Answer:
x = ± 6
Step-by-step explanation:
Hello!
Solve[tex]5x^2 = 180[/tex][tex]x^2 = 180/5[/tex][tex]x^2 = 36[/tex][tex]\sqrt{x^2} = \sqrt{36}[/tex][tex]x = \pm 6[/tex]The value of x is 6 or -6.
Hi...
Given:
[tex]\texttt{5x}[/tex]² [tex]\texttt{= 180}[/tex]
Solution:[tex]\texttt{5x}[/tex]² [tex]\texttt{= 180}[/tex]
Explanation:Divide both sides by 5
[tex]\hookrightarrow{\mathtt{\frac{5x^2}{5}} = {\mathtt{\frac{180}{5}}[/tex]
Simplify:
[tex]\hookrightarrow{\mathtt{x^2 = 36}[/tex]
[tex]\hookrightarrow{\mathtt{For \: x^2 \: = f(a) \: the \: solutions \: are \: x = \sqrt{f(a)}}[/tex] , [tex]\mathtt{- \sqrt{f(a)}}[/tex]
[tex]\hookrightarrow{\mathtt{x = \sqrt{36}}[/tex] , [tex]\mathtt{x = -\sqrt{36}}[/tex]
Factor the number: 36 = 6²
[tex]\mathtt{= \sqrt{6^2}}[/tex]
Apply radical rule: [tex]\mathtt{\sqrt[n]{a^n} \: = a}[/tex]
[tex]\mathtt{\sqrt{6^2} = 6} \\\mathtt{= 6}[/tex]
- [tex]\sqrt{36} = -6[/tex]
[tex]\boxed{\fbox{\bf{x = 6 , x = -6}}}[/tex]
Hope It Helps You...
Find the sum of the cubes of first 15 natural numbers.
The sum of the cubes of first 15 natural numbers.
Solution:[tex]( \frac{(15 \times 16)}{2} {)}^{2} [/tex]
[tex] = (15 \times 8 {)}^{2} [/tex]
=14400
Hence, the sum of the cubes of first 15 natural numbers is 14400
What is .63 as a fraction
Ava earns 9.20 per hour for the first 6 hours she works each day then time and a half.
What is her pay if she works for 9 hours?
Use the drop-down menus to identify whether the mean, median, mode, and range are always, sometimes, or never one of the data values in a data set.
the mean is
choose...
one of the data values.
the median is
choose...
one of the data values.
the mode is
choose...
one of the data values.
the range is
choose...
one of the data values.
The information shows that:
The mean is sometimes of the data values.The median is sometimes one of the data values.The mode is always one or the data values.The range is sometimes one of the data values.What is a mean?It should be noted that the mean is the average of the numbers that are given.
The median is the number in the middle when they are arranged in ascending or descending order. The mode is the number that appears most.
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(1/7x + 3/8) + (2/9x - 1/8)
Which of the following choices is a reference angle to θ = 225º?
30 degrees
45 degrees
60 degrees
90 degrees
Answer:
45 degrees
Step-by-step explanation:
A reference angle can be found by identifying its terminal side and see by what angle the terminal side is close to the x-axis.
To do this, we can subtract this given angle by the nearest 90° angle.
270° is the closest.
[tex]\textsf {Solving :}[/tex]
[tex]\implies \textsf{Reference angle = 270 - 225}[/tex]
[tex]\implies \textsf {45 degrees}[/tex]
The reference angle is the angle from the x-axis thus 45 degrees will be the reference angle to θ = 225°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
As per the given angle,
θ = 225°
It is going to the third quadrant as shown below,
The reference angle is the angle from x-axis.
The angle from the negative x-axis will be as,
180° + x = 225°
x = 225° - 180° = 45°
Hence "The reference angle is the angle from the x-axis thus 45 degrees will be the reference angle to θ = 225°".
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raw and label a model to find the value of 3··81 4·· 8. Then write and solve an equation that matches the model.
For is mathematically given as
What is the solution of an equation that matches the model.?Considering line segments from (0,0,0)origin to (3,0,0) , (3,5,1) and (0,5,1) under the infulence of force
Generally, the equation for force is mathematically given as
F = z2i + 5xyj + 2y2k
Therefore, Considering u*v
[tex]u * v = (u_1j+u_2j+u_3k) * (v_1i+v_2j+v_3k)[/tex]
[tex]u* v = u_1v_1(i * i) + u_1v_2(i * j)+u_1v_3(i * k) + u_2v_1(j * i) + u_2v_2(j * j)+u_2_3(j* k) + u_3v_1(k * i) + u_3v_2(k * j)+u_3v_3(k * k)[/tex]
Where
[tex]i * i = j *j=k * k=0[/tex]
Hence
[tex]u* v = u_1v_2k-u_1v_3j-u_2v_1k+u_2v_3i +u_3v_1j - u_3v_2i[/tex]
[tex]u = (u_1,u_2,u_3) = (0,5,1)\\\\v = (v_1,v_2,v_3) = (-3,0,0)[/tex]
The normal equation formed
-3y + 15z = 0
z= (1/5)y
Considering the level surface and differential surface area
h(x,y,z) = -y + 5z =0
[tex]dS = |grad(h)| dA[/tex]
In terms of the x and y coordinates of (3,0,0) and (3,5,1) and (0,5,1), we can state that the ranges are 0 to 3 and 5 respectively.
In conclusion,
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anyone know the answer
Answer:
y=x+4
Step-by-step explanation:
pretty sure
(x + a)(x + 3a) = x ^ 2 + bx + 75
(x+a)(x+3a)= x²+bx+75
x²+4a+3a²=x²+bx+75
by comparing 3a²=75 and b= 4a
a= ±5
possible values of b= ±20
Two possible values of b are 20 and -20.
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
Given that;
The mathematical expression as;
(x + a)(x + 3a) = x² + bx + 75
Now,
The mathematical expression is;
(x + a)(x + 3a) = x² + bx + 75
Solve the expression as;
(x + a)(x + 3a) = x² + bx + 75
x² + 3ax + ax + 3a² = x² + bx + 75
x² + 4ax + 3a² = x² + bx + 75
After comparison we get;
4a = b ... (i)
And, 3a² = 75 .. (ii)
Solve the second equation for a as;
3a² = 75
Divide by 3;
a² = 25
Take square root both side, we get;
a = ± 5
So, By equation (i) we get;
b = 4a
Substitute a = 5;
b = 4 x 5
b = 20
And, Substitute b = -5;
b = 4 x -5
b = -20
Thus, Two possible values of b are 20 and -20.
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Find a possible formula for the trigonometric function represented by the given table of values. (enter your answer in the form y = a cos(bx − c) d or y = a sin(bx − c) d. )
A function assigns the values. The function will be 8cos(2x-π)+4.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the maximum value is 12, while the minimum value is -4, therefore,
A = (Max-Min)/2 = 12-(-4)/2 = 8
D = (Max+Min)/2 = (12-4)/2 = 4
Period=π, but since x =-4 at 0 or π, therefore,
(2π/B) = π
B = 2π/π = 2
C/B = π/2, {∴At π/2 maximum}
C=π
Hence, the function will be 8cos(2x-π)+4.
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HELP
The table shows the time in minutes that Naima talked on the phone during the last 3 weeks.
Make a stem-and-leaf graph on your own paper, and then answer the question below.
Mon
Tues
Wed
Thurs
Fri
Sat
Sun
Week 1
12
15
25
45
52
30
31
Week 2
22
25
46
51
10
19
33
Week 3
44
21
30
20
10
24
52
Which stems have the same number of leaves?
a.
Stems 1 and 2 each have 5 leaves
c.
4 and 5 each have 3 leaves
b.
Stems 1 and 3 each have 4 leaves
d.
3, 4, and 5 each have 3 leaves
Please select the best answer from the choices provided
A
B
C
D
The stems that have the same number of leaves are (c) 4 and 5 each have 3 leaves
How to make the stem-and-leaf graph?The table of values is given as:
Week 1: 12 15 25 45 52 30 31
Week 2: 22 25 46 51 10 19 33
Week 3: 44 21 30 20 10 24 52
Remove the week tags:
12 15 25 45 52 30 31
22 25 46 51 10 19 33
44 21 30 20 10 24 52
Sort the data values in tens
10 10 12 15 19
20 21 22 24 25 25
30 30 31 33
44 45 46
51 52 52
Now, we can now plot the stem-and-leaf graph.
This is represented as follows:
Stem | Leaves
1 0 0 2 5 9
2 0 1 2 4 5 5
3 0 0 1 3
4 4 5 6
5 1 2 2
In the above plot, we can see that stems 4 and 5 have 3 leaves each
Hence, the stems that have the same number of leaves are (c)
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A binomial experiment has 4 trials in which p = 0.4. What is the probability of 3 successes?
The probability of 3 successes is 0.0384
How to determine the probability?The given parameters are:
Trials, n = 4Probability of success, p = 0.4The binomial probability is represented as:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x[/tex]
So, the probability of three successes is:
[tex]P(3) = ^4C_3 * 0.4^3 * (1 - 0.4)^{4 -3[/tex]
Evaluate the factors in the expression
[tex]P(3) = ^4C_3 * 0.0384[/tex]
Evaluate the combination expression
P(3) = 1 * 0.0384
Evaluate the product
P(3) = 0.0384
Hence, the probability of 3 successes is 0.0384
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Answer:
0.1536
Step-by-step explanation:
Which expression is equivalent to
(5ab)^3
30a b-7? Assume a≠0, b≠0.
1. a7b¹0/6
2. 125a¹8b21/30
3. 25a³b4/6
4. 25a9b¹0/6
The equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex]\frac{(5ab)^3}{30ab^{-7}}[/tex]
Expand the numerator
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{125a^3b^3}{30ab^{-7}}[/tex]
Divide 125 and 30 by 5
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^3b^3}{6ab^{-7}}[/tex]
Apply the law of indices
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{3-1}b^{3+7}}{6}[/tex]
Evaluate the exponent
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{2}b^{10}}{6}[/tex]
Hence, the equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]
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I don’t understand how to solve this question, can I have an explanation? I will give Brainliest.
Answer:
d
Step-by-step explanation:
the fitness grows into bodyness from good
Consider triangle ABC. What is b?
Answer:
A triangle is equal to 540° so you do 112 add 37 which equals 149° then take it away from 540 which gives you 391° as your answer
Step-by-step explanation:
Your Welcome
10m−p=−n, for m
10m−p=−n, for m
10m−p=−n, for m
10m−p=−n, for m
Answer:
[tex]m=\dfrac{-n+p}{10}[/tex]
Step-by-step explanation:Solve for 'm'
To solve for 'm', we have to isolate 'm'.
First add p to both sides to cancel (-p) in the left side10m - p = -n
10m = -n + p
Now, divide the equation by the coefficient of 'm', which 10[tex]\sf\dfrac{10m}{m}=\dfrac{-n+p}{10}\\[/tex]
[tex]\sf \boxed{\bf m = \dfrac{-n+p}{10}}[/tex]
Please help is a choose al that apply
Answer:
Your answers are:
A, B and C
Step-by-step explanation:
So 12 over 3 is equal to 4 which is a Whole number. meaning Not a fraction, an Integer is a whole number (not a fractional number) that can be positive, negative, or zero. Rational numbers would include this example as well
Hope this helped have a wonderful day/night/afternoon
B Which of the statements is true about the polygons below E D 120 degrees C 90 90 60 60 120 degrees 90 90 F D Polygon A Polygon B A. It is possible to circumscribe a circle around each polygon because they are both quadrilaterals. B. It is not possible to circumscribe a circle about either polygon because they are both quadrilaterals. C. It is possible to circumscribe a circle about the parallelogram on the left only, because opposite angles must be supplementary D. It is possible to circumscribe a circle about the rectangle because its opposite angles are supplementary
Answer:
hope you can understand
Neyha has six number cards. Here are four of Neyha's cards. 8;8;8;8 The mean of all six cards is 8 The range of all six cards is 4 What are the other two cards?
After considering the given data we come to the conclusion that the two other cards are 6 and 10, under the condition that Neyha has six number cards. Here are four of Neyha's cards. 8;8;8;8.
Let us assume that the other two cards x and y.
The given mean of all six cards is 8. Then, the sum of all six cards is 48 (8×6). We have that four of the cards are 8s.
So, the summation of these four cards is 32 (8×4).
The dedicated range of all six cards is 4. Therefore, the difference between the largest and smallest card is 4.
Furthermore, we know that four of the cards are 8s, the other two cards must be different from 8.
Hence, we can consider that x and y are the smallest and largest numbers in the set.
Here we have to apply basic algebraic expression
We can perform the setting up two equations:
x + y = 48 - 32 = 16 (the summation of x and y is equivalent to the summation of all six cards minus the summation of the four 8s)
y - x = 4 (the difference considering y and x is equal to the range of all six cards)
Evaluating these equations simultaneously gives us:
y = 10
x = 6
Therefore, the other two cards are 6 and 10.
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Find the 24th term of the sequence:
11, 16, 21, . . .
Answer:
126
Step-by-step explanation:
The difference between the first two terms of this sequence is 5 (16 - 11 = 5). The difference between the second and third terms of this sequence is also 5 (21 - 16 = 5).
So, we can assume that the difference between each term in this sequence is 5. To get from the first term (11) to the second term (16) we had to add 5 once. (or, add 5 x 1 [time])
To get from the first term (11) to third (21), we had to add 5 twice
(or, add 5 x2)
*repeated addition, such as 5+5+5 is the same thing as multiplication. If we are adding 5 three times, we will get the same outcome as 5 x 3.
So, to get from the first term (11) to the 24th term, we will have to add 5 23 times, or 5 x 23
5 x 23 = 115
11 + 115 = 126
Making 126 the 24th term of the sequence
The only contents of a bag are 4 red balls and 6 blue balls. What is the probability that two balls drawn at random from the bag will be red if the first ball drawn is not replaced
Answer:
See below ~
Step-by-step explanation:
P (first red) :
⇒ Original number of red balls / Total
⇒ 4 / 10
⇒ 0.4
⇒ 40%
===============================================================
Remember the first ball drawn is NOT replaced.
P (second red) :
⇒ Original number of red - 1 / Total - 1
⇒ 4 - 1 / 10 - 1
⇒ 3/9
⇒ 33%
find the value of 81 3x
Answer:
27 I think just divide 81 by 3
The table shows some information about the lifetimes, t, in hours, of some lightbulbs.
Frequency
Lifetime
25
47
50 < t ≤ 100
86
100
45
150 < t ≤ 200
36
200
0
250
37
300 < t ≤ 350
50
Estimate the mean lifetime of a bulb.
Give your answer rounded to 2 DP.
hours
The estimated mean lifetime of a bulb of 154.69
How to estimate the mean lifetime of a bulb?The table is given as:
Lifetime Frequency
25 < t ≤ 50 47
50 < t ≤ 100 86
100 < t ≤ 150 45
150 < t ≤ 200 36
200 < t ≤ 250 0
250 < t ≤ 300 37
300 < t ≤ 350 50
Calculate the midpoint using:
x = (Lower +Upper)/2
So, we have:
Lifetime Frequency
37.5 47
75 86
125 45
175 36
225 0
275 37
325 50
The mean value is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{37.5 * 47 + 75 * 86 + 125 * 45 + 175 * 36 + 225 * 0 + 275 * 37 + 325 * 50}{47 + 86 + 45 + 36 + 0 + 37 + 50}[/tex]
Evaluate
[tex]\bar x = \frac{46562.5}{301}[/tex]
Divide
[tex]\bar x = 154.69[/tex]
Hence, the estimated mean lifetime of a bulb of 154.69
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Decide whether quadrilateral ABCD with vertices 4(3,1), B(-1,-1) C(1,3), and D(5.5) is a rectangle, rhombus,square, or parallelogram.
Answer: rhombus
Step-by-step explanation:
By inspection, we can tell that there are no right angles, so we can determine it is not a square or a rectangle.
From the options, it is implied that it is a parallelogram, so to determine if it is a rhombus, we can determine if there is a pair of consecutive congruent sides.
By the distance formula,
[tex]AB=\sqrt{(-1-3)^{2}+(-1-1)^{2}}=\sqrt{16+4}=2\sqrt{5}\\BC=\sqrt{(-1-1)^{2}+(-1-3)^{2}}=\sqrt{4+16}=2\sqrt{5}[/tex]
As AB=BC, there is indeed a pair of consecutive congruent sides, and thus the most specific classification is a rhombus
If you apply the changes below to the quadratic parent function, f(x) = x², which of these is the equation of the new function? Shift 1 unit right. • Vertically stretch by a factor of 3. • Reflect over the x-axis. A. g(x)=-3(x-1)2 B. g(x)=-3(x+1)2 c. g(x)=-3x²-1 D. g(x) = (-3x+1)2
Equation of the new function -3(x+1)².
The correct option is (B)
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given function:
f(x) = x²
The given condition are shift one unit right+ 1.
i.e., x+1
Vertically stretch 3 units= -3
i.e., -3(x+1)
So, reflect over x- axis = square the function'
So, new function= -3(x+1)²
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Which of the following functions describes the graph of h(x)?
Answer:
2x+4/ x-1 C
Step-by-step explanation:
Because the y-intercept is -4
This table shows the number of points a high school basketball team scored during each of its last 10 games.
Which measure(s) of central tendency is most affected by the lowest score?
A. the mean
B. the median
C. the mode
D. both the mean and the median
The measure of central tendency that is most affected by the lowest score is; A: The mean.
How to find the measures of Central Tendency?
The points table is missing and so I have attached it.
The 3 main measures of central tendency are called mean, median and mode.
Now, from the table attached, if we find the average which is the mean, we will get 56.6.
Now, the mode is the number that occurs the most times. In this case, there is no mode because no number appears more than the other.
For the median, if we arrange in ascending order, we have;
42, 48, 49, 53, 55, 56, 58, 66, 68, 71.
The median = (55 + 56)/2 = 55.5
Now, if we remove the lowest score, the measure that will be most affected will be the mean as the median will only change by 0.5 to 56.
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Answer:
B
Step-by-step explanation:
Can a parabola have both a minimum and a maximum point? Explain.
question 3 help me please
Answer:
3x+(4x-1)+90°=180°{sum of angles in a triangle}
3x+4x-1+90°=180°
7x+89°=180°
7x=180°-89°
7x=91°
divide both sides by 7
x=13
Answer:
The answer is x=13
There are 973 dozen M&M's in a jar.
How many M&M's are in the jar?
Answer:
11,676 M&M's
Step-by-step explanation:
A dozen is 12
the problem is saying that in the jar, there are 973 (12-M&M's)
973 * 12 is 11676
There are 11,676 M&M's in the jar
Answer:
they are 11,676
Step-by-step explanation:
A dozen is 12 so since there are 973 dozen, we multiply by 12.