Sin and cos are trigonometry functions used to find measurements in a right triangle.
[tex]\displaystyle sin=\frac{\text{opposite side}}{hypotenuse}[/tex]
[tex]\displaystyle cos=\frac{\text{adjacent side}}{hypotenuse}[/tex]
Damek has five number cards lying on the table. There are two number cards with digit 1, two number cards with digit 2 and one number card with 0. How many different three-digit numbers can Damek form? (Number cannot being with 0).
(P.S. Is there a way to find the answer without listing all the possibilities?)
Damek can form 14 three-digit numbers from the given situation. Hence, only 14 possibilities.
There are five number cards on the table.
2- digit 1 card
1- digit 0 card
2- digit 2 card
There is a possibility of putting 1 or 2 in the hundredth place.
If 1 is put in the hundredth place then there are 3 possibilities for tenth place 1,0,2
If 1 is put there then there is a possibility of 2 numbers 0,2 in ones place
If 2 is put then there is a possibility of 3 numbers 0,1,2 in ones place
If 0 is put then there is a possibility of 2 numbers 1,2 in ones place.
So, there are 7=(2+3+2) possibilities that the hundredth place is filled by 1.
Similarly, there will be 7 possibilities that the hundredth place is filled by 2.
Hence, there are 14 possibilities as required by the problem.
So, the possibilities of 3-digit numbers are (given the number cannot start with 0) 14.
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Scalar and Matrix Multiplication
Answer:
multiply 1/2 by each element in the matrix
Step-by-step explanation:
6. 32
39 15
Which equation represents the line that passes through the point (-2.4, -7.1) and has a slope of -5.3
3. Complete the square for the following equations:
a. y = 2x² 12x + 1
b. y = 4x² + 48x - 10
Answer:
a. y = 2(x + 3)² - 17
b. y = 4(x + 6)² - 154
Step-by-step explanation:
a. y = 2x² + 12x + 1
y = 2[(x² + 6x)] + 1
y = 2[(x + 3)² - 9] + 1
y = 2(x + 3)² - 18 + 1
y = 2(x + 3)² - 17
b. y = 4x² + 48x - 10
y = 4[(x² + 12x)] - 10
y = 4[(x + 6)² - 36)] - 10
y = 4(x + 6)² - 144 - 10
y = 4(x + 6)² - 154
Which calculation correctly uses prime factorization to write square root of 48 in simplest form?
The simplest form of the square root of 48 is 4√3
Simplifying rational functionsGiven the following rational function √48
The correct prime factorization is given as;
√48 = √3×16
√48 = √16 × √3
Since the square root of 16 is 4, hence;
√48 = 4√3
Hence the simplest form of the square root of 48 is 4√3
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1) Which statement is needed to complete this syllogism? If a quadrilateral has 4 congruent sides, then it is a rhombus. If it is a rhombus, then it’s diagonals are perpendicular. Therefore, if ________________________, then it’s diagonals are perpendicular.
A) a quadrilateral has 4 congruent sides
B) it is a rhombus
C) it is a rectangle
D) it has diagonals
Statement A is needed to complete this syllogism. its diagonals are perpendicular. Therefore, if a quadrilateral has 4 congruent sides then its diagonals are perpendicular.
What is a syllogism?A logical structure for a formal argument that includes a major, minor, and conclusion.
This syllogism cannot be concluded without Statement A. The diagonals of it are parallel. As a result, a quadrilateral's diagonals are perpendicular if it has four congruent sides.
If a quadrilateral has 4 congruent sides, then it is a rhombus. If it is a rhombus, then its diagonals are perpendicular.
Therefore, if a quadrilateral has 4 congruent sides then its diagonals are perpendicular.
Hence option A is correct.
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Answer:
a quadrilateral has 4 congruent sides
Step-by-step explanation:
Syllogisms are connected by a shared statement that connects a hypothesis to a different conclusion.
This circle is centered at the origin, and the length of its radius is 8. What is
the equation of the circle?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x² + y² = 64[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Standard equation of circle is :
[tex]\qquad \tt \rightarrow \: (x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
[tex] \textsf{h = x - coordinate of centre of circle} [/tex][tex] \textsf{k = y - coordinate of centre of circle} [/tex][tex] \textsf{r = radius= 8} [/tex]Since the circle is centered at origin, h = k = 0
[tex]\qquad \tt \rightarrow \: (x - 0) {}^{2} + (y - 0) {}^{2} = {8}^{2} [/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + {y}^{2} = 64 [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
I need these answers ASAP would be very grateful for these if you would like to help me out I would appreciate it and give a good amount of points!
Answer:
5. 8π 6. 18π 7. 8.6π 8. 11/4π
Step-by-step explanation:
8. 2 3/4
2*4+3 = 11/4
Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k.
k=______.
Answer:
5
Step-by-step explanation:
Look at one of the coordinates to find k. For this example I'll look at the y-intercepts (0, 3) (for g(x)) and (0, -2) (for f(x))
g(0) = 3
g(0) = f(0) + k
3 = -2 + k
5 = k
Subtract-3x - 8 from 4x² - 7x - 2.
[tex]( {4x}^{2} - 7x - 2) - (3x - 8) \\ \\ {4x}^{2} - 7x - 2 - 3x + 8 \\ \\ {4x}^{2} - 10x + 4.[/tex]
(08.02)How many solutions are there for the system of equations of shown on the graph?
O No solution
O One solution
O Two solutions
O Infinitely many solutions
Answer: B. One solution
Step-by-step explanation: As you see, both of these lines intersect on the point (0, 3). The point where the lines intersect is the solution. Since these lines are perpendicular, they will only intersect one time. Therefore, there is only one solution, that being (0, 3).
I hope this helps!! Pls mark brainliest :)
Problem 4
(a) three friends are packing sweets into gift boxes. they agree that
each box should contain the same number of sweets, but they are
each working in separate locations with their own pile of sweets so
cannot share boxes. gwen has 286 sweets, bill has 390 sweets and
zeta has 468 sweets. if they put the largest number of sweets into
each box that they can and they use up all their sweets, how many
boxes of sweets will they pack?
(b) use the euclidean algorithm to find the highest common factor of
8008 and 24255 (you need to show all working).
Answer:
286+390+468÷3= answer
i need help with this question (answer choices 15, 5, and 12)
Answer:
x = 15
Step-by-step explanation:
the opposite angles of a cyclic quadrilateral sum to 180° , then
6x + 20 + 3x + 25 = 180 , that is
9x + 45 = 180 ( subtract 45 from both sides )
9x = 135 ( divide both sides by 9 )
x = 15
Which equation is equivalent to the given equation?
-4(X - 5) + 8x = 9x - 3
Answer:
-5x=-23
Or
X=23/5
Step-by-step explanation:
On a biased dice the probably of getting a 6 is 4/5 the dice is rolled 500 times estimate how many 6s would be riled
Answer:
400
Step-by-step explanation:
4/5×500
=400 6s would be riled
Which is true about the solution to the systems of inequalities shown?
Answer:
There are no solutions
Step-by-step explanation:
If y is greater or equal to 3x+1 it can not be less than 3x-3 since 3x-3 is 4 less than 3x+1. Therefore, there can not be any solutions for the system of inequalities.
Use the tables below to answer the following questions: a. f(h(2)) b. g(h(f(1))) c. g(g(4))
Answer:
19-73 19-73 and the other half way back home from the
to ghana 5hjgf and to the 8
please help me with my math
Answer:
x = 115
z = 27
Step-by-step explanation:
x + 65 = 180 (same side interior angles)
x = 115
x = 3z +34 (alternate interior angles)
115 = 3z + 34
3z = 81
z = 27
For the data set 7, 5, 10, 11, 12, the mean, x, is 9. What is the standard
deviation?
Answer:
Standard Deviation is s = 2.9
Step-by-step explanation:
Count = [tex]N[/tex] = 5
Mean = [tex]x^-[/tex] = 9
Variance = [tex]s^2[/tex] = 8.5
SD Formula = [tex]s = \sqrt \frac{1}{N - 1} (x_{i} - x^-)^2[/tex]
Variance Formula[tex]s^2 = \frac{(x_{i} - x^-)^2}{N- 1}[/tex]
Step 1: Calculate the variance
[tex]= \frac{(7-9)^2 + (5-9)^2 + (10-9)^2 + (11-9)^2 + (12 -9)^2 }{5-1}[/tex]
[tex]=\frac{34}{4} = 8.5[/tex]
Step 2: Apply square root/SD formula
[tex]=\sqrt{8.5} = 2.9[/tex]
Mr. Gaffy asked his students to pick a number, add
3 to it, multiply by 5 and then reduce it by 12.
Jermaine calls out his answer of 15. What number
did Jermaine start with?
Answer:
2.4
Step-by-step explanation:
We must do the inverse of every operation:
15 + 12 = 27
27/5 = 5.4
5.4 - 3 = 2.4
Given: JLM is equilateral. Z is the midpoint of JM.
Prove: JZL is congruent to MZL.
There are multiple ways to prove congruence between two triangles:
SSS - three sides are congruentSAS - two sides and the angle in between are congruentASA - two angles and the side in between are congruentAAS - two angles and one side are congruentHL - (applies only to right triangles) the hypotenuse and one leg are congruent.Keep in mind that the order of the letters matters.
Solving the Question
Given triangle JLM, we know that
S - Z is the midpoint of JM, meaning JZ is congruent to MZ.S - Both triangles share side LZ.S - Because JLM is an equilateral triangle, LJ is congruent to LM.This is only one of the ways to prove congruence with these two triangles.
A rectangular field with sides as shown below has to be fenced all around. If fencing posts have to be fixed at 1-metre intervals, how many posts are needed?
1. 167
2. 334
3. 668
4. 6840
Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
so, here
2×95 + 2×72 = 190 + 144 = 334 m
so, yes, the answer 2. 334 is correct.
The solution is Option B.
The total number of posts is the total perimeter of the rectangular field and the value of N = 334 posts
What is the Perimeter of a Rectangle?
The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
Let the number of posts be = N
Fencing posts have to be fixed at 1-metre intervals
The perimeter of the rectangular field = number of posts
Now , the equation will be
The length of the rectangular field = 95 m
The width of the rectangular field = 72 m
Perimeter P of the rectangle = 2 ( Length + Width )
Substituting the values in the equation , we get
Perimeter of the rectangle P = 2 ( 95 + 72 )
On simplifying the equation , we get
Perimeter of the rectangle P = 2 ( 167 )
Perimeter of the rectangle P = 334 m
Now , the number of posts = perimeter of the rectangular
So , the number of posts N = 334 posts
Therefore , the value of N is 334
Hence , the number of posts is 334 posts
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Which of the following rational functions is graphed below?
Answer:
B
Step-by-step explanation:
The vertical asymptotes are the red dashed lines. They are x = -4 and x = 0. Think of them as electric fences that the graph cannot touch or cross. The curve can only get closer and closer.
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Select the correct answer from each drop-down menu.
The function f is given by the table of values as shown below.
Drop down box options:
The parent function of the function represented in the table is: Linear, Exponential, Quadratic
If function f was translated down 4 units, the: x- and f(x), x, or f(x)
-values would be: divided by 4, increased by 4, decreased by 4, multiplied by 4
A point in the table for the transformed function would be : (1, 52), (2,23), (4,87), (3,29)
The above Exponential function has the parent function to be F(x).
The value will decreased by 4.A point in the table for the transformed function would be : (1, 52), What is the transformation about?The difference between successive terms is: 6, 18, 54, 162. These are known to be in the powers of 2 and therefore one can say that there is an exponential increase in the parent function.
The new function is said to g(x). Translating down by 4 means that the new y-values are 4 units lower and so the answer is that the f(x)/y-values will be decreased by 4.
Therefore, looking at the above, since g(x)=f(x)-4 one need to know the value of x, the new y-value is lower by 4 from the old one. This is the case only for (1, 52) since the old function is (1, 13).
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Match each equation to the situation it represents.
Answer:
1-3
2-2
3-1
Step-by-step explanation:
Solve the following quadratic by
completing the square.
y = x2 - 6x +2
Answer: [tex]3 \pm \sqrt{7}[/tex]
Step-by-step explanation:
[tex]1) \text{ } x^{2}-6x+2=0\\\\2) \text{ } x^{2}-6x=-2\\\\3) \text{ } x^{2}-6x+\left(\frac{-6}{2} \right)^{2}=-2+\left(\frac{-6}{2} \right)^{2}=7\\\\4) \text{ } (x-3)^{2}=7\\\\5) \text{ } x-3 =\pm \sqrt{7} \longrightarrow \boxed{3 \pm \sqrt{7}}[/tex]
PLs help answer ASAP
Answer:
The factors of the given equation are:
(11x−8)(11x+2)
Step-by-step explanation:
Since both terms are perfect squares,
Factorize using the difference of squares formula,
[tex]a^{2} -b^{2}[/tex][tex]=(a+b)(a-b)[/tex]
where a=11x−3 and b=5.
=> (11x-3+5)(11x-3-5)
=> (11x+2)(11x−8)
=>[tex](11x-3)^{2}-25[/tex]
Use the binomial theorem [tex](a-b)^{2}=a^{2} +b^{2} -2ab[/tex] to expand[tex](11x-3)^{2}-25[/tex]
=> [tex](11x^{2})+(3)^{2}- 2(11x)(3)-25[/tex]
=>[tex]121x^{2} + 9 - 66x -25[/tex]
=> [tex]121x^{2} -16+ 66x[/tex]
By the splitting method,
=> (11x−8)(11x+2)
The factors of the equation are (11x−8)(11x+2).
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Round the number to the nearest ten-thousands:
388,725
a. 400,000
b.390,000
c. 388,800
d. 389,000
Answer:
B is the correct answer
Step-by-Step:
please help in this as well thank !!
Step-by-step explanation:
4a.
the circumference of a circle is
2×pi×r
we know, r = 6 cm.
so the whole circumference is
2×pi×6 = 12×pi = 37.69911184... cm
4b.
the arc BC is the part of the full circumference that corresponds to 120° out of the 360° of a full circle.
the arc BC is then
12×pi × 120/360 = 12×p × 1/3 = 4×pi = 12.56637061... cm
the perimeter of the shaded area (pie slice) is the arc BC plus 2 radius lengths (from the arc points to the center of the circle)
12.56637061... + 2×6 = 12.56637061... + 12 =
= 24.56637061... cm
4c.
the area of a circle is
pi×r²
in our case
pi×6² = 36pi = 113.0973355... cm²
the area of the shaded area (pie slice) is the 120° part of the full 360° circle area :
36pi × 120/360 = 36pi × 1/3 = 12pi = 37.69911184... cm²
PLEASE HELP !!! which choices are equivalent to square root of -4???
Answer:
-2
Step-by-step explanation:
just a guess but it's right
