Answer:
72/24. Solution: Rewriting input as fractions if necessary: 3/2, 3/8, 5/6, 3/1. For the denominators (2, 8, 6, 1) the least common multiple ( LCM) is 24. LCM (2, 8, 6, 1) Therefore, the least common denominator ( LCD) is 24. Calculations to rewrite the original inputs as equivalent fractions with the LCD: 1 1/2.
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
The ball will be 213ft above the ground after 2.4 secs and after 5.6 seconds.
What is quadratic equation?A second-order polynomial equation in one variable with the notation x = ax2 + bx + c = 0 and a 0 is known as a quadratic equation. It is a second-order polynomial problem, which guarantees that it has at least one solution according to the fundamental theorem of algebra.
Calculations = 213 solve for t
213 = -16t² + 128t
in standard form
16t² - 128t + 213 = 0
using shridharacharya formula
t = 2.4 , 5.6
so the ball will be 213ft above the ground after 2.4 secs and after 5.6 seconds
learn more about quadratic equation here :
brainly.com/question/17177510
#SPJ1
If you make $75.00 a week at your job and want to save $250.00 over 3 months, saving an equal amount each week, how much spending money will you have each week?
The amount of spending money you will have each week is $54.17 .
How to find the spending money available?You make $75.00 a week at your job and want to save $250.00 over 3 months, saving an equal amount each week.
The amount of spending money available each week can be calculated as follows:
Therefore,
3 months = 12 weeks
let
x = amount saved every week.
Therefore,
12x = 250
x = 250 / 12
x = 20.83 dollars
Hence,
Amount of spending money each week = 75 - 20.83
Amount of spending money each week = $54.17
learn more on savings here:https://brainly.com/question/2871328
#SPJ1
show your stepsWhat is the solution of the equation?SEE IMAGE
Given the equation
[tex]\begin{gathered} 3\text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ + 3 = 27} \\ \end{gathered}[/tex]Subtract 3 from both sides
[tex]\begin{gathered} 3\text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ + 3-3 = 27}-3 \\ \\ 3\text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ = }24 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ = }\frac{24}{3} \\ \text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ = 8} \\ \end{gathered}[/tex]Raise both sides to power 5 to remove the 5th root on the left hand side
[tex]\begin{gathered} \text{ (}\sqrt[5]{(x+2)^3\text{ }})^5=8^5 \\ \\ (x+2)^3=(8^{})^5 \\ (x+2)^3=\text{ 32768} \\ \end{gathered}[/tex]Take the cube root of both sides
[tex]\begin{gathered} \sqrt[3]{(x+2)^3}^{}=\sqrt[3]{32768} \\ (x+2\text{ )= 32} \\ \end{gathered}[/tex]Subtract 2 from both sides
x + 2 = 32
x = 32 - 2
x = 30
The solution to the equation is x = 30
Can someoen answer this please
Answer:
n general, greater frequency and intensity of climate hazards are more likely to prompt people to migrate when the population is more vulnerable and has a lower capacity to adapt. Climate events can be divided into fast- and slow-onset events.
Step-by-step explanation:
Ryan is working his way through school. He works two part-time jobs for a total of 22 hours a week. Job A pays $6.20 per hour, and Job B pays $7.40 per hour. How many hours did he work at each job the week that he made $150.80.
We could write the following equations according to the problem:
Hours equation:
[tex]a+b=22[/tex]And, the payment equation: (cents)
[tex]620a+740b=1508[/tex]We could solve this system of equations using the elimination method:
[tex]\begin{cases}a+b=22 \\ 620a+740b=1508\end{cases}[/tex]We're going to multiply the first equation by -620:
[tex]\begin{cases}-620a-620b=-13640 \\ 620a+740b=15080\end{cases}[/tex]Now, we're going to sum both equations eliminating variable a, so we get a linear equation in terms of b:
[tex]\begin{gathered} 120b=1440 \\ b=12 \end{gathered}[/tex]Now we know that he did 12 hours at job b.
As he worked 22 hours in total, then he worked 10 hours at job a.
Answer:
Step-by-step explanation:
a+b = 22 -- equation 1
6.20a + 7.40b = 150.80 replacing decimals
620a + 740b = 15080 --- equation 2
From eq. 1 a = (22 - b)
putting a's value in equation 2
620(22 - b) + 740b = 15080
13640 - 620b + 740b = 15080
120b = 15080 - 13640
b = 1440/120 = 12
From equation 1 a + 12 = 22
a = 10
Verify your answer by equation 2 putting the value of a and b
620*10 + 740*12 = 15080
Hello,Can you help me with the following: Evaluate the give binomial coefficientQuestion # 63
(63)
From the question, we are to evaluate the given binomial coefficient.
(90)
( 2 )
Using the formula:
(n) = n! = n! = 1
(0) 0!(n - 0)! 1 * n!
inputting into the formula
90C2 = 90!
2!(90-2)!
90C2 = 90!
2!(88)!
90C2 = 14857159644817614973095227336
2 * 18548264225739843911479684564
90C2 = 14857159644817614973095227336
3709652845179687822959369129
90C2 = 4005
PLEASE HELP QUICK 25 POINTS
Solve the following system of equations algebraically:
y = x² - 14x + 23
y=-3x + 5
Answer:
x=9, x=2
Step-by-step explanation:
Since both expressions (x^2 - 14x + 23 and -3x+5) are equal to y, set those expressions equal to each other and solve for x.
x^2 - 14x + 23 = -3x + 5
subtract 5 from both sides
x^2 - 14x + 23 - 5 = -3x + 5 - 5
x^2 - 14x + 18 = -3x
add 3x to both sides
x^2 - 14x + 3x + 18 = -3x + 3x
x^2 - 11x + 18 = 0x
factor.
(x-9)(x-2) = 0
Because the product of these two things equals 0, we know that one of these terms must equal to zero.
x-9 = 0 or x-2 = 0
it can be either, so solve for both.
x-9 + 9 = 0 + 9 or x-2 + 2 = 0 + 2
x = 9 or x=2
Consider the following solutions Please help on my question I’m confused
The function f(x) and g(x) is given as follows:
[tex]f(x)=4x+5;\; g(x)=2x-1[/tex]The composite function is defined as:
[tex](f\circ g)(x)=f(g(x))[/tex]Replace x with g(x) in the expression given for f(x):
[tex]f(g(x))=4(g(x))+5[/tex]Substitute g(x)=2x-1 into the right-hand side of the equation:
[tex]\begin{gathered} f(g(x))=4(2x-1)+5 \\ \Rightarrow f(g(x))=8x-4+5=8x+1 \end{gathered}[/tex]Recall that,
[tex]\begin{gathered} (f\circ g)(x)=f(g(x)) \\ \Rightarrow(f\circ g)(x)=8x+1 \end{gathered}[/tex]Notice that the composite function is a polynomial function of degree one (linear).
Recall also, that the domain of all polynomial functions is the set of real numbers.
Hence, the domain of the composite function (fog)(x) is the set of real numbers.
The set of real numbers in interval form is:
[tex](-\infty,+\infty)[/tex]The answer is:
[tex]\begin{gathered} (f\circ g)(x)=\boxed{8x+1} \\ \text{The domain of }(f\circ g)(x)\text{ is }\boxed{(-\infty,+\infty)} \end{gathered}[/tex]a builder wishes to fence in 60,000 m2 of land in a rectangular shape. because of security reasons, the fence along the front part of the land will cost $2 per meter, while the fence along the other three sides will cost $1 per meter. how much of each type of fence will the builder have to buy in order to minimize the cost of the fence? what is the minimum cost?
To minimize the cost, the builder should but 200 meters of fence costs at $2 per meter and 800 meters of fence costs at $1 per meter. The minimum cost is $1,200.
Recall that if we have a function f(x), then at the extremum point, its derivative is equal to zero.
f ' (x) = 0
In the given problem, let:
p = length of the rectangle
q = width of the rectangle
Then,
p x q = 60,000 or q = 60,000/p
Assume that the front side is p, then the function that describe the cost is:
f(p,q) = 2xp + 1 x (p + q + q)
f(p,q) = 3p + 2q
f(p) = 3p + 2 x 60,000/p
f(p) = 3p + 120,000/p
Take the derivative:
f '(p) = 3 - 120,000/p² = 0
p² = 40,000
p = 200 meters
Substitute p = 200 to get q,
q = 60,000/200 = 300
Hence, the type of fences the builder have to buy to minimize the cost is:
200 meters fence with cost $2 per meter and 200+300+300= 800 meters fence with cost $1 per meter.
The minimum cost is:
f(p) = 3p + 120,000/p
f(min) = f(200) = 3x200 + 120,000/200 = $1,200
Learn more about minimum value here:
https://brainly.com/question/19203153
#SPJ4
Annie's mother asked Annie to go buy oranges, dog food, and bug spray. Each square's side length is 1 block. How many blocks will Annie have to walk in all if she visits the fruit stand, the pet store, and the supermarket, in that order, before returning home?
Here using the length of square, it is obtained that
Annie walked 14 blocks in total.
What is a square?
Square is a two dimensional four sided figure.
Here,
Length of each side of one square = 1 block
From Annie's home to the supermarket, Annie will have to walk 1 block
From Supermarket to pet store, Annie will have to walk 1 block straight and then 2 blocks to the left
From pet store to the fruit vendor, Annie will have to walk 1 block straight and then 2 blocks to the left
Total number of blocks walked by Annie from home = 1 + 1 + 2+ 1 + 2
= 7 blocks
Total number of blocks walked by Annie while returning home
= 1 + 1 + 2+ 1 + 2
= 7 blocks
Total number of blocks walked by Annie = 7 + 7 = 14 blocks
To learn more about square, refer to the link-
https://brainly.com/question/25092270
#SPJ1
Complete Question
The figure has been attached
is у = 3х3 – 3 linear?
Given the equation :
[tex]y=3x^3-3[/tex]It is a cubic function because the power of x = 3
The cubic function is not linear function
The linear function has the form : y = m * x + b
The power of x for the linear function = 1
so, the answer is : No
Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 60 yd from B and 105 yd from A, with angle ACB measuring 69.3 . How far apart are A and B (to the nearest yard)?A. 101 yardsB. 110 yardsC. 119 yardsD. 128 yards
Let's draw a diagram of this problem:
This triangle can be seen as follows:
We can use the Law of Cosines to find the length of side c, since we know the measure of angle C:
[tex]c^2=a^2+b^2-2ab\cos (C)[/tex]In our case:
[tex]c^2=105^2+60^2-2(105)(60)\cos (69.3)[/tex][tex]c^2=11025+3600-12600\cos (69.3)=14625-12600\cos (69.3)[/tex]Taking the square root of both sides we get:
[tex]c=\sqrt[]{14625-12600\cos (69.3)}[/tex]which, using a calculator or online resource to calculate the right side of the equation will give us:
[tex]c=100.9[/tex]To the nearest yard, A and B are 101 yards apart, so option A. is correct.
Susie makes bracelets to sell at a local craft fair. At each craft fair, she sells 16 more bracelets than the last time. At her first craft fair, she sold 82 bracelets. At her second craft fair, she sold 98 bracelets. At her third craft fair, she sold 114 bracelets. If this pattern continues, how many bracelets will she sell at her sixth craft fair? 120 bracelets 130 bracelets 146 bracelets 162 bracelets
Answer:
162 bracelets
Step-by-step explanation:
1st - 82 bracelets
2nd - 98
3rd - 114
4th - 130
5th - 146
6th - 162
PLEASE HELP NEED THIS NOW DUE IN AN HOUR!!
Write and simplify an expression to represent the perimeter of the triangle shown. What is the perimeter of the triangle if y equals 3 feet?
(Please show work)
The perimeter of the triangle is 31 feet when the value if y is 3 feet.
Perimeter of the triangle:
Perimeter of the triangle is obtained by the total distance around the edges of a triangle.
The standard form for the perimeter of the triangle is
P = a + b + c.
where
a, b and c refers the edges of the triangle.
Given,
Here we have the triangle with the side values are (y + 5) feet, (3y + 5) feet, and (4y - 3) feet.
Then we have to find the perimeter of the triangle when the value of y is 3 feet.
We know formula of the perimeter of triangle, so first we have to calculate the side values of it, by apply the value of y as 3,
Apply the value of y as 3 feet then we get the value of the edges are
=> y + 5 => 3 + 5 = 8 feet
=> 3y + 5 => 3(3) + 5 = 14 feet
=> 4y - 3 => 4(3) - 3 = 9 feet.
Therefore, the edges of the triangle are 9ft, 14 ft and 9 ft.
Now, we have to apply the values on the formula of the perimeter of the triangle is, then we get
=> P = 8 + 14 + 9
Then the value of P = 31
Therefore, the value of the perimeter of the triangle is 31 feet.
To know more about Perimeter of the triangle here.
brainly.com/question/28660527
#SPJ1
Simplify the expression.
negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths
The actual solution of the mathematical statement is -6.93
How to determine the actual solution?From the question, we have the following statement that can be used in our computation:
negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths
Mathematically, this statement can be expressed as
-15 + -3.7 + 9.15/5 * 3² - 4.7
Evaluate the quotient and the exponents in the expression'
So, we have
-15 + -3.7 + 1.83 * 9 - 4.7
Evaluate the product exponents in the expression'
So, we have
-15 + -3.7 + 16.47 - 4.7
Evaluate the sum and the difference
-6.93
Hence, the solution is -6.93
Read more about expressions at
brainly.com/question/4344214
#SPJ1
Hi, can you help me answer this question please, thank you
Given:
The test claims that the proportion of men who own cats is smaller than the proportion of women who owns cat.
The null and atlernative hypothesis is given as,
[tex]\begin{gathered} \mu_M=\text{ Men who own cats} \\ \mu_F=\text{ Women who own cats} \end{gathered}[/tex]So,
[tex]\begin{gathered} H_0\colon\mu_M=\mu_F_{} \\ H_1\colon\mu_M<\mu_F \end{gathered}[/tex]Answer: option c)
Answer:
what he said^^
Step-by-step explanation:
because of blablablablabla
8(y+4)-2(y-1)=70-3y
solve for y
Answer:
y = 4
Step-by-step explanation:
8(y + 4) - 2(y - 1) = 70 - 3y ← distribute parenthesis and simplify left side
8y + 32 - 2y + 2 = 70 - 3y
6y + 34 = 70 - 3y ( add 3y to both sides )
9y + 34 = 70 ( subtract 34 from both sides )
9y = 36 ( divide both sides by 9 )
y = 4
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
Width = 5.7 ft, Length = 10.5 ft
Step-by-step explanation:
Let the width be [tex]w[/tex]. Then, the length is [tex]2w-0.9[/tex].
[tex]w(2w-0.9)=59.85 \\ \\ 10w(20w-9)=5985 \\ \\ 200w^2-90w-5985=0 \\ \\ 40w^2-18w-1197=0 \\ \\ (4w+21)(10w-57)=0 \\ \\ w=5.7 (w>0) \\ \\ \implies 2w-0.9=2(5.7)-0.9=10.5[/tex]
Geo wants to buy a new home. The sales price is 185000. He has prequalified for a loan at 5.4% interest over 30 years with a 5% down payment and closing cost of 3% of the sales price. How much are the closing costs?
Answer:
$5,550.
Explanation:
The sales price = $185,000
The closing cost = 3% of the sales price.
Thus:
[tex]\begin{gathered} \text{Closing Price=3\% of }$\$185,000$ \\ =\frac{3}{100}\times185,000 \\ =0.03\times185,000 \\ =\$5,550 \end{gathered}[/tex]The closing cost is $5,550.
PLEASE ANSWER. I REALLY NEED THIS A+++
Answer: the first one is yes and the second one is no
Step-by-step explanation: that’s the answer i took the test
carmen wants to estimate the percentage of people who lease a car. she surveys 250 individuals and finds that 105 lease a car. find the margin of error for the confidence interval for the population proportion with a 95% confidence level. z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576. Use the table of common z-scores above, around the final answer of threee decimal place
Answer: 0.049
Step-by-step explanation:
Answer:
Step-by-step explanation:
0.061
Graph the equation on the coordinate plane. y=12x−3
In order to draw a straight line on a graph at least two points are needed.
The graph for the given straight line is shown in the diagram.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The given equation is as below,
y = 12x − 3
Substitute x = 0 in the above equation to get,
y = 12 × 0 - 3
=> y = -3.
Substitute y = 0 in the above equation to get,
0 = 12x - 3
=> x = 3 / 12
=> x = 1 / 4
Now, draw a line through these two points on the coordinate plane to get the graph of y = 12x − 3.
The graph of y = 12x − 3 is given in the following diagram.
Hence, the graph of the given equation is drawn by finding the intercepts.
To know more about straight line equation click on,
brainly.com/question/21627259
#SPJ1
Can you please help me
Step 1: Write out the formula for finding the area of a rhombus
[tex]\begin{gathered} \text{Area }=\frac{AC\times DB}{2} \\ \text{ Where} \\ AC\text{ and DB are the diagonals of the rhombus } \end{gathered}[/tex]Step 2: Substitute the given values to find AC
[tex]\begin{gathered} \text{ Area }=45\text{ square units} \\ DB=6\text{units} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{6AC}{2}=45 \\ 3AC=45 \\ \text{ Dividing both by 3, we have} \\ \frac{3AC}{3}=\frac{45}{3} \\ AC=15 \end{gathered}[/tex]Hence, AC is 15 unitsStella is a salesperson who sells computers at an electronics store. She makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from her sales that day. Let P represent Stella's total pay on a day on which she sells x dollars worth of computers. A graph of P is shown below. Write an equation for P then state the y-intercept of the graph and determine its interpretation in the context of the problem.
step 1
Find the slope of the line
the slope is giving by the formula
m=(y2-y1)/(x2-x1)
we need two points
From the graph we take the points
(0,80) and (4000, 140)
substitute
m=(140-80)/(4000-0)
m=60/4000
m=6/400
m=3/200
m=0.015
step 2
Find the equation of the line in slope intercept form
P=mx+b
we have
m=0.015
b=80
therefore
P=0.015x+80
Remember that the y-intercept is the value of y when the value of x is zero
In this problem
the y-intercept represent a base pay amount each day
so
$80
The height of a bridge is given by y=-3x² + x, where y is the height of the bridge (in miles) and x is the number of miles from the base of the bridge.
A. How far from the base of the bridge does the maximum height occur?
B. What is the maximum height of the bridge?
Answer:
A. (1/6) mile is the maximum height.
B. The maximum height occurs (3/36) miles from the base of the bridge.
Step-by-step explanation:
The answer of (1/6) mile to the point of maximum height is correctly given by 001466952. I'll add a little more perspective as well as a second approach in addition to graphing.
Graphing
As suggested by 001466952, one may graph the function and look for the point at which the maximum (vertex) is located. The attached graph shows this approach. The maximum height of 0.83 miles is also found on the graph [point (0.1667, 0.083)].
First Derivative
One may also take the first derivative of the function. The first derivative will provide the slope at any point x on the original curve. The slope at the vertex will be 0 (the top point where the slope turns from positive to negative). The slope will be zero at the very top.
y = -3x^2 + x
dy/dx = -6x + 1
0 = -6x+1
x = (1/6) mile
Use x = (1/6) in the original equation to find the height at this point.
y = -3x^2 + x
y = -3(1/6)^2 + (1/6)
y = (-3/36) + (6/36)
y = 3/36 or 0.083 miles from the bridge's base.
The solution is
a) The maximum height occurs at x = 1/6 where x is the number of miles from the base of the bridge
b) The maximum height of the bridge is ( 1/12 ) miles
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the height of the bridge be represented by the equation ,
y = -3x² + x be equation (1)
where y is the height of the bridge
and x is the number of miles from the base of the bridge
Now , to find the number of miles at which the maximum height occurs
Take the first derivative of the function and substitute it to 0
So , ( dy / dx ) = 0 ( at maximum height )
On simplifying the equation , we get
dy / dx = -6x + 1
when ( dy / dx ) = 0 ( at maximum height )
-6x + 1 = 0
Adding 6x on both sides of the equation , we get
6x = 1
Divide by 6 on both sides of the equation , we get
x = 1/6
Now , the maximum height of the bridge is at when x = 1/6
Substitute the value of x = 1/6 in equation (1) , we get
y = -3x² + x
y = -3 ( 1/6 )² + 1/6
y = -3/36 + 1/6
On simplifying the equation , we get
y = 3/36 miles
y = 1/12 miles
Hence , the maximum height of the bridge is 1/12 miles
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
A café has 60 tables. 35% of the tables have 2 chairs at each table. The remaining 65% of the tables have 4 chairs at each table. How many tables have 4 chairs?
The value for 39 tables have 4 chairs.
What is percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Percentage formula = (Value/Total value) × 100
Given,
total number of tables = 60
Percentage of tables have 4 chairs = 65%
Number of tables have 4 chairs = 65(60)/100
= 39
To know more about percentage, visit:
https://brainly.com/question/27574467
#SPJ1
PLEASE HELP ME OUT 12x^2+4x-1
Answer:
(6x-1)(2x+1)
Step-by-step explanation:
12x²+4x-1 (find two numbers that when you add or subtract them the ANS will be the coefficient of x and those same numbers when you multiply them the ANS will be the product of 12 and -1) then replace the middle term with those numbers.
12x²+6x-2x-1
(12x²+6x)(-2x-1)
6x(2x+1)-1(2x+1)
(6x-1)(2x+1)
Given the function () = log2( + 4) − 2 :a. On a sheet of graph paper, use transformations to graph the function. Show theasymptote on your graph using a dashed or dotted line and write its equation.b. State the domain and range of this function.c. Algebraically calculate the x-intercept of the graph of this function.
Answer:
a)
b)
[tex]Domain:(-4,\infty)[/tex][tex]Range:(-\infty,\infty)[/tex]
c) x-intercept is 0
Explanation:
Given:
[tex]f(x)=\log_2(x+4)-2[/tex]a) See below the graph of different transformations of the given function;
The equation of the vertical asymptote as shown on the graph is x = -4
b) The domain of a function is the set of possible input values for which the function is defined. The domain of a graph is the set of possible values from left to right.
Looking at the given graph, we can see that the domain of the function is;
[tex]Domain:(-4,\infty)[/tex]The range of a graph is the set of values from the bottom to the top of the graph. Looking at the graph, we can see that the range is;
[tex]Range:(-\infty,\infty)[/tex]c) We'll follow the below steps to determine the x-intercept of the function;
Step 1: Substitute f(x) with 0;
[tex]0=\log_2(x+4)-2[/tex]Step 2: Add 2 to both sides;
[tex]\begin{gathered} 0+2=\log_2(x+4)-2+2 \\ 2=\log_2(x+4) \end{gathered}[/tex]Step 3: Apply the below rule;
[tex]\begin{gathered} \log_ab=c \\ b=a^c \end{gathered}[/tex][tex]\begin{gathered} 2^2=x+4 \\ 4=x+4 \\ 4-4=x \\ 0=x \\ \therefore x=0 \end{gathered}[/tex]So the x-intercept is 0
One number is chosen from the list 2,4,6, and 8. Another is selected from the list 6, 7 and 8. Find the probability that they are the same. a. 0 b.1/6 c. 2/3 d. 1/3
There are 2 options to get the same number, they choose 6 from both lists or they choose 8 from both lists.
Then, the probability to select 6 from the first list is:
[tex]\frac{1}{4}[/tex]Because we have 4 options ( 2, 4, 6, 8) and 1 of then is number 6. At the same way, the probability to select 6 from the second list is:
[tex]\frac{1}{3}[/tex]Because there are 3 numbers and one of them is 6.
Finally, the probability to choose 6 from both lists is the multiplication of the probabilities above, so:
[tex]P_6=\frac{1}{4}\cdot\frac{1}{3}=\frac{1}{12}[/tex]We can also calculate the probability to choose 8 from both lists as:
[tex]P_8=\frac{1}{4}\cdot\frac{1}{3}=\frac{1}{12}[/tex]Because 1/4 is the probability to choose 8 from the first list and 1/3 is the probability to select 8 from the second list.
Therefore, the probability that both numbers are the same is the sum of the probability to choose 6 from both lists and the probability to choose 8 form both lists.
[tex]\begin{gathered} P=P_6+P_8 \\ P=\frac{1}{12}+\frac{1}{12} \\ P=\frac{1}{6} \end{gathered}[/tex]Answer: b. 1/6
The sum of two numbers is 38 and their product is 165. Find the larger number. PLEASE HELP
Answer:
The larger number is 33
Step-by-step explanation:
Writing and solving a system of equations
Let x and y be the numbers
sum of two numbers is 38
x+y = 38
their product is 165
xy = 165
x = 38-y
Substitute this into xy =165
(38-y) * y = 165
38y - y^2 = 165
-y^2 + 38y -165 = 0
Multiply by -1
y^2 - 38y + 165 =0
Factor
( y-33) ( y-5) = 0
Using the zero product property
y -33 =0 y-5 =0
y =33 y=5
Now we can find x for each solution
x = 38-33 =5 x = 38-5 = 33
The two numbers are 33 and 5
The larger number is 33