The value of x, in dollars, so that they have equal weekly pay is $18,000.
Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h. The domain is defined as the set of all the values that the function can input while it can be defined. The range is all the values that come out as the output of the function involved. Co-domain is a set of values that have the potential of coming out as outputs of a function.
We are given that Guy and Jim earn the same weekly pay.
Then g(x) = f(x)
So, 185 + .03x = 275 + .025x
Rearranging terms so that the x's are together and the constants are together:
0.005x = 90
∴ x = 18,000
Thus, the value of x, in dollars, so that they have equal weekly pay is $18,000.
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Which of the following is a true proportion of the figure based on the triangle proportionality theorem?
A) i/j=h/k
B) j/k=j/i
C) h/i=h/k
D) k/i=j/i
A true proportion of the figure based on the triangle proportionality theorem is: A) i/j = h/k.
What is a triangle?In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
What is the triangle proportionality theorem?The triangle proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.
Since side TU is parallel to side QR, side TU will divide both sides QS and RS proportionally in accordance with the triangle proportionality theorem as follows;
RU/QT = SU/ST ≡ i/j = h/k
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Stefan sells Jin a bicycle for $163 and a helmet for $.17 The total cost for Jin is %150
of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
The cycle originally cost $120, and he made a $60 profit by selling it for $163 with a $17 helmet.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.
Here,
The cost of bicycle=$163
Cost of helmet=$17
Total cost,
=163+17
=$180
Let the original cost be c,
180=150%*c
180=1.5c
c=$120
He made a profit,
=180-120
=$60
The original cost of cycle was $120 that he sold in $163 with the helmet of $17 making a profit of $60.
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the manager of a theater wants to know whether the majority of its patrons are adults or children. One day, 5100 tickets were sold and the receipts totaled $29,484. The adult admission is $7.50, and the children's admission is $4.50. How many adult patrons were there
By solving equations, we know that there were 2187 adult partons.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A function is an equation with a single solution for y for each value of x.
Each input of a particular type receives exactly one output when using a function.
Instead of y, a function is frequently named f(x) or g(x).
When x equals 2, we should determine our function's value because f(2) says to do so.
So, the number of adult patrons was:
Let, a be an adult and c be children.
Total tickets:
a + c = 5200
c = (5200-a)
Total amount:
7.50a + 4.50c = 29961
Replace c in the first equation with (5200-a).
7.5a + 4.5(5200-a) = 29961
7.5a + 23400 - 4.5a = 29961
7.5a - 4.5a = 29961 - 23400
3a = 6561
a = 6561/3
a = 2187
Therefore, by solving equations, we know that there were 2187 adult partons.
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Choose ALL answers that describe the polygon QRST if QR =11, RS =20, ST =11, TQ=20, QR || ST, and RS || TQ
The given polygon could be parallelogram , quadrilateral , rectangle.
What is a polygon?
In geometry, a polygonal shape could be a two-dimensional figure that's delineate by a finite range of line segments connected to make a closed two-dimensional figure chain. The delimited plane region, the bounding circuit, or the 2 along, is also referred to as a polygonal shape.
Main body:
As opposite sides of polygon QRST are parallel , it a parallelogram .
A quadrilateral is a polygon with for sides , so it also satisfies the condition.
The opposite sides of rectangle are equal and parallel , which is also satisfied.
Hence ,the given polygon could be parallelogram , quadrilateral , rectangle.
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Evaluate the expression when y=6. y^2+5y+9
Answer:
75
Step-by-step explanation:
y² + 5y + 9
since y = 6 we will just substitute for y
= (6)² + 5(6) + 9
= 36 + 30 + 9
= 66 + 9
= 75
i hope this helps
Question 3 4 pts Solve the equation for the variable. Show your work and be sure to not forget to show all of your steps. -3(3 + 6b) = 36 - 3b
Answer:
[tex]\huge\boxed{\sf b = -3}[/tex]
Step-by-step explanation:
Given equation:-3(3 + 6b) = 36 - 3b
Distribute
-9 - 18b = 36 - 3b
Add 3b to both sides
-18b + 3b - 9 = 36
-15b - 9 = 36
Add 9 to both sides
-15b = 36 + 9
-15b = 45
Divide -15 to both sides
b = 45/(-15)
b = -3[tex]\rule[225]{225}{2}[/tex]
Answer:
The value of b is -3.
Step-by-step explanation:
The equation is,
→ -3(3 + 6b) = 36 - 3b
Now the value of b will be,
→ -3(3 + 6b) = 36 - 3b
→ -3(3) - 3(6b) = 36 - 3b
→ -9 - 18b = 36 - 3b
→ -18b + 3b = 36 + 9
→ -15b = 45
→ b = -(45/15)
→ [ b = -3 ]
Hence, the value of b is -3.
There are two shapes on the coordinate plane shown. Which statement about the shapes is true? A. Shape A can be matched to shape B by reflecting it about the x-axis, then about the y-axis, and then shifting 1 on the x-axis and –3 on the y-axis. B. Shape A can be matched to shape B by reflecting about the origin and then shifting –3 on the x-axis and 1 on the y-axis. C. Shape A can be matched to shape B by reflecting it about the y-axis, then about the x-axis, and then dilating it from the origin by a factor of 2. D. Shape A can be matched to shape B by reflecting it about the y-axis, then about the x-axis, and then dilating it from the origin by a factor of .
Answer:
B. Shape A can be matched to shape B by reflecting about the origin and then shifting –3 on the x-axis and 1 on the y-axis.
Step-by-step explanation:
DIRECTIONS: Use this information to answer Parts A and B.
A faucet supplies water at a constant rate. After 3 minutes, the faucet supplies 12 liters of water.
Part A
Use the Line Tool to graph the proportional relationship that gives the number of liters of water the facet supplies, y, after x minutes.
The graph of the proportional relationship is added as an attachment
How to determine the graph of the scenarioFrom the question, we have the following parameters that can be used in our computation:
Time = 3 minutes
Supply of water = 12 litres
Using the above parameters, we have the following ordered pairs
(0, 0) and (3, 12)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (0, 0) and (3, 12)
The gradient of the line is then calculated using the following slope equation
gradient = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (3, 12)
Substitute the known values in the above equation
So, we have the following equation
gradient = (12 - 0)/(4 - 0)
Evaluate
gradient = 3
The equation of the line is then calculated as
y = gradient * x
Substitute the known values in the above equation
So, we have the following equation
y = 3 * x
Evaluate the products
y= 3x
Hence, the line equation is y= 3x
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find the missing number so that the equation has infinitely many solutions. 2x + _ = 2x - 4
Answer:
The missing number is -4.---------------------------------
For the equation to have infinitely many solutions, the variables and constants should cancel and should end up with 0 = 0. It means for any value of the variable the equation is true, i.e. both sides are equal.
Given equation:
2x + ? = 2x - 4If we solve it for ? we'll get:
? = - 48. Which is a solution of the equation y = 2x + 5? (1 point)
5,20
6,12
3,11
4,14.
I need this really quickly. Thanks to anyone willing to help.
Answer:
3,11
Step-by-step explanation:
Since y = 2x + 5, if you chose (x,y) (3,11):
11 = 2*3 + 5
11 = 6 + 5
11 = 11
Answer:
(3, 11 ) is a solution
Step-by-step explanation:
substitute the x- coordinate of the points into the equation and if the value of y obtained equals the y- coordinate then the point is a solution.
(5, 20 )
y = 2(5) + 5 = 10 + 5 = 15 ≠ 20 ← not a solution
(6, 12 )
y = 2(6) + 5 = 12 + 5 = 17 ≠ 12 ← not a solution
(3, 11 )
y = 2(3) + 5 = 6 + 5 = 11 ← solution
(4, 14 )
y = 2(4) + 5 = 8 + 5 = 13 ≠ 14 ← not a solution
Match each equation on the left with its solution on the right. No answer on the right will be used twice.
The correct match the following is shown below:
2x + 3 (x - 2) = 6 (x + 1) + x → x = -6
2x + 3 (x - 2) = 6 (x - 1) - x → All real numbers
2x + 3 (x - 2) = 6 (x - 1) + x → x = 0
2x + 3 (x - 1) = 6 (x - 1) - x → No solution.
What is equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given:
The equation is, 2x + 3 (x - 2) = 6 (x + 1) + x, 2x + 3 (x - 2) = 6 (x - 1) - x, 2x + 3 (x - 2) = 6 (x - 1) + x, and 2x + 3 (x - 1) = 6 (x - 1) - x
Solve the above equations as shown below,
2x + 3 (x - 2) = 6 (x + 1) + x
2x + 3x - 6 = 6x + 6 + x
5x - 6 = 7x + 6
7x - 5x = -6 - 6
x = -6
2x + 3 (x - 2) = 6 (x - 1) - x
2x + 3x - 6 = 6x - 6 - x
5x - 6 = 5x - 6
Infinity solutions,
2x + 3 (x - 2) = 6 (x - 1) + x
2x + 3x - 6 = 6x - 6 + x
5x - 6 = 7x - 6
x = 0
2x + 3 (x - 1) = 6 (x - 1) - x
2x + 3x - 3 = 6x - 6 - x
5x - 3 = 5x - 6
Parallel line, hence, no solution.
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A vehicle uses 1 gallons of gasoline to travel 13 miles. At this rate, how many miles can the vehicle travel per gallon of gasoline?
You may find the answer to this question in the statement of the problem, if the vehicles uses 1 gallon to travel 13 times, then it is traveling at a rate of 13 miles per gallon.
In using quarterly time series data, which quarter can serve as the base period for interpretation of dummy variables?
A. Any of the above.
B. Quarter two
C. Quarter one
D. Quarter four
E. Quarter three
In using quarterly time series data, Quarter two can serve as the base period for interpretation of dummy variables.
What do you mean by interpretation?
The process of interpreting anything involves elaborating, rephrasing, or otherwise demonstrating your own understanding of it.
Because they are explaining what someone is saying to someone who doesn't understand, a person who translates one language into another is known as an interpreter.
What are examples and variables?
A trait that is measurable and capable of taking on several values is known as a variable. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling.
The two primary categories of variables are categorical and numeric.
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If you form a triangle from two given angles measure and the length of the included side, will you always get one triangle or will you get more than one triangle?
You will always get one triangle. This is because of the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles of a triangle is always 180°.
What is known as a triangle?A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
How do triangle angles work?The inner angles of every triangle sum up to 180°, 180°, 180°, 180°. Angles in a triangle are the total (sum) of the angles at each of its three vertices.
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Jasper claims that there exists a regular polygon for which the measure of each interior angle of the polygon is four times the minimum angle of rotation about its center that carries the polygon onto itself.
For the case where Jasper's claim is true, complete the table by entering the correct information for such a regular polygon.
It is not possible for the measure of each interior angle of a regular polygon to be four times the minimum angle of rotation about its center that carries the polygon onto itself.
What is the interior angle?
The inner of the two angles formed where two sides of a polygon come together. any of the four angles formed in the area between a pair of parallel lines when a third line cuts them.
Jasper's claim is not true. The minimum angle of rotation about the center of a regular polygon that carries the polygon onto itself is called the polygon's "order of rotational symmetry." This angle is always less than or equal to 180 degrees, and it is equal to 360 degrees divided by the number of sides in the polygon.
For example, a regular hexagon has an order of rotational symmetry of 60 degrees (360 degrees / 6 sides), and a regular octagon has an order of rotational symmetry of 45 degrees (360 degrees / 8 sides).
Therefore, if the measure of each interior angle of a regular polygon is four times the minimum angle of rotation about its center that carries the polygon onto itself, then the measure of each interior angle would have to be at least 720 degrees. However, the sum of the interior angles of a regular polygon with n sides is 180(n-2) degrees, which is always less than 720 degrees for any value of n greater than 2.
Therefore, it is not possible for the measure of each interior angle of a regular polygon to be four times the minimum angle of rotation about its center that carries the polygon onto itself.
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Select the equivalent fraction for the fraction represented on the given number line.
1/2
2/6
2/3
3/6
2/6 is the equivalent fraction for the fraction represented on the given number line. So, B is the correct option
What is an equivalent fraction ?
According to equivalent fractions, two or more fractions are considered to be equal if, following simplification, both provide the same fraction. Let's imagine that a/b and c/d are two fractions. If these fractions are simplified to produce comparable fractions, such as e/f, they are then equal to one another.
For instance, if we simplify 5/15, the resulting fraction is the same as 1/3, hence that is the equivalent fraction of 1/3.
The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions. For instance, since 2/4 and 3/6 both equal the 12, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.
as 2/6 can further reduced to 1/3 which is represented on to the number line as 1/3 which is equal to 2/6
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Design An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. Another side is 12 more than three times the length of the
bottom of the triangle. The last side is 4 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.
Answer:
[tex]P_t=5x+16[/tex]
Step-by-step explanation:
The perimeter of the triangle will be the sum of all the sides,
[tex]P_t=a+b+c[/tex]
For this problem, let a=x, b=3x+12, and c=4+x. So,
[tex]P_t=(x)+(3x+12)+(4+x)\\P_t=x+3x+12+4+x\\P_t=x+3x+x+12+4\\P_t=5x+16[/tex]
What is the equation of the line through the points(0,0) and (9,-4)
Answer:
y = -4/9x
Step-by-step explanation:
You want the equation of the line through (0, 0) and (9, -4).
ProportionA line through the point (0, 0) represents a proportion. The slope of the line is the constant of proportionality, the ratio of y to x.
k = y/x = -4/9
The equation of the line is ...
y = kx
y = -4/9x
32-39 Fill in >,< or = for each prob
3
15
4
-6
-8
-15
Fill in the inequality for each problem as follows 32 > -39, 3 < 15, 4 > -6 and -8 > -15
How to fill in the correct sign for each problem?Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.
We have different inequality signs as follows:
Greater than (>)
Less than(<)
Less than or equal to (≤)
Greater than or equal to (≥)
Given:
32__-39
3__15
4__-6
-8__-15
For 32__-39:
Since 32 is greater than -39. we can write:
32 > -39
For 3__15:
Since 3 is less than 15. we can write:
3 < 15
For 4__-6:
Since 4 is greater than -6. we can write:
4 > -6
For -8__-15:
Since -8 is greater than -15. we can write:
-8 > -15
Thus, fill in for each problem accordingly
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Complete Question
Fill in >,< or = for each prob
32__-39
3__15
4__-6
-8__-15
Put the following equation of a line into slope intercept form, simplifying all fractions
20y - 4x = -160 what would be the answer
Answer:
do it yourslef
dont be silly
lol
11111111
write the equation of a line of standard form that has a slope of 4 and has same x-intercept as a line 3x+y=18
PLEASEE I WILL GIVE BRANILEST PLSS THIS IS URGENT
Answer: The slope is 3
Step-by-step explanation:
Explanation:
The slope of a line in the form
y
=
m
x
+
b
is
m
.
3
x
−
y
=
4
−
y
=
−
3
x
+
4
subtract
3
x
from both sides
y
=
3
x
−
4
multiply both sides by
−
1
what is (13.4 - 0.896 , 8.4 + 4.095) =
The difference of given decimal numbers is (12.504, 12.495).
Given that, (13.4-0.896, 8.4+4.095).
What is the difference of two decimal numbers?Subtracting decimals:
1. Write down the two numbers, one under the other, with the decimal points lined up.
2. Add zeros so the numbers have the same length.
3. Then subtract normally, remembering to put the decimal point in the answer.
Here,
13.4-0.896 =12.504
8.4+4.095 =12.495
So, (13.4-0.896, 8.4+4.095) =(12.504, 12.495)
Hence, the difference of given decimal numbers is (12.504, 12.495).
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The measure of an angle is 128.1°. What is the measure of its supplementary angle?
Answer:
Two angles are supplementary. If the measure of the angle is twice the measure of the other, find the measure of each angle.
Let the measure of one of the supplementary angles be a
.
Measure of the other angle is 2
times a
.
So, measure of the other angle is 2a
.
If the sum of the measures of two angles is 180°
, then the angles are supplementary.
So, a+2a=180°
Simplify.
3a=180°
To isolate a
, divide both sides of the equation by 3
.
3a3=180°3 a=60°
The measure of the second angle is,
2a=2×60° =120°
So, the measures of the two supplementary angles are 60°
and 120° .
Step-by-step explanation:
Hope this works!....
Divide 2x^-13x+x^2+6 by x-4
The Quadratic Equation [tex]3x^{2}-13x+6[/tex] divided by [tex]x-4[/tex] for all the values of the x(except x=4).
Let us consider [tex]3x^{2}-13x+6[/tex] as equation→(1) of a Quadratic Equation assume some values for x which is satisfies the equation and doesn't satisfy equation by "hit and trail method".
x=1 substitute in the equation (1) we get ⇒ [tex]\frac{4}{3}[/tex]
x=2 we get [tex]3(2)^{2}-13(2)+6[/tex] [tex]=4[/tex]
x=4 we get[tex]3(4)^{2}-13(4)+6[/tex] ⇒ [tex]\frac{2}{0}[/tex] which is not defined.
x=6 we get [tex]3(6)^{2}-13(6)+6[/tex] [tex]= 12[/tex]
x= -2 we get [tex]3(-2)^{2}-13(-2)+6[/tex] ⇒[tex]\frac{22}{-3}[/tex]
And so on for the remaining values of x the equation will satisfy. Except for the value x= 4 the equation doesn't satisfy because if we substitute x=4 in x-4 we get 4-4 =0 anything divided by zero is not defined.
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Divide [tex]3x^{2}-13x+6 by x-4[/tex]
Which function represents the graph?
A. y = –cos (x)
B. y = -sin (x)
C. y = cos (x)
D. y = sin (x)
How many nine-letter words can be formed from the letters of hyperbola, using each letter once per
word? The words do not have to actually spell anything, of course.
The letters of "hyperbola" can be combined into 40,320 different nine-letter words by using each letter just once.
What are the Combinations?Combinations are the procedures used in mathematics to pick k things from n different items without replacement.
The following formula computes the combinations of k items from n:
(n, k) = n! / k!×(n-k)!
There are 8 letters in the word "hyperbola",
So, there are 8 choices for the first letter, 7 choices for the second letter, and so on, down to 1 choice for the last letter.
This means that there are :
⇒ 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Therefore, 40,320 possible nine-letter words can be formed from the letters of "hyperbola" using each letter once per word.
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Use the formula A=(1+r/n)^nt to solve the compound interest problem.
Find how long it takes for 900$ to double if it is invested at 6% interest compounded monthly.
The money will double in value in approximately ? years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
The total years taken to double the money according to Compounding will be 12.5 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 6%
amount = $900
Total amount = $1800
Compounded monthly,
so formula becomes,
Total amount = amount (1+r/1200)^12t
T = A[tex](1+r/1200)^{12t}[/tex]
1800 = 900 (1+6/1200)^12t
2 = (1+1/200)^12t
2 = 1.005^12t
taking log on both sides
log 2 = 12t *log 1.005
0.3/0.002 = 12t
t = 12.5 years
Hence the time taken to double the money is 12.5 years.
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j(m) = 2^m-1
What is j (4)?
Enter your answer in the box.
j(m) = 2ᵐ ⁻ ¹
for functions you will replace the number in the brackets with the letter! so:
j(4) = 2⁴ ⁻ ¹
= 2³
= 8
A decade ago, the average class size at Newton Middle School was 30 students. Now it is 30% smaller. What is the average class size currently?
The average class size of Newton middle school is 21.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that a decade ago, the average class size at Newton Middle School was 30 students. Now it is 30% smaller.
The average class size will be calculated as,
Average class size = 30 x (70%)
Average class size = 30 x 0.7
Average class size = 21
Therefore, the average class size at Newton middle school is 21.
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Suppose a = 9 and b = 4.
Find an exact value or give at least two decimal places:
sin(A) =
cos(A) =
tan(A) =
sec(A) =
csc(A) =
cot(A) =
The trigonometric measures for the triangle in this problem are given as follows:
sin(A) = 0.9137.cos(A) = 0.4061tan(A) = 2.25.sec(A) = 2.4624.csc(A) = 1.0945.cot(A) = 0.4444.What are the trigonometric measures?The six trigonometric measures for a right triangle are given as follows:
Sine of angle: Length of opposite side to the angle divided by the hypotenuse.Cosine of angle: Length of adjacent side to the angle divided by the hypotenuse.Tangent of angle: Length of opposite side to the angle divided by the length of the adjacent side to the angle.Cossecant: One divided by the sine of the angle.Secant: One divided by the cosine of the angle.Cotangent: One divided by the tangent of the angle.From the given right triangle, the sides are given as follows:
a = 9, b = 4.
Then, applying the Pythagorean Theorem, the length of the sqis given as follows:
h² = 9² + 4²
h² = 97
h = square root of 97.
h = 9.85.
Missing InformationThe triangle is given by the image shown at the end of the answer.
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