To find Alicia's possible age, we can write an inequality based on the given information, solve it, and express Alicia's age in terms of a variable.
Explanation:To find the inequality that represents Alicia's possible age, we can start by representing Amy's age in terms of Alicia's age. Let x represent Alicia's age. Amy is eight years older than twice Alicia's age, so Amy's age is 2x + 8. The sum of their ages is less than 32, so we can write the inequality x + (2x + 8) < 32 to represent their ages. Simplifying the inequality gives us 3x + 8 < 32. We can now solve for x by subtracting 8 from both sides of the inequality: 3x < 24. Divide both sides of the inequality by 3 to isolate x: x < 8. Therefore, Alicia's possible age is less than 8, and the inequality that represents her age is x < 8.
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PLEASE HELP: Why does the AA similarity Theorem only need to identify the measurement of 2 congruent angles? Why is it not necessary to find the measurement of the third angle and show that it is also congruent to the corresponding third angle of a similar triangle?
A particle moves according to the equation x = 10t 2 where x is in meters and t is in seconds
Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth. 5x+2y=7 -2x+6=9
Answer:
y = 1.7
Step-by-step explanation:
Given : 5x+2y=7 and - 2x+6=9.
To find : Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth.
Solution : We have given
5x + 2y = 7 --------(1)
- 2x + 6y = 9 -------(2).
To make the y coefficient same multiply the equation 1 by 3.
15 x + 6y = 21 .
(+)-2x +(-) 6y = (-)9 .
______________ ( On subtracting both the equations )
17 x + 0 = 12 .
17 x = 12 .
On dividing both sides by 17
x = [tex]\frac{12}{17}[/tex].
x = 0.705
Plug x = 0.705 in equation 2 .
- 2 ( 0.705) + 6y = 9.
-1.41 + 6y = 9 .
On adding both sides by 1.41.
6y = 9 + 1.41
6 y = 10. 41
On dividing both sides by 6.
y = [tex]\frac{10.41}{6}[/tex].
y = 1.735.
Nearest tenth = 1.7
Therefore, y = 1.7.
Suppose you are given that a=5 and 4a + b=6. What can you prove by using these statements and the substitution property?
Using the values given for 'a' and the equation '4a + b = 6', we applied the substitution property to prove that the value of 'b' is -14.
Given that a=5 and 4a + b=6, we can use the substitution property to find the value of b. The substitution property allows us to replace a with 5 in the second equation.
Performing the substitution, we have:
Substitute a with 5 in 4a + b = 6, giving 4(5) + b = 6.This simplifies to 20 + b = 6.To find b, subtract 20 from both sides of the equation; b = 6 - 20.Hence, b = -14.By substituting and manipulating the equation, we prove that b equals -14 when a equals 5 and 4a + b equals 6.
Describe the possible values for x and y when ∣x − y ∣ > 0. What does it mean when ∣x − y ∣ = 0? Can ∣x − y ∣ < 0? Explain your reasoning.
The absolute value |x−y|>0 when x and y are different, |x−y|=0 when x and y are the same, and |x−y| cannot be < 0 because absolute values cannot be negative.
Explanation:The question is about absolute value, which refers to the distance of a number from zero on a number line. The notation |x−y| represents the absolute value of (x-y).
When |x−y|>0, it means that x and y are distinct from each other. For example, if x = 2 and y = 1, |x-y| equals |2-1|=1, which is indeed greater than 0. There are infinite such values for x and y as long as they are not the same.
When |x−y|=0, it implies that x and y are the same. The only way the absolute value of a number can be zero is when the number itself is zero. Therefore, this can only happen if x = y. If x and y are both 2, for example, |x-y| equals |2-2|=0.
|x−y| cannot be less than 0. The absolute value of a number can never be negative, because it represents the distance a number is from zero and distance cannot be negative.
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what is a skew line?
Skew lines are non-coplanar lines that do not intersect. For example, take a look at the image provided below. Lines m and n in the diagram do not lie on the same plane and they don't intersect. Therefore, we can say that line m is skew to line n.
What are the 3 consecutive integers of 135?
Three consecutive integers can be represented as followed.
X → first integer
X + 1 → second integer
X + 2 → third integer
Since the sum of our three consecutive integers is 135, we can set up an equation to represent this.
X + X + 1 + X + 2 = 135
-Simplify on the left-
3x + 3 = 135
-3 -3
3x = 132
÷3 ÷3 ← divide both sides by 3
X = 44
X + 1 = 45
X + 2 = 46
Therefore, the three consecutive integers are 44, 45, and 46.
There are seven vegetables. Two are squash. Two are cucumbers. The rest are carrots. You randomly choose a vegetable. Find P(cucumber). A. 1/7 B. 1/4 C. 2/7 D. 1/2
Marcus bought a shirt that was marked $28, but it was on sale for 15% off the marked price. what was the price of the shirt after the discount
Final answer:
To find the sale price of the shirt after a 15% discount on the marked price of $28, calculate the discount, subtract it from the original price, resulting in a sale price of $23.80.
Explanation:
Marcus bought a shirt that was marked $28, but it was on sale for 15% off the marked price. To calculate the price of the shirt after the discount, you first need to determine the amount of the discount. To do this, convert the percentage to a decimal by dividing by 100 (15% = 0.15) and then multiply this by the original price.
Discount amount = Original price × Discount rate
= $28 × 0.15
= $4.20.
Subtract the discount amount from the original price to find the sale price of the shirt:
Sale Price = Original price - Discount amount
= $28 - $4.20
= $23.80.
Therefore, the price of the shirt after the 15% discount is $23.80.
Please help! Which direction would the graph y= Ix-4I+3 open? a) left b) up c) right d) down
The Volume of a cube is 343ft cubed. What is the length of one side
What's the answer ????
(2h-4)11 (use the distributive property to simlify each expression)
Subtract x/x^2-36-6/x^2-36
Answer:
x + 6; where x ≠ -6, +6
Step-by-step explanation:
Which of the following statements is true about the triangles below?
triangleABC ≅ triangleABD by SSS
triangleABC ≅ triangleABD by ASA
triangleABC ≅ triangleABD by SAS
triangleABC ≅ triangleABD by AAA
Answer:
triangleABC ≅ triangleABD by ASA
Step-by-step explanation:
Took the test and it was correct
Rose likes to water ski on her sister's boat. the boat takes 3 gallons of gas each hour to run. gas costs $5 per gallon, how much money will she spend on gas to ski for 4 hours?
Two coins are knocked off a table at the same time by different forces. which coin will hit the ground first?
Final answer:
Two coins knocked off a table by different forces will hit the ground simultaneously because gravity affects each coin equally, and the horizontal and vertical components of their motion are independent. This is consistent with the universality of free fall and has been empirically demonstrated by repeated experiments.
Explanation:
Do Different Forces Affect Gravity's Impact on Falling Objects?
When two coins are knocked off a table simultaneously with different horizontal forces, their subsequent motion comprises both horizontal and vertical components. However, gravity acts only on the vertical motion, and it does so equally on both coins regardless of their horizontal velocities. According to the laws of physics, specifically Galileo's theory of falling bodies, both coins will hit the floor at the same time because the horizontal and vertical motions are independent of each other. This phenomenon is due to the universality of free fall, which states that all objects accelerate at the same rate under gravity's influence, ignoring air resistance.
An important point to note is that factors such as air resistance can affect the time it takes for objects with different shapes and surface areas to hit the ground. However, in the case of the coins, since they are identical and their shapes do not change as they fall, air resistance does not play a significant role, and thus they hit the ground simultaneously. This was demonstrated by Galileo and can be observed in everyday life, such as by dropping a shoe and a coin side by side.
Fiona is serving iced tea and lemonade at a picnic. She has only 44 cups in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of iced tea she can serve?
Answer:
[tex]x=44-y[/tex]
Step-by-step explanation:
Let x represents the number of glasses of iced tea and y represents the number of glasses of lemonade.
We have been given that Fiona is serving iced tea and lemonade at a picnic. She has only 44 cups in which to serve the drinks. We can represent this information in an equation as:
[tex]x+y=44[/tex]
Since x represents the number of glasses of iced tea, so we will solve for x by subtracting y from both sides of our equation.
[tex]x+y-y=44-y[/tex]
[tex]x=44-y[/tex]
Therefore, the equation [tex]x=44-y[/tex] represents the number of glasses of iced tea Fiona can serve.
if f(x)=5x-2, and g(x)=2x+1, find (f+g)(x)
A rare bacterial culture is being grown in a lab. As time passes, the cells multiply in a specific pattern.After 1 day, there is only 1 cell.After 2 days, there are 9 cells.After 3 days, there are 20 cells.After 4 days, there are 34 cells.How many cells will there be after seven days?
a.149B.120C. 98D.94
the equation is,
a_n = a_(n–1) + 3 * n + 2
Substituting the values
for day 4,
20 + 3*4 + 2 = 34
Thus the equation is correct
Therefore to calculate for a_n at n = 7 or a_7, we must calculate a_5 and a_6 first.
a_5 = 34 + 3*5 + 2 = 51
a_6 = 51 + 3*6 + 2 = 71
Hence,
a_7 = 71 + 3*7 + 2 = 94
Answer: D. 94
Stephanie read 72 page on sundy and 83 pages on monday about haw many pages did stephanie read during the two days
If the distance between the 2 and the 3 and the 6 and the 7 on a scale are equal, the scale would likely be at least:
Percy works two part-time jobs to help pay for college classes. On Monday, he works 3 hours at the library and 2 hours at the coffee cart and earns $36.50. On Tuesday, he works 2 hours at the library and 5 hours at the coffee cart and earns $50. His hourly wage at the library, x, and hourly wage at the coffee cart, y, can be determined using the system of equations below. 3x + 2y = 36.50 2x + 5y = 50.00 At which job does Percy earn the greater hourly wage? How much does Percy earn each hour at this job?
A) Percy earns a greater hourly wage of $7.00 at the library.
B) Percy earns a greater hourly wage of $7.00 at the coffee cart.
C) Percy earns a greater hourly wage of $7.50 at the library.
D) Percy earns a greater hourly wage of $7.50 at the coffee cart.
In the diagram below de is parallel to xy what is the value of y?
Answer:
C. 75.
Step-by-step explanation:
We have been given a diagram of two parallel lines and we are asked to find the value of y.
We can see from our given diagram that angle y and the angle that measures 105 degrees is formed inside the parallel lines and on the same side of transversal.
Since the the angles formed on the same side of transversal and inside parallel lines are called consecutive interior angles and they add up-to 180 degrees, so we can set an equation as:
[tex]y^o+105^o=180^o[/tex]
[tex]y^o+105^o-105^o=180^o-105^o[/tex]
[tex]y^o=75^o[/tex]
Therefore, the value of y is 75 degrees and option C is the correct choice.
What is the max number of slices of pizza can you get out out of 6 cuts?
the area of a rectangular field is 6603 meter squared. if the width of the field is 71 m what is it’s length
Area of rectangular field is 6603m². Given width 71m, length is 93m (6603 ÷ 71).
To find the length of the rectangular field, you can use the formula for the area of a rectangle:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
Given that the area is [tex]\( 6603 \, \text{m}^2 \)[/tex] and the width is [tex]\( 71 \, \text{m} \)[/tex], you can rearrange the formula to solve for the length:
[tex]\[ \text{Length} = \frac{\text{Area}}{\text{Width}} \][/tex]
Substitute the given values:
[tex]\[ \text{Length} = \frac{6603 \, \text{m}^2}{71 \, \text{m}} \][/tex]
[tex]\[ \text{Length} = 93 \, \text{m} \][/tex]
So, the length of the rectangular field is [tex]\( 93 \, \text{m} \).[/tex]
Estimate the area under the curve f(x) = x^2 from x = 1 to x = 5 by using four inscribed (under the curve) rectangles. Answer to the nearest integer.
Answer:
30 square units
Step-by-step explanation:
For a rectangle to be described as "inscribed" in the context of estimating the area under a curve, the entire rectangle should be positioned underneath the curve.
Therefore, as the curve of f(x) = x² is convex (concave up) in the interval [1, 5], to estimate the area under the curve by using inscribed rectangles, we can use the Left Riemann Sum.
The Left Riemann Sum is a numerical approximation method used to estimate the definite integral of a function over a given interval by dividing the interval into subintervals. It approximates the area under the curve of a function by using rectangles, where the left side of each rectangle touches the curve at the left endpoint of each subinterval.
[tex]\boxed{\begin{minipage}{11cm}\underline{Left Riemann Sum}\\\\$\displaystyle \int^b_a f(x)\; \text{d}x \approx \Delta x \left(f(x_0)+f(x_1)+f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)$\\\\$\text{where}\; \Delta x=\dfrac{b-a}{n}$\\\end{minipage}}[/tex]
The number of subintervals, n, is the number of rectangles used, and the interval is [a, b].
As the interval is [1, 5], this means that a = 1 and b = 5.
As the number of rectangles to use is 4, then n = 4.
Calculate the value of Δx:
[tex]\Delta x=\dfrac{b-a}{n}=\dfrac{5-1}{4}=\dfrac{4}{4}=1[/tex]
The given partition divides the interval [1, 5] into 4 subintervals where the width of each subinterval is one. Therefore, the left endpoints are:
[tex]x_0=1[/tex][tex]x_1=2[/tex][tex]x_2=3[/tex][tex]x_3=4[/tex]Substitute everything into the formula and solve:
[tex]\begin{aligned}\displaystyle \int^5_1 x^2\; \text{d}x &\approx 1\cdot \left(f(1)+f(2)+f(3)+f(4))\right)\\\\&=(1)^2+(2)^2+(3)^2+(4)^2\\\\&=1+4+9+16\\\\&=30\end{aligned}[/tex]
Therefore, the estimation of the area under the curve f(x) = x² from x = 1 to x = 5 using four inscribed rectangles is 30 square units.
Susie scored 85, 84,and 78 on three of the four math tests. if her average score for the four tests was 86. what was her score on the fourth test?
What are the x and y intercepts of the graph of 3x + 4y = -36?
a) x-intercept = -9, y-intercept = 12
b) x-intercept = -12, y-intercept = -9
c) x-intercept = 12, y-intercept = -9
d) x-intercept = 9, y-intercept = -12
Answer:
d
Step-by-step explanation:
The volume of a cube is 27n^27 cubic units. What is the length of one side of the cube?
3n^3 units
3n^9 units
27n^3g units
27n^9 units
Answer:
3n^9
this is answer peace