercepts.
[tex]y=-2x^2 -4x -2[/tex]
a=-2, b=-4 and c=-2
Discriminant = [tex]b^2-4ac= (-4)^2 -4(-2)(-2)=0[/tex]
Discriminant is 0 so there is only one x intercept
[tex]y=-2x^2 -16x -28[/tex]
a=-2, b=-16 and c=-28
Discriminant = [tex]b^2-4ac= (-16)^2 -4(-2)(-28)=32[/tex]
Discriminant is positive so there are two x intercepts
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a} =\frac{16+-\sqrt{32} }{2(-2)}[/tex]
We will get two values for x
x= -5.414 , x=-2.586
Two x intercepts are negative . That is the x intercepts of given graph.
[tex]y=-2x^2 +16x -28[/tex]
a=-2, b=16 and c=-28
Discriminant = [tex]b^2-4ac= (16)^2 -4(-2)(-28)=32[/tex]
Discriminant is positive so there are two x intercepts
Please help:):):) Your awesome
Answers
Answer:
Q1: 11x - 8
Q2: 2x + 10
Q3: -3v + 12
Answer:
Q1: 11x + 8
Q2: 2x + 10
Q3: 3v - 12
What is the surface area of a rectangular prism with the dimensions of: Length is 5.5, Width, 4, and Height, 3.8
Answers
Answer:
Total Area = height * width + height * length + width * length
Total Area = 3.8 * 4 + 3.8 * 5.5 + 4 * 5.5 =
15.2 + 20.9 + 22 =
58.1 square units
Step-by-step explanation:
If y varies inversely with x and y =5 when x=2.5 what is the value of y when x=20
Answers
Answer:
If x = 20, then y = 12.5/20 = 0.625
Step-by-step explanation:
The pertinent relationship is y = k/x, where k is the constant of proportionality.
Subbing 5 for y and 2.5 for x yields 5 = k/2.5, so k = 12.5.
Then the specific relationship fit to this problem is y = 12.5/x.
If x = 20, then y = 12.5/20 = 0.625
What is the exact area of a circle with radius 5?
251
15
101
10
Answers
Answer:
[tex]\large\boxed{A=25\pi}[/tex]
Step-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
We have r = 5. Substitute:
[tex]A=\pi(5^2)=25\pi[/tex]
What is the expression (3x²y³) ³
Answers
Final answer:
The expression (3x²y³) ³ is found by cubing the coefficient and multiplying each variable's exponent by 3, which results in 27x⁶y⁹.
Explanation:
When we deal with the cubing of exponentials, as in the expression (3x²y³) ³, both the numerical coefficient and the variables with their exponents are raised to the power of 3. The rules of exponents guide us to cube the number 3 and multiply the exponents of x and y by 3.
To cube the number 3, we would calculate 3³, which equals 27. For the variables, we apply the exponent to each exponent: x raised to the 2³ (which is 6) and y raised to the 3³ (which is 9). Hence, the expression (3x²y³) ³ simplifies to 27x⁶y⁹. This demonstrates that when cubing an exponential expression, we obtain a new exponent for each variable by multiplying the original exponent by 3, and we cube the numerical coefficient as well.
The number of tickets sold is an example of continuous data. True or False?
Answers
Answer:
False
Step-by-step explanation:
Continuous data is data that can take any value within a range, including non-whole number values.
Because the number of tickets sold can only take whole number values, it is not an example of continuous data.
False
I hope this helps you understand continuous data. Have a great day. :)
Answer: False
Step-by-step explanation: Continuous data is data that can be measured. The number of tickets that were sold would only be positive integers meaning that there can't be a fraction of a ticket sold. Since discrete data is data that can be counted, the number of tickets sold would be an example of data that is discrete.
solve by completing the square x^2+12x+32=0
Answers
Answer:
hello : x = - 4 or x = - 8
Step-by-step explanation:
x²+12x+32=0
(x² +2(6)(x) +6²) - 6² +32 = 0....by completing the square
(x + 6 )²- 2² = 0
(x+6-2)(x+6+2)=0 by idetity : a² - b² = (a - b ) ( a + b )
(x+4)(x+8) =0
x+4=0 or x+8= 0
x = - 4 or x = - 8
Answer:
x = - 8, x = - 4
Step-by-step explanation:
Given
x² + 12x + 32 = 0 ( subtract 32 from both sides )
x² + 12x = - 32
To complete the square
add (half the coefficient of the x- term)² to both sides
x² + 2(6)x + 6² = - 32 + 6²
(x + 6)² = - 32 + 36 = 4
Take the square root of both sides
x + 6 = ± 2 ( subtract 6 from both sides )
x = - 6 ± 2
Hence
x = - 6 - 2 = - 8
x = - 6 + 2 = - 4
solveing systems of equations by substitution y=6x-11 -2x-3y=-7
Answers
[tex]\bf \begin{cases} \boxed{y}=6x-11\\ \cline{1-1} -2x-3y=-7 \end{cases}\qquad \implies \stackrel{\textit{substituting \underline{y} in the 2nd equation}}{-2x-3\left( \boxed{6x-11} \right)=-7}[/tex]
[tex]\bf -2x-18x+33=-7\implies -20x+33=-7\implies -20x=-40 \\\\\\ x=\cfrac{-40}{-20}\implies \blacktriangleright x=2 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that }}{y=6x-11}\implies y=6(2)-11\implies y=12-11\implies \blacktriangleright y=1 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (2,1)~\hfill[/tex]
Step 1: Plug 6x - 11 in for y in the equation -2x - 3y = -7
-2x - 3(6x-11) = -7
Step 2: Distribute -3 to the numbers inside the parentheses (6x -11)
-2x - 18x + 33 = -7
Step 3: Combine like terms
x's go with x's
-20x + 33 = -7
Step 4: Subtract 33 to both sides
-20x = -40
Step 5: Isolate x by dividing -20 to both sides
x = 2
Step 6: To solve for y plug 2 in for x in the equation y = 6x - 11
y = 6(2) - 11
y = 12 - 11
y = 1
(2, 1)
Check:
1 = 6(2) - 11
1 = 12 - 11
1 = 1
-2(2) - 3(1) = -7
-4 - 3 = -7
-7 = -7
Hope this helped!
−(4.8−1.92)−((−5.4)+8.04)−1.92
please show work
Answers
ans:-7.54
do u understand
Answer:
-7.44
Step-by-step explanation:
Just do it out
i’ll mark brainliest please help
Answers
Answer:
False
Step-by-step explanation:
The distance between two points is found by
d = sqrt((y2-y1)^2 + (x2-x1)^2)
= sqrt( (4-7)^2 + (6-2)^2)
=sqrt( 3^2 +4^2)
= sqrt(9+16)
=sqrt(25)
= 5
Answer:
False
Step-by-step explanation:
Because....
[tex]\sqrt[]{(6-2)^2+(4-7)^2}[/tex][tex]\sqrt{(4)^2 +(-3)^2}[/tex][tex]\sqrt[]{16+9}[/tex][tex]\sqrt{25}[/tex] ≈ 5 NOT 6 units* Hopefully this helps:) Mark me the brainliest:)!!!
∞ 234483279c20∞
Which are the solutions of x2 = –11x + 4?
Answers
Answer:
x = 0.35 or x = -11.35
Step-by-step explanation:
Points to remember
Solution of a quadratic equation ax² + bx + c = 0
x = [-b ± √(b² - 4ac)]/2a
It is given that, x² = –11x + 4
x² + 11x - 4 = 0
To find the solution
Here a = 1, b = 11 and c = -4
x = [-b ± √(b² - 4ac)]/2a
x = [-11 ± √(11² - 4 * 1 * (-4))]/2*1
= [-11 ± √(121 + 16)]2
= [-11 ± √137]/2
= [-11 ± 11.70]/2
x = -11 + 11.70 or x = -11 - 11.70
x = 0.35 or x = -11.35
Joey can put together 4 budgets in 2 minutes. What is the unit rate for one burger?
Answers
30 seconds/per burger
Answer:
30 seconds
Step-by-step explanation:
4 burgers in 2 mins
1 burger
= 2 ÷ 4
= 0.5 min
= 30 seconds
10 points One question NEED TO SHOW WORK
Answers
Answer:
h = 3πx
Step-by-step explanation:
The volume (V) of the cylinder is calculated using the formula
V = πr²h ( r is the radius and h the height )
V = π × x² × 3x = 3πx³
The volume of the cuboid therefore has volume of 3πx³, that is
x × x × h = 3πx³
x²h = 3πx³ ( divide both sides by x² )
h = 3πx³ ÷ x² = 3πx
The length of a rectangle is 11 centimeters less than four times its width. Its area is 45 centimeters. Find the dimensions of the rectangle
Answers
Answer:
The answer is length: 9, width: 5
Step-by-step explanation:
5 x 9 = 45
5 x 4 = 20
20 - 11 = 9
Hope this helps :P
The length of a rectangle is 9 cm and width of the rectangle is 5 cm.
What is Area of Rectangle?The area of Rectangle is length times of width.
Length of a rectangle is 11 centimeters less than four times its width.
Length=4W-11
Width=W
Area=45
Area=Length×Width
=(4w-11)w
45=4w²-11w
4w²-11w-45=0
After applying a =4, b=-11 and c=-45 in the quadratic formula
we get w=5
Plug in the value of w in length
Length=4W-11
=4(5)-11
=20-11
=9
Hence, the length of a rectangle is 9 cm and width of the rectangle is 5 cm.
To learn more on Rectangle click:
https://brainly.com/question/20693059
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Why was it helpful in the paper ball situation helpful in the paper ball situation to rewrite the expression to determine specific details of the situation?
Answers
Answer:
Step-by-step explanation:
I'm not sure I know what the paper ball situation is, but I can tell you that especially when working with a set formula in physics, math or chemistry (I'd include biology if I knew any biology) that it is a good idea to write down your givens.
The equation you are given is going to fall apart once you know what your givens are and what they do.
I just looked up the Paper Ball Situation. This is a wonderful piece of physics. It immediately opened up all sorts of treasures once they experimenters thought of using tin foil. Givens are a necessity in such an experiment.
Answer:
It was helpful because it breaks things up for a better understanding.
Step-by-step explanation:
Multiply.
-8 x (-7/4)
Write your answer in simplest form.
Answers
Answer:
14
Step-by-step explanation:
Rewriting this as
-8 -7
----- · -----
1 4
makes this problem a bit easier to do. Reduce the -8/4 to -2:
-8 -7 -2(-7)
----- · ----- = ----------- = 14
1 4 1
ANSWER ASAP PLEASE
An artist is designing a kite like the one show below. Calculate the area to determine how much material she will need to create the kite.
A kite with two top triangles with height of 7 inches and a base 9.5 inches. The bottom two triangles share the base but have a height labeled 12 inches.
38 square inches
66.5 square inches
114 square inches
180.5 square inches
(Theres also a picture attatched)
Answers
Answer:
180.5 in²
Step-by-step explanation:
The area (A) of a kite is calculated as
A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ← the 2 diagonals
d₁ = 2 × 9.5 = 19 in and d₂ = 12 + 7 = 19 in
A = 0.5 × 19 × 19 = 180.5 in²
180.5 is the answer !
There are 467 sixth grade students at east side middle school. Each one needs 8 book covers. How many book covers are needed?
Answers
Around 58 book covers
what is the square root of negative 188
Answers
the square root is 13.7 hope this helps!
[tex] \sqrt{ - 188} = 13.7113092 \: i[/tex]
hope that helped you!
Evaluate 2x^-4y for x = 2 and y = 4. -64 1/8 1/2
Answers
ANSWER
[tex] \frac{1}{2} [/tex]
EXPLANATION
The given expression is;
[tex]2 {x}^{ - 4} y[/tex]
We want to find the value of this expression when x=2 and y=4.
We substitute to get,
[tex]2 {(2)}^{ - 4} (4) [/tex]
[tex]8 \times {2}^{ - 4} [/tex]
Recall that
[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]
This implies that,
[tex]8 \times {2}^{ - 4} = 8 \times \frac{1}{ {2}^{4} } [/tex]
[tex]8 \times {2}^{ - 4} = 8 \times \frac{1}{16 } = \frac{1}{2} [/tex]
Answer:
Step-by-step explanation:
How do I solve this?
Answers
Answer:
23
Step-by-step explanation:
put 3 in place of x and solve.
Answer:
f(3) = 23
Step-by-step explanation:
To evaluate f(3) substitute x = 3 into the expression
f(3) = 2(3)² + 5[tex]\sqrt{3-2}[/tex]
= (2 × 9) + (5 × [tex]\sqrt{1}[/tex])
= 18 + (5 × 1) = 18 + 5 = 23
List in order from least to greatest
Answers
Answer:-5/6 -1/6 5/3
I still need help answering these questions
Answers
Answer:
[tex]-2\frac{2}{3} y^{2} -1\frac{8}{9}y -3\frac{1}{9}[/tex]
Step-by-step explanation: