For this question we know that we have a point (-3,-2) and we want to find an equation perpendicular to the line
y=2/3x-2.
Since both lines are perpendicular we need to satisfy this:
[tex]m_1\cdot m_2=-1[/tex]With m1= 2/3. If we solve for m2 we got:
[tex]m_2=\frac{-1}{m_1}=\frac{-1}{\frac{2}{3}}=-\frac{3}{2}[/tex]And then we can find the intercept for the new line using the point given with x=-3 and y=-2 and we got this:
[tex]-2=-\frac{3}{2}(-3)+b[/tex]And solving for b we got:
[tex]b=-\frac{9}{2}-2=-\frac{13}{2}[/tex]And then our final answer would be:
[tex]y=-\frac{3}{2}x-\frac{13}{2}[/tex]The illustration below shows the graph of y as a function of x.complete the following sentences based on the graph of the function.* initially, as x increases, y (increases, decreases or stays constant).* the slope of the graph is equal to ___ for all x between x = 0 and x = 3.* starting at x = 3, the function value y (increases, decreases, or stays constant) as x increases.* the slope of the graph is equal to ___ for x between x = 3 and x = 5.* for x between x = 0 and x = 4, the function value y (≤, ≥, or =) 0.* for x between x = 4 and x = 8, the function value y (≤, ≥, or =) 0.
We will have the following:
*Initially, as x increases, y decreases.
*The slope of the graph is equal to -1 for all x between x = 0 & x = 3.
*Starting at x = 3, the function value y increases as x increases.
*The slope of the graph is equal to 3 for x between x = 3 & x = 5.
*For x between x = 0 & x = 4, the function value y ≤ 0.
*For x between x = 4 & x = 8, the function value y ≥ 0.
The volume of the right cone below is 36π units ^3. Find the value of x
The formula to find the volume of a cone is:
[tex]\begin{gathered} V=\frac{1}{3}\pi r{}{}^2h \\ \text{ Where} \\ V\text{ is the volume} \\ r\text{ is the radius} \\ h\text{ is the heigth} \end{gathered}[/tex]Then, we replace the know values in the above formula and solve for h.
[tex]\begin{gathered} V=36\pi \\ r=\frac{\text{ diameter}}{2}=\frac{6}{2}=3 \\ h=x \end{gathered}[/tex][tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ 36\pi=\frac{1}{3}\pi(3)^2x \\ 36\pi=\frac{9\pi x}{3} \\ 36\pi=3\pi x \\ \text{ Divide by }3\pi\text{ from both sides} \\ \frac{36\pi}{3\pi}=\frac{3\pi x}{3\pi} \\ 12=x \end{gathered}[/tex]AnswerThe value of x is 12 units.
Choose the equation below that represents the line passing through the point (2, -4) with a slope of(1 point)Oy=kx-3Oy -x+5Oy-1x+3Oy=1x-5
The equation of a line in slope-intercept form can be written like this:
y = mx + b
Where m is the slope and b is the y-intercept of the line.
In this case, the slope of the line is 1/2, then we can rewrite the above equation like this:
y = (1/2)x + b
We are also told that this line passes through (2, -4), by replacing 2 for x and -4 for y into the above equation, we can solve for the value of b, like this:
-4 = 2(1/2) + b
-4 = 1 + b
-4 - 1 = 1 - 1 + b
-5 = b
b = -5
Then, we can rewrite the equation of the line, like this:
y = (1/2)x - 5
Then, the last option is the correct answer
please help this is for my study guide thanks! (find volume) (don't round)
100,000π ft³
1) Let's find the volume of that Cylinder using this formula:
[tex]V=\pi r^2h[/tex]Note that the volume is the area of the base (a circle) times the height
2) Also, notice that in the picture we have the diameter, the radius is half the Diameter:
[tex]\begin{gathered} V=\pi\cdot(50)^2\cdot40 \\ V=100000\pi^{} \end{gathered}[/tex]3) So the volume is 100,000π ft³
the number of regular telephones in use is how many times the number of cellular phones? 45% regular phones15% cellular phones6% others34% Cordless phones
Solution
For this case we have the following info:
45% regular phones
15% cellular phones
6% others
34% Cordless phones
We know that the total regular of phones is 45% and the total of cellular phones are 15% then we can find the ratio like this:
45/15 = 3
The graph of y = 2x2 - 4x + 2 opens downward.true or false
The equation for the graph is :
[tex]y=2x^2-4x+2[/tex]You can graph the equation on a graph tool and view the graph as below:
From the graph, you can see that it opens upwards, so the statement is False.
Correct answer is that the graph opens upwards.
Answer choice : False
Can you please help me out with a question
S = 2(a*b + a*c + b*c)
= 2 (12*15 + 12*6 + 15*6)
= 2 (342)
= 684 ft^2
A landscape supply business charges $35 to deliver mulch. The cost of the mulch is
$29 per cubic yard. Write a linear equation to find the cost of having x cubic yards of
mulch delivered to a site.
The linear function to represent the number of mulch delivered to a site is y = 29x + 35
What is a linear function?In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
For this question, we can represent the cost of having x cubic yards of mulch delivered to a site. For a standard linear function, it can be represented as y = mx + c
m = slope
c = intercept
We can use this concept to write a linear function to represent this problem:
y = mx + c
y = 29x + 35
In this case, the slope is 29 and the intercept is 35. The slope in this situation is the cost of the mulch and the amount charged by the business is the intercept.
The equation representing this problem is y = 29x + 35
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consider the function f(x) whose second derivative is f' '(x)=4x+4sin(x). If f(0)=3 and f'(0)=4, what is f(5)?
Problem: consider the function f(x) whose second derivative is f' '(x)=4x+4sin(x). If f(0)=3 and f'(0)=4, what is f(5)?.
Solution:
Let the function f(x) whose second derivative is:
[tex]f^{\prime\prime}(x)\text{ = 4x+4sin(x)}[/tex]Now, the antiderivative (integral) of the above function would be:
EQUATION 1:
[tex]f^{\prime}(x)=\int f^{\prime\prime}(x)\text{ }dx\text{= }2x^2-4\cos (x)\text{ +C1}[/tex]where C1 is a constant because we have an indefinite integral. Now the antiderivative (integral) of the above function f´(x) is:
[tex]f(x)=\int f^{\prime}(x)\text{ }dx\text{=}\int \text{ (}2x^2-4\cos (x)\text{ +C1)}dx\text{ }[/tex]that is:
EQUATION 2:
[tex]f(x)=\text{ }\frac{2x^3}{3}-4\sin (x)+C1x+\text{ C2}[/tex]where C2 is a constant because we have an indefinite integral.
Now using the previous equation, if f(0)= 3 then:
[tex]3=\text{ C2}[/tex]Now, using equation 1 and the fact that f ´(0) = 4, then we have:
[tex]4=f^{\prime}(0)\text{= }^{}-4\text{ +C1}[/tex]That is:
[tex]4=\text{ }^{}-4\text{ +C1}[/tex]Solve for C1:
[tex]8=\text{ }^{}\text{C1}[/tex]Now, replacing the constants C1 and C2 in equation 2, we have an expression for f(x):
[tex]f(x)=\text{ }\frac{2x^3}{3}-4\sin (x)+8x+3[/tex]Then f(5) would be:
[tex]f(5)=\text{ }\frac{2(5)^3}{3}-4\sin (5)+40+3=\text{ }125.98[/tex]
then the correct answer is:
[tex]f(5)=\text{ }125.98[/tex]the table shows the number of incorrect answers given by nine students on a standardized test which of the following measures would make the number of missed questions appear as a small as possible
Let's take them one after the other
To calculate the mean:
Mean = 4 +20+ 5 +10+ 21+ 18 +10+ 11+ 16 / 9
Mean= 115/9= 12.7
To calculate the median;
Median: position (n+1)/2=(9+1)/2=5
This implies it is the fiifth value after ordering them from least to gratest
4, 5, 10, 10, 11, 16, 18, 20, 21
The fifth observation is 11, that's the median
Calculate the range;
Range = highest - lowest = 21 - 4 = 17
Mode = bi modal = 10
The answer is the Mode which is 10
The correct option is the last option : Mode
Endpoint 19,-10) Midpoint (4,8).What is the other endpoint
Let the first end point be x1 y1 and the second x2 y2 the midpoint would be
x1 + x2 / 2 y1 + y2 / 2
Hence
(19 + x2)/2 = 4
19 + x2 = 8
x2 = 8 -19
x2 = -11
(-10 + y2)/2 =8
- 10 + y2 = 8
y2 = 8 + 10
= 18
The other end point is (-11, 18)
What’s the last number in row 8 for the new number triangle I made
We have the sequence, shown as a number triangle, where in each step we add 5 (that is the constant difference).
We can write:
1
6 11
16 21 26
31 36 41 46
51 56 61 66 71
76 81 86 91 96 101
106 111 116 121 126 131 136
141 146 151 156 161 166 171 176
Answer: The last number in row 8 is 176.
Answer:
thr last number in row eight is 176
find the area of the semicircle round to the nearest tenth use 3.14 for pi do not include units with your answer 12 in
226.08
1) Since the area of the semicircle is half the circle area, then we can write:
[tex]S=\frac{1}{2}\cdot\pi\cdot r^2[/tex]2) So we can plug into that the size of that radius:
[tex]\begin{gathered} S=\frac{1}{2}\cdot\pi\cdot(12)^2 \\ S=\frac{1}{2}\cdot\pi\cdot144 \\ S=72\pi\Rightarrow S=72\times3.14\Rightarrow S=226.08 \end{gathered}[/tex]3) Hence, the area of that semicircle is 226.08 in²
Based on what you've read, decide which of the four basic operations you need to use. Then, solve the problems.
On a trip to Florida, Santina drove 203 miles and Carole drove 189 miles. How many more miles did Santina drive than Carole?
The basic operation use for the problem is subtraction.
The number of miles Santina drove than Carole is 14 miles.
How to solve problems with basic operations?Basic operations are the building blocks and rules of math.
The basic operations are addition, subtraction, multiplication, and division.
On a trip to Florida. Santina drove 203 miles and Carole drove 189 miles.
The distance in miles Santina drive than Carole is the difference between there distance travelled.
Therefore, the basic operation applied in this problem is subtraction.
Hence, let's solve it as follows:
miles Santina drove than Carole = 203 - 189 = 14 miles
Therefore, Santina drove 14 more miles.
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The basic operation used for the problem will be; subtraction. Santina drove 14 more miles than Carole.
How to solve problems with basic operations?Basic operations are the building blocks and rules of math. The basic operations are addition, subtraction, multiplication, and division.
On a trip to Florida. it is given that Santina drove 203 miles and Carole drove 189 miles.
The distance Santina drives is miles than Carole, which is the difference between their distance traveled.
Thus, the basic operation applied in this problem will be; subtraction.
Hence, let's simplify it as follows:
The miles, Santina drove = 203 - 189 = 14 miles
Therefore, Santina drove 14 more miles than Carole.
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Sales tax in South Carolina is 5%. Mr. Smith bought a new car there for $18,700. What did he pay in sales tax?
Answer: $935
Step-by-step explanation:
Mr. Smith paid $935 in sales tax
d1 = 16 m; d2 = 14 m what's the rhombus?
Step 1 : To determine the area of the rhombus
[tex]\begin{gathered} d_1=16m,d_2\text{ = 14m } \\ Area\text{ = }\frac{1}{2}\text{ }\times d_1\text{ }\times d_2 \\ Area\text{ = }\frac{1}{2}\text{ }\times\text{ 16 }\times\text{ 14} \\ Area\text{ = }\frac{224}{2} \\ Area=112m^2 \end{gathered}[/tex]Therefore the area of the rhombus = 112m²
The solution process is shown for any equation. Justify each step in the process with the appropriate property. Select the correct answer from each drop down menu.
Answer:
Explanation:
Here, we want to get the values in the segments
a) Here we would have to open up the brackets
Now, to do this, we are going to use the distributive property
By using the distributive property, we will be able to open up the brackets
Doing this, we can get the values in the brackets
So the answer here is distributive property
b) Here, we have
14 = -y after combining the like terms
The correct answer here is the subtraction property of equality
We simply subtract 3y from both sides of the equation to arrive at this answer
c) -14 = y
We have the multiplication property of equality
The reason for this is that we multiplied both sides by -1 to arrive at this answer
d) y = -14
This is the symmetric property of equality
We have this here because if two values are equal on both sides, we can switch each to the opposite sides and still retain the same equality values
Please help me with this sample question.Find f(0)Find f(1)Find f(2)
In order to find the values of f(0), f(1) and f(2), we just need to find in the graph for the value of the function (that is, the value of y) for the values of x equal to 0, 1 and 2 respectively.
Looking at the graph, for x = 0 we have y = -7, therefore f(0) = -7
For x = 1 we have y = -2, therefore f(1) = -2
For x = 2 we have y = -5, therefore f(2) = -5
Add the complex numbers 3 + 11i and -3 - 11i.6 + 0i0 + 0i0 + 22i- 9 + 121i
SOLUTION
The given complex unbers are:
[tex]3+11i,-3-11i[/tex]Add the complex numbers:
[tex]3+11i+(-3-11i)[/tex]Simplify the expression:
[tex]\begin{gathered} 3+11i-3-11i \\ =3-3+11i-11i \\ =0+0i \end{gathered}[/tex]Therefore the required answer is: 0+0i
2. Graph the following inequality on the axes provided below: 6x + 2y = 8 -10 8 6 4 2 -101-8-6 1-4-2 -2 2 4_LG_L 8 10 -4 -6 -8 -10 True or False: (1,1) is a solution to the inequality. Explain using evidence from your graph.
We are given the following inequality
[tex]6x+2y<8[/tex]Let us first convert the inequality into slope-intercept form
[tex]\begin{gathered} 6x+2y<8 \\ 2y<-6x+8 \\ y<-\frac{6x}{2}+\frac{8}{2} \\ y<-3x+4 \end{gathered}[/tex]Comparing this inequality with the standard slope-intercept form we see that
Slope = -3 and y-intercept = 4
So the graph of the inequality is
The area left to the red line represents the solution of the inequality.
Now we need to check if the point (1, 1) lies left to the red line.
We can clearly see that point (1, 1) is just left to the red line hence it is a solution.
Therefore, it is true.
Mr.Gonzalez spent $50 more than Mr.Silva on school supplies. together, they spent $174. How much money did each of them spent?
Answer: You need to spend more than $5.00
Step-by-step explanation:
Question Evaluate. 7⋅5+42−23÷4 Responses 49 49 41 41 34 34 9 9
Answer: 71.25
This is not of of the options, but is the right answer.
Step-by-step explanation:
7 x 5 + 42 - 23 / 4 =
Step 1: Make parentheses
(( 7 x 5 ) + 42) - ( 23 / 4) =
Step 2: Solve parentheses ( Multiplication and division first )
(35 + 42) - 5.75 =
Step 3: Solve parentheses ( Addition )
77 - 5.75 =
Step 4: Subtract
= 71.25
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5) 40,20,10,5, _,_,_a) Explain and Complete the sequence.B) write an explicit and recursive formula for the sequence
We have the sequence: 40, 20, 10, 5,...
Each term is half the previous term, so it is a geometrical sequence with common ratio r = 0.5.
We can not complete the sequence, as it becomes infinitely smaller and does not have a last term.
But we can write the three next terms to complete the blank spaces: 2.5, 1.25, 0.625.
We can start by writing the recursive formula. We know that each term is half the value of the previous term, so we wil have:
[tex]a_n=0.5\cdot a_{n-1}[/tex]From this recursive formula, we can deduce the explicit formula (in terms of n) as:
[tex]\begin{gathered} a_1=40 \\ a_2=0.5\cdot40=20 \\ a_3=0.5\cdot20=0.5\cdot(0.5\cdot40)=0.5^2\cdot40=10 \\ a_4=0.5\cdot10=0.5\cdot(0.5^2\cdot40)=0.5^3\cdot40 \\ \Rightarrow a_n=40\cdot0.5^{n-1} \end{gathered}[/tex]Answer:
a) Geometric sequence with r = 0.5.
The sequence first terms are: 40, 20, 10, 5, 2.5, 1.25, 0.625.
b) The recursive formula is a(n) = 0.5*a(n-1).
The explicit formula is a(n) = 40*0.5^(n-1).
Cai says you can divide both quantities in a ratio by the same non-zero number to find an equivalent ratio. Explain why cai is correct.
In this case, Cai is right.
Basically, Cai is right because a ratio is a fraction. So, if you divide the numerator and denomirator by the same number, the fraction won't be changed, in that case you would get an equivalent fraction.
For example, if we have 4/6, and we divide both numbers by 2, we get 2/3, these operations are valid because you are dividing both numbers by the same (2).
if x=2, then x^2=4, what is the inverse or give a counterexample
Step-by-step explanation:
if x = 2, then x^2 = 4, the inverse would thus be: if x^2 = 4, then x = 2.
This is partially true though since multiple values would satisfy the equation x^2 = 4, or rather 2 values. negative two and positive two. So x=2 is one solution, but just because x^2 = 4, that doesn't necessarily imply that x=2.
Which of the following is a correct interpretation of the expression -8 + (-8)?
The solution is:
*The expression describes the number that is 8 to the left of -8 on the number line. [Option A].
You want to put a 4 inch thick layer of topsoil for a new 23 ft by 31 ft garden. The dirt store sells by the cubicyards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Remember that
1 ft=12 in
1 yd =36 in
so
The garden is 23 ft by 31 ft
Convert to inches
23 ft=23*12=276 in
31 ft=31*12=372 in
Find out the volume
V=(276)*(372)*(4)
V=410,688 in3
Convert to cubic yards
410,688 in3=410,688*(1/36)^3=8.80 cubic yards
Remember that
The store only sells in increments of 1/4 cubic yards
so
The volume is 9 cubic yardsSolve for x.2x + 3 ≤ x + 5
Answer:
x ≤ 2
Explanation:
Given the inequality:
[tex]2x+3\le x+5[/tex]First, we subtract x from both sides.
[tex]\begin{gathered} 2x-x+3\le x-x+5 \\ x+3\le5 \end{gathered}[/tex]Next, we subtract 3 from both sides.
[tex]\begin{gathered} x+3-3\leqslant5-3 \\ x\leqslant2 \end{gathered}[/tex]Valentina earned some money doing odd jobs last summer and put it in a savings account that earns 7% interest compounded quarterly after 5 years there is 500.00 in the account how much did valentina earn doing odd jobs
Jane needs $20 to buy her radio.She has saved $15.What precent of the cost of the radio has she saved?
Let's begin by listing out the information given to us:
Cost of Radio (c) = $20
Jane's saving (s) = $15
% of radio cost saved = (Jane's saving / Cost of Radio) * 100%
[tex]\begin{gathered} x=\frac{s}{c}\cdot100 \\ x=\frac{15}{20}\cdot100=75 \\ x=75 \end{gathered}[/tex]Jane has saved 75% of the radio cost