Answer:
The equation for the line which passes through the points given as (a, b) and (a, b+1), is x=a, which represents a vertical line.
Step-by-step explanation:
It is given that a line passes through the points whose coordinates are (a, b) and (a, b+1).
It is asked to find the linear equation which passes through the given points.
To do so, first determine the slope of the given line using the coordinates and the formula for the slope. Accordingly, proceed to find the equation of the given line.
Step 1 of 2
Determine the slope of the line.
The points through which the line passes are given as (a, b) and (a, b+1). Next, the formula for the slope is given as,
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute b+1&b for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and a&a for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]m=\frac{b+1-b}{a-a}$\\ $m=\frac{1}{0}$[/tex]
b+1. So the equation of the line cannot be found using the general point-slope form equation.
Step 2 of 2
Write the equation of the line.
So, by definition, the line that passes through the given points is a vertical line. Now, as its x- coordinate is a, so the equation of the line is given as x=a.
Help me please!
a = 3, b = 5, and c = 7. What is m&Bº to the nearest tenth?
Answer: m∡B°=38,2°.
Step-by-step explanation:
a=3, b=5, c=7 ∡B°=?
[tex]b^2=a^2+c^2-2*a*ccosB^0\\2*a*c*cosB^0=a^2+c^2-b^2\\cosB^0=\frac{a^2+c^2-b^2}{2*a*c} \\cosB^0=\frac{3^2+7^2-5^2}{2*3*7} \\cosB^0=\frac{9+49-25}{2*3*7} \\cosB^0=\frac{33}{42} \\cosB^0=\frac{11}{14}\\[/tex]
m∡B°=arccos[tex](\frac{11}{14})[/tex]
m∡B°≈38,2°.
Good luck!
Is this right or wrong
Answer:
∠C and ∠F are right angles
Step-by-step explanation:
To prove that two triangles are congruent using HL, one must have:
a right angle congruent,a leg congruent, and the hypotenuse (the side across from the right angle) congruent.For this problem, there are two sides of the triangle already congruent: one could be the hypotenuse (if the right angle were across from it), and the other congruent side could be a leg. So, if we can prove either that angles C & F are right angles, or that angles A & D are right angles, that would be enough to use HL congruence.
Hence, from the answer choices provided, proving that angle C and angle F are both right angles would be sufficient to prove the triangles are congruent via HL congruence.
Side note: Proving angles B and E would not be enough to use HL congruence, because the hypotenuse is always across from the right angle. So, if angle B were a right angle, it would mean that side AC was the hypotenuse (which hadn't yet been proven or stated to be congruent).
While not enough to prove triangle congruence via HL, if angle B and E were congruent at all (right angles or not), it would be enough to prove that the triangles were congruent by SAS (side-angle-side) because it would have proven that two sides and the included angle were congruent.
Solve for m. 10m = 1
m = 0
m = 1
m = 2
m = 3
Answer:
wouldn't it be 0.1
Step-by-step explanation:
If geometry symbol represented as small triangle with three sides. abc geometry congruent symbol represented as two small horizontal parallel lines and a horizontal symbol s. geometry symbol represented as small triangle with three sides. dec, what is the value of x?
The value of x in the congruent triangles abc and dec is 1
How to determine the value x?The question implies that the triangles abc and dec are congruent triangles.
The congruent sides are:
ab = de
bc = ce = 4
ac = cd = 5
The congruent side ab = de implies that:
4x - 1 = x + 2
Collect like terms
4x - x = 2 + 1
Evaluate the like terms
3x = 3
Divide through by 3
x = 1
Hence, the value of x is 1
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Complete question
Two triangles, abc and cde, share a common vertex c on a grid. in triangle abc, side ab is 4x - 1, side bc is 4, side ac is 5. in triangle cde, side cd is 5, side de is x + 2, side ce is 4. If Δabc ≅ Δdec, what is the value of x? a. x = 8 b. x = 5 c. x = 4 d. x = 1 e. x = 2
IN
A graph of two functions is shown below:
g(x)
f(x)
Ox=1
Which of the following is an approximate solution for f(x) = g(x)?
Ox=-1
Ox=-4
Ox=2
62.5
45
37.5
30
225
15
-15
225-
-30
Hello,
Answer: We have f(x) = g(x) when x ≈ 1
(a) x = 1, is an approximate solution for f(x) = g(x).
Here, we have,
given that,
A graph of two functions is shown
f(x) and, g(x)
now, we have,
The graph has two functions, which are f(x) and g(x) and a graph.
In the graph, we can follow their intersections.
Those would be the parts of the line that would make the functions to have the same value.
The first intersection is really close to 1,
and second is very unclear, most likely beyond -2.5.
Since the highest number is 1 and the intersection is very close to 1,
we have to go with the approximate answer.
We have f(x) = g(x) when x ≈ 1.
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Help please !!
The graph of the invertible function f is shown on the grid below.
Answer:
4
Step-by-step explanation:
→ We go up the y axis to 6 and read of the x coordinate which is 4. This is because an inverse function does the the opposite i.e. if f ( x ) = y
f⁻¹ ( y ) = x.
TODAY, Kyle has 11 pounds to lose to get to his goal weight. Tuesday he was 196 lbs. TODAY, he is down 3 lbs.
What is Kyle’s weight today?
What is Kyle’s goal weight?
Select the correct answer.
Consider the following equation.
4(-) + 5 = 3 + 4
Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a starting point.
PLEASE HELP BEFORE TOMORROW MORNING!! I’ll give Brainiest answer!!
The solution to the graph given is 7/16.
How to illustrate the graph?It should be noted that a graph is used to show the relationship between the variables illustrated.
Here, the successive approximation is used to solve equations.
This is done by the comparison to the sequence of the known quantities.
Here, the equation given is 4(-)x + 5 = 3^x + 4. solution to the graph given is 7/16. This is based on the graph given.
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Dalinda spins a spinner 60 times. the table shows her data.
spinner
results
color spins
red
10
blue
30
yellow
15
green
5
dalinda will spin one more time,
based on her data, what is the probability that the pointer will land on blue?
od. 110
o e
10 a 1
o b. 1 / 3
o c. 1 /
The answer is 1/2 .
What is probability ?The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes. The chance that a given event will occur. The number of ways of achieving success. the total number of possible outcomes.In given question ,
Dalinda spins a spinner = 60 times.
blue = 30
The probability that the pointer will land on blue = 30 / 60 ⇒ 1/2
Therefore, the answer is 1/2 .
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Which system of equations can be used to find the roots of the equation 12 x cubed minus 5 x = 2 x squared x 6?
The system of equations used to find roots of the equation is y=12x³-5x and y=2x²+x+6.
Given the equation is 12x³-5x=2x²+x+6.
A set of equations containing one or more variables is called a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations.
Firstly, separate the given equation into two parts by equating the left-hand side and right-hand side with 0, we get
12x³-5x=0
2x²+x+6=0
Now, to make a system of equations replace 0 with y as we know that system of equations contains two variables, we get
12x³-5x=y
2x²+x+6=y
Hence, the system of equations used to find the roots of the equation 12x³-5x=2x²+x+6 is y=12x³-5x and y=2x²+x+6.
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help me please!!! 50 points
I am unfortunately not too sure about this, I have not heard of a proportional equation before even after getting my degree, because an equation usually isn't proportional, only expressions are and there are usually 2 terms.
Here's my best attempt. The first equation isn't proportional since y is inversely proportional to the 7 in the denominator. The second is proportional, and the k constant is 10.
I cannot provide any further explanations.
Let me know if this was helpful!
Answer: Since y is inversely proportional to the 7 in the denominator, the first equation cannot be a proportional expression. The k constant is 10 and the second is proportional.
Step-by-step explanation:
PLS HELP I DON’T UNDERSTAND
The question asks for the probability that a marble is NOT YELLOW
Total Marbles: orange+yellow+blue=7+3+2=12
We need to count all marbles except yellow:
orange+blue=7+2=9
Now to find the probability that is NOT YELLOW:
[tex]\frac{All Marbles Except Yellow}{Total Marbles}[/tex]= [tex]\frac{9}{12} = \frac{3}{4}[/tex]
Answer is 3/4
Hope it helps!
Alex needs to catch a train. The train arrives randomly some time between $1:00$ and $2:00$, waits for $10$ minutes, and then leaves. If Alex also arrives randomly between $1:00$ and $2:00$, what is the probability that the train will be there when Alex arrives
The probability that the train will be there when Alex arrives is 5/18
If Alex arrives at any time after 1.20pm the chances that train will be there is 1/3.
However if alex arrives at 1.00pm exactly there is no chance the train will be arrive there.
The probability that the train will be there increase linearly to 1/3 as alex's arrival time moves from 1.00pm to 1.20pm.
By arranging the probabilities over the first 20 minutes to get a 1/6 chance the train will be there if alex arrives between 1.00pm to 1.20pm
we get the final answer by
=1/3( 1/6 + 1/3 + 1/3)
=5/18
So, the probability that the train will be there when Alex arrives is 5/18
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A (not necessarily convex) 11-sided polygon can have at most how many reflex interior angles?
The value for each interior angle in the polygon will be 147.27°.
How to calculate the interior angles?The total angles in the 11 sided polygon will be:
= (n - 2) × 180
= (11 - 2) × 180
= 9 × 180°
= 1620°
Each angle will be:
= 1620°/11
= 147.27°
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3
Writing Linear Equations Using Similar Triangles
y
2
Intro
(xy)
Use similar triangles to determine the equation of the
line with a slope of 2/3 that passes through the point (0,
3).
What is the ratio of the rise to the run in the smaller
triangle in the diagram? |
What is the ratio of the rise to the run in the larger
triangle in the diagram?
What is the equation of the line in slope-intercept form?
Done
The solutions are given below:
1. 3y- 9 = 2x
2. 2/3.
3. y/x
4. y = (2/3)x + 3
What is equation of line?The equation of a line with one given point (x1, y1) is (y - y1) = m(x - x1). Here m is the slope of the line.
The complete question is:
On a coordinate plane, a line goes through (0, 3) and (x, y). A triangle has a rise of 2 and run of 3. A larger triangle has a rise of 5 and run of 7.
Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3).
What is the ratio of the rise to the run in the smaller triangle in the diagram?
What is the ratio of the rise to the run in the larger triangle in the diagram?
What is the equation of the line in slope-intercept form?
1. slope= 2/3
coordinates= (0, 3)
y-y1 = m(x-x1)
y-3 = 2/3(x-0)
y-3 = 2/3x
3y- 9 = 2x
2. The ratio of the rise to the run in the smaller triangle in the diagram
is y/x = 2/3
3. The ratio of the rise to the run in the larger triangle = y/x
4. The equation of the line in slope-intercept form is given by:
y = (2/3)x + 3
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Find the sum of a third of (a+b) and a fifth of (a+b)
Answer:
Step-by-step explanation:
X
-3
-2
Intro
-1
0
1
2
3
f(x)
-15
0
3
0
-3
O
15
Predict which statements are true about the intervals of
the continuous function. Check all that apply.
Of(x) > 0 over the interval (-3).
Of(x) ≤0 over the interval [0, 2].
Of(x) <0 over the interval (-1, 1).
Of(x) > 0 over the interval (-2, 0).
f(x) ≥ 0 over the interval [2, ..).
Done
Answer: B, D, E
Step-by-step explanation:
Statement 1 cannot be true because f(1)<0.
Statement 2 might be true.
Statement 3 cannot be true because if f is continuous, then for some value between -1 and 0, f(x) is positive by the Intermediate Value Theorem.
Statement 4 might be true.
Statement 5 might be true
GEOMETRY)
What is the equation of a circle having radius 8 and center (2,-7)?
(Picture is below) Thank you!
Answer:
(x - 2)² + (y + 7)² = 64
(fourth option listed / option D)
Step-by-step explanation:
as you likely know, the equation of a circle (centered at origin) is x²+y²=r²
now, let's say we want to write this using the center (the origin), it could look like this:
(x - 0)² + (y - 0)² = r²
(the center is 0,0)
[we write this in parentheses when we are shifting the location of a point--similar to when we move a line on a graph]
We can use this for any center, and we write our circle equation as:
(x - h)² + (y - k)² = r²
(h, k) is the center
So, let's apply the information we know
our (h, k) is (2, -7)
so let's fill that in:
(x - h)² + (y - k)² = r²
(x - 2)² + (y - -7)² = r² (simplify)
(x - 2)² + (y + 7)² = r²
now, we also know that our "r" (r is the radius) is 8, so let's fill that in too:
(x - 2)² + (y + 7)² = r²
(x - 2)² + (y + 7)² = 8² (simplify)
(x - 2)² + (y + 7)² = 64
So, we have found the equation of our circle to be:
(x - 2)² + (y + 7)² = 64
hope this helps! (and hope this makes sense) have a lovely day :)
80% of people those who purchase pet insurance are women. If the owners of 9 pet insurance are randomly selected, then find the probability that exactly 6 out of them are women. Find the quartiles of the standard normal distribution.
The probability that exactly 6 out of them are women is 0.176
According to the statement
Number of selected pet owner randomly is 9. So, Here in this case n=9.(number of randomly selected owners).
Number for which have to find the probability is 6. So, Here in this case x=6.
Find the probability by a use of BINOMIAL THEOREM
So, n!/((n-x)!*x!) = 9!/((9-6)!*6!) = 84
Now, find out the probability of success p and probability of failure (1-p)=q.
From here we get p = 0.8 and q= 0.2
Now, use p^x = (0.8)^6 = 0.2621
Then use q^(n-x) = (0.2)^(9-6) = 0.008
Now, Multiply the results obtained to get the probability is
84*0.2621*0.008 = 0.176
So, The probability that exactly 6 out of them are women is 0.176
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50 more points
sdadadada
Switch the variable x and y with each other. Then the correct option is B.
What is inverse of a function?Let the function will be
f: X → Y
Then the inverse function will be
f⁻¹: Y → X
The function is given below.
f(x) = 3x – 10
Then the inverse function of the f(x) will be
Put y in place of f(x).
x = 3y – 10
3y = x + 10
y = (x + 10) / 3
Switch the variable x and y with each other.
Then the correct option is B.
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How much water should be added to a 15 gallon solution of 35% hydrogen peroxide to create an 8% solution? how many gallons would there be of the 8% solution?
15 gallons of 35% peroxide solution contains 0.35 × 15 = 5.25 gallons of hydrogen peroxide. The rest of the volume is made up of 15 - 5.25 = 9.75 gallons of water.
If we add [tex]x[/tex] gallons of water to the solution, the amount of hyrdrogen peroxide in the solution stays the same, but the volume of water increases to [tex]9.75+x[/tex] gallons, and the total volume increases to [tex]15+x[/tex] gallons.
To get a concentration of 8% in this diluted solution, we add [tex]x[/tex] gallons of water such that
[tex]\dfrac{5.25}{15+x} = 0.08[/tex]
Solve for [tex]x[/tex].
[tex]5.25 = 0.08 (15 + x)[/tex]
[tex]5.25 = 1.2 + 0.08x[/tex]
[tex]0.08x = 4.05[/tex]
[tex]x = 50.625[/tex]
To get the desired concentration, one must add 50.625 gallons of water, and one will end up with a total volume of 65.625 gallons of solution.
Tim had 15 dollars. Paul had 6 dollars more than Tim. Rick had double Tim’s money. How much did they have ALTOGETHER?
Answer:
66 dollars
Step-by-step explanation:
15+6=22
15×2=30
15+22+30=66
Answer:
Tim had 15 dollars. Paul had 6 dollars more than Tim. Rick had double Tim’s money. How much did they have ALTOGETHER is 66 dollars.
Step-by-step explanation:
→ Is know :
Tim's money = 15 dolars Paul's money = 15 dolars + 6 dollarsRick's money = 2 × 15 dolars→ Asked :
How much did they have ALTOGETHER ?
→ Solution :
[tex] \bf{x =Tim's \: \: money + Paul's \: \: money + Rick's \: \: money }[/tex]
[tex]\bf{x =15 + (15 + 6) + (2 \times 15) }[/tex]
[tex]\bf{x =15 + 21 + 30 }[/tex]
[tex]\bf{x =36 + 30 }[/tex]
[tex]\bf{x =66 \: \: dollars }[/tex]
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VERBAL
1. Explain how to find the input variable in a word problem that uses a linear function.
Answer:
The independent variables in most cases is input variable. That is a value that does not depend on any other value and it can change independently.
Step-by-step explanation:
In the question, it is given that a problem uses an input variable.It is required to explain how to find the input variable in a word problem that uses a linear function.In order to find the input variable in a world problem, seek for the independent variable.That is a value that does not depend on any other value and it can change independently.Some other values change based on that value. In these types of functions, this value is mostly marked as x.For the training adaptation of maximum strength, what is the recommended number of repetitions per set? 1 to 5 repetitions 1 to 6 repetitions More than 15 repetitions 6 to 12 repetitions
For the training adaptation of maximum strength, 1 to 5 repetitions per set is recommended.
The one-repetition maximum test, also called a one-rep max or 1RM, is used to find out the heaviest weight you can lift just once.
If Maximal strength is desired, it is best achieved by performing repetitions at 85 to 100 % of the one-repetition maximum (1RM).
Formula to find the repetition is
weight used x (reps done x 0.33 + 1) = 1RM
so,
Reps done = {{1RM/weight used} - 1}/ 0.33
By this find the no of reps are recommended for maximum strength.
The maximum strength is achieved by doing the number of reps by 85 to 100% of the value of 1 RM.
So,
For the training adaptation of maximum strength, 1 to 5 repetitions per set is recommended.
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25) lan bikes 18 mph for 15 miles. Which is true? a. lan rode exactly 1 hour b. lan rode more than 1 hour C. lan rode less than 1 hour
Answer:
C. Ian rode less than 1 hour
Step-by-step explanation:
It never hurts to think about what the problem statement is telling you. Ian rode at a speed that would take him 18 miles in 1 hour.
InterpretationClearly, Ian would pass the 15-mile mark in a 1-hour ride before an hour had elapsed. If he only rode 15 miles, he rode less than 1 hour.
The actual time Ian rode is given by the relation between speed, time, and distance.
time = distance/speed
time = (15 mi)/(18 mi/h) = (15/18) h = 5/6 h
Ian's riding time was 5/6 of an hour, which is less than 1 hour.
can you please solve 2x+29+3x - 4
Answer:
5x + 25
Step-by-step explanation:
2x+29+3x+4
Step 1: Arrange it:- 2x+3x+29-4
Step 2:- Add and Subtract the terms:- 5x + 25
HOPE IT HELPS!
Hey there!
EQUATION:
2x + 29 + 3x - 4
COMBINE the LIKE TERMS
(2x + 3x) + (29 - 4)
2x + 3x + 29 - 4
SIMPLIFY IT!
5x + 25
Therefore, your answer should be:
5x + 25
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
(Look at picture, not this) 4. Use the following equation to perform the operations below: y = (²+5 ÷ (2+3)(2-2))-21/2₂2 4. Use the following equation to perform the operations below : y = ( ² + 5 ÷ ( 2 + 3 ) ( 2-2 ) ) - 21 / 2₂2
Thank you!
The solutions when y = 0 are x = -4.796 and x = 4.796
The graph of the functionThe function is given as:
[tex]y = (\frac{x + 5}{x + 1} \div \frac{(x + 3)(x - 2)}{(x -4)(x + 1)})- \frac{1}{x - 2}[/tex]
See attachment for the graph of the function
The vertical asymptoteWhen the function is simplified, we have:
(x +3)(x -2) at the denominator of one of the terms
Set this factor to 0
(x +3)(x -2) = 0
Expand
x + 3 = 0 and x -2 = 0
Solve for x
x = -3 and x = 2
Hence, the vertical asymptotes are x = -3 and x = 2
The feature at x = -1The feature at x = -1 is a hole and, not a vertical asymptote.
This is so because the absolute value of -1 is less than the absolute values of the vertical asymptotes at x = -3 and x = 2
The solution when y = 0From the attached graph, we have:
x = -4.796 and x = 4.796 when y = 0
Hence, the solutions when y = 0 are x = -4.796 and x = 4.796
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Two points have the coordinates P (6, -3,9) and Q (3, -6, -3). A point R divides line PQ internally in the ratio 1:2. The position vectors of P, Q and Rare p, q and r respectively.
(a) Express the position vector of p and q.
i. In terms of p and q.
ii. In terms of i, j and k
(b) Hence state the coordinates of R.
(a) i. See comment...
(a) ii. We have
[tex]\vec p = 6\,\vec\imath - 3\,\vec\jmath + 9\,\vec k[/tex]
and
[tex]\vec q = 3\,\vec\imath - 6\,\vec\jmath - 3\,\vec k[/tex]
(b) We can parameterize the line segment from P to Q by the vector function
[tex]\vec r(t) = (1-t) \vec p + t \vec q = (6-3t) \, \vec\imath + (-3-3t) \,\vec\jmath + (9-6t) \,\vec k[/tex]
with [tex]0\le t\le1[/tex]. The point R is located 1/3 of the way along this line segment, i.e. at [tex]t=\frac13[/tex], so its position vector is
[tex]\vec r\left(\dfrac13\right) = 5\,\vec\imath -4\,\vec\jmath + 7\,\vec k[/tex]
and hence its coordinates are [tex]\boxed{(5,-4,7)}[/tex].
Can someone help me out with this geometry problems? And explain how u got the answers, it’s urgent
Answer:
Step-by-step explanation:
One-third of the class grew peas, one-third grew carrots, and one-third grew beans. The class consisted of 63 students of which five-sevenths were girls. The teacher chose the three groups to be as equal in their boy-girl composition as possible. How many boys and girls were assigned to each team?
The number of boys and girls assigned to each team is 6 and 15 respectively.
FractionNumber of students in class = 63 Number of students who grows peas = 1/3 × 63= 63/3
= 21 students
Number of students who grows carrots = 21Number of students who grows beans = 21Number of girls = 5/7 × 63
= 315/7
Number of girls = 45 students
Number of boys = 63 - 45 = 18 students
If the three groups have equal composition of boys and girls, then,
Number of boys and girls in each group is 6 and 15 respectively.
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