Answer:
Step-by-step explanation:
The relationship between x and y is called a linear relationship because the points so plotted all lie on a single straight line. The number 95 in the equation y=95x+32 is the slope of the line, and measures its steepness.
The interior angle of a regular polygon is 120. Work out the number of sides of the polygon.
Answer:
6 sides
Step-by-step explanation:
The interior angle and the exterior angle sum to 180° , then
exterior angle = 180° - 120° = 60°
The sum of the exterior angles of a polygon is 360° , so
number of sides = 360° ÷ 60 = 6
Answer:
6 sides
Step-by-step explanation:
180 - 120 =60°
sum of exterior angles is 360°
therefore , 360°/60°
ans = 6 sides
Good luck :-)
Use the sum of cubes identity to write this polynomial expression in factored form:
8x3 + 27.
Answer:
[tex] {8x}^{3} + 27 \\ = {8x}^{3} + {3}^{3} \\ let : 8x \: be \: a \\ : 3 \: be \: b \\ = > {a}^{3} + {b}^{3} : \\ {(a + b)}^{3} = (a + b)( {a}^{2} + 2ab + {b}^{2} ) \\ {(a + b)}^{3} = ( {a}^{3} + 3{a}^{2} b + 3a {b}^{2} + {b}^{3} ) \\ ( {a}^{3} + {b}^{3} ) = {(a + b)}^{3} - 3ab(a + b) \\ \therefore( {8x}^{3} + 27) = {(8x + 3)}^{3} - 72(8x + 3)[/tex]
Find the components of the vertical force Bold Upper FFequals=left angle 0 comma negative 10 right angle0,−10 in the directions parallel to and normal to the plane that makes an angle of theta equals tangent Superscript negative 1 Baseline (StartFraction StartRoot 3 EndRoot Over 3 EndFraction )θ=tan−1 3 3 with the positive x-axis. Show that the total force is the sum of the two component forces. What is the component of the force parallel to the plane? left angle nothing comma nothing right angle , What is the component of the force perpendicular to the plane? left angle nothing comma nothing right angle , Find the sum of these two forces. left angle nothing comma nothing right angle
Solution :
Let [tex]$v_0$[/tex] be the unit vector in the direction parallel to the plane and let [tex]$F_1$[/tex] be the component of F in the direction of [tex]v_0[/tex] and [tex]F_2[/tex] be the component normal to [tex]v_0[/tex].
Since, [tex]|v_0| = 1,[/tex]
[tex]$(v_0)_x=\cos 60^\circ= \frac{1}{2}$[/tex]
[tex]$(v_0)_y=\sin 60^\circ= \frac{\sqrt 3}{2}$[/tex]
Therefore, [tex]v_0 = \left<\frac{1}{2},\frac{\sqrt 3}{2}\right>[/tex]
From figure,
[tex]|F_1|= |F| \cos 30^\circ = 10 \times \frac{\sqrt 3}{2} = 5 \sqrt3[/tex]
We know that the direction of [tex]F_1[/tex] is opposite of the direction of [tex]v_0[/tex], so we have
[tex]$F_1 = -5\sqrt3 v_0$[/tex]
[tex]$=-5\sqrt3 \left<\frac{1}{2},\frac{\sqrt3}{2} \right>$[/tex]
[tex]$= \left<-\frac{5 \sqrt3}{2},-\frac{15}{2} \right>$[/tex]
The unit vector in the direction normal to the plane, [tex]v_1[/tex] has components :
[tex]$(v_1)_x= \cos 30^\circ = \frac{\sqrt3}{2}$[/tex]
[tex]$(v_1)_y= -\sin 30^\circ =- \frac{1}{2}$[/tex]
Therefore, [tex]$v_1=\left< \frac{\sqrt3}{2}, -\frac{1}{2} \right>$[/tex]
From figure,
[tex]|F_2 | = |F| \sin 30^\circ = 10 \times \frac{1}{2} = 5[/tex]
∴ [tex]F_2 = 5v_1 = 5 \left< \frac{\sqrt3}{2}, - \frac{1}{2} \right>[/tex]
[tex]$=\left<\frac{5 \sqrt3}{2},-\frac{5}{2} \right>$[/tex]
Therefore,
[tex]$F_1+F_2 = \left< -\frac{5\sqrt3}{2}, -\frac{15}{2} \right> + \left< \frac{5 \sqrt3}{2}, -\frac{5}{2} \right>$[/tex]
[tex]$=<0,- 10> = F$[/tex]
What is the area of this triangle ?
Find three consecutive even integers such that the product of the second and
third integers is equal to 35.
Step-by-step explanation:
first number=x
second number=x+2
third number=x+4
(x+2)(x+4)=35
x(x+4)+2(x+4)=35
x²+4x+2x+8=35
x²+6x+8=35
x²+6x=35-8
x²+6x=33
x²+6x-33=0
using that, you can find the first number,
then use the data to find the other two.
Which expression can be used to find 80% of 120?
80% of 120
20%
20%
20%
20%
20%
Answer:
96
Step-by-step explanation:
80*120=9600 divided by 100
A surveyor leaves her base camp and drives 42km on a bearing of 032degree she then drives 28km on a bearing of 154degree,how far is she from her camp base and what is her bearing from it
Answer:
The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).
Step-by-step explanation:
The final position of the surveyor is represented by the following vectorial sum:
[tex]\vec r = \vec r_{1} + \vec r_{2} + \vec r_{3}[/tex] (1)
And this formula is expanded by definition of vectors in rectangular and polar form:
[tex](x,y) = r_{1}\cdot (\cos \theta_{1}, \sin \theta_{1}) + r_{2}\cdot (\cos \theta_{2}, \sin \theta_{2})[/tex] (1b)
Where:
[tex]x, y[/tex] - Resulting coordinates of the final position of the surveyor with respect to origin, in kilometers.
[tex]r_{1}, r_{2}[/tex] - Length of each vector, in kilometers.
[tex]\theta_{1}, \theta_{2}[/tex] - Bearing of each vector in standard position, in sexagesimal degrees.
If we know that [tex]r_{1} = 42\,km[/tex], [tex]r_{2} = 28\,km[/tex], [tex]\theta_{1} = 32^{\circ}[/tex] and [tex]\theta_{2} = 154^{\circ}[/tex], then the resulting coordinates of the final position of the surveyor is:
[tex](x,y) = (42\,km)\cdot (\cos 32^{\circ}, \sin 32^{\circ}) + (28\,km)\cdot (\cos 154^{\circ}, \sin 154^{\circ})[/tex]
[tex](x,y) = (35.618, 22.257) + (-25.166, 12.274)\,[km][/tex]
[tex](x,y) = (10.452, 34.531)\,[km][/tex]
According to this, the resulting vector is locating in the first quadrant. The bearing of the vector is determined by the following definition:
[tex]\theta = \tan^{-1} \frac{10.452\,km}{34.531\,km}[/tex]
[tex]\theta \approx 16.840^{\circ}[/tex]
And the distance from the camp is calculated by the Pythagorean Theorem:
[tex]r = \sqrt{(10.452\,km)^{2}+(34.531\,km)^{2}}[/tex]
[tex]r = 36.078\,km[/tex]
The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).
Mathssssssssssssssssssssssssss
Answer:
The value of x is 5
SOMEBODY PLEASE HELP ME!
Answer:
[tex]43.7[/tex]
Step-by-step explanation:
Since the triangles are similar, the ratio of their corresponding sides is maintained. Therefore, we can up the following proportion to solve for [tex]OP[/tex]:
[tex]\frac{9}{7}=\frac{OP}{34},\\OP=\frac{34\cdot 9}{7}=43.7142857143\approx \boxed{43.7}[/tex]
43.7
Step-by-step explanation:
Since the two are similar triangles, the ratio of the legs of one triangle is equal to the ratio of the legs of the other triangle.
OP/ON = LM/LK
OP/34 = 9/7
Solving for OP,
OP = 34(9/7)
= 43.7
if a person gives you their card number and they say you can spend a certain amount of money and u spend more is it considered stealing? or is it not because they gave u their card willingly and all u did was go over the limit.
Answer:
It would be considered stealing.
Step-by-step explanation:
They did willingly give you their card BUT, they trusted you to only spend a certain amount and not go over that certain limit. You went over the limit even though they specifically told you not to go over it so yes, it would be classified as stealing.
Pls help will mark brainliest
Answer:
1/ 4^2
Step-by-step explanation:
4^4 * 4^-6
We know that a^b * a^c = a^(b+c)
4^(4-6)
4^-2
We also know that a^-b = 1/a^b
1/4^2
Ambwene cut 3 lawns in his neighborhood on Friday and more on Saturday,
He earns $22.50 for each lawn cut. His total earning for both days is $135.
How many lawes did he cut on Saturday?
What is the solution to the inequality |X-4 <3?
Answer:
x<7
therefore {x:x<7}
Step-by-step explanation:
x-4<3
x<3+4
x<7
Please help me with this question...
Answer:
my answer is in this picture. sorry about my presentation and English
explain why 7x+3 cannot be factorised
Answer:
There is no common factor
Step-by-step explanation:
PLs! 100 points the integers 1,2,3,4,5,6,7,8 are placed in a list so that each value is either bigger than all the numbers it precedes or smaller than all the numbers it precedes. How many such lists are possible? 100 points!
2
Hope this helps! :)
______________
Answer:
you can know by the minimum number or the maximum e.g minimum 1 maximum 20 answer 20
Step-by-step explanation:
so in this kind it is 2
hope its useful
What index of y makes value1/ y^2?
Answer:
the index of y is -2
Step-by-step explanation:
[tex]y^{-2}[/tex]
=[tex]\frac{1}{y^2}[/tex]
how do i find the circumference of a circle when the given radius is 3 1\2 cm, answers in terms of π
Answer:
Circumference of circle is 9.42cm.
Step-by-step explanation:
Here we have given that A circle with having radius 3 and 1 / 2 cm. And We need to find circumference of circle.
Formula using
Circumference of circle = π × 2 × radius
substitute the value
Circumference of circle = π × 2 × 3 and 1/2 cm.
cancle the 2
Circumference of circle = π × 3 cm
Using π = 22 / 7
[tex] \small \sf \ Circumference \: of \: \: circle = \frac{ 22}{7 }×3 cm \\ [/tex]
[tex] \small \sf \ Circumference \: of \:circle = 9.42 cm[/tex]
Hence, Circumference of circle is 9.42cm.
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.
y=−9x^2+571x−3884
Write the equation for a parabola with a focus at (-4,-2) and a directrix at y = 3.
Answer:
[tex]\displaystyle y=-\frac{1}{10}x^2-\frac{4}{5}x-\frac{11}{10}[/tex]
Step-by-step explanation:
By definition, any point (x, y) on the parabola is equidistant from the focus and the directrix.
The distance between a point (x, y) on the parabola and the focus can be described using the distance formula:
[tex]d=\sqrt{(x-(-4))^2+(y-(-2))^2[/tex]
Simplify:
[tex]d=\sqrt{(x+4)^2+(y+2)^2}[/tex]
Since the directrix is an equation of y, we will use the y-coordinate. The vertical distance between a point (x, y) on the parabola and the directrix can be described using absolute value:
[tex]d=|y-3|\text{ or } |3-y|[/tex]
The two equations are equivalent. Therefore:
[tex]\sqrt{(x+4)^2+(y+2)^2}=|y-3|[/tex]
Solve for y. We can square both sides. Since anything squared is positive, we can remove the absolute value:
[tex](x+4)^2+(y+2)^2 = (y-3)^2[/tex]
Expand:
[tex](x^2+8x+16)+(y^2+4y+4)=(y^2-6y+9)[/tex]
Isolate:
[tex]x^2+8x+11=-10y[/tex]
Divide both sides by -10. Hence, our equation is:
[tex]\displaystyle y=-\frac{1}{10}x^2-\frac{4}{5}x-\frac{11}{10}[/tex]
Answer the question pleaseeeee
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 models this information.
If one of the longer si
des is 6.3 centimeters, which equation can be used to find the length of the base
Answer:
2(6.3) + b = 15.7
12.6 + b = 15.7
b = 3.1
PLEASE HELP ME 50 PTS and i'll give brainliest please help me this is the video they game me to do this hw but I still don't understand it https://youtu.be/7Uos1ED3KHI
1.) 70x/100x^2 = 7/10x
2.) 16x^3/24x = 2x^2/3
3.) 7x(2x+1)/21(2x+1) = x/3
4.) 35x - 35/x^2 - 1 = 35/x + 1
5.) x + 7/x^2 + 4x - 21 = 1/x - 3
6.) x^2 - 6x + 5 = x - 5/5
7.) x^2 - 36/x^2 - 3x - 18 = x + 6/x + 3
8.) x^2 - 3x - 10/x^2 + x - 2 = x - 5/x - 1
Mr. Ali cut a wooden plank into three parts in the ratio 2:3:8. The longest part was 72 centimeters
Answer:
117 centimeters
Step-by-step explanation:
Since the longest pieces is 72 centimeters and it’s ratio is 8, that means the individual unit of the ratio is 9 (72/8=9). You can multiply each part of the ratio by 9
2x9=18
3x9=27
We already know the third part of the ratio is 72. Add all of it together to get the original length.
18+27+72=117 cm
Please help!
Find the length of the triangle.
Answer: 12.
Step-by-step explanation: Use Pythagorean Theorem. We that a = 9, b = ?, and c = 15. Plugging that in gives us 9^2 + b^2 + 15^2. Solving for b gets us b^2 = 144. Taking the square root of both sides gets us b = 12.
(15 points!!) please help!! If you can answer the other questions on my page I will Venmo u!
Answer:
y = (x - 3)² - 4 Vertex form
(3, -4) Vertex
Step-by-step explanation:
f(x) = x² - 6x + 5
Complete the square
y = (x - 3)² + 5 - (-3)²
y = (x - 3)² + 5 - 9
y = (x - 3)² - 4 Vertex form
(3, -4) Vertex
What is the force on the surface of a square of side 5 m if the pressure acting on it is 25 pascal ?
Answer:
625 N
Step-by-step explanation:
First, find the area of the square.
Area = side x side
= 5 x 5
= 25 m²
Force = pressure x area
= 25 x 25
= 625 N
Hope this helps!
Simplify. the square root of 3 times the square root of 5
Answer:
[tex]\sqrt{15}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{3}[/tex] × [tex]\sqrt{5}[/tex] = [tex]\sqrt{3(5)}[/tex] = [tex]\sqrt{15}[/tex]
The trampoline park charges a $8 for kids and $4 for adults. Your extended family is going there to celebrate your birthday. Your family has at most $190 dollars to spend on entrance fees. You can invite at most 35 people. What are some possible combinations of adults and kids who could go to your party? Write a system of equations for this situation.
Answer:
a+k ≤ 35
8a+4k ≤ 190
Some possible combinations are 10 adults and 20 kids
5 adults and 29 kids
Step-by-step explanation:
Let k= number of kids
a = number of adults
a+k ≤ 35 since you can have at most 35
8a + 4k ≤ 190 since the most you can spend is 190
Some possible combinations are 10 adults and 20 kids
(10+30 < 35 and 8*10+4*20 = 80+80 =160< 190)
Another possible combination
5 adults and 29 kids
(5+29 < 35 and 5*10 + 4*29 =50+116=166)
Find the 10th term in the following geometric sequence.
8, 4, 2, 1,