Bashir works in a weather station and has launched a weather ballon. The height of the baloon is 4 kilometers and it is 1 kilometer from the station. In kilometers, what is the approximate distance between the station and the balloon?
(a) 3.0
(b) 3.9
(c) 4.1
(d) 5.3
Answer:
(c) 4.1 km
Explanation:
We are given that the height of the balloon is 4 km and that it is 1 km away from the station.
Setting up the diagram that describes the given scenario, we would end up with a right-angled triangle as the one shown in the attached image
where:
height of the balloon = 4 km represents one side of the triangle
distance between the base of the balloon and the station = 1 km represents the other side
distance between the balloon and the station is the length we want to find and it represents the hypotenuse of the triangle.
To get the length of the hypotenuse, we will use the Pythagorean theorem
[tex]hypotenuse = +\sqrt{(side1)^2 + (side2)^2}[/tex]
Substitute with the givens:
[tex]hypotenuse = +\sqrt{(4)^2 + (1)^2}[/tex] = √17 ≈ 4.1 km
Hope this helps :)
the point slope form of the equation of the line that passes through (-4 -3) and (12, 1) is y - 1 = 1/4 (x - 12). what is the standard form of the equation for this line?
Standard Form is ...
ax + by = c
where a ≥ 0, b > 0 (if a=0), and {a, b, c} are mutually prime integers (unless irrational numbers are involved).
You can get there from where you're starting in a couple of steps. Multiply by the least common denominator of any fractions. (Here, you multiply by 4.) Then put the variable terms on the opposite side from the constant term. Make sure the leading coefficient is positive.
... 4y -4 = x -12
... x -4y = 8 . . . . add 12-4y
I need to prove my sister wrong pleas help.
Each piece of butter is 0.4 ounces
What kind of triangle would the measurements 7ft 15ft 17ft
Answer:
This is an Obtuse triangle.
Step-by-step explanation:
A Equilateral Triangle is a triangle where all sides are equal. Here all sides are different so it is not an Equilateral Triangle.
Isosceles triangle is a triangle that has 2 sides that are equal. Here all sides are different therefore this is not an Isosceles triangle.
A right angled triangle is a triangle whose sides satisfy the following equality.
Lets say A triangle has sides a, b and c. Where c is the highest value.
Then, [tex]a^{2} +b^{2} =c^{2}[/tex]
Lets substitute the values to the above equation to see whether it the triangle we are given satisfies the above equality,
[tex]7^{2} +15^{2}[/tex] = [tex]49+225[/tex]=[tex]274[/tex]
[tex]17^{2} =289[/tex]
Therefore, [tex]7^{2} +15^{2}[/tex] ≠[tex]17^{2}
So it is not a Right Angled Triangle.
If the sum of squares of the shorter sides is greater than the square of the longer side then it is an Acute angle if not it is an obtuse angle.
[tex]7^{2} +15^{2}[/tex] = [tex]274[/tex]≤[tex]17^{2} =289[/tex]
Therefore, This is an Obtuse triangle.
please help with these two questions!! thank you so much :)
What is the solution for the equation 6x − 8 = 4x
Your answer would be x=4.
6x-8=4x
sub 6x from both sides
-8=-2x
divide by -2 both sides
x=4
Hope This Helps!!!
on Monday joe bought 10 cups of coffee and 5 doughnuts for his his office at the cost of $16.50. It turns out that the doughnuts were more popular than the office. On Tuesday he bough 5 cups of coffee and 10 doughnuts for a total of 14.25. How much was each cup of coffee
X= be coffee
Y=be donuts
Set up equations
10x+5y=16.50
5x+10y=14.25
Now multiply first equation by -2 to get a negative
(-2)10x+5y(-2)=16.50(-2)
-20x-10y=-33
Now put both equations to solve for x
-20x-10y=-33
5x+10y=14.25
___________
-15x. = -18.75
Now divide -15 bith sides to get x alone
X= -18.75/-15
X= 1.25
The cost of each coffee cup$1.25
The cost of each coffee cup will be equal to $1.25.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that on Monday joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the office. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of 14.25.
The cost will be calculated by forming linear expressions below,
X= be coffee
Y=be doughnuts
The equations can be written as,
10x+5y=16.50
5x+10y=14.25
Now multiply the first equation by -2 to get a negative.
(-2)10x+5y(-2)=16.50(-2)
-20x-10y=-33
Now put both equations to solve for x
-20x-10y=-33
5x+10y=14.25
___________
-15x. = -18.75
Now divide -15 on both sides to get x alone,
X= -18.75/-15
X= $1.25
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A culture of 2.4X10^11 bacteria is in a Petri dish A. A culture of 8X10^9 bacteria is in Petri dish B. How many times greater is the number of bacteria in Petri dish A than patri dish B. Enter your answer in standard notation in the box.
A culture of 2.4 × 10^11 bacteria is in a Petri dish A
A culture of 8 × 10^9 bacteria is in Petri dish B
Number of times number of bacteria in Petri dish A is greater than that number in Petri dish B:
[tex]\frac{Number of bacteria in Petri dish A}{Number of bacteria in Petri dish B} = \frac{2.4 * 10^11}{8 * 10^9}[/tex]
Divide 2.4 by 8 to give 0.3
Divide 10^11 by 10^9 to give 10^(11-9) = 10^2
The answer is 0.3 × 10²
Which temperature is between 12 Celsius and -10 Celsius?
The difference between 12 Celsius and -10 Celsius is 22 degrees.
There are 20 different, whole number, specific degrees between 12 and -10 Celsius.
Pls explain for each answer you pick pls
So here is how it would go
-12+12 = 08+(-8) = 0-5+-5 = -10-20+20 = 0-2000+2000 = 0if you know two points on a line, how can you find the right the rate of change of the variables being graphed?
The rate of change is the slope of a line. The slope of the line can be calculated using the formula [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. To find the slope of a line using this formula, it is necessary to know two of the points on the line.
I put this into my calculator but it keeps coming out as "error" :/ not sure if it's just my calculator or something with the problem
Find a rational number that is between 5.2 and 5.5. Explain why it is rational.
Answer:
5.3
Step-by-step explanation:
One rational number can be 5.3
It is rational because it has terminating decimal expansion
Graph y - 2 = -3/4 (x - 6) using the point and slope given in the equation.
To graph the equation, use the given slope and point to plot two points and draw a line through them.
Explanation:To graph the equation y - 2 = -3/4 (x - 6) using the given point and slope, we can follow these steps:
First, identify the slope, which is -3/4. The slope represents the rate of change of y with respect to x. In this case, for every 4 units increase in x, y will decrease by 3 units.Next, identify the given point (6, 2). This point is on the graph and will help us plot the line.Using the slope and the given point, you can plot a second point and connect the two points to draw the line.Start with the given point (6, 2) and move 4 units to the right and 3 units down to plot the second point (10, -1).Finally, draw a line through the two plotted points to represent the graph of the equation.if f(x) = 2x^2 - 3x + 4, then f(x + 3) is equal to
f(x + 3) = 2x² + 9x + 13
substitute x = x + 3 into f(x)
f(x + 3) = 2(x + 3)² - 3(x + 3) + 4 = 2(x² + 6x + 9) - 3x - 9 + 4
f(x + 3 ) = 2x² + 12x + 18 - 3x - 9 + 4 = 2x² + 9x + 13
Nancy drove from New York to Boston, a distance of 1144.97 km. She drove with a friend for the first 711.5 km, and then by herself for the remaining distance. How far did Nancy drive by herself? A. 433.47 km B. 333.47 km C. 1855.47 km D. 1856.47 km
PLEASE ANSWER
WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!
Evaluate the square root
The answer would be 9/5
Root 81 =9
Root 25 =5
14g>56 how do you solve this
To start the school year, a teacher spends $54.35 in school supplies for her classroom. During the course of the year, she will restock her supplies and will spend $22 each time she restocks the supplies. The expression below describes this situation.
22x+54.35
In this expression, what is the coefficient and what does it describe?
co·ef·fi·cient
ˌkōəˈfiSHənt/Submit
noun
1.
MATHEMATICS
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x y).
So, 22 is your coefficient.
In the mathematical expression 22x + 54.35, the coefficient is 22. It describes how much the teacher spends in dollars each time she restocks her classroom supplies. The constant term '54.35' represents the initial spending at the start of the school year.
Explanation:In the given expression 22x + 54.35, the coefficient is 22.
The coefficient, in this context, represents the cost (in dollars) that the teacher spends each time she restocks her classroom supplies. Every time the teacher purchases more supplies during the school year, she is spending $22, hence the '22' is multiply by 'x' which indicates the number of times these supplies are restocked.
The constant term '54.35', on the other hand, represents the initial amount the teacher spends at the start of the school year. To summarise, '22x' describes the total expense on supplies restocked during the year, and '54.35' is the initial expenditure.
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What’s the product of 0.54(8)
To find the product of 0.54 and 8, multiply the two numbers together. The product is 4.32.
to calculate the product of 0.54 and 8:
Start by multiplying the whole numbers:
8 * 0 = 0
Next, multiply 8 by the decimal, 0.54:
8 * 0.54 = 4.32
So, you first calculate the product of the whole numbers (8 * 0 = 0), and then you calculate the product of the decimal and the whole number (8 * 0.54 = 4.32).
When you add these results together, you get the final product, which is 4.32.
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Find two numbers a and b whose sum a+b is -5 and whose difference a−b is 1.
Your answer is
a= ____
b= ____
The answer for a would be -2 and for b it would be -3. If you added both -2 and -3 together, you would get a sum of -5, and when for the other equation, the negative in front of b will cancel out the negative in front of -3, making it 3, and when you subtract -2 and 3, you'll end up with a difference of 1. a= -2 b= -3
Is 2x/3 the same as (2/3)x ? Just wondering
the best way to understand is putting a number in place of x and seeing if they are equal to eachother so just to make it simple i'll make x=6
so your first equation is 2(6)/3 =12/3=4 now the other equation would be (2/3)6 = 6
i actually solved it putting 2 in place of x and got the same answer for both so i think they're the same
Which equation has the least steep graph?
A. Y = 4 x - 3
B. Y = -3/4x + 5
C. Y = -10x - 8
D. Y = 1/2x + 2
Option: D is the correct answer.
D) [tex]y=\dfrac{1}{2}x+2[/tex]
Step-by-step explanation:A line is said to be steepest if the modulus of the slope is greatest and it is least steep if the modulus of the slope i.e. |m| is least.
We know that the slope intercept form of a line is given by:
[tex]y=mx+c[/tex]
where m is the slope of the line and c is the y-intercept of the line.
A)
[tex]y=4x-3[/tex]
The slope of line is: 4
i.e. m=4
and |m|=4
B)
[tex]y=\dfrac{-3}{4}x+5[/tex]
the modulus of slope is:
[tex]|m|=\dfrac{3}{4}=0.75[/tex]
C)
[tex]y=-10x-8[/tex]
The modulus of slope of line is:
[tex]|m|=10[/tex]
D)
[tex]y=\dfrac{1}{2}x+2[/tex]
The slope of the line is:
[tex]|m|=\dfrac{1}{2}=0.5[/tex]
The modulus of slope of line in options D is smallest.
Hence, the line in option: D is least steep.
what is equivelent to 4.05 repeating
[tex]x=4.\overline{05}\\\\x=4.050505...\qquad|\cdot100\\\\100x=405.050505...\\\\100x-x=405.050505...-4.050505...\\\\99x=401\qquad|:99\\\\x=\dfrac{401}{99}[/tex]
the difference of two numbers is 28 find both numbers if the larger is four more than three times the smaller
Let x = the smaller number.
Let 4+3x = the larger number.
So, 28 = 4+3x - x
24 = 2x
x = 12.
The smaller number is 12, now we need to find the larger number,
4+3(12)
40
So, the numbers are 12 and 40.
The equation can be solved by setting up two equations based on the information given, and then substitifying and simplifying the equations to solve for the two numbers. The two numbers are 12 and 40.
Explanation:
The subject of this question is dealing with equations in mathematics. To problem-solve this, we can first form an equation based on the information given: The larger number is equal to 'four more than three times the smaller number' and 'the difference between the two numbers is 28'.
So we can set up two equations:
Larger Number (L) = 3* Smaller Number (S) + 4 Larger Number (L) - Smaller Number (S) = 28By substituting the first equation into the second, it resolves as:
3S + 4 - S = 28
which simplifies to:
2S = 24
So, the smaller number S = 24/2 = 12. Substituting S = 12 into the first equation gives:
L = 3*12 + 4 = 36 + 4 = 40
So the two numbers are 12 and 40.
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Whats the answer to 47+4x<7
Isolate the x. Treat the less than sign as equal sign. What you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 47 from both sides
4x + 47 (-47) < 7 (-47)
4x < -40
Next, divide 4 from both sides
(4x)/4 < (-40)/4
x < -40/4
x < -10
x < -10 is your answer
hope this helps
Graph the relation. Is the relation a function? Why or why not? {(–1, 1), (–2, 1), (–2, 2), (0, 2)} Yes; there is only one domain value for each range value. No; a domain value has two range values. Yes; there is only one range value for each domain value. No; a range value has two domain values.
{(–1, 1), (–2, 1), (–2, 2), (0, 2)}
In a function, each input has an output
Each domain has a range. In a function, range can be repeated but domain cannot be repeated. Same domain cannot have two range values.
Here domain is {-1, -2, -2, 0}
Range is { 1, 1, 2, 2}
Domain -2 is repeating so this relation is not a function
Answer : No; a domain value has two range values.
How can you put 32.3 as a mixed number in the simplest form
32.3 is a decimal number in which 3 is the digit at the tenth place.
Mixed number contains a whole number and a fraction part.
32.3 expressed as mixed fraction is [tex]32\frac{3}{10}[/tex] , here 32 is the whole number and [tex]\frac{3}{10}[/tex] is the fraction part.
[tex]\frac{3}{10}[/tex] is the fraction in the simplest form.
For this reason, 32.3 expressed as a mixed number in the simplest form is [tex]32\frac{3}{10}[/tex].
Takala put 9 marbles in the box, jackie put in 7, and laird put in 11. Then they divided the marbles evenly among themselves. How many did each person get?
Answer:
The correct answer is 9.
Step-by-step explanation:
Let's start by analyzing the information we have.
We know that Takala put 9 marbles in the box, jackie put in 7, and laird put in 11.
Before continuing, the most convenient is to add these three things:
9 + 7 + 11 = 27.
We now know that those 27 were divided equally to each other, that is 27: 3.
So we just have to divide:
27: 3 = 9
In this way we can verify that each person obtained 9.
Multiply.
4.9 X 6.7
Enter your answer in the box.
32.83 because using a calculator, you punch in numbers 4.9 and 6.7 together. Then, you press the equal sign to get 32.83