The slope-intercept form of the equation of the line with a slope of -2/5 that passes through (15, -9/2) is y = -2/5x + 3/2.
Explanation:To write the slope-intercept form of the equation of a line, we use the formula y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is -2/5. To find the y-intercept, we substitute the coordinates of the point (15, -9/2) into the equation. Thus, we have:
y = -2/5x + b
-9/2 = -2/5(15) + b
-9/2 = -6 + b
b = -9/2 + 6 = 3/2
Therefore, the equation of the line with a slope of -2/5 that passes through (15, -9/2) is y = -2/5x + 3/2.
Final answer:
The equation of the line with a slope of -2/5 that passes through (15, -9/2) in slope-intercept form is y = (-2/5)x + 3.
Explanation:
The student is asking for the slope-intercept form of an equation of a line with a given slope and a point through which it passes. The slope-intercept form is given by y = mx + b, where m represents the slope and b represents the y-intercept. Given that the slope (m) is -2/5 and the line passes through the point (15, -9/2), we can substitute the slope and the point's coordinates into the slope-intercept formula to find b. Doing so, we get -9/2 = (-2/5)(15) + b. Solving for b, we find that the intercept is 3. Finally, the equation of the line in slope-intercept form is y = (-2/5)x + 3.
9e-7=7e-11 the answer
Answer:
e=-2
Step-by-step explanation:
9e-7=7e-11
9e-7e-7=-11
2e-7=-11
2e=-11+7
2e=-4
e=-4/2
e=-2
Answer:
e=2
Step-by-step explanation:
You are told that in a billiards shot, the cue ball was shot at the eight ball, which was 8 inches away. As a result, the eight ball rolled into a pocket, which was 6 inches away.
Knowing that the angle made with the path of the cue ball and the resulting path of the eight ball is larger than 90°, it can be determined that the original distance from the cue ball to the pocket was greater than ____ inches
DISCLAIMER:
I know the answer is 10 but I don't know why, I thought I did the math right but I got 100. I'll give brainliest if you explain it well!
Answer:It is greater than 10 because as you add both distances from the image its greater than 10 by a bit, looking at the angle it gives you a bigger perspective in how far the cue ball is from the pocket
Its basically 8+6 which equals 14 but adding the way the angle is going the distance is shorter than 14 but greater than 10
Answer:
10 inches
Explanation:
correct on edge
Find the perimeter of the polygon
The perimeter of a polygon is found by adding up the lengths of all its sides. The given polygon has a perimeter of 600,000 km. A side labeled 'mfi' would be 300,000 km.
Explanation:To find the perimeter of a polygon, you add up the lengths of all its sides. In this case, the given sides of the polygon are 200,000 km, 100,000 km, and 300,000 km. So adding these together gives you a perimeter of 600,000 km for this polygon.
If you're asked to find the length of a missing side (e.g., the side labeled as 'mfi'), you can subtract the lengths of the known sides from the total perimeter. So, 600,000 km (total perimeter) - 100,000 km - 200,000 km = 300,000 km. Therefore, the length of 'mfi' is 300,000 km.
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The perimeter of the polygon shown is approximately 84.91 centimeters.
According to the given image
∠B = ∠D and AB = AD.
To find the perimeter, break the polygon into smaller shapes and find the perimeters of those shapes.
Note that triangle ABD is isosceles since AB = AD, so ∠ABD = ∠ADB. Draw imaginary segments BC and DC, which create two right triangles, ABC and ADC. Since ∠B = ∠D, it is clear that ∠ABC = ∠ADC. Additionally, it is given that BC = 8.5 cm and DC = 7.5 cm.Now, the Perimeter of triangle ABD is calculated in the following way:
AB = AD (given) = 6.5 cm
We can use the Pythagorean theorem on triangle ABD to find BD:
[tex]BD^2 = AB^2 - (\frac{1}{2} \times AD)^2\\BD^2 = 6.5^2 - (\frac{1}{2} \times 6.5)^2\\BD^2 = 25.5625\\BD \approx 5.05 cm[/tex]
So, the Perimeter of triangle ABD is
= AB + AD + BD
[tex]\approx 6.5 cm + 6.5 cm + 5.05 cm \\ \approx 18.05 cm[/tex]
Again, the Perimeter of triangle ABC is
AC = BC + AB = 8.5 cm + 6.5 cm = 15 cm
As ∠ABC is a right angle and AC is the hypotenuse, use the Pythagorean theorem to find AB:
[tex]AB^2 + BC^2 = AC^2\\AB^2 + 8.5^2 = 15^2\\AB^2 = 81\\AB = 9 cm[/tex]
Perimeter of triangle ABC
= AB + BC + AC = 9 cm + 8.5 cm + 15 cm = 32.5 cm
Perimeter of triangle ADC:
Similar to triangle ABC, find AD using the Pythagorean theorem:
[tex]AD^2 + DC^2 = AC^2\\AD^2 + 7.5^2 = 15^2\\AD^2 = 135\\AD = 3\sqrt{5} cm \approx 11.86 cm[/tex]
Perimeter of triangle ADC
= AD + DC + AC = 11.86 cm + 7.5 cm + 15 cm = 34.36 cm
Finally, to find the perimeter of the entire polygon, add the perimeters of the three triangles:
Perimeter of polygon = Perimeter of triangle ABD + Perimeter of triangle ABC + Perimeter of triangle ADC
Perimeter of polygon is
[tex]\approx 18.05 cm + 32.5 cm + 34.36 cm \approx 84.91 cm[/tex]
Therefore, the perimeter of the polygon is approximately 84.91 centimeters.
Round 1,208.7438 to the nearest hundredth.
A. 1,208.73
B. 1,208.74
C. 1,208.743
D. 1,208.75
Answer:
the answer is 1,208.74
Here’s another one thank u all for helping me. I really appreciate it!
Area = Square - Circle
Area of Square = 10² = 100 m²
Area of Circle = π(5²) = 25π m²
Area of Shaded Region = 100 - 25π = 21.5 m² approx.
answer: second choice
The solution set for -18 < 5 x - 3 is _____.
a -3 < x
b 3 < x
c -3 > x
d 3 > x
-18 < 5x - 3 Isolate/get x by itself, first add 3 to both sides of the equation
-18 + 3 < 5x - 3 + 3
-15 < 5x Divide 5 on both sides
-3 < x Your answer is A
You flip the sign [</>] if you multiply or divide a negative number to both sides of the equation.
Byron's weekly salary is $ 650. He receives a 15% pay raise. What is Byron's new weekly salary?How much was his raise?
Answer:
$747.50
Step-by-step explanation:
650×15/100=$97.50 which is then added to 650 Becoz his pay is 15% rising=747.50
.10.A cone with a height of 15 yards has a volume of 457.17 yd3 . Find the diameter of the cone
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=457.17\\ h = 15 \end{cases}\implies 457.17=\cfrac{\pi r^2(15)}{3}\implies 457.17=5\pi r^2 \\\\\\ \cfrac{457.17}{5\pi }=r^2\implies \sqrt{\cfrac{457.17}{5\pi }}=r\implies 5.39 \approx r~\hfill \boxed{\stackrel{diameter = 2r}{2(5.39) = 10.78}}[/tex]
What is 84,396 + 29,760
Answer:
114, 156
Step-by-step explanation:
Answer: 114,156
Step-by-step explanation:
To add 84,396+29,760 you must add each row.
6+0 = 6
9+6 = 15 (Carry up the one)
3+7 = 10 + 1 = 11 (Carry up the one)
4+9 = 13 + 1 = 14 (Carry up the one)
8+2 = 10 + 1 = 11
So the answer will be 114,156
What is the equation of points (8,16)
Answer:
86
Step-by-step explanation:
Can someone please help me
a^2 + b^2 = c^2
65^2 + 34^2 = c^2
4225 + 1156 = c^2
5381 = c^2
c ≈ 73.3552997404
Hope this helps! ;)
The tables below show four sets of data:
Set A
x
1
2
3
4
5
6
7
8
9
y
10
9
8
7
6
5
4
3
2
Set B
x
1
2
3
4
5
6
7
8
9
y
3
4
5
6
7
8
9
10
11
Set C
x
1
2
3
4
5
6
7
8
9
y
8
6
5
4
3.5
3
2.5
2
2
Set D
x
1
2
3
4
5
6
7
8
9
y
1
2.5
2.5
3
4
5
6
8
9
For which set of data will the scatter plot represent a positive linear association between x and y?
Set A
Set B
Set C
Set D
Answer:
B? sorry if its wrong
Step-by-step explanation:
Answer:
The answer is not set c!
Step-by-step explanation:
Triangle ABC is a right triangle.
Triangle A B C. Angle A is x degrees, B is 90 degrees, C is (x minus 10) degrees. The exterior angle to angle C is (2 x + 40) degrees.
Which equations can be used to find the value of x? Check all that apply.
x + 90 + (x minus 10) = 180
x + 90 + (2 x + 40) = 180
2 x + 80 = 180
x + 90 = 2 x + 40
(x minus 10) + 90 = 2 x + 40
The equations that can be used to the value of x are 1) x+90+(x-10)=180 and 2) x+90+(2x+40)=180.
Step-by-step explanation:
Two properties can be used to find the value of the x.
1) Sum of Interior angles of a triangle is 180°.
⇒x+90°+(x-10)°=180.
2x+80°=180°.
2x=180°-80°.
2x=100°.
x=50°.
⇒(x-10)°=40°.
2) The Angle of the straight line is 180°.
From the given diagram, BC is a straight line ray with C as intersecting point. this will result in two angles. (refer the diagram).
The sum of those two angles will be 180°.
⇒ (x-10)°+ (2x+40)°=180°.
(3x+30)°=180°.
3x=150°.
x=50°.
∴(x-10)°=40° and (2x+40)° = 140°.
∴The equations that can be used to the value of x are x+90+(x-10)=180 and x+90+(2x+40)=180.
What is the slope of y-3=-4(x-5)
Answer:
-4
Step-by-step explanation:
y-3=-4(x-5)
y=-4x+20+3
y=-4x+23
y=mx+b where m=slope and b=y-intercept
Last year a bamboo plant was 17 feet tall. It grew 10 feet this year. How tall is it now?
Answer:
27 is the right answer
Step-by-step explanation:
10+17=27 :)
What should be subtracted from 3x^2-4y^2+5xy+20 to obtain x^2+y^2+6xy+20?
Answer:
2x² − 5y² − xy
Step-by-step explanation:
3x²- 4y² + 5xy + 20
−
x² + y² + 6xy + 20
________________
2x² − 5y² − xy + 0
The graph of f(x) is shown. Estimate f(–3).
f(–3) =
The value estimated for f ( -3 ) from the graph is 12.5
Step-by-step explanation:
The function (f) in the graph defines all point sets in plane as (x, f(x)) form. The graph of equation to be the graph of function. I.e. y = f (x). Hence, graph of f is if the special case for graph of equation.
Given x = - 3 and asked to find f (-3). So, we have to see the point of y mapped (meeting point of y) on the point x = -3. In the graph, the point marked on y straight away to x = - 3 is 12.5.
Answer: 12.5
Step-by-step explanation:
it is the same as the g (x) problem. we sub -3 for x and see what the y value is on graph. At -3, y = 12.5
Brainliest? :)
Complete the square x squared +18x-64=0
Answer:
x = -9±√145 (= 3.04 or -21.04)
Step-by-step explanation:
x²+18x-64 = 0 (move the constant to the right side, add 64 to both sides)
x²+18x = 64 (divide the x-term by 2, square it, then add it to both sides)
x²+18x + (18/2)²= 64 + (18/2)² (simplify)
x²+18x + 9²= 64 + 9²
x²+18x + 9²= 64 + 81
x²+18x + 9²= 145 (simplify left side using the property (a+b)² = a²+ 2ab+b²)
(x+9)² = 145 (take square root of both sides)
x+9 = ±√145
x = -9±√145 (= 3.04 or -21.04)
In a trapezoid ABCD with legs AB and CD, the diagonals intersect each other at point O. Compare the areas of △ABO and △CDO.
ar(ΔABO) = ar(ΔCDO)
Explanation:
The image attached below.
Given ABCD is a trapezoid with legs AB and CD.
AB and CD are non-parallel sides between the parallels AD and BC.
In ΔABD and ΔACD,
We know that, triangles lie between the same base and same parallels are equal in area.
⇒ AD is the common base for ΔABD and ΔACD and they are lie between the same parallels AD and BC.
Hence, ar(ΔABD) = ar(ΔACD) – – – – (1)
Now consider ΔABO and ΔCDO,
Subtract ar(ΔAOD) on both sides of (1), we get
ar(ΔABD) – ar(ΔAOD) = ar(ΔACD) – ar(ΔAOD)
⇒ar(ΔABO) = ar(ΔCDO)
Hence, ar(ΔABO) = ar(ΔCDO).
Write the equation of a line parallel to the line y=2x that passes through the given points. a. (0,4) b.(-2,-1) c.(2,0)
Answer:
ju mmmmmmjjum,,,,i,,,,, enjoy
Step-by-step explanation:
Answer:
its option b: (-2,-1)
Step by step:
y=2x
-2=2(-1)
-2=-2
Infinitely many solutions
how do you graph the trigonometric function y= -sin(2x)+1?
Step-by-step explanation:
[tex]\displaystyle \boxed{y = -cos\:(2x - \frac{\pi}{2}) + 1} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 1[/tex]
OR
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 1[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the centre photograph displays the trigonometric graph of [tex]\displaystyle y = -cos\:2x + 1,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [centre photograph] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{4}} = \frac{\frac{\pi}{2}}{2}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = -cos\:(2x - \frac{\pi}{2}) + 1.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-\pi, 1],[/tex]from there to [tex]\displaystyle [-2\pi, 1],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 1,[/tex]in which each crest is extended one unit beyond the midline, hence, your amplitude. Now, there is one more piese of information you should know -- the sine graph in the photograph farthest to the right is the OPPOCITE of the sine graph in the photograph farthest to the left, and the reason for this is because of the negative inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of any trigonometric equation, the whole graph reflects over the midline. Keep this in mind moving forward. Now, with all that being said, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Nathan ordered one cheeseburger and one bag of chips for $3.75. Jack ordered two cheeseburgers and three bags of chips for $8.25.
Therefore the cost of a bag of chips is $0.75
therefore the cost of a cheeseburger is $3.
Step-by-step explanation:
i) let the cost of a cheesburger be x.
ii) let the cost of a bag of chips be y
iii) therefore it is given that x + y = 3.75
iv) it is also given that 2x + 3y = 8.25
v) multiplying the equation in iii) by 2 we get 2x + 2y = 7.50
vi) subtracting the equation in v) from the equation in iv) we get y = $0.75
vii) Therefore the cost of a bag of chips is $0.75
viii) Substituting the value of y found in vii) into iii) we get x = 3.
ix) therefore the cost of a cheeseburger is $3.
The diameter of a circle is 18 kilometers. What is the length of a 120° arc?
Final answer:
The length of a 120° arc in a circle with an 18-kilometer diameter is approximately 18.85 kilometers.
Explanation:
The question asks to find the length of a 120° arc, given the diameter of a circle is 18 kilometers. To solve this, we first find the radius of the circle by dividing the diameter by 2, which gives us 9 kilometers.
Knowing the circumference formula is 2πr, we calculate the circumference as 2π(9) or 18π kilometers. Since 360° represents the full circumference, a 120° arc represents one-third of the circle.
Thus, the arc's length is one-third of the circumference: ⅓(18π) = 6π kilometers, which is approximately 18.85 kilometers.
2b + 8 - 5b + 3 = -13 + 8b - 5
Answer:
The final value of [tex]b=\frac{29}{11}[/tex] .
Step-by-step explanation:
Given:
[tex]2b + 8 - 5b + 3 = -13 + 8b - 5[/tex]
We have to find the value of [tex]b.[/tex]
[tex]2b + 8 - 5b + 3 = -13 + 8b - 5[/tex]
Steps to be followed:
Step 1:Bring all the variables one left side of the equation.Subtract 8b both side.
[tex]2b + 8 - 5b + 3-8b = -13 + 8b - 5-8b[/tex]
[tex]2b - 5b -8b+ 3 +8= -13 - 5[/tex]
Step 2:Add the variable and constants on each side.[tex]2b - 5b -8b+ 3 +8= -13 - 5[/tex]
[tex]-11b+11=-18[/tex]
Step 3:Subtract 11 on both side.[tex]-11b+11=-18[/tex]
[tex]-11b+11-11=-18-11[/tex]
[tex]-11b=-29[/tex]
Step 4:Divide -11 on both sides of the equation.[tex]-11b=-29[/tex]
[tex]b=\frac{-29}{-11} =\frac{29}{11}[/tex]
So the final value of b is 29/11.
John scored 5:7 of the goals he attempted at the soccer game. During three games, if John scored 20 goals, how many did he attempt
Answer:
John scored 20 goals he attempted 28.
Step-by-step explanation:
Given:
John scored 5:7 of the goals he attempted at the soccer game.
During three games, if John scored 20 goals.
Now, to find the number of attempts.
Let the number of attempts be [tex]x.[/tex]
The number of goals = 20.
As, given John scored 5:7 of the goals he attempted at the soccer game.
So, 5 is equivalent to 7.
Thus, 20 is equivalent to [tex]x.[/tex]
Now, to solve by using cross multiplication method:
[tex]\frac{5}{7} =\frac{20}{x}[/tex]
By cross multiplying we get:
[tex]5x=140[/tex]
Dividing both sides by 5 we get:
[tex]x=28.[/tex]
Therefore, he attempt 28.
Please help me with this!
Answer:
Step-by-step explanation:
i don't know I am a forth grader
After school, Isaac skateboards directly from school to an ice cream parlor and then from the
ice cream parlor to a candy store. The ice cream parlor is 3 miles south of the school and the
candy store is 4 miles east of the ice cream parlor. What is the straight line distance between
the school and the candy store?
Answer:
The straight line distance between the school and the candy store is 5.
Step-by-step explanation:
Use Pythagorean theorem
a²+b²=c²
3²+4²=c²
9+16=c²
25=c²
5=c
The straight line distance between the school and the candy store will be 5 miles.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
After school, Isaac skateboards directly from school to an ice cream parlor and then from the ice cream parlor to a candy store.
The ice cream parlor is 3 miles south of the school and the candy store is 4 miles east of the ice cream parlor.
Then the straight line distance between the school and the candy store will be
[tex]\rightarrow \sqrt{4^2 + 3^2}\\\\\rightarrow \sqrt{16 + 9}\\\\\rightarrow \sqrt{25}\\\\\rightarrow 5[/tex]
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Jane sold 100 tickets for her school auction. Adult tickets cost $12 and the children tickets cost $8. Jane collected a total of $944. Write a system of equations for this situation
Answer:
see the explanation
Step-by-step explanation:
Let
x ----> number of adult tickets
y ----> number of children tickets
we know that
Jane sold 100 tickets for her school auction
so
[tex]x+y=100[/tex] ----> equation A
Jane collected a total of $944
[tex]12x+8y=944[/tex] ----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (36,64)
see the attached figure
therefore
The number of adult tickets sold was 36 and the number of children tickets sold was 64
What is an equivalent fraction for 5/10
Answer:
1/2
Step-by-step explanation:
5/10, 5 is HALF of ten so 1/2
orthocenter of the triangle with vertices J(1,0) H(6,0) I(3,6)
Answer:
(3, 1)
Step-by-step explanation:
The orthocenter is the point where the altitudes meet. Since all three altitudes meet there, it is only necessary to look at two of them. A graph helps immensely.
In the attached graph, we notice that segment HJ is horizontal, so the x-coordinate of the orthocenter will be that of point I (x=3).
The segment IJ has a rise of 3 for a run of 1, so its perpendicular through point H will have a rise of 1 for a run of -3. That gets you to point (3, 1) from point H, so (3, 1) is the orthocenter.