When using the substitution method to solve a nonlinear system of equations, you should first see if you can _____ one variable in one of the equations in the system?
Find three consecutive even integers such that the sum of the smallest integer and twice the median is 20 more than the largest integer
The three consecutive even integers are 10, 12, and 14.
Given that three consecutive even number the sum of the smallest integer and twice the median is 20 more than the largest integer.
Let's represent the three consecutive even integers as follows:
The smallest integer: x
The median integer: x + 2 (since it's consecutive and even)
The largest integer: x + 4 (since it's consecutive and even)
Now, we can set up the equation based on the given information:
"The sum of the smallest integer and twice the median is 20 more than the largest integer."
This can be expressed as:
x + 2(x + 2) = (x + 4) + 20
Now, we can solve for x:
x + 2x + 4 = x + 24
Combine like terms:
3x + 4 = x + 24
Subtract x from both sides:
2x + 4 = 24
Subtract 4 from both sides:
2x = 20
Now, divide by 2:
x = 10
So, the smallest integer is 10, the median integer is x + 2 = 12, and the largest integer is x + 4 = 14.
Therefore, the three consecutive even integers are 10, 12, and 14.
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PLEASE HELP!!!! The measure of an angle is x. The sum of the measure of this angle and an angle with twice the measure is the measure of an obtuse angle. Given the range of possible measures for the larger angle
At what value of x does the graph of the following function F(x) have a vertical asymptote? F(x)= 2/x-2
At a value of 2, the graph of F(x) = 2/x-2 has a vertical asymptote.
Staci has 7 more cats than Taylor. Write an expression that illustrates how many cats Staci has. use x to represent the number of cats that Taylor has
How do you factor: 12x^2-4x-40
what factors do 28 and 44 have in common?
Factors that 28 and 44 have in common are 1, 2, and 4.
Factors that 28 and 44 have in common:
1. List of Factors for 28:
1, 2, 4, 7, 14, 28
2. List of Factors for 44:
1, 2, 4, 11, 22, 44
Common Factors: 1, 2, 4
Tahmar knows the formula for simple interest is I = Prt, where I represents the simple interest on an amount of money, P, for t years at r rate. She transforms the equation to isolate P : P = i/pie . Using this formula, what is the amount of money, P, that will generate $20 at a 5% interest rate over 5 years?
r= 5% = 0.05
t = 5 years
I= 20
P=20÷(0.05×5)
P=$80
Solve the equation for the indicated variable :
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:
The y-coordinate of the solution is approximately 7.2.
Explanation:
To solve the system of equations:
1. [tex]\( 5x + 2y = 7 \)[/tex]
2. [tex]\( -2x + 6 = 9 \)[/tex]
We'll start by solving the second equation for [tex]\( x \):[/tex]
[tex]\[ -2x + 6 = 9 \][/tex]
Subtract 6 from both sides:
[tex]\[ -2x = 9 - 6 \][/tex]
[tex]\[ -2x = 3 \][/tex]
Divide both sides by -2:
[tex]\[ x = -\frac{3}{2} \][/tex]
Now that we have the value of [tex]\( x \)[/tex], we can substitute it into the first equation to find [tex]\( y \):[/tex]
[tex]\[ 5x + 2y = 7 \][/tex]
[tex]\[ 5(-\frac{3}{2}) + 2y = 7 \][/tex]
[tex]\[ -\frac{15}{2} + 2y = 7 \][/tex]
Add [tex]\( \frac{15}{2} \)[/tex] to both sides:
[tex]\[ 2y = 7 + \frac{15}{2} \][/tex]
[tex]\[ 2y = \frac{14}{2} + \frac{15}{2} \][/tex]
[tex]\[ 2y = \frac{29}{2} \][/tex]
Divide both sides by 2:
[tex]\[ y = \frac{29}{4} \][/tex]
Now, let's convert the fraction into a decimal rounded to the nearest tenth:
[tex]\[ y \approx 7.2 \][/tex]
What is the measure of DG?
In circle D, mGEC is 230 degrees
What is the measure of GDC?
what is the measure of AC?
Segment CO is congruent to segment HZ
which congruence statement is true?
A. OZ is congruent to CO
B. CH is congruent to COZ
C. CH is congruent to HZO
D. CO is congruent to HZ
in circle K, what is the value of x?
A. x=30
B. x=25
C. x=20
D. x=15
It can be deduced that the value of angle GDC is 110°.
How to calculate the anglesThe value of minor arc DG will be;
= 2 × 55°
= 110°
The value of AC will be:
= 230° + AC = 360°
AC = 360° - 230°
AC = 130°
Lastly, since segment CO is congruent to segment HZ, CO is congruent to HZ.
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A plant has a height of 8 1/4 inches what is the height of the plant after it grows 1 7/8 inches?
The height of the plant after it grows 1 7/8 inches is 81/8 inches.
Explanation:To find the height of the plant after it grows 1 7/8 inches, we need to add 1 7/8 to the current height of 8 1/4. First, we can convert 8 1/4 to an improper fraction by multiplying the whole number (8) by the denominator (4) and then adding the numerator (1). This gives us 33/4 inches. Next, we can add 1 7/8 by finding a common denominator (8) and adding the numerators (1+7=8). So, 1 7/8 is equivalent to 15/8. Adding 33/4 and 15/8, we first need to find a common denominator which is 8. Multiplying the numerator and denominator of 33/4 by 2 gives us 66/8. Now, we can add 66/8 and 15/8 to get a total of 81/8 inches. Therefore, the height of the plant after it grows 1 7/8 inches is 81/8 inches.
Final answer:
After adding the growth of 1 7/8 inches to the original plant height of 8 1/4 inches, the new height of the plant is calculated to be 10 1/8 inches.
Explanation:
To calculate the new height of the plant after it grows an additional 1 7/8 inches, we simply need to add this growth to the plant's original height of 8 1/4 inches. The sum of these two measurements will give us the plant's total height.
Begin by converting the mixed numbers to improper fractions to make addition easier: 8 1/4 inches becomes 33/4 inches and 1 7/8 inches becomes 15/8 inches. Next, find a common denominator and add the two fractions.
Common denominator for 4 and 8 is 8.Convert 33/4 to an equivalent fraction with a denominator of 8, which is 66/8.Add 66/8 inches and 15/8 inches.(66/8) + (15/8) = 81/8 inches.Now, convert the improper fraction back to a mixed number to determine the plant's new height:
81 divided by 8 is 10 with a remainder of 1.So, 81/8 inches is equal to 10 1/8 inches.Therefore, after growing an additional 1 7/8 inches, the plant's new height is 10 1/8 inches.
Write the function y = 3(x - 1)2 + 2 in standard form.
What integer is equivalent to 25 3/2
Answer: 13
25 3/2 = 26.5
26.5 is basically 26 1/2
26 1/2 = 13
Which of the following is not a good plan for achieving goals? a. Set goals higher than what you feel you can achieve. b. Be positive about achieving your goals. c. Continue to monitor your plan for achieving your goals. d. Keep reminding yourself of your goals.
Answer: Set goals higher than what you feel you can achieve.
Step-by-step explanation:
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Select all the expressions that cannot be factored using intergal coefficients and intergal constants
A. X^2 + 5x + 3
B. 25 - 20x + 4x^2
C. -2x^2 + 7x - 3
D. 2x^2 - 5x + 4
The area of a rug is 36 square feet. the length of the rug is 5 feet longer than the width. what is the width of the rug?
The Porters’ food, clothing, and medical expenses are not fixed expenses. Explain what type of expense they are, and why.
Food, clothing, and medical are variable expenses because they occur regularly but can change from month to month.
The Porters’ food, clothing, and medical expenses are variable expenses.
A fixed expenses are the expenses that are constant and doesn't change while the variable expenses are those that are not fixed since they change.In this case, Porters’ food, clothing, and medical expenses are variable expenses since they can change every month.Read related link on:
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The ratio of red to blue m7m's in a jar is 5:7. if there are 108 m&m's in the jar, how many are red
What does the notation f prime of x mean?
Final answer:
The notation f'(x) represents the derivative of the function f with respect to x, signifying the rate of change of the function or the slope of the tangent to its curve at a specific point.
Explanation:
The notation f prime of x, often written as f'(x), represents the derivative of the function f with respect to x. This concept is a fundamental part of calculus, which deals with the rate at which quantities change. The derivative f'(x) is the instant rate of change of the function f(x) at a particular value of x, or the slope of the tangent line to the curve f(x) at that point.
For example, if f(x) = x2, then the derivative f'(x) would equal 2x, as the rate of change of x2 with respect to x is 2x. This means that for every unit increase in x, the value of x2 increases by an amount corresponding to 2x.
The derivative can also be understood in the context of physics, where it might represent things like velocity, which is the derivative of position with respect to time. Regardless of the context, f'(x) is about understanding how a function changes at a specific point.
1. The perimeter of a rectangular garden is 690 ft. The short sides are each 55 ft. long. What's the length the other 2 sides? Which equation models the situation?
a) 55+2x=690
b) 55+x=690
c) 2(55)+2x=690
d) 55(x-2)=690
2. Two boys took turns driving home. Will averaged 52 miles per hour. Jim averaged 44 miles per hour and drove 2 hours longer than Will. X is the Will time drove, with D being the length of the trip in miles. The trip was 352 miles. If Jim's equation was 44(X+2)=D-52X. Which equation models the situation?
a) 143
b) 209
c) 238
d) 191
Why is it important to take note of skipped check numbers?
A. Skipping a check wastes the check and will end up costing money.
B. Locating skipped checks helps to identify where the fees come from.
C. Skipped checks were written for more money than was available in the account.
D. A skipped check has not been cashed or deposited.
Answer:
D. A skipped check has not been cashed or deposited.
Step-by-step explanation:
We can say that a skipped check number means the check has not been cashed yet.
If we see the check book and there is a gap between the check numbers that you have written, then that means the missing number checks are not processes yet. The processing can be depositing or withdrawing/cashing.
So, the correct answer here is D. A skipped check has not been cashed or deposited.
Find the rate of change of the surface area of a sphere with respect to the radius r. what is the rate when r = 6?
Final answer:
The rate of change of the surface area of a sphere with respect to its radius is 8πr. For a sphere with a radius of 6, this rate is 48π square units per unit of radius.
Explanation:
The surface area S of a sphere is given by the formula S = 4πr², where r is the radius of the sphere. To find the rate of change of the surface area with respect to the radius, we need to differentiate the surface area formula with respect to r. This calculation gives us dS/dr = 8πr. When r = 6, the rate of change, or the derivative evaluated at this radius, is dS/dr = 8π(6) which equals 48π.
So, the rate of change of the surface area of a sphere with respect to its radius when r = 6 is 48π square units per unit of radius.
If an item is 1/3 off, to calculate the final price simply divide the original price by 3. true or false
Answer:
False.
Step-by-step explanation:
If an item is [tex]\frac{1}{3}[/tex] off thats how much you are not paying from the original price of the item, to calculate how much are you paying after the disccount you can do 2 things.
The first one is multiplying the price by [tex]\frac{1}{3}[/tex] and then substracting that from the original price, that will give you the final price.
Or you can simply multiply the original price by 2/3 which is what you have to pay for the item in terms of fractions, and you´d get the final price.
4.5(8-x) + 36=102-2.5(3x+24)
what’s x?
24 golf balls and 18 golf clubs how many bundles of golf balls and clubs can she make with nothing left over
24 -18 = 6
24/6 =4
18/6 =3
6 bundles with 4 balls and 3 clubs each
How do you simplify 25-4x-15/4
What is the exact value of sin30
Mrs. Decker walks for 30 minutes each day as often as possible. What is an equation that relates the number of days d that Mrs. Decker walks and the number of minutes m that she spends walking?