Jared wrote an equation for the perimeter of an equilateral triangle as 3x = 20. What does x represent in his equation?
Answer:
The length of a side of the triangle.
Step-by-step explanation:
An equilateral triangle has 3 equal sides so the x would be equal to one side of the triangle.
Which equation is satisfied by all of the plotted points?
A. y = 2x
B. y = x + 3
C. y = 2x + 1
D. y = -2x
E. y = x
F. y = 3x -3
The answer is y= -2x
A student is running a 10-kilometer race. He runs 1 kilometer every 4 minutes. Select the function that describes his distance from the finish line.
f(x) = - 1 over 4x + 4
f(x) = - 1 over 10x + 4
f(x) = - 1 over 10x + 10
f(x) = - 1 over 4x + 10
Answer:
Option D is correct
[tex]y =-\frac{1}{4}x+10[/tex]
Step-by-step explanation:
Slope intercept form:
The equation of line is given by:
[tex]y=mx+c[/tex] .....[1]
where, m is the rate or slope and c is the y-intercept or initial value.
As per the statement:
Here, y represents the distance in kilometer and x represents the time in minutes.
A student is running a 10-kilometer race
⇒y(0) = b = 10 km
It is also given that he runs 1 kilometer every 4 minutes.
Now, with each passing minute the student is getting closer and closer to the finish line which was 10 kilometers away when the race started. Thus, as the race progresses, the distance between the student and the finish line will decrease.
[tex]m =-\frac{1}{4}[/tex]
Substitute these in [1] we have;
[tex]y = -\frac{1}{4}x+10[/tex]
Therefore, the function that describes his distance from the finish line is, [tex]y = -\frac{1}{4}x+10[/tex]
How to find the product of rational expressions
Find the number of years it would take for $1,200 to earn simple interest of $324 at an annual interest rate of 6% per year.
What is 4/5 4/5 as a mixed number fraction?
Please help me
All of the following are equivalent except _____.
2%
0.2
1/50
0.02
After 3 years, what is the total amount of a compound interest investment of $5,000 at 4% interest, compounded quarterly?
$5,203.71
$5,360.68
$20,480,000
$5,634.13
The perimeter of the rectangle below is 128 units. Find the length of side VW .
Write your answer without variables.
simplify please I need help don't get it
25% of what number is 17
Solve for x.
−5x−4(x−6)=−3
Enter your answer in the box.
x =
Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y.
750x + 17y = 141.61
300x + 30y = 75.90
Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina’s solution?
a. The cost of electricity is $0.17 per unit.
b. The cost of natural gas is $0.20 per unit.
c. The cost of electricity is $0.72 per unit.
d. The cost of natural gas is $0.83 per unit.
D: The cost of natural gas is $0.83 per unit.
Answer:
Option d is correct
The cost of natural gas (y) = $0.83 per unit
Step-by-step explanation:
Given the system of equation:
750x + 17y = 141.61 ......[1]
300x + 30y =75.90 ......[2]
where x is the cost of electricity and y is the costs of natural gas.
Multiply equation [1] by 30 and equation [2] by 75 we get;
[tex]30 \cdot (750x + 17y) = 30 \cdot 141.61[/tex]
Simplify:
22500x + 510y = 4248.3 ......[3]
[tex]75 \cdot (300x + 30y) = 75 \cdot 75.90[/tex]
Simplify:
22500x + 2250y = 5692.5 .......[4]
Subtract equation [3] from [4] we get;
1740 y = 1444.2
Divide by 15 both sides, we get
116 y = 96.28
Since, Katrina solves the above system using linear equation and arrives at the equation :
116 y = 96.28
Division property of equality states that divide the same number to both sides of an equation:
Divide by 116 to both sides of an equation, to solve for y;
[tex]\frac{116 y}{116} =\frac{96.28}{116}[/tex]
Simplify:
y = 0.83 where y represents the cost of natural gas
Therefore, the cost of natural gas y ,is, $ 0.83 per unit.
how do u right this Seven less than the quotient of x and 9
Answer:
(x÷9)−7 is your answer.
which is greater 14 ounces or 0.4 kilograms
After converting 0.4 kilograms to ounces using the appropriate conversion factors, it is determined that 0.4 kilograms is slightly greater than 14 ounces.
Explanation:To determine which is greater, 14 ounces or 0.4 kilograms, we first need to use the appropriate conversion factors to compare the two measurements in the same unit. Since 1 pound is equivalent to 0.4536 kilograms, and 1 pound is also equal to 16 ounces, we need to convert one of the measures so that both are in either ounces or kilograms for a direct comparison.
Converting 0.4 kilograms to ounces:
1 kilogram is approximately 2.20462 pounds (since 1 pound is 0.4536 kg).So, 0.4 kilograms is 0.4 * 2.20462 pounds, which is approximately 0.882 pounds.Next, we convert 0.882 pounds to ounces by multiplying by the conversion factor of 16 ounces per pound: 0.882 * 16 = 14.11 ounces (approximately).Now we have both weights in ounces, and we can see that 14.11 ounces is slightly more than 14 ounces. Therefore, 0.4 kilograms is greater than 14 ounces.
Learn more about Unit Conversion here:https://brainly.com/question/19420601
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The daily rainfall during a two week period in April was: 1, 0.5, 0.3, 0, 0 ,0, 1.2, 3, 0, 1.1, 0.7, 2, 1.3, 2 inches. What was the mode during this two week period?
Answer: 0.3 is the mode
Step-by-step explanation: The mode is what number shows up the most and 0.3 shows up 3 times.
0 shows up twice
How many times does 59 go into 295?
your new cell phone plan charges $50 per month for 400 minutes of talk time. the plan charges $0.10 for each additional minute you talk. you use 50 additional minutes this month. what is your bill for the month?
Answer:
$55
Step-by-step explanation:
What is the length of the altitude of the equilateral triangle below
Answer
Find out the altitude of the equilateral triangle .
To proof
By using the trignometric identity.
[tex]tan\theta = \frac{Perpendicular}{base}[/tex]
As shown in the diagram
and putting the values of the angles , base and perpendicular
[tex]tan 60^{\circ} = \frac{a}{4\sqrt{3}}[/tex]
[tex]tan 60^{\circ} = \sqrt{3}[/tex]
solving
[tex]\sqrt{3} = \frac{a}{4\sqrt{3}}[/tex]
[tex]a = \sqrt{3}\times 4 \sqrt{3}[/tex]
As
[tex]\sqrt{3}\times \sqrt{3} = 3[/tex]
put in the above
a = 4 × 3
a = 12 units
The length of the altitude of the equilateral triangle is 12 units .
Option (F) is correct .
Hence proved
Answer:
F. 12
Step-by-step explanation:
We have been given an image of a triangle and we are asked to find the length of the altitude of our given triangle.
Since we know that altitude of an equilateral triangle splits it into two 30-60-90 triangle.
We will use Pythagoras theorem to solve for the altitude of our given triangle.
[tex]\text{Leg}^2+\text{Leg}^2=\text{Hypotenuse}^2[/tex]
Upon substituting our given values in above formula we will get,
[tex](4\sqrt{3})^2+a^2=(8\sqrt{3})^2[/tex]
[tex]16*3+a^2=64*3[/tex]
[tex]48+a^2=192[/tex]
[tex]48-48+a^2=192-48[/tex]
[tex]a^2=144[/tex]
Upon taking square root of both sides we will get,
[tex]a=\sqrt{144}[/tex]
[tex]a=12[/tex]
Therefore, the length of the altitude of our given equilateral triangle is 12 units and option F is the correct choice.
21. The Johnsons framed a family picture to hang on the wall. The perimeter of the frame is 72 inches. Use the formula P = 2 l + 2 w to find the length of the frame if the width is 14 inches. 21. The Johnsons framed a family picture to hang on the wall. The perimeter of the frame is 72 inches. Use the formula P = 2 l + 2 w to find the length of the frame if the width is 14 inches.
7.What are the steps that you would follow to recreate a triangle using a protractor, a string, and the AAS Congruence Theorem?
ANSWER:
To construct a triangle given one side and the angle at each end of it with compass and straightedge or ruler. It works by first copying the line segment to form one side of the triangle, then copy the two angles on to each end of it to complete the triangle. Follow these steps to draw the recreate a triangle using a protector, a string and angle, angle side congruence theorem.
STEP-BY-STEP EXPLANATION:
Step 1: You will need to choose two angle and one length for both triangle. Noted that the two angle and one length must be the same for both triangle.
Step 2: Draw a long line on a paper
Step 3: Use a ruler to measure the length ,and then make a mark on the string.
Step 4: Use the string to mark on the long line.
Step 5: Use a protractor to measure
Step 6: Use AAS Congruence Theorem to prove that both triangle are congruent.
A piece of furniture has a retail price of $3,200 and is on sale at a 30% discount. how much money will be saved if the piece of furniture is purchased at the sale price?
A rectangle's length is 4 feet more than its width. If the area of the rectangle is 396 square feet, what is its width, in feet?
How many regions would a net for a three-dimensional solid like the one shown have?
Answer:
A
Step-by-step explanation:
Write the trigonometric expression in terms of sine and cosine, and then simplify.
csc2 x − cot2 x
Let w represent the possible weights of boxes on a delivery truck. For this type of delivery, the weight of the box must be within 8 pounds of a standard lifting weight of 48 pounds. Write an inequality to describe the possible weights of boxes.
A. |w – 48| ≥ 8
B. |w – 48| ≤ 8
C. |w – 48| < –8
D. |w – 48| > –8
Which number belongs to the solution set of the equation below? x - 7 = 35
A) 22
B) 28
C) 42
D) 41
9x-3y=3; 3x+8y=-17
I want to know the steps and answers
A company introduces a new product for which the number of units sold S is
S(t)= 200 ( 5- 9/(2+t))
where t is the time in months
(a) Find the avg. value of S(t) during the first year.
(b) During what month does S'(t) equal the avg value during the first year? ...?
3 times a number divided by 2