If the slope of the line that goes through the points (2, 7) and (5, a) is -3, what is the value of a?
Answers
Answer:
a = -2
Step-by-step explanation:
I graphed the given point (2,7) and then I used that point and plugged the point and the slope into the point-slope formula, which is (y-y₁)=m(x-x₁). Then, I just looked for where x=5 on the line and it was -2
Related Questions
The profit from a business is
described by the function
P(x) = -5x² + 30x + 8, where x
is the number of items made,
in thousands, and P(x) is the
profit in dollars. How many
items will maximize the profit?
Answers
First of all we will understand the question!!
The question is saying that you are given a function and you have to find the value of x which will give the maximum profit... Lets solve it by finding the extrema using the vertex
[tex] \rm \: p(x) = - 5 {x}^{2} + 30x + 8[/tex]
Identify the coefficients a and b of the quadratic function[tex] \rm \: p(x) = { - 5x}^{2} + 30x + 8 \\ \rm \: a = - 5 \: and \: b \: = 30[/tex]
Since a<0, the function has the maximum value at x, calculated by substituting a and b into x=-b/2a[tex] \rm \: x = \frac{30}{ 2 \times (- 5)} [/tex]
Solve the equation for x[tex] \rm \: x = 3[/tex]
The maximum of the quadratic function is at x=3what is the perimeter of the triangle
Answers
How is 0.136¯¯¯¯ written as a fraction in simplest form?
Enter your answer in the box.
Answers
Answer:
[tex]\frac{3}{22}[/tex]
Step-by-step explanation:
the bar above 36 means that the digits 36 are being repeated
we require 2 equations with the repeating digits placed after the decimal point.
let x = 0.13636.. ( multiply both sides by 10 and 1000 )
10x = 1.3636... (1)
1000x = 136.3636... (2)
subtract (1) from (2) thus eliminating the repeating digits
990x = 135 ( divide both sides by 990 )
x = [tex]\frac{135}{990}[/tex] = [tex]\frac{3}{22}[/tex] ← in simplest form
The great pyramid of giza has a square base. the length of each side of the base is approximately 230 meters. the height of the pyramid is approximately 147 meters. using these dimensions, what is the volume, in cubic meters, of the pyramid?
Answers
Answer:
2,592,100 m³
Step-by-step explanation:
The volume of the pyramid can be found by using the given dimensions in the formula for the volume of a square pyramid.
__
formulaV = 1/3s²h
where s is the side length of the square base, and h is the height.
applicationUsing the given dimensions, s = 230 m, h = 147 m, we find the volume to be ...
V = 1/3(230 m)²(147 m) = 2,592,100 m³
The volume of the pyramid is 2,592,100 cubic meters.
Which equation can be simplified to find the inverse of y=x^2-7
Answers
You just switch X with Y
A number cube with the numbers 1 through 6 is rolled. What is the theoretical probability, as a decimal, of the number cube showing a 1? Round the decimal to the nearest hundredth
Answers
Answer:
0.17 (rounded)
Step-by-step explanation:
There's only one way a 1 can appear on a number cube out of 6 possible sides. Thus, the theoretical probability of the number cube showing a 1 is 1/6, or 0.17 rounded.
Quadrilateral RSTU is a rectangle and m/RVU = 72°.
What is m/VRU?
Answers
Answer: [tex]18^{\circ}[/tex]
Step-by-step explanation:
In triangle RUV, angle RUV is a right angle (and thus measures 90 degrees), and angle RVU measures 72 degrees.
Since angles in a triangle add to 180 degrees, angle VRU measures
180-90-72=18 degreesA timer is started and a few moments later a model airplane is launched from the ground. Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−12)2+81
. Which of the following statements is true?
The airplane reaches its minimum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
The airplane reaches its minimum height of 81 feet in 12 seconds.
The airplane reaches its maximum height of 12 feet in 81 seconds.
Answers
The statement which is true is the airplane reaches its maximum height of 81 feet in 12 seconds.
Since the height of the plane is a function given by a parabola, we need to know the equation of a parabola in vertex form
What is the equation of a parabola in vertex form?The equation of a parabola with vertex (h,k) is given by y = a(x - h) + k
Since the height (in feet) of the airplane as a function of time (in seconds after the timer was started) is given by the equation h(t) = −(t − 12) + 81
Since this is the equation of a parabola in vertex form, comparing h with y, we have that a = -1, h = 12 and k = 81Since a = -1 < 0 this implies that the point (h, k) = (12, 81) is a maximum pointSo, the statement which is true is the airplane reaches its maximum height of 81 feet in 12 seconds.
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Which expression is equivalent to startfraction startroot 10 endroot over rootindex 4 startroot 8 endroot?
Answers
The expression that is equivalent to √10 / (4√8) is given as √5 / 8
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the equation:
√10 / (4√8)
Simplifying:
= √10 / (4√(4 * 2))
= √10 / (8√2)
= √5 / 8
The expression that is equivalent to √10 / (4√8) is given as √5 / 8
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What characteristics do all points in Quadrant I share?
A. The x-coordinate is positive and the y-coordinate is positive.
B. The x-coordinate is negative and the y-coordinate is negative.
C. The x-coordinate is positive and y-coordinate is negative.
D. The x-coordinate is negative and y-coordinate is positive.
Answers
Answer:
Option A
Step-by-step explanation:
Remember the things.
In Q1
x>0,y>0in Q2
x<0,y>0in Q3
x<0,y<0in Q4
x>0,y<0Answer:
A. The x-coordinate is positive and the y-coordinate is positive.
Step-by-step explanation:
The Cartesian plane is divided into four regions by the x-axis and y-axis.
These regions are called "quadrants".
Quadrant I is the top right region, where x and y coordinates of points are positive.
From here, move in a counterclockwise direction.
Therefore, Quadrant II is the top left region, where the x-coordinate is negative and the y-coordinate is positive.
Quadrant I → (x, y)
Quadrant II → (-x, y)
Quadrant III → (-x, -y)
Quadrant IV → (x, -y)
What substitution should be used to rewrite 6(x 5)2 5(x 5) – 4 = 0 as a quadratic equation?
Answers
Don’t know how to solve.
Answers
Answer:
$122.88
Step-by-step explanation:
the phone decreases by 20% each year , that is
(100 - 20)% = 80% = [tex]\frac{80}{100}[/tex] = 0.8
the phone reduces by a factor of 0.8 each year , then after 4 years
value = $300 × [tex](0.8)^{4}[/tex] = $122.88
Select the correct answer.
The Cohen family started their wheat farm in 1995. The equation models the number of bushels of wheat they produced each year, where t
is the number of years since 1995.
C(t) = 7,000+500 In(t+1)
The Mason family also started their wheat farm in 1995. The graph models the number of bushels of wheat they produced each year, where t
is the number of years since 1995.
M(1)
12,000
8,000
4,000
-24-168
16 24
4,000
-8,000+
12,000
Which statement is true about the quantity of wheat the two farms will produce as the years pass?
OA The wheat production of both farms will continue to increase each year without bound.
OB. The Cohen farm's wheat production will continue to increase each year without bound, while the Mason farm's wheat
production will approach a stable amount.
OC. The Mason farm's wheat production will continue to increase each year without bound, while the Cohen farm's wheat
production will approach a stable amount.
O D.
The wheat production of both farms will approach a stable amount as the years pass.
Answers
The wheat production of both farms will approach a stable amount as the years pass.
What is an exponential function?
An exponential function is one that is steadily increasing or decreasing. We can see that in this case there is a positive sign indicating an increase.
Thus, from the graph, we can see that, the wheat production of both farms will approach a stable amount as the years pass.
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write a polynomial that represents the length of the rectangle
help please !!
Answers
Answer:
[tex]\textsf{Length}=0.8x^2-0.7x+0.7\quad \sf units[/tex]
Step-by-step explanation:
Area of a rectangle = width × length
Therefore, to find the length of the rectangle, we need to divide the area by the width.
Using long division:
[tex]\large\begin{array}{r}0.8x^2-0.7x+0.7\phantom{)} \\x+0.5{\overline{\smash{\big)}\,0.8x^3-0.3x^2+0.35x+0.35\phantom{)}}}\\-~\phantom{(}\underline{(0.8x^3+0.4x^2)\phantom{-b))))))))))))))}}\\0-0.7x^2+0.35x+0.35\phantom{)}\\ \underline{-~\phantom{()}(-0.7x^2-0.35x)\phantom{-b)))))}}\\ 0.7x+0.35\phantom{)}\\\underline{-~\phantom{()}(0.7x-0.35)}\\ 0\phantom{)}\end{array}[/tex]
Therefore, the length of the rectangle is:
[tex]0.8x^2-0.7x+0.7[/tex]
What is this and how do you solve it
Answers
b²-4ac is the discriminant (D)!
you use it when you have a second degree function and want to find the x. If:
D<0 -> no x that we can find
D=0 -> 1 answer for x
D>0 -> 2 answers for x
when your D is = or > 0 then you use these formulas to find the x:
x1= (-b-VD)/2a
x2= (-b+VD)/2a
example1:
f(x)=2x²+3x+4=0
D= b²-4ac
= 3²-4×2×4
=9- 32
=-23
-> no answers for x
example2:
f(x)=2x²+5x+2=0
D= 4²-4×2×2
= 25-16
=9
x1= (-b-VD)/2a
= (-5-3)/4
= -8/4
=-2
x2= (-b+VD)/2a
= (-5+3)/4
=-2/4
=-1/2
Market research shows that 30% of consumers are likely to purchase an electronic tablet for younger children under age 10. However, only 2% of consumers are likely to buy a laptop for children under the age of 10. On the other hand, for children ages 10 – 17, 50% of consumers are likely to buy a tablet and 40% are likely to buy a laptop. If a family has a five-year-old son and a 13-year-old daughter, what is the probability of both children receiving a tablet?
Answers
Answer:
see the attachment photo!
11. 6.2 m B 1.8m Calculate the value of x. NOT TO SCALE
Answers
Answer:
24.19
Step-by-step explanation:
[tex] \tan(x) = \frac{6.2}{13.8} \\ x = { \tan}^{1} \frac{6.2}{13.8} \\ x = 24.19320899[/tex]
or the value of x can be 24.20
4 people completed their work in one hour how will it take 3 people to finish it give your answer in minutes
Answers
it would be 45 minutes
-7x + 13 > 41 what is the answer
Answers
Answer:
x < -4
Step-by-step explanation:
-7x>28
7x<-28
x<-4
please give brainliest!
hope this helps :)
Selma's house is 1,450 cm long. How many meters
long is Selma's house?
Answers
Answer:
14.5 Meters
Step-by-step explanation:
1 centimeter= 0.01 Meters
1450 cm x 0.01 =14.5
Ari said there are three possible outcomes when you
spin this spinner twice: two reds, a yellow and a red,
or two yellows.
So, the probability of getting two yellows is 1/3
Do you agree or disagree? Explain your thinking
Please answer fast :(
Answers
========================================================
Reason:
Ari hasn't considered the case of "red and yellow" which is almost identical to "yellow and red".
It helps to lay out a two by two table. Along the rows and columns, you'll have "red" and "yellow". See below.
Then inside the table are the list of all outcomes in the form (x,y) where x is the horizontal component along the columns, and y is the vertical component along the rows.
Example: if x = red and y = red, then we have the outcome (x,y) = (red, red)
As the table shows, we have 4 outcomes. Therefore the probability of getting two yellows is 1/4
Technically the (red, yellow) = (yellow, red) since ultimately order doesn't matter in this case. For some probability problems, order will matter. But again, order doesn't matter here and it means that we can treat these two situations the same. So I can see why Ari thinks there are only three outcomes.
--------------------------------
Here's another way to look at it:
The probability of landing on yellow is 1/2 assuming red and yellow are equally likely.
This means the probability of two yellow in a row is (1/2)*(1/2) = 1/4
Each is spin is independent of any other.
Acellus
Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent?
Answers
Solution:
The right angle sides of two triangles are equal to each other and the included angle on both sides is 90 degrees so the two large triangles are congruent
I need help with 7 8 and 9 question perimeter and area
Answers
The perimeter and area of the equilateral, isosceles and right angled triangle are 16.2mm 12.6mm², 15.2in and 9.61in², 21.47yds and 16.81yds² respectively.
What is the area of the equilateral, isosceles and right angle triangle?Note that:
The perimeter of an Equilateral triangle is expressed as P = 3a
The area of an Equilateral triangle is expressed as A = ((√3)/4)a²
Where a is the dimension of the side.
The perimeter of an Isosceles triangle is expressed as P = 2a + b
The area of an Isosceles triangle is expressed as A = (ah)/2
Where b is the slant height, a is the dimension of the base and h is the height.
The perimeter of a Right angled triangle is expressed as P = a + b + c
The area of a Right angled triangle is expressed as A = (ab)/2
Where a and b is the dimension of the two sides other than the hypotenuse and c is the hypotenuse.
For the Equilateral triangle.
Given that;
a = 5.4mmPerimeter P = ?Area A = ?Perimeter P = 3a
P = 3 × 5.4mm
P = 16.2mm
Area A = ((√3)/4)(5.4mm)²
A = ((√3)/4)( 29.16mm² )
A = 12.6mm²
The Perimeter and Area of the Equilateral triangle are 16.2mm 12.6mm² respectively.
For the Isosceles triangle.
Given that;
Base a = 3.4inSlant height b = 5.9inPerimeter P = ?height h = ?Area A = ?Perimeter P = 2a + b
P = 2(b) + a
P = 2(5.9in) + 3.4in
P = 11.8in + 3.4in
P = 15.2in
The height h is the imaginary line drawn upward from the center of a.
First, we calculate the height using Pythagorean theorem
x² = y² + z²
Where x = b = 5.9in, y = a/2 = 3.4in/2 = 1.7in, and z = h
(5.9in)² = (1.7in)² + h²
34.81in² = 2.89in² + h²
h² = 34.81in² - 2.89in²
h² = 31.92in²
h = √31.92in²
h = 5.65in
Now, the area will be;
A = (ah)/2
A = (3.4in × 5.65in )/2
A = 19.21in²/2
A = 9.61in²
The Perimeter and Area of the Isosceles triangle are 15.2in and 9.61in² respectively.
For the Right angled triangle.
Given that;
a = 8.2ydsb = 4.1ydsc = 9.17ydsPerimeter P = ?Area A = ?Perimeter P = a + b + c
P = 8.2yds + 4.1yds + 9.17yds
P = 21.47yds
Area A = (ab)/2
A = ( 8.2yds × 4.1yds)/2
A = ( 33.62yds²)/2
A = 16.81yds²
The Perimeter and Area of the Right angled triangle are 21.47yds and 16.81yds² respectively.
Therefore, the perimeter and area of the equilateral, isosceles and right angled triangle are 16.2mm 12.6mm², 15.2in and 9.61in², 21.47yds and 16.81yds² respectively.
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Question 5 of 10
What is the surface area of the cube below?
OA. 20 units²
B. 8 units²
C. 24 units²
OD. 12 units²
SUBMIT
Answers
Answer:
S=6a^2
S=6×2^2
S=6×4=24
The right answer is C
Answer:
24 units²
Explanation:
The surface area of cube is 6(side)²
Here given:
a = 2
The surface area:
= 6(2)^2
= 6(4)
= 24
In class 8 A, there are 20 students, 55% students are present on Wednesday. Find out how many people are present that day? How many people are absent on that day?
Answers
Answer:
11 students are present and 9 are absent.
What is the next fraction in this sequence? Simplify your answer.
13/23, 1/2, 10/23, 17/46,
...
Submit
Answers
Answer:
7/23
Step-by-step explanation:
Each answer is 1.5/23 less than the previous
17/46 - 1.5/23 = 17/46 - 3/46 = 14/46 = 7/23
how do you find the breadth of the area in a square
Answers
Answer:
A = l x b
Step-by-step explanation:
Area = length x breath
So find the area and length and work it out by dividing area by length.
Could anyone give me the answer to this question?
Answers
Answer:
36
Step-by-step explanation:
[tex]\angle AOC[/tex] is made up of s + r, and since r is [tex]\frac{3}{5}[/tex] of [tex]\angle AOC[/tex] we know r must be the remaining [tex]\frac{2}{5}[/tex] of [tex]\angle AOC[/tex].
We can solve for [tex]\angle AOC[/tex] by using this equation:
[tex]\frac{2}{5}\angle AOC = 24\\(\frac{2}{5}\angle AOC)\frac{5}{2} = (24)\frac{5}{2}\\ \boxed{\angle AOC = 60}[/tex]
1. 2 fifths of [tex]\angle AOC[/tex] is 24
2. multiply both sides by [tex]\frac{5}{2}[/tex] to isolate [tex]\angle AOC[/tex]
3. [tex]\angle AOC[/tex] is 60°
We can now solve for r
[tex]r = \frac{3}{5}\angle AOC\\r = \frac{3}{5}(60)\\\boxed{r = 36}[/tex]
1. the equation the problem gave us
2. substitute [tex]\angle AOC[/tex] for 60 (we solved for it before)
3. [tex]r[/tex] is 36°
Help will mark brainliest!
Answers
a) The compound interest equation is [tex]C = 4250 \cdot 0.9675^{t}[/tex].
b) There is an approximate loss of $ 987.16.
c) The stock will take approximately 12.979 to decrease by half.
How to find stock losses by compound interest model
Compound interest model represents the gain of a deposit as a function of the number of periods and initial amount. The model is represented below:
[tex]C = C_{o}\cdot (1+r)^{t}[/tex] (1)
Where:
[tex]C_{o}[/tex] - Initial capital, in monetary units.[tex]r[/tex] - Interest rate.[tex]t[/tex] - Period number.[tex]C[/tex] - Current capital, in monetary units.Capital decreases in time when interest rate is a negative number. The equation that models the situation is [tex]C = 4250 \cdot 0.9675^{t}[/tex] and the current capital after eight years is:
C = 4250 · 0.9675⁸
C = 3262.84
That represents an approximate loss of $ 987.16.
And the number of periods required to decrease the capital by half is:
[tex]2125 = 4250 \cdot 0.9675^{t}[/tex]
[tex]0.5 = 0.9675^{t}[/tex]
㏒ 0.5 = t · log 0.9675
t ≈ 20.979
The stock will take approximately 12.979 to decrease by half.
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Eliminate the parameter:
x = (3t+ 2)² y = t - 2
Answers
Solve for t in terms of y :
[tex]y = t - 2 \implies t = y + 2[/tex]
Substitute this into the parametric equation for x :
[tex]x = (3t + 2)^2 \implies x = (3(y + 2) + 2)^2 \implies \boxed{x = (3y+8)^2}[/tex]