Tony because he spent $19 while Mario spent $18. To explain, you would multiply 3 by $4 because Tony bought 3 of the $4 packs of pencils. Therefore, he would have spent $12. In addition, add $7 to $12, you get $19. On the other hand, Mario bout 4 of the $6 binders. That would mean he spent $24 on binders However, he had a $6 coupon which means he can take $6 off the total price of $24. That would mean subtracting $6 from $24. That would get Mario $18
Find the constant of proportionality for the table and write in the form y = kx.
A) y = 9x
B) y = 10x
C) y = 90x
D) y = 1/10x
Please give an honest answer = )
Answer:
B) y = 10x
Step-by-step explanation:
It should not be too hard for you to determine that every number on the bottom row is the same as the number on the top row with a zero appended.
Appending a zero to a number is the same as multiplying it by 10. For example, ...
... 90 = 10·9
... y = 10x
_____
In case that observation doesn't work out for you, you can always solve the given equation for k, then choose values from the table to fill in.
... y = kx
... k = y/x . . . . . divide by the coefficient of k, which is x
Fill in values from the table
... k = 20/2 = 10 . . . . . . from the second column
Now put this value where k is in the equation. After you do that, you know ...
... y = 10x
slope = (30 - 20)/(3 - 2) = 10 /1 = 10
equation
y = 10x
Answer
B) y = 10x
Forty-eight pounds of sand are used to fill 12 bags. Miranda uses the five-step problem-solving plan. After completing the Solve step, how many pounds of sand should she find each bag will hold? Enter you answer in the box.
Hi
Here is the solution.
To find how much sand is in each bag we have to divide the weight of the sand by number bags.
Each bag hold = 48/12 = 4 pounds.
That's the answer.
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Two planes left the same airport traveling in opposite directions. The first plane left at 9:00 a.m. and 2.25 hours later, the two planes were 1825 miles apart. The second plane left at 10:00 a.m. and its average rate was 108 miles per hour slower than the first plane's average rate. Let x represent the first plane's average rate.
What was the first plane's average rate?
Enter an equation that can be used to solve this problem in the first box.
Solve for x and enter the first plane's average rate in the second box.
Answer:
(a) 1825 = 2.25x + (2.25-1)(x -108)
(b) 560 mi/h
Step-by-step explanation:
(a) distance = speed·time
The first plane's speed is x. The distance it travels in 2.25 hours is 2.25x.
The second plane's speed is x-108. It travels only 1.25 hours (since it started an hour later). The distance it travels is then (2.25 -1)(x -108).
The problem statement tells us the total of the distances traveled by the two planes is 1825 miles, so we can write the equation ...
... 1825 = 2.25x + (2.25 -1)(x -108)
(b) Simplifying the equation gives ...
... 1825 = 3.50x -135
To solve this 2-step equation, we add 135, then divide by 3.50.
.. 1960 = 3.50x
... 1960/3.50 = x = 560
The first airplane's speed is 560 mph.
Check
In 2.25 hours, the first plane travels (560 mi/h)·(2.25 h) = 1260 mi.
In 1.25 hours, the second plane travels (452 mi/h)·(1.25 h) = 565 mi.
Then 2.25 hours after the first plane leaves, the planes are 1260 +565 = 1825 miles apart, as given in the problem statement.
The first plane's average rate is 560 mph. The equation that can be used to solve this problem is 2.25x + 1.25(x - 108) = 1825
To solve this problem, we need to set up an equation based on the information given.
First, let x represent the first plane's average rate in miles per hour (mph).The first plane left at 9:00 a.m. and traveled for 2.25 hours at x mph.The second plane left at 10:00 a.m., which is 1.25 hours before the distance was measured. Its speed is x - 108 mph (108 mph slower than the first plane).Using the distance formula (Distance = Speed x Time), we can write the distances covered by both planes.The first plane covered a distance of 2.25x miles.The second plane covered a distance of 1.25(x - 108) miles.The total distance between the two planes is the sum of their traveled distances: 2.25x + 1.25(x - 108) = 1825 miles.Simplifying the equation gives us:
2.25x + 1.25x - 135 = 1825
3.5x - 135 = 1825
Adding 135 to both sides:
3.5x = 1960
Dividing by 3.5:
x = 560
Therefore, the first plane's average rate was 560 mph.
(Fifty points.)
Two functions, P and Q, are described as follows:
Function P
y = 5x + 3
Function Q
The slope is 2 and the y-intercept is 4.
How much more is the slope of function P than the slope of function Q?
A. 3
B. 5
C. 7
D. 8
A
the equation of a line in ' slope-intercept form ' is
y = mx + c ( m is the slope and c the y-intercept )
y = 5x + 3 is in this form with slope m = 5
function Q has equation y = 2x + 4
the slope of function P is 3 more than function Q
(1.18×103)⋅(9.1×10−6)
Your answer would be
10330.9
answer: 3767.74
work:
(1.18 × 103) ⋅ (9.1 × 10 − 6)
121.54 ⋅ (91 − 60)
121.54 ⋅ 31
3767.74
hope this helps! comment if the problems seems wrong :) ❤ from peachimin
Graph the following lines and write the equation in slope-intercept form. e Through the point (2,7.5) with an x intercept of −1.
You can start with the 2-point form of the equation for a line:
... y = (y₂ -y₁)/(x₂ -x₁)·(x -x₁) +y₁
Filling in the given values, you get
... y = (0 -7.5)/(-1 -2)·(x -(-1)) +0
... y = 2.5(x +1) . . . . . simplify a bit
... y = 2.5x +2.5 . . . . slope-intercept form
First you find the slope with the 2 points: (2, 7.5) and (-1, 0)
y1-y2/x1-x2 so 7.5-0/2-(-1) which equals 2.5
Next you solve the slope intercept form equation to get b
y=m*x+b (m is the slope and b is the intercept)
7.5=2.5*2+b
b=2.5
So the equation is y=2.5x+2.5
Solve the system Solve the system of equations of equations
{y= 2x+7 y = 25−x
A (19, 6)
B (6, 19)
C (-6, -19)
D (19, -6)
E none of these
B
since both equations express y in terms of x we can equate the right sides
2x + 7 = 25 - x ( add x to both sides )
3x + 7 = 25 ( subtract 7 from both sides )
3x = 18 ( divide both sides by 3 )
x = 6
substitute x = 6 into either of the 2 equations for y
y = 2x + 7 = ( 2 × 6 ) + 7 = 12 + 7 = 19
solution is (6, 19 )
Fab Pool Cleaning Service charges $35 per month plus a $50 equipment fee for cleaning the pool. Perfect Pools offers a $40 a month service plus a $35 equipment fee. In how many months will the cleaning costs be the same? What will the cost be?
In order to solve this problem, we the cost of both to equal each other, so we need to set up two expressions that will equal each other.
Let t = time in months.
The cost of Fab Pool can be represented by the expression 35t + 50
The cost of Perfect Pools can be represented by the expression by 40t + 35.
Now that we have the cost for each, we need to find when they are the same, so we set the expressions equal to each other.
35t + 50 = 40t + 35
Now we solve like a regular equation
50 = 5t + 35
15 = 5t
t = 3
At three months, the cleaning costs will be the same.
Hey there!!
Fab pool service costs $35 per month, this is a variable, the number of month could change and $50 for equipment. And perfect pools cost $40( a variable ) and $35 for equipment.
Let's take the number of month as 'm'.
The question asks us to find the number of months at which both of these costs become equal.
As the question states, we will have to equate both the sums or the values.
Total cost = Cost for month + Cost for equipment.
Fab pool :
Cost per month = $35
Cost for equipment = $50
Total cost = 35 × ( the number of months ) + 50
Perfect pools :
Cost for month = $40
Cost for equipment = $35
Total cost = 40 × ( the number of months ) + 35
We have taken the number of months as 'm'.
Now, plugging in the values :
Fab pools : 35m + 50
Perfect pools : 40m + 35
Equating this :
... 35m + 50 = 40m + 35
Subtracting 35m on both sides :
... 50 = 5m + 35
Subtracting 35 on both sides:
... 15 = 5m
Dividing by 5 on both sides :
... m = 3
Hence, the number of months is 3.
Hope it helps!!
How do I solve for x here? Use the properties of logarithms to find a value for x. Assume a,b, and M are constants.
[tex]ln(a*b^{x}) = M[/tex]
The answer in the back of the textbook is [tex]x=\frac{M-ln(a)}{ln(b)}[/tex]
But I am unsure how to get to that solution. Do I start with ln(a) + ln(b)^x?
Yes, you're right! The first step is rewriting the equation as
[tex] \ln(a) + \ln(b^x) = M [/tex]
Subtract [tex] \ln(a) [/tex] from both sides:
[tex] \ln(b^x) = M-\ln(a) [/tex]
Use the property [tex] \ln(a^b) = b\ln(a) [/tex] to rewrite the equation as
[tex] x\ln(b) = M-\ln(a) [/tex]
Divide both sides by [tex] \ln(b)[/tex]
[tex] x = \dfrac{M-\ln(a)}{\ln(b)} [/tex]
Alternative strategy:
Consider both sides as exponents of e:
[tex] e^{\ln(ab^x)} = e^M [/tex]
Use [tex] e^{\ln(x)} = x [/tex] to write
[tex] ab^x = e^M [/tex]
Divide both sides by a:
[tex] b^x = \dfrac{e^M}{a} [/tex]
Consider the logarithm base b of both sides:
[tex] x = \log_b\left(\dfrac{e^M}{a}\right) [/tex]
The two numbers are the same: you can check it using the rule for changing the base of logarithms
To solve ln(a*b^x) = M, apply the log properties to get ln(a) + x*ln(b) = M, isolate x to get x*ln(b) = M - ln(a), and divide by ln(b) to find x = (M - ln(a))/ln(b).
To solve the equation ln(a*b^x) = M for x, begin by applying the property that the logarithm of a product is equal to the sum of the logarithms. That is, ln(xy) = ln(x) + ln(y). Therefore, we can write:
ln(a*b^x) = ln(a) + ln(b^x)
The logarithm of a power allows us to move the exponent to the front of the log, hence:
ln(b^x) = x * ln(b)
Now, our equation becomes:
ln(a) + x * ln(b) = M
We can isolate x by subtracting ln(a) from both sides:
x * ln(b) = M - ln(a)
Finally, divide both sides of the equation by ln(b) to solve for x:
x = (M - ln(a)) / ln(b)
solve the equation. 3(2k-9)+4=5-2(k+7) (show work please)
Hey there!!
Given equation :
... 3 ( 2k - 9 ) + 4 = 5 - 2 ( k + 7 )
Using the distributive property :
... 6k - 27 + 4 = 5 - 2k - 14
Combining the like terms :
... 6k - 23 = -2k - 9
Adding 2k on both sides :
... 8k - 23 = -9
Adding 23 on both sides :
... 8k = 24
Dividing by 8 on both sides :
... k = 24 / 8
... k = 3
The required answer is 3.
Hope my answer helps!!
Which answers are examples of the Law of Detachment?
Select each correct answer.
If it snows tomorrow, then my dentist appointment will be canceled. If my dentist appointment is canceled, then I will clean under my bed. Therefore, if it snows tomorrow, then I will clean under my bed.
Jonathan’s cars are all white. Sarah is driving one of Jonathan’s cars. Therefore, Sarah is driving a white car.
If an object is a square, then it is a rhombus. If it is a rhombus, then it is a quadrilateral. Therefore, if an object is a square, then it is a quadrilateral.
If two angles are vertical angles, then they have the same measure. Angle A and angle B are vertical angles. So, the measure of angle A is equal to the measure of angle B.
the answer is b and d!
The examples of the Law of Detachment are:
1. If it snows tomorrow, then my dentist appointment will be canceled.
If my dentist appointment is canceled, then I will clean under my bed. Therefore, if it snows tomorrow, then I will clean under my bed.
3. If an object is a square, then it is a rhombus. If it is a rhombus, then it is a quadrilateral. Therefore, if an object is a square, then it is a quadrilateral.
What is Law of Detachment?It states that if a conditional statement (if-then statement) is known to be true and its hypothesis (the "if" part) is true, then the conclusion (the "then" part) can be validly inferred as true.
The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then the conclusion must also be true. In both the first and third examples, the statements follow this pattern.
So, the examples of the Law of Detachment are:
If it snows tomorrow, then my dentist appointment will be canceled.If my dentist appointment is canceled, then I will clean under my bed. Therefore, if it snows tomorrow, then I will clean under my bed.
If an object is a square, then it is a rhombus. If it is a rhombus, then it is a quadrilateral. Therefore, if an object is a square, then it is a quadrilateral.Learn more about Law of Detachment here:
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Write the equation of the line in slope intercept form
Using Rise/Run, the answer would be y= -3/4x + 3.
y = - [tex]\frac{3}{4}[/tex] x + 3
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-interceot )
to calculate m use the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (4, 0 ) ← 2 points on line
m = [tex]\frac{0-3}{4-0}[/tex] = - [tex]\frac{3}{4}[/tex]
the line crosses the y- axis at (0, 3 ) → c = 3
y = - [tex]\frac{3}{4}[/tex] x + 3 ← in slope-intercept form
To travel 100 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 42 miles riding a bicycle. Sue travels 19 miles per hour faster than Doreen. Find the times and rates of both girls.
Let us assume Doreen rate = x miles per hour.
Sue travels 19 miles per hour faster than Doreen.
Therefore,
Rate of Sue = (x+19) miles per hour.
We know time, rate and distance relation as
Time = Distance / rate.
Therefore, time taken by Doreen to travel 42 miles at the rate x miles per hour =
[tex]\frac{42}{x}[/tex].
And time taken by Sue to travel 100 miles at the rate (x+19) miles per hour =
[tex]\frac{100}{(x+19)}[/tex].
Sue takes 3 hours less time than it takes Doreen.
Therefore,
[tex]\frac{42}{x}-\frac{100}{(x+19)}=3[/tex]
We need to solve the equatuion for x now.
[tex]\frac{42}{x}-\frac{100}{\left(x+19\right)}=3[/tex]
[tex]\mathrm{Find\:Least\:Common\:Multiplier\:of\:}x,\:x+19:\quad x\left(x+19\right)[/tex]
[tex]\mathrm{Multiply\:by\:LCM=}x\left(x+19\right)[/tex]
[tex]\frac{42}{x}x\left(x+19\right)-\frac{100}{x+19}x\left(x+19\right)=3x\left(x+19\right)[/tex]
[tex]42\left(x+19\right)-100x=3x\left(x+19\right)[/tex]
[tex]-58x+798=3x^2+57x[/tex]
[tex]3x^2+57x=-58x+798[/tex]
[tex]3x^2+57x-798=-58x+798-798[/tex]
[tex]3x^2+57x-798=-58x[/tex]
[tex]\mathrm{Add\:}58x\mathrm{\:to\:both\:sides}[/tex]
[tex]3x^2+57x-798+58x=-58x+58x[/tex]
[tex]3x^2+115x-798=0[/tex]
[tex]\mathrm{Solve\:with\:the\:quadratic\:formula}[/tex]
[tex]\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-115+\sqrt{115^2-4\cdot \:3\left(-798\right)}}{2\cdot \:3}:\quad 6[/tex]
[tex]x=\frac{-115-\sqrt{115^2-4\cdot \:3\left(-798\right)}}{2\cdot \:3}:\quad -\frac{133}{3}[/tex]
[tex]x=6,\:x=-\frac{133}{3}[/tex]
We can't take rates as negative numbers.
So, the rate of Doreen (x) = 6 miles per hour.
Rate of Sue = x+19 = 6+19 = 25 miles per hour.
Time taken by Doreen @ 6 miles per hour to cover 42 miles = 42/6 = 7 hours.
Time taken by Sue @ the rate 25 miles per hour to cover 100 miles = 100/25 = 4 hours.
The graph of F(x), shown below, has the same shape as the graph of G(x) = 3x2, but it is shifted down 1 unit. What is its equation? F(x) = _____
A. F(x) = 3(x + 1)2
B. F(x) = 3x2 + 1
C. F(x) = 3x2 - 1
D. F(x) = 3(x - 1)2
Answer:
[tex]F(x)=3x^2-1[/tex]
Step-by-step explanation:
We have been given the function [tex]G(x)=3x^2[/tex], it is shifted down 1 unit. Now, whenever a function is shifted up or down we just the idea of vertical shift which says:
To shift a function up by 'k' units we use:
[tex]g(x)+k[/tex]
To shift a function down by 'k' units we use:
[tex]g(x)-k[/tex]
Here, in our case we have to shift the function down by 1 unit, so we will subtract 1 from the function:
[tex]F(x)=G(x)-1=3x^2-1[/tex]
So the required function is [tex]3x^2-1[/tex].
Write an equation of the line passing through each of the following pairs of points. g (−6, −5), (−4, −3)
The require line is passing through the points [tex](-6,-5)[/tex] and [tex](-4,-3)[/tex].
We can use the following formula to find the equation of the line passing through a pair of points:
[tex]y-y_1=m(x-x_1)[/tex] .................equation (1)
Where 'm' is slope of the line which is defined as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Now, lets say point [tex](x_1, y_1)[/tex] is [tex](-6,-5)[/tex] and point [tex](x_2,y_2)[/tex] is [tex](-4,-3)[/tex].
We will calculate the slope of the line now:
[tex]m=\frac{-3-(-5)}{-4-(-6)} =\frac{-3+5}{-4+6} =\frac{2}{2} =1[/tex]
So, the slope of the required line is 1.
Now, plugging the value of the slope in equation 1, we get:
[tex]y-(-5)=1(x-(-6))[/tex]
[tex]y+5=x+6[/tex]
[tex]y=x+6-5[/tex]
[tex]y=x+1[/tex]
Therefore, the equation of the line passing through the points [tex](-6,-5)[/tex] and [tex](-4,-3)[/tex] is [tex]y=x+1[/tex].
To verify if the equation of line is correct or not, you can plug in any of the points in the equation and compare both the sides:
Lets plug in (-6,-5) in the equation:
[tex]-5=-6+1=-5[/tex]
Hence, the equation of the line is correct.
What is the sum of two solutions of the quadratic equation ax^2+bx+c=0
Try this option:
According to the properties of the quadratic equation the sum of its roots is '-b', in other words x₁+x₂= -b
Answer: -b
if we were to use the quadratic formula, we would get that the roots are
[tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
or that the 2 seperate roots are
[tex]\frac{-b+\sqrt{b^2-4ac}}{2a}[/tex] and [tex]\frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
if we sum these, then the [tex]\sqrt{b^2-4ac}[/tex] bits will cancel and we wil be left with
[tex]\frac{-b-b}{2a}[/tex] or [tex]\frac{-2b}{2a}[/tex] or [tex]\frac{-b}{a}[/tex]
the sum of the solutions is [tex]\frac{-b}{a}[/tex]
PLEASE HURRY ON TIME LIMIT
Which pair of points should be used to find the line of best-fit for the scatterplot?.
J and L
J and M
K and L
K and M
I would say K and M
By eye this looks like the line would pass through points with approximately an equal amount of points above and below the line of best fit
K and M are pair of points which should be used to find the line of best-fit for the scatterplot, option d is correct.
To choose the pair of points that should be used to find the line of best fit, we look for two points on the scatterplot that are representative of the general trend and capture the spread of the data.
The pair of points K and M should be used.
By selecting these two points, we can establish a line that best approximates the overall relationship between the variables.
These points are typically chosen from the extremes of the scatterplot or from points that are evenly distributed across the range of the data. Choosing K and M allows us to incorporate a range of data points, providing a more accurate representation of the overall trend.
By using these two points, we can calculate the slope and intercept of the line of best fit using various regression techniques, such as linear regression.
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Let f(x) = cos(x). Solve the equation f(x) = 0 on [0, 2π). (Enter your answers as a comma-separated list.)
[tex]\frac{\pi }{2}[/tex], [tex]\frac{3\pi }{2}[/tex]
solve cosx = 0
x = [tex]cos^{-1}[/tex](0) = [tex]\frac{\pi }{2}[/tex], [tex]\frac{3\pi }{2}[/tex]
The solutions to the trigonometric equation: 0.5π radians, 1.5π radians.
How to solve a trigonometric equation
In this question we find the case of a trigonometric equation whose solution must be found:
cos (2π · x / T) = 0
Solution:
2π · x / T = cos⁻¹ 0
2π · x / T = 0.5π + i · π, where i is an integer.
2π · x = π · T · (0.5 + i)
[tex]x = \frac{T\cdot (0.5 + i)}{2}[/tex]
Where T is the period of the trigonometric equation.
If we know that T = 2π, then the solutions to the trigonometric equations are:
x = π · (0.5 + i)
x₁ = 0.5π, x₂ = 1.5π
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Point A is located at (1, 10) and point B is located at (20, 18).
What point partitions the directed line segment AB⎯⎯⎯⎯⎯ into a 2:5 ratio?
(1025, 22)
(737, 1557)
(637, 1227)
(5, 1715)
Since the answer choices differ in their first coordinate, it is sufficient to determine that one. The 2:5 ratio means the distance from A to the point is 2/(2+5) = 2/7 of the total distance A to B.
The x-distance from A to B is 20 -1 = 19 units. 2/7 of that is (2/7)·19 = 38/7 = 5 3/7. Adding this value to the x-coordinate of A gives the x-coordinate of the point of interest: 1 +5 3/7 = 6 3/7.
The appropriate answer choice is ...
... (6 3/7, 12 2/7)
Answer:
(6 3/7, 12 2/7)
Step-by-step explanation: because I got it right
the ratio of the measure of a base angle in an isosceles triangle to the measure of the vertex angle is 1:7
Assuming you require the measure of the angles
let x represent each equal base angle then vertex = 7x
The sum of the angles in a triangle = 180°, hence
x + x + 7x = 180
9x = 180 ( divide both sides by 9 )
x = 20
the base angles = 20° and the vertex = 140°
The ratio of the measure of a base angle in an isosceles triangle to the measure of the vertex angle is 1:7. The measure of the base angle is 1/7 times the measure of the vertex angle.
Explanation:In an isosceles triangle, the base angles are congruent, meaning they have the same measure. Let's denote the measure of the base angle as x degrees and the measure of the vertex angle as y degrees. According to the given ratio, we have the equation:
x : y = 1 : 7
To find the exact measures of the angles, we can set up the equation:
x/y = 1/7
Multiplying both sides by y, we get:
x = y/7
Therefore, the measure of the base angle is 1/7 times the measure of the vertex angle.
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The graph of an equation is shown below:
Based on the graph, which of the following represents a solution to the equation?
(−2,−3)
(3, 1)
(1, 3)
(3, 2)
pleaseee help will give brainliest
(1, 3 )
to determine if the given points are a solution to the equation
They must lie on the given line to be a solution
the only one that is on the line is (1, 3 ) and is therefore the only solution
Allison has 5 time as many baseball cards as football cards. In all,she has 120 baseball and football cards. How many baseball cards does Allison have?
100
let the number of football cards be x then she has 5x baseball cards
the total cards she has is 120, hence
x + 5x = 120
6x = 120 ( divide both sides by 6 )
x = 20
Allison has 20 football cards and 5 × 20 = 100 baseball cards
b=baseball cards
f=football cards
b=5f she has 5 times as many baseball cards as football cards so we multiply the football cards by 5 to make them equal
b+f=120 there are 120 football and baseball cards total
5f+f = 120 substitute 5f everywhere you see a b
6f = 120 combine like terms
f=20 divide by 6
there are 20 football cards
b=5f
b=5(20)
there are 100 baseball cards
In ∆ABC, the altitudes from vertex B and C intersect at point M, so that BM = CM. Prove that ∆ABC is isosceles.
Final answer:
To prove that triangle ABC is isosceles, we can use the fact that the altitudes from vertex B and C intersect at point M and BM = CM. Since BM = CM and the two triangles share the side BM, we can conclude that ΔBMC and ΔBMA are congruent by Side-Side-Side Congruence (SSS). Therefore, the corresponding angles and sides of the two triangles are congruent, meaning that AB = AC, and triangle ABC is isosceles.
Explanation:
To prove that triangle ABC is isosceles, we can use the fact that the altitudes from vertex B and C intersect at point M and BM = CM.
When the altitudes from vertex B and C intersect at point M, it creates two right triangles, ΔBMC and ΔBMA.
Since BM = CM and the two triangles share the side BM, we can conclude that ΔBMC and ΔBMA are congruent by Side-Side-Side Congruence (SSS).
Therefore, the corresponding angles and sides of the two triangles are congruent, meaning that AB = AC, and triangle ABC is isosceles.
Solve the equation.
y + 6 = –3y + 26
y = –8
y = –5
y = 5
y = 8
For this case we have the following equation:
[tex]y + 6 = -3y + 26[/tex]
To clear the value of and we have the following steps:
1st step:
We subtract 6 on both sides of the equation:
[tex]y + 6-6 = -3y + 26-6\\y = -3y + 20[/tex]
2nd step:
We subtract "y" from both sides of the equation:
[tex]y-y = -3y-y + 20\\0 = -4y + 20[/tex]
3rd step:
We add [tex]4y[/tex] to both sides of the equation:
[tex]0 + 4y = -4y + 4y + 20\\4y = 20[/tex]
4th step:
We divide between 4 sides of the equation:
[tex]\frac{4y}{4}=\frac{20}{4}\\y = 5[/tex]
Thus, the value of y is 5.
Answer:
[tex]y = 5[/tex]
Option C
Answer:
Step-by-step explanation:
5
assume that when adults with smartphones are randomly selected, 44% use them in meetings or classes. If 10 adult smartphones users are randomly selected find the probability that fewer than 3 of them
Solution: The given random experiment follows Binomial distribution with [tex]n=10,p=0.44[/tex]
Let [tex]X[/tex] be the number of adults who use their smartphones in meetings or classes.
Therefore, we have to find:
[tex]P(X<3)[/tex]
We know the binomial model is:
[tex]P(X=x)=\binom{n}{x} p^{x} (1-p)^{n-x}[/tex]
[tex]\therefore P(X<3) = P(X=0)+P(X=1) +P(X=2)[/tex]
[tex]=\binom{10}{0}0.44^{0}(1-0.44)^{12-0}+\binom{10}{1}0.44^{1}(1-0.44)^{10-1}+\binom{10}{2}0.44^{2}(1-0.44)^{10-2}[/tex]
[tex]=1 \times 1 \times 0.0030 + 10 \times 0.44 \times 0.0054 + 45 \times 0.1936 \times 0.009672[/tex]
[tex]=0.0030+0.0238+0.0843[/tex]
[tex]=0.1111[/tex]
Therefore, the probability that fewer than 3 of them is 0.1111
A one-celled organism measures 32 mm in length in a photograph. If the photo has been enlarged by a factor of 100, what is the actual length of the organism?
32 mm = length × 100
(32 mm)/100 = length . . . . . divide both sides by 100
0.32 mm = length
The actual length of the organism is 0.32 mm.
Let L be the actual length. Then 100 L = 32 mm, and so L = 3 1/8 mm or 3.125 mm.
What is the domain of the given function?
{x | x = –6, –1, 0, 3}
{y | y = –7, –2, 1, 9}
{x | x = –7, –6, –2, –1, 0, 1, 3, 9}
{y | y = –7, –6, –2, –1, 0, 1, 3, 9}
For this case we have:
Let [tex]y = f (x)[/tex] be a given function, where:
x is an independent variable y it is a dependent variableBy definition, the domain of a function is represented by the values associated with the independent variable, that is, the values of x.
Therefore, the domain of the given function is represented by:
[tex]{x | x = -6, -1, 0, 3}[/tex]
Answer:
[tex]{x | x = -6, -1, 0, 3}[/tex]
Answer:
Its A for Edgenuit
Plz plz help for brainlest!!
1.) Give the coordinate rule for translation right 10 Units
2.) Give the coordinate rule for a translation up 10 units
1.) Translation to the right increases the x-coordinate value.
... (x+10, y)
2.) Translation up increases the y-coordinate value.
... (x, y+10)
What is the value of x?
Enter your answer in the box.
We can see that
there are six sides
so, n=6
so, firstly we will find total angle
total angle =(n-2)*180
total angle =(6-2)*180
total angle =720
so, sum of all angles must be 720
so, we get
[tex]x+120+100+128+133+112=720[/tex]
now, we can solve for x
[tex]x+593=720[/tex]
[tex]x=127[/tex].............Answer
To determine whether a number is written in scientific notation, what test can you apply to the first factor, and what test can you apply to the second factor?
(A) Is the first factor of this form?
[minus sign] <digit> [<decimal point> [<digit> ...]]
where square brackets show optional items, and "..." shows items that repeat as much as you may like.
(B) Is the second factor of this form?
10^<integer>