The equation of line is y = -x/10 + -29/10.
Given,
The equation of a line that is perpendicular to y = 10x
and, passes through the (1, -3)
To find the equation of line.
Now, According to the question:
Find the slope of the line that is perpendicular to y = 10x;
m = - 1/10
We know that, Slope of line is ;
y = mx + c
m = -1/10
x = 1
y = -3
Substitute and calculate
- 3 = -1/10 + b
b = -29/10
Now, y = mx + b
Substitute all the values in above slope equation:
y = -x/10 + -29/10
Hence, The equation of line is y = -x/10 + -29/10.
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1. Consider the graph f(x) = 34. Describe how to graph thetransformation f(x – 3) + 2.
If the graph shows a constant function, the value of f(x) will always be the same no matter which value does x take. It means: to graph the transformation of this function do an horizontal translation right 3 units (which would show the same graph, basically) and then do a vertical translation up 2 units
.Find the area of the sector with radius 4 and central angle, ∅= 45°
Remember that the formula for the area of a sector is:
[tex]A=\frac{\pi\cdot r^2\cdot\theta}{360}[/tex]Where:
• r, is the radius
,• Theta ,is the central angle (in degrees)
Using this formula and the data given,
[tex]\begin{gathered} A=\frac{\pi\cdot4^2\cdot45}{360} \\ \rightarrow A=2\pi \end{gathered}[/tex]I got the picture and will send it to you show the coordinates of the points that create the shape of the image
We have the following:
[tex]\begin{gathered} P(1-1,-3+3)\rightarrow P^{\prime}(0,0) \\ Q(3-1,-1+3)\rightarrow Q^{\prime}(2,2) \\ R(4-1,-3+3)\rightarrow R^{\prime}(3,0) \end{gathered}[/tex]now,
The answer is:
A sector of a circle has a central angle of 60∘ . Find the area of the sector if the radius of the circle is 9 cm.
Step-by-step explanation:
area of a sector is theta ÷360 ×πr²
12. A teacher weighed 148 lbs. in 1999 and weighs 190 lbs. In 2020. What was the rate ofchange in weight?
Given,
The weight of the teacher in 1999 is 148 lbs.
The weight of the teacher in 2020 is 190 lbs.
The rate of change in weight is,
[tex]\begin{gathered} \text{Rate of change=}\frac{190-148}{2020-1999} \\ =\frac{42}{21} \\ =2 \end{gathered}[/tex]The teacher gained 2 pounds per year.
Hence, option A is correct.
[tex]8.25 \div 6[/tex]8.25 divid by 6
We want to calculate the following number
[tex]\frac{8.25}{6}[/tex]To make the calcul.ation easier, we will transform the number 8.25 into a fraction. Recall that
[tex]8.25=\frac{825}{100}[/tex]So, so far, we have
[tex]\frac{8.25}{6}=\frac{\frac{825}{100}}{6}[/tex]Also, recall that
[tex]6=\frac{6}{1}[/tex]So, we have
[tex]\frac{\frac{825}{100}}{6}=\frac{\frac{825}{100}}{\frac{6}{1}}[/tex]Now, recall that when we divide fractions, we have
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]In this case, we have a=825,b=100,c=6,d=1.
So we have
[tex]undefined[/tex]Two functions are shown. f(x) = 29(0.5)* g(x) = 18x + 14 What is the value of f(2) + g(4)?
Answer:
93.25
Explanation:
Given the below functions;
[tex]\begin{gathered} f(x)=29(0.5)^x \\ g(x)=18x+14 \end{gathered}[/tex]To be able to find the value of f(2) + g(4), we have to 1st determine the value of f(2) and f(4) as shown below;
[tex]\begin{gathered} f(2)=29(0.5)^2=29\ast0.25=7.25 \\ g(4)=18(4)+14=72+14=86 \end{gathered}[/tex]Let's go ahead and find the value of f(2) + g(4);
[tex]f(2)+g(4)=7.25+86=93.25[/tex]Can you Help me with this i cannot do ir
To translate f(x) 4 units down we subtract 4 from f(x):
[tex]f(x)-4.[/tex]Now, to reflect f(x)-4 over the x-axis we multiply by -1:
[tex]-1(f(x)-4)=-f(x)+4.[/tex]Answer:
[tex]g(x)=-\sqrt[3]{x-2}+4.[/tex]question 5 only. determine the missing side length QP. the triangles are not drawn to scale.
This is a simple question.
First, we can see both triangles are proportional, it means it has the same relation between its sides even if one is in a large scale and the other on a a small scale.
Now we can identify which side corresponds to which side. Once side AC is the longest one for triangle ABC it means its equivalent for triangle PQR is the side RP, so the equivalent for side AB is side QP. Once we know that we can write the following relation and calculate:
Susanna has played the piano for s years. Patrick has played the piano for 4 more than twice the number of years that susanna has been playing the piano. which expression correctly shows the number of years that Patrick has been playing the piano.2s + 44s + 22 (s + 4)(s - 4) ÷ 3none of the above
Given data:
The expression for Patrick paly Piano is,
[tex]P=2s+4[/tex]Thus, the first option is correct.
determine the solution,if it exists,for each system of linear equation. Verify your solution on the coordinate plane. x + 3 = y 3x + 4y = 7
then
[tex]\begin{gathered} 3\mleft(y-3\mright)+4y=7 \\ 3y-9+4y=7 \\ 7y-9=7 \\ 7y-9+9=7+9 \\ 7y=16 \\ \frac{7y}{7}=\frac{16}{7} \\ y=\frac{16}{7} \end{gathered}[/tex]replacing in x
[tex]undefined[/tex]Which of the following tables represents a function?
Answer:
Table A represents a function
Step-by-step explanation:
Table A represents function because it is the only table that doesn't repeat an output or input number.
Solve the inequality for x and identify the graph of its solution.|x+ 2] < 2Choose the answer that gives both the correct solution and the correct graph.
| x + 2 | < 2
-2 < x + 2 < 2
-2 - 2 < x + 2 < 2 - 2
-4 < x < 0 This is the inequality
Letter B is the right choice.
Solve the problem. Use 3.14 as the approximate value of pie
The volume of a cylinder is calculated using the formula:
[tex]V=\pi r^2h[/tex]where r is the radius of the cylinder and h is the height.
From the question, we have the following parameters:
[tex]\begin{gathered} diameter=4.8 \\ \therefore \\ r=\frac{4.8}{2}=2.4 \\ and \\ h=6.66 \end{gathered}[/tex]Therefore, we c n calculae tehe volume of a cylinder to be:
[tex]\begin{gathered} V=3.14\times2.4^2\times6.66 \\ V=120.455424 \end{gathered}[/tex]For four cylinders, the combined volume will be:
[tex]\begin{gathered} V=120.455424\times4 \\ V=481.821696 \end{gathered}[/tex]The volume i 481 .82 cubic inches.
Sue would like to join a gym. Gym A has a $56 joining fee with $3 per visit. Gym B has a $30 joining fee with a $5 per visit. Let x represent the number of visits. After how many visits would the cost of the two gyms be the same?
Let x represent the number of visits it will take for the cost of the two gyms to be the same.
Gym A has a $56 joining fee with $3 per visit. This means that the cost of x visits of gym A would be
3 * x + 56
= 3x + 56
Gym B has a $30 joining fee with a $5 per visit. This means that the cost of x visits of gym B would be
5 * x + 30
= 5x + 30
For both costs to be the same, it means that
3x + 56 = 5x + 30
5x - 3x = 56 - 30
2x = 26
x = 26/2
x = 13
After 13 visits, the cost of the two gyms would be the same
what is the area of a triangle with the legth of 8in,12in,6in
Area is
[tex]A=\frac{1}{2}bh=\frac{1}{2}\times6\times8=\frac{48}{2}=24[/tex]answer: 24 sq in
A friend plans to purchase a 72-inch tv at a particular store for a cost of $1500. The store is offering 25% off any one item. He also has an internet coupon for an additional 10% off any discounted price. How much will your friend save (a) in dollar amount and (b) in percent?
the The Solution.
The marked price of the 72-inch TV = $1500
25% discount makes the actual discount to be:
[tex]\begin{gathered} \text{Actual Discount = 25 \% of 1500} \\ \text{ = }\frac{25}{100}\times1500=\text{ \$375} \end{gathered}[/tex]So, the discounted price will now be
Discounted price = 1500 - 375 = $1125
He has an additional 10% internet coupon discount on already dicounted price ($1125) .
[tex]\begin{gathered} \text{Additional discount = 10\% of 1125} \\ \text{ =}\frac{10}{100}\times1125=\text{ \$112.50} \end{gathered}[/tex]a. The friend will save
[tex]\begin{gathered} 375+112.50 \\ =\text{ \$487.50} \end{gathered}[/tex]b. in percentage, he saved
[tex]\frac{487.5}{1500}\times100=32.5\text{ \%}[/tex]Therefore, the correct answers are:
a. $487.50
b. 32.5%
6-Find the measure of ∠AEB.A. 122°B. 132°C. 142°D. 152°7-Find the measure of ∠BEC.A. 58 °B. 48°C. 38°D. 28°8-Find the measure of ∠CED.A. 52 °B. 48 °C. 42 °D. 32°9-Find the measure of ∠FEB.A. 142°B. 180°C. 90°D. 0°10-Find the measure of ∠FED.A. 0°B. 180°C. 45°D. 90°
The answer for 6 is C. 142°
Explanation
∠AEB = 180 - ∠AEF (Sum of angle on a straight line)
∠AEB = 180 - 38 = 142°
15% of $764.69rounded to the nearest cent.
Percentage is expressed in terms of 100. To find 15% of 764.69, we would multiply ratio of 15% to 100% by 764.69. Thus, we have
15/100 * 764.69
= 114.7035
Calculate the average rate of change for the function f(x) = 3x4 − 2x3 − 5x2 + x + 5, from x = −1 to x = 1.
a
−5
b
−1
c
1
d
5
Average rate of change for the function f(x) = 3x⁴ -2x³ -5x² +x +5 from
x =-1 to x=1 is equal to -1.
As given in the question,
Given function :
f(x) = 3x⁴ -2x³ -5x² +x +5
Formula for average rate of change for (a, f(a)) and (b, f(b))
[f(b) -f(a)] / (b-a)
Substitute the value of a=-1 and b=1
f(-1)=3(-1)⁴ -2(-1)³-5(-1)² +(-1) +5
= 3+2-5-1+5
=4
f(1)=3(1)⁴ -2(1)³-5(1)² +(1) +5
= 3-2-5+1+5
= 2
Average rate of change = (2-4)/(1-(-1))
= -2/2
=-1
Therefore, average rate of change for the function f(x) = 3x⁴ -2x³ -5x² +x +5 from x =-1 to x=1 is equal to -1.
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How to draw the graphs of the following non-linear functions?y=x^2 + 1y=3^x + 1
The first step is to substitute values of x into each equation.
For y = x^2 + 1,
if x = - 2, y = (- 2)^2 + 1 = 4 + 1 = 5
if x = - 1, y = (- 1)^2 + 1 = 1 + 1 = 2
if x = 0, y = (0)^2 + 1 = 0 + 1 = 1
if x = 1, y = (1)^2 + 1 = 1 + 1 = 2
if x = 2, y = (2)^2 + 1 = 4 + 1 = 5
We would plot the corresponding values of x and y on the graph as shown below
For y = 3^(x + 1),
if x = - 2, y = 3^(-2 + 1) = 3^-1 = 0.33
if x = - 1, y = 3^(-1 + 1) = 3^0 = 1
if x = 0, y = 3^(0 + 1) = 3^1 = 3
if x = 1, y = 3^(1 + 1) = 3^2 = 9
if x = 2, y = 3^(2 + 1) = 3^3 = 27
We would plot the corresponding values of x and y on the graph as shown below
a coyote can run a hundred one in 5.3 seconds a jack-rabbit can run 75 m in 4.7 seconds compared their unit speeds to determine which animal is faster round to the nearest whole unit Blank#1 Coyote speedBlank#2 Jack Rabbit speedBlank#3 Which one is faster
Answer
Coyote's speed = 19 m/s
Jack Rabbit's speed = 16 m/s
The Coyote is faster since 19 > 16.
Explanation
To answer this, we need to note that the relationship between speed, distance and time is given as
Speed = (Distance/Time)
For the Coyote,
Distance = 101 m
Time = 5.3 seconds
Speed = (Distance/Time)
Coyote's speed = (101/5.3) = 19 m/s
For the Jack Rabbit,
Distance = 75 m
Time = 4.7 seconds
Speed = (Distance/Time)
Jack Rabbit's speed = (75/4.7) = 16 m/s
Since 19 m/s is evidently greater than 16 m/s, we can conclude that the Coyote is faster than the Jack Rabbit.
Hope this Helps!!!
Evaluate the expression (4x^3y^-2)(3x^-2y^4) for x = –2 and y = –1.
Answer:
3x−2y)(4x+3y)
It can be written as =3x(4x+3y)−2y(4x+3y)
By further calculation =12x
2
+9xy−8xy−6y
2
So we get =12x
2
+xy−6y
2
identify the slope: 6x - 2y = -6
The slope = 3
Explanations:Note that:
The slope - Intercept form of the equation of a line takes the form y = mx + c
where m is the slope and
c is the intercept
The given equation is:
6x - 2y = -6
The equation can be re-written as:
2y = 6x + 6
2y / 2 = 6x/2 + 6/2
y = 3x + 3
The slope, m = 3
The intercept, c = 3
There are 6 dogs and 2 mice. Write a ratio for the number of ears to th number of paws. * 6:2 3 people are in a room. Write a ratio to represent the number of finger
each dog has 4 paws, then 6 dogs have 6*4 = 24 paws
each mouse has 4 paws, then 2 mice have 2*4 = 8 paws
Total number of paws: 24 + 8 = 32 paws
each dog has 2 ears, then 6 dogs have 6*2 = 12 ears
each mouse has 2 ears, then 2 mice have 2*2 = 4 ears
total number of ears: 12 + 4 = 16 ears
The ratio for the number of ears to the number of paws: 16/32 = 1/2 or 1:2
(8-4) mulitiply (3-2)=
An object is dropped from 27 feet below the tip of the pinnacle atop a 1471-ft tall building. The height h of the object after t seconds is giveh= - 16t^2 + 1444. Find how many seconds pass before the object reaches the ground.How many seconds pass before the object reaches the ground
The Solution:
Given:
[tex]h=-16t^2+1444.[/tex]We are required to find t when h = 0.
[tex]\begin{gathered} -16t^2+1444=0 \\ \\ -16t^2=-1444 \end{gathered}[/tex]Divide both sides by -16.
[tex]t^2=\frac{-1444}{-16}=90.25[/tex][tex]\begin{gathered} t=\sqrt{90.25} \\ \\ t=9.5\text{ or }t=-9.5 \end{gathered}[/tex]Thus, the correct answer is 9.5 seconds.
what is the sum of 141.2-79.83
Given:
141.2 - 79.83
Here, we are to subtract 79.83 from 141.2
Let's evaluate the given expression.
We have:
[tex]\begin{gathered} 141.20 \\ -79.83 \\ _{\text{ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}} \\ \text{ 61.37} \end{gathered}[/tex]ANSWER:
61.37
a. Create a perfect square trinomial.
b. Factor the perfect square trinomial you created in 1a.
a. Create a difference of two squares.
b. Factor the difference of two squares you created in 2a.
a. Describe at least one similarity between the perfect square trinomial and the difference of squares. You can use either the form you wrote in 1a and 2a, or you can use their factored form from 1b and 2b. Write your answer using complete sentences.
b. Describe at least one difference between the perfect square trinomial and the difference of squares. You can use either the form you wrote in 1a and 2a, or you can use their factored form from 1b and 2b. Write your answer using complete sentences.
A factored perfect square might look like (x+a)(x+a) or (x-a)(x-a) [or (ax+b)(ax+b) but keep it simple]. Then, distribute.
A factored difference of two squares might look like (x+a)(x-a). Then, distribute.
(pick a number for a)
1.
a. One example of a perfect square trinomial is: x² + 6x + 9.
b. The factored trinomial above is: (x + 3)².
2.
a. One example of a difference of two squares is: x² - 4.
b. The factored difference of squares above is: (x - 2)(x + 2).
3.
a. The similarity is that the first term is positive for both cases.
b. The difference is that the final term is positive for perfect square trinomials and negative for the difference of squares.
Perfect square trinomialsThere are two examples of perfect square trinomials, the square of the sum and the square of the subtraction, as follows:
Square of the sum: (a + b)² = a² + 2ab + b².Square of the subtraction: (a - b)² = a² - 2ab + b².The left side is the factored form and the right side is the expanded form.
Hence one example of a perfect square trinomial is given as follows:
(x + 3)² = x² + 6x + 9.
Difference of two squaresA difference of two squares is factored as follows:
x² - y² = (x + 2)(x - 2)
Hence one possible example is:
x² - 4 = (x + 2)(x - 2).
Compared to the perfect square trinomial, we have that:
The similarity is that the first term in any of the two polynomials will always be positive.The difference is in the last term, for the perfect square it will always be positive (+ b²) and for the difference of two squares it will always be negative (- b²).More can be learned about perfect square trinomials at https://brainly.com/question/14584348
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Write an equation for the graph below in point-slope form and then solve rewrite in slope-intercept form.
We are given the graph of a line and we are asked to determine its equation in point-slope form.
The general form in slope point form of a line is:
[tex]y-y_0=m(x-x_0)[/tex]Where:
[tex]\begin{gathered} m=\text{ slope} \\ (x_0,y_0)\text{ is apoint in the line} \end{gathered}[/tex]to determine the slope we will use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where:
[tex](x_1,y_1);(x_2,y_2)=\text{ points on the line}[/tex]We will choose two points on the line from the graph:
[tex]\begin{gathered} (x_1,y_1)=(0,1) \\ (x_2,y_2)=(2,2) \end{gathered}[/tex]Now, we plug in the values in the formula for the slope:
[tex]m=\frac{2-1}{2-0}=\frac{1}{2}[/tex]Now, we substitute the value of the slope in the equation of the line:
[tex]y-y_0=\frac{1}{2}(x-x_0)[/tex]Now, we plug in the first point we choose for the line:
[tex]\begin{gathered} y-1=\frac{1}{2}(x-0) \\ \\ y-1=\frac{1}{2}x \end{gathered}[/tex]And thus we have determined the equation of the line in point-slope form.
The slope-intercept form is the following:
[tex]y=mx+b[/tex]To convert this equation to slope-intercept form, we will take the previous equations and we will add 1 to both sides:
[tex]y=\frac{1}{2}x+1[/tex]And thus we have determined the slope-intercept form of the equations of the line.