What is the perimeter of △LMN?
A. 8 units
B. 9 units
C. 6 + √10 units
D. 8 + √10 units
we know that
The distance 's formula between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step [tex]1[/tex]
Find the distance MN
[tex]M(-2,1)\\N(-1,4)[/tex]
Substitute in the distance's formula
[tex]d=\sqrt{(4-1)^{2}+(-1+2)^{2}}[/tex]
[tex]d=\sqrt{(3)^{2}+(1)^{2}}[/tex]
[tex]dMN=\sqrt{10}\ units[/tex]
Step [tex]2[/tex]
Find the distance NL
[tex]N(-1,4)\\L(2,4)[/tex]
Substitute in the distance's formula
[tex]d=\sqrt{(4-4)^{2}+(2+1)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(3)^{2}}[/tex]
[tex]dNL=3\ units[/tex]
Step [tex]3[/tex]
Find the distance LM
[tex]L(2,4)\\M(-2,1)[/tex]
Substitute in the distance's formula
[tex]d=\sqrt{(1-4)^{2}+(-2-2)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(-4)^{2}}[/tex]
[tex]dLM=5\ units[/tex]
Step [tex]4[/tex]
Find the perimeter of the triangle LMN
we know that
The perimeter of a triangle is equal to the sum of the three length sides
In this problem
[tex]Perimeter=MN+NL+LM[/tex]
substitute the values in the formula
[tex]Perimeter=(\sqrt{10}+3+5)\ units[/tex]
[tex]Perimeter=(8+\sqrt{10})\ units[/tex]
therefore
the answer is the option D
the perimeter of the triangle LMN is equal to [tex](8+\sqrt{10})\ units[/tex]
Luis starts at one corner of a square field and walks 80 feet along one side to another corner of the field. He turns 90° and walks 60 feet, and then walks straight back to where he started.
What is the area of the part of the field he walked around?
A.
140 ft²
B.
280 ft²
C.
320 ft²
D.
2400 ft²
1/2 x 80 x 60 = 2400 square feet was the area
Determine which package of laundry soap is the better buy: 65 ounces for 6.99 of 120 ounces of 12.99
A package of organic strawberries costs $1.50 while they are in season and $2.25 when they aren’t in season what is the percent increase?
Answer:50 percent
Step-by-step explanation:You need to subtract 2.25 and 1.50 and get 0.75 then divide it to 1.5 and 0.5 then convert it into decimal form and its 50%.
How do you solve x+2a=16+ax-6a ?
You drive your car for 4.5 hours at an average speed of 70 miles per hour how far did you go
the columns in any data table represent __________ in a controlled experiment. a variables b controls
Answer:
A) Variables
A) Independent
A) X
Step-by-step explanation:
I need help with #7 please help
If ray BD bisects angle CBE, ray BC is transparent to ray BA, angle CBD = (3x + 25) degrees, and angle DBE = (7x - 19) degrees, find angle ABD
Answer: The required measure of angle ABD is 148°.
Step-by-step explanation: Given that ray BD bisects angle CBE, ray BC is transparent to ray BA.
Also,
[tex]m\angle CBD=(3x+25)^\circ,~~m\angle DBE=(7x-19)^\circ,~~m\angle ABC=90^\circ.[/tex]
We are to find the measure of angle ABD.
Since ray BD bisects angle CBE, so we have
[tex]m\angle CBD=m\angle DBE\\\\\Rightarrow (3x+25)^\circ=(7x-19)^\circ\\\\\Rightarrow 3x+25=7x-19\\\\\Rightarrow 7x-3x=25+19\\\\\Rightarrow 4x=44\\\\\Rightarrow x=\dfrac{44}{4}\\\\\Rightarrow x=11.[/tex]
So, we get
[tex]m\angle CBD=(3\times11+25)^\circ=58^\circ.[/tex]
Therefore,
[tex]m\angle ABD=m\angle ABC+m\angle CBD=90^\circ+58^\circ=148^\circ.[/tex]
Thus, the required measure of angle ABD is 148°.
If Maria earned $60 in interest over a 4-year period at a 4% simple annual interest rate, how much did she originally deposit in savings?
A.
$160
B.
$320
C.
$375
D.
$800
Answer:
the answer is c} 375
Suppose that a new fuel-efficient European car travels an average of 26 kilometers on 1 liter of gas. If gas costs 1.50 euros per liter, how much will it cost to drive 300 kilometers in dollars?
19.04 dollars.
The student is asking how to calculate the cost of driving 300 kilometers in a fuel-efficient car, with the cost given in dollars instead of euros. To calculate this, we need to perform several steps:
First, calculate the total liters of gasoline needed to drive 300 kilometers in a car that consumes 1 liter per 26 kilometers.Next, calculate the total cost in euros.Finally, convert euros to dollars.Step-by-step, this calculation is:
Fuel Required: 300 km \/ 26 km/l = 11.54 liters (approximately).Total Cost in Euros: 11.54 liters * 1.50 euros/liter = 17.31 euros.Exchange Rate: Assuming an exchange rate of 1 euro = 1.10 dollars (this rate would need to be checked for the current value as it fluctuates).Total Cost in Dollars: 17.31 euros * 1.10 dollars/euro = 19.04 dollars.Therefore, it will cost approximately 19.04 dollars to drive 300 kilometers.
Daphne paid $68a month for 2 years for internet service. How much did she pay in total?
The minute hand of a clock is 6 inches long. how far does the tip of the minute hand move in 15 minutes? how
Answer:
The tip of the minute hand moves approximately 37.7 inches in 15 minutes.
Explanation:
To find how far the tip of the minute hand moves in 15 minutes, we can use the formula for the circumference of a circle:
[tex]\[ \text{Circumference} = 2 \pi r \][/tex]
Where:
- [tex]\( r \)[/tex] is the length of the minute hand (radius of the circle).
Given:
- The length of the minute hand, [tex]\( r = 6 \)[/tex] inches.
Substitute the given value into the formula:
[tex]\[ \text{Circumference} = 2 \pi \times 6 \][/tex]
[tex]\[ \text{Circumference} = 12 \pi \][/tex]
So, the tip of the minute hand moves a distance of [tex]\( 12 \pi \)[/tex] inches in 15 minutes.
To approximate this value:
[tex]\[ 12 \pi \approx 37.7 \][/tex] inches (rounded to one decimal place).
Write an algebraic expression, 1 less than the quotient of a number n and 6
The expression for the 1 less than the quotient of a number n and 6 is n/6 - 1.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The word expression:
1 less than the quotient of a number n and 6:
Here n is the number:
A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56 etc. are the numbers.
The quotient of a number n and 6 = n/6
1 less than the quotient of a number n and 6:
n/6 - 1
If in the linear expression, one variable is present, then the expression is known as the linear expression in one variable.
Thus, the expression for the 1 less than the quotient of a number n and 6 is n/6 - 1.
Learn more about the expression here:
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HELP!!! WILL GIVE 20 POINTS AND BRAINLIEST!!!!
Algebra 2 Will give brainiest
if f (x) =15x-7 then f^-1(x)=
For the function f (x) = 15x - 7, the value of f ⁻¹ (x) is,
⇒ f ⁻¹ (x) = (x + 7) / 15
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = 15x - 7
Now, We can find the inverse of f (x) as;
⇒ f (x) = 15x - 7
Substitute y = f (x),
⇒ y = 15x - 7
Solve for x;
⇒ y + 7 = 15x
⇒ x = (y + 7) / 15
Hence, We get;
⇒ f ⁻¹ (x) = (x + 7) / 15
Thus, The inverse function is,
⇒ f ⁻¹ (x) = (x + 7) / 15
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Which graph represents the solution set of the system of inequalities?
{y<2/3x
y≥−x+2
Answer:
Last graph is the answer.
Step-by-step explanation:
The inequalities are y < [tex]\frac{2}{3}x[/tex] and y ≥ -x + 2
Now first inequality y < [tex]\frac{2}{3}x[/tex] will represent a dotted line passing through origin and a point (3, 2)
This inequality will be in the form a dotted line and shaded area will be below the line.
Second inequality is y ≥ -x + 2
Line representing the inequality will be solid in shape and shaded area will be above this line.
Common shaded area of both the inequalities matches with the last option.
Therefore, Last option (second row last figure) will be the answer.
A line passes through (2, −1) and (4, 5).
Which answer is the equation of the line?
A. −3x+5y=−13
B. −3x+y=−7
C. −3x+y=17
D. −3x+5y=13
The magnitude, M, of an earthquake is defined to be M=log I/S, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 35 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.
log(35) = 1.544
rounded to nearest tenth = 1.5
Answer: The magnitude of the earthquake that is 35 times more intense than a standard earthquake=1.5
Step-by-step explanation:
Given : The magnitude M of an earthquake is defined to be [tex]M=\log \frac{I}{S}[/tex]---(1)
, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and
S is the intensity of a “standard” earthquake, which is barely detectable.
If the magnitude of an earthquake that is 35 times more intense than a standard earthquake
⇒Intensity of earthquake I=35 S
Substitute the value of I in (1), we get [tex]M=\log(\frac{35S}{S})=\log(35)=\log(5\times7)=1.544068[/tex] [tex]\approx1.5[/tex]
∴ The magnitude of the earthquake that is 35 times more intense than a standard earthquake=1.5
Eight plus the quotient of a number and 3 is -2
Help please thanks...............
okay this is the last one i already know how to distribute and such i was just wondering what's my next step
You have 480 feet of fencing to enclose a rectangular garden. you want the length of the garden to be 30 feet greater than the width. find the length and width of the garden if you use all of the fencing.
What is the value of y?
Enter your answer in the box.
Five times the sum of a number and 4 is -15
If a polygon has 5 sides is it a regular pentagon
Write an equation of the line that has a slope of 3 and contains the point (2,5) in point-slope form.
enter the coordinates of the point (−5, 1) after a 180° rotation about the origin. ( , )
(5,-1) because it would turn the points to their opposite "charge" and turn the positive to a negative and a negative to a positive
In your own words, write the rules for multiplying integers. Then write the rules for dividing integers.
best answer gets brainliest