[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the slope of the line passing through the point (1,2) and (5,4)
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
Formula used, here [tex]\bf{\dfrac{y2-y1}{x2-x1}[/tex]
_______________________________________________________
[tex]\bf{\dfrac{4-2}{5-1}[/tex] | simplify
[tex]\bf{\dfrac{2}{4}[/tex] | reduce
[tex]\bf{\dfrac{1}{2}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Slope:\dfrac{1}{2}[/tex]
[tex]\boxed{\bf{aesthetic\not101}}[/tex]
Answer:
1/2
Step-by-step explanation:
Subtract the second point on the you axis and
A horse holds the all time record for running a 2 kilometer race in 1 min and 59.4 sec. which conversions are necessary to find the horses average speed for the race in miles per hour?
To calculate the average speed of the horse in miles per hour, holding the all-time record for running a 2-kilometer race in 1 min and 59.4 sec, we do the necessary conversions over distance from kilometers to miles and over time from minutes and seconds to hours.
The average speed thus calculated is 393.2722 miles per hour.
The average speed of any object is the ratio of the total distance the object travels, and the total time taken by the object to cover that distance.
Thus, Average speed = Total Distance/Time taken.
In the question, we are informed that a horse holds the all-time record for running a 2-kilometer race in 1 min and 59.4 sec.
We are asked for the necessary conversions required to calculate the average speed of the horse for the race in miles per hour.
The necessary conversions that will be required will be:
Distance: 2 kilometers to miles.
Time: 1 minute 59.4 secs to hours.
To convert from kilometers to miles, we follow the conversion rate:
1 kilometer = 0.621371 miles.
Thus, distance = 2 kilometers = 2 * 0.621371 miles = 1.24274 miles.
For the time, we first convert seconds to time, using the conversion rate:
1 second = 1/60 minutes,
Therefore, 59.4 seconds = 59.4/60 minutes = 0.99 minutes.
Thus, the total time = 1.99 minutes.
To convert from minutes to hours, we follow the conversion rate:
1 minutes= 1/60 hours.
Thus, time = 1.99 minutes = 1.99/60 hours = 0.03316 hours.
Thus, the average speed of the horse = Distance/Time = 1.24274/0.003316 miles per hour = 393.2722 miles per hour.
Thus, to calculate the average speed of the horse in miles per hour, holding the all-time record for running a 2-kilometer race in 1 min and 59.4 sec, we do the necessary conversions over distance from kilometers to miles and over time from minutes and seconds to hours.
The average speed thus calculated is 393.2722 miles per hour.
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HELLPPPPPPPP !!!!!!???
Answer:
C
Step-by-step explanation:
12 /13 is definitely less than 36/30 because 36/30 = 1 1/5
solve this trigonometry question, please by an easy method.
And
sin39=6/yy=6/sin39y=9.5Answer:
x = 7.41 (nearest hundredth)
y = 9.53 (nearest hundredth)
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)From inspection of the triangle:
[tex]\theta[/tex] = 39°O = 6A = xH = yTo find x, use the tan trigonometric ratio:
[tex]\implies \tan 39^{\circ}=\dfrac{6}{x}[/tex]
[tex]\implies x=\dfrac{6}{\tan 39^{\circ}}[/tex]
[tex]\implies x=7.409382939...[/tex]
Therefore, x = 7.41 (nearest hundredth)
To find y, use the sin trigonometric ratio:
[tex]\implies \sin 39^{\circ}=\dfrac{6}{y}[/tex]
[tex]\implies y=\dfrac{6}{\sin39^{\circ}}[/tex]
[tex]\implies y=9.534094374...[/tex]
Therefore, y = 9.53 (nearest hundredth)
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This problem is lowkey tricky. Can someone help me out
Answer:
x = 10
Step-by-step explanation:
Proof: If a line is parallel to one side of the triangle, then it divides the other two sides proportionally.
6/9 = x/15
9x = 90
x = 10
Tina spent a total of $14.90 on 4 identical notebooks and 3 identical pencils. She
had some money left. If she bought another identical pencil, she would have $0.30
left. If she bought another identical notebook instead, she will be short of $1.50.
How much more does a notebook cost than a pencil?
$14.90 spent with the amount left for an extra pencil or notebook being $0.30 or $1.50 short respectively indicates that a notebook costs $1.8 more than a pencil.
Which method can be used to calculate the difference in costs?Let x represent the cost of a notebook and let y represent the cost of a pencil. The following equations can be obtained;
4•x + 3•y = 14.9...(1)
Let a represent the total money Tina has, which gives;
4•x + 4•y = a - 0.3...(2)
5•x + 3•y = a + 1.5...(3)
Subtracting equation (2) from equation (3) gives;
5•x - 4•x + 3•y - 4•y = a - a + 1.5 - (-0.3) = 1.8
Which gives;
x - y = 1.8...(4) From the above, we have that the difference between the cost of a notebook and pencil is 1.8Multiplying equation (4) by 4 and subtracting the result to equation (1) gives;
4 × (x - y) = 4 × 1.8 = 7.2
4•x - 4•y = 7.2
4•x - 4•x + 3•y - (-4•y) = 14.9 - 7.2 = 7.7
7•y = 7.7
y = 7.7 ÷ 7 = 1.1The cost of a pencil, y = $1.1x - y = 1.8
x = 1.8 + 1.1 = 2.9
Cost of a notebook, x = $2.9The difference between the cost of a notebook and the cost of a pencil is therefore;
x - y = $2.9 - $1.1 = $1.8
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HELP ASAP
What is the solution to the inequality below?
12+x23(x-6)
OA. x≤ 12
OB. x≤ 5
OC. x≤ 15
OD. x≤9
The solution to the inequality is x ≤ 15
How to solve the inequality?The inequality is given as:
12 + x ≥ 3(x-6)
Open the bracket
12 + x ≥ 3x - 18
Evaluate the like terms
-2x ≥ -30
Divide by -2
x ≤ 15
Hence, the solution to the inequality is x ≤ 15
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Write the ratio of sin X and cos X
The ratio of sin X and cos X are as follows;
sin X = √119 / 12
cos X = 5 / 12
How to find the sides of right angle triangle?Right angle triangle has one of its angle as 90 degrees. The side and angles can be found using trigonometric ratios.
Therefore,
sin X = opposite / hypotenuse
sin X = √119 / 12
Therefore,
cos X = adjacent / hypotenuse
cos X = 5 / 12
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(1) Triangle ABC is an isosceles triangle.
Find the altitude h.
B
45°
Step-by-step explanation:
45+45
90
I guess is the answer
Plis help! Will give brainliest!
Answer: 7) Step 1 8) Step
Step-by-step explanation:
The answer to 7 is 11. The error starts in step 1, as you can see youre supposed to do 8 divided by 2 plus 3 times 3 minus 2, instead it seems like 3+3 were added instead of becoming 9 thus the answer becomes 7.
The answer to 8 is also 11. 18-14/2 is 11.
can someone please help me
The answer is [tex]11c^3[/tex].
The cost of a 6 ounce can of tomato paste is 29
cents. A 16 ounce can sells for 65 cents.
Which is the better deal?
Answer:
16 ounce can sells for 85 cents
Step-by-step explanation:
29cents / 6 ounce = 4.833cents/ounce
65cents / 16 ounce = 4.0625cents/ounce
4.0625 < 4.833
then:
the better deal is:
16 ounces per 65 cents
Evaluate the following expression. -8 \times (-10 + (-7))−8×(−10+(−7))minus, 8, times, left parenthesis, minus, 10, plus, left parenthesis, minus, 7, right parenthesis, right parenthesis
The value of the given expression is 136
Simplifying an expressionFrom the question, we are to evaluate the give expression
The given expression is
−8×(−10+(−7))
The expression can be simplified as follows
−8×(−10+(−7))
−8×(−10−7)
−8×(−17)
= 136
Hence, the value of the given expression is 136
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A quadratic sequence is defined as:2;12;28;50
Calculate the first difference between Tn and Tn-1 where Tn= 688
The first difference between Tn and Tn-1 where Tn= 688 is 88 if the quadratic sequence is defined as:2;12;28;50
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
The quadratic sequence:
2, 12, 28, 50
a + b + c = 2
10, 16, 22 (first difference)
3a + b = 10
6, 6 (second difference)
2a = 6
a = 3
b = 1
c = -2
Tterm:
T(n) = 3n² + n - 2 = 688 (given)
After solving the quadratic equation:
n = 15, n = -46/3(n cannot be nagatve)
n = 15
n - 1 = 14
T(14) = 600
T(n) - T(n-1) = 688 - 600 = 88
Thus, the first difference between Tn and Tn-1 where Tn= 688 is 88 if the quadratic sequence is defined as:2;12;28;50
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Step 1: Place the graph paper in landscape orientation. Measure from the top left hand corner 6 inches right and 5 inches down. This will be your starting point for
your diagram.
Step 2: Using a ruler and index card/protractor create an isosceles Right triangle. Drawing the triangles legs 1 inch straight up from the starting point and 1 inch to the
right of the starting point. Connect the endpoints of the two segments to create your right isosceles triangle.
Step 3: On a separate piece of paper, use the Pythagorean Theorem to calculate the length of the hypotenuse. You only need to do this for the first 8 if you discover a
pattern.
Step 4: Using your original Right triangle, add another leg measuring 1 inch and right angle to the hypotenuse of your original Right triangle. Connect the endpoints
to form a new hypotenuse for your new Right triangle.
Step 5: Show the calculations to find the length of the new hypotenuse.
Step 6: Continue to repeat this process of connecting and drawing new triangles with a side length of 1 inch, using the previous hypotenuse as the other side. Draw
triangles until you are able to measure the square root of 17. You must show all calculations (Step 3) on a separate piece of paper.
T
How to determine the hypotenuse?Step 1 and 2: Draw an isosceles right triangle
See attachment (figure 1) for this triangle
The legs of this triangle have a length of 1 inch
Step 3: The hypotenuse
This is calculated using the following Pythagoras theorem
[tex]h^2 = 1^2 + 1^2[/tex]
This gives
[tex]h = \sqrt 2[/tex]
Step 4: Draw another isosceles right triangle
Add 1 inch to one of the legs
See attachment (figure 2) for this triangle
The legs of this triangle have lengths of 1 inch and 2 inches, respectively
This hypotenuse is calculated using the following Pythagoras theorem
[tex]h^2 = 2^2 + 1^2[/tex]
This gives
[tex]h = \sqrt 5[/tex]
Step 5: Draw another isosceles right triangle
Add 1 inch to one of the legs
See attachment (figure 3) for this triangle
The legs of this triangle have lengths of 1 inch and 3 inches, respectively
This hypotenuse is calculated using the following Pythagoras theorem
[tex]h^2 = 3^2 + 1^2[/tex]
This gives
[tex]h = \sqrt {10[/tex]
Step 6: Draw another isosceles right triangle
Add 1 inch to one of the legs
See attachment (figure 4) for this triangle
The legs of this triangle have lengths of 1 inch and 4 inches, respectively
This hypotenuse is calculated using the following Pythagoras theorem
[tex]h^2 = 4^2 + 1^2[/tex]
This gives
[tex]h = \sqrt{[17[/tex]
See that the hypotenuse is the square root of 17
Hence, the right triangle whose legs are 1 inch and 4 inches has an hypotenuse of √17
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Select the function that represents a geometric sequence.
OA. A(n) = P+ (n-1)i P, where n is a positive integer
B. A(n) = (n-1)(P. )", where n is any real number
O C. A(n) = P(1 + i)-1, where n is a positive integer
OD. A(n) = n+ (P-1)i P, where n is a positive integer
The function that represents a geometric sequence is given by:
C. [tex]A(n) = P(1 + i)^{n-1}[/tex], where n is a positive integer.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
Following this pattern, a function that is also a geometric sequence is:
C. [tex]A(n) = P(1 + i)^{n-1}[/tex], where n is a positive integer.
For the function, we have that:
[tex]a_1 = P, q = 1 + i[/tex].
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What is the sum of a° + b°?
180°
We need more information to solve this problem.
The answer depends on the values of the individual angles.
360°
Answer:
a=70°
b=120°
we know,
a+b
=70+120
=190
the inverse of the relation y=2x+3 can be obtained graphically by:
A. a reflection in the yaxis
B. a reflection in the line y= 1/2x
C. a reflection in the line y=√x
D. a reflection in the line y= x
Answer:
a reflection in the line y=x
Step-by-step explanation:
The inverse relation of an equation is when the x and y are swapped. For this reason it's going to be reflected over the y=x line. You can also use an online graphing tool to show this as well:
Need help with this problem
Answer:graph a
Step-by-step explanation:
bc if you subtract 3
from 2 you find the one you line your numbers up with
there were three parts to Rita's race. she ran the first part, which was 4/9 of the total distance, in 20 minutes. She ran the second part, which was 2/5 of the remaining distance, in 12 minutes. She finally ran the third part in 15 minutes at a speed of 300 meters per minute.
a) How long was the third part of the race?
20+12+15= 32+15 = 47 minutes in total
300 meters per minute
300 * 47 = 14100 meters in total
with this we can see the first race was 4/9 that distance meaning the first race was 6266.6 meters long
14100 - 6266.6 = 7833.3
2/5 of 7833.3 is 3133.32
therefore 7833.3 - 3133.32 will give the distance of the third part of the race
meaning of course the answer is 4699.98 or rounding up 4700 meters for the third race
AC is a tangent to the circle below at point B.
Calculate the sizes of angle x, angle y and angle z.
Justify each of your answers.
[tex]y=78^{\circ}[/tex] (alternate interior angles theorem)
[tex]x=78^{\circ}[/tex] (alternate segment theorem)
[tex]z=24^{\circ}[/tex] (angles in a triangle add to 180 degrees)
Man's needs help ASAP
A linear function graph of the x-axis and y-axis has a diagonal line that passes the x-axis at (minus 0.5, 0), and the y-axis at (0, 1) In the function above, the slope will be multiplied by 2, and the y-value of the y-intercept will be increased by 3 units. Which of the following graphs best represents the new function?
A. X
B. Z
C. W
D. Y
The graph that best describes the new function is shown in the image attached below.
How to Determine the Graph of a Linear Function?The equation for a linear function with a slope of m and y-intercept of b is represented as y = mx + b.
Given a linear function graph passes the points (-0.5, 0) and (0, 1):
Y-intercept (b) = 1 (value of y when x = 0)
Slope (m) = change in y/change in x = (1 - 0)/(0 - (-0.5)) = 2
If the slope (1) is multiplied by 2, the new slope would be: 2
If the y-intercept (2) is increased by 3 units, the new y-intercept would be: 5
The equation of the new function would be: y = 2x + 5
The graph that best represents the function is shown in the image attached below.
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PLEASE HELP ITS URGENT i need number 20 & 21
!!!!!
Answer:
Put the equations in the form y=mx+c and after that, take any two values for x, fill in the equation of y=mx+c to get the corresponding y coordinate and take any value for y, to get the corresponding x coordinate. For this example i took x=0 and y=0, feel free to try it again with any other value. If you get a fraction and don't what to work with fractions, just do a trial and error till you get a whole number (as i did for Question 21 for the x and y coordinates)
Evan has a storage unit that he keeps all his garden tools in. It measures 4 feet by 312 feet by 2 feet.A prism has a length of 4 feet, height of 2 feet, and width of 3 and one-half feet.What is the maximum amount of supplies that the storage unit can hold
The maximum amount of supplies that the storage unit can hold is 28 ft³
How to calculate the volume of a rectangular prism?
For us to calculate the volume or amount of space in Evan's prism, we will first of all calculate the volume of rectangular prisms. Formula is;
V = Length × width × height.
We are given;
length = 4 feet
width = 3.5 feet
height of the prism = 2 feet.
Thus;
V = 4 * 3.5 * 2
V = 28 ft³
Thus, the maximum amount of supplies that the storage unit can hold is 28 ft³
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Pls help to find the coordinate on the line. Will mark brainliest. Thank you!!!
The coordinate of point R is 11/40, so the correct option is C.
How to find the coordinate of point R?
On the number line we can see that:
M = -1/4
T = 5/8
There are 5 segments between T and M, and the difference between T and M is:
5/8 - (-1/4) = 5/8 + 2/8 = 7/8
The measure of each segment will be equal to:
m = (7/8)/5 = 7/(8*5) = 7/40
Now, coordinate R is 2 segments to the left of T, so the coordinate of point R is given by:
R = 5/8 - 2*(7/40)
R = 25/40 - 14/40 = 11/40
The correct option is C.
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Simplify
(7.5x² +5.4x +3.7) (7.4x² -2.1x +7.7)
Answer:
55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49
Step-by-step explanation:
To simplify this equation, follow these steps:
(7.5x² +5.4x +3.7) (7.4x² -2.1x +7.7)
Multiply 7.5x² by all the terms in the right parenthesis.
7.5x² (7.4x² -2.1x +7.7)=55.5[tex]x^{4}[/tex] - 15.75x³+ 57.75x²
Then multiply 5.4x by all the terms in the right parenthesis.
5.4x(7.4x²-2.1x+7.7)=39.96x³-11.34x²+41.58x
Now multiply 3.7 by all the terms in the right parenthesis.
3.7(7.4x²-2.1x+7.7)=27.38x²-7.77x+28.49
Add all of those answers together.
55.5[tex]x^{4}[/tex] - 15.75x³+ 57.75x²+39.96x³-11.34x²+41.58x+27.38x²-7.77x+28.49=
=55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49
The answer is 55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49
Hope this helps!
If not, I am sorry.
31. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
31. f(-1) = 4 and f(5) = 1
Answer:
The required linear equation satisfying the given conditions f(-1)=4 and f(5)=1 is [tex]$y=\frac{-1}{2} x+\frac{7}{2}$[/tex]
Step-by-step explanation:
It is given that f(-1)=4 and f(5)=1.
It is required to find out a linear equation satisfying the conditions f(-1)=4
and f(5)=1. linear equation of the line in the form
[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$[/tex]
Step 1 of 4
Observe, f(-1)=4 gives the point (-1,4)
And f(5)=1 gives the point (5,1).
This means that the function f(x) satisfies the points (-1,4) and (5,1).
Step 2 of 4
Now find out the slope of a line passing through the points (-1,4) and (5,1),
[tex]$$\begin{aligned}&m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\&m=\frac{1-4}{5-(-1)} \\&m=\frac{-3}{5+1} \\&m=\frac{-3}{6} \\&m=\frac{-1}{2}\end{aligned}$$[/tex]
Step 3 of 4
Now use the slope [tex]$m=\frac{-1}{2}$[/tex] and use one of the two given points and write the equation in point-slope form:
[tex]$(y-1)=\frac{-1}{2}(x-5)$[/tex]
Distribute [tex]$\frac{-1}{2}$[/tex],
[tex]$y-1=\frac{-1}{2} x+\frac{5}{2}$[/tex]
Step 4 of 4
This linear function can be written in the slope-intercept form by adding 1 on both sides,
[tex]$$\begin{aligned}&y-1+1=\frac{-1}{2} x+\frac{5}{2}+1 \\&y=\frac{-1}{2} x+\frac{5}{2}+\frac{2}{2} \\&y=\frac{-1}{2} x+\frac{7}{2}\end{aligned}$$[/tex]
So, this is the required linear equation.
The farmer wants ratio horses : cows to equal 5 : 3.
He keeps his 45 horses but buys some cows.
Work out the number of cows he must buy.
Answer
He needs to buy 27 Cows
Step-by-step explanation:
if the ratio from horses to cows is 5-3 then you multiply 5 by the number to get 45 and also multiply it by 3
5 x 9 = 45
3 x 9 = 27
Solve x≥0 or x≥−5 and write the solution in interval notation.
The solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.
The interval notations are used to represent numbers between two numbers excluding or including the numbers as per the use. We use the following four interval notations:
[a, b] ⇒ All numbers between a and b including both a and b.
(a, b) ⇒ All numbers between a and b excluding both a and b.
(a, b] ⇒ All numbers between a and b excluding a but including b.
[a, b) ⇒ All numbers between a and b including a but excluding b.
We are asked to write the solution for x ≥ 0 and x ≥ -5 in the interval notation.
We first write each inequality in interval notation:
x ≥ 0 ⇒ x are all numbers greater than 0 including 0. This can be written in the interval notation as [0, ∞). We don't include ∞ as it is indeterminant.
x ≥ -5 ⇒ x are all numbers greater than -5 including -5. This can be written in the interval notation as [-5, ∞). We don't include ∞ as it is indeterminant.
Now, we are asked to solve for x ≥ 0 or x ≥ -5. Since it is 'or', we take unions of the two sets, that is the solution is:
[0, ∞) ∪ [-5, ∞) = [5, ∞).
Therefore, the solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.
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If 55% of the people at a certain conference are doctors, 49% are women, and 29% are female doctors, what is the probability that a person selected at random at this conference is a doctor or woman (or both)?
[tex]doctors = 55\% \\ woman = 49\% \\ both = 29\%[/tex]
[tex]p(a) =0.55 + 0.49 - 0.29 \\ p(a) = 0.75[/tex]
[tex]\frac{x^{2}-5x+6}{2x^{2}-7x+6 }[/tex]
whats the simplest form and the exclusions aka holes
Answer:
[tex]\frac{x-3}{2x-3}[/tex]. hole or removable discontinuity at x=2
Step-by-step explanation:
Well generally if you want the simplest form, you factor each the denominator and numerator and then see if you can cancel any of the factors out (because they're in the denominator and numerator)
So let's start by factoring the first equation:
[tex]x^2-5x+6[/tex]
Now let's find what ac is (it's just c since a=1...)
[tex]AC= 6[/tex]
List factors of -6
[tex]\pm1, \pm2, \pm3, \pm6[/tex].
Now we have to look for two numbers that add up to -5. It's a bit obvious here since there isn't many factors, but it's -2 and -3, and they're both negative since 6 is positive, and -5 is negative...
So using these two factors we get
[tex](x-2)(x-3)[/tex]
Ok now let's factor the second equation:
[tex]2x^2-7x+6[/tex]
Multiply a and c
[tex]AC = 12[/tex]
List factors of 12:
[tex]\pm1, \pm2, \pm3, \pm4, \pm6, \pm12[/tex].
Factors that add up to -7 and multiply to 12:
[tex]-3\ and\ -4[/tex]
Rewrite equation:
[tex]2x^2-4x-3x+6[/tex]
Group terms:
[tex](2x^2-4x)+(-3x+6)[/tex]
Factor out GCF:
[tex]2x(x-2)-3(x-2)[/tex]
Rewrite:
[tex](2x-3)(x-2)[/tex]
Now let's write out the equation using these factors:
[tex]\frac{(x-2)(x-3)}{(2x-3)(x-2)}[/tex].
Here we can factor out the x-2 and the simplified form is:
[tex]\frac{x-3}{2x-3}[/tex]
So we can "technically" define f(2) using the most simplified form, but it's removable discontinuity, so it has a hole as x=2. since it makes (x-2) equal to 0 (2-2) = 0.