For the right triangles below, find the exact values of the side lengths a and h. If necessary, write your responses in simplified radical form. pad 309 8 Х X S 45° 0 60° 3 h
Answers
First Triangle:
This is a special right-angled triangle and is known as 45°-45°-90° triangle
To solve for any side length, we can use the following procedure.
As you can see, the sides opposite to the 45° are equal and in this case, both are 3
Then the side opposite 90° will be
[tex]3\sqrt[]{2}[/tex]Therefore, the side a = 3√2
Second Triangle:
This is a special right-angled triangle and is known as the 30°-60°-90° triangle.
To solve for any side length, we can use the following procedure.
As you can see, the side opposite the 30° is the smallest.
The side opposite the 60° is 2 times the side 30°
The side opposite the 90° is √3 times the side 30°
For the given case, we want to know the side opposite of side 30°
We are given the side opposite the 60° that is 8
[tex]\begin{gathered} 2h=8 \\ h=\frac{8}{2} \\ h=4 \end{gathered}[/tex]Therefore, side h = 4
Related Questions
Priya starts with $50 in her bank account. She then deposits $20 each week for 12 weeks. Write an equation that represents the relationship between the dollar amount in her bank account and the number of weeks of saving.
Answers
Answer: d=50+20w
D(deposit) = 50(starting amount)+20(added amount)w(multiply 20 by the amount of weeks, 12, and this is your equation.)
if you cant read it it says : Use the distributive property for the expression 4(m + 7) - 6(4-) and simplify
Answers
Explanation
The distributive property tells us how to solve expressions in the form of a(b + c)
[tex]a(b+c)=ab+ac[/tex]Then,
Step 1
apply distributive property operate
[tex]\begin{gathered} 4(m+7)-6(4-m) \\ 4\cdot(m)+4\cdot7-6(4)+6(m) \\ 4m+28-24+6m \end{gathered}[/tex]
Step 2
add similar terms
[tex]\begin{gathered} 4m+28-24+6m \\ 10m+4 \end{gathered}[/tex]so, the answer is
[tex]D)10m+4[/tex]I hope this helps you
While shopping for supplies for the party, she is trying to decide which soda is the better deal. She can buy a 138 ounce bottle of soda for $3.20 or she can buy twelve 12ounce cans of cola for $3.60. Find the unit rate for the bottle.
Find the unit rate for the cans.
Answers
Answer:
The unit rate for the bottle is $0.023/oz
The unit rate for the cans is $0.025/oz
Step-by-step explanation:
Cans oz/can Total oz Price ($) Cost ($/oz)
1 138 138 3.20 $0.023
12 12 144 3.60 $0.025
The unit rate for the bottle is $0.023/oz
The unit rate for the cans is $0.025/oz
The unit rate for the bottle is $0.023/oz
The unit rate for the cans is $0.025/oz
Solve for x and then give the m∠G?
Enter your answer in the box.
Answers
first the sum of all angles of in triangle is 180 degree.
x+(3x+25)+(x-5)=180
x+3x+25+x-5=180
4x+25+x-5=180
4x+x+25-5=180
5x+20=180
5x=180-20
5x=160
x=32 degree and
the angle of G is 3(32)+25=121 degree
A particle travels along the x-axis such that its position at time t is given by the function x(t) = 2t2 + t. What is the average speed of this particle over the interval 2 ≤ t ≤ 10?
4
25
32
200
Answers
Answer:
25.
Step-by-step explanation:
At time 2, x(t) = 2(2)^2 + 2 = 10
At time 10, x(t) = 2(10)^2 + 10 = 210.
Average speed for this interval
distance / time
= (210 - 10) / (10 - 2)
= 200/8
= 25.
if a test yields almost identical scores when it is retaken after a two-month interval, we can say that the test is
Answers
Yield testing is a technique for figuring out the precise quantity of raw materials required to make a specific quantity of finished product.
What exactly is a yield test?The amount of food material available for consumption after it has been prepared, processed, and changed into the completed product is referred to as yield.Yield testing is a method of determining the precise amount of raw materials needed to produce a certain amount of final product.AP weight minus waste equals EP weight.Calculate your yield percentage by dividing the edible product weight by 100. EP weight x AP weight x 100 = yield% is the formula.Therefore, yield testing is a method of determining the precise amount of raw materials needed to produce a certain amount of the final product.
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Which step shows the result of applying the subtraction property of equality? one-fourth (12 x 8) 4 = 3 step solution 1 3 x 2 4 = 3 2 3 x 6 = 3 3 3 x = negative 3 4 x = negative 1 step 1 step 2 step 3 step 4
Answers
The step 3 follow the subtraction property of equality.
Given,
The Equation is : 1/4 (12x + 8) + 4 = 3
There is some steps:
Step Solution
1 3x + 2 + 4 = 3
2 3x + 6 = 3
3 3x = -3
4 x = -1
To find the which step shows the result of applying the subtraction property of equality?
Now, According to the given steps:
From the table, we can know
From Step 2: 3x + 6 = 3
Subtract 6 on both sides
3x + 6 - 6 = 3 - 6
3x = -3
Hence, The step 3 follow the subtraction property of equality.
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i need to know if they are functions, please say
function A:(function or not a function)
function B:(function or not a function)
Answers
Answer:
First one is a function, second one is not, since it assigns more than one y value for x values.
Step-by-step explanation:
A function means for every x value, at most 1 y value exists. This is clearly not the case for the bottom figure. You can test it with an imaginary vertical line. There should be zero or one intersections.
what are the maximum dimensions of a div with the following properties?div.container { min-height: 150px; max-height: 600px; min-width: 300px; max-width: 900px;
Answers
Max width = 900px
600 x 900 or 540 000px
Simplify as far as possible without a calculator.
5
√
3
(
2
√
3
−
3
√
7
)
Answers
After simplification this 5√3(2√3−3√7) we get, -38.71
5√3(2√3−3√7) is a linear equation.
What is linear equation?
An equation between two variables that, when plotted on a graph, produces a straight line or say first degree equation is known as linear equation.
Let's simply this 5√3(2√3−3√7)
=> 5√3 * 2√3 - 3√7 * 5√3
=> 5*2*√3*√3 - 3 * 5 √7 * √3
=> 10 * 3 - 15 * 1.732 * 2.645
=> 30 - 68.717
=> -38.717 or -38.71
Therefore, the value of 5√3(2√3−3√7), after simplification we get -38.71
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NEED THIS ASAP 50 POINTS UWU
Which property of equality should you apply to keep the equation 22 . a = 242 in balance when solving?
The division property of equality
The subtraction property of equality
The reflexive property
The substitution property of equality
Answers
A property of equality that you should apply to keep the equation 22 . a = 242 in balance when solving include the following: A. The division property of equality.
What is the subtraction property of equality?In Mathematics and Geometry, the subtraction property of equality states that the two (2) sides of an algebraic expression or equation would still remain equal even when the same number has been subtracted from both sides of an equality.
Based on the information provided above, we can logically deduce the following equation:
22 . a = 242
22 × a = 242
By applying the division property of equality, we have the following:
a = 242/22
a = 11.
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On Monday morning, Mr. Descartes asked his Algebra II students whether they had gone to the carnival in town over the weekend.
"I did," said Kristen. "I went on the Teacups ride twice, the rollercoaster twice, and the Spinning Vortex once. I had a lot of fun for only $20."
"I went on those rides, too!" exclaimed Jorge. "Just once each on the Teacups and rollercoaster, but three times on the Spinning Vortex, all for $25."
"I did five Teacup rides," said Lakesha. "And two rollercoaster rides, and one Spinning Vortex. I spent $29."
Marc listed off the same rides. "Three Teacups for me, plus two rollercoasters, plus two rides on the Spinning Vortex, all for - "
"You don't need to say," interrupted Mr. Descartes. "I know how much you spent."
How much are the rides? How much did Marc spend?
• A. Teacups: $2; rollercoaster: $5; Spinning Vortex: $6; Marc spent $26.
• B. Teacups: $2; rollercoaster: $5; Spinning Vortex: $6; Marc
spent $28.
• C. Teacups: $3; rollercoaster: $4; Spinning Vortex: $6; Marc
spent $29.
• D. Teacups: $3; rollercoaster: $4; Spinning Vortex: $6; Marc spent $30.
Answers
Answer:
C.
Step-by-step explanation:
You can assign each variable a ride, let's say the teacup is t, the roller coaster is r, and the spinning vortex is s. Now we can create algebraic expressions to find the values of each ride :
Kristen: 2t+2r+s=20
Jorge: t+r+3s=25
Lakesha: 5t+2r+s=29
Now we can use elimination to find each variable:
2t+2r+s=20
-2t-2r-6s=-50
The t and r cancel out, so find s
-5s=-30
s=6, so the spinning vortex is $6.
Now, substitution
2t+2r+s=20 -5t-2r-s=-29
2t+2r+6=20 -5t-2r-6=-29
2t+2r=14 -5t-2r=-23
2t=-2r+14
t=-r+7
Now plug in for t
-5(-r+7)-2r=-23
5r-35-2r=-23
3r=12
3r/3=12/3
r=4, which means the roller coaster is $4
Now we can just plug in both of those and solve for t with any equation
t+r+3s=25
t+4+3(6)=25
t+4+18
t+22=25
t=3
Now we know that the teacups have to be $3, the rollercoaster has to be $4, and the spinning vortex has to be $6. Marc's equation is:
3t+2r+2s = Money marc spent
Plug in the values
3(3) + 2(4) + 2(6) = Money marc spent
9+8+12 = Money marc spent
29 = Money marc spent
Marc spent $29, your answer is C
To solve a system of equations _______________ means that we will use some algebraic manipulation to find the solution(s). there are two techniques for solving algebraically: _______________ and _______________.
Answers
To solve a system of equations algebraically means that we will use some algebraic manipulation to find the solution(s). there are two techniques for solving algebraically: elimination and substitution.
The theory of linear systems serves as the foundation for the field of linear algebra, which is used in most branches of modern mathematics.
Computational methods for getting the solutions, which are essential to the disciplines of engineering, physics, biochemistry, computer science, and economics, are included in numerical linear algebra. It is useful to approximate a system of nonlinear equations by a linear system when developing a mathematical model or computational modelling of a relatively complex system (see linearization).The easiest method for resolving a system of linear equations is to repeatedly remove variables. This method is described in the sentences that follow.The first equation's variables should each be solved for in relation to one another.In the following equations, substitute this expression in its place. As a result, the system of equations contains one less equation and unknown.Hence the two ways an algebraic equation can be solved is by elimination and substitution.
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How do you decide which operations to use when writing an equation?
Answers
Answer:The order of operations tells us the order to solve steps in expressions with more than one operation.
Step-by-step explanation: First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right.
Rewrite 8-1/2 as an improper fraction.
Answers
Answer:
[tex]\frac{15}{2}[/tex]
Step-by-step explanation:
8 - [tex]\frac{1}{2}[/tex]
= [tex]\frac{16}{2}[/tex] - [tex]\frac{1}{2}[/tex]
= [tex]\frac{15}{2}[/tex]
Answer:
The answer is 17/2
Step-by-step explanation:
You get that by multiplying the whole number 8 by the denominator of the fraction, and that will be equal to 16 and the 1 from the numerator of the fraction 1/2, so the equation will look like 16+1=17. Your new numerator 17.
Jerrod brought 48 cupcakes to school. At school, he gave 3 cupcakes to
each student in his class. He has 6 cupcakes remaining. How many
students are in Jerrod's class?
Answers
it should be 14 students i think
Hope this help you
Suppose n represents an integer. Then the next integer can be represented by the expression n+1. Write a linear expression that represents the sum of any two consecutive integers. Then use the expression to make an argument about whether the sum of any two consecutive integers is even or odd. Explain your reasoning.
Answers
The expression 2n + 1 will produce both odd and even numbers based on the choice we have made.
Expression:
An expression is a mathematical expression consisting of numbers, operations, and one or more variables.
Given,
Suppose n represents an integer. Then the next integer can be represented by the expression n+1.
Here we need to write the linear equation for these two consecutive integers.
Then we have to use the expression to make an argument about whether the sum of any two consecutive integers is even or odd.
Let n represents the first integer and n+1 is the second integer.
Then the linear equation for these two consecutive integer is
=> n + (n + 1)
=> 2n + 1
Now we have to take the value of n and n + 1 as, 2 and 3,
Then we apply the value to the expression,
=> 2(2) + 3
=> 4 + 3
Similarly, if we take the value as 5 and 6,
Then we get,
=> 2(5) + 6
=> 10 + 6
=> 16
So, based on the given details the equation givens both odd and even number based on the number our choices.
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On a map, two cities are 2.8 inches apart. The map has a scale of 1 inch to 25 miles. How far apart, in inches, would the same two cities be on a map that has a scale of 1 inch to 40 miles?
Answers
When a scale of 1 inch to 40 miles apart then distance = 112 miles .
We have been give that
If 1 inch = 25 miles,
Then 2.8 inches would be 25 miles multiplied by 2.8 since each of those 2.8 inches is 25 miles.
2.8 x 25 = 70.
70 miles.
The same two cities be on a map that has a scale of 1 inch to 40 miles
Then 1 inch= 40 miles,
then 2.8 inches would be 40 miles multiplied by 2.8 since each of those 2.8 inches is 40 miles.
2.8 x 40 = 112.
112 miles.
Hence , Distance equals 112 miles when measured on a scale of 1 inch to 40 miles apart.
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if y=-2 when x=4, find y when x =7
Answers
As x and y vary inversely as each other , if x=7 then y = -8/7.
in the question ,
it is given that
x and y vary inversely ,
So , x * y = k
given that , when x = 4 , the value of y = -2 .
Substituting , 4 * (-2) = k
k = -8
so , the constant of variation (k) = -8 .
in order to find value of y when x = 7 ,
we substitute x=7 and k = -8 in the relation xy = k
we get , 7 * y = (-8)
Dividing both sides by 7 we get
7y/7 = -8/7
on simplifying we get ,
y = -8/7
Therefore , as x and y vary inversely as each other , if x = 7 then y = -8/7 .
The given question is incomplete , the complete question is
If y varies inversely as x, and y = -2 when x = 4 find y when x = 7 .
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Max loves fishing. He and his family chartered a fishing boat that left Florida and traveled towards the Bahama Islands at an average speed of 10 km/hour. Some time later a cruise ship left traveling in the same direction but at an average speed of 14 km/hour. After traveling for ten hours the cruise ship caught up with the fishing boat. How long did the fishing boat travel before the cruise ship caught up?
Answers
The fishing boat traveled for 14 hours before the cruise ship caught up.
In this question, we have been given Max and his family chartered a fishing boat that left Florida and traveled towards the Bahama Islands at an average speed of 10 km/hour.
After some time, a cruise ship left traveling in the same direction but at an average speed of 14 km/hour.
The cruise ship caught up with the fishing boat after traveling for 10 hours.
Let a cruise traveled 'm' km after 10 hours.
Using the formula of speed,
speed = distance / time
14 = m / 10
m = 14 * 10
m = 140 km
This means, a cruise traveled 140 km in 10 hours.
Now, we find the time needed for a fishing boat to cover 140 hours.
speed = distance / time
10 = 140/t
t = 140 / 10
t = 14 hours
Therefore, the fishing boat traveled for 14 hours before the cruise ship caught up.
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Brady loves to go fishing he goes every weekend this weekend he caught 4 less fish than he did last weekend he caught 7 fish this weekend write and solve and equation to determine how many fish he caught last weekend let f represent the number of fish
Answers
Find the LCM of 4 and 14
Answers
Mia, this is the solution:
4 = 2 * 2
14 = 2 * 7
Therefore, we have:
2 = two ocurrences (the higher number)
7 = one ocurrence
LCM = 2 * 2 * 7
LCM = 28
The perimeter of the rectangle is
A) 9.49
B) The p
C) 18.97
The area of the rectangle
A) 18.5
B) 20
C) 40
Please answer ASAP
Answers
The area and the perimeter of the rectangle is found as 13.12 sq. unit and 21.77 units respectively.
What is termed as the rectangle?A rectangle is a quadrilateral with parallel sides that are equal to one another and all four vertices that are 90 degrees apart. degrees. As a result, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal as well as parallel, it is also known as a parallelogram.For the given question;
To find the perimeter of the rectangle ABCD, first find the length of the sides.
Using the distance formula, find the length DA and DC,
DA = √(x2 - x1)² + (y2 - y1)²
Put the coordinate of the point D and A.
DA = √(8 - 1)² + (2 - 0)²
DA = √49 + 4
DA = √53 units.
Now, length DC
DC = √(3 - 1)² + (3 - 0)²
DC = √4 + 9
DC = √13 units.
For the rectangles;
DA = CB = √53 units.
DC = AB = √13 units.
Perimeter = DA + CB + DC + AB
Perimeter = 2√53 + 2√13 units
Perimeter = 2(√53 + √13) units.
Perimeter = 21.77 units.
Area = (1/2) base × height
Area = (1/2) CB × CD
Area = (1/2) × √53 × √13
Area = 26.24/2
Area = 13.12 sq. unit.
Thus, the area and the perimeter of the rectangle is found as 13.12 sq. unit and 21.77 units respectively.
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What is the surface area of this rectangular pyramid? 4 mm
4 mm 4 mm
Answers
The formula for calculating the total surface area of a rectangular pyramid using its length, width, and height is provided as T.S.A. = lw + l[(w/2)2 + h2] + w[(l/2)2 + h2], where l is the length of the rectangular base, w is its width, and h is its height.
What is the Rectangular Pyramid?Pyramids are three-dimensional constructions with triangle-shaped faces and a base with a polygonal shape. A pyramid is referred to as a rectangular pyramid if its base is also rectangular. All pyramids have triangular sides, despite the fact that their bases are rectangular. The height of the pyramid is indicated by the top vertex, also known as the apex. The volume of a rectangular pyramid can be calculated using the formula V=1/3lwh, where l denotes the length of the base, w its width, and h its height.To learn more about Rectangular Pyramid refer :
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Autumn and her children went into a bakery and she bought $5 worth of donuts and cookies. Each donut costs $1 and each cookie costs $0.50. She bought a total of 6 donuts and cookies altogether. Graphically solve a system of equations in order to determine the number of donuts, x, and the number of cookies, y, that Autumn bought.
Answers
Autumn bought 4 Donuts and 2 Cookies worth of 5 dollars.
What are simultaneous equations?We know two simultaneous equations have a unique solution when they intersect at a point,
when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.
Given, Autumn and her children went into a bakery and she bought $5 worth of donuts and cookies.
Each donut costs $1 and each cookie costs $0.50. She bought a total of 6 donuts and cookies altogether.
Let us denote no. of Donuts by x and no. of Cookies by y.
∴ x + y = 6...(i) and x + 0.5y = 5...(ii).
Subtracting eqn(ii) from eqn(i) we get y = 2 and substituting the value of y in eqn(i) we get x = 4.
Autumn bought 4 Donuts and 2 cookies with 5 dollars.
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An A.P has 17 terms and a common difference of -4 determine the first and the last termif the A.P is 107.1
Answers
Answer:
Below in bold.
Step-by-step explanation:
The sum of 17 terms is 107.1.
Sn = (n/2)[2a + (n-1)d] where a = first term and d = common difference
(17/2) (2a + (17-1)(-4)) = 107.1
8.5(2a -64) = 107.1
17a - 544 = 107.1
17a = 651.1
a = 38.3 = First term
The last term is the 17th so
L = a + (n - 1) d
= 38.3 + 16*-4
= -25.7.
Write an equasion of the line that passes through (0,-2) and (4,10)
Answers
Answer:
12.649
Step-by-step explanation:
we can use Pythagoras to solve this; simply by forming a triangle of the difference between the x and y values. (I added a lil-sketch of it).
So, we just need to find the length of the two sides:
Vertical side: 12
Horizontal side: 4
Thus;
[tex]4^{2} + 12^{2} = c^{2} \\160 = c^{2}\\Side c is equal to 12.649 (in whatever unit given)[/tex]
8x^4+7x^3+2x^4+6+4x^3
Answers
You have the following algebraic expression:
[tex]\begin{gathered} 8x^4+7x^3+2x^4+6+4x^3 \\ \end{gathered}[/tex]The previous expression can be simplified by taking into account, that for the simplification you sum or subtract (depending of signs) similar terms. Remind that similar terms are those one which has the same variable with the same exponent. In this case you have similar terms with variable x and exponent 4, furthermore you have similar terms with variable x and exponent 3. Then you sum this terms and you obtain:
[tex]\begin{gathered} 8x^4+7x^3+2x^4+6+4x^3 \\ =8x^4+2x^4+7x^3+4x^3+6 \\ =10x^4+11x^3+6 \end{gathered}[/tex]where you have summed 8x^4 + 2x^4 = 10x^4, and 7x^3 + 4x^3 = 11x^3.
Hence, the simplied expression is 10x^4 + 11x^3 + 6
A store owner paid $225 wholesale price for a TV. They need to make a 65% profit on the sale of the TV. What will a customer pay for the TV after it is marked up 65% and they pay sales tax of 9%?
Answers
The customer will pay $391.5 after it is marked up to 65% and the sale tax of 9%.
When a consumer buys a good or service from a retailer, sales tax, which is estimated as a percentage, is added to the cost of the item.
Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.
The wholesale price paid by a store owner is $225.
The store owner needs to make a profit of 65%.
Then, the profit will be:
= 225 × 65% = $146.25
And, amount of tax the customer will pay will be:
= $225 × 9% = $20.25
Therefore, the price at which the customer will buy the TV will be:
= $225 + profit + sales tax
= $225 + $146.25 + $20.25
= $391.5
Hence, the customer will pay $391.5 for the TV.
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You have a function that takes in an X value and produces a Y value. The x value equals 7 times the y value, plus 18 more. What's the x value when the y value equals 6?
Answers
The value of x from the given function is 60.
Given that, the x value equals 7 times the y value, plus 18 more.
What is the function?A function in math means a correspondence from one value x of the first set A to another value y of the second set B. It relates inputs to outputs.
Now, the x value equals 7 times the y value, plus 18 more
x=7y+18
Put y=6 in the obtained function, that is
x=7(6)+18
⇒ x = 42+18
⇒ x = 60
Therefore, the value of x from the given function is 60.
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