To solve the inequality and graph its solution, solve the two separate inequalities: 2t + 1 > 9 and -18 > 5t - 3. The solution is t > 4 or t < -3.6. Graph the solution by plotting the points 4 and -3.6 on a number line, and shading the area to the right of 4 and the left of -3.6.
Explanation:To solve the inequality and graph its solution, we need to solve the two separate inequalities:
1) 2t + 1 > 9
2) -18 > 5t - 3
For the first inequality, we can subtract 1 from both sides and divide by 2 to obtain t > 4.
For the second inequality, we can add 3 to both sides and divide by 5 to obtain t < -3.6.
Thus, the solution to the original inequality is t > 4 or t < -3.6.
To graph the solution, we would plot the points 4 and -3.6 on a number line, and shade the area to the right of 4 and the left of -3.6.
To solve the inequalities 2t + 1 > 9 and –18 > 5t – 3, we must solve each separately, and since it's an 'or' inequality, we combine the solution sets. The solutions are t > 4 and t < -3. Graphically, these solutions represent non-overlapping shaded regions on a number line.
Explanation:To solve the inequality 2t + 1 > 9 or –18 > 5t – 3, we need to consider them separately as each inequality represents a different solution set.
For the first inequality:
Subtract 1 from both sides to obtain 2t > 8.Divide by 2 to isolate t, yielding t > 4.For the second inequality:
Add 3 to both sides to get –15 > 5t.Divide by 5, which flips the inequality because we are dividing by a positive number, resulting in t < –3.We interpret these results as two separate conditions:
t > 4: This suggests that t is any value greater than 4.t < –3: This suggests that t is any value less than -3.Since the original statement uses 'or', the solution set includes all the values that satisfy either inequality. Therefore, graphically, we would show these on a number line with a shaded region to the right of 4 and another shaded region to the left of -3. The areas do not overlap because there are no t values that can simultaneously be greater than 4 and less than -3.
The lengths of the sides of a triangle are 10, 13, and 19. Classify the triangle as acute, right or obtuse.
jason deposit $5000 in a bank account that will pay him 4% simple interest annually if jason deposits no more than the initial $5000, how much money will be in the account at the end of five years ? (the formula for simple interest is l = prt or interest = principal * rate * time. use a decimal to express the interest when using that formula.)
What is the value of x?
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x =
Two intersection lines. Angle formed at the top is labeled 2 x plus 2 degrees. Angle formed at the bottom is labeled 3 x minus 52 degrees.
Diagram is in the attachment below
Three consecutive odd integers whose sum is 243
Final answer:
The three consecutive odd integers whose sum is 243 are 79, 81, and 83. The integers were found using the algebraic expression for consecutive odd numbers and solving for the sum equal to 243.
Explanation:
To find three consecutive odd integers whose sum is 243, we can represent the first of these integers as 'n', the second as 'n + 2', and the third as 'n + 4', since each consecutive odd integer is 2 more than the previous one. The equation we would use to portray their sum is:
n + (n + 2) + (n + 4) = 243
Simplifying the equation, we combine like terms:
3n + 6 = 243
Next, we subtract 6 from both sides to isolate the 3n term:
3n = 243 - 6
3n = 237
Now we divide by 3 to solve for n:
n = 237 / 3
n = 79
The first odd integer is 79, the second odd integer is 79 + 2 = 81, and the third odd integer is 79 + 4 = 83.
Therefore, the three consecutive odd integers are 79, 81, and 83.
The area of a rectangular field is 8624 yd^2. If the length of the field is 98 yards, what is its width
The width of the rectangular field is 88 yards.
Explanation:To find the width of the rectangular field, we can use the formula for the area of a rectangle: Area = length x width.
In this case, the area is given as 8624 yd² and the length is given as 98 yards. So, we can rearrange the formula to solve for the width: width = Area / length.
Plugging in the values, we have width = 8624 yd² / 98 yds. Dividing these values gives us the width of the field: width = 88 yards.
Create the quadratic function that contains the points (0, -2), (1, 0) and (3, 10). Show all of your work for full credit
According to an almanac, 80 % of adult smokers started smoking before turning 18 years old. (a) if 400 adult smokers are randomly selected, how many would we expect to have started smoking before turning 18 years old? (b) would it be unusual to observe 360 smokers who started smoking before turning 18 years old in a random sample of 400 adult smokers? why?
Based on the 80% figure, we'd expect 320 out of 400 adult smokers to have started before they turned 18. Observing 360 in this situation could be unusual but would require a statistical test to confirm.
Explanation:This question pertains to concepts of probability and statistics. If 80% of adult smokers began smoking before they turned 18, then in a group of 400 randomly selected adult smokers, we would expect 80% (or 0.8) of that 400 to have started smoking before the age of 18. This means 320 out of the 400 individuals started smoking before turning 18.
As for the second part of the question, if we observed 360 smokers out of 400 who started smoking before turning 18, this number is higher than our expectation of 320. This could be seen as unusual, but it also might occur by chance. To determine how unusual it is, we would typically conduct a statistical test, which would require additional information not provided in the question.
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Area of a square with sides of length 1/3 yard .
how did you get 1/9
Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. r = 2.7 meters, s = 4.32 meters
a. 1.6 radians
b. 0.37 radians
c. 3.5 radians
d. 1.35 radians
Answer:
The correct option is a.
Step-by-step explanation:
Given information: radius r =2.7 meters, arc length s = 4.32 meters.
The formula of arc length is
[tex]s=r\theta[/tex]
where, r is radius and θ is central angle in radians.
Using the above formula we get
[tex]4.32=2.7\times \theta[/tex]
Divide both sides by 2.7.
[tex]\frac{4.32}{2.7}=\theta[/tex]
[tex]1.6=\theta[/tex]
The value of the central angle is 1.6 radians. Therefore option a is correct.
the sum od the squares of two consecutive even integers is 164. Find the integers.
The consecutive even integers whose squares sum to 164 are [tex]\(8\) and \(10\) or \(-10\) and \(-8\).[/tex]
Let the two consecutive even integers be [tex]\( x \) and \( x + 2 \).[/tex]
The sum of their squares is given by:
[tex]\[ x^2 + (x + 2)^2 = 164 \][/tex]
Expanding and simplifying this equation:
[tex]\[ x^2 + (x^2 + 4x + 4) = 164 \]\[ 2x^2 + 4x + 4 = 164 \]\[ 2x^2 + 4x + 4 - 164 = 0 \]\[ 2x^2 + 4x - 160 = 0 \]\[ x^2 + 2x - 80 = 0 \][/tex]
Now, solve the quadratic equation [tex]\( x^2 + 2x - 80 = 0 \).[/tex] We use the quadratic formula [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \),[/tex] where [tex]\( a = 1 \), \( b = 2 \), and \( c = -80 \).[/tex]
[tex]\[ x = \frac{-2 \pm \sqrt{2^2 - 4 \cdot 1 \cdot (-80)}}{2 \cdot 1} \]\[ x = \frac{-2 \pm \sqrt{4 + 320}}{2} \]\[ x = \frac{-2 \pm \sqrt{324}}{2} \]\[ x = \frac{-2 \pm 18}{2} \][/tex]
This gives us two solutions:
[tex]\[ x = \frac{-2 + 18}{2} = \frac{16}{2} = 8 \]\[ x = \frac{-2 - 18}{2} = \frac{-20}{2} = -10 \][/tex]
So, the two pairs of consecutive even integers are [tex]\( 8 \) and \( 10 \), or \( -10 \) and \( -8 \).[/tex]
Therefore, the integers are [tex]\( 8 \) and \( 10 \), or \( -10 \) and \( -8 \).[/tex]
Which statements are true based on the diagram? Check all that apply.
How many inches are in a yard?
What number completes the list of prime factors for 36?
3.3.2.?
How many 1/2 foot pieces can be cut from 6 foot ribbon?
what is the measure ?
A biologist studied the populations of black bear and brown bears over a 10 year period. the biologist modeled the populations, in thousands with the following polynomials where X is time , in years. BLACK BEARS : 2.3x^2-5.6X+2.3 BROWN BEARS:2.4X^2+7.2X+0.97 What polynomial models the total number of brown and black bears ? A.) 4.7x^2+1.6x+3.27 B.) 4.7x^2-1.6x-3.37 C.) 4.7x^2+1.6x-3.37 D.) 4.7x^2-1.6x+3.37 i need help ??
What is 0.074¯¯¯¯¯ expressed as a fraction?
the average heart pumps about 80ml of Blood each contraction. if your heart rate was 70 beats per minute, calculate the volume of Blood your heart pumps in one minute when you are resting. show your calculation.
at this rate how much blood would your heart pump in one hour? show your calculation.
Answer:
Step-by-step explanation:33
What is the standard deviation for the data set?
212, 249, 212, 248, 239, 212, 216, 234, 248
Express your answer as a decimal to the nearest tenth.
Enter your answer in the box.
What is the standard deviation for the data set?
212, 249, 212, 248, 239, 212, 216, 234, 248Answer:16.9
Step-by-step explanation:
What is happening to this graph when the x values are between -1 and 1
Find the exact length of the curve. y2 = 4(x + 1)3, 0 ≤ x ≤ 1, y > 0
To find the exact length of the curve, we can use the concept of arc length. The formula for the arc length of a curve y = f(x) on the interval [a, b] is given by: L = ∫√(1 + (f'(x))^2) dx, where f'(x) is the derivative of f(x). In this case, y2 = 4(x + 1)3 can be rewritten as y = 2√(x + 1)^3. Taking the derivative of y with respect to x, we get y' = 3(x + 1)^(3/2). Plugging this into the formula for arc length: L = ∫√(1 + (3(x + 1)^(3/2))^2) dx = ∫√(1 + 9(x + 1)^3) dx. We can then evaluate this integral over the interval [0, 1] to find the exact length of the curve.
Explanation:To find the exact length of the curve y2 = 4(x + 1)3, 0 ≤ x ≤ 1, y > 0, we can use the concept of arc length. The formula for the arc length of a curve y = f(x) on the interval [a, b] is given by:
L = ∫√(1 + (f'(x))^2) dx, where f'(x) is the derivative of f(x).
In this case, y2 = 4(x + 1)3 can be rewritten as y = 2√(x + 1)^3. Taking the derivative of y with respect to x, we get y' = 3(x + 1)^(3/2). Plugging this into the formula for arc length:
L = ∫√(1 + (3(x + 1)^(3/2))^2) dx = ∫√(1 + 9(x + 1)^3) dx
We can then evaluate this integral over the interval [0, 1] to find the exact length of the curve.
PLEASE PLEEEASE HELP ME IM BEGGING YOU WITH ALL MY HEART YOU GET 20 POINTS Solve for m:(m-4)^3 = (1/8)^-1
In MNO NM=3 cm NO=4cm and MO=5 cm list the angels in order from smallest to largest
The triangle is a right triangle as the sides follow the Pythagorean theorem. The angles opposite the sides are 90° (largest), 53.13°, and 36.87° (smallest), listed from largest to smallest based on side lengths.
The student's question involves a triangle with sides of lengths 3 cm, 4 cm, and 5 cm and asks for the angles to be listed from smallest to largest. Since these side lengths satisfy the Pythagorean theorem (32 + 42 = 52), the triangle is a right triangle, with the right angle opposite the longest side, MO. Using the properties of a right triangle, we can determine that the smallest angle is opposite the shortest side, NM, and the next larger angle is opposite the intermediate side, NO.
To find the actual angle measurements, we would typically use trigonometric ratios such as sine, cosine, or tangent. However, since this is a 3-4-5 triangle, we already know that the angles are 90° for the right angle, and 36.87° and 53.13° for the other two angles, respectively. Thus, the angle opposite NM (3 cm) is the smallest, the angle opposite NO (4 cm) is larger, and the angle opposite MO (5 cm) is the largest, at 90 degrees.
The angle measurements in a right triangle will always follow this pattern based on the lengths of the sides, making it a straightforward matter to list them from smallest to largest.
not sure what this question is asking...
Find n for a series for which a649-14-01-00-00_files/i0160000.jpg = 30, d = -4, and Sn = -210.
Answer:
b.
21
Step-by-step explanation:
What are the zeros of the function?
f(t)=t^2−13t+36
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i need to know what “x” in the angle measures
You withdrew $36.25 from your checking account. Now your balance is -$14.75. Write and solve an equation to find the amount of money in your account before you withdrew the money?
Consider the proof. Given: In △ABC, BD ⊥ AC Prove: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A) Statement Reason 1. In △ABC, BD ⊥ AC 1. given 2. In △ADB, c2 = x2 + h2 2. Pythagorean thm. 3. In △BDC, a2 = (b – x)2 + h2 3. Pythagorean thm. 4. a2 = b2 – 2bx + x2 + h2 4. prop. of multiplication 5. a2 = b2 – 2bx + c2 5. substitution 6. In △ADB, cos(A) = 6. def. cosine 7. ccos(A) = x 7. mult. prop. of equality 8. a2 = b2 – 2bccos(A) + c2 8. ? 9. a2 = b2 + c2 – 2bccos(A) 9. commutative property What is the missing reason in Step 8?
Solution: The missing reason in Step 8 is substitution of [tex]x=c\cos (A)[/tex].
Explanation:
The given steps are used to prove the formula for law of cosines.
From step 5 it is noticed that our equation is
[tex]a^2=b^2-2bx+c^2[/tex] ..... (1)
From step 7 it is noticed that the value of [tex]x[/tex] is [tex]c\cos (A)[/tex].
So by substituting [tex]c\cos (A)[/tex] for [tex]x[/tex] in equation (1) we get the equation of step 8, i.e.,
[tex]a^2=b^2-2bc\cos (A)+c^2[/tex]
Hence, the missing reason in Step 8 is substitution of [tex]x=c\cos (A)[/tex].
The missing reason in Step 8 of the proof for the Law of Cosines is substitution, where x is replaced with cc cos(A) in the expression.
Explanation:The missing reason in Step 8 of the proof that shows how the Law of Cosines is derived, a2 = b2 + c2 – 2bc cos(A), is the substitution property. In Step 7, we established that c cos(A) is equal to x. Thus, for Step 8, when we replace x with cc cos(A) in the expression b2 – 2bx + c2, we effectively utilize substitution to arrive at the expression a2 = b2 – 2bccos(A) + c2.
jude earns $54 interest each year on an investment. his principal was $1800. what is jude's interest rate?
Jude's interest rate will be 3% for the principal of $1800 on an investment.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.
To find Jude's interest rate, we need to set up an equation using the information given. Let R be the interest rate.
The interest earned is equal to the principal times the interest rate, so the equation is:
Interest = Principal × Rate
Substituting the given values, we have:
54 = 1800 × R
Dividing both sides by 1800 gives:
R = 54 / 1800
R = 0.03, or 3%.
Therefore, for an investment of $1800, the interest rate will be 3%.
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