Answers
SOLUTION:
The graph of g(x) is the graph of f(x) translated 5 units to the left.
Thus, the equation is;
[tex]g(x)=(x+5)^2[/tex]Related Questions
Two similar triangular regions are prepared for development. Grassland Forest 45 yd 60 ya Grassland Perimeter = 240 yd Grassland Area = 2400 yd2 a. It costs $6 per foot to install fencing. How much does it cost to surround the forest with a fence? It costs $ b. The cost to prepare 1 square yard of grassland is $15 and the cost to prepare 1 square yard of forest is costs more to prepare?
Answers
Notice that both regions are right triangles.
As for Grassland, its area is given by the formula:
[tex]\begin{gathered} A_G=\frac{1}{2}bh,A_G=2400 \\ \Rightarrow\frac{1}{2}bh=2400 \\ \Rightarrow b=\frac{4800}{h}=\frac{4800}{60}=80 \\ \Rightarrow b=80 \end{gathered}[/tex]Then, the base of Grassland is equal to 80.
Furthermore, we can use the Pythagorean theorem to find the value of its hypotenuse:
[tex]\text{hypotenuse}=\sqrt[]{80^2+60^2}=100[/tex]With this, we have found all the sides of the Grassland triangle, which is:
And the Forest triangle is similar to the Grassland triangle; then, their corresponding sides have the same ratio
Consider the diagram:
Then, due to the similarity between the triangles:
[tex]\begin{gathered} \frac{45}{60}=\frac{x}{80} \\ \Rightarrow x=80\cdot\frac{45}{60}=60 \end{gathered}[/tex]And
[tex]\begin{gathered} \frac{45}{60}=\frac{y}{100} \\ \Rightarrow y=\frac{4500}{60}=75 \end{gathered}[/tex]Then, the Forest triangle is:
a) The perimeter of the Forest triangle is
[tex]\begin{gathered} P_F=45+75+60=180yd \\ \Rightarrow P_F=180\cdot3=540ft \end{gathered}[/tex]540ft, and, since the fence is $6 per foot, we need
[tex]540\cdot6=3240[/tex]$3240 to surround the whole Forest triangle.
b)
The cost of fencing around the forest is $3240 and cost to prepare the grassland is $15750 more than to prepare the forest.
What are similar triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Given that, Two similar triangular regions are to be prepared for development, the grassland and forest have side length 45 yd 60yd respectively Grassland Perimeter = 240 yd Grassland Area = 2400 yd²
We know that, in similar triangles, the ratio of corresponding sides are equal to the ratio of their perimeters and the ratio of square corresponding sides are equal to the ratio of theirs areas.
Let the perimeter of the forest be x,
Therefore, 45/60 = x/240
x = 180 yd = 540 ft
Since, cost of fencing is $6/foot
Therefore, cost of fencing the forest = 6*540 = $3240
And, Let the area of forest be y,
(45/60)² = y/2400
9/16 = y/2400
y = 1350 yd²
Since, the cost of preparing the forest and the grassland is $15/yd
Therefore, the cost of preparing the forest = 1350*15 = $20250
And the cost of preparing the grassland = 2400*15 = $36000
Therefore, cost to prepare the grassland is $15750 more than to prepare the forest.
Hence, The cost of fencing around the forest is $3240 and cost to prepare the grassland is $15750 more than to prepare the forest.
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I need help with this question please! I have options to choose from also. Also the graph below the wording is just option A
Answers
The correct option is D
Explanation:Given the function:
[tex]f(x)=x^2-5x+6[/tex]This may be written as:
[tex]y=x^2-5x+6[/tex]For x = -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
we need to find the corresponding values for y.
For x = -5
y = (-5)^2 - 5(-5) + 6
= 56
For x = -4
y = (-4)^2 - 5(-4) + 6
= 42
For x = -3
y = (-3)^2 - 5(-3) + 6
= 30
For x = -2
y = (-3)^2 - 5(-2) + 6
= 20
For x = -1
y = (-1)^2 - 5(-1) + 6
= 12
For x = 0
y = (0)^2 - 5(0) + 6
= 6
For x = 1
y = (1)^2 - 5(1) + 6
= 2
For x = 2
y = (2)^2 - 5(2) + 6
= 0
For x = 3
y = 3^2 - 5(3) + 6
= 0
For x = 4
y = 4^2 - 5(4) + 6
= 2
For x = 5
y = 5^2 - 5(5) + 6
= 6
By inspection, we see that the correct option is D
Evaluate: 6+ [8x(5-1)]
Answers
6+ [8x(5-1)]
First, solve the parenthesis:
6+ [8x4]
Then the brackets:
6+ 32
Finally, add both numbers.
38
choose the correct value on each side of the equation.
Answers
Answer:
442.12
Expalanation:
Given the expression
458.13 + y = 900.25
We are to look for the value of y
Subtract 458.13 from bith sides of the equation:
458.13 + y - 458.13 = 900.25 - 458.13
y = 442.12
Hence the correct value is 442.12
.13 from bith sides of the equation:
458.13 + y - 458.13 = 900.25 - 458.13
Why do dividing functions have 4 end behaviors
Answers
Since the dividing function has discontinuity in x and y, we can see that it would have 4 end behaviours
I need help with my math
Answers
From the question, we can deduce the answer using indices which deals with power of numbers, e.g
[tex]\frac{5^2.5^3}{5^4}=\frac{5^{2+3}}{5^4}=\frac{5^5}{5^4}=5^{5-4}=5^1=5[/tex]Also, for the next one,
[tex]\frac{9^4.9^6}{9^8}=\frac{9^{4+6}}{9^8}=\frac{9^{10}}{9^8}=9^{10-8}=9^2[/tex]This applies to every other ones provided in the question,
Considering Option D,
[tex]\begin{gathered} \frac{b^{2k}.b^{3k}}{b^{4k}} \\ \text{where k is 2,} \\ \frac{b^{2(2)}.b^{3(2)}}{b^{4(2)}}=\text{ }\frac{b^4.b^6}{b^8}=\frac{b^{4+6}}{b^8}=\frac{b^{10}}{b^8}=b^{10-8}=b^2 \\ \text{Where k=2, Option D is favoured} \end{gathered}[/tex]Since the equation D favours the solution,
Hence, the best option is D.
Find the scale factor for 8 in : 2 ft
Answers
Explanation
to solve this we need to get the ratio, to do this get the same unit measure in both sides of the quotient
so
[tex]8\text{ in : 2 ft}[/tex]since
[tex]1\text{ ft=12 in}[/tex]replace,
[tex]\begin{gathered} 8\text{ in : 2 ft} \\ 8\text{ in : 2}(12\text{ in)} \\ 8\text{ in: 24 in} \\ \text{divide both sides by 8} \\ \frac{8\text{ in}}{8}=\frac{24\text{ in}}{8} \\ 1\text{ in:3 in} \end{gathered}[/tex]it means the scales factor is
[tex]1\colon3[/tex]1) What is the value of u? A) 32° B) 34 C) 36° D) 68°
Answers
Triangle XYZ is an isosceles triangle, then ∠Z and ∠X (also called u) measure the same.
The addition of the internal angles of a triangle is equal to 180°:
∠X + ∠Y + ∠Z = 180°
Replacing with ∠X = ∠Z = u, and ∠Y = 112°:
u + 112° + u = 180°
2u + 112° = 180°
2u = 180° - 112°
2u = 68°
u = 68°/2
u = 34°
Nine hundred people who attended a movie were asked whether they enjoyed it. The table shows the results.Did Not EnjoyTotalChildrenAdultsTotalEnjoyed461277738114162900How many more children were surveyed than adults? Enter a numerical answer only
Answers
Given:
Total number of people that attended = 900
The total number of adults that attended = 277 + 114 = 391
Total number of children that attended = Total number of people - number of adults
= 900 - 391 = 509
To find how many more children were surveyed than adults, subtract the number of adults from the number of children.
Thus, we have:
Number of children surveyed than adults = 509 - 391 = 118
Therefore, 118 more children were surveyed more than adults.
Let's complete the table below:
ENJOYED DID NOT ENJOY TOTAL
CHILDREN 461
I need to show you a pic of the question
Answers
To answer this question, we need to identify two points on the graph. These points are:
(4, 7) and (0, -9). These points are easy to identify, and a line is defined by two points.
We are going to use the two-point equation of the line to finally find the slope-intercept form of the line.
The formula to find the line is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]We have two points, and we need to label them as follows:
(4, 7) ---> x1 = 4, y1 = 7
(0, -9) ---> x2 = 0, y2 = -9
Then, we have:
[tex]y-7=\frac{-9-7}{0-4}(x-4)\Rightarrow y-7=\frac{-16}{-4}(x-4)\Rightarrow y-7=4(x-4)[/tex]Then, we have:
[tex]y-7=4x-16\Rightarrow y=4x-16+7\Rightarrow y=4x-9[/tex]Therefore, the equation of the line is equal to:
[tex]y=4x-9[/tex]We need to write:
• In the first box ---> ,4
,• In the second box --->, -9
Solve the compound an equality. Write the solution in interval notation.
Answers
Step 1: Write the two inequalities equations
[tex]4u\text{ + 1 }\leq\text{ -3 -2u }\ge\text{ 10}[/tex]Step 2: Solve the two inequalities separately
[tex]\begin{gathered} 4u\text{ + 1 }\leq\text{ -3} \\ 4u\text{ }\leq\text{ -3 -1 } \\ 4u\text{ }\leq\text{ -4} \\ u\text{ }\leq\text{ }\frac{-4}{4} \\ u\text{ }\leq\text{ -1} \end{gathered}[/tex][tex]\begin{gathered} -2u\text{ }\ge\text{ 10} \\ \text{When you divide inequalities by -2, the sign will change} \\ \frac{-2u}{-2}\text{ }\leq\text{ }\frac{10}{-2} \\ u\text{ }\leq\text{ -5} \end{gathered}[/tex]
Final answer
[tex](-\infty,\text{ -5\rbrack}[/tex]Or
[tex]\lbrack\text{ x }\leq\text{ -5\rbrack or ( -}\infty,\text{ -5)}[/tex]What is the difference between 3xg and gº? .
Answers
EXPLANATION
The difference is that 3*g is a multiplication that give us a Real number and g° is a degree number.
Calculate the sum of interior angles of a 6 sided polygon
Answers
The sum of interior angles of a polygon can be calculated using the formula below.
[tex]\begin{gathered} S\text{ = }(n-2)\times180^0 \\ \text{Where; } \\ S\text{ = sum of interior angles of the polygon } \\ n\text{ = number of sides of the polygon} \end{gathered}[/tex]For the given question the polygon is 6 sided, so;
[tex]n\text{ = 6}[/tex]Substituting the value of n into the formula, we have;
[tex]\begin{gathered} S\text{ = (6-2)}\times180^0 \\ S\text{ = 4}\times180^0 \\ S=720^0 \end{gathered}[/tex]Therefore, the sum of interior angles of a 6 sided polygon is 720 degree
[tex]S=720^0[/tex]Find the equation for the line with the given properties. Sketch the graph of the line. Passes through (2, -5) and (7,3)
Answers
We have to find the equation of the line that passes through points (2,-5) and (7,3).
We can start by calculating the slope m as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-5)}{7-2}=\frac{3+5}{5}=\frac{8}{5}[/tex]With one point and the slope, we can write the line equation in slope-point form and then rearrange it:
[tex]\begin{gathered} y-y_2=m(x-x_2) \\ y-3=\frac{8}{5}(x-7) \\ y-3=\frac{8}{5}x-\frac{56}{5} \\ y=\frac{8}{5}x-\frac{56}{5}+3\cdot\frac{5}{5} \\ y=\frac{8}{5}x-\frac{56}{5}+\frac{15}{5} \\ 5y=8x-56+15 \\ 5y=8x-41 \\ -8x+5y+41=0 \\ 8x-5y-41=0 \end{gathered}[/tex]The equation in general form is 8x-5y-41 = 0.
We can sketch it as:
Identify the parent function of f(x) = -×^2+2
Answers
The given function is
[tex]f(x)=-x^2+2[/tex]The parent function refers to the simplest function possible.
Hence, the parent function is[tex]f(x)=x^2[/tex]A cylindrical can has a radius of 6 inches and a height of 15 inches. Find the volumeof the can.
Answers
let's remember the formula to find the volume of a cylinder
Let's apply the formula with the values that we have in the problem.
The volume of the cylindrical can is 540π inches^3 or 1696.46 inches^3.
In order for th parallelogram tobe a square, x = = [? ]°4x+17°
Answers
We know that the diagonals of a square bisects it's angles and every angles of square are 90°.
The diagnol bisects the parallelogram in two equal parts.
The angle obtained are,
[tex]4x+17^{\circ}[/tex]The sum of the angles are 90 deg.
[tex]4x+17+4x+17=90^{\circ}[/tex][tex]8x+34=90^{\circ}[/tex][tex]8x=56^{\circ}[/tex][tex]x=7^{\circ}[/tex]Thus the value of x is 7 deg.
the difference of a number and 6 is the same as 5 times the sum of the number and 2. what is the number? a. -4 b. -2 c. -1d. 1
Answers
Let x represent the number.
the difference of a number and 6. This would be expressed as
x - 6
5 times the sum of the number and 2. This would be expressed as
5(x + 2)
Since both expressions are the same, it means that
x - 6 = 5(x + 2)
We would open the bracket on the right hand side by multiplying each term inside the bracket by the term outside the bracket. It becomes
x - 6 = 5x + 10
5x - x = - 6 - 10
4x = - 16
x = - 16/4
x = - 4
The correct option is A
One canned juice drink is 20% orange juice, another is 10% orange juice. How many liters of each should be mixed together in order to get 10L that is 11% orangeNice?
Answers
Let:
x = Liters of 20% orange juice
y = Liters of 10% orange juice
z = Liters of 11% orange juice
so:
[tex]0.2x+0.1y=10\cdot0.11[/tex]so:
[tex]\begin{gathered} 0.2x+0.1y=1.1 \\ y=10-x \\ so\colon \\ 0.2x+0.1(10-x)=1.1 \\ 0.2x+1-0.1x=1.1 \\ 0.1x=0.1 \\ x=\frac{0.1}{0.1} \\ x=1 \\ so\colon \\ y=10-1=9 \end{gathered}[/tex]Answer:
1 liters of 20% orange juice
9 liters of 10% orange juice
Read the following conjectures and decide if they are true or false: • Angles that are adjacent angles share a vertex. • All right angles are supplementary angles. • The square of all odd numbers is an odd number • The product of an even number and odd number is even Counterexamples:
Answers
1) Angles that are adjacent share a common vertex = True
Points to know about adjacent angles:
They have a side in common
They have a common vertex
They do not overlap
2) All right angles are supplementary angles = False
Right angles = 90 degrees (they are complementary)
3) The square of all odd numbers is an odd number = True
All odd numbers take the form 2n + 1 (notice the offshoot of 1)
The square of odd numbers will be :
(2n + 1) ² = 4n ² + 4n + 1 (this also has an offshoot of 1)
This means that both an odd number and its square are odd
4) The product of an even number and an odd number is even = True
find the measure of all labeled angles in the diagram
Answers
Answer:
∠1 = 127°
∠2 = 53°
∠3 = 127°
∠4 = 37°
∠5 = 53°
∠6 = 90°
∠7 = 37°
∠8 = 143°
∠9 = 37°
∠10 = 143°
Explanation:
If two angles form a straight line, they add to 180°, so ∠1, ∠2, and ∠3 can be calculated as:
∠1 = 180 - 53 = 127°
∠2 = 180 - ∠1 = 180 - 127 = 53°
∠3 = 180 - 53 = 127°
Then, ∠5 is corresponding to 53° because they are in the same relative position. It means that these angles have the same measure, so:
∠5 = 53°
On the other hand, ∠6 is opposite to the right angle, so it has the same measure, then:
∠6 = 90°
∠4, ∠5, and ∠6, form a straight line, so:
∠4 = 180 - ∠5 - ∠6
∠4 = 180 - 53 - 90
∠4 = 37°
Finally, the sum of the interior angles of a triangle is also 180°, so the measure ∠7 will be equal to:
∠7 = 180 - ∠2 - ∠6
∠7 = 180 - 53 - 90
∠7 = 37°
So, the measures of ∠8, ∠9, and ∠10 will be equal to:
∠8 = 180 - ∠7 = 180 - 37 = 143°
∠9 = 180 - ∠8 = 180 - 143 = 37°
∠10 = 180 - ∠7 = 180 - 37 = 143°
Therefore, the answers are:
∠1 = 127°
∠2 = 53°
∠3 = 127°
∠4 = 37°
∠5 = 53°
∠6 = 90°
∠7 = 37°
∠8 = 143°
∠9 = 37°
∠10 = 143°
Determine whether the sample is biased or unbiased. Explain You want to estimate the number of students in your school who drive their own cars to school.You survey every 8th person who enters the cafeteria for lunch.
Answers
You want to estimate the number of students in your school who drive their own cars to school.You survey every 8th person who enters the cafeteria for lunch.
Determine whether the sample is biased or unbiased.
Explain
It is biased because the whole population was not properly represented in the sample study.
More and more people are purchasing food from farmers' markets. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 5% each year. If there are 7,700 farmers' markets this year, how many will there be in 5 years?
Answers
Given:
A market researcher predicts that the number of farmers' markets will increase by 5% each year
There are 7,700 farmers' markets this year
we will the number of farmers' markets after 5 years
So, we will use the following formula:
[tex]A=P\cdot(1+r)^t[/tex]We will calculate (A) when P = 7700, r = 5% and t = 5
so,
[tex]A=7700\cdot(1+\frac{5}{100})^5=7700\cdot1.05^5=9827.368[/tex]Rounding to the nearest whole number
so, the answer will be 9827
Can you help meSolve(2/9)³+13⁰
Answers
737/729
1) Let's solve that expression with two powers.
[tex]\begin{gathered} (\frac{2}{9})^3+13^0 \\ \text{Any power raised to 0 is =1} \\ (\frac{8}{729})+1 \\ \text{LCM 1 and 729}=729 \\ \frac{\square}{729} \\ \\ \text{Let's divide 729 by 729 and multiply by 8} \\ \frac{(\frac{729}{729\text{ }}=1\text{ }\times8)}{729} \\ \frac{8}{729} \\ \frac{\frac{729}{1}=\text{ 729 x 1}}{729}=\frac{729}{729} \\ \text{Hence,} \\ \frac{8}{729}+\frac{729}{729}=\frac{737}{729} \end{gathered}[/tex]2) So the answer to that expression, considering that any number raised to 0 is equal to 1 and taking the LCM (Least Common Multiple) to turn those fractions into one with the same denominator and then sum turns out to be 737/729
A washer and dryer cost $911 combined the washer cost $61 more than the dryer. What is the cost of the dryer?
Answers
ANSWER:
$425
STEP-BY-STEP EXPLANATION:
Let w be the price of the washer and d be the price of the dryer, we can establish the following system of equations:
[tex]\begin{gathered} w+d=911 \\ \\ w=d+61 \end{gathered}[/tex]We substitute the second equation into the first and solve for d, like this:
[tex]\begin{gathered} d+61+d=911 \\ \\ 2d=911-61 \\ \\ d=\frac{850}{2} \\ \\ d=\text{\$}425 \end{gathered}[/tex]Therefore, the price of the dryer is $425.
Determine if the following equation is linear if the equation is linear converted to standard form AX+by=c
Answers
Given the equation:
[tex](-10+y^2)-y^2=-7x+10[/tex]To determine if the equation is a linear equation, the first step is to simplify it. To do so, erase the parentheses and simplify the like terms:
[tex]\begin{gathered} (-10+y^2)-y^2=7x+10 \\ -10+y^2-y^2=7x+10 \\ -10+0y^2=7x+10 \\ -10+0y=7x+10 \end{gathered}[/tex]The terms "+y²" and "-y²" canceled each other, this is why the variable y is multiplied by zero. Then the only variable left is "x", which suggests that the equation represents a vertical line.
To write this equation in standard form, you have to pass the x-term to the left side of the equation and the constant to the right side of it:
[tex]\begin{gathered} -10+0y=-7x+10\text{ \rightarrow add 10 to both sides of the equation} \\ -10+10+0y=-7x+10+10 \\ 0y=-7x+20\text{ \rightarrow add 7x to both sides of the equation} \\ 0y+7x=-7x+7x+20 \\ 0y+7x=20 \\ 7x+0y=20 \end{gathered}[/tex]The line written in standard form is 7x+0y=20.
Vertical lines are considered to be linear equations.
Find two points on the line to graph the function Any lines orCurves will be drawn once all required points are plotted
Answers
ANSWER:
A: (4, 9)
B: (-1, -3)
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]q(x)=4x-\frac{(3+8x)}{5}[/tex]We determine the two points when x = 4 and when x = -1, like this:
[tex]\begin{gathered} q(4)=4\cdot4-\frac{\left(3+8\cdot4\right)}{5}\: \\ \\ q(4)=16-\frac{3+32}{5}=16-7 \\ \\ q(4)=9 \\ \\ A=(4,9) \\ \\ q(-1)=4\cdot\left(-1\right)-\frac{\left(3+8\cdot(-1)\right)}{5}\: \\ \\ q(-1)=-4-\frac{3-8}{5} \\ \\ q(-1)=-4-(-1)=-4+1 \\ \\ q(-1)=-3 \\ \\ B=(-1,-3) \end{gathered}[/tex]Therefore point A is (4, 9) and point B is (-1, -3)
which equation had a graph that is a parabola with vertex at (-1,-1)
Answers
After solving all the equations, we can conclude that equation (D) [y = (x + 1)² - 1] had a graph that is a parabola with vertex (-1, -1).
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the form of the equation of the vertical parabola:
y = a(x - h)² + kWhere h and k are the vertexes.Now, calculate each equation as follows:
(A) y = (x - 1)² + 1
Vertex: (1, 1)Then, the wrong answer.(B) y = (x - 1)² - 1
Vertex: (1, -1)Then, the wrong answer.(C) y = (x + 1)² + 1
Vertex: (1, 1)Then, the wrong answer.(D) y = (x + 1)² - 1
Vertex: (-1, -1)Then, this is the correct option.Therefore, after solving all the equations, we can conclude that equation (D) [y = (x + 1)² - 1] had a graph that is a parabola with vertex (-1, -1).
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Complete question:
Which equation has a graph that is a parabola with a vertex at (–1, –1)?
A.y = (x – 1)2 + 1
B.y = (x – 1)2 – 1
C.y = (x + 1)2 + 1
D.y = (x + 1)2 – 1
Suppose z varies directly with x and inversely with the square of y. If z = 18 when I = 6 and y = 2, what is z when I 7 and y = 7? Z =
Answers
It is given that z varies directly with x and inversely with the square of y so it follows:
[tex]z=k\frac{x}{y^2}[/tex]It is also given that z=18 when x=6 and y=2 so it follows:
[tex]\begin{gathered} 18=k\frac{6}{2^2} \\ k=\frac{18\times4}{6} \\ k=12 \end{gathered}[/tex]So the equation of variation becomes:
[tex]z=12\frac{x}{y^2}[/tex]Therefore the value of z when x=7 and y=7 is given by:
[tex]\begin{gathered} z=\frac{12\times7}{7^2} \\ z=\frac{12}{7} \\ z\approx1.7143 \end{gathered}[/tex]Hence the value of z is 12/7 or 1.7143.
15h - 13h - h + 3= 7
Answers
Answer:
[tex]h=4[/tex]Explanation: We need to solve for h in the given equation, which is:
[tex]15h-13h-h+3=7[/tex]Isolating unknowns and constants:
[tex]\begin{gathered} 15h-13h-h+3=7\rightarrow15h-14h+3=7 \\ \therefore\rightarrow \\ 15h-14h=7-3=4 \\ \therefore\rightarrow \\ 15h-14h=4 \end{gathered}[/tex]Simplifying gives:
[tex]\begin{gathered} 15h-14h=4 \\ \therefore\rightarrow \\ h=4 \end{gathered}[/tex]