Answer:
Constant: A numerical value
Coefficient: The constant preceding the variables in a product
Variable: a letter or symbol used to represent and unknown
Expression: A mathematical phrase that cannot be determined by true or false
Algebraic expression: A mathematical expression containing one or more variables
Step-by-step explanation:
Please show full SOLUTIONS!! I WILL MARK BRAINLIEST FOR THE BEST ANSWER. THANKS
The orthocentre for the triangle ABC is (1.85, 5.88).
Triangle ABC has vertices at A(2, 8), B(6, 2) and C(-3, 2).
We need to use analytical geometry to determine the coordinates of the orthocentre.
How to find the orthocentre using analytical geometry?Steps to find the orthocentre:
Step 1: First, we will find the slopes of any two sides of the triangle (say AC and AB).
Step 2: Next, we can find the slopes of the corresponding altitudes. Remember that if two lines are perpendicular to each other, they satisfy the following equation.
Step 3: Next, we will use the slope-point form of the equation of a straight line to find the equations of the lines that are coincident with the altitudes BE and AD.
Step 4: Next, we can solve the equations of BE and CF simultaneously to find their solution, which gives us the coordinates of the orthocentre H.
Now, the slope of AC=2-8/-3-2=6/5 and the slope of BE=5/6.
The slope of AB=2-8/6-2=-6/4=-3/2 and the slope of CF=-2/3
The slope of BE=y-2/x-6=5/6
⇒6x-5y-26=0----(1)
The slope of CF=y-2/x+3=-2/3
⇒-2x-3y=0----(2)
By solving (1) and(2), we get
y=26/14=13/7=1.85 and x=5.88
Therefore, the orthocentre for the triangle ABC is (1.85, 5.88).
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A store carries chocolate, vanilla, peppermint, and lemon candies. One day, the store clerk notices that he has fifteen candies total. Furthermore, the number of peppermint and lemon candies together is twice the number of chocolate and vanilla candies together, and there are eight more peppermint candies than lemon candies. How many lemon candies are there
The total number of lemon candies is 1, solved using the linear equation in one variable 3l + 12 = 15, where l is the number of lemon candies.
We assume the number of chocolate candies to be c.
We assume the number of vanilla candies to be v.
We assume the number of peppermint candies to be p.
We assume the number of lemon candies to be l.
The total number of candies is given as 15.
This can be represented by the linear equation: c + v + p + l = 15 ... (i).
The number of peppermint candies and lemon candies together is given to be twice the number of chocolate and vanilla candies together.
This can be represented by the linear equation: p + l = 2(c + v) ... (ii).
There are eight more peppermint candies than lemon candies.
This can be represented by the linear equation: p = l + 8.
Substituting p = l + 8 in (ii), we get,
l + 8 + l = 2(c + v),
or, 2(l + 4) = 2(c + v),
or, c + v = l + 4.
Substituting c + v = l + 4, and p = l + 8, in (i), we get:
l + 4 + l + 8 + l = 15,
or, 3l + 12 = 15,
or, 3l = 15 - 12 = 3,
or, l = 3/3 = 1.
Therefore, the total number of lemon candies is 1, solved using the linear equation in one variable 3l + 12 = 15, where l is the number of lemon candies.
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write an exponential function that includes the following given pair of points.
(-3,16) and (-2,8)
There are 24 boys and serveral girls in a class.They sit in pairs so that exactly one fourth of the boys sit with a girl and exactly one half of the girls sit with a boy. How many students in the class?
Please explain it step-by-step. I will give you a brainlist!
Answer:
36 total students in the class
Step-by-step explanation:
Analyze the boysThere are 24 boys in the class.
Since they sit in pairs, and exactly 1/4 of the boys sit with a girl, then one-quarter of the 24 boys sits with a girl.
1/4 * 24 = 6, so 6 of the boys sit with a girl. Reflexively, 6 girls sit with a boy.
Analyze the girls
Since the problem states that exactly half of the girls sit with a boy, then half of the total number of girls is 6 (since we know that exactly 6 girls were sitting with a boy).
1/2 * x = 6
Multiplying both sides by 2...
x=12
So there are 12 girls total in the class, half (6) of whom sit with a boy.
Find the totalThere are 24 boys total in the class, one-quarter (6) of whom sit with a girl. The rest of the boys (18) sit in pairs with another boy (9 pairs), and the rest of the girls (6) sit with another girl (3 pairs).
Since there are 12 girls total and 24 boys total in the class, the total number of students is the sum of 12 and 24
12+24 =36 total students in the class
Find two consecutive even numbers such that the sum of 3 times the smaller and 5 times thelarger is106.
Answer:
12 and 14
Step-by-step explanation:
The first number can be assigned x, the second will be assigned x+2 so that it will be even.
3(x)+5(x+2) = 106
3x+5x+10 = 106
8x = 96
x = 12
x+2 = 14
The two consecutive even numbers such that the sum of three times the smaller and five times the larger is 106 are 12 and 14, computed using the linear equation in one variable 3x + 5(x + 2) = 106.
We are given two consecutive even numbers, thus the larger number will be two more than the smaller one, as consecutive even numbers differ by two.
We assume the smaller number to be x.
Thus, the larger number = x + 2.
We have been given that three times the smaller number summed with five times the larger number results in 106.
This can be shown by the linear equation in one variable:
3x + 5(x + 2) = 106.
To find the numbers, we need to solve this linear equation in one variable as follows:
3x + 5(x + 2) = 106,
or 3x + 5x + 10 = 106 {Simplifying},
or, 8x + 10 = 106 {Simplifying},
or, 8x + 10 - 10 = 106 - 10 {Subtracting 10 from both sides of the equation},
or, 8x = 96 {Simplifying},
or, 8x/8 = 96/8 {Dividing both sides of the equation by 8},
or, x = 12 {Simplifying}.
Thus the smaller number, x = 12.
The larger number, x + 2 = 12 + 2 = 14.
Thus, the two consecutive even numbers such that the sum of three times the smaller and five times the larger is 106 are 12 and 14, computed using the linear equation in one variable 3x + 5(x + 2) = 106.
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help
me help me help
Answer:
SSS similarity
Step-by-step explanation:
From the smaller triangle to the larger triangle, the ratio of each pair of corresponding sides is 2.
for what values of b will f(x)=log b x be a decreasing function?
Answer:
Step-by-step explanation:
Can someone please help me figure out if there similar and then the rest
The figures have corresponding sides that are proportional, therefore, they are similar figures.
What are Similar Figures?When two figures are similar to each other, the corresponding sides are proportional to each other.
The two figures given have two opposite sides that are parallel and congruent to each other. Therefore:
DA/VS = 21/7 = 3
AB/ST = 15/5 = 3
Thus, we can conclude that since their corresponding sides are proportional, therefore, they are similar to each other.
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Solve the following
2(x+6)-10=12
⊰________________________________________________________⊱
Answer:
x=5
Step-by-step explanation:
Apply the distributive property,
2(x+6)-10=12
2x+12-10=12
Collect a few like terms
2x+2=12
Subtract 2 from both sides
2x=10
Divide the equation by 2.
x=5
Done!!
⊱______________________________________________________⊰
2(x+6) - 10 = 12
2(x+6) = 22
x+6 = 11
x = 11 - 6 = 5
x = 5
An ellipse has a center at the origin, a vertex along the major axis at (10, 0), and a focus at (8, 0).
Which equation represents this ellipse?
[tex]\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1[/tex] is the equation of the ellipse.
What is the equation of an Ellipse ?The equation of an ellipse is given by
[tex]\rm \dfrac{ (x-h)^2 }{a^2} + \dfrac{ (y-k)^2}{b^2} = 1[/tex]
here
(h,k) is the center
c = is the distance between center to focus
c = [tex]\rm \sqrt{a ^2 - b^2}[/tex]
as the a = 10 , component length
and c = 8
8 = [tex]\rm \sqrt{10 ^2 - b^2}[/tex]
8² = 10² -b²
b² = 36
b = 6
h = 0 ,k = 0
Substituting the values given
[tex]\rm \dfrac{ (x-0)^2 }{10^2} + \dfrac{ (y-0)^2}{6^2} = 1[/tex]
[tex]\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1[/tex]
Therefore the equation of the ellipse has been determined.
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What are the coordinates of a point P(x, y)
reflected across the y-axis? Across the x-axis?
Use reflection notation to write your answer.
[tex]R_{x-axis}[/tex] means [tex]P(x,y) \longrightarrow P'(x,-y)[/tex].
[tex]R_{y-axis}[/tex] means [tex]P(x,y) \longrightarrow P'(x,-y)[/tex]
Which equation accurately represents this statement? Select three options. Negative 3 less than 4.9 times a number, x, is the same as 12.8. Negative 3 minus 4.9 x = 12.8 4.9 x minus (negative 3) = 12.8 3 + 4.9 x = 12.8 (4.9 minus 3) x = 12.8 12.8 = 4.9 x + 3
Equations b,c, and e accurately represent this statement.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
The three equation accurately represents this statement is;
4.9 x-(-3) = 12.8
3+ 4.9 x = 12.8
12.8 = 4.9 x +3
Hence, equations b,c, and e accurately represent this statement.
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Calculate the ninth term of the sequence:
3, 8, 13, 18, 23, 28, 33, 38, ...
Answer:
43
Step-by-step explanation:
sequence: +5
∴ninth term of sequence = 38+5
= 43
Part B Which value is closest to the product 0.04 × 8.01?
A. 32
B. 3.2
C. 0.032
D. 0.32
Answer:
D
Step-by-step explanation:
this is because when multipled you get 0.3204 so u round and it becomes 0.320
Answer:
D
Step-by-step explanation:
0.04 x 8.01 = [tex]\dfrac{4}{100} . \dfrac{801}{100}[/tex]
[tex]=\dfrac{3204}{10000}\\\\\\0.3204[/tex]
I have a bag with blue marbles and yellow marbles in it. At the moment, the ratio of blue marbles to yellow marbles is 8:5. If I remove 12 blue marbles and add 21 yellow marbles, the ratio will be 1:3. How many blue marbles were in the bag before I removed some
There were 15 blue marbles in the bag before removing some
Let B=blue marbles and Y= yellow marbles
The ratio of B to Y is
[tex]\frac{B}{Y} =\frac{8}{5}[/tex]
If we remove 12 blue marbles and add 12 yellow marbles,
the ratio will be
[tex]\frac{B-12}{Y+21} =\frac{1}{3}[/tex]
[tex]3(B-12)=1(Y+21)[/tex]
[tex]3B-36=Y+21\\[/tex]
[tex]3(\frac{8}{5}Y)-36=Y+21[/tex]
[tex]\frac{24}{5}Y-Y=21+36[/tex]
[tex]\frac{19}{5}Y=57[/tex]
[tex]Y=\frac{57*5}{19}\\[/tex]
[tex]Y=15[/tex]
[tex]B=\frac{8}{5} (15)\\B=24[/tex]
Hence, there were 15 blue marbles in the bag before removing some
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If there are 36 eggs in 3 egg cartons, how many eggs are in 6 egg cartons? eggs
Step-by-step explanation:
36 eggs in 3 cartons.
now we double the cartons, so, we need to double the eggs too, because there is a direct relationship between cartons and the number of eggs.
so. in 2×3 cartons are then 2×36 = 72 eggs.
Write an equation of the perpendicular bisector of the segment with the endpoints (3,5) and (9,−1). HELP!!!!!
The equation of the perpendicular bisector of the segment with the endpoints (3,5) and (9,−1) is y = x + 8
Equation of a lineThe equation of a line in slope intercept form is expressed as;
y = mx + b
The equation of the perpendicular bisector will be given as y = -1/m x+ b
where
m is the slope
b is the y-intercept
Determine the slope
Slope = -1-5/9-3
Slope = -6/6
Slope = -1
For the y-intercept
-1 = -1(9) + b
-1 = -9 + b
b = 8
Determine the equation
y = -1/m x + b
y = -1/(-1) x + 8
y = x + 8
Hence the equation of the perpendicular bisector of the segment with the endpoints (3,5) and (9,−1) is y = x + 8
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Match the systems of equations with their solution sets.
The Solution set 1 , 2 , 3, 4 matches with equations 4 , 1 , 2 , 3
What are System of Equations ?The system of equations are the set of equations that have common solution.
The set of equations given are
y+5 = x² - 3x
2x +y = 1
On subtracting equation 1 from 2
5 - 2x = x² -3x -1
x² -x -6 = 0
(x-3)(x +2) = 0
x = 3 , -2
At x = 3 , -2; y = -5 , 5
The set of equation are
y -17 = x²-9x
-x +y =1
-17 +x = x² -9x -1
x²-10x +16 = 0
x² - 8x -2x +16 = 0
(x -8) (x-2) = 0
at x = 2 ,8 ; y = 3 ,9
The set of equation is
y +12 = x²+x
x +y =3
12 - x = x²+x -3
x²+2x -15=0
x² +5x -3x -15 = 0
x(x+5) -3(x+5) = 0
(x-3)(x+5) = 0
x = 3 ,-5
At x = 3 , -5 , y = 0,8
The set of equation is
y-15 = -x² +4x
x +y = 1
-15 -x = -x²+4x -1
x²-5x -14 = 0
x² -7x +2x -14 = 0
x(x-7) +2(x-7) = 0
(x +2) (x-7) = 0
x = -2 , 7
at x = -2 , 7 ; y = 3 ,-6
Therefore the Solution set 1 , 2 , 3, 4 matches with equations 4 , 1 , 2 , 3
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can anyone help me find its Area and perimeter? im so confused please also explain it!!
Topic= Measurement Area, volume & capacity
Answer:
See below
Step-by-step explanation:
Diameter of the semi circles = 15 - 3-3 = 9mm
radius = 4.5 mm
area of rectangle tha goes through the semicircles = 5 x 15 = 75 mm^2
area of two semicircles =
area of circle with radius 4.5 = pi r^2 = 63.62 mm^2
total area = 75 + 63.62 = `38.62 mm^2
Perimeter Two small side rectangles = 2 * (3+5+3) =26 mm
perimeter of cicle with diameter 9 = pi * d = 9pi = 28.27 mm
total perimeter = 54.27 mm
(check my math !)
Why can't [tex]x^2-5x-1[/tex] be factored?
Answer:
Step-by-step explanation:
Discussion.
Not directly. But the quadratic formula can do it. But that's not your question.
the factors you get must contain the factors for 1 which are 1 and - 1
These factors must add to - 5. There's no way that will happen with 1 and - 1 and you would be creative math if you tried to say that you could make one of the factors (x -1-1-1-1-1-1). That creates a whole new question.
A particular industrial product is shipped in lots of 20. Testing to determine whether an item is defective is costly, and hence the manufacturer samples his production rather than using a 100 percent inspection plan. A sampling plan constructed to minimize the number of defectives shipped to customers calls for sampling five items from each lot and rejecting the lot if more than one defective is observed. (If rejected, each item in the lot is tested.) If a lot contains four defectives, what is the probability that it will be rejected
The probability that the sample will be rejected if five items from 1 lot is selected is 26/15504.
Given Industrial product is product in lots of 20. If sample contains more than one defective then the lot will be rejected.
Probability is the chance of happening an event among all the events possible. The probability lies between 0 and 1. The formula of calculating probability is as under:
Probability= number of items/ total items.
Sample from 1 lot =5
Samples in 1 lot=20
Lot will be rejected when 1 sample, 2 sample , 3 sample, 4 sample or all the samples are defective.
Probability that the lot will be rejected=[tex](5C_{2} +5C_{3} +5C_{4} +5C_{5})/20C_{5}[/tex]
=(10+10+5+1)/15504
=26/15504
Hence the probability that lot will be rejected if the lot is rejected if more than one defective is observed is 26/15504.
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Find the value of x to the nearest tenth.
Answer:
Its 31.0 as the the two triangles are similar and the scale factor is 2
How many $4$-digit positive integers exist that satisfy the following conditions: (A) Each of the first two digits must be $1$, $4$, or $5$, and (B) the last two digits cannot be the same digit, and (C) each of the last two digits must be $5$, $7$, or $8$
Answer:
54 possibles
Step-by-step explanation:
Digit ONE 3 choices
Digit two 3 choices
digit three 3 choices
digit four 2 choices
3 x 3 x 3 x 2 = 54 choices meet all of the conditions
A hydro company is laying down power lines in the ground. They have two sections of cable so far that are 325.0 m and 430.0 m long. These two sections of power lines meet at an angle of 23°. How much extra cable is necessary to connect the two pieces of existing cable? Round to the nearest metre.
The length of extra cable that is required to connect the two pieces of existing cable is equal to 182 meters.
How to determine the length of extra cable?In order to determine the length of extra cable that is required to connect the two pieces of existing cable, we would apply the law of cosine as follows:
B² = A² + C² - 2(A)(C)cosB
Substituting the given parameters into the formula, we have;
B² = 325.0² + 430.0² - 2(325.0)(430.0)cos23
B² = 105,625 + 184,900 - 279,500(0.9205)
B² = 290,525 - 257,279.75
B² = 33,245.25
B = √33,245.25
B = 182.33 ≈ 182 meters.
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A teacher puts students names in a hat and chooses without looking to get a sample of 3 students
What type of sample is this?
Question:
A teacher puts students' names in a hat and chooses without looking to get a sample of 3 students. What type of sample is this?
Answer:
Simple random
5. A boy gets 29 marks out of 50 in his maths ex-
am. What percentage did he score?
Answer:
58%
Step-by-step explanation:
29 / 50 * 100% = 58 % ( rather pathetic score, huh?)
Answer:
58%
Step-by-step explanation:
the boy gets 29 marks out of 50
Then
He gets 29 × 2 marks out of 50 × 2
Then
He gets 58 marks out of 100
Therefore
He scored 58%
3x − 12y = −21,
−x + 4y = 7
find x and y intercept
If triangle PQR is an obtuse triangle and angle P is obtuse, then angle Q must be
Answer:
Angle Q is acute.
Step-by-step explanation:
In an obtuse triangle, there is one obtuse angle and the other two angles are acute.
It will take 29.4 years for the population of Africa to be two times what it is today. This reflects:
It will take 29.4 years for the population of Africa to be two times what it is today. This reflects: doubling time.
Doubling time is the time it takes for a particular amount of size or value to double at a given growth rate. By applying the 70 rules, we can find the doubling time of the exponentially increasing population. To do this, divide 70 by the growth rate (r).
Rule of 70 is a simplified way to determine the doubling time using the equation doubling time = 70 / r. Where r is the percentage growth rate of the population. For example, if the population of 10 species increases by 2 individuals per year, the r value will be 20%.
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A car insurance company has determined that 9% of all drivers were involved in a car accident last year. among 14 drivers living on one particular street, 3 were involved in a car accident last year. If 14 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?
a) 0.094.
b) 0.906.
c) 0.126.
d) 0.393.
The probability of getting 3 or more who were involved in a car accident last year is 0.126.
Given 9% of the drivers were involved in a car accident last year.
We have to find the probability of getting 3 or more who were involved in a car accident last year if 14 were selected randomly.
We have to use binomial theorem which is as under:
n[tex]C_{r}p^{r} (1-p)^{n-r}[/tex]
where p is the probability an r is the number of trials.
Probability that 3 or more involved in a car accident last year if 14 are randomly selected=1-[P(X=0)+P(X=1)+P(X=2)]
=1-{[tex]14C_{0}0.9^{0} (0.1)^{14} +14C_{1} (0.9)^{1} (0.1)^{13} +14C_{2} (0.9)^{2} (0.1)^{12}[/tex]}
=1-{1*0.2670+14!/13!*0.9*0.29+14!/2!12!*0.0081*0.2358}
=1-{0.2670+0.3654+0.2358}
=1-0.8682
=0.1318
Among the options given the nearest is 0.126.
Hence the probability that 3 or more are involved in the accident is 0.126.
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