The surface area S of sphere is given by
[tex]S=4\pi r^2[/tex]In our case
[tex]S=324\pi[/tex]Then, we have
[tex]324\pi=4\pi r^2[/tex]By moving 4Pi to the left hand side, we have
[tex]\frac{324\pi}{4\pi}=r^2[/tex]We can cancel Pi out in numerator and denominator, then ,we get
[tex]\begin{gathered} \frac{324}{4}=r^2 \\ 81=r^2 \\ \text{therefore} \\ r=\sqrt[]{81} \end{gathered}[/tex]and the answer is r= 9 kilometers, that is, the radius is 9 km
Solve algebraicallyX+4=-2
SOLUTION:
Step 1:
In this question, we are given the following:
Solve algebraically
[tex]x\text{ + 4 = -2}[/tex]Step 2:
The details of the solutio are as follows:
[tex]\begin{gathered} x\text{ + 4 = -2} \\ collecting\text{ like terms, we have that:} \\ x\text{ = - 2 - 4} \\ x\text{ = - 6} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]x\text{ = - 6}[/tex]Are the triangles similar?.. help me with this problem! Thank you :)
In similar triangles, corresponding sides are always in the same ratio.
Find the ratio of corresponding sides in the given triangles, to identify corresponding sides the greater side in one triangle is corresponding with the greater side of the other triangle.
[tex]\begin{gathered} \frac{QR}{TU}=\frac{28}{8}=\frac{7}{2} \\ \\ \frac{RP}{US}=\frac{21}{6}=\frac{7}{2} \\ \\ \frac{PQ}{ST}=\frac{14}{4}=\frac{7}{2} \end{gathered}[/tex]As the ratio of corresponding sides is the same, triangle PQR is similar to triangle STUFor similar triangles the corresponding angles are equal.
Corresponding angles for triangles PQR and STU:
P and S
Q and T
R and U
[tex]\begin{gathered} \angle P=\angle S=70º \\ \angle Q=\angle T \\ \angle R=\angle U=46º \end{gathered}[/tex]The sum of the interior angles in any triangle is always 180º:
[tex]\begin{gathered} \angle P+\angle Q+\angle R=180º \\ \angle Q=180º-\angle P-\angle R \\ \angle Q=180º-70º-46º \\ \angle Q=64º \\ \\ \angle Q=\angle T=64º \end{gathered}[/tex]Lucy's mom started a 529 college fund for her when she was 4 years old inorder to save money for college. She put $9,000 into an account that earnsa 5% compounded annually. Lucy wants to know how much money she willhave when she is 18. Look at her work below.Is her solution correct? If not, describe the mistake(s) in her work.y = 900011+ 9(e)y = 9000 (1.5) 18y = 8133010 26.92
Explanation:
P = $9000
i = 5% 0.05
We nee to apply the formula:
[tex]\begin{gathered} \frac{FV}{(i+i)^n}=\text{ PV} \\ FV\text{ = }PV\text{ }(1+i)^n \\ FV=9000(1+0.05)^{18}\text{ } \end{gathered}[/tex][tex]undefined[/tex]graph the line y=-4x
Solution
x=-2 , y = 8
x=-1, y= 4
x=0, y=0
x= 1, y= -4
x= 2, y=-8
In the picture shown b and F are midpoints solve for x
ANSWER:
x = 10
EXPLANATION:
Given:
Recall that the Midpoint Theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side.
We can go ahead and solve for x as seen below;
[tex]\begin{gathered} BF=\frac{1}{2}*AE \\ \\ 23=\frac{1}{2}*(5x-4) \\ \\ 23*2=5x-4 \\ \\ 46=5x-4 \\ \\ 5x=46+4 \\ \\ 5x=50 \\ \\ x=\frac{50}{5} \\ \\ x=10 \end{gathered}[/tex]Therefore, the value of x is 10
Which of the following options results in a graph that shows exponentialdecay?5 pointsO f(x) 0.4(0.2)^xf(x) = 4(4)^xf(x) = 0.7(1.98)^xOf(x) = 5(1+.1)^x
Answer
Option A is the answer.
f(x) = 0.4(0.2)ˣ
The value carrying the power of x is less than 1, so, this expression represents exponential decay.
Explanation
The key to knowing which expression is represents an exponential decay or exponential growth is the value of the number carrying the power of x.
If that number is greater than 1, then it represents exponential growth.
But, if that number is lesser than 1 (but greater than 0), then it represents exponential decay.
(2)ˣ represents exponential growth.
(0.5)ˣ represents exponetial decay.
f(x) = 0.4(0.2)ˣ
The value carrying the power of x is less than 1, so, this expression represents exponential decay.
f(x) = 4(4)ˣ
The value carrying the power of x is greater than 1, so, this expression represents exponential growth.
f(x) = 0.7(1.98)ˣ
The value carrying the power of x is greater than 1, so, this expression represents exponential growth.
f(x) = 5(1 + .1)ˣ
The value carrying the power of x is greater than 1, so, this expression represents exponential growth.
Hope this Helps!!!
A group of five will rent a car for a spring break trip and divide the costs associated with the car among them. The rental costs $480 for the week. Insurance is an additional $175, they estimated they’ll use 120 gallons of gas, and gas costs around $2.80 per gallon. Estimate how much each friend will pay for the cost associated with the car
Solution:
Given:
[tex]\begin{gathered} car\text{ rental cost}=\text{ \$}480 \\ Insurance=\text{ \$}175 \\ Gas=120\times2.80=\text{ \$}336 \end{gathered}[/tex]Thus, the total cost associated with the car is;
[tex]480+175+336=\text{ \$}991[/tex]Each friend will pay;
[tex]\frac{991}{5}=\text{ \$}198.20[/tex]Therefore, each friend will pay $198.20
Classify the polynomial as constant, linear, quadratic, cubic, or quartic, anddetermine the leading term, the leading coefficient, and the degree of thepolynomial.g(x) = - 2x^4 - 6
Given:
[tex]g(x)=-2x^4-6[/tex]To classify: The polynomial name, degree, leading term, and leading coefficient
Explanation:
Since the degree of the polynomial is the highest or the greatest power of a variable in a polynomial equation.
Here, 4 is the greatest power of a variable x.
So, the degree of the polynomial is 4.
As we know,
The leading term is the term containing the highest power of the variable.
So, the leading term is,
[tex]-2x^4[/tex]Since the coefficient of the term of the highest degree in a given polynomial is -2.
So, the leading coefficient is -2.
Since the degree of the polynomial is 4.
So, the given polynomial is a quartic polynomial.
Final answer: Option C. Quartic polynomial.
6. Write the equation of the line below. 1-10 7 6 5 3 2 का 2 3 4 5 6 7 8 9 10
Let the two points in the graph are (0,7) and (1,3).
Then, the slope of the line is,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{3-7}{1-0} \\ m=-4 \end{gathered}[/tex]Use the equation y=y1=m(x-x1) to find the equation of the line.
[tex]\begin{gathered} y-7=-4(x-0)\text{.} \\ y-7=-4x \\ y=-4x+7 \end{gathered}[/tex]Therefore, the equation of the line is y=-4x+7.
Use the given row transformation to transform the following matrix.
The 2 x 2 matrix is given
[tex]\begin{bmatrix}{2} & {8} \\ {10} & {7} \\ {} & {}\end{bmatrix}[/tex]The row transformation given is:
[tex]\frac{1}{2}R_1[/tex]this means we take half of all the elements of Row 1
The process is shown below:
[tex]\begin{gathered} \begin{bmatrix}{\frac{1}{2}\times2} & {\frac{1}{2}\times8} & \\ {10} & {7} & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{1} & {4} & \\ {10} & {7} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]Hence, the final matrix Row 2 is same as previous matrix, but Row 1 is half of the elements of previous matrix.
Answer:
[tex]\begin{bmatrix}{1} & {4} & \\ {10} & {7} & {} \\ {} & {} & {}\end{bmatrix}[/tex]11/8 Percent / Valuehow can I find it please help me understand it
20 candies represent 3%
Explanation:Sincne 15% = 100
Let x% = 20, then
100x = 20 * 15
100x = 300
x = 300/100 = 3
Therefore, 20 candies represent 3%
what is the factor of the expression of 39-13 using gcf
We are asked to find out the GCF of the given expression
[tex]39-13[/tex]GCF (greatest common factor) is the greatest common factor between two or more numbers.
To find the GCF, let us first list out the common factors of both numbers
Factors of 13 = 1, 13
Factors of 39 = 1, 3, 13, 39
Now which factor is common to both and is greatest?
Yes, it is 13
Therefore, the GCF of the given expression is 13
[tex]39-13=13(3-1)[/tex]Evaluate the function.
f(x)=(x−7)2+4
for f(−6)
f(−6)
Answer:
F(-6) = 173
Hope this helps!
The steps to derive the quadratic formula are shown below:Step 1 ax2 + bx + c = 0Step 2 ax2 + bx = - CStep 3Provide the next step to derive the quadratic formula.
Here, we are given the first two steps to derive the quadratic formula:
Step 1: ax² + bx + c = 0
Step 2: ax² + bx = -c
Let's determine the next step to derive the quadratic formula.
To provide the next step, let's divide all terms by a:
We have:
Step 3.
[tex]\begin{gathered} \frac{ax^2}{a}+\frac{bx}{a}=-\frac{c}{a} \\ \\ \frac{x^2}{a}+\frac{b}{a}x=-\frac{c}{a} \end{gathered}[/tex]Therefore, the next step to derive the quadratic formula is:
[tex]\frac{x^2}{a}+\frac{b}{a}x=-\frac{c}{a}[/tex]ANSWER:
[tex]\frac{x^2^{}}{a}+\frac{b}{a}x=-\frac{c}{a}[/tex]log 2-log 5 can also be written as ?.
The formula for difference of two logarthimic terms are,
[tex]\log a-\log b=\log (\frac{a}{b})[/tex]Determine the expression for log 2 -log 5.
[tex]\log 2-\log 5=\log (\frac{2}{5})[/tex]Answer: log(2/5)
if you travel 35 miles per hour for 4.5 hours hovú far will you travle
We need to multiply 4.5 hours by 35 miles per hour, as follows:
[tex]4.5\text{ hours}\cdot35\frac{miles}{hour}=157.5\text{ miles}[/tex]You will travel 157.5 miles
Help with Algebra 2 question.14) An angle is in standard position and is terminal side pauses through point (-2,5), find sec.
Given:
An angle is in standard position and is terminal side passes through the point (-2,5),
Required:
To find the value of the secant function.
Explanation:
The value of the secant function is given as:
[tex]sec\theta=\frac{r}{x}[/tex]Where
[tex]r=\sqrt{x^2+y^2}[/tex]Consider x= -2 and y = 5
Now calculate the value of r by using the formula:
[tex]\begin{gathered} r=\sqrt{(-2)^2+(5)^2} \\ r=\sqrt{4+25} \\ r=\sqrt{29} \end{gathered}[/tex]Thus the required value is:
[tex]sec\theta=\frac{\sqrt{29}}{-2}[/tex]Final Answer:
[tex]sec\theta=-\frac{\sqrt{29}}{2}[/tex]Five hundred students in your school took the SAT test. Assuming that a normal curve existed for your school, how many of those students scored within 2 standard deviations of the mean? (Give the percent and the number.)
In order to find the percentage of students within 2 standard deviations, let's look at the z-table for the percentages when z = -2 and z = 2.
From the z-table, we have that the percentage for z = -2 is 0.0228 and for z = 2 is 0.9772.
The percentage between z = -2 and z = 2 is given by:
[tex]0.9772-0.0228=0.9544[/tex]Therefore the percentage is 95.44%.
Now, calculating the number of students within this percentage, we have:
[tex]500\cdot0.9544=477.2[/tex]Rounding to the nearest whole, we have 477 students.
If D and R denote the degree and radian measure of an angle, then prove that D/180=R/pie
Given: D and R denote the degree and radian measure of an angle
To Determine: The prove that D/180=R/pie
Solution
Please note that
[tex]180^0=\pi radians[/tex]So
[tex]1^0=\frac{\pi}{180^}radian[/tex]Then
[tex]\begin{gathered} D^0=D\times\frac{\pi}{180}radian \\ D^0=\frac{D\pi}{180}radians \end{gathered}[/tex]Therefore
[tex]\frac{D\pi}{180}=R[/tex]Let us divide both sides by pie
[tex]\frac{D\pi}{180}\div\pi=R\div\pi[/tex][tex]\begin{gathered} \frac{D\pi}{180}\times\frac{1}{\pi}=R\times\frac{1}{\pi} \\ \frac{D}{180}=\frac{R}{\pi} \end{gathered}[/tex]Hence, the above help to prove that D/180 = R/pie
Segment XY measures 5cm. How long is the image of XY after a dilation with: A scale factor of a?
The image of the XY will be 5 times larger than the after dilation.
What is dilation?
resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.
The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.
Segment XY mesured as 5cm
It will undergo dilation.
If X(0,0) and Y(x,y)
XY = √x²+y²
The factor we need to multiply, a
X'(0,0), Y'(ax,ay)
So the X'Y'=√a²x²+a²y²
X'Y'=a√x²+y²
X'Y'=aXY = 5a
Hence the image of the XY will be 5 times larger than the after dilation.
Learn more about dilation, by the following link
https://brainly.com/question/20137507
#SPJ1
all of the Patron in part shade and rewrite (x × y)^nas a product of two single powers
we have
(2*3)^5
we know that
(2*3)^5=(2^5)(3^5)
Rewrite each term as product of two single powers
so
(2^5)(3^5)=(2^3)(2^2)(3^3)(3^2)
Part c
we have
10^2/10^0
when divide, subtract the exponents
so
10^(2-0)
10^2
another way
Any number elevated to zero is equal to 1
so
10^0=1
substitute
10^2/1=10^2
Part f
we have
(2/3)^5
we know that
(2/3)^5=2^5/3^5
Can you please write the basic equation forConstant parent functionInverse sine parent functionInverse cosine parent function Inverse tangent parent function
• In order to understand this, we need to know that an inverse trigonometric function “undo” what the original trigonometric function
• e.g Trig function : inverse of trig. function .
Explanations :(a) Inverse sine parent function:The inverse y = six x parent function will be
[tex]\begin{gathered} y=sinx^{-1}\text{ ; meaning } \\ x\text{ = sin y } \end{gathered}[/tex]• y = sinx ^-1 , has domain at [-1;1] and range at (-/2; /2)
(b)Inverse cosine parent functionthe inverse of y = cos x parent function will be :
[tex]\begin{gathered} y=cosx^{-1};\text{ meaning } \\ x\text{ = cos y } \end{gathered}[/tex]• y = cosx^-1 , has domain at [-1;1] and range at (0;)
(c)Inverse tangent parent function
The inverse of y = tan x parent function will be :
[tex]\begin{gathered} y=tanx^{-1\text{ }},\text{ meaning } \\ x\text{ = tan y } \end{gathered}[/tex]• y = tanx^-1 has domain at (-∞;∞) and range at (- /2 ; /2)
see the graphs below that shows the asympotes of the trigonometric function.Parabola in the form x^2=4pyIdentify Vertex, value of P, focus, and focal diameter.Identify endpoints of latus rectumWrite equations for the directrix and axis of symmetry X^2= -12y
Answer:
(a)
• The vertex of the parabola, (h,k)=(0,0)
,• The value of p = -3
• The focus is at (0,-3).
,• The focal diameter is 12
(b)The endpoints of latus rectum are (-1/12, -1/6) and (-1/12, 1/6).
(c)See Graph below
(d)
• I. The equation for the directrix is y=3.
,• II. The axis of symmetry is at x=0.
Explanation:
Given the equation of the parabola:
[tex]x^2=-12y[/tex]For an up-facing parabola with vertex at (h, k) and a focal length Ipl, the standard equation is:
[tex](x-h)^2=4p(y-k)[/tex]Rewrite the equation in the given format:
[tex]\begin{gathered} (x-0)^2=4(-3)(y-0) \\ \implies(h,k)=(0,0) \\ \implies p=-3 \end{gathered}[/tex]• The vertex of the parabola, (h,k)=(0,0)
,• The value of p = -3
The focus is calculated using the formula:
[tex]\begin{gathered} (h,k+p) \\ \implies Focus=(0,0-3)=(0-3) \end{gathered}[/tex]• The focus is at (0,-3).
Focal Diameter
Comparing the given equation with x²=4py, we have:
[tex]\begin{gathered} x^2=4ay \\ x^2=-12y \\ 4a=-12 \\ \implies a=-3 \\ \text{ Focal Diameter =4\mid a\mid=4\mid3\mid=12} \end{gathered}[/tex]The focal diameter is 12
Part B (The endpoints of the latus rectum).
First, rewrite the equation in the standard form:
[tex]\begin{gathered} y=-\frac{1}{12}x^2 \\ \implies a=-\frac{1}{12} \end{gathered}[/tex]The endpoints are:
[tex]\begin{gathered} (a,2a)=(-\frac{1}{12},-\frac{1}{6}) \\ (a,-2a)=(-\frac{1}{12},\frac{1}{6}) \end{gathered}[/tex]The endpoints of latus rectum are (-1/12, -1/6) and (-1/12, 1/6).
Part C
The graph of the parabola is given below:
Part D
I. The equation for the directrix is of the form y=k-p.
[tex]\begin{gathered} y=0-(-3) \\ y=3 \end{gathered}[/tex]The equation for the directrix is y=3.
II. The axis of symmetry is the x-value at the vertex.
The axis of symmetry is at x=0.
write the thirteen million, three hundred two thousand, fifty in expanded form.
Let's begin by listing out the information given to us:
[tex]13,302,050=13,000,000+300,000+2,000+0+50[/tex]thirteen million = 13,000,000
three hundred and two thousands = 300,000 + 2,000
fifty = 50
13,302,050 = 13,000,000 + 300,000 + 2,000 + 50
I need help please, it’s my math assignment also can you add simple answers
a)
Step 1:
Draw the scatter diagram from the table
x represents days and y represent set up time
Step 2:
b)
Draw the scatter diagram
Step 3:
c)
Pick two points from the graph to find the linear equation
Points (2 , 16 ) and (6, 11)
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \frac{y\text{ - 16}}{x\text{ - 2}}\text{ = }\frac{11\text{ - 16}}{6\text{ - 2}} \\ \frac{\text{y - 16}}{x\text{ - 2}}\text{ = }\frac{-5}{4} \\ \frac{y-16}{x-2}\text{ = -1.25} \\ y\text{ - 16 = -1.25x + 2.5} \\ y\text{ = -1}.25x\text{ + 18.5} \end{gathered}[/tex]The equation is y = -1.25x + 18.5
6. F(x) is the function that determines the absolute value of the cube of the input. Part 1. Evaluate: F(5) Part 2. Evaluate: F(-7) Part 3. Determine: F(5). F(-7) Or is the function defined by the following graph. The graph window is:
We have that F(x) is the function that determines the absolute value of the cube of the input, then we have that f(x) is:
[tex]f(x)=\lvert x^3\rvert[/tex]Part 1. Evaluate F(5): x = 5
[tex]f(5)=\lvert5^3\rvert=\lvert125\rvert=125[/tex]Part 2. Evaluate F(-7): x = -7
[tex]f(-7)=\lvert-7^3\rvert=\lvert-343\rvert=343[/tex]Part 3. Evaluate F(5)xF(-7)
[tex]f(5)\cdot f(-7)=125\cdot343=42875[/tex]The cost of any soda from a soda machine is $0.50. The graph representing this relationship is shown below. Soda Machine Total Cost 3 2 Number & Sodas 6 6 What is the slope of the line that models this relationship?
Answer:
The slope of the line is;
[tex]m=\frac{1}{2}=0.5[/tex]Explanation:
Given the attached graph.
Recall that the formula for calculating the slope m of a line is;
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]From the graph, let us select two points on the line;
We have;
[tex]\begin{gathered} (2,1)\text{ } \\ \text{and} \\ (4,2) \end{gathered}[/tex]The slope can then be calculated by substituting this points into the formula;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{4-2} \\ m=\frac{1}{2}=0.5 \end{gathered}[/tex]Therefore, the slope of the line is;
[tex]m=\frac{1}{2}=0.5[/tex]while shopping at a 30% off sale, Robin was told that the sale price would saver her $6 on her purchase. Since the original price tag was missing, she had to calculate the price. what was the original price.
To do this, let x be the original price. Since the sale price would save you $ 6 on your purchase and this equates to 30% off, then using the rule of three you can find the original price, like this
[tex]\begin{gathered} \text{ \$6}\Rightarrow30\text{ \%} \\ x\Rightarrow100\text{ \%} \\ x=\frac{100\text{ \%}\cdot\text{ \$6}}{30\text{ \%}} \\ x=\text{ \$}\frac{600}{30} \\ x=\text{ \$20} \end{gathered}[/tex]Therefore, the original price was $20.
Verifying you have
[tex]\text{ \$20}\ast30\text{ \%= \$20}\cdot\frac{30}{100}=\text{ \$20}\cdot0.3=\text{ \$6}[/tex]Which was the $6 that Robin saved on his purchase.
For each equation chose the statement that describes its solution
GIven:
The equations
[tex]\begin{gathered} -6(u+1)+8u=2(u-3) \\ 2(v+1)+7=3(v-2)+2v \end{gathered}[/tex]Required:
Find the correct solution.
Explanation:
The equations,
[tex]\begin{gathered} -6(u+1)+8u=2(u-3) \\ -6u-6+8u=2u-6 \\ -6u+8u=2u \\ -8u+8u=0 \\ 0=0 \\ Hence,\text{ true for all }u. \end{gathered}[/tex]And
[tex]\begin{gathered} 2(v+1)+7=3(v-2)+2v \\ 2v+2+7=3v-6+2v \\ 9=3v-6 \\ 3v=15 \\ v=5 \end{gathered}[/tex]Answer:
[tex]\text{ In equation 1, equation is true for all }u\text{ and equation 2 is true for }v=5.[/tex]Fill in the blanks (B1, B2, B3) in the equation based on the graph.(a-B1)2 + (y-B2)² = (B3)²8182=83=Blank 1:
Given: a circle is given with center (3,-3) and equation
[tex](x-B_1)^2+(y-B_2)^2=(B_3)^2[/tex]Find:
[tex]B_{1,\text{ }}B_{2,}B_3[/tex]Explanation: the general equation of the circle with center (a,b) and radius r is
[tex](x-a)^2+(y-b)^2=r^2[/tex]in the given figure the center of the circle is at (3,-3)
so the equatio of the circle becomes
[tex](x-3)^2+(y+3)^2=(3)^2[/tex]on comparing eith the given equation we get
[tex]B_1=3,\text{ B}_2=-3\text{ and B}_3=3[/tex]