Answer:
The first set: 8, 15, and 17.
Step-by-step explanation:
Pair: 8, 15, 17By the pythagorean theorem, a triangle is a right triangle if and only if
[tex]\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2[/tex].
In this case,
[tex]\text{longest side}^2 = 17^2 = 289[/tex].
[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}[/tex].
In other words, indeed [tex]\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2[/tex]. Hence, 8, 15, 17 does form a right triangle.
Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two
Pair: 10, 15, 20Factor out the common factor [tex]2[/tex] to simplify the calculations.
[tex]\text{longest side}^2 = 20^2 = 400[/tex]
[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}[/tex].
[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].
Hence, by the pythagorean theorem, these three sides don't form a right triangle.
Pair: 12, 18, 22[tex]\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121[/tex].
[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}[/tex].
[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].
Hence, by the pythagorean theorem, these three sides don't form a right triangle.
Pair: 7, 9, 11[tex]\text{longest side}^2 = 11^2 = 121[/tex].
[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}[/tex].[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].
Hence, by the pythagorean theorem, these three sides don't form a right triangle.
The length of a vegetable garden is 6 feet longer than its width. If the area of the garden is 135
square feet, find its dimensions.
Assign a variable, write an equation, solve the equation, and state the answer.
The width of the garden is 9 feet.
The length of the garden is 15 feet.
Step-by-step explanation:
The vegetable garden is in rectangular shape since the measure of length and width are different.Let 'x' be the width of the gardenlength = (x+6) feetArea = 135 sq.feetArea of the rectangle = length[tex]\times[/tex]width
⇒ 135 = (x+6)x
⇒ 135 = x² + 6x
⇒ x²+6x-135 = 0
Using factorization method,
x²+6x-135 = 0
⇒ (x+15)(x-9) = 0
∴ x = -15 and x = 9
The width of the garden is 9 feet.
The length of the garden is (x+6) = 15 feet.
By assigning a variable to the width of the garden and using the provided length and area, we can create and solve an equation which tells us that the width of the garden is 9 feet and the length is 15 feet.
Explanation:Let's assign the width of the vegetable garden as 'x', so the length of the garden would be 'x + 6' feet because we know it is 6 feet longer than the width. The area of a rectangle is computed by multiplying the length and the width. So, the equation we come up with, based on the question, is 'x(x + 6) = 135' square feet.
Let's solve this equation. We first expand the multiplication on the left-hand side which gives us 'x2 + 6x = 135'. By rearranging this equation, we set it to zero: 'x2 + 6x - 135 = 0'. Subsequently, we can factor this equation to ' (x - 9)(x + 15) = 0'. Setting each factor equal to zero gives us the solutions 'x = 9' or 'x = -15'. However, since a negative width doesn't make sense in this context, we discard '-15'. Therefore, the width of the garden is 9 feet, and the length is 9 + 6 = 15 feet.
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trent's mom sAID HE COULD SPEND NO MORE THAN $12 for rides at the carnival. if the rides cost $0.75 each, how many rides can he go on?
What Is 6 divided by 2/6?
Can you explain step by step please
Answer:
18Step-by-step explanation:
[tex]\frac{6}{\frac{2}{6} } =6*\frac{6}{2} =6*3=18[/tex]
Answer:
18
Step-by-step explanation:
6/(2/3)
Turn 6 into a fraction first.
(6/1) / (2/6)
(6/1) x (6/2)
36/2
18
Find the volume of the cone. Round your answer to the nearest hundredth. A. 88.49 B. 132.73 C. 176.98 D. 353.95
The missing figure is attached down
The volume of the cone is 88.49 cm³ to the nearest hundredth ⇒ A
Step-by-step explanation:
The formula of the volume of a cone is V = [tex]\frac{1}{3}[/tex] πr²h, where
r is the radius of its baseh is the length of its heightFrom the attached figure:
∵ The diameter of the base of the cone is 6.5 cm
∵ The radius = [tex]\frac{1}{2}[/tex] diameter
∴ r = [tex]\frac{1}{2}[/tex] × 6.5 = 3.25 cm
∵ The length of the height of the cone = 8 cm
- Substitute r and h in the formula of the volume above
∵ V = [tex]\frac{1}{3}[/tex] × π × (3.25)² × 8
∴ V = 88.48819308 cm³
- Round it to the nearest hundredth
∴ V = 88.49 cm³
The volume of the cone is 88.49 cm³ to the nearest hundredth
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What is the value of y?
Enter your answer in the box.
Answer:64
Step-by-step explanation:
Add 79 with 37 an you will get 116 you need to know the total angle for a triangle is 180 so 180 minus 116 is 64
The measure of the angle y for the triangle is 64°.
What is the angle of a triangle?The triangle is a shape having three sides and the sum of the angles of the triangle is always equal to 180°.
Here in the given triangle, the two angles are 79° and 37°. The measure of the unknown angle y° will be calculated as:-
y + 79 + 37 = 180
Now solve for the value of angle y below,
y = ( 180 - 79 - 37 )
y = 64°
Therefore, the measure of the angle y for the triangle is 64°.
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What is the measure of all angles. HELP ASAP! Will someone answer this for me like right now. Thanks
Answer:
∠ ABC = ∠ DBE = 65°
∠ ABD = ∠ CBE = 115°
Step-by-step explanation:
See the diagram attached to this question.
Now, ∠ ABC and ∠ DBE are two vertically opposite angles.
So, 3x + 38 = 5x + 20
⇒ 2x = 18
⇒ x = 9
So, ∠ ABC = ∠ DBE = 3(9) + 38 = 65° (Answer)
Again, ∠ ABC and ∠ ABD are supplementary angles.
Then, ∠ ABC + ∠ ABD = 180°
⇒ ∠ ABD = 180° - 65° = 115°
And ∠ ABD = ∠ CBE {Vertically opposite angles}
So, ∠ ABD = ∠ CBE = 115° (Answer)
Which equation can be simplified to find the inverse of y = 5x2 + 10?
f^-1(x) = sq.rt 5(x - 10)/5, sq.rt 5(x - 10)/5 is the inverse of y = 5x^2 +10
Step-by-step explanation:
interchanging the variables
x = 5y^2 + 10
5y^2 +10 = x
5y^2 = x - 10
dividing by 5
5y^2/5 = x/5 + -10/5
y^2 = x/5 + - 10/5
y^2 = x/5 - 2
y = 5 (x-10) 0/5 (sq.rt)
g(5x^2 + 10) = 5x/5
g(5x^2 + 10) = x
f^-1(x) = sq.rt 5(x - 10)/5, sq.rt 5(x - 10)/5 is the inverse of y = 5x^2 +10
Answer:
its A i took the test on Eg2020
Find the value of 49/ 50 ÷ 7/ 6 using any method. Type your answer as a fraction in simplest form.
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Simplify the resulting fraction.
Explanation:To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. So, the reciprocal of 7/6 is 6/7. Therefore, 49/50 ÷ 7/6 = 49/50 x 6/7. When we multiply the numerators (49 x 6) and the denominators (50 x 7), we get 294/350. This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 14. Therefore, 294/350 simplifies to 21/25.
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the depth of a diver is directly proportional to the time since the diver entered the water if it took the diver 45 minutes to reach a depth of 80 ft what is the time it will take to reach a depth of 250 feet
Answer:
1125/8 minutes
Step-by-step explanation:
45/80=x/250
cross product
80*x=45*250
80x=11250
x=11250/80
x=1125/8
Final answer:
To calculate the time it will take for the diver to reach a depth of 250 feet based on the given information.
Explanation:
The depth of a diver is directly proportional to the time since the diver entered the water.
To find the time it will take to reach a depth of 250 feet, we can set up a proportion using the given information: 80 ft / 45 min = 250 ft / x min. Cross-multiply and solve for x to find the time.
Therefore, the time it will take to reach a depth of 250 feet is approximately 140.6 minutes.
Justin wanted to wrap his moms birthday present shaped like a rectangular prism with pretty paper. The box is 2.1 feet long, 2.7 feet wide, And 3.2 feet high. What is the total surface area of the box?
Answer:
42.06 ft²
Step-by-step explanation:
2 sides = 2(2.7 ft × 3.2 ft) = 2 × 8.64 ft² = 17.28 ft²
Front + back = 2(2.1 ft × 3.2 ft) = 2 × 6.72 ft² = 13.44 ft²
Top + bottom = 2(2.1 ft × 2.7 ft) = 2 × 5.67 ft² = 11.34 ft²
Total area = 42.06 ft²
A the slope of f(x) is greater than the slope of g(x)
B the slope of f(x) is less than the slope of g(x)
C the slope of f(x) is equal than the slope of g(x)
The slope of g(x) is undefined
To find the slope of g(x), use the slope formula(m):
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] And plug in two points, I will use:
(0, 2) = (x₁, y₁)
(5, 4) = (x₂, y₂)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{4-2}{5-0}[/tex]
[tex]m=\frac{2}{5}[/tex]
You could do the same to find f(x) by finding two points and using the slope formula, or you could use this to tell visibly:
[tex]m=\frac{rise}{run}[/tex]
Rise is the number of units you go up(+) or down(-) from each distinguished point
Run is the number of units you go to the right from each distinguished point
If you look at the graph, you can see the points (0, -1) and (3, 1). From each point, you go up 2 units and to the right 3 units (you can make sure by using another point). So the slope of f(x) is [tex]\frac{2}{3}[/tex]
Whichever line looks more vertical(and is positive) has the greater slope. So the slope of f(x) is greater than the slope of g(x). The answer is option A
Find the area of the region bounded by the line y=3x−6 and line y=−2x+8. a) the x-axis.
Answer:
[tex]\displaystyle A = \frac{12}{5}[/tex]
General Formulas and Concepts:
Math
Number LinePre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Terms/CoefficientsFactoringCoordinates (x, y)Solving systems of equations using substitution/eliminationSolving systems of equations by graphingFunction NotationInterval NotationCalculus
Integration
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Splitting Integral]: [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
f(x) is always top functiong(x) is always bottom function"Top minus Bottom"Step-by-step explanation:
Step 1: Define
Identify bounded region. See attached graph.
y = 3x - 6
y = -2x + 8
Bounded by x-axis and between those 2 lines (already pre-determined; taking an integral always takes it to the x-axis).
Step 2: Analyze Graph
See attached graph.
Looking at our systems of equations on the graph, we see that our limits of integration is from x = 2 to x = 4.
We don't have a continuous top function through the interval [2, 4] (it switches from y = 3x - 6 to y = -2x + 8), so we need to split it into 2 integrals to find the total area.
We can either use the graph and identify the intersection point, which is x = 2.8, or we can solve it algebraically (systems of equations - substitution method):
Substitute in y: 3x - 6 = -2x + 8[Addition Property of Equality] Add 2x on both sides: 5x - 6 = 8[Addition Property of Equality] Add 6 on both sides: 5x = 14[Division Property of Equality] Divide 5 on both sides: x = 14/5Our 2 intervals would be [2, 14/5] and [14/5, 4] for their respective integrals.
Step 3: Find Area
Our top functions are the linear lines y = 3x - 6 and y = -2x + 8 and our continuous bottom function is the x-axis (x = 0).
We can redefine the linear lines as f₁(x) = 3x - 6, f₂(x) = -2x + 8, and g(x) = 0.
Integration
[Area of a Region Formula] Rewrite/Redefine [Int Prop SI]: [tex]\displaystyle A = \int\limits^b_a {[f_1(x) - g(x)]} \, dx + \int\limits^c_b {[f_2(x) - g(x)]} \, dx[/tex][Area of a Region Formula] Substitute in variables: [tex]\displaystyle A = \int\limits^{\frac{14}{5}}_2 {[(3x - 6) - 0]} \, dx + \int\limits^4_{\frac{14}{5}} {[(-2x + 8) - 0]} \, dx[/tex][Integrals] Simplify Integrands: [tex]\displaystyle A = \int\limits^{\frac{14}{5}}_2 {[3x - 6]} \, dx + \int\limits^4_{\frac{14}{5}} {[-2x + 8]} \, dx[/tex][Integrals - Algebra] Factor: [tex]\displaystyle A = \int\limits^{\frac{14}{5}}_2 {[3(x - 2)]} \, dx + \int\limits^4_{\frac{14}{5}} {[-2(x - 4)]} \, dx[/tex][Integrals] Simplify [Int Prop MC]: [tex]\displaystyle A = 3 \int\limits^{\frac{14}{5}}_2 {[x - 2]} \, dx - 2 \int\limits^4_{\frac{14}{5}} {[x - 4]} \, dx[/tex][Integrals] Integrate [Int Rule RPR]: [tex]\displaystyle A = 3(\frac{x^2}{2} - 2x) \bigg| \limits^{\frac{14}{5}}_2 - 2(\frac{x^2}{2} - 4x) \bigg| \limits^4_{\frac{14}{5}}[/tex][Integrals] Evaluate [Int Rule FTC 1]: [tex]\displaystyle A = 3(\frac{8}{25}) - 2(\frac{-18}{25})[/tex][Expression] Multiply: [tex]\displaystyle A = \frac{24}{25} + \frac{36}{25}[/tex][Expression] Add: [tex]\displaystyle A = \frac{12}{5}[/tex]We have found the area bounded by the x-axis and linear lines y = 3x - 6 and y = -2x + 8.
Topic: Calculus BC
Unit: Area between 2 Curves, Volume, Arc Length, Surface Area
Chapter 7 (College Textbook - Calculus 10e)
Hope this helped!
Answer:
A = 12/5 units
Step-by-step explanation:
USING ALGEBRA:
We can find the intersection point between these two lines;
y = 3x - 6y = -2x + 8Set these two equations equal to each other.
3x - 6 = -2x + 8Add 2x to both sides of the equation.
5x - 6 = 8Add 6 to both sides of the equation.
5x = 14Divide both sides of the equation by 5.
x = 14/5Find the y-value where these points intersect by plugging this x-value back into either equation.
y = 3(14/5) - 6Multiply and simplify.
y = 42/5 - 6Multiply 6 by (5/5) to get common denominators.
y = 42/5 - 30/5Subtract and simplify.
y = 12/5These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.
Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.
Set both equations equal to 0.
(I) 0 = 3x - 6Add 6 both sides of the equation.
6 = 3xDivide both sides of the equation by 3.
x = 2Set the second equation equal to 0.
(II) 0 = -2x + 8Add 2x to both sides of the equation.
2x = 8Divide both sides of the equation by 2.
x = 4The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.
The height of the triangle is 12/5 units.
Formula for the Area of a Triangle:
A = 1/2bhSubstitute 2 for b and 14/5 for h.
A = (1/2) · (2) · (12/5)Multiply and simplify.
A = 12/5The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.
Match each function with its inverse function.
Answer:
check the photo.
Step-by-step explanation:
The inverse of the function
f(x) = ax + b is g(x) = (x/a) - (b/a)
(learn it by heart)
Solve and simplify: 5/6 x 3/4
A.5/8
B.18/20
C.1/2
D.20/18
Answer: 5/8
Step-by-step explanation:
5*3=15
6*4=24
Get 15/24 simplify and get 5/8
How to simplify it?
Divide 15 and 3
Divide 24 and 3
Get 5/8
Which decimal is greater than 24.07 and less than 24.075
Answer:
24.071
Step-by-step explanation:
Let f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11
Answer:
Since this dude got a Bird Brain I got ya'll
Step-by-step explanation:
Whats in Bold is what you put in the drop down menu. :)
So, f(3) = 26. This means that after 3 months, the number of products sold were 26,000.
If f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11 the sale after three months will be 26 thousand.
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Finding profit, populations, and distance traveled are some applications of functions. By entering a number into the formula, locating the independent variable on a table or graph, and then computing the resulting dependent variable, functions are employed.
It is given that,
f(t)=5t+11
So for the given condition after three months,
Substitute the value of t as 3,
f(3)=5(3)+11
f(3)=15+11
f(3)=26
Thus, if f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11 the sale after three months will be 26 thousand.
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Bally manufacturing sent intel corporation an invoice for machinery with a $15,200 list price. Bally dated the invoice August 14 with 5/10 EOM terms. Intel receives a 40% trade discount. Intel pays the invoice on August 27. What does Intel pay Bally?
Answer:
9120
Step-by-step explanation:
Write an equation in two variables that also has (1,3)as a solution.
Answer:
Step-by-step explanation:
x+2y=7
Final answer:
To write an equation with (1,3) as a solution, choose an arbitrary slope and use the given point to solve for the y-intercept, forming a complete linear equation.
Explanation:
To write an equation in two variables that has (1,3) as a solution, you start by understanding linear equations in the form y = mx + b, where m is the slope, and b is the y-intercept. Given the point (1,3), we can choose an arbitrary slope (for example, 2) and plug the point into the equation to solve for b.
Note: y = 2x + b, and with the point (1,3), substituting x with 1 and y with 3 gives 3 = 2(1) + b, which simplifies to b = 1. Therefore, an example equation that fits the criteria is y = 2x + 1.
can someone please help me with this?
tysm!
Answer:
yes
Step-by-step explanation:
Answer:
Area of shades region [tex]=45[/tex] square inches
Step-by-step explanation:
In the given figure accordingly, we have to find the Area of the shaded region
Area of shaded region= Area of big triangle - Area of the small triangle.
Area of a triangle= [tex]\frac{1}{2} *base*altitude[/tex]
Altitude is the perpendicular height of the triangle from its top to base.
Base of big triangle=12 inches, Altitude of big triangle=6+3= 9 inches
Area of Big triangle
[tex]=\frac{1}{2}* 12*9\\\\=6*9\\\\=54[/tex]
Base of small triangle= 6 inches, Altitude of small triangle= 3 inches
Area of the small triangle=
[tex]=\frac{1}{2} *6*3\\\\=3*3\\\\=9[/tex]
Area of shades region [tex]=54-9\\[/tex]
[tex]=45[/tex] square inches
[tex](s^{2} -2s-9) + (2s^{2} - 6s^{3} +s)[/tex]
Question:
Simplify [tex]\left(s^{2}-2 s-9\right)+\left(2 s^{2}-6 s^{3}+s\right)[/tex]
Answer:
The solution is [tex]-6 s^{3}+3 s^{2}-s-9[/tex]
Explanation:
The expression is [tex]\left(s^{2}-2 s-9\right)+\left(2 s^{2}-6 s^{3}+s\right)[/tex]
Let us simplify the expression by removing the parentheses, [tex](a)=a[/tex]
Thus, the expression becomes,
[tex]s^{2}-2 s-9+2 s^{2}-6 s^{3}+s[/tex]
Let us group the like terms, we get,
[tex]-6 s^{3}+s^{2}+2 s^{2}-2 s+s-9[/tex]
Adding the similar terms, we have,
[tex]-6 s^{3}+3 s^{2}-s-9[/tex]
Thus, the solution of the expression [tex]\left(s^{2}-2 s-9\right)+\left(2 s^{2}-6 s^{3}+s\right)[/tex] is [tex]-6 s^{3}+3 s^{2}-s-9[/tex]
When Carrie mows a lawn, she charges a flat fee of $5 plus an hourly rate, R. Carrie worked 2 hours at her last job. She charged a total of $20.00 for all lawns she mowed. Which equation represents what Carrie charged as an hourly rate?
A. 5 + r = 20
B. 5 + 2r = 20
C. 5r + 2 = 20
D. 20 + 2r = 5
Answer:
option B.) 5 + 2r = 20 is correct
Step-by-step explanation:
Carrie mows a lawn, she charges a flat fee of $5 plus an hourly rate, r.
The amount Carrie earns for mowing lawns for t number or hours
= 5 + rt
Carrie worked for 2 hours and charged a total of $20.
Therefore we can write
20 = 5 + r [tex]\times[/tex] 2 [tex]\Rightarrow[/tex] 20 = 5 + 2r
Therefore option B.) 5 + 2r = 20 is correct
1. How far does the tip of a 12 cm
long minute hand on a clock move
in 45 minutes?
Answer:
Therefore the tip of the minute hand on the clock moves 56.57 cm in 45 minutes.Step-by-step explanation:
Using this formula to find the length of the arc
Arc length = [tex]2\pi r (\frac{\theta}{360} )[/tex]
Here [tex]\theta = \frac{360}{60}\times 45[/tex] [for 45 minutes]
[tex]=270^\circ[/tex]
Radius(r) = length of the minute hand = 12 cm
The length of the arc is = [tex]2\pi \times 12\times \frac{270}{360}[/tex]
= 56.57 cm
Therefore the tip of the minute hand on the clock moves 56.57 cm in 45 minutes.
-5w = -24.5 what is it.
Answer:
w=4.9
Step-by-step explanation:
If you are solving for w, you want to isolate the variable. If it is easier to write it out, it would look something like this..
-5 x w = -24.5
To get w by itself, use the inverse of multiplication, which is division. Divide the expression to the left of the equal sign by -5. Remember, what you do to one side, you must do to the other. When you divide -24.5 by -5, you end up with
w=4.9
123
23
1
+(−123
23
1
)123, start fraction, 1, divided by, 23, end fraction, plus, left parenthesis, minus, 123, start fraction, 1, divided by, 23, end fraction, right parenthesis?
Answer:
Neither positive nor negative—the sum is zero.
Step-by-step explanation:
Final answer:
The mathematics problem involves cancelled positive and negative numbers. Adding a number to its negative results in zero. Therefore, the expression simplifies to zero.
Explanation:
The question provided appears to be a mathematics problem that involves adding a number and its negative equivalent. Specifically, it looks like the sum of 123 and 1/23 plus the negative of 123 and 1/23 is being asked.
When you sum a number and its negative, they cancel each other out, resulting in zero. This is because the definition of a negative number is that it's the additive inverse of its positive counterpart, meaning when the two are added together, their sum is zero. The calculation is straightforward:
123 and 1/23 + (-123 and 1/23) = 0.
Jonah is going to the store to buy candles. Small candles cost $2.50 and large candles cost $7.00. He needs to buy at least 20 candles, and he can spend no more than 80 dollars. Make this into a system of linear inequalities to model each situation. DEFINE YOUR VARIABLES! (No Solving is required, just equation.)
The system of linear inequalities are:
[tex]a + b \geq 20\\\\2.50a + 7b\leq 80[/tex]
Solution:
Let "a" be the number of small candles bought
Let "b" be the number of large candles bought
Cost of each small candle = $ 2.50
Cost of each large candle = $ 7
He needs to buy at least 20 candles
Therefore, number of small candles and number of large candles bought must be at least 20
Thus, we frame a inequality as:
[tex]a + b\geq 20[/tex]
"at least" means greater than or equal to
Here, we used "greater or equal to" symbol because, he can buy 20 candles or more than 20 candles also
He can spend no more than 80 dollars
Which means, he spend maximum 80 dollars or less than 80 dollars also
So we have to use "less than or equal to" symbol
Thus, we frame a inequality as:
Number of small candles bought x Cost of 1 small candle + number of large candles bought x Cost of 1 large candle [tex]\leq[/tex] 80
[tex]a \times 2.50 + b \times 7 \leq 80\\\\2.50a + 7b\leq 80[/tex]
Thus the system of linear inequalities are:
[tex]a + b \geq 20\\\\2.50a + 7b\leq 80[/tex]
Dalton has 7 bills, all tens and twenties, that total $100 in value. How many of each bill does he have?
Dalton has 4 ten-dollar bills and 3 twenty-dollar bills.
Explanation:To find out how many of each bill Dalton has, we can set up a system of equations.
Let's assume Dalton has x number of ten-dollar bills and y number of twenty-dollar bills. The total number of bills he has is given as 7, so we have the equation: x + y = 7.
Additionally, the total value of the bills is given as $100. Since each ten-dollar bill is worth 10 dollars and each twenty-dollar bill is worth 20 dollars, we have the equation: 10x+20y = 100.
Now we can solve the system of equations to find the values of x and y.
Multiplying the first equation by 10 to eliminate x, we have: 10x + 10y = 70.
Subtracting this equation from the second equation, we get: 10x + 20y - (10x + 10y) = 100 - 70.
Simplifying, we have: 10y = 30.
Dividing both sides of the equation by 10, we find that y = 3.
Substituting this value back into the first equation, we can solve for x: x + 3 = 7.
Subtracting 3 from both sides, we find that x = 4.
Therefore, Dalton has 4 ten-dollar bills and 3 twenty-dollar bills.
HELP PLZ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! NEED ASAP
Answer:
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Step-by-step explanation:
bc its the only reasonable one
What is -3(4x-2)-2x ?
Step-by-step explanation:
[tex] - 3(4x - 2) - 2x \\ \\ = - 12x + 6 - 2x \\ \\ = - 14x + 6[/tex]
5. What is the solution to the system? *
Captionless Image
6. Explain what your solution means in terms of the scenario. *
Answer:
This is what I came up with
5. (6,32)
6. That means that when six kites are order it would be the same cost from each company
Step-by-step explanation:
The solution y = 3x + 12 represents a linear relationship between two variables in the given scenario, with an initial cost of $12 and an additional cost of $3 for each unit increase in the independent variable "x." The interpretation of this relationship depends on the specific context of the problem.
The given system of equations can be written in slope-intercept form, which is in the form y = mx + b, where "m" represents the slope of the line, and "b" represents the y-intercept. In this context, the system is as follows:
4 = 3m + b
12 = b
We can solve this system to find the values of "m" and "b."
First, we already know that b = 12 from the second equation.
Now, substitute this value into the first equation:
4 = 3m + 12
Next, isolate "3m" by subtracting 12 from both sides of the equation:
3m = 4 - 12
3m = -8
Finally, divide both sides by 3 to solve for "m":
m = -8/3
So, we have found that m = -8/3 and b = 12.
Now, let's interpret the solution in the context of the scenario:
The equation y = 3x + 12 represents the relationship between "x" (which could represent a quantity like time or another variable) and "y" (which could represent a cost, height, or another quantity). In this specific case, it seems like the equation describes a linear relationship between two variables.
In terms of the scenario, it could mean that there is an initial cost of $12 (the y-intercept) and an additional cost of $3 for each unit increase in "x." This interpretation depends on the context of the problem. For example, if "x" represents the number of items purchased, then $12 could be an initial fee, and $3 could be the cost per item.
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The question probable may be:
find the system to the solution you have to put in into slope intersecpt form so y=mx+b
so 4=m(3)+b
12=b
y=3x+12 Explain what your solution means in terms of the scenario. *
Write equivalent fractions to 7.15
Answer:
2 examples would be
7 3/20
or
7 9/60.
Step-by-step explanation:
0.15 = 15/100
= 3/20.
So 7.15
= 7 3/20
Answer:
Step-by-step explanation:
7.15 to fraction
= 7.15 × (100/100)
= 715/100
= 143/20
= 7 3/20