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.)
Your parents have decided to buy a new Toyota 4Runner for 25,635. According to the dealer, the car will depreciate in value approximately $3,000 per year. Write and solve a linear equation to find how many years it will be until the car is worth $3,135
What is happening to this graph when the x values are between -1 and 1
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.
The lengths of the sides of a triangle are 10, 13, and 19. Classify the triangle as acute, right or obtuse.
What are the zeros of the function?
f(t)=t^2−13t+36
Enter your answers in the boxes.
PLEASE PLEEEASE HELP ME IM BEGGING YOU WITH ALL MY HEART YOU GET 20 POINTS Solve for m:(m-4)^3 = (1/8)^-1
Area of a square with sides of length 1/3 yard .
how did you get 1/9
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.
what is the measure ?
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]
Find the area enclosed between f(x)=0.3x2+7 and g(x)=x from x=−4 to x=8.
To find the area enclosed between two functions, we calculate the definite integral of the absolute difference between the functions over the given interval. The area is equal to the integral of ∣f(x) - g(x)∣, split into two parts where g(x) ≥ f(x) and g(x) < f(x), then added together. The enclosed area for the given functions is 82.26 square units.
Explanation:To find the area enclosed between the functions f(x) = 0.3x^2+7 and g(x) = x from x = -4 to x = 8, we need to calculate the definite integral of the absolute difference between the two functions over the given interval.
The area is equal to the integral of ∣f(x) - g(x)∣ from x = -4 to x = 8. We can split the integral into two parts where g(x) ≥ f(x) and g(x) < f(x), then evaluate each separately. Finally, we add the two areas together.
After evaluating the integrals, we find that the area enclosed between the two functions is 82.26 square units.
Learn more about Finding the area enclosed between two functions here:https://brainly.com/question/36023284
#SPJ11
How many 1/2 foot pieces can be cut from 6 foot ribbon?
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?
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.
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:
You purchased merchandise from a suppler and failed to pay the invoice amount $310 by the last day of the credit period, August 12. Calculate the total amount you must pay on October 15 if the suppler charges 18% interest on past-due accounts.
△BCD is a right triangle. The length of the hypotenuse is 20 centimeters. The length of one of the legs is 15 centimeters. What is the length of the other leg? Enter your answer, as a decimal rounded to the nearest tenth, in the box
Answer:
13.2 cm
Step-by-step explanation:
b = [tex]\sqrt{c^{2} - a\\^{2} }[/tex]
b = [tex]\sqrt{20^{2} - 15\\^{2} }[/tex]
b = [tex]\sqrt{400-225\\} \\[/tex]
b = [tex]\sqrt{175}[/tex]
b = 13.228
b= 13.2 cm
:) good luck on the rest!
Which statements are true based on the diagram? Check all that apply.
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%.
Learn more about the simple interest here:
brainly.com/question/22621039
#SPJ6
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
Write an explicit formula for the sequence 4,-1,-6,-11,-16 then find a14
What is 0.074¯¯¯¯¯ expressed as a fraction?
What number completes the list of prime factors for 36?
3.3.2.?
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.
For the weight of the box that she measured, Beatriz determined the margin of error as 23.5 pounds to 24.5 pounds. What was the greatest possible error for her actual measurement? 0.5 pounds 1 pound 24 pounds 24.5 pounds
Answer:
Option A - 0.5 pounds
Step-by-step explanation:
Given : Beatriz determined the margin of error as 23.5 pounds to 24.5 pounds.
To find : What was the greatest possible error for her actual measurement?
Solution :
To find the margin of error first we find the median of the given numbers.
Median of 23.5 and 24.5
[tex]M=\frac{23.5+24.5}{2}=\frac{48}{2}=24[/tex]
So, the Greatest possible error is 24.5-24 = 0.5 pounds
Therefore, option A is correct.
not sure what this question is asking...
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.
Create the quadratic function that contains the points (0, -2), (1, 0) and (3, 10). Show all of your work for full credit
What is the value of x?
Enter your answer in the box.
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