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[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]
Find the equation of a line parallel to y-5=6x-10 that passes through (4,10)
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond[/tex]
❖ If lines are parallel to each other, they have the same slope.
So the slope of the line parallel to y-5=6x-10 is 6.
Now, since we're also given the point crossed by the line, we write the equation in point-slope form:-
[tex]\sf{y-y_1=m(x-x_1)}[/tex]
Substitute 10 for y₁, 6 for m and 4 for x₁:-
[tex]\sf{y-10=6(x-4)}[/tex]
On simplification,
[tex]\sf{y-10=6x-24}[/tex]
Adding 10 to both sides results in:-
[tex]\sf{y=6x-14}[/tex]
So we conclude that Option A is correct.
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10. The following measurements from yaw marks left at the scene of an accident were taken by law
enforcement officers. Using a 31-ft-long chord, the middle ordinate measured approximately 3
ft. The drag factor for the road surface is 1.02.
a. Determine the radius of the yaw mark to the nearest tenth of a foot.
1
Determine the minimum snood that it
The radius of the yaw mark to the nearest tenth of a foot is 11.2 ft
The minimum speed 11.1634 miles per hour.
What is Yaw mark?Yaw marks are always curved. They are, initiated by a steering input. They're what's left from a tire that is still rolling but is simultaneously sliding laterally.
The formula for determining radius from a chord and middle ordinate is
[tex]r^{2}= \frac{c^{2}}{8m}+\frac{m}{2}[/tex]
To find the radius of the yaw mark, we have to use the formula
[tex]r^{2}= \frac{c^{2}}{8m}+\frac{m}{2}[/tex]
where c is the length of the chord and m is the middle ordinate
As the tires leave a yaw mark with a 31 foot chord and a middle ordinate of 3 feet.
So,
[tex]r^{2}= \frac{31^{2}}{8*3}+\frac{3}{2}[/tex]
[tex]r^{2}= 40.041 +1.5\\r^{2}=41.541[/tex]
Now to find the minimum speed, we are going to use the formula: [tex]s=\sqrt{15fr}[/tex]
where 'f' is drag factor and 'r' is the radius
drag factor is 0.2, f=0.2
and r= 41.541 ft
So, [tex]s=\sqrt{15* 0.2*41.541}\\s=\sqrt{124.623}\\s= 11.1634 mph[/tex]
The minimum speed before the brakes are applied was 11.1634 miles per hour.
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How tall is Merapi in Indonesia?
A. 2,698 meters
B. 3,000 meters
C. 5,201 meters
D. 26.2 miles
The function h(x) is a translation of the exponential function g(x) = 2(3)x − 4. What's h(x) if the translation is a vertical stretch by a factor of 2, a vertical shift upward 9 units, and a horizontal shift to the right 7 units? Question 11 options: A) h(x) = 4(3)x − 7 + 9 B) h(x) = 4(3)x − 9 + 7 C) h(x) = 4(3)x – 7 + 7 D) h(x) = 4(3)x + 7 − 9
The function h(x) is a translation of the exponential function [tex]g(x) = 2(3)^{x - 4}[/tex] , is [tex]h(x) = 4(3)^{x + 7} - 9[/tex]
What are exponential functions?When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.
There usual form is specified below. They are written in several such equivalent forms.
The function h(x) is a translation of the exponential function given as
[tex]g(x) = 2(3)^{x - 4}[/tex]
We have to determine, the h(x) if the translation is a vertical stretch by a factor of 2, a vertical shift upward of 9 units, and a horizontal shift to the right 7 units.
The function h(x) is vertically stretched by 2.
[tex]h(x) = 2 (2(3)^{x - 4})\\\\h(x) = 4((3)^{x - 4})[/tex]
Vertically shift upward by 9,
[tex]h(x) = 4((3)^{x - 4})\\\\h(x) = 4((3)^{x - 4})- 9[/tex]
And a horizontal shift to the right 7 units,
[tex]h(x) = 4((3)^{x - 7})- 9[/tex]
The function h(x) is a translation of the exponential function [tex]g(x) = 2(3)^{x - 4}[/tex] , is [tex]h(x) = 4(3)^{x + 7} - 9[/tex]
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Let U=(1,2,3,4,5,6,7,8,9,10) Let A = {2,4,6,8,10}. Let B=(1,3,4,6,9} Determine (A - B)'.
A - B is the complement of B in A; in other words, all the elements of A that do not belong to B.
Since A ∩ B = {4, 6}, we have
A - B = {2, 8, 10}
Then the complement of A - B, denoted (A - B)' is all the elements of the universal set U that do not belong to A - B.
(A - B)' = {1, 3, 4, 5, 6, 7, 9}
Identify the slope and y-intercept of the line whose equation is given. Write the y-intercept as an ordered pair. (Remember the slope-intercept form is y = m x + b)
y = StartFraction 5 Over 6 EndFraction + StartFraction x Over 3 EndFraction
a.
slope = Negative StartFraction 5 Over 6 EndFraction; y-intercept (0, One-third)
b.
slope = Five-sixths; y-intercept (0, One-third)
c.
slope = Negative one-third; y-intercept (0, Five-sixths)
d.
slope = One-third; y-intercept (0, Five-sixths)
The slope of the given linear equation is 1/3 and the y-intercept will be 5/6. Then the correct option is D.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
Identify the slope and y-intercept of the line whose equation is given. Write the y-intercept as an ordered pair.
The linear equation is given below.
[tex]\rm y =\dfrac{5}{6} + \dfrac{x}{3}[/tex]
Then the slope of the equation will be 1/3.
And the y-intercept will be 5/6.
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Answer:
d
Step-by-step explanation:
Write the symbolic expression for each of the following descriptions, then get rid of the radical and make them exponential expressions in fractional form.
11. The eighth root of fifty-seven to the sixth degree
12. The square root of Y to the fourteenth degree
13. The nth root of m to the o plus p degree.
14. The fifth root plus x of eighty-one to the third power.
15. The cube root of five squared.
Answer:
11. [tex]57^{6/8}[/tex]
12. [tex]Y^{14/2}[/tex]
13. [tex]m^{\frac{o+p}{n}}[/tex]
14. [tex]81^{\frac{3}{50+x}}[/tex]
15. [tex]5^{2/3}[/tex]
Step-by-step explanation:
When converting from radicals to rational exponents, there's a quick, easy rule to remember:
[tex]\sqrt[n]{x} =\sqrt[\text{index}]{\text{radicand}}[/tex] the exponent is [tex]\frac{\text{power}}{\text{root}}[/tex][tex]\sqrt[n]{x} = x^{1/n}[/tex]The "power" represents the exponent of the radical/radicand, while the "root" represents the index.
11. the eight root of fifty-seven to the sixth degree.
Write the expression in radical form: [tex]\sqrt[8]{57^6}[/tex]Rewrite using the exponent rule (power over root): [tex]57^{6/8}[/tex]12. the square root of Y to the fourteenth power.
Write the expression in radical form: [tex]\sqrt[2]{Y^{14}}[/tex]Rewrite using the exponent rule (power over root): [tex]Y^{14/2}[/tex]13. the nth root of m to the o plus p degree.
Write the expression in radical form: [tex]\sqrt[n]{m^{o+p}}[/tex]Rewrite using the exponent rule (power over root): [tex]m^{\frac{o+p}{n}}[/tex]14. The fifth root plus x of eighty-one to the third power.
Write the expression in radical form: [tex]\sqrt[5+x]{81^{3}}[/tex]Rewrite using the exponent rule (power over root): [tex]81^{\frac{3}{50+x}}[/tex]15. The cube root of five squared.
Write the expression in radical form: [tex]\sqrt[3]{5^{2}}[/tex]Rewrite using the exponent rule (power over root): [tex]5^{2/3}[/tex]Will a pencil of length 19cm fit in the beaker without poking out of the top?
Answer:
Pencil will poke out everytime, no matter if it lays diagonally, or strictly vertically, because pencil's length is greater than the height and diagonal of the beaker
i need this answer quickly
Solve 2x - 8 ≥ 22 - 4x.
A. x ≥ 5
B. x ≥ -15
C. x ≤ 5
D. x ≤ -15
Answer:
A. x ≥ 5
Step-by-step explanation:
Given :
2x - 8 ≥ 22 - 4x
Add 8 to each side :
2x - 8 + 8 ≥ 22 - 4x + 8
2x ≥ 30 - 4x
Add 4x to each side :
2x + 4x ≥ 30 - 4x + 4x
6x ≥ 30
Divide both sides by 6 :
1/6 x 6x ≥ 1/6 x 30
x ≥ 5
what is he inverse of the function f(x) = 1/2x+10?
Find the area of the figure. (Sides meet at right angles.) 3yd 5yd 5yd 8yd 8yd
Answer:
39 yd²
Step-by-step explanation:
Two rectangles can be formed here.
One smaller of the dimensions 5 × 3 yd
And another of 8 × 3 yd.
Total area = 5×3 + 8×3 (area of rect. = l×b)
= 15 + 24
= 39 yd²
NEED THIS TOO GRADUATE PLS HELP
5x - 3y = 16
4x - 2y = 14
The system when solved is
(-3, -13)
(-5, 17)
(5, -3)
(5, 3)
Determine the intercepts of the line. Do not round your answers. y-6=4(x+5)y−6=4(x+5)
Find the slope of the line graphed below
picture is attached
Answer: The answer is D.
Answer:
it is d cause i really need to be nice so i think it is d
Please help me, I need it asap
Answer:
70°Step-by-step explanation:
We can see that
111 and A are of same value as vertical anglesThe angle formed by intersecting chords measures the half the sum of intercepted arcs.
[tex](152 + ?)/2=111 \\152 + ? = 2*111\\152 + ? = 222\\? = 222 - 152\\? = 70[/tex]A cylinder has a base diameter of 12 inches and a height of 13 inches. What is its volume in cubic inches, to the nearest tenths place?
The volume of the given cylinder.
Solution:First, we'll have to find the raduis.
[tex]d = 2r [/tex]
[tex]r = \frac{12}{2} [/tex]
[tex]r = 6 \: in [/tex]
Now, we can work out the volume.
[tex]V = \pi {r}^{2} h[/tex]
[tex]V = \pi \times {6}^{2} \times 13[/tex]
[tex]V = 1470.26536 \: {in}^{3} [/tex]
[tex]\large\boxed{\sf{V = 1470.3 \: {in}^{3}}}[/tex]
Hence, the volume of the given cylinder is 1470.3 cubic inches.
What is the distance between point C (-4,-6)and point D(1,6)
Answer:
the distance between the CD points is 5
Step-by-step explanation:
(-4,-6) (1,6)
it takes 4 to get from -4 to 0 plus 1 to get to 1
so 4+1=5
Class A has 15 pupils and class B has 29 pupils. Both classes sit the same maths test. The mean score for class A is 35. The mean score for class B is 36. What is the mean score (rounded to 2 DP) in the maths test across both classes?
Answer:
35.66
Step-by-step explanation:
Don't work with the mean given at first
1. Multiply the mean of class A by the number of students in class A
35 times 15=525
2. Multiply the mean of class B by the number of pupils in class B
36 times 29=1044
3. Add the answers you got
1044+525
4.Add the pupils of both classes
29+15=44
5.Then divide the total grades and pupils
1569/44 =35.659
6 Then round off
=35.66
URGENT PLEASE ANSWER. PHOTO OF PROBLEM ATTACHED. BRAINLIEST TO FIRST CORRECT ANSWER.
Answer:
27.23 inches
Step-by-step explanation:
question wants circumference over 2π/3 radians
2π/3 times 180/π = 120 degrees
120 is 1/3 of 360
so question wants 1/3 of the circumference
circumference is π times diameter
π times 26 = 81.6814089933
81.6814089933 divided by 3 =
27.2271363311 =
27.23
Find the sum and express it in simplest form. (3a2+2a)+(5a2-a-7)
Done
[tex] \pink{\underline{\boxed{8a²+a-7}}}[/tex]
Solution :-
[tex]\Longrightarrow\sf{(3a ^2 + 2a) + (5a^2 -a-7)}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{3a^2+ 2a + 5a^2-a-7}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{8a^2+2a-a-7}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex] \Longrightarrow\sf{8a^2+1a-7}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{8a^2+a-7}[/tex]
[tex]\red{━━━━━━━━━━━━━━━━━━━━━━}[/tex]
Which statement best describes ratio
100 POINTS!!! VERY URGENT
Answer:
D) (f o g)(x) = 10x² - 60x + 93
Step-by-step explanation:
f(x) = 10x² + 3
g(x) = x - 3
⇒ (f o g)(x)
⇒ f(x - 3)
⇒ f(x - 3) = 10(x - 3)² + 3
⇒ f(x - 3) = 10(x² - 6x + 9) + 3
⇒ f(x - 3) = 10x² - 60x + 90 + 3
⇒ (f o g)(x) = 10x² - 60x + 93
Answer:
[tex]\textsf{D)} \quad (f \circ g)(x)=10x^2-60x+93[/tex]
Step-by-step explanation:
[tex]\textsf{If }\:f(x)=10x^2+3\:\textsf{ and }\:g(x)=x-3\:\textsf{ then}:[/tex]
[tex]\begin{aligned}(f \circ g)(x) & = f[g(x)]\\ & = f(x-3)\\& = 10(x-3)^2+3\\& = 10(x^2-6x+9)+3\\& = 10x^2-60x+90+3\\& = 10x^2-60x+93\\\end{aligned}[/tex]
Miguel is designing shipping boxes that are rectangular prisms. The shape of one box, with height h in feet, has a volume defined by the function V(h) = h(h - 7)(h - 11). Graph the function. What is the maximum volume for the domain 0 < h < 11? Round to the nearest cubic foot.
Answer:
96 ft³
Step-by-step explanation:
A graphing calculator conveniently graphs this function. It shows the maximum volume is about 96 ft³.
5. John is now three times as old as Bill.
In four years, John will be only twice
as old as Bill. Find John's age.
6
A. 4
B.
C.
8
D. 10
E. 12
Answer:
12 is johns age
Step-by-step explanation:
all you have to do is multiply johns age times 3 then you get your anser
Which is a property of polygons?
A polygon has a maximum of 100 sides
A polygon is a solid figure
A polygon is a open figure
A polygon is a plane figure
Answer:
A polygon is a plane figure.
Step-by-step explanation:
This means it is a 2 dimensional shape that lies flat, it has length and width, it has area but no thickness.
There is no max number of sides, so the first answer is not right.
In math, saying it is solid means its 3-d, so that is not right (it's only 2-d)
Saying its open, means that somewhere on the shape, the sides don't meet up at a corner, like an animal corral with the gate left open. So that's not right. Part of the definition of a polygon is that it is closed.
It is a 2-d shape with straight sides and closed, it lies flat in a plane. The last answer is correct.
Answer:
A polygon is a plane figure.
IF the sum of four times a number and four less than three times a number is seventeen what is the number
Answer: 3
Step-by-step explanation: This equation can be written as 4x+3x-4=17
We can now solve.
Moving the 4 to the other side (adding) and we get 21.
Now we have 4x+3x. Adding like terms, we get 7x = 21. Now we divide by 7.
X = 3.
What is the sum of the fractions?
Answer:
-3/4
Step-by-step explanation:
Problem
-1 1/4 + 1/2
Comment
This combined with the number line is to help you visualize how fractions can be represented and how you find their sum.
The rule is move left when the number is minus. Move right when the number is plus.
so -1 1/4 = (4*-1 -1 )/4 = - 5/4
Start at 0 and move left. The number beside - 1 on the number line is -5/4 Put an arrowhead on the line you just drew. The arrowhead should be just about -5/4.
Each mark on the number line is 1/4 away from the next quarter on the number line.
1/2 = 2/4
So since 1/2 is plus, you move right. You need 2 marks right of -5/4. You will find that is at -3/4
PLEASE HELP ME OR I WILL GET IN TROUBLE PLEASE
kevin and anita are writing poems. kevin has no poems to start and writes three new poems each day anita has four poems to start and writes two new poems each day. After how many days will they have the same number of poems in their collections?
ANSWER
A) 1day
B) 2days
C) 3days
D) 4days
Answer:
4 days
Step-by-step explanation:
Answer:
D)
Step-by-step explanation:
Kevin starts with 0 poems but increases 3 each day
Let kevin = x
y = 3x
Anita has 4 poems to start with but increases 2 each day
Let anita = y
y = 2x + 4
As seen on this graph:
The point of intersection is (4,12)
The x axis being the number of days.
Thus the answer is D)
ANSWER THIS CORRECTLY FOR BRAINLIEST!!!!
Answer:
3052.08
Step-by-step explanation:
in a group of 60 workers they get paid an average of 80$ a day per person.
if some earn $75 a day and the rest earn $100 a day, how many earn $75 a day
Answer:
48 workers earn $75 a day.
Step-by-step explanation:
Let x people earn 75 a day then 60-x earn 100 dollars a day.
Average is $80 a day so total paid out to the 60 workers
= 60*80 = $4800.
So 75x + 100(60-x) = 4800
75x + 6000 - 100x = 4800
6000 - 4800 = 100x - 75x
1200 = 25x
x = 48.