Equations that have the roots of x = 2 and x = -2 are:
(A) x² - 4 = 0(D) 4x² = 16What exactly are equations?In mathematical formulas, the equals sign is used to indicate that two expressions are equal. A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation. Like 3x + 5 = 15, for instance. Equations come in a wide variety of forms, including linear, quadratic, cubic, and others. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.So, equations true for x = 2 and x = -2 are:
Roots of x = -2:
x² = 4x² - 4 = 0Roots of x = 2:
x² = 4Now, multiply 4 on both sides as follows:
4x² = 16Therefore, equations that have the roots of x = 2 and x = -2 are:
(A) x² - 4 = 0(D) 4x² = 16Know more about equations here:
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Correct question:
Which equations are true for x = –2 and x = 2? Select two options
A. x2 – 4 = 0
B. x2 = –4 3
C. x2 + 12 = 0
D. 4x2 = 16
E. 2(x – 2)2 = 0
which statement is true if the graph of the linear function passes through the points (-1, -6)and (5,6) function first if needed
The correct option is C
Explanation:We check through each of the options to see if they are true
Option A is not true
The slope of the graph is as follows:
(6 - (-6))/((5 - (-1))
= (6 + 6)/(5 + 1)
= 12/6
= 2
Option B is not true
The zero of the graph is the point on the x-axis where y = 0, this is x = 2
Option C is true
The x-intercept is the point where the graph crosses the x-axis. This is (2, 0)
Option D is not true
Question Solve: s + 159 = 25.
We have to solve for s:
[tex]\begin{gathered} s+159=25 \\ s+159-159=25-159 \\ s=-134 \end{gathered}[/tex]Answer: s = -134
An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in tall, and the initial velocity of the ball is 30 ft per sec. The height s of the ball in feet isgiven by the equation s= -2.7t^2 + 30t + 6.5, where t is the number of seconds after the ball was thrown. Complete parts a and b.a. After how many seconds is the ball 18 ft above the moon's surface?After ____ seconds the ball will be 18 ft above the moon's surface.(Round to the nearest hundredth as needed. Use a comma to separate answers as needed.)
In order to find when the ball will be 18 ft above the moon's surface, we need to equal the expression to 18
[tex]18=-2.7t^2+30t+6.5[/tex]then, solve the associated quadratic expression
[tex]\begin{gathered} 0=-2.7t^2+30t+6.5-18 \\ 0=-2.7t^2+30-11.5 \\ using\text{ }the\text{ }quadratic\text{ }formula \\ x=\frac{-30\pm\sqrt{(30)^2-4\ast(-2.7)\ast(-11.5)}}{2\ast(-2.7)} \\ x_1\cong0.40 \\ x_2\cong10.72 \end{gathered}[/tex]answer:
after 0.40 seconds the ball will be 18 ft above the surface
let f(x) = 10x-10. Find the value of (f o f^-1) (-10)a)0b)1c)10d)-10
Solution
We are given the following expression to evaluate:
[tex]\begin{gathered} f(x)=10x-10 \\ \\ \text{ Find:} \\ (f\mathrm{}f^{-1})(-10) \end{gathered}[/tex]- In order to solve this question, we should apply the following theorem:
[tex]f(f^{-1})(x)=x_{}[/tex]- Thus, in order to solve the question, we simply substitute x = -10. This is done below:
[tex]\begin{gathered} f(f^{-1})(x)=x \\ \text{put }x=-10 \\ \\ f(f^{-1})(-10)=-10\text{ (OPTION D)} \end{gathered}[/tex]Final Answer
The answer is:
[tex]f(f^{-1})(-10)=-10\text{ (OPTION D)}[/tex]Re-write the equation in slope-intercept form: 3x - 2y =6
To write it in the slope intercept form we have to slove the equation to y:
[tex]\begin{gathered} 3x-2y=6\rightarrow \\ 2y=3x-6 \\ y=\frac{3}{2}x-3 \end{gathered}[/tex]differentiate y=4x√3x²-8x
Okay, here we have this:
Considering the provided function, we are going to perform the requested operation, so we obtain the following:
[tex]\begin{gathered} y=4x\sqrt{3}x^2-8x \\ \\ y=4\sqrt{3}x^3-8x \\ \\ \frac{dy}{dx}=\frac{d}{dx}(4\sqrt{3}x^3)-\frac{d}{dx}(8x) \\ \\ \frac{dy}{dx}=12\sqrt{3}x^2-8 \end{gathered}[/tex]Finally we obtain that dy/dx is equal to: 12sqrt(3)x^2-8
find the length between the big circle and small circle.
First, we will calculate the hypotenuse of the first triangle
[tex]\begin{gathered} \cos 51=\frac{11}{h} \\ h=\frac{11}{\cos51} \\ h=17.48 \\ \end{gathered}[/tex]Now let's calculate the angle a
[tex]\begin{gathered} a=180-64-54 \\ a=65 \end{gathered}[/tex]Total result
T = 17.48+12.204+2.62+4.72
T = 37.024
The answer would be 37.024
for all triangles input data entered: side a, b and angle γ.
Calculation of the third side c of the triangle using a Law of Cosines
[tex]c^2=a^2+b^2-2ab\cos \gamma[/tex]From the graph identify the zeros of the quadratic function
The zeros of the function are the points where it crosses the x axis:
Answer: (1,0) and (3,0)
In a direct variation, y = -18 when x = -3. Write a direct variation equation that shows therelationship between x and y.Write your answer as an equation with y first, followed by an equals sign.Submit
The direct variation between y and x has the following
Thursday: Word Problems 1 The plant growth is proportional to time. When Tia bought the plant, it measured 2 cm. It measured 2.5 cm exactly one week later. If the plant continues to grow at this rate, determine the function that represents the plant's growth.
We have the next informtion
initial measure = 2 cm
after
Suppose that the functions g and h are defined for all real numbers x as follows. 9g(x) = 2x ^ 2 h(x) = x - 3Write the expressions for (hg)(x) and (h + g)(x) and evaluate (h - g)(- 3) .
Given
[tex]\begin{gathered} g(x)=2x^2 \\ h(x)=x-3 \end{gathered}[/tex]To write the expressions of
[tex]\begin{gathered} (h\cdot g)(x) \\ (h+g)(x) \end{gathered}[/tex]And to evaluate,
[tex](h-g)(-3)[/tex]Explanation:
It is given that,
[tex]\begin{gathered} g(x)=2x^2 \\ h(x)=x-3 \end{gathered}[/tex]Then,
[tex]\begin{gathered} (h\cdot g)(x)=h(x)\cdot g(x) \\ =\left(x-3\right)\cdot\left(2x^2\right) \\ =2x^3-6x^2 \end{gathered}[/tex]Also,
[tex]\begin{gathered} (h+g)(x)=h(x)+g(x) \\ =(x-3)+2x^2 \\ =2x^2+x-3 \end{gathered}[/tex]And,
[tex]\begin{gathered} (h-g)(-3)=h(-3)-g(-3) \\ =(-3-3)-2(-3)^2 \\ =-6-(2\times9) \\ =-6-18 \\ =-24 \end{gathered}[/tex]Hence, the answer is,
[tex]\begin{gathered} (h\cdot g)(x)=2x^3-6x^2 \\ (h+g)(x)=2x^2+x-3 \\ (h-g)(-3)=-24 \end{gathered}[/tex]Help Please!!use the drawing to form the correct answers on the graph complete the function table for the given domain and plot the points on the graph
The Solution:
The given function is
[tex]f(x)=-x^2+2x+5[/tex]Step 1:
We shall complete the table.
Explanation of how the table was completed:
Substituting each value of x to obtain the corresponding value of y.
[tex]\begin{gathered} f(-1)=-(-1)^2+2(-1)+5=-1-2+5=2 \\ f(0)=-(0)^2+2(0)+5=5 \\ f(1)=-(1)^2+2(1)+5=-1+2+5=6 \\ f(2)=-(2)^2+2(2)+5=-4+4+5=5 \\ f(3)=-(3)^2+2(3)+5=-9+6+5=2 \end{gathered}[/tex]3. A savings account is started with an initial deposit of $1500.The account earns 1.8% interest compounded annually.(a) Write an equation to represent the amount of money inthe account as a function of time in years. 5 Points(B) how much more interest would be earned if the initial deposit is allowed to earn interest for 20 years vs 10 years
a) We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
where
A = the total amount in the account at the end of t years
r = interest rate
n = the periodic interval at which it was compounded
P = the principal or initial amount deposited
From the information given,
P = 1500
r = 1.8/100 = 0.018
n = 1 because it is compounded once in a year
Thus, an equation to represent the amount of money in the account as a function of time in years ia
A = 1500(1 + 0.018/1)^1 * t
A = 1500(1.018)^t
B) If t = 20, then
A = 1500(1.018)^20
A = 2143.12
The interest earned would be the total amount - the principal
Interest earned after 20 years = 2143.12 - 1500 = 643.12
If t = 10, then
A = 1500(1.018)^10
A = 1792.95
Interest earned after 10 years = 1792.95 - 1500 = 292.95
Thus, the difference in interest earned between both years is
643.12 - 292.95
= $350.17
46. Identify the center and radius of a circle given the equation is (x - 2)^2 + (y + 4)^2= 36
Answer: Center: (2, –4); Radius: 6.
Explanation
The equation of a circle in standard form is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) is the center and r is the radius. Thus, in our given equation:
[tex]\left(x-2\right)^2+(y+4)^2=36[/tex]• h = 2
,• k = –4 (it is negative as negative sign times negative sign equals positive sign)
,• r² = 36
Therefore, the center is (2, –4) and the radius is:
[tex]r^2=36[/tex][tex]\sqrt{r^2}=\sqrt{36}[/tex][tex]r=6[/tex]Triangle ABC has coordinates A(-6,2), B(-3,6), and C(5,0). Find the perimeter of the triangle. Express your answer in simplest radical form.
we must know the measure of each side, for this we must calculate the distance between points
the formula is
[tex]d=\sqrt[]{(x1-x2)^2+(y1-y2)^2}[/tex]AB
[tex]\begin{gathered} \sqrt[]{(-6-(-3))^2+(2-6)^2} \\ \sqrt[]{25} \\ AB=5 \end{gathered}[/tex]AC
[tex]\begin{gathered} \sqrt[]{(-6-5)^2+(2-0)^2} \\ \sqrt[]{125} \\ AC=5\sqrt[]{5} \end{gathered}[/tex]BC
[tex]\begin{gathered} \sqrt[]{(-3-5)^2+(6-0)^2} \\ \\ \sqrt[]{100} \\ BC=10 \end{gathered}[/tex]now add all sides to find the perimeter
[tex]\begin{gathered} 5+5\sqrt[]{5}+10 \\ \end{gathered}[/tex]the perimeter is
[tex]15+5\sqrt[]{5}\approx26.18[/tex]If each side of an equilateral triangle is 2 inches long, then what is the area of the triangle?
Solution:
The image below represents the equilateral triangle of 2 inches long
From the triangle above, the given values include
[tex]\begin{gathered} a=2in \\ b=2in \\ c=2in \end{gathered}[/tex]Concept:
To calculate the area of the triangle, we will use Heron's formula below
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where,s = semi perimter} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]Step 1:
Calculate the semi perimeter s
[tex]\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{2in+2in+2in}{2} \\ s=\frac{6in}{2} \\ s=3in \end{gathered}[/tex]Step 2:
Substitute the value of s,a,b,c in the heron's formula
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A=\sqrt[]{3(3-2)(3-2)(3-2)} \\ A=\sqrt[]{3\times1\times1\times1} \\ A=\sqrt[]{3} \\ A=1.73in^2 \end{gathered}[/tex]Hence,
The area of the triangle = 1.73 squared inches
Is the LCD Going to be 5 • 7 •z = 35 ?
To add these fractions, we can do the following steps.
Step 1: Simplify each fraction.
[tex]\frac{25}{5y}=\frac{5\cdot5}{5y}=\frac{5}{y}[/tex][tex]\frac{64}{8y}=\frac{8\cdot8}{8y}=\frac{8}{y}[/tex]Step 2: We add the numerators since the fractions have the same denominator.
[tex]\frac{5}{y}+\frac{8}{y}=\frac{5+8}{y}=\frac{13}{y}[/tex]Therefore, the result of adding the fractions is 13/y.
6:4= :2 I dont know what that is
Answer: x = 3
Let the missing number be x
6 : 4 = x : 2
ratio is the same as fraction
6/4 = x/2
Step2 : cross multiply
x * 4 = 6 * 2
4x = 12
Divide both sides by 4
4x/4 = 12/4
x = 3
Therefore, the missing number is 3
I need help please Question 9 Help for my homework
Given the figure of a triangular prism.
We will find the amount of wood to make the wooden play block
So, we will find the volume of the given block
As shown: the triangular side has a base of 4 cm and a height of 6 cm
The area of the triangular base =
[tex]\frac{1}{2}*4*6=12\text{ }cm^2[/tex]the length between the triangular sides = 12 cm
So, the volume = base area * length =
[tex]12*12=144\text{ }cm^3[/tex]So, the answer will be the first option 144 cm³
7. Let f(x) = 3x and g(x) = (x + 2)^2. Find the value of (f og)(-5)A.135B. -27 C. 169. D.27.
f(x)= 3x
g(x)= (x+2)²
What is the sum of the first 19 terms of the sequence 9,2,-5,-12....2SEE ANSWERS
ANSWER
-1026
EXPLANATION
The sum of the first n terms in an arithmetic sequence is,
[tex]S_n=\frac{n(a_1+a_n)}{2}[/tex]As we can see, we have to find the nth term of the sequence,
[tex]a_n=a_1+(n-1)d[/tex]In this case, the first term is 9 and the common difference is -7 - note that each term is the previous one minus 7. So the formula for the nth term is,
[tex]a_n=9-7(n-1)[/tex]We have to find the 19th term,
[tex]a_{19}=9-7(19-1)=9-7\cdot18=9-126=-117[/tex]So the sum of the first 19 terms is,
[tex]S_{19}=\frac{19\cdot(9+(-117))}{2}=\frac{19\cdot(9-117)}{2}=\frac{19\cdot(-108)}{2}=\frac{-2052}{2}=-1026[/tex]Hence, the sum of the first 19 terms of the given sequence is -1026.
Hannah reads at a constant rate of 3 pages every 8 minutes. Write an equation that shows the relationship between p, the number of pages she reads, and m, the number of minutes she spends reading. Report a probler
Since we have that Hannah reads 3 pages every 8 minutes, we will construct the function by first knowing how many pages she reads in 1 minute, that is:
She reads 3/8 pages each minute, then we will construct the function as follows:
[tex]p=\frac{3}{8}m[/tex]Where p is the number of pages and m is the number of minutes that she reads. We can see that this describes is if we solve for 1 minute and 8 minutes. If we solve for 1 minute, we get she read 3/8 pages and if we replace 8 minutes, we will get that she reads 3 pages.
if a=5x-2 and b=5x-22 , what is the value of x ?
Trigonometry
We are given the following condition:
sin (a) = cos (b)
Since both angles are acute, the following relationship must apply:
a = 90° - b
Both angles must be complementary
Substituting the values for each angle:
a = 5x - 2
b = 5x - 22
We have:
5x - 2 = 90 - (5x - 22)
Removing brackets:
5x - 2 = 90 - 5x + 22
Adding 5x:
5x - 2 + 5x = 90 + 22
Adding 2:
5x + 5x = 90 + 22 + 2
Simplifying:
10x = 114
Dividing by 10:
x = 114/10
x = 11.4
Correct choice: C)
Which is not a true equation?O A. -12 · 4 = -3O B. 100 = -25 = -4O C. -72 = -9 = 80 D. –32 - 0 = 32
In the last option:
-32 / 0 = 32
But we can not divide by 0, it is undefined in mathematics, so this is not a true equation.
Answer: Option D
guys please help
60% of = 45
Answer:
Step-by-step explanation:
Answer: 75
Use the equation is/of = %/100
Plug in the numbers to get 45/x = 60/100
Cross Multiply and you get 60x = 4500
Divide both sides by 60
X = 75.
Create an expression that can be used to find the value of x
There are two possible expressions that can help to calculate "x"
First
[tex]\begin{gathered} \text{ cos 28 = }\frac{42}{x} \\ \text{ } \end{gathered}[/tex]Second
[tex]\text{ sec 28 = }\frac{x}{42}[/tex]Both are possible to find "x".
Counting in bases less than ten
Answer:
Step-by-step explanation:
84649347
l will send u the pic
as they are in the same line, the measures of angles AOD and angle DOC they measure 180°
Suppose f(x)=5x+6 . Describe how the graph of g compares with the graph of f . g(x)=f(x+5)
g(x) = f(x) + 5 relates to f(x) by shifting f(x) 5 units up.
What is a function?The link between two independent variables and one dependent variable is described by a mathematical expression, rule, or law (the dependent variable).
An example of a rule is a function, which produces one output for a single input. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. We can infer that y is a function of x because x is the input value.
The function is given as:
f(x) = 5x+6
g(x) = f(x)+5
this gives,
g(x) = 5x+6+5
g(x) = 5x+11
g(x) = f(x) + 5 relates to f(x) by shifting f(x) 5 units up.
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Two investments are made summing up to 8,800. For a certain year, theseinvestments yield P1,326 in simple interest. Part of the investment is allotted for14% and part for 16%. Find the amount invested at each rate
Given:
a.) Two investments are made summing up to 8,800.
b.) For a certain year, these investments yield P1,326 in simple interest.
c.) Part of the investment is allotted for 14% and part for 16%.
Recall: The simple interest formula.
[tex]\text{ I = Prt}[/tex]Where,
I = interest
P = principal amount
r = interest rate
t = time (in year)
Step 1:
P = 8,800
But it's been made into two investments.
Let,
A = investment 1
B = investment 2
We get,
A + B = 8,800 = P (Equation 1)
Step 2:
Part of the investment is allotted for 14% and part for 16%.
Thus,
For investment 1:
Ia = Art = A(14/100)(1) = 0.14A
For investment 2:
Ib = Brt = B(16/100)(1) = 0.16B
We get,
0.14A + 0.16B = 1,326 (Equation 2)
Step 3:
Substitute Equation 1 to Equation 2.
A + B = 8,800
A = 8,800 - B
0.14A + 0.16B = 1,326
0.14(8,800 - B) + 0.16B = 1,326
1,232 - 0.14B + 0.16B = 1,326
0.02B = 1,326 - 1,232
0.02B = 94
0.02B/0.02 = 94/0.02
B = 4,700
Let's now find A.
A + B = 8,800
A + 4,700 = 8,800
A = 8,800 - 4,700
A = 4,100
In Summary:
The amount invested at 14% is 4,100
The amount invested at 16% is 4,700