The perimeter of the larger triangle is 51
Here, we want to calculate the perimeter of the larger triangle
From the smaller triangle, we can see that its shortest side is 4
The shortest side of the larger triangle is 12
This shows that the scale of the larger to the smaller is 3 to 1
Mathematically, what this means is that, by multiplying the length of the smaller triangle by 3, we can get the sides of the larger
Hence, what we have at this point is that the sides of the larger triangle are 12 by 18 by 21
Mathematically, the perimeter of a triangle can be calculated by adding the length of the sides together
With respect to this question, the perimeter of the larger triangle will be;
12 + 18 + 21 = 51
What is 1.57828282E5And 6.82e-8 in standard form
The standard form of a number converts a large number in short form using the power of 10.
First number is:
1.57828282E5
As you mentioned the numbers are technology generated hence E^x = 10^x. For example, in Matlab, you can write 10^5 as E^5.
Hence, the standard form of the number would be
1.57828282 x 10^5
While the ordinary form would be
157828.282
Similarly, the standard form of the second number would be:
6.82 x 10^-8
(Exponential Regressions)The accompanying table shows the number of bacteria present in a certain cultureover a 4 hour period, where x is the time, in hours, and y is the number ofbacteria. Write an exponential regression equation for this set of data, rounding allcoefficients to the nearest hundredth. Using this equation, determine the number ofbacteria present after 16 hours, to the nearest whole number.
Answer:
[tex]\begin{gathered} (a)y=460.30(1.10)^x \\ (b)2115\text{ bacteria} \end{gathered}[/tex]Explanation:
Part A
An exponential regression is of the form:
[tex]y=AB^x[/tex]We plug this data into an exponential regression calculator:
To the nearest hundredth, the values obtained are:
[tex]\begin{gathered} A\approx460.30 \\ B\approx1.10 \end{gathered}[/tex]An exponential regression equation for this set of data is:
[tex]y=460.30(1.10)^x[/tex]Part B
After 16 hours, when x=16
[tex]\begin{gathered} y=460.30(1.10)^{16} \\ y\approx2115\text{ (to the nearest whole number)} \end{gathered}[/tex]After 16 hours, the number of bacteria present is 2,115.
For an unknown parent function f(x), write a function g(x) that is:-vertically stretched by a factor of 2,- shifted up 5 units, and - shifted right 4 units. Explain how your function accomplishes these transformations.
Given the parent function to be:
[tex]f(x)[/tex]Write the function g(x), when the parent function is
1. vertically stretched by a factor of 2 - Multiply the parent function by 2
[tex]g(x)=2f(x)[/tex]2. Shifted up 5 units - Add 5 units outside of the parent function
[tex]g(x)=2f(x)+5[/tex]3. Shifted right 4 units - Subtract 4 from within the parent function
[tex]g(x)=2f(x-4)+5[/tex]Therefore, the transformation of the parent function f(x) to g(x) is
[tex]g(x)=2f(x-4)+5[/tex]3/5t+ 7 = -8 What is t
The equation to solve is:
[tex]\frac{3}{5t}+7=-8[/tex]We take "7" to the right hand side:
[tex]\begin{gathered} \frac{3}{5t}+7=-8 \\ \frac{3}{5t}=-8-7 \\ \frac{3}{5t}=-15 \end{gathered}[/tex]Now, we cross multiply:
[tex]\begin{gathered} 3=5t\times-15 \\ 3=-75t \end{gathered}[/tex]Now we divide by -75 to solve for t:
[tex]\begin{gathered} 3=-75t \\ t=-\frac{3}{75} \end{gathered}[/tex]Which values are solutions to the inequality below? √x≤=4 check all that apply: A. 20 B. 12 C. 2 D. 5 E. -1. F. NO SOLUTIONS.
we can replace the value of X for each option and check the inequality
A.20
[tex]\begin{gathered} \sqrt[]{20}\le4 \\ 4.47\le4 \end{gathered}[/tex]the inequality is wrong because 4.47 is greater than 4
B.12
[tex]\begin{gathered} \sqrt[]{12}\le4 \\ 3.46\le4 \end{gathered}[/tex]The inequality is right because 3.46 is less than 4
C.2
[tex]\begin{gathered} \sqrt[]{2}\le4 \\ 1.41\le4 \end{gathered}[/tex]The inequality is right because 1.41 is less than 4
D.5
[tex]\begin{gathered} \sqrt[]{5}\le4 \\ 2.23\le4 \end{gathered}[/tex]inequality is right because 2.23 is less than 4
E. -1
[tex]\sqrt[]{-1}\le4[/tex]we can calculate the root of a negative number then the option is wrong
It’s two-parter question I would like the answer and how to solve
Answer:
x > 10 ; D
Step-by-step explanation:
Which of the following expressions could be used to determine the exact value of cos 240°?
The formula we will use is the one of cos2x:
2x=240
x=120
The formula is: cos2x = 2cos²x - 1
cos240 = 2cos²(120) - 1
Assume lines that look tangent, are tangent.Find the value of x.(The ones that are crossed out don’t need answered)
Take into account that for secant and tangent lines related to circles, use the following formula:
x = 1/2·(larger arc - smaller arc)
Then, you have, for the first circle:
larger arc = 360° - 124° = 236°
smaller arc = 124°
x = 1/2·(236° - 124°)
x = 1/2·(112°)
x = 56°
For the second circle, the value of x is the same that the given arc:
x = 124°
For the fourth circle:
larger arc = 171°
smaler arc = 67°
x = 1/2·(171° - 67°)
x = 1/2·(104°)
x = 52°
For the fifth circle:
x = 1/2·(101° + 39°)
x = 70°
what is the equation fir the graph below1. y=2/5x+42. y= -2/5x+43. y= 4/1x-2/54. y= -5/2x+4
y = -2/5 x + 4 (option 2)
Explanation:Equation of line: y = mx + b
m = slope, b = y-intercept
Slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]Using points (5, 2) and (0, 4)
[tex]\begin{gathered} x_1=5,y_1=2,x_2=0,y_2\text{ = }4 \\ \text{slope = }\frac{4-2}{0-5}=\text{ }\frac{2}{-5} \\ \text{slope = -2/5} \end{gathered}[/tex]The y -intercept is point the line crosses the y axis. The point is at y = 4
b = 4
The equation of the line becomes:
y = -2/5 x + 4 (option 2)
Solve for x and y:x – 3y = -83x + 2y = 31Select one:a. (-11,-1)b.(11,-1)c. (5,8)d. (7,5)
We have two unknowns (x and y) and 2 equations.
We will clear one unknown in the first equation and then replace it in the second.
Then, we can solve for the other variable and solve backwards.
The first equation is:
[tex]\begin{gathered} x-3y=-8 \\ x=3y-8 \end{gathered}[/tex]We replace the value of x in the second equation:
[tex]\begin{gathered} 3x+2y=31 \\ 3(3y-8)+2y=31 \\ 9y-24+2y=31 \\ 11y=31+24 \\ 11y=55 \\ y=\frac{55}{11} \\ y=5 \end{gathered}[/tex]Then, with y=5, we can calculate the value of x:
[tex]x=3y-8=3\cdot5-8=15-8=7[/tex]The solution (x,y) is (7,5). The answer is Option D.
use the graph below to find the point of intersection for the functions .
The equations are in the slope-intercept form:
y= mx+b
Where:
m= slope ( rise / run )
b= y-intercept (where the line crosses the y axis)
Graph:
Both functions intersect at the point (-1,3)
Evaluate the factorial expression.10!/7!
To evaluate the expression we need to remember that:
[tex]n!=n(n-1)![/tex]Then we have:
[tex]\frac{10!}{7!}=\frac{10\cdot9!}{7!}=\frac{10\cdot9\cdot8!}{7!}=\frac{10\cdot9\cdot8\cdot7!}{7!}=10\cdot9\cdot8=720[/tex]Therefore:
[tex]\frac{10!}{7!}=720[/tex]Find the midpoint of the two points below. Type your answer as a point (x,y) without any spaces between your characters. Be sure to include the parentheses and a comma between your x and y values. If a value is not an integer then type your answer as a decimal rounded to the nearest hundredth.(0,7) and (4,-9)The midpoint is Answer
We will use the following formula for the coordinates of the midpoint (l,m) of a segment with endpoints (x,y) and (z,k):
[tex]\begin{gathered} l=\frac{x+z}{2}, \\ m=\frac{y+k}{2}\text{.} \end{gathered}[/tex]Substituting the given points in the above formula we get:
[tex]\begin{gathered} l=\frac{0+4}{2}=\frac{4}{2}=2, \\ m=\frac{7+(-9)}{2}=\frac{-2}{2}=-1. \end{gathered}[/tex]Answer: The midpoint is
[tex](2,-1)\text{.}[/tex]Wendy is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, she spent a total of $100. Wendy will be earning a base salary of $70 per month from the gym, plus an additional $3 for every class she teaches. If Wendy teaches a certain number of classes during her first month as an instructor, she will earn back the amount she spent on certification. How much will Wendy's expenses and earnings be?
Write a system of equations, graph them, and type the solution.
Wendy's expenses and earnings be will becomes $100 once she completed 10 classes.
What is meant by the term system of equations?System of equations, also known as simultaneous equations, Two or even more equations to just be solved together in algebra. The number of equations should then equal the number of uncertainties for a system to produce a unique solution.The information regarding the teaching classes at a local gym by kickboxing instructor is given-
Total amount spent = $100.
Basic salary of Wendy = $70.
Additional salary = $3 for each class.
Let 'x' be the number of classes during first month.
The, the equation forms as;
100 = 70 + 3x (equation)
Simplifying,
x = 30/3
x = 10 (solution)
The graph is shown.
Wendy's expenses and earnings be will becomes $100 once she completed 10 classes.
To know more about the system of equations, here
https://brainly.com/question/25976025
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P varies jointly with Q and R,and P=6 when Q=3 and R=12.Find P Q=4 and R=16
Answer:
10.67
Explanation:
We're told that P varies jointly as Q and R, this can be represented as shown below;
[tex]\begin{gathered} P\propto QR \\ P=\text{kQR} \end{gathered}[/tex]where k = constant of proportionality
Given P = 6, Q = 3 and R = 12, let's go ahead and solve for k;
[tex]k=\frac{P}{QR}=\frac{6}{3\times12}=\frac{6}{36}=\frac{1}{6}[/tex]Knowing k = 1/6, let's solve for P when Q = 4 and R = 16;
[tex]P=\frac{1}{6}\times4\times16=\frac{64}{6}=10.67[/tex]Favorite coffee flavor a survey was taken asking the favorite flavor of a coffee drink a person prefers. The responses were C=caramel, H=hazelnut, M=mocha, P equals plain, And V=vanilla
It is given that Favorite coffee flavor a survey was taken asking the favorite flavor of a coffee drink a person prefers. The responses were
C=caramel, H=hazelnut, M=mocha, P equals plain, And V=vanilla
The given data is;
C M M C H H C C H M
H P V H P H V H H H
C V M H V H P C H C
H H V C H P P
Number of Caramel favorite person = 8
Number of Hazelnut favorite person = 15
Number of Mocha favorite person = 4
Number of plain favorite person = 5
Number of Vanila favorite person = 5
..
8What is the slope of the line that passes through the points (-2, 5) and (3, 4) in the standard (x,y) plane?
Answer
Slope = -(1/5) = -0.20
Explanation
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (-2, 5) and (3, 4)
[tex]\text{Slope = }\frac{4-5}{3-(-2)}=\frac{-1}{3+2}=\frac{-1}{5}[/tex]Hope this Helps!!!
What is the value of x when f(x) = 9?
ANSWER :
A. 2
EXPLANATION :
From the problem, we have the function :
[tex]f(x)=3^x[/tex]when f(x) = 9 :
[tex]\begin{gathered} f(x)=3^{^x} \\ 9=3^x \end{gathered}[/tex]Note that 9 is 3^2
[tex]\begin{gathered} 9=3^x \\ 3^2=3^x \\ \text{ Since the bases are equal, the exponents are equal too.} \\ 2=x \\ x=2 \end{gathered}[/tex]x+4y=4 I know how to solve it. But how. how do you plot it on a graph?
In order to plot it, we start by solving for y:
[tex]\Rightarrow4y=4-x\Rightarrow y=1-\frac{x}{4}[/tex]After this we simply replace values for x and we will get values for y inordered pairs, the
Can someone walk me through this? I know it’s familiar but I can’t recall how to do it.
18 dimes and 6 quarters
1) Let's recall that 1 dime = $0.10 and a quarter is $0.25
2) We can solve this by writing a Linear System of Equations:
[tex]\begin{gathered} x+y=24 \\ 0.1x+0.25y=3.3 \end{gathered}[/tex]Note that the second equation relates the quantities in dollars, 330 cents is the same as $3.30.
2.2) So now let's solve it using the Elimination Method multiplying one of those equations by -0.1:
[tex]\begin{gathered} 0.1x+0.25y=3.3 \\ -0.1x-0.1y=-2.4 \\ ---------------- \\ 0.15y=0.9 \end{gathered}[/tex]Let's divide both sides by 0.15:
[tex]\begin{gathered} \frac{0.15y}{0.15}=\frac{0.9}{0.15} \\ y=6 \end{gathered}[/tex]So we have 6 coins of quarters, now let's plug into the original equation x+y=24 to get the number of dimes:
[tex]\begin{gathered} x+6=24 \\ x+6-6=24-6 \\ x=18 \end{gathered}[/tex]3) Hence, there are 18 dimes and 6 quarters
Pay Cut Todd works for a computer firm, and last year he earned a salary of $120,000. Recently, Todd was required to take a 15% pay cut. Find Todd's salary after the pay cut.
Given:
The salary of Todd last year, C=$120,000.
The percentage rate of pay cut, R=15%.
Todd's salary after the pay cut can be calculated as,
T=C x (100-R)/100
T=120000 x (100-15)/100
T=120000 x 85/100
T=102000
Therefore, Todd's salary after the pay cut is $102000.
Solve for y:x/y = h-k
We have to solve for y:
[tex]\begin{gathered} \frac{x}{y}=h-k \\ x=(h-k)\cdot y \\ \frac{x}{h-k}=y \\ y=\frac{x}{h-k} \end{gathered}[/tex]Answer: y = x / (h-k)
Solve the equation by factoring: x2 - 5x - 14 a. X = -2 or 7 b. X = 2 and - 7 c. x = -2 or -7 d. X = 2 or 7
We need to solve the quadratic equation:
x^2 - 5 x - 14 = 0 by factoring.
So we look for a pair of factors whose product is -14 and when combined render - 5. So we find the pair "-7 and 2"
Their product = (-7) * 2 = -14
combining them we get: -7 + 2 = -5
So we used them to split the middle term in the equation:
x^2 - 5 x - 14 = 0
x^2 - 7 x + 2 x - 14 = 0
Factor by grouping:
x ( x - 7) + 2 x - 14 = 0
x (x - 7) + 2 (x - 7) = 0
(x - 7) (x + 2 ) = 0
Then for this product to render zero, (x - 7) must be zero (so x = 7)
or (x + 2) is zero (and therefore x = -2)
Then we look for the answers x = -2 or x = 7
This coincides with answer (a) in your list.
evaluate the expression x² + y²/10when x = 6 and y =8
The given expression is
[tex]\frac{x^2+y^2}{10}[/tex]Let's replace x = 6 and y = 8.
[tex]\frac{6^2+8^2}{10}=\frac{36+64}{10}=\frac{100}{10}=10[/tex]Hence, the evaluation gives 10.If she is working alone, Sylvia can pick a pint of raspberries in 20 minutes. If Jasmine and Sylvia work together, they can complete the job in 8 minutes. How long would it take Jasmine to pick a pint of raspberries working alone?
Given that:
- Sylvia can pick a pint of raspberries in 20 minutes working alone.
- Jasmine and Sylvia can complete the job in 8 minutes if they work together.
You can use the following Rate for Work Formula in order to solve the exercise:
[tex]\frac{t}{a}+\frac{t}{b}=1[/tex]Where "t" is the time for objects A and B to complete the work together, "a" is the time needed for object A to complete the work alone, and "b" is the time for object B to complete the work alone.
In this case, you can identify that:
[tex]\begin{gathered} t=8\text{ } \\ a=20\text{ } \end{gathered}[/tex]Therefore, by substituting values into the formula and solving for "b", you can determine how long it would take (in minutes) for Jasmin to pick a pint of raspberries working alone:
[tex]\frac{8}{20}+\frac{8}{b}=1[/tex][tex]\frac{8}{b}=1-\frac{8}{20}[/tex][tex]\frac{8}{b}=1-\frac{8}{20}[/tex][tex]8=(\frac{3}{5})(b)[/tex][tex](8)(\frac{5}{3})=b[/tex][tex]b\approx13.3[/tex]Hence, the answer is:
[tex]13.3\text{ }minutes\text{ \lparen Approximately\rparen}[/tex]find the constant rate of change and interpret its meaning
The constat rate is given by the slope of the line. By definition, the slope of the line is defined as follows:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]Where (X1,Y1) and (X2,Y2) are given points on the line. In our case, for example, we can take the points:
(X2,Y2) =(4,50)
(X1,Y1)=(2,70)
Replacing the previous data in the equation of the slope we obtain:
[tex]rate=m\text{ = }\frac{Y2-Y1}{X2-X1}=\frac{50-70}{4-2}=\frac{-20}{2}\text{ =-10 ft/s}[/tex]Then, we can conclude that the constant rate is
-10 ft /s : a descent of 10 ft per second.
If EF = 2x - 12 FG = 3x - 15. and EG = 23, find the values of x. EF, and FG. The drawing is not to scale. x =3, EF = 8, FG = 15 Ox=10, EF = 32, FG = 45 O x =3, EF = -6, FG = -6 x =10, EF = 8, FG = 15
We have the next information
EF=2x-12
FG=3x-15
EG=23
With the information above we can have the next equation in order to find x
2x-12+3x-15=23
Then we sum similar terms
5x-27=23
then we isolate the x
5x=23+27
5x=50
x=10
then we substitute the value of x for each segment
EF=2x-12=2(10)-12=20-12=8
FG=3x-15=3(10)-15=30-15=15
Find the value of f(-6).yy = f(x)108642-10-8-6-422468.10-2-4-6-8
The given graph is a downward parabola.
The roots of the equation is -2 and -8, and the vertex is (-5,7).
The general root form of parabola will be,
a(x-(-2))(x-(-8))=a(x+2)(x+8).
The value of a can be determined from the coordinate of vertex,
[tex]\begin{gathered} y=a(x+2)(x+8) \\ 7=a(-5+2)(-5+8) \\ 7=a\times(-3)(3) \\ a=\frac{-7}{9} \end{gathered}[/tex]Thus, the required quadratic is,
[tex]f(x)=\frac{-7}{9}(x+2)(x+8)[/tex]The value of f(-6) can be determined as,
[tex]\begin{gathered} f(-6)=\frac{-7}{9}(-6+2)(-6+8) \\ =6.22 \end{gathered}[/tex]Thus, the requried value of f(-6) is 6.22.
Don’t know how to do this some help would be nice pls and thanks
Looking at the graph, f(2) means that the function is evaluated at x = 2.
Using this information, we need to identify the corresponding y-value on the graph, just like the image below:
We conclude that f(2) = -5
1,898,130,000,000,000,000,000,000,000 in scientific notation (round to two digts after the decimal
in scientific notation is
[tex]1.89\times10^{27}[/tex]