point slope form = y-(-43)=[tex]-\frac{2}{21}[/tex](x-3)
slope intercept form = -[tex]\frac{152}{7}[/tex]=c
What is slope?Finding the ratio of "vertical change" to "horizontal change" between any two unique locations on a line yields the slope. Occasionally, the ratio is written as a quotient (also known as a "rise over run"), which produces the same number for every two unique points on the same line. Negative "rise" refers to a diminishing line. The line could be functional, established by a road surveyor, or depicted in a graphic that represents a road or a roof as a description or a design.
The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope. A line's direction might be either horizontal, ascending, decreasing, or vertical
If a line is rising from left to right, it is increasing. Since m>0, the slope is positive.
If a line decreases from left to right, it is said to be diminishing. The slope is inverse, or m0.
A line has zero slope if it is horizontal. This function has a fixed value.
A line's slope is ambiguous if it is vertical.
Slope= [tex]\frac{x-x1}{y-y1}[/tex]= [tex]\frac{3-5}{-22+43}[/tex]=[tex]\frac{-2}{21}[/tex]
point slope form= y-(-43)=[tex]-\frac{2}{21}[/tex](x-3)
slope intercept formy=mx+c
-22=[tex]-\frac{2}{21}[/tex]*3+c
-22+[tex]\frac{2}{7}[/tex]=c
-[tex]\frac{152}{7}[/tex]=c
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An apartment building has 32 one-bedroom
apartments, 24 two-bedroom apartments,
and 16 three-bedroom
apartments.
How many bedrooms are in the building?
Answer:
128
Step-by-step explanation:
You want the total number of bedrooms in a mix of 1-, 2-, and 3-bedroom apartments.
BedroomsThe total number will be the sum of the products ...
1 × number of 1-bedroom apartments = 1 × 32 = 32
2 × number of 2-bedroom apartments = 2 × 24 = 48
3 × number of 3-bedroom apartments = 3 × 16 = 48
That total is ...
32 +48 +48 = 128
There are 128 bedrooms in the apartment building.
The dash triangle is a dilation image of the solar triangle with a center at the origin. Is a dilation and enlargement or a reduction find the scale factor of the dilation.
Because the scaling factor is a whole number, which is 3, the enlargement of the dashed triangle is a dilatation.
Recall:
Dilation enlarges or shrinks a figure or shape.The original image prior to any reduction or expansion is the image of a dilatation.The new image created following any necessary reduction or enlargement is the scale copy.Any side length of the new image divided by the corresponding side length of the old image gives the scale factor.The dilation is a reduction if the scale factor is a fraction.The dilatation is an enlargement if the scale factor is a whole number.Thus:
For the dashed triangle, measure the separation between the points (2, -2) and (0, -2).
(2, -2) to (0, -2) is separated by 2 units.Using the coordinates (6, -6) and (0, -6) for the solid triangle, calculate the equivalent distance:
(6, -6) and (0, -6) are separated by 6 units.Scale factor = 6/2 = 3
The dilation is an enlargement because the scale factor is a whole number.
In conclusion, the enlarged dashed triangle indicates a dilatation because the scale factor, which is 3, is a whole number.
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What is the answer to # 11?
Answer:
40
Step-by-step explanation:
Go through PEMDAS
Exponents: 4∧0 = 1 and 1³ = 1
Multiply: 4 × 5 = 20 × 2 = 40
Add: 1 + 40 = 41
Subtract: 41 - 1 = 40
Find the value of x
A. x = 20
b. x = 32
c. x = 24
d. x = 28
Using proportions, it is found that the value of x would be 28.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We have been given two triangle, we need to find the value of x.
Then using proportions;
12/(x-7) = 8 / 14
Cross multiplication;
12 (14/8) = x - 7
3 (14/2) = x - 7
21 = x - 7
x = 21 + 7
x = 28
Therefore, the value of x is 28.
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What is the
Range??
Help me out plsss
Answer:
1≤x≤|R+
Step-by-step explanation:
since range is from the y axis
the starting point is 1 UpTo positive real numbers and it doesn't include 0
help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!
Answer:
It would take [tex]2.7[/tex] seconds, correct to 1 decimal place/nearest tenth.
Step-by-step explanation:
Step 1: Understanding the formula
The formula is given as [tex]h=16t^{2}[/tex], where [tex]h[/tex] represents the height, and [tex]t[/tex] represents the time.
Step 2: Substituting and solving
The question asks for the time that would take when the height is [tex]117~\text{feet}[/tex].
So, substitute [tex]117[/tex] for [tex]h[/tex] in the formula, since [tex]h[/tex] denotes the height:
[tex]h=16t^{2}\\117=16t^{2}[/tex]
Now, let's solve the equation to find the time, [tex]t[/tex]:
[tex]117=16t^{2}\\\\\text{Divide by 16 on both sides of the equation:}\\\frac{117}{16}=\frac{16t^{2}}{16}\\\\\text{Simplify:}\\7.3125=t^{2}\\\\\text{Square root both sides of the equation:}\\\sqrt{7.3125}=\sqrt{t^{2}}\\\\\text{Calculate:}\\2.7 \approx t\\\\\text{Rearrange the equation:}\\t\approx2.7[/tex]
So, it takes about [tex]2.7[/tex] seconds to travel [tex]117[/tex] feet, according to the formula.
What is the equation of the line?
does the data give evidence of an association between scoring at least 21 points and the football team winning the game? there is a strong, negative association. there is a strong, positive association. there is a weak, negative association. there is a weak, positive association.
Considering the relative frequencies in this problem, the association between scoring 21 points and winning the game is as follows:
There is a strong, positive association.
What is a relative frequency?The relative frequency of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
From the table given at the end of the answer, we have that when the team scored at least 21 points, an interval composed of 28 games, the team won 25 games and lost only 3, hence the relative frequency of wins when the team scores at least 21 points is of:
25/28 = 0.8929 = 89.29%.
Due to this high frequency of wins, there is a strong and positive association between scoring 21 points and winning the game
What is the missing information?The table with the team's results is given by the image at the end of the answer.
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how many solutions are in 7x-4=-3x+5+10x
Which recursive sequence would sequence 5,-8,5
The recursive sequence that defines 5, -8, 5, is given by:
[tex]a_n = -a_{n-1} - 3[/tex]
In which the first term is of [tex]a_1 = 5[/tex].
What is a recursive sequence?A recursive sequence, in general terms, can be defined as follows:
[tex]a_n = f(a_{n - 1))[/tex]
In which the first term [tex]a_1[/tex] is given.
This rule means that the nth term of the sequence is a function depending on the previous term, the (n-1)th term of the function.
In the context of this problem, the sequence is given as follows:
5, -8, 5.
From the first to the second term, the number changed the signal and was subtracted by 3, and the same is true for the second to third term, as follows:
-5 - 3 = -8.-(-8) - 3 = 8 - 3 = 5.Then the recursive rule for the sequence is given as follows:
[tex]a_n = -a_{n-1} - 3[/tex]
With first term of [tex]a_1 = 5[/tex].
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The difference between the total surface area and curved
surface area of a hemisphere is 154 cm2, find its volume.
If the difference between the total surface area and curved surface area of a hemisphere is 154 cm2, then its volume is 718.66 cm³
What is hemisphere?In general, the term "hemisphere" refers to the lower half of the earth, such as the northern or southern hemispheres. A hemisphere, however, is a 3D figure that is created by splitting a sphere into two equal halves, each with one flat side, and is known as such in geometry.
In everyday life, we encounter a variety of objects that have a hemisphere shape, such as a cherry that is shaped like a hemisphere when cut in half or a grapefruit that has a hemisphere shape when cut in half.
The difference between the total surface area and curved surface area of a hemisphere is 154cm.
Total Surface Area of Hemisphere = 3πr²
And Curved Surface Area of Hemisphere = 2πr²
It is Given that
Total Surface Area of Hemisphere - Curved Surface Area of Hemisphere. = 154.
Substituting the values, we get,
⇒ 3πr² - 2πr² = 154
⇒ πr² = 154
⇒ r² = 154/π
⇒ r² = 154 × (7/22)
⇒ r² = 7 × 7
⇒ r = 7.
Now, lets find the volume which is
Volume of Hemisphere = 2/3πr³
V = 2/3π(7)³
V = 2/3(22)(7)²
V = 2156/3
V = 718.66 cm³
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BRAINLY IF CORRECT!!
In △ A B C , A B = 7 , B C = 12 , and m ∠ A B C = 82 ∘
In △ D E F , D E = 7 , E F = 12 , and m ∠ D E F = ( 2 x − 6 ) ∘
A C > D F.
What is the range of possible values for x?
(a) 44 < x < 180
(b) 3 < x < 44
(c) 0 < x < 44
d) none of these
(e) x > 44
(f) 44 < x < 93
(g) x < 44
3 < x < 44
=============================================================
Explanation:
For triangles ABC and DEF we have these two pairs of congruent sides
AB = DE = 7BC = EF = 12In between sides AB and BC is angle ABC = 82
In between sides DE and EF is angle DEF = 2x-6
Since AC > DF, this must mean angle ABC is larger than angle DEF. This is because the longer a side is, the larger the opposite angle will be.
Therefore, this leads to angle ABC > angle DEF
--------------------------------------------------
This is what the steps will look like
angle ABC > angle DEF
angle DEF < ABC
0 < angle DEF < angle ABC
0 < 2x-6 < 82
0+6 < 2x-6+6 < 82+6
6 < 2x < 88
6/2 < 2x/2 < 88/2
3 < x < 44
x is between 3 and 44, excluding both endpoints.
In a Sports league each team has 36 players and 3 coaches. There are also a number of team assistants. The ratio of team assistants to players is 1/6. What is the ratio of coaches to assistants?
Answer:
1/2
Step-by-step explanation:
We know that each team has the following:
36Players + 3Coaches + ?Assistants = Sports League
We know that the ratio of assistants to players is 1/6, rewrite the equation accordingly:
36Players + 3Coaches + 6Assitants = Sports League
Now find the ratio of coaches to assistants:
3Coaches / 6Assistants = 1/2
HELP ME PLEASE! My exams tmrw can someone explain one of these
Pls answer the question on the image attatched.
Step-by-step explanation:
loga(x) calculates simply the exponent of a needed to get x as result.
so, 5 "to the power of the exponent of 5 needed to get 7" is 7 (we give 5 the exponent that it needs to create 7, so it creates 7).
the same thing with 2, where we give 2 the exponent it needs to create 1/49. so, it creates 1/49.
we get therefore
7 × 1/49 = 7/49 = 1/7
A college has 19 engineering students for every 81 students enrolled. if the college has 750 students, approximately how many are engineering students
The total number of engineering students is 176 approximately among the 750 students enrolled in the college by using the proportionate formula.
It is mentioned here that a college has 19 students of engineering for every 81 students who got enrolled.
Therefore the ratio of engineering students to total number of students is as follows:
No. of engineering students = 19
Total number of students = 81
Ratio = [tex]\frac{19}{81}[/tex]
Now if the total number of students that the college has is 750 then the number of engineering students can be found by using the proportionate formula as the ratio of the engineering to the total students will remain same.
Total number of students = 750
Let the number of engineering students be y
Ratio = [tex]\frac{y}{750}[/tex]
Comparing it with the above ratio and using the proportionate formula,
[tex]\frac{19}{81} = \frac{y}{750}[/tex]
⇒ y = [tex]\frac{19*750}{81}[/tex]
⇒ y = 175.925
So approximately 176 were the engineering students among 750 students enrolled.
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Help please i forgot about this
Whats the product of 3 plus 4
whats 5 times 8
Not sure how to solve this? Any tips are helpful!
Question 12
REASONING Given: 2a²
a
= 72. Conjecture: a = 6. Write a counterexample.
A counterexample to show that 2a^2 = 72 where a = 6 is that a = -6 will still arrive at 72
What is counterexample?This is a term that counters a statement. we can therefore say that counterexample is one that proves a statement to be false.
How to write the counterexamplegiven data
2a² = 72
Conjecture: a = 6
The counterexample is a = -6
substituting a = -6 into the given equation
= 2a²
= 2 * ( -6 )^2
= 2 * ( 36 )
= 72
Since a = -6 gave same answer of 72 as a = 6 then a = -6 is the counterexample
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[3^2 x (189 divided by 9] -30
Step-by-step explanation:
[tex]3 {}^{2} (189 \div 9) - 30 \\ 9 \times 189 \div 9 - 30 \\ 189 \div 1 - 30 \div 1 \\ 189 - 30 \div 1 \\ = 159[/tex]
according to bodmas
Answer:
159
Step-by-step explanation:
Using BODMAS - Bracket Of Division Multiplication Addition Subtraction
Step 1: Bracket
189/9=21
Hence [3^2 x (21)]-30
Step 2:
3^2= 9
Step 3: Calculate within parentheses [9* 21] : 189
9*21=189
Step 4: Open bracket
[189]-30=159
what is the perimeter for a rectangle with a length of 12x - 7 and a width of 5
The perimeter of the rectangle given its dimensions is 24x - 4.
What is the perimeter?A rectangle is a two-dimensional quadrilateral with four right angles that sum up to 360 degrees. A rectangle has two diagonals of equal length that bisect each other at right angles.
The perimeter of rectangle is the sum of the lengths of the four sides of the rectangle.
Perimeter of a rectangle = 2 x (length + width)
2 x [(12x - 7) + 5)
2 x (12x - 2)
24x - 4
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find the equation of the line
Answer:
1 is 2 and 2 is 2
Step-by-step explanation:
Two pools are being filled with water. To start, the first pool had 728 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 23 liters per minute. Water is being added to the second pool at a rate of 37 liters per minute.
Let x be the number of minutes water has been added.
(a)
For each pool, write an expression for the amount of water in the pool after x minutes.
Amount of water in the first pool (in liters) = ____
Amount of water in the second pool (in liters) = ____
(b)
Write an equation to show when the two pools would have the same amount of water.
______________
Two pools are being filled with water. To start, the first pool had 728 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 23 liters per minute. Water is being added to the second pool at a rate of 37 liters per minute.
Let x be the number of minutes water has been added.
(a)
For each pool, write an expression for the amount of water in the pool after x minutes.
Amount of water in the first pool (in liters) = 23x + 728
Amount of water in the second pool (in liters) = 37x
(b)
Write an equation to show when the two pools would have the same amount of water.
this is when:
23x + 728 = 37x
subtract 23x from both sides:
23x + 728 - 23x = 37x - 23x
728 = 14x
divide both sides by 14:
728/14 = 14x/14
x = 52
So, pools are equal after 52 minutes.
Guys i need help is this right?
The range of the function in this situation as required in the task content is; Choice D; 0 ≤ y ≤ 3.
How to determine the range of a function?It follows from the task content that the range of the function described by the situation is to be determined.
The set of all possible output values of a function, otherwise termed the dependent variable, y is called the Range.
It follows that since the distance he has remaining, y is a function of how long he has been riding the bike, x and it's said that; the boy lives 3 miles from the library; the range of the function described is; Choice D ; 0 ≤ y ≤ 3.
Please Note: The term, domain encompasses the set of all possible input values, otherwise termed the independent variable, x.
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multiple choice in a single football game, a team scored 14 points from touchdowns and made x field goals, which are worth three points each. the team scored 23 points. how many field goals did the team make? a. 2 b. 3 c. 4 d. 5
The number of field goals the team made in the game is equal to b. 3
The number of field goals the team made can be determined using an algebraic expression. An algebraic expression can be defined as an expression or equation that consists of both letters and numbers in it.
If the team scored 14 points from touchdowns and made x goals which are worth three points each, then an algebraic expression can be given as;
3(x) + 14 = 23
Solving for x;
3x = 23 - 14
3x = 9
x = 9 ÷ 3
x = 3
Hence, the team made a total of 3 field goals that are worth three points each.
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Describe how to solve the following:
a. 2√25
b. √150
Answer:
10 and 5[tex]\sqrt{6}[/tex]
Step-by-step explanation:
these cannot be solved as they are not equations, but can be simplified
using the rule of radicals
[tex]\sqrt{ab}[/tex] ⇔ [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex]
then
2[tex]\sqrt{25}[/tex] = 2 × 5 = 10
[tex]\sqrt{150}[/tex]
= [tex]\sqrt{25(6)}[/tex]
= [tex]\sqrt{25}[/tex] × [tex]\sqrt{6}[/tex]
= 5[tex]\sqrt{6}[/tex]
PLEASE HELP I NEED THIS VERY VERY SOON!!!!
Tim and Jim leave Chicago traveling in opposite
directions. Jim travels 65 mph and Tim travels
63 mph. In how many hours will they be 1056
miles apart?
The formula for time, t = d/s which means time exists equivalent to distance divided by speed.
The times taken to travel 441 miles apart exists 8.25 hours
What is the time formula?Time can be defined as the dimension based on which the evolution of any system takes place. It can be measured in terms of seconds, minutes, hours, days, weeks, months, and years.
The formula for time, t = d/s which means time exists equivalent to distance divided by speed.
Given: Train running in the opposite direction
Speed of one train (S1) = 65 mph
Speed of one train (S2)= 63 mph
Distance to be covered = 1056 miles
Train exists running in the opposite direction, so their relative speed = (S1 + S2)
Relative speed = (65 + 63) = 128 mph
Now, time is taken to travel 1056 miles apart
Time = Distance / relative speed
Time = 1056/128 = 8.25 hours
Therefore, the times taken to travel 441 miles apart exists 8.25 hours
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Which number is closest to √30 ?
5.4
6.2
6.1
5.8
Answer: 5.4
Step-by-step explanation:
[tex]29.16 < 30 < 30.25 \implies 5.4 < \sqrt{30} < 5.5[/tex]
The volume of this cube is 729 cubic yards. What is the value of y?
()) y =
yards
Corinne made $60,400 last year. She received a 2% annual raise. What will her new salary be for the upcoming year?
Answer:
61608 i believe
Step-by-step explanation:
2% of 60400= 1208
60400+1208=61608