Answer:
C
Step-by-step explanation:
Answer:
C: Yes, the terms can be regrouped and still be equivalent.
Step-by-step explanation:
Most terms can be regrouped and still be equivalent.
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
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]
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 = - 18Which 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
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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.
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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]
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
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
The expression x^2 - 10x + 24 is equivalent to
Answer:
[tex](x−6)(x−4)[/tex]
Step-by-step explanation:
[tex]x^2 - 10x + 24[/tex]
[tex] {x}^{2} −6x−4x+24[/tex]
[tex]x(x−6)−4(x−6)[/tex]
[tex](x−6)(x−4)[/tex]
Hope it is helpful...Answer:
(x - 4 )(x - 6 )
Step-by-step explanation:
[tex]x^2 - 10x + 24 \\\\=x^2 - 6x - 4x +24 \\\\=x(x - 6) -4(x - 6) \\\\=(x - 4)(x-6) \\[/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)
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.
What is v6/v5 in simplest radical form?
Answer: [tex]\sqrt{30}/5[/tex]
Step-by-step explanation:
You should get this answer because the simpliest form of a radical is that you shouldn't have any radical in the denominator. In order to get rid of the radical sign in the denominator, you have to multiply the numerator and the denominator with the [tex]\sqrt{5}[/tex].
Look at the image below for further explanation
What else would need to be congruent to show that ABC= DEF by ASA?
B
E
10
10
45
A
с
45
F
O A. ZBE ZE
B. AC = DF
C. ZA ZD
O D. BC = EF
Answer:
Option A
then you would have an angle, a side and another angle (ASA) next to each other
Opt.B would be a second sude (SAS)
Opt.C is already given
Opt.D seems to be like (A-S-S). no pun intended.
The additional information need to be added to show the given triangles congruent is angle B = angle E
What are congruent triangles?Triangles are said to be congruent if their corresponding sides and angles are congruent.
Given is a pair of triangles, Δ ABC and Δ DEF, in this angle A = angle D and AB = DE = 10,
We need to find one more reason to make them congruent by ASA rule,
In ASA rule of congruence, we have two corresponding angles congruent in the triangles and a side between them need to be congruent,
Here, the pair of two angles should be ∠ A and ∠ D and ∠ B and ∠ E, because the congruent sides AB and DE are in mid of them.
Hence, the additional information need to be added to show the given triangles congruent is angle B = angle E
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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 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]
help please on all of these
the answer is on the picture
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 :)
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)
PLEASE HELP Assume the line of best fit for a data set is given by y = 32x+ 25. What data
points are predicted by the line of best fit? Check all that apply.
A. (9,326)
B. (10,345)
C. (7,224)
D. (6,217)
Answer:
B
Step-by-step explanation:
the answer is B
If you substitute 10 in the equation
32(9)+25=345
Answer:
B and D
Step-by-step explanation:
Substitute the values in y = 32x+ 25
A. 9, 326
326=32(9)+25
326 don't equal to 315
A is not
B. 10, 345
345=32(10)+25
345=345
B is a point on the line of best fit.
C. (7,224)
244= 32(7)+ 25
244 don't equal to 249
D. (6,217)
217= 32(6)+ 25
217=217
D is a point on the line of best fit.
Brainliest please
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
[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
which of the following is most likely the next step in the series?
Answer:
D
Step-by-step explanation:
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
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.
pls answer this question correctly pls .
Answer:
Step-by-step explanation:
Fraction Decimal Percentage
[tex]\frac{19}{100}[/tex] [tex]0.19[/tex] [tex]19 \%[/tex]
[tex]\frac{3}{10}[/tex] [tex]0.3[/tex] [tex]3 0\%[/tex]
[tex]\frac{49}{100}[/tex] [tex]0.49[/tex] [tex]49 \%[/tex]
[tex]\frac{7}{100}[/tex] [tex]0.07[/tex] [tex]7 \%[/tex]
Answer:
First row: 19%
Decimal for 3/10: 0.3
Fraction for 0.49: 49/100
Percentage for 0.49: 49%
Decimal for 7/100: 0.07
Fraction for 7/100: 7&
Also 3% should be 30%. Just to point that out :)
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
Si: Tg θ =√2 ∧ θ es agudo √7 Calcular: A = 3(Sen θ + Cos θ) - √7
Answer:
[tex]A \approx 1.488[/tex]
Step-by-step explanation:
Por definición de razones trigonométricas, tenemos las siguientes identidades:
[tex]\tan \theta = \frac{y}{x} = \sqrt{2}[/tex] (1)
[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (2)
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (3)
Si [tex]\theta[/tex] es agudo, entonces [tex]x, y > 0[/tex].
De (1), suponemos [tex]x = 1[/tex] que [tex]y = \sqrt{2}[/tex], entonces los valores de las funciones seno y coseno:
[tex]\sin \theta = \frac{\sqrt{2}}{\sqrt{5}} = \sqrt{\frac{2}{5} }[/tex]
[tex]\sin \theta = \frac{\sqrt{10}}{5 }[/tex]
[tex]\cos \theta = \sqrt{\frac{1}{5} }[/tex]
[tex]\cos \theta = \frac{\sqrt{5}}{5}[/tex]
Por último, calculemos [tex]A[/tex]:
[tex]A = 3\cdot \left(\frac{\sqrt{10}}{5} + \frac{\sqrt{5}}{5} \right) - \sqrt{7}[/tex]
[tex]A \approx 1.488[/tex]
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 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.
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).
