Answers
Related Questions
Evaluate.
(1.8)(3 2/3−6)
Enter your answer as a simplified mixed number in the box.
Answers
Answer:
-4 1/5
Step-by-step explanation:
Lets start with the mixed number minus the whole number: 3 2/3 - 6 equals -7/3 that multiplied by 1.8 is -4.2. Which as a mixed number is -4 2/10 which can be simplified to -4 1/5
:D
When a number contains both an integer (whole number) and a correct fraction, it is known as a mixed number or mixed fraction.
Evaluate ?A mixed number is said to be in its simplest form if its fractional part's highest common factor, or HCF, is 1.When mixed numbers are simplified, the fraction's value doesn't change.We can assert that the actual mixed number and the simplified mixed number are fractions of the same size.
A mixed fraction is one that is represented by both its quotient and remainder.
A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.An amalgam of a whole number and a legal fraction is a mixed fraction.
Evaluate.
(1.8)(3 2/3−6)
= -4.2
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Evaluate 4y0 + x^1 if x =9 and y=5
Answers
Step 1: Problem
\(\text{Evaluate 4y}^0+x^1\text{ if x = 9 and y = 5}\)Step 2: Concept
Substitute the values of x and y in the expression.
Step 3: Method
\(\begin{gathered} x\text{ = 9 and y = 5} \\ 4y^0+x^1 \\ =\text{ 4 }\times5^0+9^{1\text{ }} \\ =\text{ 4 }\times\text{ 1 + 9} \\ =\text{ 4 + 9} \\ =\text{ 13} \end{gathered}\)Step 4: Final answer
13
4y^0 + x^1 with x = 9 and y = 5.
First, every number (except 0) to the power of 0 = 1
We substitute x = 9
4 x 1 + 9^1
= 4 + 9 = 13.
a taylor polynomial (and later, a taylor series) centered at x=0 is often called a maclaurain polynomial (or series). find the maclaurin polynomials of orders n=0,1,2,3, and 4,
Answers
The Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 can be obtained by expanding the function around x = 0 using the Taylor series. Here they are:
Order n = 0:
P0(x) = f(0)
Order n = 1:
P1(x) = f(0) + f'(0)x
Order n = 2:
P2(x) = f(0) + f'(0)x + (f''(0)x^2)/2
Order n = 3:
P3(x) = f(0) + f'(0)x + (f''(0)x^2)/2 + (f'''(0)x^3)/6
Order n = 4:
P4(x) = f(0) + f'(0)x + (f''(0)x^2)/2 + (f'''(0)x^3)/6 + (f''''(0)x^4)/24
Note that f'(0) represents the derivative of the function evaluated at x = 0, f''(0) represents the second derivative evaluated at x = 0, and so on.
These polynomials can be used to approximate the function near x = 0. The higher the order of the polynomial, the closer the approximation to the actual function.
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the orginal price of a computer game is 45$ the price marked down by 18$ what precent of the original price is the markdown
Answers
Answer: 40%
Step-by-step explanation:
these cones are similar. find the volume of the smaller cone. round to the nearest tenth.
Answers
Answer:
Volume of the smaller cone = 8.34 cm³
Step-by-step explanation:
"If two figures are similar, their dimensions will be proportional.
Following this rule,
Ratio of the dimensions of two cones = \(\frac{\text{Radius of the large cone}}{\text{Radius of the small cone}}\)
= \(\frac{r_2}{r_1}\)
= \(\frac{5}{2}\)
= 2.5
Similarly, "ratio of the volumes of two similar figures is cube of the dimensional ratio".
Ratio of the volumes = (ratio of the dimensions)³
\(\frac{V_1}{V_2}=(2.5)^3\)
\(\frac{131}{V_2}=15.625\)
\(V_2=\frac{131}{15.625}\)
= 8.384 cm³
≈ 8.4 cm³
Therefore, volume of the smaller cone is 8.4 cm³.
lori took a trip during her recent trip to NYC. They charged a flat rate of $2.50, plus an additional $3.00 per mile. Lori only has $20
Answers
Explanation
We know we can use slope intercept form
y = mx + b
m = 3.00 per mile, this is the rate or slope
b= 2.50, the y intercept or flat fee that doesn’t change
y = $20, the total she has to spen
≤ is less than or equal to sign because the amount has to be less than or equal to $20
We are looking for “x” the amount of miles
3.00x + 2.50 ≤ $20
Subtract 2.50 from each side to isolate the variable
3.00x + 2.50 - 2.50 ≤ $20 - 2.50
Simplify
3.00x ≤ $17.50
Divide both sides by 3.00 to solve x
3.00/3.00x ≤ 17.50 / 3.00
x ≤ 5.83 miles
What is P(A ∩ B)?
A) 1/10
B) 1/2
C) 3/10
D) 4/5
Answers
Answer:
A)
\(P(A ∩ B) = \frac{2}{20} \\ = \frac{1}{10} \)
I NEED HELP!!
Drag and drop numbers into the boxes so that the paired values are in a proportional relationship.
х
2
4
?
7
9
Y
1
2
3
3.5
?
Answers
Answer:
The first blank would be x=6
the other blank would be 9=4.5
Step-by-step explanation:
if you look at the table, you can see that when you insert a number as x (A.K.A the number "two") the number is divided by 2, so in the y row, its half the number that x was.
2÷1=1
4÷2=2
6÷2=3
7÷2=3.5
9÷2=4.5
Hope this helps!
assume that the test scores of a college entrance exam fits a normal distribution. the mean test score is 72, and the standard deviation is 5. what is the percentage of students scoring 84 or more in the exam?
Answers
The percentage of students scoring 84 or more in the exam is 99.18%.
Given, Mean test score = 72,
Standard deviation = 5.
We are supposed to find the percentage of students scoring 84 or more in the exam.
To find the percentage of students scoring 84 or more in the exam, we will use the following steps:
First, we need to find the z-score associated with 84.
Let us assume that z is the z-score corresponding to the value 84, then;
z = (84 - 72) / 5 = 2.4
Now, we have the value of z, we can find the percentage of students scoring 84 or more in the exam using the normal distribution table.
The percentage is the area under the normal distribution curve to the right of the z-score.
To find the area using the normal distribution table, we need to look for the value 2.4 in the z-table. Since 2.4 is not exactly listed in the z-table, we will use the value for 2.4 closest to it.
Using the z-table, the value closest to 2.4 is 0.9918.
Therefore, the percentage of students scoring 84 or more in the exam is;
P(Z > 2.4) = 0.9918 × 100 = 99.18%.
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A consumer's utility function is U=In(xy2). Find the values of x and y which maximize U subject to the budgetary constraint 6x + 3y = 72. Use the method of Lagrange to solve this problem, and y(Simpli
Answers
Using the method of Lagrange, the maximum utility is achieved when x = 6 and y = 6, with a maximum utility value of ln(6*6^2) = ln(216).
To maximize the utility function U = ln(xy^2) subject to the budgetary constraint 6x + 3y = 72, we can use the method of Lagrange multipliers. We define the Lagrangian function L = ln(xy^2) + λ(6x + 3y - 72), where λ is the Lagrange multiplier. To find the critical points, we take partial derivatives of L with respect to x, y, and λ, and set them equal to zero. Taking the partial derivative with respect to x gives y^2/x = 6λ, and the partial derivative with respect to y gives 2y/x = 3λ. Solving these equations simultaneously, we find x = 6 and y = 6. Substituting these values into the budgetary constraint, we confirm that the constraint is satisfied. Finally, substituting x = 6 and y = 6 into the utility function, we get U = ln(6*6^2) = ln(216), which represents the maximum utility attainable under the given constraint.
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Sara threw 6 darts at this dartboard, and they all hit the target. Which of the following numbers could have been her score: 4,24,29,31,56
Answers
Answer:
everything but 4 and 31!
Step-by-step explanation:
24: 9+9+1+1+1+3
29: 9+5+5+1+1+3
56: 9×6
A company expects that the number N(x) of a product sold during a week is related to the amount spent on advertising by the function N(x)=-6x3+180x²+2250x + 13,000, where x (with 0 ≤x≤25) is the amount spent on advertising in thousands of dollars. What is the point of diminishing returns?
The point of diminishing returns is
(Simplify your answer. Type an ordered pair. Do not use commas in the individual coordinates.)
Answers
The point of diminishing returns is (20.98, 21247.3).
The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.
Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.
The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:
0 = -18x² + 360x + 2250
Dividing by -18 simplifies the equation:
0 = x² - 20x - 125
Using the quadratic formula, we find the solutions to the equation:
x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)
x₁,₂ = 10 ± 5√5
Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.
To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:
N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8
N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8
From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.
To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).
Hence, the point of diminishing returns is approximately (20.98, 21247.3).
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If the price of a business math text rose to $120 and this was 10% more than the original price what was the original selling price?
Answers
Step-by-step explanation:
120*10% =12
10% percent *120
= (10/100)*120
= (10*120)/100
= 1200/100 = 12
120 - 12 = 108.00 is original price of math text
Dr. Peters and Dr. Paul have a psychotherapy practice together. They both met with Sarah, and while Dr. Peters thought Sarah had ADD, Dr. Paul diagnosed her with GAD. Based on this disagreement, which of the following diagnostic measurements do Dr. Peters and Dr. Paul NOT have?
a. diagnostic validity
b. assurance
c. reliability
d. predictability
Answers
Dr. Peters and Dr. Paul do not have diagnostic validity measurement in this scenario.
Diagnostic validity refers to the accuracy of a diagnostic assessment in correctly identifying a particular condition or disorder. It involves determining whether a diagnosis aligns with the true condition or not. In this case, Dr. Peters and Dr. Paul disagree on the diagnosis for Sarah, indicating a lack of diagnostic validity. They have differing opinions on whether she has ADD or GAD, suggesting that at least one of their diagnoses is incorrect. Therefore, they do not have diagnostic validity in this context.
On the other hand, assurance, reliability, and predictability are not necessarily affected by the disagreement between Dr. Peters and Dr. Paul. Assurance relates to the confidence and trustworthiness in the diagnosis and treatment provided by healthcare professionals. Reliability refers to the consistency and stability of diagnostic assessments, ensuring that repeated evaluations yield similar results. Predictability involves the ability to forecast the course and outcome of a condition or disorder based on the diagnosis. While the specific diagnoses may differ between Dr. Peters and Dr. Paul, these aspects are not inherently compromised by their disagreement.
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Last week, Erik ran 3 miles. This week, he plans to run 2 7/8 times as far as last week. How many miles does Erik plan to run this week?
Answers
Erik plans to run approximately 8.63 miles this week.
To find out how many miles Erik plans to run this week, we need to multiply the distance he ran last week (3 miles) by 2 7/8, which is the factor by which he plans to increase his distance. To do this, we first need to convert the mixed number 2 7/8 into an improper fraction:
2 7/8 = (2 x 8 + 7) / 8 = 23/8
Now we can multiply:
3 miles x 23/8 = (3 x 23) / 8 = 69/8 miles
This means that Erik plans to run 69/8 miles, or 8 5/8 miles, this week. This is a mixed number, which means that Erik plans to run 8 whole miles and 5/8 of a mile.
Alternatively, we can express 69/8 as a decimal by dividing the numerator (69) by the denominator (8):
69/8 ≈ 8.63
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There were some people on a bus. Half of the people get off at the first stop and 11 people get on. Now there are 20 people on the bus. How many people were on the bus to begin with?
Answers
Answer:
18 people
Step-by-step explanation:
18/2=9
9+11=20
Answer:
18.
Step-by-step explanation:
this is because in order to find out how many were on the bus, you simply do 20 - 11 = 9. Than you must multiply 9 by 2 which equals 18. That gives you your answer.
help help helpppppp.fasttttttt.
Answers
Answer:
23.6
Step-by-step explanation:
\(c=2\pi r\)
The diameter of the cirle is 7.5 m. To find the radius you would take half of the diameter.
7.5 / 2 = 3.75
\(c=2\pi 3.75\)
Then you multiply them
your answer is
23.5619
then you round
23.6
Hope this helps!
Given the right angle DEF what is the value of cos (F)
Answers
The answer to this is A
find each sum. The large square represents 1, the larger rectangle represents 0.1 and the smaller rectangle represents 0.001.
Answers
Spanish: Siento algo que me mueve
Un ritmo que me hace bailar
Tomen todos su pareja
Todos vamos a gozar
Baila, baila esta cumbia
Mueve, mueve la cintura
Todos, las manos en alto
Y griten, griten con locura
Baila, baila esta cumbia
Un ritmo, ritmo sin igual
Nadie se quede sentado
Todos vamos a bailar
Siento algo que me mueve
Un ritmo que me hace bailar
Tomen todos su pareja
Todos vamos a gozar
Baila, baila esta cumbia
Mueve, mueve la cintura
Todos, las manos en alto
Y griten, griten con locura
¡Hey!, ¡hey!, ¡hey!, ¡hey!
¡Hey!, ¡hey!, ¡hey!, ¡hey!
¡Hey!
Baila, baila esta cumbia
Un ritmo, ritmo sin igual
Nadie se quede sentado
Todos vamos a bailar
Baila, baila esta cumbia
Un ritmo, ritmo sin igual
Nadie se quede sentado
Todos vamos a bailar
Baila, baila esta cumbia (baila esta cumbia conmigo)
Un ritmo, ritmo sin igual
Nadie se quede sentado (mueve la cintura)
Todos vamos a bailar
Baila, baila esta cumbia
Un ritmo, ritmo sin igual
Nadie se quede sentado (baila esta cumbia conmigo)
Todos vamos a bailar
Baila, baila esta cumbia (mueve la cintura)
Un ritmo, ritmo sin igual
Englis:I feel something that moves me
A rhythm that makes me dance
Take all your partner
We are all going to enjoy
Dance, dance this cumbia
Move, move your waist
Everyone, hands up
And scream, scream with madness
Dance, dance this cumbia
A rhythm, rhythm like no other
No one stay seated
We are all going to dance
I feel something that moves me
A rhythm that makes me dance
Take all your partner
We are all going to enjoy
Dance, dance this cumbia
Move, move your waist
Everyone, hands up
And scream, scream with madness
Hey! Hey! Hey! Hey!
Hey! Hey! Hey! Hey!
Hey!
Dance, dance this cumbia
A rhythm, rhythm like no other
No one stay seated
We are all going to dance
Dance, dance this cumbia
A rhythm, rhythm like no other
No one stay seated
We are all going to dance
Dance, dance this cumbia (dance this cumbia with me)
A rhythm, rhythm like no other
Nobody stay seated (move the waist)
We are all going to dance
Dance, dance this cumbia
A rhythm, rhythm like no other
Nobody stay seated (dance this cumbia with me)
We are all going to dance
Dance, dance this cumbia (move your waist)
A rhythm, rhythm like no other
Volume = 1243.44 in3
Height = 11 in
Solve this equation and you have the answer:
3.14 • 11 • r2 = 1243.44
Radius = in
Answers
The radius of the cylinder is approximately 5.88 inches.
What are equivalent equations?
Equivalent equations are algebraic equations that are having identical roots or solutions.
We can solve the given equation to find the radius of the cylinder using the volume and height information
3.14 * 11 * r² = 1243.44
First, divide both sides by 3.14*11 to isolate r²:
\(r^2 = 1243.44 / (3.14 * 11)\)
r² ≈ 34.585
Taking the square root of both sides, we get:
r ≈ 5.88
Hence, the radius of the cylinder is approximately 5.88 inches.
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solve by substitution
1. 6x+ 5y=7 x-y=3
2. 3a +2b =4 2a + b=6
3. 2x + y= 4 4x -y=2
Answers
Answer:
1. y = 11
x = -48
2. a =8
b= -10
3. x= 1
y= 2
Step-by-step explanation:
1 . 6x + 5y = 7
x-y= 3
6x+5y = 7
6x-6y =18
-1y = - 11
6x + 5y = 7
y = 11
6x + 55 = 7
6x = -48
x = -48
The ________ identifies the number of standard deviations a particular value is from the mean of its distribution.
Answers
The z-score, also known as the standard score, is a statistical measure that identifies the number of standard deviations a particular value is from the mean of its distribution.
It is calculated by subtracting the mean from the value and then dividing the result by the standard deviation.
The z-score is a useful tool in statistics because it allows for the comparison and interpretation of values across different distributions. By converting values into standardized units, it provides a standardized reference point for assessing how extreme or typical a particular observation is within its distribution.
A positive z-score indicates that the value is above the mean, while a negative z-score indicates that the value is below the mean. The magnitude of the z-score indicates the distance of the value from the mean in terms of standard deviations.
The z-score is commonly used in hypothesis testing, confidence intervals, and determining percentiles in a distribution. It helps in understanding the relative position of an observation and provides a standardized measure of its deviation from the mean.
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2. Make subsets from the set below.
{red, blue, pink, green}what is the answer
Answers
Answer:
{} , {red}, {blue}, {pink}, {green} , {red, blue}, {red, pink}, {red, green}, {blue, pink} , {blue, green} , {pink, green}, {red, blue, pink}, {red, pink, green}, {blue, pink, green}, {red, blue, green}, {red, blue, pink, green}
Step-by-step explanation:
Given set is:
{red, blue, pink, green}
First of all, we have to calculate the number of subsets
In the given set,
n = 4
So the number of subsets will be: 2^4 = 16
The subsets are:
{} , {red}, {blue}, {pink}, {green} , {red, blue}, {red, pink}, {red, green}, {blue, pink} , {blue, green} , {pink, green}, {red, blue, pink}, {red, pink, green}, {blue, pink, green}, {red, blue, green}, {red, blue, pink, green}
Geometry Unit 5 Test: Similarity Score 5) Similar Triangles Using a 2-column proof, prove that Triangle UTR is similar to Triangle VSR Then, separate from the proof, find the value of x with the information given. UR = 40 ft; RT = (3x+6) ft; VR = 25 ft; SR = 15 ft X= BONUS OPPORTUNITY Score
Answers
To prove that Triangle UTR is similar to Triangle VSR, we must show that all three corresponding angles are congruent and that the corresponding sides are proportional. Here's the 2-column proof:
Statement | Reason
--- | ---
1. ∠UTR ≅ ∠VSR | Given
2. ∠URT ≅ ∠VRS | Vertical angles are congruent
3. ∠RTU ≅ ∠RSV | Vertical angles are congruent
4. ∆UTR ≅ ∆VSR | Angle-Angle (AA) Similarity Theorem
Now, to find the value of x, we can set up a proportion using the corresponding sides UT and VS:
UT/VS = RT/SR
Substituting the given values, we get:
40/25 = (3x+6)/15
Simplifying, we can cross-multiply and solve for x:
600 = 25(3x+6)
600 = 75x + 150
450 = 75x
x = 6
Therefore, the value of x is 6.
BONUS OPPORTUNITY Score: Good job! You earned a perfect score of 5 for your Similarity proof and for solving for x correctly.
To prove that Triangle UTR is similar to Triangle VSR using a 2-column proof, we will first use the Side-Side-Side (SSS) Similarity Theorem. This theorem states that if the corresponding sides of two triangles are proportional, then the triangles are similar.
1. List the given information:
- UR = 40 ft
- RT = (3x + 6) ft
- VR = 25 ft
- SR = 15 ft
2. Write a 2-column proof:
| Statement | Reason |
|------------------------------|--------------------------------|
| 1. UR = 40 ft | Given |
| 2. RT = (3x + 6) ft | Given |
| 3. VR = 25 ft | Given |
| 4. SR = 15 ft | Given |
| 5. UR/VR = RT/SR | Using given information |
| 6. 40/25 = (3x + 6)/15 | Substituting values from 1-4 |
| 7. 8/5 = (3x + 6)/15 | Simplifying the ratio in step 6|
| 8. Triangle UTR ~ Triangle VSR| SSS Similarity Theorem |
Now that we have proven the triangles are similar, we can find the value of x:
8/5 = (3x + 6)/15
Multiply both sides by 15 to clear the denominator:
15 * (8/5) = (3x + 6)
24 = 3x + 6
Now, subtract 6 from both sides:
24 - 6 = 3x
18 = 3x
Finally, divide both sides by 3 to solve for x:
18 / 3 = x
x = 6
So, the value of x is 6.
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1
(n+2)
п+2) + 4 = 3n — 5
2
Answers
Answer:
2.4 that what I got
Step-by-step explanation:
Answer:
n=29
Step-by-step explanation:
PLS HELP QUICKLY
Which pair of functions are inverses of each other?
5
O A. f(x) = -2 and g(x) = +2
B. f(x) = 7x-2 and g(x) = 2
C. f(x) =x/5+ 6 and g(x) = 5x - y
D. f(x) = 3+ 6 and g(x) = 6x³
Answers
Answer: B
\(f(x) = 7x-2\) and \(g(x) = \frac{x+2}{7}\)
How to solve:
check if the composite functions of f(x) and g(x) are equal to x (this means they are inverses)
f[g(x)] = x
g[f(x)] = x
Step-by-step explanation:
Checking A.
\(f(x) = \frac{5}{x} -2\)
\(g(x) = \frac{x+2}{5}\)
\(f(g(x)) = f(\frac{x+2}{5} ) = \frac{5}{\frac{x+2}{5} } -2\)
This does not equal x, so we know these are not inverses
Checking B.
\(f(x) = 7x-2\)
\(g(x) = \frac{x+2}{7}\)
\(f(g(x)) = f(\frac{x+2}{7} ) = 7(\frac{x+2}{7}) - 2 = x+2-2 = x\)
\(g(f(x)) = g(7x-2) = \frac{7x-2 + 2}{7} = \frac{7x}{7} = x\)
since both f(g(x)) = x and g(f(x)) = x, we can determine that they are inverses of each other.
Need help ASAP!! Please!! Will mark brainliest
Answers
Answer:
D. 37.68
Step-by-step explanation:
Circumference of a circle is 2 x pi x radius
your radius is 6 bc its half of your diameter is 12
when you multify them together, it gives you ab 37.68
Robert is told the size of angle BAC in degrees and he is then asked to calculate
the length of the line BC. He uses his calculator but forgets that his calculator
is in radian mode. Luckily he still manages to obtain the correct answer. Given
that angle BAC is between 10° and 15°, use graphing software to help you find
the size of angle BAC, correct to 2 decimal places.
Answers
The measure of angle BAC is of 14.48º, considering the relations in a right triangle.
What are the relations in a right triangle?There are three relations in a right triangle, presented as follows:
The sine of an angle of the triangle is represented by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle of the triangle is represented by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle of the triangle is represented by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.Using a ruler, it is found that the length of the opposite side to angle BAC, of CB, is of 1.5 cm, hence the following relation is established, considering the hypotenuse of 6 cm.
sin(x) = 1.5/6
In which x is the measure of angle BAC.
x can be isolated applying the arc sine function, which is the inverse of the sine, hence:
x = arcsin(1.5/6)
x = 14.48º.
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Sandy's 8th grade class receives $13.50 for every 5 boxes of chocolates that they sell. Which graph shows this relationship with the same unit rate?
Answers
Answer:
See Explanation
Step-by-step explanation:
Incomplete Question: This question requires options
Let the amount received be represented with y
Let the number of boxes be represented with x
From the question, we have that:
x = 5 ; y = 13.50
Multiply the values of x and y by 2Similarly,
x = 10; y = 27
This gives:
\((x_1,y_1) = (5,13.5)\)
\((x_2,y_2) = (10,27)\)
The slope of the graph is calculated as follows:
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
\(m = \frac{27 - 13.5}{10 - 5}\)
\(m = \frac{13.5}{5}\)
\(m = 2.7\)
The equation of the graph is calculated as follows:
\(y - y_1 = m(x - x_1)\)
Substitute values for m, x1 and x2
\(y - 13.5 = 2.7 * (x - 5)\)
Open Brackets
\(y - 13.5 = 2.7x - 13.5\)
Collect Like Terms
\(y = 2.7x - 13.5 + 13.5\)
\(y = 2.7x\)
The above equation can be used to determine the graph
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Angles p and q are complementary. p is four times the size of q. what is the size of q.
Answers
Angles p and q are complementary, which means that their sum is equal to 90 degrees. Let's assume the size of angle q is x degrees. Since p is four times the size of q, we can write the equation p = 4q.
To find the size of q, we need to substitute the value of p in terms of q into the equation for the sum of the angles: p + q = 90.
Substituting 4q for p, we get:
4q + q = 90
Combining like terms:
5q = 90
To solve for q, we divide both sides of the equation by 5:
q = 90/5
Simplifying:
q = 18
Therefore, the size of angle q is 18 degrees.
when angles p and q are complementary and p is four times the size of q, the size of angle q is 18 degrees.
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