Answers
-----------------------------------------------
Explanation:
Let
P = area of triangle ABC
Q = area of triangle ACD
The two areas mentioned above are in ratio 1.5:1 which basically means
P = 1.5*k
Q = 1*k
for some value k
Notice how P/Q = (1.5k)/(1k) = 1.5 which proves that P:Q = 1.5:1
We can find the value of k by determining the area of triangle ABC
P = area of triangle ABC
P = (base)*(height)/2
P = 36*10/2
P = 360/2
P = 180
If P = 180, then
P = 1.5*k
1.5*k = 180
k = 180/1.5
k = 120
Telling us that
Q = 1*k
Q = 1*120
Q = 120
Q = area of triangle ACD
area of triangle ACD = 120
note how P/Q = 180/120 = 1.5 so P:Q = 1.5:1
We'll use this area to find the base of triangle ACD which is AD
Area of Triangle ACD = (base)*(height)/2
120 = AD*10/2
120*2 = AD*10
240 = AD*10
240/10 = AD
24 = AD
AD = 24
Related Questions
find the difference (-ab+9a-1)-(5ab-3)
Answers
Hope this helps!! ;))
Have a grat day!! <3
Amy and Ebony are shopping. Amy has $77. Together, Amy and Ebony have less than $172. If x represents the amount of money Ebony has, which of the following inequalities represents this information?
A.) $77 + x > $172
B.) $172 + x < $77
C.) $77 + x < $172
D.) x - $77 < $172
Answers
Ebony = x
Together, Amy and Ebony have less than $172:
Amy + Ebony < $172
$77 + x < $172 (Answer C)
1) Given that lines L and M are parallel, which of the statements is true? A) ∠ DEF ≅ ∠ EBC B) ∠ ABC ≅ ∠ DEF C) ∠ ABC ≅ ∠ EBC D) ∠ BEF ≅ ∠ ABC
Answers
What fraction of a batch of trail mix consists of peanuts
Answers
This will be tha answer I tjink
The fraction of a batch of trail mix consisting of peanuts is 43/6.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Number of cups for peanuts = 2(2/3)
Total number of cups in the trial mix.
= 2(2/3) + 3/4 + 2(1/2) + 1(1/4)
= 8/3 + 3/4 + 5/2 + 5/4
= (32 + 9 + 30 + 15)/12
= 86/12
= 43/6
= 7(1/6)
Thus,
The fraction of peanuts is 43/6.
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Hot air is less dense than cool air, so hot air will rise above cool air. Increasing the air temperature inside a hot air balloon makes it lighter than the surrounding air, so the balloon can lift up. The density of hot air is about 0.25 kg/m^3 less than that of cool air, which means a cubic meter of hot air can lift about 0.25 kg. What is the minimum volume of hot air needed to lift a hot air balloon carrying 800 kg?
Answers
The minimum volume of hot air needed to lift a hot air balloon carrying 800 kg is 3200 m³.
Explanation:The minimum volume of hot air needed to lift a hot air balloon carrying 800 kg can be calculated by using the density difference between hot air and cool air. Given that the density of hot air is about 0.25 kg/m³ less than that of cool air, we can calculate the volume of hot air needed.
Let V be the volume of hot air needed. The weight of the hot air balloon is equal to the weight of the cool air displaced by the hot air balloon. So we can set up the equation 800 kg = ((V + 1) - V) x 0.25 kg/m³, where 1 represents the volume of the hot air balloon itself.
Simplifying the equation, we have 800 kg = 0.25 kg/m x 1 m³, which gives us V = 800/0.25 = 3200 m³. Therefore, the minimum volume of hot air needed to lift the hot air balloon carrying 800 kg is 3200 m³.
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A circle is increased to have a circumference that is 4 times larger than the original. Which of the following options best describes the change in the radius of the original circle? increased by a factor of 8 increased by a factor of 4 increased by a factor of 16 increased by a factor of 12
Answers
Answer:
Increased by a factor of 4
Step-by-step explanation:
Jennifer bought a thousand inch roll of ribbon for $21.00. If she cuts the ribbon into 75 equal hair ribbons, how much did she spend per ribbon?
Answers
Hope I helped brainliest pts pls
Mike says that 3/3 of his fraction model is shaded blue. Ryan says that 6/6 of the same model is shaded blue. Are the two fractions equivalent?
Answers
Hope this helped!
the fish tank in Paul's bedroom has a pump that will recirculate 75 gallons of water in 1/4 of an hour. Find the unit rate in gallons per hour.
a. 5 gallons per hour
b. 18.75 gallons per hour
c. 300 gallons per hour
d. 187.5 gallons per hour
Answers
(1/4) hour---------> 0.25 hour
if the pump recirculate 75 gallons of water in -------------> 0.25 hour
X gallons of water in-----------------------------------------> 1 hour
X=75/0.25----------> x=300 gallons /hour
the answer is 300 gallons /hour
Find the distance between the points (2, 3) and (2, 8).
A) 2
B) 5
C) 10
D) 15
Answers
In this case:
square root (2-2) ^2 + (8 - 3)^2
square root of (0)^2 + (5)^2
square root of 25 = 5
So the distance is 5
The value of the distance between the points (2, 3) and (2, 8) is,
⇒ d = 5 units
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
To find the distance between the points (2, 3) and (2, 8).
Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Thus, The value of the distance between the points (2, 3) and (2, 8) is,
⇒ d = √(2 - 2)² + (8 - 3)²
⇒ d = √5²
⇒ d = 5 units
Thus, The value of the distance between the points (2, 3) and (2, 8) is,
⇒ d = 5 units
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Gcf of 28x3 and 16x2y2
Answers
The greatest common factor (GCF) of [tex]28x^{3}[/tex] and [tex]16x^{2} y^{2}[/tex] is the greatest common factor (GCF) of and [tex]16x^{2} y^{2}[/tex] is [tex]4x^{2}[/tex] .
To find the greatest common factor (GCF) of [tex]28x^{3}[/tex] and [tex]16x^{2} y^{2}[/tex]
, we need to identify the common factors between the two expressions.
The prime factorization of is [tex]2.2.7.x.x.x.[/tex]
The prime factorization of [tex]16x^{2} y^{2}[/tex] is [tex]2.2.2.2.x.x.y.y.[/tex]
Now, let's identify the common factors:
Both expressions have [tex]2.2.x.x[/tex] in common.
So, the greatest common factor (GCF) of and [tex]16x^{2} y^{2}[/tex] is [tex]4x^{2}[/tex] .
COMPLETE QUESTION:
Circle the GCF of [tex]28x^{3}[/tex] and [tex]16x^{2} y^{2}[/tex]
[tex]28x^{3}[/tex]: [tex]2.2.7[/tex].*•*•*
[tex]16x^{2} y^{2}[/tex]:[tex]2.2.2.2.x.x.y.y[/tex]
Alexander found the means-to-MAD ratio of two data sets to be 3.4
What can he conclude about the distributions?
A.
They are similar.
B.
They are somewhat similar.
C.
They are different.
D.
They are identical.
Answers
Answer: the answer is c
Step-by-step explanation:
A candy wrapping robot can wrap 434 pieces of candy in five minutes. How many pieces of candy can it wrap in any number of minutes
Answers
y=86.8x (y is total candies wrapped, x is the number of minutes)
The table shows the profit from a school book fair based on the number of books sold. What is the rate of change for the function represented in the table?
$0.50
$0.67
$1.07
$1.50
Book sold Profit f(x)
(X)
100 ║ $50.00
250 ║ $275.00
300 ║ $350.00
350 ║ $425.00
answer is A-$0.50
Answers
You are given a table
[tex]\begin{array}{cc}\text{Number of books sold} & \text{Profit}\\100 & \$50\\250 & \$275\\300 & \$350\\350 & \$450\end{array}[/tex]
The rate of change for the function represented in the table can be calculated using the formula
[tex]\dfrac{y_{i+1}-y_i}{x_{i+1}-x_i},[/tex]
where i=1,2,3.
1. When i=1,
[tex]\dfrac{y_2-y_2}{x_2-x_1}=\dfrac{275-50}{250-100}=\dfrac{225}{150}=1.5[/tex]
2. When i=2,
[tex]\dfrac{y_3-y_2}{x_3-x_2}=\dfrac{350-275}{300-250}=\dfrac{75}{50}=1.5[/tex]
3. When i=3,
[tex]\dfrac{y_4-y_3}{x_4-x_3}=\dfrac{425-350}{350-300}=\dfrac{75}{50}=1.5[/tex]
Then the rate of change is $1.5
Answer: correct choice is D.
The rate of change for the function is [tex]\$ 1.5[/tex]
The rate of change for the function is calculate by the formula
[tex]\frac{y_{n+1}-y_n}{x_{n+1}-x_n}[/tex]
Where [tex]n=1,2,3[/tex].
A) when [tex]n=1[/tex]
[tex]\frac{y_{1+1}-y_1}{x_{1+1}-x_1}=\frac{y_{2}-y_2}{x_{2}-x_2}[/tex]
[tex]\dfrac{275-50}{250-100}=\dfrac{225}{100}[/tex]
Hence Rate of change when [tex]n=1[/tex] is [tex]1.5[/tex]
B)when [tex]n=2[/tex]
[tex]\frac{y_{2+1}-y_2}{x_{2+1}-x_2}=\frac{y_{3}-y_2}{x_{3}-x_2}[/tex]
[tex]\dfrac{350-275}{300-250}=\dfrac{75}{50}[/tex]
Hence Rate of change when [tex]n=2[/tex] is [tex]1.5[/tex]
C) when [tex]n=3[/tex]
[tex]\frac{y_{3+1}-y_3}{x_{3+1}-x_3}=\frac{y_{4}-y_3}{x_{4}-x_3}[/tex]
[tex]\dfrac{425-350}{350-300}=\dfrac{75}{50}[/tex]
Hence Rate of change when [tex]n=3[/tex] is [tex]1.5[/tex]
So the rate of change for function represented in the table is same for different value of [tex]n[/tex] i.e, [tex]\$ 1.5[/tex].
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Find the discriminant of the quadratic $3x^2 - 7x + 6.$
Answers
3 x^2 - 7 x + 6 = 0
Divide both sides by 3:
x^2 - (7 x)/3 + 2 = 0
Subtract 2 from both sides:
x^2 - (7 x)/3 = -2
Add 49/36 to both sides:
x^2 - (7 x)/3 + 49/36 = -23/36
Write the left hand side as a square:
(x - 7/6)^2 = -23/36
Take the square root of both sides:
x - 7/6 = (i sqrt(23))/6 or x - 7/6 = -(i sqrt(23))/6
Add 7/6 to both sides:
x = 7/6 + (i sqrt(23))/6 or x - 7/6 = -(i sqrt(23))/6
Add 7/6 to both sides:
Answer: x = 7/6 + (i sqrt(23))/6 or x = 7/6 - (i sqrt(23))/6
Answer:
Discriminant of the quadratic is-23
Step-by-step explanation:
The given quadratic function is [tex]3x^2-7x+6[/tex]
Comparing with the expression [tex]ax^2+bx+c[/tex]
a = 3, b = -7, c = 6
The discriminant of the quadratic is given by [tex]D=b^2-4ac[/tex]
Substituting the known values, discriminant of the quadratic is
[tex]D=(-7)^2-4(3)(6)\\\\D=49-72\\\\D=-23[/tex]
Therefore, discriminant of the quadratic is-23
can you help me..Pls work it out
Answers
You start off at -20 on the number line. Then move over to the right 16 places and you get to -4 on the number line. Then move to the left 5 spots and you'll land on -9
Or you can think of -20+16 as 20-16 = 4 and just make the result negative. So we would have -20+16-5 turn into -4-5. At this point, we add the numbers to get 4+5 = 9 and the result is negative because we're adding two negatives. So that's why the answer is -9
What's the formula for finding the surface area of a prism and the formula for the surface area of a triangular prism??
Answers
The formula A=1/2 bh
Answer:
i) The general formula to find the surface area of a prism = ph + 2B
ii) The area of the triangular prism = ph + 2([tex]\frac{1}{2} bh[/tex])
Step-by-step explanation:
A prism is a three-dimensional figure. The surface area of a figure is the sum of all the areas of its sides.
For example, rectangular prism has 6 sides, to find the surface of rectangular prism, we need to find the area of each side and add them together to get the surface area.
So, the general formula to find the surface area of a prism = ph + 2B, where "p" is the perimeter of the base, "h" is the height of the prism and B is the area of the base.
Now let's find the area of triangular prism.
In the triangular prism, there are two triangles and three rectangles.
Area of a triangle = [tex]\frac{1}{2} bh[/tex]
So, the area of the triangular prism = ph + 2([tex]\frac{1}{2} bh[/tex])
what is the value of x if
6x +4=4x-2
Answers
-3*6 +4=-14
4*-3 -2=-14
Hope that helps!
2x = -6
Divide by 2
x = -3
_____
When you don't know where to start on a linear equation, you can just subtract the expression on one side so you have an expression equal to zero. Here (below), we choose to subtract (4x -2), the expression on the right, because 4x has a smaller coefficient of x than does 6x. The result will be an x-term with a positive coefficient. (Planning ahead.)
(6x +4) -(4x -2) = 0
2x +6 = 0
Now, you have a variable term and a constant term. In either order, subtract the constant term and divide by the coefficient of the variable term.
2x = -6
x = -3
or
x +3 = 0
x = -3
_____
Remember always and truly: whatever you do to one side of the equation, you must also do to the other side.
Here, for example, when I say "subtract such-and-such", it means "subtract such-and-such from both sides of the equation."
There are folks who will tell you "move such-and-such to the other side and change its sign." Don't even begin to think that way. If you already have been told that, immediately drop that habit of thought.
WHATEVER YOU DO TO ONE SIDE OF THE EQUATION, YOU MUST ALSO DO TO THE OTHER SIDE. This rule is the entire basis for solving algebraic equations.
2 - 4x = 14 A) -4 B) -3 C) 0 D) 3 Eliminate
Answers
Hope this helps
subtract 2 from both sides
-4x = 12
divide both sides by -4
x= -3
ANSWER: B) -3
Hope this helps! :)
which expression is equivalent to 20-4x/4
a. 5-x
b. 5-4x
c. 20-x
d. 80-16x
Answers
The expression (20-4x)/4 equals 5 - x.
Given is an expression (20-4x)/4 we need to find an equivalent expression to it,
A mathematical expression or equation that is equivalent to another expression or equation is one that has the same value or meaning.
In other words, if two phrases yield the same result or depict the same mathematical relationship, they are deemed equal.
So,
By multiplying each word in the brackets by 4, it is possible to simplify the formula (20-4x)/4.
This results in:
(20/4) - (4x/4)
Simplifying even more
5 - x
Therefore, the expression (20-4x)/4 equals 5 - x.
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The westside bakery uses 440 pounds of flour to make 1,000 loaves of bread.Each loaf contains the same amount of flour.How many pounds of flour are used in each loaf of bread
Answers
x= # of pounds of flour per loaf
440/1000= x/1
cross multiply
(440*1)= (1000*x)
440= 1000x
divide both sides by 1000
440/1000= x
0.44= x
x= 0.44 pounds
ANSWER: 0.44 pounds of flour are used in each loaf.
Hope this helps! :)
Final answer:
Each loaf of bread from the Westside bakery contains 0.44 pounds of flour.
Explanation:
To determine the amount of flour used in each loaf of bread, we need to divide the total amount of flour used by the number of loaves produced. In this case, the bakery uses 440 pounds of flour to make 1,000 loaves of bread. So, to find out the amount of flour used in each loaf, we divide 440 by 1,000.
440 ÷ 1,000 = 0.44 pounds of flour
Therefore, each loaf of bread contains 0.44 pounds of flour.
Carlos and Maria drove a total of 233 miles in 4.4 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary.
Answers
Equation 1: x + y = 4.4
x = 4.4 - y
Equation 2: 55x + 50y = 233
55(4.4 - y) + 50y = 233
242 - 55y + 50y = 233
-5y = 233-242
-5y = -9
y=9/5 or 1.8 hours Maria drove
To find time Carlos drove:
x=4.4 - 1.8
x = 2.6 hours
Answer:
Time of driving of Maria = 1.8 hours
Step-by-step explanation:
Let a be time drove by Carlos and b be the time drove by Maria.
Carlos and Maria drove a total of 233 miles in 4.4 hours.
Total time = 4.4 hours
a + b = 4.4 ------------------eqn 1
Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour.
Speed of Carlos = 55 miles per hour
Speed of Maria = 50 miles per hour
Total distance = 233 miles
That is
55 a + 50 b = 233----------------------eqn 2
eqn 1 x 50
50 a + 50 b = 220---------------------------eqn 3
eqn 3 - eqn 2
55 a + 50 b - 50 a - 50 b = 233 - 220
5a = 13
a = 2.6
Substituting in eqn 1
2.6 + b = 4.4
b = 1.8
Time of driving of Maria = 1.8 hours
What is the upper quartile of the data represented in the following box-and-whisker plot?
8
12
16
20
Answers
In a box and whiskers plot, the point on the right edge of the box is called the upper quartile. In this case, that value is 12. It represents the median of the upper half of the set of data.
Answer:
Step-by-step explanation:
12
please help! determine whether the number is closest to 0, or 1. explain why. (a. 10/9) (b. 9/16) (c. 2/15) theyre not answer choices.
Answers
A number greater than 1 is closer to 1 than to 0.
A number between 0 and half is closer to 0 than to 1.
A number between half and 1 is closer to 1 than to 0.
Now we need to see if the given numbers are less than 0, greater than 1, between 0 and half, or between half and 1.
a. 10/9 is greater than 1, so it is closer to 1 than to 0.
b. 9/16 is between half and 1, so it is closer to 1.
c. 2/15 is between 0 and half, so it is closer to 0.
What is the answer to 3(t-7)=6t
Answers
3(t) = 3t
3(-7) = -21
3t -21 = 6t
isolate the -21 by subtracting 3t from both sides
-21 + 3t = 6t
-21 + 3t (-3t) = 6t (-3t)
-21 = 3t
divide 3 from both sides to isolate the t
3t = -21
3t/3 = -21/3
t = -21/3
t = -7
t = -7 is your answer
hope this helps
Which number produces a rational number when added to 1/2?
Answers
Adding any rational number to 1/2 results in another rational number, because rational numbers can always be expressed as fractions with integers as numerators and denominators, making addition straightforward by finding a common denominator.
Any number that can be expressed as a fraction where both the numerator and denominator are integers (excluding zero as the denominator) will produce a rational number when added to 1/2. For example, adding 1/2 to 3 (which is the same as 3/1) will yield 3 1/2 or 7/2, still a rational number. By definition, rational numbers include integers, finite decimals, and repeating or terminating decimals, as they can all be represented as fractions.
Understanding Rational Numbers:
To solve the more difficult problem, one might need to find common denominators when working with more complex fractions. For instance, adding 1/2 to 2/3 requires a common denominator: 3/6 + 4/6 = 7/6. The key point here is that when you add any rational number to another rational number (like 1/2), the result will be rational because you can find a common denominator and then add the numerators, keeping that same common denominator.
A campground consists of 5 square campsites arranged in a line along a beach. The distance from the edge of a campsite to the water at the end of the beach is 4 yd. The area of the campground, including the beach, is 950 sq yd. What is the width of one campsite?
A. 14.35 yd
B. 13.93 yd
C. 11.93 yd
Answers
To find the width of one campsite, we subtract the area of the beach from the total area and divide by 5 (the number of campsites). We set up a quadratic equation and solve for the width, finding that it is approximately 13.93 yd.
Explanation:The student's question is about finding the width of one campsite in a linear arrangement of five campsites along a beach. Given that the area of the campground, including the beach, is 950 sq yd and the distance from the edge of a campsite to the water is 4 yd, we can set up an equation to find the total width of the five campsites. The total width of the campsites will be the total area minus the area of the beach, divided by the length of the campsites (which is 5 times the width of one campsite).
Let's call the width of one campsite 'w'. The area of the beach is 5w * 4 yd, since it extends the entire length of the campsites and is 4 yd wide. Therefore, the area of just the campsites is 950 sq yd - 5w * 4 yd. Since we have five campsites, all of equal width, the total width of the campsites is 5w. So we can set up the following equation:
950 - 5w * 4 = 5w2
Now solve for w:
950 - 20w = 5w25w2 + 20w - 950 = 0Using the quadratic formula, we find that w is approximately 13.93 yd, so the correct answer is B. 13.93 ydB. 13.93 yd. The approximate width of one campsite is 13.81 yards.
Explanation:To find the width of one campsite, we need to divide the area of the campground by the number of campsites. The given area of the campground is 950 sq yd, and there are 5 campsites. So, the area of one campsite is 950 sq yd / 5 = 190 sq yd. Since the campsite is square, the width and length are equal. Let's assume the width of one campsite is 'x' yards. Then the equation becomes x^2 = 190. By taking the square root of both sides, we get x = √190 ≈ 13.81 yards. Therefore, the approximate width of one campsite is 13.81 yards.
Which statements about the opposite of −12 are true?
Select each correct answer.
A. −12 and its opposite are on located on the same side of zero on a number line
B. The opposite of −12 is -1/12
C.−12and its opposite are located the same distance from zero on a number line.
D.The opposite of the opposite of −12 is −12
Answers
I need to know the answer
Answers
Greyson's mom used 4 out of 12 eggs to make pancakes. Then she used 3 out of 12 eggs to make cupcakes. What fraction of a dozen eggs did she used in all? ( Hint: 1 dozen = 12)
Answers
NBDHBbhjnsjkbhBSDBWjcd
Well . . .
4 out of 12 eggs makes the fraction 4/12 for pancakes.
3 out of 12 eggs makes the fraction 3/12 for cupcakes.
4/12 + 3/12 + 7/12
If you don’t know how to do it here you go judging by how easy the question is -
Only add the numerator (top) and keep the denominator (bottom) the same.
Hope this helps :)