Solve the system by substitution.
x - 2y = 4
2x - 6y = 8
Calculate the difference 12.0875 – 7.50 using significant digits.
A. 4.5
B. 4.587
C. 4.59
D. 4.6
C. 4.59
Step-by-step explanation:Significant digits are digits expressing precision of a measurement. Non-zero digits are always significant but zeroes can be either included or ignored. For instance, zeroes that comes before other digits aren't significant. For example 0.058 has two significant digits. In this exercise, we have two numbers:
12.0875
7.50
The number 12.0875 has five significant digits while 7.50 has three significant digits. If we add or subtract two numbers, the least number of decimal places (that isn't the same as significant digits) in any of the two numbers must be the same as the number of decimal places in the result. Hence, for 12.0875 we have four decimal places and for 7.50 we have two decimal places. Therefore, the result must have two decimal places:
12.0875 - 7.50 = 4.59
Mark raises guppies in an aquarium. He finds out that guppies reproduce very rapidly, and the number quadruples every month. He starts out with only 2 guppies, and the function y equals 2 times 4 to the x models the number of guppies he will have after x months. Which graph represents this function?
Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100.
Answer:
Step-by-step explanation:
We will make a substitution to make our work easier (when we get there). We also need to know that
[tex]i^2=-1[/tex]
We will use that as another substitution. First, let's make the job of factoring a bit easier. Here's the first substitution. We will let
[tex]x^4=u^2[/tex]
Therefore,
[tex]x^2=u[/tex]
Now we will write the polynomial in terms of u instead of x:
[tex]f(x)=u^2+21u-100[/tex]
Solve for the values of u by setting the polynomial equal to 0 and factoring. When you factor, you will get:
[tex](u+25)(u-4)[/tex]
But don't forget that
[tex]x^2=u[/tex]
so we have to put those back in now:
[tex](x^2+25)(x^2-4)=0[/tex]
By the Zero Product Property, either
[tex]x^2+25=0[/tex] or
[tex]x^2-4=0[/tex]
We will factor the first term. Solving for x-squared gives us:
[tex]x^2=-25[/tex] and
x = ±√-25
which simplifies down to
x = ±√-1 × 25
we can sub in an i-squared for the -1:
x = ±√[tex]i^2*25[/tex]
The square root of i-squared is "i" and the square root of 25 is 5, so
x = ±5i
The next one is a bit easier. If
[tex]x^2=4[/tex], then
x = ±2
You can see you have 4 solutions. But you knew that already, since this is a 4th degree polynomial. The types of solutions are: 2 real, 2 imaginary
What are the coordinates for this graph!
The population of wild horses on a wildlife refuge decreased from 110 to 99 in a year. If this trend were to continue, what exponential equation could be used to predict the horse population in the future?
y = 110(1.1)^x
y = 99(0.9)^x
y = 99(1.1)^x
y = 110(0.9)^x,
The exponential equation for this situation is y = 110(0.9) ^x. This is because 110 is the principal or the initial number of horses and y is the resultant population after a certain number of years X with a rate of 0.9. Note that the rate is less than 1 which means that the population is decreasing as time goes by.
Answer:
The person is right.
Step-by-step explanation:
Look at his profile.
The formula v =sqrt 64h can be used to find the velocity, v, in feet per second, of an object that has fallen h feet. Find the velocity of an object that has fallen 75 feet. Round to the nearest tenth.,
I’m not sure how to use integration to solve this question (4)
A circle of radius 1 centered at (4, 0) is rotated about the y-axus. Draw a picture of the three-dimensional shape that is produced when the circle is rotated about the y-axis. In two or more complete sentences, describe the three-dimensional shape. Upload both parts A and B as your final answer.
When a circle rotates around the y-axis, it forms a three-dimensional object known as a cylinder. The cylinder will have a radius of 1 and height equal to the diameter of the circle, which is 2.
Explanation:When a circle of radius 1 centered at (4,0) is rotated about the y-axis, the three-dimensional shape that is produced is known as a cylinder.
This cylinder would have a radius of 1, and its height would be equal to the length of the diameter of the original circle, which is 2 units (from -1 to 1 along the x-axis).In terms of the visual representation, imagine a circle on a piece of paper, now pick up the paper and rotate it about the line that is the y-axis. The paper, on which the circle is drawn, forms a cylindrical shape when rotated. The edges of the paper represent the bases of the cylinder and the surface of the paper forms the curved surface of the cylinder.Learn more about 3D Shapes after Rotation here:
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The following sequence is an arithmetic sequence what comes next ? 7,___,17
Since this is an arithmetic sequence, you can conclude that the addition to the number is constant.
Let x = the number asked
k = constant number added to the sequence
7 + k = x
x + k = 17
Solve the system of equation:
7 + k + k = 17
7 + 2k = 17
2k = 10
k = 5
Therefore, the missing number is 12 (7 + 5).
a factory worker can make 14 products in 45 minutes. what is the worker's unit rate?
emily is converting 9 feet per hour into inches per minute. which conversion factor should she use
The diameter of a sphere is 21.6 cm. What is the sphere's volume? Round to the nearest tenth, if necessary.
Most flat screen TVs today are made with an aspect ratio (ratio of the length to the height) of 16:9. Xenock Electronics' top selling TV is their 28-inch model, whose viewing area has a length of 24 inches and a height of 13.5 inches. This TV costs $226.99. They have three main competitors that claim to offer a better deal per viewing area. Phil's Supercenter claims their 18-inch model, whose viewing area length is of the length of Xenock's 28-inch model, is a better deal per viewing area at $152.99. Tyler's Electronics claims their 33-inch model, whose viewing area height is 20% taller than Xenock's 28-inch model, is a better deal per viewing area at $276.99. Beltre's Superstore claims their 82-inch model, whose viewing area dimensions are 300% as large as Xenock's 28-inch model, is a better deal per viewing area at $2,079.99. List the TV's in order of best deal per viewing area. Assume all TV's have the same aspect ratio.
Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95. (2 points)
Question 1 options:
1) 203
2) 197
3) 168
4) 163,
Answer: 197
Step-by-step explanation: I took the test :)))
pls help me with this one question
2. Solve 10^6x = 93. Round to the nearest ten-thousandth. (1 point)
11.8109
1.0986
13.3801
0.3281
3. Use a graphing calculator. Solve 5.5^3x = 805 by graphing. Round to the nearest hundredth. (1 point)
2.91
3.92
1.31
0.97,
1. B
2. D
3. C
4. A
5. B
ESKETIT
Which of the following is true for the angular momentum of a rotating bicycle wheel?
(Points : 1)
It is a vector that points in the direction the bike would travel.
It is a vector that points along the axis of rotation perpendicular to the wheel.
It is a vector pointing radially outward from the center to the edge of the wheel.
It is a scalar.,
Expand the logarithmic expression.
log5(7)a^5
A. log57 • 5log5a
B. log57 + 5log5a
C. 7log5a^5
D. log57 – 5log5a
Answer: is b. log57 + 5log5a
This is a word problem where you have to create an equation and a solution to.
"Michaela and Aleah play on the same basketball team. In one game Michaela scored one fifth of the team's points and Aleah scored one tenth's of the teams points. Together they scored a total of 42 points. How many points did the team score?"
(I might find an equation for it, but I doubt it so if anyone is good with creating equations for word problems please help me!!)
-matty
To solve this word problem, set up the equation (1/5) x + (1/10) x = 42 and solve for x. The team scored 140 points.
Explanation:To solve this word problem, we can start by letting the total number of points scored by the team be represented by 'x'. Since Michaela scored one-fifth of the team's points, her score can be represented as (1/5)x. Similarly, Aleah's score can be represented as (1/10)x. Together, their scores add up to 42 points, so we can set up the equation:
(1/5)x + (1/10)x = 42
To simplify the equation, we can find a common denominator of 10:
(2/10) x + (1/10) x = 42
Combining like terms, we get:
(3/10) x = 42
To isolate x, we can multiply both sides of the equation by 10/3:
x = 42 * (10/3)
Simplifying further, we get:
x = 140
Therefore, the team scored 140 points.
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What is the value of n? Enter you answer in the box.
Please help! Even just explaining how to do it will help a lot.
Answer:
The value of n is [tex]n=4[/tex]
Step-by-step explanation:
we know that
The intersecting chords theorem states that the products of the lengths of the line segments on each chord in a circle are equal
so
In this problem
[tex](n+2)16=(n+8)8[/tex]
solve for n
[tex]16n+32=8n+64[/tex]
[tex]16n-8n=64-32[/tex]
[tex]8n=32[/tex]
[tex]n=4[/tex]
what is: 2/3 X 5/6 X 14 =
this is so that i can help a 5th grader. and i am horrible at fractions. please show work and or explain how to do it. so that i can show her how to do it as well.,
If △STU ~ △XYZ, which statements must be true? Check all that apply. ∠S ≅ ∠X ∠T ≅ ∠Y ST = XY SU = XZ
Two triangles are similar if and only if there corresponding angles are congruent and the ratio of there corresponding sides are equal. Triangle STU is similar to triangle XYZ than [tex]\rm \angle S \cong \angle X[/tex] , [tex]\rm \angle T \cong \angle Y[/tex] and [tex]\rm \dfrac{ST}{XY}=\dfrac{TU}{YZ}=\dfrac{SU}{XZ}[/tex].
Given :
[tex]\rm \Delta STU \sim \Delta XYZ[/tex]
Two triangles are similar if and only if there corresponding angles are congruent and the ratio of there corresponding sides are equal.
Now, it is given that triangle STU is similar to triangle XYZ. This condition is only true when:
[tex]\rm \angle S \cong \angle X[/tex][tex]\rm \angle T \cong \angle Y[/tex][tex]\rm \dfrac{ST}{XY}=\dfrac{TU}{YZ}=\dfrac{SU}{XZ}[/tex]It can be conclude that if triangle STU is similar to triangle XYZ than [tex]\rm \angle S \cong \angle X[/tex] , [tex]\rm \angle T \cong \angle Y[/tex] and [tex]\rm \dfrac{ST}{XY}=\dfrac{TU}{YZ}=\dfrac{SU}{XZ}[/tex] . Therefore, the correct option is A), C) and D).
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The radius of a circle is equal to half of its diameter. What is the RADIUS of this circle?
Water is flowing into a 50-gallon bathtub at a rate of 2.3 gallons per minute (gpm). To the nearest minute, how long will it take to completely fill the bathtub?
A. 48 minutes
B. 22 minutes
C. 26 minutes
D. 115 minutes
Which is an example of the associative property?
A) x + 5 = 5 + x
B) (x + 3) + 7 = x + (3 + 7)
C) 3 • (x + 5) = 3 • x + 15
D) If x = a, and a = 7, then x =
Think it’s b not sure though
Cara muffin recipe calls for 1 1/2 cups of flour for the muffins and 1/4 cup flour for the topping.If she makes 1/2 of the original recipe.How much flour will she use.
The amount of cups of flour needed to make 1/2 of the original recipe is 7/8 cups.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Recipe:
Amount of flour for muffins = [tex]1\frac{1}{2}[/tex] = 3/2 cups
Amount of flour for toppings = [tex]\frac{1}{4}[/tex] = 1/4 cups
The total amount of flour:
= 3/2 + 1/4
= (12 + 2) / 8
= 14 / 8
= 7/4 cups
We see that the total amount of flour needed to make one Cara muffin recipe is 7/4 cup of flour.
To make 1/2 of the original recipe.
The amount of flour needed:
1 recipe = 7/4 cups
Divide both sides by 2.
1/2 recipe = 1/2 x 7/4 cups
1/2 recipe = 7/8 cups
Thus,
The amount of cups of flour needed to make 1/2 of the original recipe is 7/8 cups.
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Choose the correct product of (7x − 3)(7x + 3). 49x2 + 9 49x2 − 42x + 9 49x2 − 9 49x2 + 42x + 9
Final answer:
The product of the binomials (7x - 3)(7x + 3) is calculated using the difference of squares formula, resulting in 49x² - 9.
Explanation:
To find the correct product of the binomials (7x − 3)(7x + 3), we use the difference of squares formula, a² - b² = (a - b)(a + b). In this case, a is 7x and b is 3. Thus, the product is:
(7x − 3)(7x + 3) = (7x)² - (3)²
= 49x² - 9
Therefore, the correct product is 49x² - 9.
What is the value of x? The figure shows 2 right triangles, triangle K L J with right angle J and triangle L J M with right angle M. The measure of angle L K J is 30 degrees. The measure of angle L J M is 45 degrees. The length of side K L is 8 square root 2. The length of side L M is x. Enter your answer in the box.