The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle?
5 StartRoot 2 EndRoot units
4 StartRoot 3 EndRoot units
10 StartRoot 2 EndRoot units
16 StartRoot 5 EndRoot units
Answers
Answer:The perimeter of parallelogram PQRS = 2\sqrt{10}+8\sqrt{2} ⇒
2nd answer
Step-by-step explanation:* Lets revise some properties of the parallelogram
- Each two opposite sides are parallel
- Each two opposite sides are equal
- Its perimeter is the twice the sum of two adjacent sides
* Lets solve the problem
∵ PQRS is a parallelogram
∵ The length of side SR is
∵ The length of side QR is
∵ SR and RQ are two adjacent sides
∵ The perimeter of parallelogram PQRS = 2(RQ + SR)
∴ The perimeter of parallelogram PQRS =
∵ =
∵ =
∴ The perimeter of parallelogram PQRS =
Answer:
Option B.
Step-by-step explanation:
It is given that the sides of an equilateral triangle are 8 units long.
Draw an altitude of the triangle.
Altitude of an equilateral triangle is perpendicular bisector.
Let x be the length of the altitude of the triangle.
According to the Pythagoras theorem
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
Using Pythagoras theorem we get
[tex]8^2=4^2+x^2[/tex]
[tex]64=16+x^2[/tex]
[tex]64-16=x^2[/tex]
[tex]48=x^2[/tex]
Taking square root on both sides.
[tex]\sqrt{48}=x[/tex]
[tex]4\sqrt{3}=x[/tex]
The length of the altitude of the triangle is 4√3 units.
Therefore, the correct option is B.
Related Questions
What number would x be for 2x+1/3 and 2x be the same equation
Answers
Answer:
No solution.
Step-by-step explanation:
2x+1/3=2x
1/3=2x-2x
1/3=0
no solution
Complete the statement below to explain how this model shows that 2/3÷3/4=8/9
Answers
To reciprocal the term for dividing, then multiply both fractions and get the solution to model 2/3 ÷ 3/4 = 8/9.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
The numeral model is given in the question following:
⇒ 2/3 ÷ 3/4 = 8/9
According to the given question, the required solution would be as:
Find the reciprocal in this situation to divide by a fraction:
3/4 divided by 2/3
This would be: 2/3 x 4/3
When you multiply the components, you get 8/9.
Thus, to reciprocal the term for dividing, then multiply both fractions and get the solution.
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Final answer:
To show that 2/3 divided by 3/4 equals 8/9, we multiply 2/3 by the reciprocal of 3/4, which is 4/3, yielding the answer 8/9. This illustrates that division by a fraction involves multiplying by its reciprocal.
Explanation:
To explain how the model shows that 2/3 ÷ 3/4 = 8/9, we need to understand division of fractions and the concept of reciprocals. Division of fractions is the same as multiplying by the reciprocal of the divisor. The reciprocal of 3/4 is 4/3. Therefore, to divide 2/3 by 3/4, we multiply 2/3 by 4/3:
(2/3) × (4/3) = 8/9
This demonstrates that dividing by a fraction is equivalent to multiplying by its reciprocal. We can also use familiar scenarios to rationalize the answer. For instance, we know that half of one half (1/2 × 1/2) equals one quarter (1/4) and this helps us understand the process - we are scaling a number by another when we multiply fractions.
When discussing multiplication and division of fractions, it is useful to remember that these operations are fundamentally linked; division is essentially multiplication by a reciprocal. Hence, dividing 2/3 by 3/4 is the same as multiplying 2/3 by the reciprocal of 3/4, which is 4/3, resulting in 8/9.
2kilogram convert into g
Answers
Answer:
The answer is 2000 g
Step-by-step explanation:
We use the following equivalence:
1 kg-------1000g
2kg----- X = (2kgx1000g)/1kg= 2000g
It took a car 5 days to travel 1459 miles. What was this car average speed in miles per hour ?
Answers
Answer:
12.1583333333 miles/hr.
Step-by-step explanation:
24 * 5 = 120 hrs
1459/120 = 12.1583333333
Answer:
12.158 miles/hour
Step-by-step explanation:
[tex]\frac{1459 miles}{5 days} = 291.8 miles/day\\\frac{291.8 miles}{1 day} x \frac{1 day}{24 hours} = 12.158 miles/hour[/tex]
6 dollars of 3 cans of tuna in a unit rate
Answers
The unit rate is $2 per can.
Step-by-step explanation:
You divide 6 by 3 which then equals 2.
Answer:
$2.00 per can
Step-by-step explanation:
if f(x)=4/x+2 and g is the inverse of f, then g'(10)=
Answers
Answer:
The value of g'(10)=[tex]\frac{(-1)}{16}[/tex]
Step-by-step explanation:
Given function is f(x)=[tex]\frac{4}{x} + 2[/tex]
Take f(x)=y
y=[tex]\frac{4}{x} + 2[/tex]
Subtract 2 from both side.
y-2=[tex]\frac{4}{x}[/tex]
x=[tex]\frac{4}{y-2}[/tex]
The inverse of f(x) is written as [tex] \frac{4}{y-2}[/tex]
It is said as g is inverse of f
g(y)=\frac{4}{y-2}[/tex]
g(y)=[tex]\frac{4}{y-2}[/tex]
g(10)=[tex]\frac{4}{10-2}[/tex]
g(10)=[tex]\frac{1}{2}[/tex]
Differentiating both sides we get,
g'(y)=[tex]\frac{4(-1)}{(y-2)^{2}}+0[/tex]
g'(y)=[tex]\frac{(-4)}{(y-2)^{2}}[/tex]
To find g'(10)=[tex]\frac{(-4)}{(10-2)^{2}}[/tex]
g'(10)=[tex]\frac{(-1)}{16}[/tex]
Solve the problem.
6. John bought three cups of root beer. Two of the cups were smalls and the last
was a large. All the cups together add up to 52 fl. oz. of root beer. If the large can hold 36 fl. oz.
of root beer, how much root beer can a small cup hold.
Answers
Answer:
the small cup of root beer can hold 8 fl. oz
Step-by-step explanation:
52-36=16
16/2=8
Each small cup holds 8 fl. oz. Together they hold 16 fl. oz. Plus 36 fl. oz. Which equals 52 fl. oz.
Shawn hikes up a mountain, back down the other side, then around the front of the mountain back to his truck. How far did he go if n = 5 and m = 6?
Answers
Answer:
The distance Shawn went is 40.
Step-by-step explanation:
Given:
N= 5 and M =6
Mountain hike = N = 5
Back down the other side = 2N+1 = 2×5 + 1 = 10 + 1 =11
From Mountain back to truck = 4M = 4×6 = 24
We need to find the total distance he went and can be calculate by adding Mountain hike with back down the other side and then from Mountain back to truck.
Total distance Shawn went = Mountain hike+ Back down the other side + From Mountain back to truck = 5 + 11 + 24 = 40
Hence Shawn went the distance of 40.
Over the course of a year, a company goes from 115 employees to 124 employees.
Use the drop-down menus to build an equation that could be used to find the percent change, p, in the number of employees
Answers
Answer:
on the top is 124 - 115 whille in the bottom is 115
Step-by-step explanation:
To calculate the percent change in the number of employees, use the formula (Change in Quantity / Original Quantity) × 100. The original number of employees is 115, and it increased to 124, resulting in a change of 9. The percent change is approximately 7.83%.
Explanation:To find the percent change in the number of employees, you can use the following formula:
Percent Change (p) = (Change in Quantity / Original Quantity) × 100
In this case, the Original Quantity is the number of employees at the start of the year (115) and the Change in Quantity is the difference between the number at the end of the year (124) and the number at the start of the year (115).
So, we calculate Change in Quantity as 124 - 115 = 9.
Now, using the formula:
p = (9 / 115) × 100
Calculating this gives us the percentage change:
p = (9 / 115) × 100 ≈ 7.83%
The percent change in the number of employees is approximately 7.83%.
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2. One of the most common mutagens in
our environment, that we are exposed
to everyday we are outside in the
sunlight, is
O UV radiation
infrared radiation
Answers
Answer:
Ultraviolet (UV) radiation.
Step-by-step explanation:
Mutagen is part of genetics, it is chemical or physical agent which are present in atmosphere and causes changes or mutation in the genetic materials i.e. in DNA (these changes can be permanent as well). Example of mutagen are radioactive substances, ultraviolet radiation, etc.
UV radiation is an electromagnetic radiation which is present in sunlight. It is a strong mutagen which is when absorbed by DNA can cause extreme damage, for example, uncontrolled division of skin cell can cause skin cancer, that's the reason why UV radiation is the most common mutagen to which we are exposed to when we are outside in the sunlight.
mr morton sold bird houses to stores. he started the week with 60. he sold 10 to one store and divided the rest between 5 other stores. how many birdhouses did he sell to each of the other 5 stores?
Answers
Answer:
10
Step-by-step explanation:
Mr morton initially had 60 bird houses.
He sold 10 to one store.
So left number of birdhouses = 60 - 10 = 50.
He sold them equally to 5 stores,
So, each of them will get [tex]\frac{50}{5}[/tex] = 10 bird houses.
So,
He sold 10 birdhouses to each of the other 5 stores.
INEQUALITIES-PLEASE HELP! Tricia receives a $5 allowance every week. She also earns $6.50 for every hour that she baby-sits. Next week she wants to earn at least $21.25 to buy a present. Please write an inequality to math this equation.
Answers
Answer:
6.50x + 5 = 21.25 is the answer
Step-by-step explanation:
x=2.5
The inequality that represents Tricia's goal to earn at least $21.25 through her $5 allowance and $6.50 per hour from babysitting is E = 5 + 6.50h ≥ 21.25, where h represents the number of hours she babysits.
The student's question asks for an inequality to represent the situation where Tricia receives a $5 weekly allowance and earns $6.50 for each hour she babysits. The goal is to earn at least $21.25 to buy a present.
Let's denote the number of hours Tricia babysits as h. The inequality representing her total earnings E from both her allowance and babysitting will be:
E = 5 + 6.50h ≥ 21.25
This inequality implies that the sum of Tricia's weekly allowance ($5) and her babysitting earnings ($6.50 per hour multiplied by the number of hours h) should be at least $21.25.
Rammy has $9.60 to spend on some peaches and a gallon of milk. Peaches
cost $1.20 per pound, and a gallon of milk costs $3.60.
The inequality 1.20x+ 3.60 39.60 models this situation, where x is the
number of pounds of peaches.
HEF
Solve the inequality. How many pounds of peaches can Rammy buy?
Answers
Answer:
[tex]\large \boxed{\text{5.00 lb}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcl}1.20x + 3.60 & \leq & 9.60\\1.20x & \leq & 6.00\\x &\leq & \mathbf{5.00}\\\end{array}\\\text{Rammy can buy $\large \boxed{\textbf{5.00 lb}}$ of peaches.}[/tex]
Check:
[tex]\begin{array}{rcl}1.20(5.00) + 3.60 & \leq & 9.60\\6.00 + 3.60 & \leq & 9.60\\9.60 & \leq & 9.60\\\end{array}[/tex]
OK.
The number of pounds of peaches that Rammy can buy is 5 pounds.
Based on the information given in the question, the equation to solve the question will be:
1.20x + 3.60 ≤ 9.60
Collect like terms
1.20x ≤ 9.60 - 3.60
1.20x ≤ 6.00
Divide both side by 1.20
1.20x/1.20 ≤ 6.00/1.20
x ≤ 5.00
Therefore, the number of pounds of peaches that Rammy can buy is 5 pounds
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Mrs. William shops at a store that has an annual membership fee of $30. today she paid her annual membership and bought several fruit baskets costing $15 each as gifts for her co-workers. her total was $105. solve the equation 15b+ 30=105 to find the number of fruit baskets mrs. Williams purchased.
Answers
Number of fruit baskets purchased by Mrs. William is 5
Solution:Given that
Annual membership fee of store where Mrs. William shops = $30
Cost of one fruit basket which Mrs. William as gifts for her co-workers = $15
Total amount spent by Mrs. William = $150
Given that "b" represents number of basket purchased
Equation which models the above scenario is as follows
15b+ 30=105 ------ (1)
Where b represents number of fruit basket purchased by Mrs. William
Need to calculate number of fruit basket purchased by Mrs. William
For which we need to solve equation (1) for b
On solving we get
15b+ 30 = 105
On Subtracting 30 from both sides we get
15b + 30 – 30 = 105 – 30
=> 15b = 75
On dividing both sides by 15 we get
[tex]\begin{array}{l}{\frac{15 b}{15}=\frac{75}{15}} \\\\ {=>b=5}\end{array}[/tex]
As variable "b" represents number of basket purchased, hence we can conclude that number of fruit baskets purchased by Mrs. William is 5
What is y+2=⅞(x-3) in standard form?
Answers
Answer:
7x - 8y = 37
Explanation:
y+2 = ⅞(x-3) (distribute ⅞ -- x times 7/8, -3 times 7/8)
y+2 = ⅞x - 21/8 (subtract ⅞x from both sides)
y+2-⅞x = -21/8 (subtract 2 from both sides)
y-⅞x = -37/8 <--- result of -21/8 - 2
Multiply both sides by 8 to get ride of fractions
8y - 7x = -37 (rearrange)
-7x + 8y = -37
It's better to have a positive coefficient for x if you can. So multiply both sides by -1. That just means changing the sign of every term on both sides, you get
7x - 8y = 37
Factor −1/2 out of −1/2x+6.
The factored expression is
Answers
Final answer:
To factor −1/2 out of −1/2x+6, we identify the common factor, divide each term by −1/2, and write the expression as −1/2 times the simplified expression. The result is −1/2(x − 12).
Explanation:
To factor −1/2 out of −1/2x+6, we can think of pulling out the −1/2 as a common factor from both terms in the expression. Here's a step-by-step breakdown:
Identify the common factor in both terms. In this case, the common factor is −1/2.Divide each term by −1/2 (which is the same as multiplying by −2).Write the original expression as the product of the common factor and the simplified expression.Applying these steps, we get:
−1/2x divided by −1/2 equals x.6 divided by −1/2 equals −12.The factored expression is then −1/2(x − 12).So, −1/2x+6 factored with −1/2 taken out is −1/2(x − 12).
Which of the following problems can be solved by finding 4 divided by 2/3?
A. 4 people equally share 2/3 of a pizza. How much of the pizza does each person eat?
B. How many 2/3 cup servings of soup are in 4 cups of soup?
C. A pie recipe requires 2/3 pounds of apples. How many apples are needed for 4 pies?
D A family ate 2/3 of a 4 foot sandwich. How much did he they eat?
Arthur chose A as the correct answer. How did he get that answer?
Answers
Step-by-step explanation:
Arthur got because a pizza is shared by 4 people. however only
2/3 of the pizza is there so it is divided by the four people.
The correct option is b.
The correct problem that can be solved by calculating 4 divided by 2/3 is determining the number of 2/3 cup servings of soup in 4 cups. By understanding how division of fractions work, we can see that there are 6 such servings in 4 cups.
Explanation:The subject matter of the question is related to basic division and fractions. Specifically, it's asking about when we would need to find the result of 4 divided by 2/3. Given the answer choices, option B is the correct one. The question here is not about sharing a pizza or calculating the quantity of apples for pies, or the amount of sandwich eaten. It's rather about how many 2/3 cup servings fit within 4 cups of soup. When we do the division 4 ÷ 2/3, we're essentially figuring out how many 2/3s there are in 4. This concept can be a bit tricky because dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of 2/3 is 3/2, so 4 × 3/2 = 6. Hence, there are 6 servings of 2/3 cup soup in 4 cups.
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Solving systems by substitution
X=y-11
2x+3y=8
Answers
Answer:
x=-5, y=6. (-5, 6).
Step-by-step explanation:
x=y-11
2x+3y=8
--------------
2(y-11)+3y=8
2y-22+3y=8
5y-22=8
5y=8+22
5y=30
y=30/5=6
x=6-11=-5
-6(y+5)-24=66 find the value of y
Answers
Answer:
y=-20
Step-by-step explanation:
-6(y+5)-24=66
-6y-30-24=66
-6y-54=66
-6y=66+54
-6y=120
y=120/-6=-20
What is the solution to this equation x - 12 = - 4
Answers
Answer:
x = 8Step-by-step explanation:
x - 12 = -4 add 12 to both sides
x - 12 + 12 = -4 + 12
x = 8
Add 12 to -4
X=8
A wooden beam is left parenthesis 6 y squared plus 5 y plus 1 right parenthesis6y2+5y+1 meters long. If a piece of length left parenthesis y squared minus 12 right parenthesisy2−12 meters is cut off, express the length of the remaining piece of beam as a polynomial in y.
Answers
Answer:
5y² + 5y - 11
Step-by-step explanation:
The length of a wooden beam is as a function of y
L(y) = 6y² + 5y + 1
and a piece of length y² - 12 is cut off the remaining piece is
6y² + 5y + 1 - y² - 12 = 5y² + 5y - 11
To find the remaining length of the wooden beam, subtract the length of the cut-off piece from the original polynomial. Simplify the expression to get the final answer: 5y² + 5y + 13 meters. This represents the remaining length of the beam.
Finding the Remaining Length of the Wooden Beam:
We start with the original length of the wooden beam given by the polynomial 6y² + 5y + 1 meters.
We need to subtract the length of the piece that was cut off, which is given by the polynomial y² - 12 meters.
First, write down the original length of the beam:
6y² + 5y + 1
Next, identify the length of the piece cut off:
y² - 12
Subtract the second polynomial from the first:
(6y² + 5y + 1) - (y² - 12)
Simplify the expression by combining like terms:
6y² - y² = 5y²
5y remains unchanged.
1 - (-12) = 1 + 12 = 13
So, the remaining length of the beam is:
5y² + 5y + 13
The remaining length of the wooden beam, expressed as a polynomial in y, is 5y² + 5y + 13 meters.
use the method of completing the square to solve y²+y-7=0
Answers
Answer:
y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2
Step-by-step explanation:
Solve for y:
y^2 + y - 7 = 0
Add 7 to both sides:
y^2 + y = 7
Add 1/4 to both sides:
y^2 + y + 1/4 = 29/4
Write the left hand side as a square:
(y + 1/2)^2 = 29/4
Take the square root of both sides:
y + 1/2 = sqrt(29)/2 or y + 1/2 = -sqrt(29)/2
Subtract 1/2 from both sides:
y = sqrt(29)/2 - 1/2 or y + 1/2 = -sqrt(29)/2
Subtract 1/2 from both sides:
Answer: y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2
Answer:
y=sqrt(29)/2-1/2, -sqrt(29)/2-1/2
Step-by-step explanation:
y^2+y-7=0
completing the square,
(b/2)^2=(1/2)^2=1/4
(y+1/2)^2=7+1/4
(y+1/2)^2=28/4+1/4
(y+1/2)^2=29/4
y+1/2=sqrt(29/4)
y=sqrt(29/4)-1/2
y=sqrt(29)/2-1/2
y=-sqrt(29)/2-1/2
What’s 333x333 please I need to know
Answers
Answer:
110889
Step-by-step explanation:
Answer:
110,889 is the answer dude..
please help. If you answer correctly and give an explanation I'll give you 5 stars, thanks, and brainliest.
solve the equation:
2x + 1-x/4 = 3
or
[tex]2x + \frac{1-x}{4} = 3[/tex]
Answers
The solution of the equation is [tex]x=\frac{11}{7}[/tex]
Step-by-step explanation:
To simplify an equation of x
Simplify each side of the equationCollect x in side and the numerical terms in the other sideFind the value of x∵ The equation is [tex]2x + \frac{1-x}{4}=3[/tex]
- Multiply all terms of the equation by 4 to cancel the denominator
of the 2nd term in the left hand side
∵ The equation is [tex]4(2x) +4 (\frac{1-x}{4})=4(3)[/tex]
∴ 8x + (1 - x) = 12
∴ 8x + 1 - x = 12
- Add like terms
∴ (8x - x) + 1 = 12
∴ 7x + 1 = 12
- Subtract 1 from both sides
∴ 7x = 11
- Divide both sides by 7
∴ [tex]x=\frac{11}{7}[/tex]
The solution of the equation is [tex]x=\frac{11}{7}[/tex]
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Calculate the constant of variation if y varies directly as x. PLEASE GIVE EXPLANATION
Answers
Answer:
[tex]k = - \frac{3}{2}[/tex]
Step-by-step explanation:
If y varies directly with x, then from the relation of direct variation we can write y ∝ x
Now, converting the variation relation to equation relation,
⇒ y = kx ........... (1) {Where k is the constant of variation}
Now, given that at y = - 3, x = 2 and this solution will satisfy the equation (1).
Hence, - 3 = 2k
⇒ [tex]k = - \frac{3}{2}[/tex] (Answer)
you miss3 out of 7 on a science quiz and 9 out of 23 on math quiz which quiz has a higher percent of correct answers
Answers
Science Quiz: 42.8571429%
Math Quiz: 39.1304348%
Take the amount of answers correct out of the total, divide it, and then multiply by 100. In this case, Science has a higher score.
The percentage of correct answers for the science quiz is 57.14%, while for the math quiz it's 60.87%. Therefore, the student had a higher percentage of correct answers on the math quiz.
Explanation:You determine the percentage of correct answers on each quiz by dividing the number of correct answers by the total number of questions on each quiz respectively.
For the science quiz, you answered 4 out of 7 questions correctly since you missed 3 out of 7. The percentage of correct answers for the science quiz is thus (4/7)*100 = 57.14%.
For the math quiz, you answered 14 out of 23 questions correctly since you missed 9 out of 23. The percentage of correct answers for the math quiz is thus (14/23)*100 = 60.87%.
Therefore, you had a higher percentage of correct answers on the math quiz than on the science quiz.
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Thank you! Please do both
Answers
Answer:
my 12 inch pito that pito good
Which expression is equivalent to the expression (-18) - 64n?
A -2(9 - 32n)
B 2(9 - 32n)
C -2(9 + 32n)
D 2(9 + 32n)
Answers
Answer:
C) -2(9+32n)
Step-by-step explanation:
(-18)-64n=-18-64n
---------------------------
A) -2(9-32n)=-18+64n
B) 2(9-32n)=18-64n
C) -2(9+32n)=-18-64n
D) 2(9+32n)=18+64n
-----------------------------------
The answer is C.
One day, the high temperature was 84 degrees and the low temperature was 68 degrees. Write a compound inequality to represent the day’s temperatures
Answers
Answer:
x > 68 and x < 84
Step-by-step explanation:
Given: △AKM, KD ⊥ AM , AK = 6, KM = 10, m∠AKM = 93º Find: KD
Answers
The length of KD in triangle △AKM, with AK = 6 and KM = 10, and m∠AKM = 93° is 10, since KD is the height of a right triangle and KM is the hypotenuse.
The question asks to find the length of KD in triangle △AKM where KD is perpendicular to AM. Given AK = 6, KM = 10, and m∠AKM = 93º, we can solve for KD using trigonometric ratios.
Since KD ⊥ AM, we have a right triangle △KDM.
We know the hypotenuse KM and angle AKM, so we can use the sine function, where sin(AKM) = opposite/hypotenuse, to find the length of KD. The sine of angle AKM (which is slightly adjusted from 93º to 90º since we are looking for the height in a right triangle) gives us:
sin(90º) = KD/ KM
We know sin(90º) = 1 and KM = 10, so:
1 = KD / 10
Therefore, KD = 10.