Answers
Answer:
Gradient of Line ⊥ to AB = m = 3
B) y = 3x+11
Step-by-step explanation:
A) Firstly, finding the slope of AB
Gradient = [tex]\frac{rise}{run}[/tex]
Gradient = [tex]\frac{y2-y1}{x2-x1}[/tex]
Gradient = [tex]\frac{-2-2}{7+5}[/tex]
Gradient = [tex]\frac{-4}{12}[/tex]
Gradient = [tex]\frac{-1}{3}[/tex]
Now, the line has a gradient of negative reciprocal to this one which is perpendicular to AB
So,
Gradient of Line ⊥ to AB = m = 3
B) Equation of line ⊥ to AB:
Gradient = m = 3
Now, Point = (x,y) = (-2,5)
So, x = -2, y = 5
Putting this in slope-intercept form to get b
=> [tex]y = mx+b[/tex]
=> 5 = (3)(-2) + b
=> 5+6 = b
=> b = 11
Now, Putting m and b in the slope intercept form to get the required equation:
=> [tex]y = mx+b[/tex]
=> y = 3x+11
Related Questions
I get how to solve for angle A but wht about angle B? PLS PROVIDE AN EXPLAINATION
Answers
Se tiene el mismo número de cajas de manzanas que de limones. Si en una caja de manzanas caben 13 unidades y en una de limones caben 17, ¿cuántas cajas de cada tipo de fruta se tienen si hay un total de 180 frutas?
Answers
Answer: 6 cajas de cada tipo de fruta.
Step-by-step explanation:
En cada caja de manzanas, tenemos 13 manzanas.
En cada caja de limones, tenemos 17 limones.
Si el numero total de cajas es C, entonces el numero total de manzanas es:
C*13
y el numero total de limones es: C*17.
Si en total tenemos 180 frutas, entonces tenemos que:
C*13 + C*17 = 180
C*(13 + 17) = 180
C*30 = 180
C = 180/30 = 6
Tenemos 6 cajas de cada tipo de fruta.
Answer:
[tex]\large \boxed{\text{6 boxes of apples and 6 boxes of lemons}}[/tex]
Step-by-step explanation:
Let m = the number of boxes of apples. Then
13m = the number of apples
Let l = the number of boxes of lemons. Then
17l = the number of lemons and
13m + 17l = the total number of fruits
You have two conditions:
[tex]\begin{array}{rrclr}(1) & m & = &l\\(2) & 13m + 17l & = & 180\\\end{array}[/tex]
Solve the equations for m and l
[tex]\begin{array}{rrcll}(1) & m & = & l&\\(2) & 13m + 17l & = & 180\\(3)&13m +17m & = & 180 & \text{Substituted (1) into (2)}\\&30m& = &180 &\text{Simplified}\\(4)&m& = &\mathbf{6} &\text{Divided each side by 30}\\& 6& = &l& \text{Substituted (4) into (1)}\\& l& = &\mathbf{6}& \\\end{array}\\\text{You have $\large \boxed{\textbf{6 boxes of apples and 6 boxes of lemons}}$}[/tex]
Check:
[tex]\begin{array}{ccc}6 = 6 & \qquad & 13(6) + 17(6) = 180\\& \qquad & 78 + 102 =180\\& \qquad & 180 = 180\\\end{array}[/tex]
It checks.
A grasshopper makes jumps that are either 17 or 19 cm in length, in either direction (forwards or backwards). Is it possible for the grasshopper to cover a distance of 101 cm in 100 jumps?
Answers
Answer: No. The grasshopper cannot cover exactly 101 cm in exactly 100 jumps.
Step-by-step explanation:
If the grasshopper makes 50 forward jumps of 19 cm and 50 backward jumps of 17 cm (in any order) the jumps total 950-850 for a net result of 100.
Changing to any other amount just gets farther away from the goal.
A system of equations yields no solution of integers.
x + y ==100
19x - 17y =101
You can try it, but the result has a decimal. This grasshopper cannot make partial jumps!
A force of 90 Newton's is applied to a 20cm2 surface. The force applied is then increased by 5 Newton's and the surface is increased by 5cm2 what percentage does the outcome decrease by
Answers
Answer:
15.56%
Step-by-step explanation:
The force applied, F, to the surface is 90N.
The area, A, of the surface is [tex]20 cm^2[/tex] = [tex]0.002m^2[/tex]
The pressure on the surface is:
P = F / A = 90 / 0.002 = 45000 Nm^2
The force is increased by 5N, the new force is 95N.
The surface area is increased by 5 cm^2 = 0.0005 m^2. The new surface area is 0.0025 m^2.
The pressure is now:
P = 95 / 0.0025 = 38000 Nm^2
The percentage decreased is gotten by dividing the difference in the two values by the old value and then multiplying by 100.
=> Difference = 45000 - 38000 = 7000
% decrease is therefore:
= 7000 / 45000 * 100 = 15.56%
There was a 15.56% decrease.
The ratio of the applied force to the area to which the force is applied,
gives the amount of pressure applied.
The outcome decreases by [tex]\underline{15.\overline 5 \%}[/tex]
Reasons:
[tex]\mathrm{Pressure, P} = \dfrac{Force, \, F}{Area, \, A}[/tex]
The initial force, F₁ = 5 N
The initial area, A₁ = 20 cm²
[tex]\mathrm{ } P_1=\dfrac{F_1}{A_1 }[/tex]
[tex]\mathrm{The \ initial \ pressure \ on \ the \ surface \ is \ } P_1=\dfrac{90 \ N}{0.002 \ m^2} = 45,000 \ Pa[/tex]
The new force, F₂ = F₁ + 5 N = 90 N + 5 N = 95 N
The new area, A₂ = A₁ + 5 cm² = 20 cm² + 5 cm² = 25 cm²
The new pressure after the increase is given by the equation;
[tex]\mathrm{ } P_2=\dfrac{F_2}{A_2 }[/tex]
[tex]\mathrm{The \ surface \ pressure \ after \ the \ increase\ is \ } P_2=\dfrac{95 \ N}{0.0025 \ m^2} = \mathbf{38,000 \ Pa}[/tex]
[tex]Percentage \ change = \dfrac{New \ value - Initial \ value}{Initial \ value} \times 100[/tex]
[tex]Percentage \ change = \dfrac{38,000 - 45,000}{45,000} \times 100 = 15.\overline 5 \%[/tex]
The outcome decreases by 15.[tex]\overline 5 \%[/tex]
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The dimensions of a triangle are represented by the functions shown. Which function represents the area of the triangle, ? h(x) = 12x2 + 6x h(x) = 12x2 – 6x h(x) = 24x2 – 12x h(x) = 12x – 6
Answers
Answer:
h(x) = 12x – 6
Step-by-step explanation:
To know which is the function that represents the area of a triangle, you take into account the degree of the given polynomials.
If the degree is 2, the graph of the function is a parabola.
If the degree is 1, the graph of the function is a line.
By comparing all functions you can conclude that only the last option (h(x)=12-x-6) is convenient to construct a triangle. The y-intersect of the function is at y=-6, the slope is positive and the x-intersect is x=1/2. This forms a triangle in the fourth quadrant of the coordinate system.
Answer:
B. g(x) = 12x2 – 6x
Step-by-step explanation:
correct on edge 2020
10.
0.7 + 3.89 is closest to which letter on the number line above?
a. G
b. H
c. 1
d. J
Answers
Answer:
G
Step-by-step explanation:
Looking at the confidential explaniation, 0.7 + 3.89 would be 4.59z
Can you solve (x-5)^2=3
Answers
Answer:
x = 6.73 (corrected to 3 significant figures.)
Step-by-step explanation:
(x-5)^2=3
Square root both sides of the equation.
[tex]\sqrt{(x-5)^2} =\sqrt{3}[/tex]
[tex](x-5) = \sqrt{3}[/tex]
Add 5 to both sides.
[tex]x = \sqrt{3} + 5[/tex]
x = 6.73 (corrected to 3 significant figures.)
Answer:
x=-22 or -13
Step-by-step explanation:
(x-5)^2=3
Or,x^2-10x+25=3
Or,x^2-10x=3-25
Or,x (x-10)=-22
Either
x=-22
Or,
x-10=-22
x=-22+10
x=-12
x=-22,-12
Please help me with a explanation
Answers
Answer:
x = -3 or x = 3
Step-by-step explanation:
Subtract 9 from both sides.
x^2 - 9 = 0
Factor the left side. There is no common factor of the terms. It is a binomial which is the difference of two squares, so it factors into the product of a sum and a difference.
(x + 3)(x - 3) = 0
Set each factor equal to zero.
x + 3 = 0 or x - 3 = 0
Solve each equation.
x = -3 or x = 3
By what percent did the price of a cup of
coffee increase if its price was increased
from $1.25 to $1.35?
A. 7%
B. 8%
C. 10%
D. 12%
Answers
Answer:
8%Option B is the right option.
solution,
Old price=$ 1.25
New price=$ 1.35
Now,
percentage increase:
[tex] \frac{new \: price - old \: price}{old \: price} \times 100 \: percent \\ = \frac{1.35 - 1.25}{1.25} \times 100 \: percent \\ = \frac{0.1}{1.25} \times 100 \: percent \\ = 8 \: percent[/tex]
Hope this helps..
Good luck on your assignment..
Answer:
B.8%
Step-by-step explanation:
First, you figure out that the price increased by ten cents by subtracting the old price from the new one.
Then you figure out what one percent of 1.25 is by dividing it by 100 to get 0.0125.
Finally you can plug in each answer and multiply it with 0.0125 so you end up with 10 cents or 0.1.
8 is the correct answer.
A model of a tower block is made with a scale of 1 : 60. The volume of themodel is 36 000 cm3. Calculate the volume of the actual tower block in m3
Answers
Answer:
7776 m^3
Step-by-step explanation:
The ratio of volumes is the cube of the scale factor. Here, the actual tower has dimensions 60 times those of the model, so the actual volume is ...
(36,000 cm^3)(60^3) = 7.776·10^9 cm^3
= 7.776·10^9(10^-2 m)^3
= 7776 m^3
The actual tower block has a volume of 7776 m^3.
Answer:
Therefore, volume of actual tower = 2.16 m³
Step-by-step explanation:
Scale of model to actual tower = 1:60
This means that the actual tower is larger than the model tower by a scale of 60 times
To calculate the volume of the actual tower, the following steps are used:
1 cm³ of model tower = 60 cm³ of actual tower
∴ 36,000 cm³ of model tower = 60 × 36,000 = 2,160,000 cm³
converting to m³
100 cm = 1 m
(100 cm)³ = (1 m)³
1,000,000 cm³ = 1 m³
∴ 1 cm³ = [tex]\frac{1}{1,000,000} m^{3}[/tex]
∴ 2,160,000 cm³ = [tex]\frac{2,160,000}{1,000,000} m^{3}[/tex] = 2.16 m³
Therefore, volume of actual tower = 2.16 m³
X+(-13) = -5
if anyone can help me out , thank you <3
Answers
Answer:
x=8.
Step-by-step explanation:
x+(-13)=-5 makes x =8.
reason:
(-13)+??=-5.
-5+8=-13
therefore x=8
OAB is a sector of a circle with radius 9cm and center O. The angle at O is 30°.
Answers
Answer:
Area of sector = 21.195 cm²
length of arc = 4.71 cm
Step-by-step explanation:
Given:
Radius of circle (r) = 9 Cm
Angle at O = 30°
Find:
Area of sector.
length of arc.
Computation:
⇒ Area of sector = [θ/360]πr²
Area of sector = [30/360]3.14(9)²
Area of sector = 21.195 cm²
⇒ length of arc = [θ/360]2πr
length of arc = [30/360]2(3.14)(9)
length of arc = 4.71 cm
The graph of g(x) = x - hl+k is shown on the coordinate grid. What must be true about the signs of h and k
Answers
Answer:
Option: The sign of h must be negative, and the sign of k must be positive.
Answer:
D.The sign of h must be negative and the signal of k must be positive *it’s for sure the answer
Step-by-step explanation:
Which equation represents a graph with a vertex at (-1,6)?
Answers
Answer:
B. [tex]y = 3x^2 -6x -3[/tex]
Step-by-step explanation:
Well, we can use the following formula to find the x coordianate of the vertex -b / 2a.
So let’s start with a)
-6 / 6
-1
A. is wrong because its vertex starts with -1.
b)
6 / 6
1
now that we have our x coordinate we can plug it into the equation to get our y.
3 - 6 - 3
So the y coordinate is -6.
Hence, the answer choice B. [tex]y = 3x^2 -6x -3[/tex]
look at the image below.
A bag contains 1 blue, 2 green, 3 yellow, and 3 red marbles, as shown. I WILL GIVE BRAINLIEST 1 blue marble, 2 green marbles, 3 yellow marbles, and 3 red marbles. Which best describes the complement of choosing a red marble? choosing a green or blue marble choosing any marble choosing a blue, green, or yellow marble choosing a yellow marble
Answers
Green/blue marble=1/3 chance
Any Marble= 9/9 chance
Blue/Green/Yellow= 2/3 chance
Yellow= 1/3 chance
Answer:
B.
choosing any marble
Step-by-step explanation:
slove all of it please 100 points
Answers
Answer:
Step-by-step explanation:
5x+y-7=0 isolate y
y=-5x+7 (m=-5,b=7)
9x+7y-14=0
7y=14-9x ( divide both sides by 7)
y=-9x/7 +14/7
y=-9/7 + 2 (m=-9/7, b=2)
x+y=1000
4x+3y=3600 ( multiply the first equation by 3 to eliminate y)
3x+3y=3000
4x+3y=3600 ( subtract the two equations)
3x+3y-(4x+3y)=3000-3600
3x+3y-4x-3y=-600
-x=-600
x=600 ( substitute x in the equation)
x+y=1000
600+y=1000
y=1000-600=400
check : x+y=1000 , (600+400)=1000
check : 4x+3y=3600 = (4(600)+3(400))=2400+1200=3600
how many tickets are sold :
adults x=600/4=150
kids (y)=400/3=133 tickets+1 dollars left
unless( x represent kids then x=200, y represent adult = 100)
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
Question 1:
[tex]5x+y-7=0[/tex]
Write in slope intercept form.
[tex]y=-5x+7 \\m=-5,b=7\\9x+7y-14=0[/tex]
Write in slope intercept form.
[tex]7y=14-9x\\y=-9x/7 +14/7\\y=-9/7 + 2\\m=-9/7, b=2[/tex]
Question 2:
[tex]x+y=1000\\4x+3y=3600[/tex]
[tex]3x+3y=3000\\4x+3y=3600\\3x+3y-(4x+3y) = 3000-3600\\3x+3y-4x-3y=-600\\-x=-600\\x=600[/tex]
[tex]x+y=1000\\600+y=1000\\y=1000-600=400[/tex]
Tickets sold:
Adults:
[tex]x=600[/tex]
Kids:
[tex]y=400[/tex]
Help me out please if anybody can
Answers
Answer:
The correct choices are;
g(0) = 0
g(1) = 1
and ;
g(-1) = 1
Step-by-step explanation:
In this question, we are to select the correct options.
So let’s take a look at the options
The term g(0) is correct
We can see that the base of the graph is sitting on the origin. At the point where x = 0, then g(x) is also = 0
g(1) is not equal to -1.
g(1) is equal to 1, mark the point 1 on the positive x-axis and trace towards the graph.
g(4) = -2 is another wrong option
The graph has no values on the negative y-axis i.e its smallest value is 0
g(1) = 1 is correct
We can trace this out from the graph
g(-1) = 1 is also correct. This is also traceable from the graph also
HELP ME ASAP pls !!
evaluate the function for the given value: f(x)=2x2-5x-17, find f(-3)
Can You please show step by step I want to understand everything :)
Answers
Answer:
16
Step-by-step explanation:
2x² - 5x - 17
Put x as -3 and solve.
2(-3)² - 5(-3) - 17
2(9) - (-15) - 17
18 + 15 - 17
= 16
‼️‼️‼️PLEASE HELP ‼️‼️ I NEED HELP ASAP PLEASE ‼️‼️‼️‼️
Answers
Answer:
C. g(x)=1/3x^2
Step-by-step explanation:
let g(x)= ax^2
It bases through the point (3,3) × -x 3= a×3^2
-x 3= a×9 -x
a= 3/9=1/3
g(x)=1/3x^2
A 7-column table with 2 rows. Column 1 is labeled Sample with entries catfish, all fish. Column 2 is labeled 1 with entries 3, 20. Column 3 is labeled 2 with entries 5, 20. Column 4 is labeled 3 with entries 7, 20. Column 5 is labeled 4 with entries 5, 20. Column 6 is labeled 5 with entries 6, 20. Column 7 is labeled 6 with entries 8, 20. The mean number of catfish in all 6 samples is approximately 5.7. If 200 fish are in the pond, which proportion can be used to predict the number of catfish in the population? StartFraction 5.7 over 20 EndFraction = StartFraction x over 200 EndFraction StartFraction 5.7 over 20 EndFraction = StartFraction 200 over x EndFraction StartFraction 34 over 20 EndFraction = StartFraction x over 200 EndFraction StartFraction 8 over 20 EndFraction = StartFraction 20 over x EndFraction
Answers
Answer: The correct option is 5.7/20 = x/200
Step-by-step explanation: Please refer to the diagram attached for more details.
From the 7-column by 2-row table drawn, you can determine that the mean number of catfish as given in the question is derived as follows;
Mean = Summation of observed data / Number of observations
Mean = (3 + 5 + 7 + 5 + 6 + 8)/6
Mean = 34/6
Mean = 5.6667
Mean ≈ 5.7
Also the mean number of all fish is derived as follows;
Mean = Summation of observed data / Number of observations
Mean = (20 + 20 + 20 + 20 + 20 + 20)/6
Mean = 120/6
Mean = 20
Using relative frequency, we can confidently predict the number of catfish population in the pond. This simply means, if the mean number of catfish is 5.7 and the mean number of all fish is 20, then the relative frequency would be 5.7 over 20 of the total fish population.
Hence, if there is a total of 200 fish in the pond then to predict the proportion which would be catfish can be expressed as follows;
StartFraction 5.7 over 20 EndFraction = StartFraction x over 200 EndFraction.
OR better expressed as;
5.7/20 = x/200
Answer:
5.7/20 = x/200
Step-by-step explanation:
HELP ASAP PLEASE What is the measure of yz (the minor arc) in the diagram below? A.168 B.42 C.192 D.84
Answers
Answer:
B
Step-by-step explanation:
The measure of the tangent- chord angle XYZ is half the measure of its intercepted arc, thus
arc YZ = 2 × 84° = 168° → B
Which number doesn't belong?
Why?
3x
-3
- 3x?
- 5x
Answers
Answer:
-3 does not belong because it is not an algebraic expression unlike the others.
-3 dose not belong because it is an algebraic expression and you can also tell cause it ha no X
How many 6-digit numbers can be created using 8,0,1,3,7, and 5 if each number is used only once?
Answers
There’s 6 numbers that can be used.
The first digit can be any of the 6
The 2nd digit can be any of the 5 left
The 3rd digit can be any of the 4 left
The 4th did fit can be any of the 3 left
The 5th digit can be any of the 3 left
The 6th digit would be the last number left.
Total combinations = 6 x 5 x 4 x 3 x 2 x 1 = 720
Brainly
Simplify: 24-45-9+100
Answers
Answer:
answer will be 70
Step-by-step explanation:
First of all simplify this 24-45
youll get -21
then, simplify-21-9
you'll get -30
and finally simplify-30+100
you'll get 70
Answer:
Step-by-step explanation:
Bodmas rule
+ comes first
100+(-9)
100-9
91
24-45+91
91+(-45)
91-45
46
24+46
70
Therefore answer = 70
Plss mark as Brainliest
There are 90 students in 5th Grade. 10% of them were absent today. How many students were present .
Answers
Answer:
81 students.
Step-by-step explanation:
If 10% of the 90 students were absent, then that means that 9 students were absent. To find the number of students present, simply subtract.
90 - 9 = 81.
- Hope this helped.
According to the U.S. Department of Agriculture, Alabama egg farmers produce millions of eggs every year. Suppose egg production per year in Alabama is normally distributed, with a standard deviation of 83 million eggs. If during only 3% of the years Alabama egg farmers produce more than 2,655 million eggs, what is the mean egg production by Alabama farmers?
Answers
Answer:
The mean egg production 2499 million
Step-by-step explanation:
P(Z > a) = 3% = 0.03
P(Z > a) = 1 - ∅(a)
1 - ∅(a) = 0.03
∅(a) = 1 - 0.03
∅(a) = 0.97
Checking the normal distribution curve, for ∅(a) = 0.97, z = 1.88
This means that area under the normal curve is 3% (0.03) to the right of z = 1.8808
X = μ + (zб)
X = 2,655 millions
б = 83 million
2655 = μ + (1.88 * 83)
2655 = μ + 156.04
μ = 2655 - 156.04
μ = 2498.96
The mean egg production, is therefore, 2499 million
Which of the following investments could be represented by the function A = 250(1 + 0.08/12)12 × 4?
Answers
hello,
the first term is 250 so this is the initial invested amount
[tex](1+\dfrac{0.08}{12})^{12}=(1+\dfrac{8\%}{12})^{12}[/tex]
is to compute 8% annual interest compounded monthly (there are 12 months in a year)
and then multiply by 4 means that it is computed for 4 years so
finally the answer is
$250 is invested at 8% annual interest compounded monthly for 4 years
hope this helps
Which is closest to the total length of the six cars?
A 12.3 ft
B 15.8 ft
C 25.6 ft
D 32.5 ft
Answers
Answer:
d = 32.5 ft
Step-by-step explanation:
The closest to the total length of the six cars is 32.5 ft.
What are trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
Given that, a roller costar making a right triangle's hypotenuse with the height and the base,
We need to find the length of the all the six cars, we will find it, by considering the whole scenario as a right-angled triangle and the roller costar be the hypotenuse,
Here using the concept of Trigonometric Ratios
Sin 38° = 20 / the length of the cars
The length of the cars = 20 / Sin 38°
= 32.5
Hence, the closest to the total length of the six cars is 32.5 ft.
Learn more about Trigonometric Ratios click;
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Answer?someone help me
Answers
Answer:
The angles in the diagram add up to 90°
To find x add the two angles and equate them to 90°
That's
8x + 50 = 90
8x = 90-50
8x = 40
Divide both sides by 8
8x/8 = 40/8
x = 5
Hope this helps you
what number decreased by 6 equals 3 times the number
Answers
Answer:
-3
Step-by-step explanation:
x-6=3x
2x=-6
x=-3
The required number is -3 decreased by 6 equals 3 times.
A number to be determine when decreased by 6 equals 3 times the number.
What is arithmetic?it explores the numbers of operations according to the statements.
Let the number be x,
Now,
x-6=3x
x= -3
Thus, the required number is -3 decreased by 6 equals 3 times.
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