if its diameter is 9, that means its radius is half that, or 4.5.
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4.5 \end{cases}\implies \begin{array}{llll} SA=4\pi (4.5)^2\implies SA=81\pi \\\\\\ SA\approx 254.47~in^2 \end{array}[/tex]
The surface area of the basketball with diameter of 9 in will be 254.34 in².
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given that, a basketball has a diameter of 9 inches we need to find its surface area,
Since, the basketball is in the shape of the sphere and the surface area of the sphere = 4π×radius²
Therefore, the surface area of the basketball =
= 4×3.14×(9/2)²
= 4×3.14×4.5×4.5
= 254.34 in²
Hence the surface area of the basketball with diameter of 9 in will be 254.34 in².
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Solve: log8 (x - 4) = 2
Answer:
x = 68
Explanation:
⇒ log₈(x - 4) = 2
apply log rules: logₐN = x then N = aˣ
⇒ (x - 4) = 8²
simplify
⇒ x - 4 = 64
add 4 on both sides
⇒ x = 64 + 4
add the integers
⇒ x = 68
Answer:
x = 68
Step-by-step explanation:
Given equation:
[tex] \rm log_{8}(x - 4) = 2[/tex]
To Find:
Value of x
Solution:
Rewrite the equation in exponential form which is equivalent to b^y = x.
[tex] \implies {8}^{2} = x - 4[/tex]
Now find the value of x.
[tex] \implies \:64 = x - 4[/tex]
Transpose 4 from RHS to LHS, make sure to change its sign from (-) to (+) .
[tex] \implies \: 64 + 4 = x[/tex]
Overturn the equation
[tex] \implies \: x = 68[/tex]
Thus, value of x is 68.
A patch of farmland is currently worth $78,125. The expected increase in its market value can be modeled by the function below, where t is the time in years. How many years will it take for the farmland's market value to reach $125,000?
The number of the years to take for the farmland's market value to reach $125,000 will be 19 years.
The missing function will be given below.
[tex]\rm p(t) = 78,125\ e^{0.025t}[/tex]
What is an exponent?Let a is the base and x is the power of the exponent function and b is the y-intercept. The exponent is given as
y = aˣ
A patch of farmland is currently worth $78,125. The expected increase in its market value can be modeled by the function below.
[tex]\rm p(t) = 78,125\ e^{0.025t}[/tex]
Then the number of the years to take for the farmland's market value to reach $125,000 will be
[tex]\rm 78,125 \ e^{0.025t} = 125,000\\\\e^{0.025t} = 1.6[/tex]
Then take log on both sides, then we have
0.025t lne = ln 1.6
0.025t = 0.47
t = 18.8
t = 19 years
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What is the scale factor if a 8 in. by 10 in. photograph is enlarged to a poster that is 6 ft. by 7.5 ft.?
9
1/9
1.33
1/1.33
Solve for x: 2 over 3 (x − 4) = 2x.
[tex] \frac{2}{3} (x - 4) = 2x \\ \frac{2}{3} x - \frac{8}{3} = 2x \\ \frac{2}{3} x - 2x = \frac{8}{3} \\ \frac{2}{3} x - \frac{6}{3} x = \frac{8}{3} \\ \frac{ - 4}{3} x = \frac{8}{3} \\ - 12x = 24 \\ x = \frac{24}{ - 12} \\ x = - 2[/tex]
What is the equation of the parabola with focus (3,0) and directrix x= -3?
Check the picture below, so the parabola looks more or less like so, with a "p" distance of 3 and the vertex at the origin, keeping in mind the vertex is half-way between the focus point and the directrix.
[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=0\\ k=0\\ p=3 \end{cases}\implies 4(3)(x-0)~~ = ~~(y-0)^2\implies 12x=y^2\implies x=\cfrac{1}{12}y^2[/tex]
If f(x) = 2x² + 1, what is f(x) when x = 3?
0 1
07
O 13
19
Answer:
f(x)=19
Step-by-step explanation:
2(3)²+1
2(9)+1
19
The value of function at x = 3 is,
⇒ f (3) = 19
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = 2x² + 1
Now, Substitute x = 3 in above function,
⇒ f (x) = 2x² + 1
⇒ f (3) = 2 × 3² + 1
⇒ f (3) = 19
Thus, The value of function at x = 3 is,
⇒ f (3) = 19
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If you multiply four negative numbers, what is the sign of the product?
If you multiply five negative numbers, what is the sign of the product?
Based on the answers to these questions and the product rules, write a general rule for the sign of the product based on the number of
negative numbers in the expression.
Answer:
positive
Step-by-step explanation:
(-a) (-a) (-a) (-a) = a
(-a)(-a) = a
a (-a) = -a
-a (-a) = a --> positive sign
If you multiply four negative numbers, what is the sign of the product?
You can test this with numbers, the easiest with -1:
(-1)(-1)(-1)(-1) = (1)(-1)(-1) = (-1)(-1) = 1
General:
(-a)(-b)(-c)(-d) = abcd
The sign of the product of four negative numbers is positive.
If you multiply five negative numbers, what is the sign of the product?
Testing with -1:
(-1)(-1)(-1)(-1)(-1) = (1)(-1)(-1)(-1) = (-1)(-1)(-1) = (1)(-1) -1
General:
(-a)(-b)(-c)(-d)(-e) = -abcde
The sign of the product of five negative numbers is negative.
General rule: The product of an even number of negative numbers is positive. The product of an odd number of negative numbers is negative.
Consider the diagram and proof by contradiction.
Given: △ABC with ∠B ≅ ∠C
Prove: AB ≅ AC
Triangle A B C is shown. Angles A B C and B C A are congruent.
Which would prove that AB ≅ AC?
converse of the isosceles triangle theorem
substitution
definition of congruency
converse of the triangle parts relationship theor
The correct statement is that it is done by the converse of the triangle parts relationship theorem. The correct answer is option D.
The complete answer is given below and the figure is attached with the answer.
Consider the diagram and proof by contradiction.
Given: △ABC with ∠B ≅ ∠C
Prove: AB ≅ AC
It is given that ∠B ≅ ∠C. Assume AB and AC are not congruent. If AB > AC, then m∠C > m∠B by ________. If AC > AB, then m∠B > m∠C for the same reason. However, using the given statement and the definition of congruency, we know that m∠B = m∠C. Therefore, AB = AC and AB ≅ AC.
What is the missing reason in the proof?
the converse of the triangle parts relationship theorem
substitution
definition of congruency
the converse of the isosceles triangle theorem
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
Isosceles triangle two sides of the triangle are equal and their opposite angles too.
Given
△ABC with ∠B ≅ ∠C
Prove that
AB ≅ AC
How to give a conclusion?
From the definition of the Isosceles triangle, it is proved that if ∠B ≅ ∠C Then AB ≅ AC. We know that if the length o the side increases then the opposite angle decreases. It is done by the converse of the triangle parts relationship theorem.
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Find the inverse equations for f and g.f(x)=3x+5g(x)=x2−6Explain your process. Then write about the relationship between the functions and their inverses. Does the domain and range of all functions and inverses follow a pattern?View keyboard shortcuts
[tex]g = \frac{x}{5} - \frac{6}{5x} - \frac{3}{5} [/tex]
Step-by-step explanation:
[tex]3 + 5g = \frac{ {x}^{2} - 6 }{x} \\ 5g = x - \frac{6}{x} - 3 \\ g = x - \frac{ \frac{6}{x} - 3}{5} \\ g = \frac{x}{5} - \frac{ \frac{6}{x} }{5} - \frac{3}{5} [/tex]
Solve for x. Round to nearest tenth
SOMEONE PLEASE HELP ME WITH THIS ILL GIVE YOU BRAINLIST ANSWER
Image above
Answer: the answer to your question is 42.2
Step-by-step explanation:25 x 25 + 34 X 34 = c^2
Answer:
20
Step-by-step explanation:
34 + 90 = 124
180-124 = 56 degrees
c = 56 degrees
to find x we need to use sin
sin = SOH (Sin = opposite/hypotenuse
sin 56 = x/25
sin 56 x 25 = x
x = 20.72593931
x = 20 (rounded to the nearest 10th)
hope this helped :)
SOMEONE PLEASE HELP ASAPP PLEASEEE
ILL GIVE BRAINLIEST AND POINTS!!!
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The shaded region in the graph represents the solutions of this system of linear inequalities:
y ___
4x + ___
y ≤ ___
x + ___
Note: Use the symbols <, >, <=, and >= for inequality signs.
Based on the calculations, the solutions of this system of linear inequalities are equal to:
y < 4x + 5y ≤ 2x + 3 What is an inequality?An inequality simply refers to a mathematical relation that's used to compare two (2) or more integers (variables) in an equation based on any of the following:
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).In order to determine the solutions of this system of linear inequalities, we would find the slope of each line.
For line A, we have:
Slope, m = (11 - 3)/(4 - 0) = 8/4
Slope, m = 2.
Mathematically, the standard equation of a line is given by y = mx + b.
y = 2x + 3
y ≤ 2x + 3.
For line B, the slope is equal to 4. Also, the y-intercept from the graph is equal to 5.
Therefore, the standard equation of a line is given by:
y = 4x + 5
y < 4x + 5
In conclusion, the solutions of this system of linear inequalities are equal to:
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Solve for x. Each figure is a trapezoid. # 18 has a midsegment.
13)
Question 13
[tex]{12x+2}=\frac{18+34}{2}\\\\12x+2=26\\\\12x=24\\\\x=\boxed{2}[/tex]
Question 14
Base angles of an isosceles trapezoid are congruent, so:
[tex]73x+1=74\\73x=73\\x=\boxed{1}[/tex]
the normal yearly growth of a plant is 60 inches, the normal Grove was 10 inches more than twice the amount of last year, what was the growth of the plant last year
The growth of the plant is 25 inches last year.
Explanation:
Suppose the growth of the plant last year was y.
From the given situation, the normal growth was 10 inches more than twice the amount of last year.
So the equation will be
= 10 + 2y = 60
= 2y = 50
= y= 25 inches.
Therefore , the growth of the plant was 25 inches last year.
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What is the volume, in cubic centimeters, of a right square pyramid
with base edges that are 64 cm long and a slant height of 40 cm
The volume of the right squared pyramid with the given base edges and slant height is 32768 cubic centimeters.
What is the volume of right square pyramid?The volume of a square pyramid is expressed as;
V = (1/3)a²h
Where a is the base length and h is the height of the pyramid
Given that;
Base edges of the square base a = 64cmSlant height s = 40cmHeight of the pyramid h = ?Volume = ?First, we determine the height of the pyramid using Pythagorean theorem.
c² = a² + b²
c = s = 40cma = half of the base length = a/2 = 64cm/2 = 32cmb = h(40cm) = (32cm)² + h²
1600cm² = 1024cm² + h²
h² = 1600cm² - 1024cm²
h² = 576cm²
h = √576cm²
h = 24cm
Now, we calculate the volume of the right square pyramid;
V = (1/3)a²h
V = (1/3) × (64cm)² × 24cm
V = (1/3) × 409664cm² × 24cm
V = 32768cm³
Therefore, the volume of the right squared pyramid with the given base edges and slant height is 32768 cubic centimeters.
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Aleka earns her regular pay or $14 per hour for up to 40 hours of work per week. For each hour over 40 hours of work per week, Aleka earns 14 times her regular pay. How much does Aleka earn in a week in which she works 48 hours?
a. $576
b. $672
c. $728
d. $744
e. 1008
If Aleka earns her regular pay or $14 per hour for up to 40 hours of work per week. For each hour over 40 hours of work per week, Aleka earns 14 times her regular pay. Then $728 she earns in a week in which she works 48 hours
What is equation?Two or more expressions with an equal sign is called as Equation.
Given that Aleka earns her regular pay or $14 per hour for up to 40 hours of work per week.
14x40=560
For each hour over 40 hours of work per week, Aleka earns 14 times her regular pay.
Fourteen plus seven equal to twenty one
14+7=21
Twenty one times of eight is equal to one hundred sixty eight
21x8=168
Now let us add five hundred sixty and one hundred sixty eight
560+168=728
Hence she earns $728 in a week in which she works 48 hours.
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Recipe 3:
For every 2 tablespoons of chocolate
use 5 ounces of milk.
5 ounces
then for 5 tablespoons you use 12.5 ounces of milk
A plane, initially traveling 150 mi/hr due
east, suddenly enters a region where the
wind is blowing at 50 mi/hr 38° north of
east.
What is the resultant speed of the plane?
[?] mi/hr
Round to the nearest hundredth.
The resultant speed of the plane is 100 mi/hr along the northeast direction.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken
First, we need to find our coordinate axis, we will define the x-axis as the east and the y-axis as the north.
We are given that the plane travels at 150 mi/hr at 100° east of north, notice that if we measure from the positive x-axis, this is equivalent to an angle of -10°.
Then the x-component of the velocity ;
150mi/hr x cos(-10°) = 147.7 mi/hr
The y-component of the velocity;
150mi/hr x sin(-10°) = -26 mi/hr.
So, the vector is:
V = 147.7 mi/hr, -26 mi/hr
Now we know that the wind blowing at 50mi/hr at southwest, exactly southwest would be at an angle of 225°,
Thus, the components of the vector are:
x-component: 50mi/hr x cos(225°) = -35.4 mi/hr
y-component: 50mi/hr x sin(225°) = -35.4 mi/hr.
So, the vector is:
W = < -35.4 mi/hr, -35.4 mi/hr>
The sum of the vectors gives the total velocity of the plane in the wind is;
V + W = < 147.7 mi/hr -35.4 mi/hr , -26 mi/hr -35.4 mi/hr >
V + W = <112.3 mi/hr, -61.4 mi/hr>
The direction of a vector is;
θ = Atan(y/x)
Then, in this case the direction of the plane is:
θ = Atan(-61.4 mi/hr/112.3 mi/hr) = -28.7°
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help me with this question
Answer:
a) 150
b) 2650
Step-by-step explanation:
6% of 2500 is 150
150 + 2500 = 2650
The rectangle is 93 m long and 70 m wide what is the area if you use 3.14 for pie
Answer:
i might just be mind numb right now but you don't use pie on rectangles for area
Area = 6510
Step-by-step explanation:
A = L x W
A = 93 x 70
A = 6510
work out the value of T using the formula T=3x^{2]p-2p when p= -1?
The solution of the equation when p = -1 is [tex]T=3x^{-2}[/tex]
How to determine the value of the equation?The equation is given as:
[tex]T=3x^{2p}[/tex]
The value of p is -1.
So, we have:
[tex]T=3x^{2*-1}[/tex]
Evaluate the product
[tex]T=3x^{-2}[/tex]
Hence, the solution of the equation when p = -1 is [tex]T=3x^{-2}[/tex]
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By selling an article for $250, a man makes a profit of 25%. what was the cost price of the article.
Answer:
200 dollars
Step-by-step explanation:
Let's say p equals the cost price of the article. Since the man made 25% profit, that means he got 100% of what he originally paid plus another 25% of what he originally paid. In other words, he sold the article for 125% of the original price. Converting that to a decimal we get:
250=p*1.25
Some simple division gets us a cost price of 200 dollars.
3x=3(x-1)
Step by step ( 20 pts )
Answer:
No solution.
Step-by-step explanation:
[tex]\textbf{Given that,}\\\\~~~~~~~~3x = 3(x-1)\\\\\\\implies \dfrac{3x}3 = \dfrac{3(x-1)}{3}~~~~~~~~~~~~~~~~~;\textbf{Dividing both sides by 3}\\\\\\\implies x = x-1\\\\\\\implies x-x = x-1-x~~~~~~~~~~~~~;\textbf{Subtracting}~ x ~ \textbf{from both sides} \\\\\\\implies 0 = -1\\\\\\\textbf{Which is not true, so there are no solutions.}[/tex]
Expand (x^22-3x^5 + x^-2 - 7) * (5x^4).
Can someone please explain in detail how to remove the parentheses step by step?
Let's see
[tex]\\ \rm\Rrightarrow (x^{22}-3x^5+x^{-2}-7)5x^4[/tex]
Use distributive law
a(b+c)=ab+ac[tex]\\ \rm\Rrightarrow 5x^{22+4}-15x^{5+4}+5x^{-2+4}-35x^4[/tex]
[tex]\\ \rm\Rrightarrow 5x^{26}-15x^9+5x^2-35x^4[/tex]
Answer:
[tex]5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]
Step-by-explanation:
Given expression:
[tex](x^{22}-3x^5 + x^{-2} - 7) (5x^4)[/tex]
Use the Distributive Property Law (b ± c)a = ab ± ac
to remove the parentheses:
[tex]\implies 5x^4 \cdot x^{22}-5x^4 \cdot 3x^5+5x^4 \cdot x^{-2}-5x^4 \cdot 7[/tex]
Simplify by multiplying the coefficients of each term:
[tex]\implies 5x^4 \cdot x^{22}-15x^4 \cdot x^5+5x^4 \cdot x^{-2}-35x^4[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]:
[tex]\implies 5x^{4+22}-15x^{4+5}+5x^{4-2}-35x^4[/tex]
[tex]\implies 5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]
I need help on this 1 question. Thank you.
Answer: 5/6, 3/4, 4/12
Step-by-step explanation:
Convert them all into a common denominator, 12.
5/6=10/12, 3/4=9/12, and 4/12 stays the same. 10>9, and 9>4
When a die is rolled, what is the theoretical probability that number five will be rolled?
Answer: 1/6
Step-by-step explanation: there is 6 faces on a standard die, one of them is 5.
the product of two numbers is 16/9. if one of the numbers is 5/2, find the other number
Answer:
[tex] \frac{32}{45} [/tex]
Step-by-step explanation:
if the multiplication of two numbers is 16)9, and one of the numbers is 5/2. then the other number can be found by dividing the number from the product to get the other number.
The surface area of Earth is about 196.9 million square miles. The land area is about 57.5 million square miles and the rest is water. What is the probability that a meteorite will hit water?
Brian usually brushes his teeth in the morning, but 10% of the time he forgets. What is the probability that he will forget to brush his teeth three days in a row (Assume that forgetting one day does not influence any other day.)
Using it's concept, it is found that there is a 0.001 = 0.1% probability that he will forget to brush his teeth three days in a row.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, for each day, there is a 0.1 probability that he forgers to brush his teeth, and days are independent, hence for 3 consecutive days the probability is given by:
p = (0.1)³ = 0.001.
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Can someone help me with this question
The probability that the selected element is a member of A n B is 2/9
How to complete the number line?The elements of the set are given as:
E = {1,2,3,4,5,6,7,8,9}
A = {1,3,4,8,9}
B = {2,4,9}
Using the above parameters, we have:
A only = {1, 3, 8}
B only = {2}
A and B = {4, 9}
None = {5,6,7}
The above dataset is the represented using the attached Venn diagram
How to determine the probability?
In (a), we have:
A and B = {4, 9}
E = {1,2,3,4,5,6,7,8,9}
The probability is then calculated as:
P(A n B) = n(A n B)/n(E)
This gives
P(A n B) = 2/9
Hence, the probability is 2/9
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