Find the equation for the line that passes through the point (-4,1), and that is perpendicular to the line with the equation
Answers
EXPLANATION
Given:
Point ( - 4, 1)
⇒x = -4 and y = 1
Perpendicular equation
3/4 x + y = -5/4
We need to re-write the above equation in the form y = mx + b
y = -3/4 x -5/4
Compare the above with y=mx + b where m is the slope and b is the intercept.
slope(m) = -3/4
Slope of vertical lines are inverse of one another.
This implies that the slpe of our new equation is:
[tex]m=\frac{-1}{m}=\frac{-1}{-\frac{3}{4}}=\frac{4}{3}[/tex]Next, is to find the intercept of the new equation.
We can find this by substituting m = 4/3 , x = -4 and y = 1 into y=mx + b and then solve for b.
That is;
[tex]\begin{gathered} 1=\frac{4}{3}(-4)+b \\ \\ 1=-\frac{16}{3}+b \\ \\ 1+\frac{16}{3}=b \\ \\ b=\frac{3+16}{3} \\ \\ b=\frac{19}{3} \end{gathered}[/tex]We can proceed to form the new equation by simply substituting the values of m and b into y=mx + b
Hence, the equation is:
[tex]y=\frac{4}{3}x+\frac{19}{3}[/tex]Related Questions
For the following figure, complete the statement for the specified points.RPoints R, S, and Tareneither collinear nor coplanarboth collinear and coplanarcollinearcoplanar
Answers
First we need to define what collinear and coplaner means.
It is said that 3 or more points are collinear if they all lie on the same line.
From the diagram, point R, S, T do not lie on the same line.
Hence point R, S and T are not collinear
For a point or line to be coplaner, it must line in the same plane
Also looking at the diagram, points R, S, T do not lie in the same plane.
Hence
Heather dropped a water balloon over the side of her school a height of 80 feet. The approximate height of the balloon at any point during it's fall can be represented by the following quadratic equation: h=-16t^2+80. About how long did it take for the balloon to hit the ground.A.1.73B.2.24C.2.45D.2.83
Answers
h = - 16t^ 2 + 80
[tex]h=-16t^2\text{ + 80}[/tex]The balloon will hit the ground when the height = 0
[tex]\begin{gathered} 0=-16t^2\text{ + 80} \\ \text{collect like terms} \\ \\ 16t^2\text{ = 80} \\ \text{Divide both sides by 16} \\ t^2\text{ = }\frac{80}{16} \\ t^2\text{ = 5} \\ t\text{ =}\sqrt[]{5} \\ t\text{ = 2.236} \\ t\text{ = 2.24} \end{gathered}[/tex]The correct option is B = 2.24
Simplify: 2x^2 + 19x + 35/2x^2 +11x +15 a) 7/3b) 19x + 35/11x + 15c) 2x + 7/2x + 3d) x + 7/x + 3
Answers
SOLUTION
We want to simplify
[tex]\frac{2x^2+19x+35}{2x^2+11x+15\text{ }}[/tex]Factorising the numerator and denominator, we have
[tex]\begin{gathered} \frac{2x^2+19x+35}{2x^2+11x+15\text{ }} \\ \frac{2x^2+14x+5x+35}{2x^2+6x+5x+15\text{ }} \\ \frac{2x(x+7)+5(x+7)}{2x(x+3)+5(x+3)} \\ \frac{(2x+5)(x+7)}{(2x+5)(x+3)} \end{gathered}[/tex]Canceling out the common factor which is
[tex]2x+5[/tex]We have our answer as
[tex]\frac{x+7}{x+3}[/tex]Hence the answer is option D
The rectangular rug has side lengths of 3 and 4 ft. What is the length of the diagonal? Draw a picture of the problem and solve. Round to the nearest tenth
Answers
ANSWER
The length of the diagonal is 5 ft
EXPLANATION
The diagram of the rug with the diagonal is:
The diagonal and the sides form a right triangle, so we can use the Pythagorean theorem to find x, the length of the diagonal:
[tex]\begin{gathered} x^2=3^2+4^2 \\ x=\sqrt[]{9+16} \\ x=\sqrt[]{25} \\ x=5 \end{gathered}[/tex]If you randomly select a letter from the phrase "Ichiro Suzuki is at the top of the lineup," what is theprobability that you select a consonant? (Your answer must be in the form of a reduced fraction.)Submit Question
Answers
Given the phrase "Ichiro Suzuki is at the top of the lineup", you can identify that:
- The total number of letters the phrase has is:
[tex]Total=33[/tex]- The number of consonants the phrase has is:
[tex]Consonants=18[/tex]Therefore, you can find the probability that you select a consonant by dividing the number of consonants in the phrase by the total number of letters:
[tex]P=\frac{18}{33}[/tex]You can reduce the fraction by dividing the numerator and the denominator by 3:
[tex]\begin{gathered} P=\frac{18\div3}{33\div3} \\ \\ P=\frac{6}{11} \end{gathered}[/tex]Hence, the answer is:
[tex]P=\frac{6}{11}[/tex]consider the equation -4x+3y=7. Assume that y is a function of x. rewrite the equation using function notation F(x)
Answers
y=(7+4x)/3
y=F(x)
Answer: F(x)=(7+4x)/3
What is the greatest common factor of the polynomial: 35y + 5y + 157 "
Answers
The greatest common factor of the expression is:
[tex]5y^3[/tex]This comes from the fact that 5 is the greatest common factor of the constants, whereas y^3 is the greatest common factor of the variable.
Which of the following is equivalent to 10^4 x 10^3? A 10^7 B 20^12 C 20^7 D 10^12
Answers
Explanation
Let's remember some properties for the exponents
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ \frac{a^m}{a^n}=a^{m-n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]hence
let's calculate the product
[tex]\begin{gathered} 10^4\cdot10^3 \\ 10^4\cdot10^3=10^{4+3}=10^7 \\ 10^4\cdot10^3=10^7 \end{gathered}[/tex]therefore, the answer is
[tex]A)10^7[/tex]I hope this helps you
Find and simplify the difference quotient for the following function
Answers
Therefore:
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4x^2-8xh-h^2+7x+7h+4-(-4x^2+7x+4)}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{7h-8xh-h^2}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{h(7-8x-h)}{h} \\ \frac{f(x+h)-f(x)}{h}=7-8x-h \end{gathered}[/tex]Solve 2(x-6)+7x = 5-3(x-2)
Answers
To solve x, let's eliminate the parenthesis first by multiplying 2 and -3 to it.
[tex]2x-12+7x=5-3x+6[/tex]Next, let's combine all like terms on either side. We will move -3x to the left side of the equation and -12 to the right side of the equation. Note that when a term crosses the equal symbol, the sign reverses. From -3x to +3x and from -12 to +12.
[tex]2x+7x+3x=5+6+12[/tex]Next, add the terms on both sides.
[tex]12x=23[/tex]Lastly, divide both sides by 12 to isolate x.
[tex]\begin{gathered} \frac{12x}{12}=\frac{23}{12} \\ x=\frac{23}{12} \end{gathered}[/tex]The value of x is 23/12.
Let's check if this is right by substituting the value of x to the equation.
[tex]\begin{gathered} 2(\frac{23}{12}-6)+7(\frac{23}{12})=5-3(\frac{23}{12}-2) \\ 2(-\frac{49}{12})+\frac{161}{12}=5-3(-\frac{1}{12}) \\ -\frac{98}{12}+\frac{161}{12}=5+\frac{3}{12} \\ \frac{63}{12}=\frac{63}{12} \\ \frac{21}{4}=\frac{21}{4} \end{gathered}[/tex]Since we got the same 21/4 on both sides of the equation, our x value 23/12 is correct.
34. A school admissions office accepts 2 out of every 7 applicants. Given that the school accepted 630 students, how many applicants were NOT accepted? F. 140 180 490 J. 1,260 K. 1,575
Answers
We were told that the school admissions office accepts 2 out of every 7 applicants. Thus, the probability that the school accepts an applicant is 2/7
There are only two outcomes. It is either the school accepts an applicant or it doesn't. If the school accepts 630 students, It means that 2/7 of the total number of applicants were accepted
Assuming the totla number of applicants is x, it means that
2/7 * x = 630
2x = 630 * 7 = 4410
x = 4410/2
x = 2205
The total number of applicants is 2205
The number of applicants that were not accepted is
2205 - 630 = 1575
1575 applicants were not accepted
What expression represents the sum of ages of Hugo and his two siblings?
Answers
The correct option is D
The sum of their ages is 3x + 8
Explanation:Given that Hugo's age = x
Jasmine's age = x + 3
Manny's age = (x + 3) + 2 = x + 5
The sum of their ages is:
x + (x + 3) + (x + 5)
= x + x + x + 3 + 5
= 3x + 8
The boxplot below shows salaries for Construction workers and Teachers.
Answers
First, let's identify each element in a box plot:
Looking at the first box plot (Construction, Jennie), the first quartile is 30, and looking at the second box plot (Teacher, Markos), the first quartile is 25.
Since the first quartile represents the salary, that means Jennie makes more money, and the amount she does more is $5000.
(The graph shows the money in thousands)
x-5=11;x=5Determine if the value of x is a solution to the equation
Answers
Given data:
The given expression is x-5=11.
Substitute 5 for x in the above expression.
5-5=11
0=11
As LHS is not equal to RHS so x=5 is not the solution of the given exprression.
Thus, x=5 is not the solution.
Solve the equation. |k + 6| = 3
Question 7 options:
{–3, 9}
{–3, 3}
{–9, –3}
{all real numbers greater than or equal to –9 and less than or equal to –3}
Answers
Step-by-step explanation:
k= {-3,-9}
Because || always gets positive numbers.
For example |-5|=5, and |5|=5.
so |-9+6|=|-3| which is |-3|=3
and |-3+6|=|3| which is equal to 3.
Answer:
c) k = {-9,-3}
Step-by-step explanation:
Given equation,
→ |k + 6| = 3
Now the value of k will be,
→ |k + 6| = 3
→ k + 6 = 3 || → -(k + 6) = 3
→ k = 3 - 6 || → -k = 3 + 6
→ [ k = -3 ] || → [ k = -9 ]
Hence, value of k is -3 & -9.
Use the distributive property of multiplication to find 6x14.
Answers
Answer
6 × 14
= 6 × (7 + 7)
= (6 × 7) + (6 × 7)
= 42 + 42
= 84
Explanation
Distributive property is used to open brackets. For example, the expression
a (b + c) can be solved using the distributive property to multiply into the bracket.
a (b + c) = ab + ac
So,
6 × 14
= 6 × (7 + 7)
= (6 × 7) + (6 × 7)
= 42 + 42
= 84
Hope this Helps!!!
12.The graph of y=x + 3 is a vertical translation ofthe graph of y = x + 1, 2 units upward. Examine the intercepts of both linesand state another way that the geometric relationship between the two graphscan be described.
Answers
The graph of y=x + 3 is a vertical translation of
the graph of y = x + 1, 2 units upward. Examine the intercepts of both lines
and state another way that the geometric relationship between the two graphs
can be described.
we have
step 1
y=x+3
Find the x-intercepts
Value of x when the value of y is equal to zero
For y=0
0=x+3
solve for x
x=-3
step 2
y=x+1
Find the x-intercepts
Value of x when the value of y is equal to zero
For y=0
0=x+1
x=-1
step 3
The graph of y=x+3 is a horizontal translation 2 units at left of the graph of y=x+1
The rule is
(x,y) -------> (x-2,y)
Each ticket to a matinee movie costs $8. Part A: Complete this table relating the number of movie tickets bought, m, to the total cost, c, of the tickets. m C 4 6 9 Part B: Write an equation that models this situation, using the variables m and c. Answer: Brandy thinks the number of movie tickets bought depends on the total cost of the movie tickets. Brandy's brother thinks the total cost of the movie tickets depends on the number of movie tickets bought Part C: Whose thinking is correct, Brandy's, her brother's, or both? Explain how you know.
Answers
Part A
Since each ticket costs $8, we need to add $8 for each plus ticket one buys:
[tex]\begin{gathered} 1\text{ ticket: \$}8 \\ 2\text{ tickets: \$}8+\text{ \$}8=\text{ \$}16 \\ 3\text{ tickets: \$}16+\text{ \$}8=\text{ \$}24 \\ 4\text{ tickets: \$}24+\text{ \$}8=\text{ \$}32 \\ 6\text{ tickets: \$}32+\text{ \$}16=\text{ \$}48 \\ 9\text{ tickets: \$}48+\text{ \$}24=\text{ \$}72 \end{gathered}[/tex]Therefore, we have:
Part B
Notice that, instead of summing (8+8+8+...) we can multiply $8 by the number of tickets bought m to obtain the total cost c.
Thus, we have:
[tex]c=m\times\text{ \$}8[/tex]Part C
The equation above (c = m x $8) shows that the total cost c depends on the number of tickets bought.
However, we write that relation in another way:
[tex]m=c\div\text{ \$}8[/tex]Thus, if we know the total cost, we can divide it by $8 to find the number of tickets bought. Then, we can say that the number of tickets boght m depends on the total cost c.
Therefore, both thoughts are correct.
Please be clear with the answer thank you bye-bye bye-bye
Answers
Solve the system of equations:
3x + 3y = 3
5x + y = 13
Solving the second equation for y:
y = 13 - 5x
Substituting in the first equation:
3x + 3(13 - 5x) = 3
Opeating:
3x + 39 - 15x = 3
Simplifying:
-12x + 39 = 3
Subtracting 39:
-12x = -36
Dividing by -12:
x = -36 / (-12)
x =3
Substituting in the equation for y:
y = 13 - 5(3)
y = -2
Answer: x = 3, y = -2
Answer: x = 3, y = -2
Step-by-step explanation:
Using the graph, determine the coordinates of the x-intercepts of the parabola.10984-10-98-7 -6-5-427 8 9103 410-8-10
Answers
The x-intercepts are the points where the parabola crosses the x-axis,
Also, the y coordinate is always zero,
By looking at the graph we can see that the parabola crosses the x-axis at x = 4 and x= 6
X-intercepts = (4,0) and (6,0)
31/32 - > Identify the ordered pairs in the graph. Then identify the domain and range. Is this a function? 7) 8) Domain: Domain: Range: that Range: Function? Function? O Type here to search gi 3
Answers
7)
The ordered pairs are:
(-4, -2), (-2, 1), (0, -1), (-3, 0), and (-3,2)
Domain = {-4, -3, -2, 0}
Range = {-2, -1, 0, 1, 2}
A function must map every element of the domain to a unique number in the range
But here -3 is mapped to 0 and 2.
Hence it is not a function
8)
The ordered pairs are:
(-2, 3), (-1,-1), (0,-1), (1,-3), (3, 1)
Domain = {-2, -1, 0, 1, 3}
Range = {-3, -1, 1, 3}
In this case, every element of the domain is mapped to a unique
ut -The ordered pairs are:
The perpendicular bisectors of triangle ABC intersect at point G and are shown in blue. Find BG
Answers
Answer:
9
Explanation:
A perpendicular bisector of a triangle is a line that is perpendicular to the side and passes through the midpoint of the triangle.
So when three perpendicular bisectors of the sides of a triangle meet at a point in a triangle, that point is called a circumcenter.
From the circumcenter theorem, we know that the circumcenter is equidistant from the vertices of a triangle, that is, the circumcenter is the same distance from each of the vertices of the triangle.
Looking at the given triangle, we can see that G is the circumcenter of the triangle because all the perpendicular bisectors DG, EG, and FG meet at this point.
We can see that AG is 9 which is the distance from vertex A to the circumcenter, G, since the circumcenter is equidistant from the vertices of a triangle according to the circumcenter theorem, therefore, BG will also be 9.
Venus' orbital speed is approximately 210 kilometers in 6 seconds. Earth's orbital speed is approximately 270 kilometers in 9 seconds. Which planet travels at a faster speed per second?
Answers
We know that
• Venus' orbital speed is 210 kilometers in 6 seconds.
,• Earth's orbital speed is 270 kilometers in 9 seconds.
First, we have to divide the numbers to find the ratio
[tex]\begin{gathered} \frac{210}{6}=35 \\ \frac{270}{9}=30 \end{gathered}[/tex]As you can observe, Venus has greater speed because it's 35 kilometers per second.
Hence, the answer is Venus.Based on the end behavior, what is the graph of function R?
Answers
As given by the question
There are given that the function
[tex]f(x)=-x^3+3x^2+x-3[/tex]Now,
The graph of the given function is shown below:
Hence, the correct option is C.
Answer:
C
Step-by-step explanation:
Trust
What is the volume of the cone when the radius is 10 and the height is 18
Answers
The volume of the cone is given by the formula:
Analyze the diagram below and complete the instructions that follow./Find the value of x.A.4B.5C.6D.9Please select the best answer from the choices providedABCD
Answers
ANSWER
EXPLANATION;
Apply Pythagora's rule to find the value of x
[tex]\begin{gathered} \text{ Pythagora's rule} \\ \text{ Hypotenuse}^2\text{ = opposite}^2\text{ + adjacent}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{ Hypotenuse = }\sqrt{117} \\ \text{ Opposite = x} \\ \text{ Adjacent = \lparen x + 3\rparen} \end{gathered}[/tex][tex][/tex]Jeremy is given the choice between two chocoletes,chocolates, and Y. Which..........
Answers
To determine which option is correct, we first need to find the volume of both chocolate.
The volume of X:
The shape is a square-based pyramid. The volume is given by
[tex]\begin{gathered} V_x=\frac{1}{3}\times base\text{ area }\times height \\ V_x=\frac{1}{3}\times l\times b\times h \end{gathered}[/tex]From the diagram,
l = 5 cm
b = 6 cm
h = 10 cm
Substituting,
[tex]\begin{gathered} V_x=\frac{1}{3}\times5\times6\times10 \\ V_x=100\operatorname{cm}^3 \end{gathered}[/tex]The volume of Y:
The shape is a triangular-based pyramid. The volume is given by
[tex]\begin{gathered} V_y=\frac{1}{3}\times base\text{ area }\times height \\ V_y=\frac{1}{3}\times\frac{1}{2}\times b\times l\times h \end{gathered}[/tex]From the diagram,
l = 8 cm
b = 7.5 cm
h = 10 cm
[tex]\begin{gathered} V_y=\frac{1}{3}\times\frac{1}{2}\times7.5\times8\times10 \\ V_y=100\operatorname{cm}^3 \end{gathered}[/tex]From here, the volumes of both chocolates are the same.
Therefore, the chocolate he picks does not matter as both volumes are equivalent.
The SECOND OPTION is correct.
O 9,976 15) An air-conditioning fan makes 125 revolutions per second. How many revolutions will it make if it runs for 30 minutes?
Answers
An air-conditioning fan makes 125 revolutions per second. How many revolutions will it make if it runs for 30 minutes?
we know that
1 min=60 sec
we have
125 rev/sec
so
1 sec=1/60 min
substitute
125 rev/sec=125/ (1/60)=7,500 rev/min
Multiply by 30 min
7,500*30=225,000 rev
therefore
the answer is225,000 revolutionsA nurse measured The blood pressure of each person who visit a hair clinic and created a relative frequency histogram for the systolic blood pressure readings approximately what percentage of the people had a systolic blood pressure Reading between 110 and 139 inclusive
Answers
Given a relative frequency histogram for the systolic blood pressure readings.
We will find the percentage of the people who had a systolic blood pressure reading between 110 and 139
As shown:
The percentage of people who had a systolic blood pressure reading between 110 and 119 = 0.35
The percentage of people who had a systolic blood pressure reading between 120 and 129 = 0.25
The percentage of people who had a systolic blood pressure reading between 130 and 139 = 0.15
So, the answer will be = 0.35 + 0.25 + 0.15 = 0.75
So, the answer will be option 3) 75%
6. You deposit $1000 a year into an account. This account earns 8% interest compounded yearly,(20 points)a) how much will you have after 10 years?b) How much total money did you put in the account.c) How much total interest did you earn?
Answers
Compound interest formuae :
A = P ( 1+r/100)^ n or A = P( 1+i)^n or A = P ((1 + i )^n -1 )/i
we will use the highlighted formular due to compounded yearly statement on the question:
where A = Accumulated amount;
P = original amount invested/ (borrowed )
n = number of years
r = interest rate as a percentage
i = r/100
Answer to (a )
A = P ((1 + i )^n -1 )/i
where n = 10; i = 8/100 =0.08 ; P = 1000
A = 1000 ( 1 + (8/100))^10 -1)/ 0. 08
A =1000 ( 14.48)
A =$14486.56
b. 1000 X 10 = $12000
c. you earned interest of $14486 - $12000 = $2486