A 13-feet ladder is placed 5 feet away from a wall. What is the height at which the top of the ladder reaches the wall?
Answers
Draw the situation for a better understanding:
To find the height at which the top of the ladder reaches the wall use pythagorean theorem:
[tex]\begin{gathered} h=\sqrt[]{13^2-5^2} \\ h=\sqrt[]{169-25} \\ h=\sqrt[]{144} \\ h=12 \end{gathered}[/tex]The height at which the top of the ladder reaches the wall is 12 ft.
Related Questions
Determine the value of b for which x = 1 is a solution of the equation shown.
2x + 14 = 10x + b
b=
Answers
Answer
Step-by-step explanation:
solve for b.
2x+14=10x+b
Step 1: Flip the equation.
b+10x=2x+14
Step 2: subtract 10x from both sides.
b+10x+−10x=2x+14+−10x
b=−8x+14
Answer:
b=−8x+14
What is the value of y in the solution set of the system of linear equations shown below?y = -x + 124x - 2y = 36A.10B. 8C. 6D. 2
Answers
y = 2 (option D)
Explanation:y = -x + 12
4x - 2y = 36
rewriting the equations:
y + x = 12 ....equation 1
-2y + 4x = 36 ....equation 2
Using elimination method:
we will be eliminating y. So we need to make the coefficient of y to be the same in both equation. We will be multiplying the first equation by 2.
2y + 2x = 24 ....equation 1
-2y + 4x = 36 ....equation 2
Add both equations:
2y + (-2y) + 2x + 4x = 24 + 36
2y-2y + 6x = 60
6x = 60
x = 60/6 = 10
Insert the value of x in any of the equation. Using equation 2:
4(10) - 2y = 36
40 -2y = 36
-2y = 36 - 40
-2y = -4
y = -4/-2
y = 2 (option D)
What is the output value for the following function if the input value is 5?y = 4x - 34223172
Answers
Answer:
17
Explanation:
Given the function:
[tex]y=4x-3[/tex]When the input value, x = 5
[tex]\begin{gathered} y=4x-3 \\ =4(5)-3 \\ =20-3 \\ =17 \end{gathered}[/tex]The output value if the input value is 5 is 17.
5/6+1/3×5/8 i need help
Answers
We will solve as follows:
[tex]\frac{5}{6}+\frac{1}{3}\cdot\frac{5}{8}=\frac{5}{6}+\frac{5}{24}=\frac{4}{4}\cdot\frac{5}{6}+\frac{5}{24}[/tex][tex]=\frac{20}{24}+\frac{5}{24}=\frac{25}{24}[/tex]Find the median and mean of the data set below: 3, 8, 44, 50, 12, 44, 14 Median Mean =
Answers
the median is 25, because:
[tex]=\frac{3+8+44+50+12+44+14}{7}=\frac{175}{7}=25[/tex]the mean value is :
[tex]14[/tex]Use the figure below to find the value of x. (x + 20) y (x + 10° (y – 40)
Answers
Answer:
The value of x is 75;
[tex]x=75[/tex]Explanation:
From the diagram;
[tex](x+20)^0+(x+10)^0=180^0[/tex]Reason; supplementary angles.
Solving the equation, we have;
[tex]\begin{gathered} x+x+20+10=180 \\ 2x+30=180 \\ 2x=180-30 \\ 2x=150 \\ x=\frac{150}{2} \\ x=75 \end{gathered}[/tex]Therefore, the value of x is 75;
[tex]x=75[/tex]Please help, algebra 1, i dont know how to begin to solve it :/ thank you thank you.Simplify:
Answers
Given the expression:
[tex](x^2-4x^3)+(5x^3+3x^2)[/tex]You can simplify it as follows:
1. Distribute the positive sign. Since the sign between the parentheses is positive, it does not change the signs of the second parentheses:
[tex]=x^2-4x^3+5x^3+3x^2[/tex]2. Add the like terms.
By definition, like terms have the same variables with the same exponent.
In this case, you need to add the terms with exponent 3 and add the terms with exponent 2. Notice that:
[tex]\begin{gathered} -4x^3+5x^3=x^3 \\ \\ x^2+3x^2=4x^2 \end{gathered}[/tex]Then, you get:
[tex]=x^3+4x^2[/tex]Hence, the answer is:
[tex]=x^3+4x^2[/tex]5 ptsIn Ms. Johnson's class a student will get 3 points forhaving their name on their paper and 4 points for eachquestion that is correct. In Mr. Gallegos class, a studentwill get 7 points for having their name on their paper and2 points for each question correct. Which inequalitycould be used to determine x, the number of questionsthat would give you a higher grade in Ms. Johnson'sclass?
Answers
In Ms. Johnson's class a student will get 3 points for
having their name on their paper and 4 points for each
question that is correct. In Mr. Gallegos class, a student
will get 7 points for having their name on their paper and
2 points for each question correct. Which inequality
could be used to determine x, the number of questions
that would give you a higher grade in Ms. Johnson's
class?
we have
Ms. Johnson's class
3+4x
Mr. Gallegos class
7+2x
so
the inequality is given by
3+4x > 7+2x
solve for x
4x-2x > 7-3
2x>4
x> 2
the number of question must be greater than 2
Mary Bought her car for $20,000. After 5 years she decided to sell her car for a 25% increase invalue. What is the price that Mary decided to sell her car for?
Answers
Original Car price = $20,000
Price increase after 5 years = 25%
To calculate the price after 5 years, first multiply the original price (20,000) by the percentage increase in decimal form ( divided by 100) to obtain the increase amount:
20,000 x (25/100) = 20,000 x 0.25 = $5000
Finally, add the increase amount to the original price:
20,000+5,000 = $25,000
Suppose that you follow the same path on the return trip from Dubuque to Council Bluffs. What would be thetotal number of (actual) miles for the round trip?
Answers
We know the trip from Council Bluffs to Dubuque had a total distance of 348 miles; if we take the same route to go back this will mean that we need to travel the same distance, 348 miles. The total distance then we will be 696 miles.
A rectangle with an area of 20 square units is dilated by the scale factor of 3.5. find the area of the new rectangle
Answers
We are given the area of a rectangle. The area of a rectangle is the product of the length and the height. Therefore, we have:
[tex]A=lh[/tex]If we scale the rectangle by a factor of 3.5 this means that we multiply the length and the height by 3.5, like this:
[tex]A^{\prime}=(3.5l)(3.5h)[/tex]Solving the product:
[tex]A^{\prime}=12.25lh[/tex]Since "lh" is the original area we have:
[tex]A^{\prime}=12.25A[/tex]Now, we substitute the value of the original area:
[tex]A^{\prime}=12.25(20)[/tex]Solving the operations:
[tex]A^{\prime}=245[/tex]Therefore, the new area is 245 square units.
The current in a simple electrical circuit is inversely proportional to the resistance. If thecurrent is 30 amperes (an ampere is a unit for measuring current) when the resistance is 5ohms, find the current when the resistance is 7.8 ohms.
Answers
Hello there. To solve this question, we'll have to remember some properties about inversely proportional terms.
Let's start labeling the terms:
Say Current is given by I, Resistance is given by R and voltage is given by V.
By Ohm's Law, we know that:
[tex]V=R\cdot I[/tex]In fact, this is the definition we need to find the answer.
But, to understand why the question mention the fact that they are inversely proportional, note:
We say two numbers x and y are inversely proportional when:
[tex]x\cdot y=k[/tex]Their product is equal to a constant. k is the constant (of proportionality).
Now, using the given values in the question, we can solve this question.
If the current is 30 ampère when the resistance is 5 ohms, we have to find the current when the resistance is 7.8 ohms.
First scenery:
[tex]V=30\cdot5[/tex]Multiply the numbers
[tex]V=150[/tex]Second scenery:
[tex]V=7.8\cdot I[/tex]Plugging V = 150, we get:
[tex]150=7.8\cdot I[/tex]Divide both sides of the equation by a factor of 7.8
[tex]I=\frac{150}{7.8}[/tex]Simplify the fraction by a factor of 2
[tex]I=\frac{75}{3.9}[/tex]Using a calculator, we get the following approximation
[tex]I\approx19.2\text{ A}[/tex]A is for Ampère.
In order for the parallelogram to be a rhombus, x equals?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
parallelogram diagram
Step 02:
geometry:
solve for x:
(5x + 25)° = (12x + 11)°
5x + 25 = 12x + 11
25 - 11 = 12x - 5x
14 = 7x
14 / 7 = x
2 = x
The answer is:
x = 2
IF P(A)=0.2 P(B)=0.1 and P(AnB)=0.07 what is P(AuB) ?A.0.13 B. 0.23 C. 0.3 D.0.4
Answers
ANSWER
P(AuB) = 0.23
STEP-BY-STEP EXPLANATION:
Given information
P(A) = 0.2
P(B) = 0.1
P(AnB) = 0.07
What is P(AUB)
[tex]P(\text{AuB) = P(A) + P(B) }-\text{ P(AnB)}[/tex]The next step is to substitute the above data into the formula
[tex]\begin{gathered} P(\text{AuB) = 0.2 + 0.1 - 0.07} \\ P(\text{AuB) = 0.3 - 0.07} \\ P(\text{AuB) = 0.23} \end{gathered}[/tex]Write the percent as fraction or mixed number in simplest form 750%
Answers
Answer
[tex]7\frac{1}{2}[/tex]Explanation
The 750 percent as a fraction or mixed number in simplest form is calculated as follows:
[tex]750\%=\frac{750}{100}=\frac{75}{10}=\frac{15}{2}=7\frac{1}{2}[/tex]3, -10, 16, -36, 68, ___-3, 12, -33, 102, -303, ___Identify a pattern in each list of numbers. Then use this pattern to find the next number.
Answers
As for the sequence 3,-10,16,-36,68,..., notice that
[tex]\begin{gathered} 3-13=-10 \\ -10+26=-10+2(13)=-10+2^1(13)=16 \\ 16-52=16-4(13)=16-2^2(13)=-36 \\ -36+104=-36+8(13)=-36+2^3(13)=68 \end{gathered}[/tex]Therefore, the next term is
[tex]68-2^4(13)=68-16(13)=-140[/tex]The answer is -140.
Regarding the second pattern, notice that
[tex]\begin{gathered} -3+15=12 \\ 12-45=12-3(15)=12-3^1(15)=-33 \\ -33+135=-33+9(15)=-33+3^2(15)=102 \\ 102-405=102-27(15)=102-3^3(15)=-303 \end{gathered}[/tex]Then, the next term of the sequence is
[tex]-303+3^4(15)=912[/tex]The answer is 912
Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a = 3.0, b = 4.0, C = 58°
Answers
Answer
A = 46.3°
B = 75.7°
c = 3.5
Explanation
We will be using both Cosine and Sine rule to solve this.
For Cosine rule,
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the Cosine rule is given as
c² = a² + b² - 2ab Cos C
a = 3.0
b = 4.0
C = 58°
c² = 3² + 4² - 2(3)(4)(Cos 58°)
c² = 9 + 16 - (24)(0.5299)
c² = 25 - 12.72 = 12.28
c = √12.28 = 3.50
To find the other angles, we will now use Sine Rule
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is given as
[tex]\frac{\text{ Sin A}}{a}=\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]So, we can use the latter parts to solve this
[tex]\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]B = ?
b = 4.0
C = 58°
c = 3.5
[tex]\begin{gathered} \frac{\text{ Sin B}}{4}=\frac{\text{ Sin 58}\degree}{3.5} \\ \text{ Sin B = }\frac{4\times\text{ Sin 58}\degree}{3.5}=0.9692 \\ B=Sin^{-1}(0.9692)=75.7\degree \end{gathered}[/tex]We can then solve for Angle A
The sum of angles in a triangle is 180°
A + B + C = 180°
A + 75.7° + 58° = 180°
A = 180° - 133.7° = 46.3°
Hope this Helps!!!
Find a unit vector u with the same direction as v = : (-3, 8)
Answers
Given:
The vector
[tex]v=<-3,8>[/tex]Required:
To find the unit vector u with the same direction.
Explanation:
Unit formula is the vector is divided by its magnitude.
Now the magnitude of v is,
[tex]\begin{gathered} mag.v=\sqrt{(-3)^2+8^2} \\ =\sqrt{9+64} \\ =\sqrt{73} \end{gathered}[/tex]Now the unit vector is,
[tex]u=<-\frac{3}{\sqrt{73}},\frac{8}{\sqrt{73}}>[/tex]Final Answer:
[tex]u=<-\frac{3}{\sqrt{73}},\frac{8}{\sqrt{73}}>[/tex]4(x - 3) - (x - 5) = 0
Answers
4(x - 3) - (x - 5) = 0
Solving for x:
4(x - 3) - (x - 5) = 0
4x - 12 - x + 5 = 0
4x - x = 12 - 5
3x = 7
x = 7/3
Answer:
x = 7/3 = 2.33
How many different amounts of money can be made
with six pennies, two nickels, and one quarter?
Answers
Based on the number of pennies, nickels, and quarters, the number of different amounts of money that can be made are 42.
How to find the different amounts that can be made?First, find out the number of ways to select the different amounts.
There are six pennies so there are 7 ways to collect them including:
(0 times, 1 time, 2, 3, 4, 5, 6)
There are 3 ways to collect nickels and there are two ways to collect quarters.
The number of different amounts of money that can be made are:
= 7 x 3 x 2
= 42 different amounts of money
Find out more on pennies at https://brainly.com/question/2874020
#SPJ1
What are the possible values for the missing term of the geometric sequence? .004, _____, .4.04.04, -.04.0004.0004, -.0004
Answers
By definition, in a Geometric sequence the terms are found by multiplying the previous one by a constant. This constant is called "Common ratio".
In this case, you know these values of the set:
[tex]\begin{gathered} .004 \\ .4 \end{gathered}[/tex]Notice that you can set up this set with the value given in the first option:
[tex].004,.04,.4[/tex]Now you can check it there is a Common ratio:
[tex]\begin{gathered} \frac{0.04}{0.004}=10 \\ \\ \frac{.4}{0.04}=10 \end{gathered}[/tex]The Common ratio is:
[tex]r=10[/tex]Therefore, it is a Geometric sequence.
Apply the same procedure with each option given in the exercise:
- Using
[tex].004,.04,-.04,.4[/tex]You can notice that it is not a Geometric sequence, because:
[tex]\begin{gathered} \frac{-.04}{.04}=-1 \\ \\ \frac{.4}{-.04}=-10 \end{gathered}[/tex]- Using
[tex].004,.0004,.4[/tex][tex]\begin{gathered} \frac{.0004}{.004}=0.1 \\ \\ \frac{4}{.0004}=1,000 \end{gathered}[/tex]Since there is no Common ratio, if you use the value given in the third option, you don't get a Geometric sequence.
- Using this set with the values given in the last option:
[tex].004,.0004,-.0004,.4[/tex]You get:
[tex]\begin{gathered} \frac{.0004}{.004}=0.1 \\ \\ \frac{-.0004}{.0004}=-1 \end{gathered}[/tex]It is not a Geometric sequence.
The answer is: First option.
There is sales tax of $9.00 on an item t that costs $ 120.00 before tax. The sales tax on a different item is $ 19.05. How much does the second item cost before tax?
Answers
SOLUTION:
Step 1:
In this question, we are given that:
There is sales tax of $9.00 on an item that costs $ 120.00 before tax.
The sales tax on a different item is $ 19.05.
We are meant to find how much the second item cost before tax.
Step 2:
Assuming that there is an equal percentage of tax,
and let the second item cost before tax be y,
then we have that:
[tex]\frac{9}{120}\text{ = }\frac{19.05}{y}[/tex]Cross-multiply, we have that:
[tex]\begin{gathered} 9\text{ x y = 19.05 x 120} \\ 9y\text{ = 2286} \\ \end{gathered}[/tex]Divide both sides by 9, we have that:
[tex]\begin{gathered} y\text{ = }\frac{2286}{9} \\ y\text{ = 254} \end{gathered}[/tex]CONCLUSION:
The cost of the second item before tax = $ 254
If Triangle ABC is dilated by a scale factor of 3 and the length of side AB is 15 inches, what is the length of side A'B'? Complete the statement: The length of side A'B' would be inches. Your answer
Answers
If Triangle ABC is dilated by a scale factor of 3 and the length of side AB is 15 inches, what is the length of side A'B'? Complete the statement: The length of side A'B' would be inches.
To find out the length side of A'B' multiply the length side AB by the scale factor
so
A'B'=3*(15)=45 inches
Compute the sums below. (Assume that the terms in the first sum are consecutive terms of an arithmetic sequence.) 9 + 4 + (-1) + ... + (-536)
Answers
SOLUTION
The terms below make an A.P. Now we are told to find the sum of the AP.
Sum of an AP is given by
[tex]S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack}[/tex]Where S = sum of the AP, a = first term = 9, d = -5, n= ?
So we have to find n first before we can find the sum. The nth term which is the last term = -536. So we will use it to find the number of terms "n"
[tex]\begin{gathered} \text{From T}_{n\text{ }}=\text{ a +(n-1)d where T}_{n\text{ }}=\text{ -536} \\ -536\text{ = 9+(n-1)-5} \\ -536\text{ = 9-5n+5} \\ -536\text{ = 14-5n} \\ -5n\text{ = -536-14} \\ -5n\text{ = -550} \\ n\text{ = 110} \end{gathered}[/tex]Now let's find the sum
[tex]\begin{gathered} S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack} \\ S\text{ = }\frac{110}{2}\lbrack2\times9\text{ + (110-1)-5\rbrack} \\ S\text{ = 55\lbrack{}18+(119)-5\rbrack} \\ S\text{ = 55\lbrack{}18 - 595\rbrack} \\ S\text{ = 55}\times-577 \\ S\text{ = -31735} \end{gathered}[/tex]Therefore, the sum = -31735
i need help solving this and also what does the 2 that's on the top of some letters mean
Answers
given the expression :
[tex]a-bc^2[/tex]We need to evaluate the expression when :
[tex]\begin{gathered} a=3 \\ b=2 \\ c=-1 \end{gathered}[/tex]So, substitute with a , b and c at the expression
The result will be :
[tex]\begin{gathered} a-bc^2 \\ =3-2\cdot(-1)^2 \\ =3-2\cdot1 \\ =3-2 \\ \\ =1 \end{gathered}[/tex]There is another expression :
[tex]c^2+a^2b[/tex]By substitute with the values of a, b and c
so, the result will be :
[tex]\begin{gathered} c^2=(-1)^2=1 \\ a^2=3^2=9 \\ \\ c^2+a^2b=1+9\cdot2=1+18=19 \end{gathered}[/tex]I need to know how to 53 evaluate the inverse trigonometric function give answers in both radians and degrees
Answers
GIVEN:
We are given the following trigonometric expression;
[tex]Tan^{-1}(-1)[/tex]Required;
We are required to evaluate and answer both in radians and in degrees.
Step-by-step solution;
We shall begin by using the trig property;
[tex]tan^{-1}(-x)=-tan^{-1}(x)[/tex]Therefore, we now have;
[tex]tan^{-1}(-1)=-tan^{-1}(1)[/tex]We now use the table of common values and we'll have;
[tex]tan^{-1}(1)=\frac{\pi}{4}[/tex]Therefore;
[tex]-tan^{-1}(1)=-\frac{\pi}{4}[/tex]We can now convert this to degrees;
[tex]\begin{gathered} Convert\text{ }radians\text{ }to\text{ }degrees: \\ \frac{r}{\pi}=\frac{d}{180} \end{gathered}[/tex]Substitute for r (radian measure):
[tex]\begin{gathered} \frac{-\frac{\pi}{4}}{\pi}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\div\frac{\pi}{1}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\times\frac{1}{\pi}=\frac{d}{180} \\ \\ -\frac{1}{4}=\frac{d}{180} \end{gathered}[/tex]Now we can cross multiply;
[tex]\begin{gathered} -\frac{180}{4}=d \\ \\ -45=d \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} radians=-\frac{\pi}{4} \\ \\ degrees=-45\degree \end{gathered}[/tex]Which ordered pair is a solution tothe system of inequalities shown?
Answers
We want to know which ordered pair is a solution of the system of inequalities shown:
[tex]\begin{cases}x-4y\ge0 \\ x-y<-1\end{cases}[/tex]For doing so, we will try to solve both inequalities for one variable, in this case, we will use y.
On the first equation:
[tex]\begin{gathered} x-4y\ge0 \\ x\ge4y \\ y\le\frac{x}{4} \end{gathered}[/tex]On the second equation:
[tex]\begin{gathered} x-y<-1 \\ x+1-y<0 \\ x+1And joining those two results we get:[tex]x+1Now we check each of the ordered pairs, if they hold the condition above:For (0, 2)
We have that x=0, and y=2. Thus,
[tex]\begin{gathered} x+1=1 \\ \frac{x}{4}=0 \\ \text{And as }2>0,\text{ (0, 2) is NOT a solution of the system.} \end{gathered}[/tex]For (-3, 8)
In this case, x=-3 and y=8.
[tex]\begin{gathered} x+1=-2 \\ \frac{x}{4}=-\frac{3}{4} \\ \text{As }8>-\frac{3}{4},\text{ this means that (-3, 8) is NOT a solution of the system.} \end{gathered}[/tex]For (2,5)
In this case, x=2 and y=5.
[tex]\begin{gathered} x+1=3 \\ \frac{x}{4}=\frac{2}{4}=\frac{1}{2} \\ \text{As }5>\frac{1}{2}\text{ this means that (2, 5) is NOT a solution of the system.} \end{gathered}[/tex]For (-7, -4)
In this case, x=-7 and y=-4.
[tex]\begin{gathered} x+1=-6 \\ \frac{x}{4}=-\frac{7}{4} \\ \text{As }-6<-4\le-\frac{7}{4},\text{ (-7, -4) is a SOLUTION of the system.} \end{gathered}[/tex]For (6, -1)
We have that x=6 and y=-1.
[tex]\begin{gathered} x+1=7 \\ \frac{x}{4}=\frac{6}{4}=\frac{3}{2} \\ \text{As }7>-1,\text{ (6, -1) is NOT a solution of the system. } \end{gathered}[/tex]Thus, the ordered pair which is a solution of the system is (-7, -4).Find the surface area of the triangular prism. 13 in. 5 in. 4 in. 12 in.
Answers
The first face is a triangle with height 5in and base 12in
Traingular face area = 1/2 x bh
=1/2 x 12 x 5
= 30 in^2
The area of the other triangular base = 30 in^2
Area of left side face = Length x breadth
= 5 x 4 = 20in^2
Area of the slant face = Length x breadth
= 13 x 4 = 52in^2
Area of the bottom face = Length x breadth
= 12 x 4 = 48in^2
Total surface area = 30 in^2 + 30 in^2 + 20in^2 + 52in^2 + 48in^2
=180in^2
Consider the line y= 3/5x-3Find the equation of the line that is parallel to this line and passes through the point (3, 4).Find the equation of the line that is perpendicular to this line and passes through the point (3, 4).
Answers
a) y = 3/5x + 11/5
b) y = -5/3x + 9
Explanation:[tex]\begin{gathered} a)\text{ }y\text{ = }\frac{3}{5}x\text{ - 3} \\ \text{compare with equation of line:} \\ y\text{ = mx + b} \\ m\text{ =slope, b = y-intercept} \\ m\text{ =slope = 3/5} \\ b\text{ = -3} \end{gathered}[/tex]For a line to be parallel to another line. the slope of the 1st line will be equalt to the slope of the 2nd line:
slope of 1st line = 3/5
So, the slope of the 2nd line = 3/5
Given point: (3, 4) = (x, y)
To get the y-intercept of the second line, we would insert the slope and the point into the equation of line
[tex]\begin{gathered} y\text{ = mx + b} \\ 4\text{ = }\frac{3}{5}(3)\text{ + b} \\ 4\text{ = 9/5 + b} \\ 4\text{ - }\frac{\text{9}}{5}\text{ = b} \\ \frac{20-9}{5}\text{ = b} \\ b\text{ = 11/5} \end{gathered}[/tex]The equation of line parallel to y = 3/5x - 3:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = }\frac{3}{5}x\text{ + }\frac{11}{5} \end{gathered}[/tex][tex]b)\text{ line perpendicular to y = 3/5x - 3}[/tex]For a line to be perpendicular to another line, the slope of one will be the negative reciprocal of the second line
Slope of the 1st line = 3/5
reciprocal of 3/5 = 5/3
negative reciprocal = -5/3
slope of the 2nd line (perpendicular) = -5/3
We need to get the y-intercept of the perpendicular line:
[tex]\begin{gathered} \text{given point: (3,4) = (x, y)} \\ y\text{ = mx + b} \\ m\text{ of the perpendicular = -5/3} \\ 4\text{ = }\frac{-5}{3}(3)\text{ + b} \\ 4\text{ = -5 + b} \\ 4\text{ + 5 = b} \\ b\text{ = 9} \end{gathered}[/tex]The equation of line perpendicular to y = 3/5x - 3:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = }\frac{-5}{3}x\text{ + 9} \end{gathered}[/tex]Solve for z. 24z - 48 = 16z + 112
Answers
Answer: z = 20
Explanation:
The given equation is
24z - 48 = 16z + 112
Subtracting 16z from both sides of the equation, we have
24z - 16z - 48 = 16z - 16z + 112
8z - 48 = 112
Adding 48 to both sides, we have
8z - 48 + 48 = 112 + 48
8z = 160
Dividing both sides by 8,
8z/8 = 160/8
z = 20
