Answer:
Yes, It is a Right Triangle.
Step-by-step explanation:
The hypotenuse is the longest side of the triangle, so for this problem we set the hypotenuse's value to 18.2
From there it doesn't matter which side is which, as both will undergo the same operations.
If the following equation is true, then it is a right triangle.
7²+16.8²= 18.2²
49 + 282.24 = 331.24
The equation is True.
It is a right-angled Triangle.
samantha recieved $500 as a graduation present and decided to invest it in an account that is compounded continuously. how much will be in the account at the end of 5 years if the interest rate is 3%
Answer:
$2,226.20
Step-by-step explanation:
[tex]a_{5}[/tex] = 500e^5(0.03)
If a line has a slope of 3, what is the slope of a line perpendicular to it?
Answer:
- [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]
Here m = 3 , then
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{3}[/tex]
If this trapezoid is moved through the
translation (x+3, y-2), what will the
coordinates of C'be?
5
00
NO
A
D
1
-7 -6 -5
4
-3
1
2
3
4
-2 -1 0
-1
C' = (1, [?])
-2
Given:
The rule of translation is:
[tex](x+3,y-2)[/tex]
The trapezoid ABCD on the graph.
To find:
The coordinates of the point C'.
Solution:
From the given graph, it is clear that the coordinates of point C are (-2,4).
The rule of translation is:
[tex](x,y)\to (x+3,y-2)[/tex]
Using this rule of translation, we get
[tex]C(-2,4)\to C'(-2+3,4-2)[/tex]
[tex]C(-2,4)\to C'(1,2)[/tex]
Therefore, the coordinates of the point C' are (1,2).
2. Find the perimeter of a triangle with vertices A(–3, 5), B(–3, 2), and C(1, 2).
Answer:
12 units
Step-by-step explanation:
the perimeter = 3 + 4 + 5 = 12 units
The perimeter of a triangle is 12 cm.
To find the perimeter of the triangle.
What is triangle?
A triangle has three sides, three vertices, and three angles. The sum of the three interior angles of a triangle is always 180°.
Use the distance formula to find the length between point A and B, B and C, C and A. Then add all three lengths together to get the perimeter.
Distance = √ ( (x2 - x1)2 + (y2 - y1)2 )
Points A and B:
d = √(-3 +3)2 + (2 - 5)2
d = √ 0 + 9
d = √9
d = 3
Points B and C:
d = √ (1+ 3)2 + (2 -2)2
d = √ 16 + 0
d = √ 16
d = 4
Points C and A:
d = √ (-3 - 1)2 + (2 -5)2
d = √ 16 + 9
d = √ 25
d = 5
Perimeter= 3 + 5 + 4 = 12
So, the perimeter of a triangle is 12 cm.
Learn more about triangle here:
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6. The diagram on the right shows right-angled triangles POR
and PRS. Given that tan 0 =
3
4
in em, the length of
(a) PR
(b) RS
Q
9 cm
R
Answer:
The answer is below
Step-by-step explanation:
Trigonometric ratios shows the relationship between the sides of a right angled triangle and its angles. Some trigonometric ratios are:
sinθ = opposite / hypotenuse, cosθ = adjacent / hypotenuse; tanθ = opposite / adjacent.
In triangle PQR:
tanθ = QR / PQ
substituting gives:
3/4 = 9 / PQ
PQ = 9 * 4 / 3 = 12 cm
Applying Pythagoras in triangle PQR gives:
PR² = PQ² + QR²
PR² = 12² + 9²
PR² = 144 + 81 = 225
PR = 15 cm
Also in triangle PRS:
PS = (5/3)PR = (5/3)*15 = 25 cm
PS² = PR² + RS²
25² = 15² + RS²
625 = 225 + RS²
RS² = 400
RS = 20 cm
If f(x) = 2x-5, then f(4) is ___.
Answer:
3
Step-by-step explanation:
f(x) = 2x-5
Let x = 4
f(4) = 2*4 - 5
Multiply
f(4) = 8 -5
Subtract
f(4) = 3
Choose the function that is a "parent function". O f(x) = x=3 o f(x) = (x - 3)2 O o f(x)= X O f() = x-31
Answer:
option D is the correct answer I think so
HELP ME!
Line segment EQ consists of the points ____________. ???
Answer:
{F, G, H, I, J, K, L, M, N, O, P}
are the points between segment EQ :)
Which describes the
correlation shown in the scatterplot? help pls
Answer:
B
Step-by-step explanation:
There is a negative correlation. The direction of a line if we plot it generally through thi scatter plot would be going down, negative.
Answer:
Negative Correlation
Step-by-step explanation:
Because the graph shows that the y axis is on 4 and then goes down to 2
Which of the following steps were applied to ABCD to obtain A'B'C'D
Answer:
B. 3 units right and 4 units up
The correct steps were applied to ABCD to obtain A'B'C'D is,
⇒ 3 units right and 4 units up
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
We have to given that;
Translation applied to ABCD to obtain A'B'C'D.
Now, We get;
Coordinate of A = (2, 3)
Coordinate of A' = (5, 7) = (2 + 3, 3 + 4)
Hence, The correct steps were applied to ABCD to obtain A'B'C'D is,
⇒ 3 units right and 4 units up
Learn more about the transformation visit:
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solve it : -
[tex] \sqrt{27 \times3 } [/tex]
_______
Answer:
9
Step-by-step explanation:
sqrt(27*3)
sqrt(81)
sqrt(9*9)
9
Answer:
9
Step-by-step explanation:
27 * 3 = 81
√81 = 9
Which of the following are solutions to the quadratic equation? Check all that
apply.
x2 + 8x + 16 = 7
Answer:
x=-9/10
Step-by-step explanation:
2x+8x+16=7
Step 1: Simplify both sides of the equation.
2x+8x+16=7
(2x+8x)+(16)=7(Combine Like Terms)
10x+16=7
10x+16=7
Step 2: Subtract 16 from both sides.
10x+16−16=7−16
10x=−9
Step 3: Divide both sides by 10.
10x/10
=
−9/10
x=-9/10
Answer:
x = - 4 ± [tex]\sqrt{7}[/tex]
Step-by-step explanation:
Given
x² + 8x + 16 = 7 ( subtract 16 from both sides )
x² + 8x = - 9
Using the method of completing the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(4)x + 16 = - 9 + 16
(x + 4)² = 7 ( take the square root of both sides )
x + 4 = ± [tex]\sqrt{7}[/tex] ( subtract 4 from both sides )
x = - 4 ± [tex]\sqrt{7}[/tex]
Then
solutions are x = - 4 - [tex]\sqrt{7}[/tex] , x = - 4 + [tex]\sqrt{7}[/tex]
What happens if simultaneous Equations have two of the same variable like below? How would I solve it?
6A + 4B + 5C = 390
6A + 4B + 5.75C = 405
Answer:
C = 20
Step-by-step explanation:
What happens if simultaneous Equations have two of the same variable like below? How would I solve it?
6A + 4B + 5C = 390
6A + 4B + 5.75C = 405
Step 1
We solve for C first
6A + 4B + 5C = 390....Equation 1
6A + 4B + 5.75C = 405... Equation 2
We substract Equation 1 from Equation 2
0.75C = 15
C = 15/0.75
C = 20
solve for x: 3(x-5)+4x-2=4
Answer:
x = 3
Step-by-step explanation:
3(x−5)+4x−2=4
Step 1: Simplify both sides of the equation.
3(x−5)+4x−2=4
(3)(x)+(3)(−5)+4x+−2=4(Distribute)
3x+−15+4x+−2=4
(3x+4x)+(−15+−2)=4(Combine Like Terms)
7x+−17=4
7x−17=4
Step 2: Add 17 to both sides.
7x−17+17=4+17
7x=21
Step 3: Divide both sides by 7.
7x
7
=
21
7
x=3
Which of the following is the line of symmetry for the figure shown below?
B.
A. Line A
O
B. Line B
C. Line C
O D. This figure is not symmetrical.
Answer:
Line A
Step-by-step explanation:
A line of symmetry is a line that divides a shape into exactly two equal halves.
A triangle is a polygon with three sides and three angles. A scalene triangle has no lines of symmetry, an isosceles triangle has more than one line of symmetry while an equilateral triangle has three lines of symmetry.
From the diagram we can see that line A divides the figure into two equal halves, hence line A is the line of symmetry.
Miyoko's goal is to earn more than this week. She earns for every day she works as a cryptographer, and
earns for every day she works as a geologist.
Write an inequality that represents the number of days Miyoko should work as a cryptographer and as a
geologist to achieve her goal.
Answer:
$250*C + $180*G = $950
Step-by-step explanation:
Solving for G, it is G = (950 - 250C)/180
Solving for C, it is C = (950 - 180G)/250
which of the following is most likely the next step in the series?
Answer:
D
Step-by-step explanation:
What is the direct variation between x and y when x=7 and y=3 1/2?
Answer:
[tex]{ \tt{y \: \alpha \: x }} \\ { \tt{y = kx}} \\ \\ { \bf{3 \frac{1}{2} = k \times 7 }} \\ { \bf{k = \frac{1}{2} }} \\ \\ { \tt{y = \frac{1}{2}x }} \\ \\ { \tt{y = 0.5x}}[/tex]
[tex] \frac{1.107}{123} \times \frac{1.998}{333} = [/tex]
Answer:
45Step-by-step explanation:
[tex]\frac{1.107}{123} \times \frac{1.998}{333} = [/tex]
[tex] = > 9 \times 6[/tex]
[tex] = 45[/tex]
Answer:
Step-by-step explanation:
[tex]\frac{1.107}{123}*\frac{1.998}{333}= 0.009 * 0.006 = 0.000054[/tex]
1107÷ 123 = 9
The dividend has 3 decimal places. So, take 3 decimal places from the right towards left in the result 0.009
1.107 ÷ 123 = 0.0009
0.009 * 0.006
First multiply 9 * 6 = 54
Now, count the number of decimal place in the multiplicands. 0.009 has 3 decimal places and 0.006 has 3 decimal places. So totally, 3+ 3 = 6 decimal places in the result
0.009 * 0.006 = 0.000054
Work out the sum of 1/4 1/6 and 1/3
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4} +\frac{1}{6} +\frac{1}{3}[/tex]
4 = 2 × 2 × 1
6 = 2 × 3 × 1
3 = 3 × 1
GCF = 1
4 × 6 × 3 = 72
[tex]\frac{18}{72} +\frac{12}{72} +\frac{24}{72}[/tex]
[tex]\frac{18+12+24}{72}[/tex]
[tex]\frac{54}{72}[/tex]
54 = 2 × 3 × 3 × 3
72 = 2 × 2 × 2 × 3 × 3
GCF = 2 × 3 × 3
GCF = 18
[tex]\frac{\frac{54}{18} }{\frac{72}{18} }=\frac{3}{4}[/tex]
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{Looking for your LCD (Least Common Denominator) of each fraction}\downarrow\\\\\\\mathsf{\dfrac{1}{4}=\dfrac{3}{12}}\\\\\\\mathsf{\dfrac{1}{6}=\dfrac{2}{12}}\\\\\\\mathsf{\dfrac{1}{3}=\dfrac{4}{12}}\\\\\\\\\\\large\textsf{The LCD is \underline{12}}[/tex]
[tex]\mathsf{\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{3}}[/tex]
[tex]\mathsf{= \ \dfrac{1\times3}{4\times3}+\dfrac{1\times2}{6\times2}+\dfrac{1\times4}{3\times4}}[/tex]
[tex]\large\textsf{Solving for the numerators (TOP numbers)}\downarrow\\\\\mathsf{1\times3=\boxed{\bf 3}}\\\\\mathsf{1\times2=\boxed{\bf 2}}\\\\\mathsf{1\times4=\boxed{\bf 4}}[/tex]
[tex]\large\textsf{Solving for the denominators (BOTTOM numbers)}\downarrow\\\\\mathsf{4\times3=\boxed{\bf 12}}\\\\\mathsf{6\times2=\boxed{\bf 12}}\\\\\mathsf{3\times4=\boxed{\bf 12}}[/tex]
[tex]\mathsf{=\ \dfrac{3+2+4}{12}}[/tex]
[tex]\large\textsf{Solving for your numerator (TOP number) }\downarrow\\\\\\\mathsf{3+2+4}\\\\\mathsf{= 5+4}\\\\\mathsf{= \boxed{\large\textsf{\bf 9}}}[/tex]
[tex]\mathsf{=\ \dfrac{9}{12}}[/tex]
[tex]\mathsf{\dfrac{9\div3}{12\div3}}\\\\\\\\\mathsf{9\div3= \boxed{\large\textsf{\bf 3}}}\\\\\mathsf{12\div3=\boxed{\large\textsf{\bf 4}}}[/tex]
[tex]\mathsf{= \dfrac{3}{4}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: }\boxed{\mathsf{\bold{ \dfrac{9}{12}\ or\ \dfrac{3}{4}}\ either\ of\ those\ fractions\ should\ work\ because}}}}\\\boxed{\boxed{\large\textsf{they are equal to each other!}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The probability that a certain football team wins a match is 2/3.Given that the team plays 4 matches, find the probability that the team wins 1)more than half of the number of matches played
Answer:
The probability is 32/81
Step-by-step explanation:
We know that:
The probability that the team wins is p = 2/3
Then the probability of not winning is q = 1 - p = 1 - 2/3 = 1/3
The team plays 4 matches.
We want to find the probability that the team wins 1 more than half of the number of matches played.
So if there are 4 matches, the half is 2 matches
one more than half is then 3 matches.
Let's assume that the team wins the first 3 matches, and does not win the last match.
match one, the team wins with prob: P₁ = 2/3
match two, the team wins with prob: P₂ = 2/3
match three, the team wins with prob: P₃ = 2/3
match four, the team wins with prob: P₄ = 1/3
The joint probability is the product of all the individual probabilities:
P = (2/3)*(2/3)*(2/3)*(1/3)
Now we must also considerate the permutations, we have the cases:
the team does not win the fourth match
the team does not win the third match
the team does not win the second match
the team does not win the first match
So we have just four permutations, then the total probability is:
probability = 4*P = 4*(2/3)*(2/3)*(2/3)*(1/3) = 4*(8/81) = (32/81)
The plans for a new aquarium call for 2 hallways of exhibits leading out of a circular main room as shown. What is the value of x? Give reason
Answer:
[tex]x =23^o[/tex]
Step-by-step explanation:
Given
See attachment
Required
Find x
To solve for x, we make use of:
[tex]5x + 65= 180[/tex] --- angle on a straight line
[tex]5x = 180-65[/tex]
[tex]5x = 115[/tex]
Solve for x
[tex]x = 115/5[/tex]
[tex]x =23^o[/tex]
which is the value of x in the equation-3/4 = x/24 A. -32 B. -18 C. 18 D. 32
Answer:
-18 =x
Step-by-step explanation:
-3/4 = x/24
Using cross products
-3*24 = 4*x
-72 = 4x
Divide each side by 4
-72/4 = 4x/4
-18 =x
Answer:
B. -18
Step-by-step explanation:
-3/4 = x / 24solve the proportion using cross multiplication
-3 × 24 = 4 × x-72 = 4xswap the side
4x = -72divide both side by 4
4x / 4 = -72/4x = - 18Victor also saw a jacket he liked while he was shopping. The jacket has a price tag of $75.00 and was marked for 30% off. How much money will the jacket cost after the sale?
Respuesta:
$ 52.5
Explicación paso a paso:
Dado
Costo de la chaqueta = $ 75
Mark off = 30%
Descuento = 30% de $ 75
Precio de descuento = 0,3 * 75
Precio de descuento = $ 22.5
Costo después de la venta = $ 75 - $ 22.5
Costo después de la venta = $ 52.5
Por lo tanto, el costo después de la venta es de $ 52.5
The two cross sections shown are taken parallel to their respective bases. The cross sections have the same area. If the heights of the two solids are equal, find the volume of the cylinder. Round your answer to the nearest hundredth. A. 465.10cm3 B. Please select the best answer from the choices provided A B C D
Answer:
489.40 cm³
Step-by-step explanation:
Since the cross section is parallel to their respective bases, hence:
Area of the cylinder cross section = area of the circular base = πr²
where r is the radius of the cylinder base.
Area of other cross section = area of rectangle base = 3.8 cm * 8.1 cm
Since both cross sections have same area, hence:
Area of cylinder cross section = Area of rectangle base
πr² = 8.1 * 3.8
r² = 9.8
r = 3.1 cm
Volume of the cylinder = πr²h = π(3.1)²(15.9) = 489.40 cm³
Which of the following pairs of functions are inverses of each other
Answer:
[tex]f(x) = 5x -11[/tex] and [tex]g(x) = \frac{x + 11}{5}[/tex]
Step-by-step explanation:
Required
The inverse pairs
Solving (a):
[tex]f(x) = 5x -11[/tex] [tex]g(x) = \frac{x + 11}{5}[/tex]
Calculate the inverse of f(x)
[tex]f(x) = 5x -11[/tex]
Replace f(x) with y
[tex]y = 5x - 11[/tex]
Swap x and y
[tex]x = 5y - 11[/tex]
Solve for y
[tex]5y = x + 11[/tex]
[tex]y = \frac{x + 11}{5}[/tex]
So, we have:
[tex]g(x) = \frac{x + 11}{5}[/tex]
Hence, f(x) and g(x) in (a) are inverse functions
Others are not
john bought a new game system for $529 how much is he in debt
Answer:
Depending on how much he had before he bought the game system.
Rami is solving the equation for x .
–6x – 1 = 5
–6x – 1 Empty square 1 = (5 Empty square 1)
–6x = 6
–6x Empty circle – 6 = 6 Empty circle –6
x = –1
Which operation symbols should Rami write in the Empty squareand the Empty circle?
Answer:
Empty square = +
Empty Circle = ÷
Step-by-step explanation:
In order to eliminate the extra numbers from the equation you have to do the opposite of the problem. So...
-6x-1=5
-6x -1+1 = 5+1 (eliminating the 1 from the -6x side and adding it to the other side)
-6x = 6
-6x ÷ -6 = 6 ÷ -6 ( eliminating the-6 so that one side just has x)
so... x= -1
Answer: Option B is your correct answer.
Tính :
a) (a+b+c)^2
b) (a-b-c)^2
c) (a+b-c)^2
d) (a-b+c)^2
Answer:
a.) a² + b² + c ² + 2ab + 2ac + 2bc
b.) a² + b² + c² - 2ab - 2 ac + 2bc
c ) a² + b² + c² + 2ab - 2ac - 2bc
d.) a² + b² + c² - 2ab + 2ac - 2bc
Step-by-step explanation:
Use ( a + b + c )² = a² + b² + c² + 2 × ab + 2 × ac + 2 × bc to expand all these expressiona) ( a + b + c )²
= a² + b² + c² + 2 × ab + 2 × ac + 2 × bc
= a² + b² + c ² + 2ab + 2ac + 2bc
b.) ( a - b - c )
= a² + ( - b )² + ( - c)² + 2a ( -b ) + 2a(-c) + 2(-b)(-c)
= a² + b² + c² - 2ab - 2 ac + 2bc
c.) ( a + b - c )²
= a² + b² + ( -c)² + 2ab + 2a ( - c) + 2 b( -c)
= a² + b² + c² + 2ab - 2ac - 2bc
d.) (a - b + c ) ²
= a² + ( -b)² + c² + 2a(-b) + 2ac + 2c( -b)
= a² + b² + c² - 2ab + 2ac - 2bc
help please on all of these
the answer is on the picture
