To find the length of the hypotenuse in a right-angled triangle with sides measuring 7ft and 4ft, use the Pythagorean Theorem: 7² + 4²= c², which gives us the hypotenuse length of approximately 8.06 feet.
The question is asking for the length of the hypotenuse of a right-angled triangle when the lengths of the other two sides are known (7ft and 4ft).
To find the hypotenuse, we use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is expressed as a² + b² = c².
By applying the Pythagorean Theorem:
72 + 42 = c²
49 + 16 = c²
65 = c²
c = √65 ≈ 8.06 ft
Therefore, the length of the hypotenuse is approximately 8.06 feet.
The graph models the function f(x) = 2(1/2)x. What is the domain and range of the function?
A-Domain: x < 0; Range: y > 0
B-Domain: x > 0; Range: all real numbers
C-Domain: all real numbers; Range: y > 0
D-Domain: all real numbers; Range: y ≥ 0
Please explain with the answer !!
Hello!
Given the function, [tex]f(x) = 2(\frac{1}{2})^{x}[/tex], notice that the function f(x) is an exponential function.
All exponential functions have a horizontal asymptote at y = 0, and this means that the graph never goes over the line y = 0. Therefore, the range is less than zero, but never equal to zero.
Also, this means that the domain of the function f(x) is all real numbers because as we substitute positive x-values into the function, the graph goes closer to zero, but never across zero. But, if we substitute negative x-values into the equation, it goes to infinity.
Therefore, the answer is choice C. The domain of f(x) is all real numbers, and the range is y > 0.
We want to find the domain and range of the given equation.
We will see that the correct option is C:
Domain: all real numbers;
Range: y > 0
First, we need to define what these are.
For a given function y = f(x), the domain is the set of all the possible x-values we can input on the function, and the range is the set of the possible outcomes.
We have the exponential equation:
f(x) = 2*(1/2)^x
To get the domain we start by assuming that the domain is the set of all real numbers, and then we see if the equation has a problem for a given value of x, then we remove that from the domain.
But here we have x on the exponent, so there are no value of x that causes problems, thus the domain is the set of all real numbers.
To get the range we can look at the graph, we can see that the range goes from near 0 to infinity, so we can say that:
range = y > 0.
(note that the function tends asymptotically to zero, meaning that it never becomes equal to zero).
Then the correct option is C:
Domain: all real numbers;
Range: y > 0
If you want to learn more, you can read:
https://brainly.com/question/21853810
A company sells lab equipment. The daily revenue and costs are modeled by the functions below where x is the number of units sold.
Pleeeeaaasssseeeee help! <3 I'm just trying to graduate.thanks.
Subtract the cost from the revenue:
(-0.32x^2+270x) - (70x+52)
270x - 70x = 200x
The answer would be -0.32x^2 + 200x + - 52
Answer:
P(x) = -0.32x² + 200x + (-52)
Step-by-step explanation:
A company sells lab equipment. Daily revenue and costs are modeled by the function as given in the question.
Revenue: R(x) = -0.32x² + 270x
Cost : C(x) = 70x + 52
Here x = Number of units sold.
Now we have to determine the function P(x) for daily profit.
Since Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = (-0.32x² + 270x) - (70x + 52)
= -0.32x² + 270x - 70x - 52
P(x) = -0.32x² + 200x - 52
Therefore, answer will be P(x) = -0.32x² + 200x + (-52)
plzzz help - i will mark brainest
1.-Write the recursive rule of the sequence 9, 3, 3, 9,... −− .
________________________________________
2.-A line has an x-intercept of (4, 0) and a y-intercept of (0, 12). Find the slope of the line.
________________________________________
3.-A horizontal line includes the points (0, -5 ) and ( 2, -5 ) Find the slope of the line.
Answer:
1. You divide by 3 then multiply by 1 and multiply by 3 again
2. Slope of -3
3. Slope of 0
Step-by-step explanation:
Determine the equation of the ellipse.
Answer:
A) x²/25 + y²/9 = 1
Step-by-step explanation:
The major axis length is the sum of distances to the foci from the ellipse, 10. So the semi-major axis has length 10/2 = 5. The foci are on the x-axis, so the ellipse is oriented horizontally.
The semi-minor axis is the other leg of the right triangle having the focus and center as one leg, and the semi-major axis as the hypotenuse. This is obviously a 3-4-5 triangle, so the semi-minor axis length is 3.
When the ellipse is horizontal, the formula for it is ...
... (x/(semi-major axis))² + (y/(semi-minor axis))² = 1
... (x/5)² + (y/3)² = 1
... x²/25 + y²/9 = 1
A rectangular field is three times as long as it is wide. If the perimeter of the field is 600 feet, what are the dimensions of the field?
Final answer:
To find the dimensions of the field with a perimeter of 600 feet where the length is three times the width, solve the equation derived from the perimeter formula. The width comes out to be 75 feet and the length 225 feet.
Explanation:
The question is about finding the dimensions of a rectangular field that is three times as long as it is wide, with a total perimeter of 600 feet. First, let's denote the width of the field as W and the length as 3W since the length is three times the width. The formula for the perimeter of a rectangle is 2(length + width), which in this case is 2(3W + W) = 8W. Given that the perimeter is 600 feet, we can set up the equation 8W = 600. Solving this for W gives us W = 75 feet. Therefore, the length, being three times the width, is 225 feet.
So, the dimensions of the field are 75 feet in width and 225 feet in length.
whats the answer math will give brainliest
[tex]ax^2+bx+c=0\\\\\text{From quadratic formula the roots are equal:}\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\ \text{and}\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\text{We have}\ 2x^2+7x-15=0\\\\a=2,\ b=7,\ c=-15\\\\\text{and}\ r,\ s\ \text{are two solution}\\\\\sqrt{b^2-4ac}=\sqrt{7^2-4(2)(-15)}=\sqrt{49+120}=\sqrt{169}=13\\\\x_1=\dfrac{-7-13}{2(2)}=\dfrac{-20}{4}=-5\\\\x_2=\dfrac{-7+13}{2(2)}=\dfrac{6}{4}=\dfrac{3}{2}\\\\\dfrac{3}{2}>-5\ \text{therefore}\ r=\dfrac{3}{2}\ \text{and}\ s=-5.[/tex]
[tex]r-s=\dfrac{3}{2}-(-5)}=\dfrac{3}{2}+5=\dfrac{3}{2}+\dfrac{10}{2}=\dfrac{13}{2}\\\\Answer:\ \boxed{B)\ \dfrac{13}{2}}[/tex]
What are the first four terms of the sequence shown below?
an = 5n ‒ 1
A.
‒1, 4, 9, 14
B.
4, 9, 14, 19
C.
5, 6, 7, 8
D.
6, 11, 16, 21
[tex]a_n=5n-1\\\\a_1=5(1)-1=5-1=4\\\\a_2=5(2)-1=10-1=9\\\\a_3=5(3)-1=15-1=14\\\\a_4=5(4)-1=20-1=19\\\\Answer:\ B.\ \{4,\ 9,\ 14,\ 19\}[/tex]
Taxi A charges $0.20 per mile and an initial fee of $4. Taxi B charges $0.40 per mile and an initial fee of $2. Write an inequality that can determine when the cost of Taxi B will be greater than Taxi A. A) 0.20x + 4 > 0.40x + 2 B) 0.20x + 4 < 0.40x + 2 C) 0.20x + 0.40x > 4 + 2 D) 0.20x + 0.40x < 4 + 2
The expression for the cost of Taxi B is 0.40x + 2. The expression for the cost of Taxi A is 0.20x + 4. The inequality asks for when the cost of Taxi B will be greater than Taxi A, so you write it as 0.40x + 2 > 0.20x + 4, or 0.20x + 4 < 0.40x + 2.
The answer is B) 0.20x + 4 < 0.40x + 2.
Answer: B. [tex]0.20x+4<0.40x+2[/tex]
Step-by-step explanation:
let x denotes the number of mile taxi runs.
Given : Taxi A charges $0.20 per mile and an initial fee of $4.
i.e. the expression to show total charge by Taxi A will be :[tex]0.20x+4[/tex]
Taxi B charges $0.40 per mile and an initial fee of $2.
i.e. the expression to show total charge by Taxi B will be :[tex]0.40x+2[/tex]
Now, the inequality that can determine when the cost of Taxi B will be greater than Taxi A will be :-
[tex]0.20x+4<0.40x+2[/tex]
Hence, B is the correct answer.
If 45 Cookies will serve 15 student do you live students,how many cookies are needed for 30 students?
90
divide 45 cookies by 15 to obtain cookies per student then multiply this amount by 30 to obtain cookies for 30 students
15 students → 45 cookies
30 students → 45 × [tex]\frac{30}{15}[/tex] = 90 cookies
Rhino can run at speed about 28 miles per hour what is the speed in feet per second to the nearst whole number
(28 mph) x (5,280 ft/mi) / (60 min/hr) / (60 sec/min) = 41 feet per second
2 3 of the children at a school are scared of snakes, 1 3 are scared of spiders, and 1 6 are scared of snakes and spiders. What fraction of those who are scared of spiders are also scared of snakes?
The fraction of those who are scared of spiders and also scared of snakes is 1/2.
What are Fraction?A fraction is a way of representing a part of a whole or a division of quantities. It consists of two components: a numerator and a denominator, separated by a horizontal line called a fraction bar.
We have,
1/3 of the children are scared of spiders and 1/6 of both snakes and spiders, we can find the fraction of those who are scared of spiders and snakes by dividing the overlap by the total number scared of spiders.
Fraction scared of spiders and snakes
= (Overlap) / (Total scared of spiders)
Overlap = 1/6
Total scared of spiders = 1/3
Fraction scared of spiders and snakes = (1/6) / (1/3) = (1/6) * (3/1) = 1/2
Therefore, the fraction of those who are scared of spiders and also scared of snakes is 1/2.
Learn more about Fraction here:
https://brainly.com/question/10354322
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Final answer:
Half of the children who are scared of spiders are also scared of snakes, calculated by dividing the fraction of children scared of both by those scared of spiders.
Explanation:
To find the fraction of those who are scared of spiders that are also scared of snakes, we start with the information that 2/3 of the children are scared of snakes, 1/3 are scared of spiders, and 1/6 are scared of both snakes and spiders. Since we want to find out the fraction of those scared of spiders (1/3 of the total) who are also scared of snakes, we focus on the 1/6 portion that represents children scared of both. This fraction is relative to the whole group. To express it as a fraction of just those scared of spiders, we divide the fraction of both phobias (1/6) by the fraction scared of spiders (1/3).
Calculation: (1/6) ÷ (1/3) = (1/6) * (3/1) = 1/2.
Therefore, 1/2 of those who are scared of spiders are also scared of snakes.
Kayla has budgeted $400 for day trips during the summer. She needs at least $100 available at the end of summer to buy scrapbooks to memorialize her travels. If Kayla spends $60 for each day trip, what is the greatest number of trips that she can take without exceeding her budget?
A) 3
B) 4
C) 5
D) 7
400-100=300
300÷60=5
5 trips
Answer:- C) is the right answer. She can take 5 trips without exceeding her budget .
Explanation:-
Given: Budget for trips = $400
Amount needed by Kayla at the end of the trip= $100
Thus the exact amount she spends on trips= $400-$100= $300
Amount spend for each day trip = $ 60
Then The number of trips she can take[tex]=\frac{\text{Amount spend on trips }}{\text{Amount for each trip}}=\frac{300}{60}=5[/tex]
Thus she can take 5 trips without exceeding her budget .
please help asap 30 pts
[tex]14-4y\geq38\qquad|\text{subtract 14 from both sides}\\\\-4y\geq24\qquad|\text{change the signs}\\\\4y\leq-24\qquad|\text{divide both sides by 4}\\\\y\leq-6\\\\Answer:\ \boxed{d.\ y\leq-6}[/tex]
Which system of linear inequalities is graphed?
{y>3x−2
{x+2y<4
{y<3x−2
{x+2y>4
{y≤3x−2
{x+2y≥4
{y≥3x−2
{x+2y≤4
The system of linear inequalities that are graphed are {y≥3x−2 and x+2y≤4
In order to get the required system of inequalities, we need to get the equations of both lines.
For the line with having the coordinate points (0, 2) and (4, 0)
The standard form of the expression will be y = mx+b
m = 0-2/4-0
m = -2/4
m = -1/2
The y-intercept "b" is 2 (the point where the line cuts the y-axis)
The equation of the line will be y = -1/2x + 2
2y = -x + 4
x + 2y = 4
Since the line is a solid line and shaded towards the negative side of the graph, the given inequality expression will be x+2y ≤ 4
For the line with having the coordinate points (0, -2) and (2, 4)
The standard form of the expression will be y = mx+b
m = 4+2/2-0
m = 6/2
m = 3
The y-intercept "b" is -2 (the point where the line cuts the y-axis)
The equation of the line will be y = 3x-2
Since the line is a solid line and shaded towards the positive side of the graph, the given inequality expression will be y≥3x−2
Learn more here: https://brainly.com/question/9134439
Joseph completed the two-way table on the left about the social networking habits of his classmates as follows:
Step 1: 85 – 30 = 55
Step 2: 80 – 55 = 25
Step 3: 140 – 80 = 60
Step 4: 60 – 30 = 30
Step 5: 25 + 30 = 55
Choose ONE OPTION from BELOW
The student made...
A) and error in step 1
B) and error in step 2
C) an error in step 3
D) an error in step 4
E) an error in step 5
F) no error
Joseph made no error.
The answer is F) no error
Answer:
Option: F is the correct answer.
F) No error.
Step-by-step explanation:
We are given the steps that Joseph used while solving as:
Step 1: 85 – 30 = 55
Step 2: 80 – 55 = 25
Step 3: 140 – 80 = 60
Step 4: 60 – 30 = 30
Step 5: 25 + 30 = 55
Clearly the steps involves simple addition as well as subtraction of the mathematical numbers.
Hence all his steps are correct as he has not committed any wrong operation.He evaluated the expressions in the right manner.
Hence, the answer is:
Option: F
Jake recorded a special album in honor of mother’s day his mom was so excited she purchased 40% of the copies in the store she has 80 copies of the cd how many cds did the stores have for sale
Answer:
200 CD's.
Step-by-step explanation:
Jake recorded a special album in honor of mother's day. His mom was so excited that she purchased 40% of the copies in the store.
we have tell the total number of CD's in the store.
Let total number of CD's available in the store was = A
Then 40% of the total numbers of CD's = A×40% = 0.04 A
Since 0.04A = 80
A = 80/0.04 = 200
Therefore there were 200 CD's in the store for the sale.
Math, Not sure how to do this one help me out please?
You need to know the 30-60-90 triangles rules for lengths. (b, b√3, 2b)
the given side length of corresponds to the 30° angle. So, b = 8
side y corresponds to the 60° angle so it is b√3. Since we determined that b = 8, then b√3 is 8√3.
side x corresponds to the 90° angle so it is 2b. Since we determined that b = 8, then 2b = 2(8) = 16
Answer: x = 16, y = 8√3
Solve the following equation: 3(3x−8)+4x = −2(12 −7x)−x
A. No solution
B. x = 13
C. All Real Numbers
D. x = 2
3(3x - 8) + 4x = -2(12 - 7x) - x
9x - 24 + 4x = -24 + 14x - x distributed 3 on the left and -2 on the right
- 24 + 13x = -24 + 13x added like terms on the left and the right
-13x -13x
-24 = -24
TRUE
A true statement means infinitely many solutions (aka All Real Numbers)
Answer: C
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
Solve the equation.
x^2 + 10x + 24 = 0
A) -12 and 2
B) 12 and -2
C) -4 and -6
D) 4 and 6
[tex]x^2 + 10x + 24 = 0\\\\x^2+2x+12x+24=0\\\\x(x+2)+12(x+2)=0\\\\(x+12)(x+2)=0\\\\x=-12 \vee x=-2\Rightarrow \text{A}[/tex]
2a=0.38
a= ?
Hey can you guys help please
Josh was born on 30/06/03. How old is he on the 1 september 2015
Josh would be 15 years old
He would be 12 years old on 1 September, 2015.
Given the following perfect square trinomial, fill in the missing term.
x2 − 16x + ____
Answer:
[tex]x^{2}-16x+64[/tex]
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
1. You have the following perfect square trinomial given in the problem:
[tex]x^{2}-16+[/tex]
2. To fill the missing term, you must divide the coefficient -16 by 2 and then you must square it, as following:
[tex](\frac{-16}{2})^{2}=(-8)^{2}=64[/tex]
Which of the following are ordered pairs for the equation y = -4x + 5?
(0,5) (1,1) (-1,9)
(0,5) (-1,-1) (-1,-9)
(0,5) (1,-1) (-1,9)
(0,5) (-1,1) (-1,-9)
(0, 5), (1, 1 ), ( - 1, 9 )
to test the points substitute the x-coordinate into the equation and if the value is equal to the y- coordinate then it is an ordered pair
(0, 5 ) → y = 0 + 5 = 5 ← ordered pair
(1, 1 ) → y = - 4 + 5 = 1 ← ordered pair
(- 1, 9 ) → y = 4 + 5 = 9 ← ordered pair
( - 1, - 1 ) → y = 4 + 5 = 9 ← not an ordered pair
( - 1, - 9 ) → y = 4 + 5 = 9 ← not an ordered pair
(1, - 1 ) → y = - 4 + 5 = 1 ← not an ordered pair
(- 1, 1 ) → y = 4 + 5 = 9 ← not an ordered pair
William earned $9.50 an hour he worked 40 hours one week
Which values of P and Q result in an equation with no solutions? Px+40=Qx+20
Answer:
When P and Q are equal there is no solution exist.
For example - (0,0) , (1,1)
Step-by-step explanation:
Given : Equation [tex]Px+40=Qx+20[/tex]
To find : Which values of P and Q result in an equation with no solutions?
Solution :
In the given equation [tex]Px+40=Qx+20[/tex]
P, Q, x are variable.
We have to find the values at which the equation has no solutions.
[tex]Px+40=Qx+20[/tex]
[tex]Px+20=Qx[/tex]
[tex]20=Qx-Px[/tex]
[tex]20=x(Q-P)[/tex]
If Q=P then (Q-P)x = 0 for all x
Thus the original equation has no solutions.
For example,
Put x=1 and Q=1
[tex]x+40=x+20[/tex]
[tex]40\neq 20[/tex]
There is no solution.
There are 10 less red skittles than orange skittles. The orange skittles are also twice the number of ed skittles. Find the number of red and orange skittles
Answer: red = 10, orange = 20
Step-by-step explanation:
Let R represent the # of red skittles and G represent the # of orange skittles
there are 10 less red skittles than orange skittles: R = G - 10
orange skittles are twice the red skittles: G = 2R
Use substitution to solve the system:
R = (2R) - 10
-R -R
0 = R - 10
+10 +10
10 = R
G = 2R = 2(10) = 20
Answer:30
Step-by-step explanation:
20+10=30
Which of the following is the equation of a line in slope intercept form for a line with slope = 2/3 and y-intercept at (0,-2)
*(The Answer)*= [tex]y = \frac{2}{3} x-2[/tex]
*(Equation)*= The equation for slope-intercept form is [tex]y=mx+b[/tex]
*(Additional Information)*= m = slope, and b = y-intercept
Hope this helps
Person who answered: BangtanBoyScouts
Answer: The correct option is
(C) [tex]y=\dfrac{2}{3}x-2.[/tex]
Step-by-step explanation: We are given to select the equation of a line in slope-intercept form with slope [tex]\dfrac{2}{3}[/tex] and y-intercept at (0, -2).
We know that
the slope-intercept form of the equation of a line with slope m and y -intercept at the point (0, c) is given by
[tex]y=mx+c.[/tex]
For the given line, we have
[tex]\textup{slope, }m=\dfrac{2}{3},\\\\\\\textup{y-intercept},~(0,c)=(0,-2)\\\\\Rightarrow c=-2.[/tex]
Therefore, the equation of the line in slope-intercept form is
[tex]y=mx+c\\\\\Rightarrow y=\dfrac{2}{3}x+(-2)\\\\\\\Rightarrow y=\dfrac{2}{3}x-2.[/tex]
Thus, the required equation of the line in slope-intercept form is [tex]y=\dfrac{2}{3}x-2.[/tex]
Option (C) is CORRECT.
A japanese bullet train averages 162 miles per hour. About how many minutes would it take to travel 80 miles?
1. Solve for x. Show each step of the solution
4.5(8 - x) + 36 = 102 - 2.5(3x + 24)
Final answer:
We solved the algebraic equation to find that the solution is x = -10. Each step involved distributing, combining like terms, and isolating the variable.
Explanation:
Let's solve the algebraic equation step-by-step:
Distribute the multiplication over the brackets: 4.5(8 - x) + 36 = 102 - 2.5(3x + 24).Multiply the terms inside the brackets by the coefficients: 36 - 4.5x + 36 = 102 - 7.5x - 60.Combine like terms on both sides: -4.5x + 72 = 42 - 7.5x.Add 7.5x to both sides and subtract 72 from both sides to isolate the variable term: 3x = -30.Finally, divide both sides by 3 to solve for x: x = -10.The solution to the equation is x = -10, which you can verify by plugging it back into the original equation.
Can someone help me with this math question pls?
Solution is attached below