Complementary angle add up to 90 degrees.
Angle A = x + 6
Angle B = x
They both add up to 90.
x + 6 + x = 90
2x + 6 = 90
2x = 90 - 6
2x = 84
x = 84/2
x = 42
Angle A = x + 6
Angle A = 42 + 6
Angle A = 48 degrees
I need help with this
If .... a-b=5 Then what is 2(a-b) ??
Answer: 10
Step-by-step explanation:
if we know a-b=5, to get the answer of 2(a-b) multiply 5 by 2.
Answer:
10
Step-by-step explanation:
a-b=5
Multiply each side by 2
2(a-b) = 2*5
2 (a-b) = 10
Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?
O 1-6 - 751, - 6 + V51)
O 1-6 - 121, -6 + V21)
O 16 - 151,6 + V51)
O (6 - 121,6 + V21)
Answer:
(6-[tex]\sqrt{21}[/tex]) (6+[tex]\sqrt{21}[/tex])
Step-by-step explanation:
The solution set of the equation x2 = 12x – 15 is O (6 - 121,6 + V21).
The answer is option D.
What is a quadratic equation?
A quadratic equation is an equation that can be rearranged in standard form.
ax²+bx²+c=0
The solution gives two values of the single variable.The values are real root and non-real roots.Calculation
equation x2 = 12x - 15
can be written as
x² - 12x = -15
On square by adding (-b/2)2 on both sides of the equation
x²- 12x + (-12/2)² = -15 + (-12/2)²
We get
⇒ x² - 12x + (-6)² = -15 + (-6)²
⇒ x²- 12x + 36 = -15 + 36
⇒ (x - 6)2 = 21
Taking square root on both sides
⇒x - 6 = ± √21
⇒x - 6 = √21 and x - 6 = - √21
⇒x = (6 + √21 ) and x = (6 - √21)
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A roller coaster carries riders up a ramp that is 39 meters long. This ramp
forms a right triangle with the ground and a vertical support beam. What is
the height of the support beam?
Support
Roller coaster 9
Ground
15 m
OOOO
A. 36 m
24 m
C. 42 m
D. 54 m
Answer:
A. 36
Step-by-step explanation:
By using hypotenuse theorem we can find the height of the support.
In hypotenuse we square both the given measures, then subtract them. if slant measure is given we subtract the square of the other side from the square of the slant and find the square root of the result. if we have to find the slope, then we add the squares of the 2 given sides and find the square root of the result.
so, in this case:
(39×39) - (15×15)
=1521 - 225
=1296
= square root of 1296
= 36
Hope it helps u ....
The quotient of 20 and 3 more than x is 4. Find x.
Answer:
x=2
Step-by-step explanation:
Quotient means division
20/(x+3) =4
Multiply each side by (x+3)
(x+3)*20/(x+3) =4(x+3)
20 = 4(x+3)
Divide each side by 4
20/4 = 4(x+3)/4
5 = x+3
Subtract 3 from each side
5-3 = x+3-3
2 =x
If the domain of the square root function f(x) is x<7, which statement must be true?
7 is subtracted from the x-term inside the radical.
The radical is multiplied by a negative number.
7 is added tihe radical term.
The x-term inside the radical has a negative coefficient.
Answer:
The x-term inside the radical has a negative coefficient
Step-by-step explanation:
The argument of a square root should be ALWAYS greater or equal to zero. If the domain of the function is x<7, rearranging, we have: 0<x-7
Therefore the argument is: x-7, and the function is: y = √(x-7)
The statement "The x-term inside the radical has a negative coefficient" is the right answer.
A kayak rental company charges $25.00 to rent a kayak and $3.50 for each half hour it is used.
Which linear function best represents the total cost of renting a kayak for 4 hours?
r (t) = 3.50t + 25
r(4) = 39
r (t) = 25t +3.5
R(8) = 203.5
r(t) = 25t + 3.5
r(4) = 103.5
r(t) = 3.50t +25
r(8) = 53
Answer:
Option D (r(t) = 3.50t +25 ; r(8) = 53)
Step-by-step explanation:
The fixed cost to rent the kayak $25. This is the cost which remains fixed irrespective of the usage of the kayak. The variable cost of using the kayak is the cost which depends on the usage of the kayak. It is mentioned that the kayak is used for 4 hours and the company charges $3.5 for every half hour. The cost function is given by:
r(t) = 25 + 3.5t ; there r is the total cost of using the kayak and t is the number of half-hours the kayak is used.
4 hours means that there are 8 half-hours. Therefore, t=8. Put t=8 in r(t).
r(8) = 25 + 3.5*(8) = 25 + 28 = 53.
Therefore, Option D is the correct answer!!!
Answer:
The Answer would be D.
r(t) = 3.50t +25
r(8) = 53
Step-by-step explanation:
The Rental Company charges a fixed price of $25 to rent the kayak, as well as an additional $3.50 for each half hour. So the only variable we are looking at would be the amount of time the kayak was rented. We can model this question with the following equation.
[tex]f(x) = 25 + 3.50x[/tex]
with x being the time the kayak was rented in 30 min intervals. Since the kayak was rented for 4 hours we can multiply this by 2 to get 8 (30 min intervals). Now we can plug this into the formula and solve it.
[tex]f(8) = 25 + 3.50(8)[/tex]
[tex]f(8) = 25+ 28[/tex]
[tex]f(8) = 53[/tex]
So to rent the kayak for 4 hours it would cost $53
Find the missing side of the triangle.
Answer:
x=1
Step-by-step explanation:
Since you know two sides and are trying to find the missing side, you can use the Pythagorean Theorem. So fashion the equation like this:
x^2 + 3^2 = sqrt10^2. After simplify, which leads to x^2 + 9 =10. Then have the variable to one side by subtracting 9 on both sides. This leads to x^2=1. Finally, square root both sides which leads to 1. Note that any root of 1 is 1. So your answer becomes x=1.
Hope this helps!
need someone to teach/explain how to do these problems: asap
Answer:
The farthest Left
Step-by-step explanation:
The second equation, y<x+1, means that every y value will be less than the x value +1. Since it is less than, and not less than or equal to, the graph is represented by the dotted line and not a solid line. Moving on to the next problem, we have to get it in slope-intercept form. We start with x-4y is less than or equal to 4. We need to separate the x and y, so we add 4u to the negative 4y, cancelling it out, but what we do to one side, we have to do to the other, so we add 4y, making our equation x is less than or equal to 4y + 4. Next, we need to get the y by itself, so we subract 4 from the y side, cancelling it out and subtract it from the other side, which leaves us with x-4 is less than or equal to 4y. 4y is just 4 times y so we divide it by four on both sides to get y is greater than or equal to 1/4x-1. Since the solution can be equal to, we make the line solid and when we plot both lines, we get the graph furthest to the left.
What is the maximum number of turns for the graph of f(x)=x^4+3x^2?
Answer:
The turns of a graph is represented by the number of maximum or minimum that the function has.
If we differenciate f(x) we get:
f'(x)=4x^3+6x
f'(x)=2x(2x^2 + 3)
Therefore f'(x) =0, when x=0. Given that negative roots are not defined.
Therefore, the number of turns will be given by the number of solutions of f'(x) which is 1.
Attached you find the graph of the function which confirms the number of turns.
If the function had other solutions, the maximum number of turns it could have is 3! because f'(x) is a third degree polynomial, therefore it can't have more than 3 solutions!
Un triángulo tiene un área de 48 cm2 y una base de 6cm . Encuentra la longitud de la altura.
Sloane believes there is a correlation between the number of texts sent in class and GPA. She collected data and found that the line of best fit for the data can be modeled by the equation y = 4.0 − 0.5x.
Identify and interpret the slope in this scenario.
a. The slope is −4.0. Starting at 0.5, the GPA will decrease by 4.0 for every text sent in class.
b. The slope is −0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class.
c. The slope is 4.0. Starting at 0.5, the GPA will increase by 4.0 for every text sent in class.
d. The slope is 0.5. Starting at 4.0, the GPA will increase by 0.5 for every text sent in class.
Answer: b. The slope is -0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class.
Step-by-step explanation:
We know that the equation of a line in intercept form is given by :-
[tex]y=mx+c[/tex], where m is the slope and c is the y-intercept. (i)
Given : Sloane believes there is a correlation between the number of texts sent in class and GPA. She collected data and found that the line of best fit for the data can be modeled by the equation :-
[tex]y = 4.0-0.5x[/tex]
When we compare it to (i), we get
m=-0.5 and c=4.0
It means the slope is -0.5 and the function is starting at 4.0 and the GPA will decrease by 0.5 for every text sent in class (since its negative).
The correct option is B which is ''The slope is −0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class''.
Given
The data can be modeled by the equation;
[tex]\rm y = 4.0 - 0.5x[/tex]
How to determine the slope of the line?The standard form of the linear equation is;
[tex]\rm y = mx+c[/tex]
Where m is the slope of the equation and c is the intercept.
On comparing the given equation with the standard equation;
[tex]\rm y = 4.0 - 0.5x\\\\y = -0.5x+4.0[/tex]
The slope of the line m is -0.5 and intercept c is 4.0.
Hence, the slope is −0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class.
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Complete the recursive formula of the arithmetic sequence 14, 30, 46, 62, ....
d(1) =
d(n) = din - 1)+
Answer:
They are adding 16 to the number each time. So the next number in the sequence would be 78.
Step-by-step explanation:
d(1) = 14
d(n) = d (n-1) + 16
14 + 16 = 30
30 + 16 = 46
46 + 16 = 62
62 + 16 = 78 and so on...
The recursive formula of the arithmetic sequence is [tex]d_{n}=d_{n-1} +16[/tex].
What is recursive formula?A recursive formula is a formula that defines any term of a sequence in terms of its preceding term(s).
The recursive formula of an arithmetic sequence is, [tex]a_{n}=a_{n-1} +d[/tex]
From the question
14, 30, 46, 62, .......
d = [tex]62-46 =46-30=30-14=16[/tex]
d = 16
As per sequence
d(1) = 14
[tex]d_{n}-d_{n-1} =d=16[/tex]
[tex]d_{n}=d_{n-1} +16[/tex]
The recursive formula of the arithmetic sequence is [tex]d_{n}=d_{n-1} +16[/tex].
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f(x)=25x^2-10x+1 what is the the value of the discriminant of f
Answer:
0
Step-by-step explanation:
Quadratic equation
[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]
The discriminant is the part of the quadratic formula within the square root symbol: [tex]{b^{2}-4*a*c}[/tex]. The discriminant indicates if there are two solutions, one solution, or none.
The discriminant can be positive, zero or negative which determines how roots exist for the given quadratic equation.
So, a positive discriminant tell us that the quadratic has two different real solutions.
A discriminant of zero tell us that the quadratic has two real and equal solutions.
And a negative discriminant tell us that none of the solutions are real numbers.
In this case: 25x^2-10x+1=0
We can see that
a= 25 b=-10 c=1
Using: [tex]{b^{2}-4*a*c}[/tex]
We have [tex]-10^{2}-4* 25*1 =100-100=0[/tex]
the answer is zero, so the quadratic has two real and equal solutions
Answer:
What is the value of the discriminant of f?
0
How many x-intercepts does the graph of f?
1
Step-by-step explanation:
I promise you i just got this question and this is the answer
The graph for the equation y=-x+2 is shown. If another equation is graphed so that the system has an infinite number of solutions, which equation could that be?
A. y=-2(x-1)
B. y=-(x+2)
C. y=-1/4(4x-8)
D. y=-1/2(x+4)
Answer:
C
Step-by-step explanation:
Note that C is exactly -1/4(4x-8) = -1/4*4x -1/4*(-8) = -x+2, so the system with C is the same equation twice, and obviously has an infinite number of solutions.
help please its URGENT!!!!!!!!
This is a relation but not a function.
Functions must have that there is a unique y for a given x, which clearly doesn't work here because all lines of a given x have 2 y-values. However, it is a relation because there is a given set of points which are defined to be within the set of the ellipse (if it's defined which members of two sets, the range and domain, go together, then you have a relation)
iam thinking its D but iam not 100% sure.
Which of the following shows the length of the third side, in inches, of the triangle below?
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{61}\\ a=adjacent\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ \sqrt{61^1-11^2}=a\implies \implies \sqrt{3600}=a\implies 60=a[/tex]
An equation is shown below: 2(3x − 5) = 1 Which of the following correctly shows the first two steps to solve this equation? Step 1: 6x − 10 = 1; Step 2: 6x = 11 Step 1: 6x − 5 = 1; Step 2: 6x = 6 Step 1: 5x − 3 = 1; Step 2: 5x = 4 Step 1: 5x − 7 = 1; Step 2: 5x = 8
Answer:
A: Step 1: 6x − 10 = 1; Step 2: 6x = 11
Step-by-step explanation:
First: remove parentheses by multiplying factors.
6x - 10 = 1
Second: Move the constants to the right side of the equation
6x = 1 + 10
6x = 11
Answer: The correct answer is "Step 1: 6x − 10 = 1; Step 2: 6x = 11"
Step-by-step explanation:
3x-2y=-1 Y=-x+3 is (1,2) a solution of the system
Answer:
Yes
Step-by-step explanation:
To be a solution of the system, it has to satisfy both the equations.
Let's check first one:
3x - 2y = -1
3 (1) - 2(2) = 3 - 4 = -1
So correct (satisfies).
Now, 2nd one:
y = -x + 3
y = -(1) + 3
y = -1 +3
y = 2
Yes, this is satisfied.
Hence, (1,2) IS A SOLUTION OF THE SYSTEM
The line graph shows the number of members during the first few months of a photography club. Describe the data. Then predict the number of members for the sixth month.
Thus, based on the observed pattern and the linear model, we can expect the Photography Club to have 13 members in the sixth month.
Based on the updated coordinate points provided for the graph, which are (1,4), (2,5), (3,7), (4,9), and (5,11), we can describe the data and predict the number of members for the sixth month as follows:
1. Describe the Data:
- At month 1, there are 4 members.
- At month 2, there is an increase to 5 members.
- At month 3, there are 7 members.
- At month 4, there are 9 members.
- At month 5, there are 11 members.
2. Identify the Pattern:
- From month 1 to 2, the increase is 1 member.
- From month 2 to 3, the increase is 2 members.
- From month 3 to 4, the increase is 2 members.
- From month 4 to 5, the increase is 2 members.
3. Predict the Number of Members for the Sixth Month:
- We observe that after the first month, the number of members increases by 2 each month.
- Assuming the pattern continues, we can predict that in the sixth month, the number of members will increase by 2 from the fifth month.
Therefore, the predicted number of members for the sixth month would be:
[tex]\[ 11 \text{ members at month 5} + 2 \text{ increase} = 13 \text{ members at month 6} \][/tex]
We can plot the provided data points and extend the line to the sixth month to visually confirm our prediction. Let's do that.
The linear model fitted to the given data points predicts approximately 12.6 members for the sixth month. Since the number of members must be a whole number, we can round this to 13 members.
Which set of fractions is ordered from greatest to least?
A
two over three, three over eight, five over twelve
B
five over twelve, three over eight, two over three
C
two over three, five over twelve, three over eight
D
three over eight, two over three, five over twelve
Answer:
That would be C.
Step-by-step explanation:
Hope this helps!
The set of fractions {2/3, 5/12, 3/8} is ordered from greatest to least. which is the correct answer would be an option (C).
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
What is descending order?Descending order is defined as when numbers (or other items) are arranged from the largest numbers to the least numbers, it is said to be in descending order.
What is ascending order?Ascending order is defined as when numbers (or other items) are arranged from the least numbers to the largest numbers, it is said to be in ascending order.
According to option (C),
two over three, five over twelve, three over eight
2/3, 5/12, 3/8
⇒ 2/3 < 5/12 <3/8
Therefore, the set of fractions is ordered from greatest to least.
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What is the measure of <7?
Answer:
120
Step-by-step explanation:
<2 = 120 degrees
<3 = <2 vertical angles
Assuming b is parallel to c
<3 = <6 alternate interior angles
<6 = <7 vertical angles
<2 = <7 =120
How do I solve this equation 4x^2-12x+29=20
[tex]4x^2-12x+29=20 \\4x^2-12x+9=0\\(2x-3)^2=0\\2x-3=0\\2x=3\\x=\dfrac{3}{2}[/tex]
With these kind of equations you want to use the quadratic formula. These problems take time, so don't fret you'll get there! :)
Quadratic formula:
-b +- √b^2-4(a)(c)
--------------------------
2(a)
Next find your a, b, and c!
a= 4
b=12
c=29
Time to plug those answers in.
12 +- √(-12)^2-4(4)(9)
-------------------------------
2(4)
Next solve everything in the radical first! Then the bottom.
12 +- √144-144
----------------------- ~ x=12/8 ~ x=3/2
8
You get: x=3/2!
On three rolls of a single die, you will lose $19 if a 3 turns up at least once, and you will win $5 otherwise. What is the expected value of the game?
Let X be the random variable for the amount won on a single play of this game.
Answer:
-16 cents
Step-by-step explanation:
We are given that on three rolls of a single die, you will lose $19 if a 3 turns up at least once, and you will win $5 otherwise.
We are to find the expected value of the game.
P (at least one 5 in three rolls) = 1 - P (no. of 3 in three) = [tex]1-(\frac{3}{6} )^2[/tex] = 0.875
P (other results) = 1 - 0.875 = 0.125
Random game value = -19, +5
Probabilities: 0.875, 0.125
Expected game value (X) = 0.875 × (-19) + 0.125 × (5) = -16 cents
Therefore, every time you play the game, you can expect to lose 16 cents
Answer:
It is expected to lose 5.10 dollars
Step-by-step explanation:
The probability of getting a 3 by throwing a die once is 1/6.
By throwing it 3 times the probability of not getting a 3 is:
[tex]P=(\frac{5}{6}) ^ 3 =0.5787[/tex]
Then the probability of obtaining a three at least once in the 3 attempts is:
[tex]P'=(1-0.5787)=0.421[/tex]
So if X is the discrete random variable that represents the amount gained in a single move of this game, the expected gain E(X) is:
[tex]E(X)=P'*(X') + P*(X)[/tex]
[tex]E(X) =0.421'*(-19) + 0.5787*(5)\\\\E(X) =-\$5.10[/tex]
An experiment was conducted, and it was determined that plants that received more than two hours of sunlight per day grew larger than plants that received less than two hours of sunlight per day. Which of the following best describes this situation?
A)This is an example of correlation and causation.
B)This is an example of correlation.
C)This is an example of causation.
D)This is not an example of causation or correlation.
Answer:
C). This is an example of causation
Step-by-step explanation:
Causation : It can be defined as the one event is the result of the other event. It is simply the cause and its effect. There is a causal relation between the two events.
Correlation : It can described the direction of the relation between two or more events or variables.
The conclusion of the experiment is that the plant that received more than two hours of sunlight in each day grew more than the plants that received less than two hours of sunlight in each day.
This is the cause of one event and its effect on the other event.
So option C is correct because sunlight causes plants to grow.
So option C). This is an example of causation.
Answer:
C( This is an example of causation
PLEASE ANSWER FAST
EASY QUESTION
50 POINTS
Complete the sentence. A secant is a
________ in the plane of a circle that
intersects the circle at exactly
________ points.
Answer:
A Secant is a line in the plane of a circle that intersects the circle at exactly two points
Step-by-step explanation:
A line intersecting in two points is called a secant line, in one point a tangent line and in no points an exterior line. A chord of a circle is the line segment that joins two distinct points of the circle. A chord is therefore contained in a unique secant line and each secant line determines a unique chord.
8. A patient is told to take 12 1/2 grains (gr) of aspirin qd (every day). If the
aspirin tablets contain 5 gr each, how many tablets must the patient
take qd?
Answer:
The patient must take [tex]2\frac{1}{2}\ tablets[/tex] per day
Step-by-step explanation:
we know that
12 1/2 grains (gr) of aspirin is equal to 12.5 grains
using proportion
Let
x -----> the number of aspirin tablets
[tex]\frac{1}{5} \frac{tablet}{gr} =\frac{x}{12.5} \frac{tablets}{gr} \\ \\x= 12.5/5\\ \\x=2.5\ tablets[/tex]
Convert to mixed number
[tex]2.5=2\frac{1}{2}\ tablets[/tex]
What is the domain of f(x)?
Answer:
A
Step-by-step explanation:
what’s 11/5 simplified ?
The simplified form of the fraction 11/5 is determined as 2 1/5.
What is simplification of an expression?Simplification refers to the process of reducing an expression, equation, or fraction into its simplest or most concise form.
Fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). This reduces the fraction to its simplest form.
The given fraction expression;
11/5
This expression is simplified as follows;
11/5 = 2 remainder 1
The final expression becomes;
11/5 = 2 1/5
Thus, the simplified form of the expression 11/5 is determined as 2 1/5.
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Find the value of x (really need help with this)
Answer:
x=-7
Step-by-step explanation:
The sum of the angles of a triangle are 180 degrees
40 + x+57 + 90 =180
Combine like terms
187 +x = 180
Subtract 187 from each side
187-187 +x = 180-187
x = -7