The given functions are
f(x) = x^2 - 5
g(x) = 3x - 1
To find 2g(f(- 5)), we would first find f(- 5)
To find f(- 5), we would substitute x = - 5 into f(x) = x2 - 5. It becomes
f(- 5) = (- 5)^2 - 5
f(- 5) = 25 - 5
f(- 5) = 20
Then, we would substitute f(- 5) = 20 into g(x) = 3x - 1
Thus,
g(f(- 5) = 3*20 - 1
g(f(- 5) = 60 - 1
g(f(- 5) = 59
Therefore,
2g(f(- 5)) = 2 * 59 = 118
Solve the system of equations 2x - 3y = 4 and 9x - 8y = - 26 by combining the
equations.
[tex]\sf \Large \boxed{\sf +}\\ \sf \Large \boxed{\sf +}\\\\ \sf \Large \boxed{\sf 11x+-11y=-22}\\\\ 2x+9x-3y-8y=4-26\\Combine\\11x-11y=-22\\Simplify\\x-y=-2\\x=y-2\\Plug\ the\ value\ in\ the\ equation\\2(y-2)-3y=4\\2y-4-3y=4\\-y-4=4\\-y=8\\y=-8\\Solve\ for\ x\\9x-8(-8)=-26\\9x+64=-26\\9x=-90\\x=-10[/tex]
The length of your step is 34 inches (in.). If you walk 10,000 steps in a day, how many feet (ft.) will you walk? ?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
step length = 34 inches
walking = 10000 steps
Step 02:
feet to inches
1 feet = 12 inches
1 step --------------- 34 inches
10000 steps ------- x
1 * x = 10000 * 34
x = 340000
340000 inches * ( 1 feet / 12 inches)
28333.33 feet
The answer is:
You will walk 28333.33 feet .
You want to enlarge a picture by a factor of 4.5 from its current size of 4 inches by 6 inches. What is the size of the enlarged picture?a. 18 in. by 27 in.b.8.5 in. by 10.5 in.c. 18 in. by 10.5 in.d. 8.5 in. by 27 in.
If we want to enlarge the picture by a factor of 4.5, the perimeter will also increase by the factor of 4.
[tex]\begin{gathered} \text{New dimension =}4.5\text{ (old dimension)} \\ \text{New dimension=4.5 (4 by 6)} \\ \text{New dimension=18 inches by 27 inches} \end{gathered}[/tex]Hence, the correct option is Option A
If the ones digit in a two-digit number is even, the number is a composite number. Which odd ones digit also tells you the number must be a compositenumber? Explain.
Okay, here we have this:
Considering that a composite number is a number that is not prime, the only number one of the units that tells us that a two-digit number is composed is 5, since every number ending in 5 is a multiple of 5.
find the slope of the line that passes through these two points (0, -2) (5, 3) slope= ?
Find the slope of the line that passes through these two points
P1 = (0, -2)
P2 = (5, 3)
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{3-(-2)}{5-0} \\ m=\frac{3+2}{5} \\ m=\frac{5}{5} \\ m=1 \end{gathered}[/tex]The slope would be 1
40 model A cars were sold that week. what else can you say about this bar model?
From the diagram
Ratio of model A car to model B car = 4:6
Ratio of model A to model B = 4:6
Ratio of model B to model A = 6:4
Ratio of model A to total = 4:10
Ratio of model B to total = 6:10
If 40 model A cars sold
I know that 60 model B cars was sold.
40. Circle A has a radius 4 inches. Is each statement about circle A true?
The first statement is about the diameter of the circle.
The diameter of a circle is always the double of its radius.
So if circle A ras a radius of 4 inches, its diameter is:
[tex]\text{diameter}=2\cdot\text{radius}=2\cdot4=8\text{ inches}[/tex]So the first statement is true (YES)
The second statement is about the area of the circle. The area of a circle is given by the following equation:
[tex]Area=\pi\cdot r^2[/tex]If the radius of the circle is 4 inches, we have:
[tex]\text{Area}=\pi\cdot4^2=16\pi[/tex]So the second statement is also true (YES)
The third statement is about the volume of a cylinder with a height of 6 inches and the circle A as the base. The volume of a cylinder is given by the equation:
[tex]\text{Volume}=\pi\cdot r^2\cdot h[/tex]Using the radius = 4 inches and the height = 6 inches, we have:
[tex]\begin{gathered} \text{Volume}=\pi\cdot4^2\cdot6 \\ \text{Volume}=\pi\cdot16\cdot6=96\pi \end{gathered}[/tex]The volume is not 64pi, so this statement is false (NO).
I need help with this question please. This is non graded.
To determine the factor of the given polynomial, first, we rewrite it as follows:
[tex](16x^2+4x)+(-20x-5).[/tex]Now, notice that:
[tex]\begin{gathered} 16x^2+4x=4x(4x^+1), \\ -20x-5=-5(4x+1). \end{gathered}[/tex]Factoring out the 4x+1, we get:
[tex](16x^2+4x)+(-20x-5)=(4x-5)(4x+1).[/tex]Answer: [tex](4x+1).[/tex]1-38. Given f(x)=2x-7, complete parts (a) through (C). HomeworkHelpa. Compute f(0).b. Solve f(x)=0.c. What do the answers to parts (a) and (b) tell you about the graph of y=f(x)?
the Part a. Compute f(0). We have to evaluate the function for x = 0.
[tex]f(0)\text{ = 2(0) - 7 = 0 - 7 = -7}[/tex]Therefore, f(0) = -7.
Part b. Solve f(x) = 0.
[tex]f(x)=\text{ 2x - 7 }=\text{ 0}[/tex]To solve the equation 2x - 7 = 0, we have to add 7 to both sides of the equation, and then dividing the equation by 2:
[tex]2x\text{ - 7 + 7 = 7 }[/tex][tex]2x\text{ = 7 }\Rightarrow x\text{ = }\frac{7}{2}[/tex]So, x = 7/2.
Part c.
Part a tells us that the graph of the function is evaluated in zero, the value for the function is -7. When x = 0, the value for y = -7. This is the intercept of the linear function.
Part b tells us that when y = 0, the value for x = 7/2.
The line passes through points (0, -7) and (7/2, 0). These are the points on y-axis and x-axis, respectively.
Simplify using exponential notation. 5a^6 x 7a^7
Given:
[tex]5a^6\times7a^7[/tex]Let's simplify using exponential notation.
To simplify, multiply the the base, then use law of indicies to add the exponents
We have:
[tex]undefined[/tex]Practice questions to use for study guide/ my notes please help want to Ace test!
We have, From the graph it can be seen that when x tends to zero on the right, y
I need to solve this problem and name the concepts used in the problem
In a pie chart, the sum of the angles for each variable or item is 360 degrees. also, the total percentage is 100
Looking at each flavor,
27% chose Glazier freeze, = 27/100 * 360 = 97.2 degrees
25% chose Fierce grape = 25/100 * 360 = 90 degrees
15.5% chose Extreme Citrico = 15.5/100 * 360 = 55.8 degrees
13.5% chose Cool Blue = 13.5/100 * 360 = 48.6 degrees
11.5% chose Lemon ice = 11.5/100 * 360 = 41.4
We want to determine the degrees for others
Therefore,
97.2 + 90 + 55.8 + 48.6 + 41.4 + others = 360
333 + others = 360
others = 360 - 333
others = 27 degrees
The correct option is C
The concept used is converting the given percentages to degrees and equation them to 360 degrees
100% is equivalent to 360 degrees
Dr. Wells saw 960 patients last year. This year, the number of patients he saw was 25%higher. How many patients did Dr. Wells see this year?
.Since the old number of patients is 960
Since it is increasing by 25%, then
We will find the amount of 25% of 960, then add it to 960
[tex]\begin{gathered} I=\frac{25}{100}\times960 \\ I=240 \end{gathered}[/tex]Add it to 960 to find the new number of patients
[tex]\begin{gathered} N=960+240 \\ N=1200 \end{gathered}[/tex]Dr Wells saw 1200 patients
Sketch one cycle of the graph of each function 16. y= -2 sin 8x
Answer:
• Amplitude = 2
,• Period = π/4
Explanation:
Given the function:
[tex]y=-2\sin(8x)[/tex]In order to sketch the graph of y, we need to find its amplitude and period.
Comparing the function with the general sine function:
[tex]y=a\sin(bx+c)+d[/tex]We have that:
[tex]\begin{gathered} Amplitude=|a|=|-2|=2 \\ Period=\frac{2\pi}{|b|}=\frac{2\pi}{8}=\frac{1}{4}\pi \end{gathered}[/tex]Next, using these values, we sketch one cycle of the graph below:
Find from first principles the derivative of f:x maps to (x+2)all squared
Given:
[tex]f(x)=(x+2)^2[/tex]Required:
To find the first principles
Explanation:
First principle,
[tex]\lim_{h\to0}\frac{f(x+h)-f(x)}{h}[/tex][tex]=\lim_{h\to0}\frac{(x+h+2)^2-(x+2)^2}{h}[/tex][tex]=\lim_{h\to0}\frac{x^2+(h+2)^2+2x(h+2)-x^2-4-4x}{h}[/tex][tex]=\lim_{h\to0}\frac{h^2+4+4h+2xh+4x-4-4x}{h}[/tex][tex]\begin{gathered} =\lim_{h\to0}\frac{h^2+4h+2xh}{h} \\ \\ =\lim_{h\to0}\frac{h(h+4+2x)}{h} \\ \\ =\lim_{h\to0}(h+4+2x) \\ =2x+4 \end{gathered}[/tex]Final Answer:
[tex]2x+4[/tex]At a particular restaurant, each mozzarella stick has 100 calories and each slider has
200 calories. A combination meal with mozzarella sticks and sliders is shown to have
1500 total calories and 9 more mozzarella sticks than sliders. Determine the number
of mozzarella sticks in the combination meal and the number of sliders in the
combination meal.
There are
mozzarella sticks and
sliders in the combination meal.
The 1,500 calories in the combination meal and the amount of calories per mozzarella stick and per each slider gives an equation with the following solution;
There are 11 mozzarella sticks and 2 sliders in the combination meal.
What is a mathematical equation?An equation in mathematics is a statement that two mathematical expressions are equal.
The number of calories in each mozzarella stick = 100
Number of calories in each slider = 200
Number of calories in the combination meal = 1,500
Number of mozzarella sticks in the combination meal = 9 + The number of sliders
Let s represent the number of sliders in the combination meal, we have;
Number of mozzarella in the combination meal = s + 9
The equation that gives the amount of calories in the meal is therefore;
200·s + 100·(s + 9) = 1,500
200·s + 100·s + 900 = 1,500
300·s = 1,500 - 900 = 600
s = 600 ÷ 300 = 2
The number of sliders in the combination meal, s = 2
The number of mozzarella in the meal = 2 + 9 = 11
Learn more about writing equations in algebra here;
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A SHADED REGION IS DESCRIBED BY THE FOLLOWING INEQUALITIES:X> OR EQUAL 0 , Y> OR EQUAL 0 , X+2Y< OR EQUAL TO 4 , X-Y< OR EQUAL 1 WHAT ARE ITS CORNER POINTS?
Its corner points (0, 0), (2, 1), (0, 2), (1, 0)
From the question, we have
All the points should be positive, as we can see after carefully examining the equation.
There are two approaches to approach this problem. The first is to solve the equations, create a graph, and make a decision.
The alternative is to just plug the points into the equations and check to see if the conditions are met; this method is quicker for tests with MCQs.
As a result, option B is correct.
Inequalities:
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. The different inequality symbols, properties, and methods for resolving linear inequalities in one variable and two variables will all be covered in this article along with examples.
Complete question: A shaded region is described by the following inequalities: x 20, y 20, x + 2y s 4, X y sl. What are its corner points? a. (0, 0), (1, 0), (0; 1), (0, 2) b. (0, 0), (2, 1), (0, 2), (1, 0) c. (0, 0), (4, 0), (0, 2), (2, 1) d. (0, 0), (1, 0), (2, 1), (0, 1) e. (0, -1), (2, 1), (0, 2)
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When 27 is subtracted from the square of anumber, the result is 6 times the number. Findthe negative solution.
Given: A statement, "When 27 is subtracted from the square of a
number, the result is 6 times the number."
Required: To determine the number.
Explanation: Let the number be x. Then according to the question-
[tex]x^2-27=6x[/tex]Rearranging the equation as -
[tex]x^2-6x-27=0[/tex]The quadratic equation can be simplified as follows-
[tex]\begin{gathered} x^2-9x+3x-27=0 \\ x(x-9)+3(x-9)=0 \\ (x+3)(x-9)=0 \\ x=-3\text{ or }x=9 \end{gathered}[/tex]Final Answer: The negative solution is-
[tex]x=-3[/tex]Please see the picture below. Indeed help with parts of the question
Given
[tex]\frac{(x-4)^2}{4}-\frac{y^2}{9}=1[/tex]Find
Values of a and b for this conic section
Explanation
As we know the standard equation for conic section is given by
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]where (h , k) be the vertex
vertices (h+a , k) and (h-a , k)
given equation can be rewrite as
[tex]\frac{(x-4)^2}{2^2}-\frac{y^2}{3^2}=1[/tex]on comparing , we get
a = 2 and b = 3
Final Answer
Therefore , the value of a = 2 and b = 3
need answer with steps[tex]( - 3 - 5i) + (4 - 2i)[/tex][tex](7 + 9i) + ( - 5i)[/tex]
We are given the following complex numbers
[tex](-3-5i)+(4-2i)[/tex]To perform the addition of the complex numbers, simply add the like terms together.
[tex](-3-5i)+(4-2i)=(-3+4)+(-5i-2i)=(1-7i)[/tex]Similarly,
[tex](7+9i)+(-5i)=\mleft(7\mright)+\mleft(9i-5i\mright)=(7+4i)_{}[/tex]Therefore, the result of the complex addition is
[tex]\begin{gathered} 19.\: (1-7i) \\ 20.\: (7+4i) \end{gathered}[/tex]A kitty in a tuxedo walks into a bank deposit of $4000 in an investment account. the account earns 8% interest, compounded monthly. after 10 years how much money will the fancy kitty have?
Answer:
The amount of money Kitty would have is;
[tex]\text{ \$}8,878.56[/tex]Explanation:
Given that Kitty invested $4000 into an account that earns 8% interest compounded monthly for 10 years;
[tex]\begin{gathered} \text{ Principal P = \$4000} \\ \text{ Rate r = 8\% = 0.08} \\ \text{ Time t =10 years} \\ \text{ number of times compounded per time n = 12} \end{gathered}[/tex]Applying the formula for compound interest;
[tex]F=P(1+\frac{r}{n})^{nt}[/tex]Substituting the given values;
[tex]\begin{gathered} F=4000(1+\frac{0.08}{12})^{12(10)} \\ F=4000(1+\frac{0.08}{12})^{120} \\ F=4000(2.2194) \\ F=\text{ \$}8,878.56 \end{gathered}[/tex]Therefore, the amount of money Kitty would have is;
[tex]\text{ \$}8,878.56[/tex]Please Help me solve I know I am supposed to use the quadratic formula But I’m still not getting the right answers
To find the maximum profit we need to maximize the function.
First we need to find the critical points, to do this we need to find the derivative of the function:
[tex]\begin{gathered} \frac{dy}{dx}=\frac{d}{dx}(-2x^2+105x-773) \\ =-4x+105 \end{gathered}[/tex]now we equate it to zero and solve for x:
[tex]\begin{gathered} -4x+105=0 \\ 4x=105 \\ x=\frac{105}{4} \end{gathered}[/tex]hence the critical point of the function is x=105/4.
The next step is to determine if the critical point is a maximum or a minimum, to do this we find the second derivative:
[tex]\begin{gathered} \frac{d^2y}{dx^2}=\frac{d}{dx}(-4x+105) \\ =-4 \end{gathered}[/tex]Since the second derivative is negative for all values of x (and specially for x=105/4) we conclude that the critical point is a maximum.
Hence the function has a maximum at x=105/4. To find the value of the maximum we plug the value of x to find y:
[tex]\begin{gathered} y=-2(\frac{105}{4})^2+105(\frac{105}{4})-773 \\ y=605.125 \end{gathered}[/tex]Therefore the maximum profit is $605
What is the equation of the line that passes through the given points (2,3) and (2,5)
Solution:
The equation of a line that passes through two points is expressed as
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ where \\ (x_1,y_1)\text{ and} \\ (x_2,y_2)\text{ are the coordinates of the points } \\ through\text{ which the line passes} \end{gathered}[/tex]Given that the line passes through the points (2,3) and (2, 5), this implies that
[tex]\begin{gathered} x_1=2 \\ y_1=3 \\ x_2=2 \\ y_2=5 \end{gathered}[/tex]By substitution, we have
[tex]\begin{gathered} y-3=\frac{5-3}{2-2}(x-2) \\ \Rightarrow y-3=\frac{2}{0}(x-2) \\ multiply\text{ through by zero} \\ 0(y-3)=2(x-2) \\ \Rightarrow0=2x-4 \\ add\text{ 4 to both sides} \\ 0+4=2x-4+4 \\ \Rightarrow4=2x \\ divide\text{ both sides by the coefficient of x, which is 2} \\ \frac{4}{2}=\frac{2x}{2} \\ \Rightarrow x=2 \\ \end{gathered}[/tex]Hence, the equation of the line that passes through the given points (2,3) and (2,5) is
[tex]x=2[/tex]Solve (x+2<5) u ( x-7>6)
You have the following opeartion between sets:
(x + 2 < 5) U (x - 7 > 6)
In order to find the solution to the previoues expression, you first find the solutionof each inequality, just as follow:
x + 2 < 5 subtract 2 both sides
x < 5 - 2
x < 3
The solution interval is (-∞,3)
x - 7 > - 6 add 7 both sides
x > - 6 + 7
x > 1
The solution interval is (1, ∞)
Then, you have:
(-∞,3) U (1,∞)
which is the same that:
{x| x<3 or x>1}
Write an equation to find the necessary score on the final exam for a student to earn an A (90%) in the class.
For the given table:
We will find the necessary score on the final exam for a student to earn an A (90%) in the class.
so,
The equation will be:
[tex]92\cdot(0.2)+95\cdot(0.3)+88\cdot(0.2)+x\cdot(0.3)=90[/tex]now, solve the equation to find x:
[tex]\begin{gathered} 64.5+0.3x=90 \\ 0.3x=90-64.5 \\ 0.3x=25.5 \\ x=\frac{25.5}{0.3} \\ \\ x=85 \end{gathered}[/tex]So, the answer will be:
The student needs a score of 85% on the final exam to earn a 90%
In scientific notation, what is the product of 5.78 x 10^5 and 8.04 x 10^-2
The given numbers are
5.78 x 10^5 and 8.04 x 10^-2
We would simplify the exponents by applying one of the laws of exponents which states that
a^b x a^c = a^(b + c)
By applying this law, the expression becomes
5.78 x 8.04 x 10^(5 + - 2)
46.4712 x 10^(5 - 2)
46.4712 x 10^3
The product in scientific notation is
46.4712 x 10^3
5.Find the measures of themissing side of the righttriangle usingPythagorean Theoremequation.106K
Pythagoras Theorem:
In a right angle triangle, the sum of square of base and perpendicular is equal to the square of Hypotenuse .
Hypotenuse² = Perpendicular² + base²
In the given figure, we have:
Base = k
Hypotenuse = 10
Perpendicular = 6
Substitute the valus and solve for k,
[tex]\begin{gathered} \text{Hypotenuse}^2=Perpendicular^2+Base^2 \\ 10^2=6^2+k^2 \\ 100=36+k^2 \\ k^2=100-36 \\ k^2=64 \\ k=\sqrt[]{64} \\ k=8 \\ \text{Base, k = 8} \end{gathered}[/tex]The missing side is 8
Answer: 8
A fence is purchased and constructed as shown. There are 250 feet of fence used for the chorale. Determine the values for x and y that will maximize the area. Round your answers to the nearest tenth if needed. Type the value for the x dimension in the first blank (you do not need to type x = , but label your answer). Type the value for y in the second blank (you do not need to type y =, but label your answer).
2x + 3y = 250
y = (250 - 2x)/3 (1)
S = x * y
= (-2/3x + 250/3)*x
= -2/3(x - 125/2)^2 + 125^2/6
x = 125/2
Replacing the value of x in (1)
y = 125/3
show that the triangles are similar by measuring the lengths of their sides and comparing the ratios of their corresponding sides
ANSWER
EXPLANATION
The ratio between corresponding sides of similar triangles is constant - in other words, the ratio between each pair of corresponding sides gives the same value.
As shown in the questions, the ratios between corresponding sides are,
[tex]\begin{gathered} \frac{DE}{AB}=\frac{3}{2}=1.5 \\ \frac{DF}{AC}=\frac{1.5}{1}=1.5 \\ \frac{EF}{BC}=\frac{2.4}{1.6}=1.5 \end{gathered}[/tex]Since the three ratios between corresponding sides are the same, 1.5, the triangles are similar.
Nintendo previously projected that it would sell 19 million units of the console for the year ending in March. If it ended up selling 26.5 million after several upward versions to the forecast. How many selling off were their estimate