Answer: a=-3b
2
Step-by-step explanation:
get all letters on the same side so:
7a-5a (because when you cross the = you do the opposite)=-b+2b
2a=b
you are solving for a so: 2a/2=b/2
so the 2 cancel out and you have a=1/2b
You and your friend get the same magazine. You spend $15 for twelve issues. Your friend pays $1.50 per issue but gets the first two issues free. How many issues will your friend get if he also spends $15?
In this ordered pair (4,-5) which number is the ordinate
In the ordered pair (4, -5), the number -5 is the ordinate, which represents the vertical position of a point in a coordinate system.
In the ordered pair (4,-5), the number -5 is the ordinate. In a coordinate system, ordered pairs are used to define locations with two values: the x-coordinate and the y-coordinate. The first number in the pair represents the x-coordinate, which is the horizontal position, and the second number represents the y-coordinate, which is the vertical position, also known as the ordinate.
In this context, the ordinate is the position relative to the horizontal axis in a two-dimensional space. It indicates how far up or down a point lies from the horizontal (x) axis. Hence, in the ordered pair (4, -5), -5 is the ordinate. If a point is above the x-axis, its ordinate is positive; if it's below, as in this case, it's negative.
The variance represents how the data is distributed around the mean
b. the variance is always equal to the mean squared (μ2)
c. the variance is negative whenever the mean of x is negative
d. the variance is the value of x that is most likely to occur in the data.
A rectangular fountain display has a perimeter of 400 feet and an area of at least 9100 feet. describe the possible widths of the fountain
what are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotensue is 15 units long?
Answer:
For plato users the correct option is D.
Step-by-step explanation:
D. 4.9 units, 14.2 units
Simplify the fraction
what is 16 over 38
Irst. write an expression for the probability that both socks are bl
A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has 15 minutes per session of strength-training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength-training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week. Which statement describes when the plans are based on the same number of aerobic exercise sessions?
A. Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.
B. Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
C. Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.
D. Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.
HELPPPPP PLEASEEEEEE
The average (A) of two number,M and N, is given by the formula A=m+n/2. Find the average of the two numbers 36 and 72.
Answer: 54
Step-by-step explanation:
Average = Total/ total number
Average= 36 +72/2
= 108/2
= 54
54 is the average of the two numbers 36 and 72.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We need to find the average of the two numbers 36 and 72.
The average (A) of two number, M and N, is given by the formula A=m+n/2
Let m = 36
n=72
Now to find the average of two numbers we have to plug in these values in the formula
A=36+72/2
=108/2
=54
Hence, 54 is the average of the two numbers 36 and 72.
To learn more on Statistics click:
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Sammy has a 10-foot ladder, which he needs to climb to reach the roof of his house. the roof is 12 feet above the ground. the base of the ladder must be at least 1.5 feet from the base of the house. how far is it from the top of the ladder to the edge of the roof? draw a sketch.
a cylinder. With a diameter of 6cm and a height of 10cm. Can you help me work out the volume of this cylinder to 1 decimal place please?
Final answer:
The volume of a cylinder with a diameter of 6 cm and a height of 10 cm is 282.8 cm³, calculated using the formula V = πr²h and rounding to one decimal place.
Explanation:
To calculate the volume of a cylinder, we use the formula V = πr²h where V is the volume, r is the radius of the base, and h is the height of the cylinder. In this case, we have a cylinder with a diameter of 6 cm, which means the radius r is half of that, or 3 cm. The height h is 10 cm. So, the volume is calculated by:
V = π × (3 cm)² × 10 cm
Substituting 3.142 for π, we get:
V = 3.142 × 9 cm² × 10 cm
V = 3.142 × 90 cm³
V = 282.78 cm³
Therefore, the volume of the cylinder rounded to one decimal place is 282.8 cm³.
If a radical is multiplied by a number or variable, you should put the number or variable _____ the radical sign.
Final answer:
Numbers or variables are placed outside of the radical sign when multiplied by a radical. This representation indicates that the entire radical, not just the number inside, is to be multiplied by that number or variable.
Explanation:
If a radical is multiplied by a number or variable, you should put the number or variable outside the radical sign. In mathematics, multiplication or division by the same number on both sides of an equation does not change the equality. When you multiply a radical by a number or variable, you are essentially multiplying the contents inside the square root by that number or variable, but outside of the radical sign to maintain proper order of operations.
When writing an expression involving radicals mathematically, numbers or variables outside the radical do not directly interact with the values inside until simplification or further operations are performed. For example, if you're multiplying 3 by √2, you would write it as 3√2, not √(3×2). The multiplication of the coefficient (the number in front of the radical) applies to the entire radical, not just the number inside it.
In a cross-country race with 35 participants , the mean finish time was 21 minutes . Which statement must be true?
A-the most common finish time was 21 minutes
B-at least one participant finished in exactly 21 minutes.
C-over half of the participants finished in less than 21 minutes.
D-if no participants finished in less than 21 minute, than everyone finished in exactly 21 minutes
use prime factorization to find gcf of 57 and 27
On traditional maps, Earth is represented in a flat plane, or by Euclidean geometry. However, a globe is a more accurate model that comes from elliptical geometry. How does a globe represent the fact that there are no parallel lines in elliptical geometry? The equator is not parallel to any other latitudinal lines. The North and South Poles are never connected by a geodesic. The geodesics connecting the North and South Poles never intersect. The geodesics connecting the North and South Poles intersect at both of the Poles.
Answer:
D. The geodesics connecting the North and South Poles intersect at both of the Poles
Step-by-step explanation:
Answer:
D) The geodesics connecting the North and South Poles intersect at both of the Poles.
Step-by-step explanation:
got it right on edge 2021 :)
Find the measure of each indicated angle
Answer:64
Step-by-step explanation:
36+84+x=180
x=180-120
x=60
right angle 90=x+y=60+y
y=90-60=30
y+86+?=180
30+86+?=180
?=180-116
?=64
What is the limit ? And how do I get the answer?
what is 4,548 in expanded form ?
−3/4(x+2)=6 solve for x
Find the tax on a dinette set with a cash price of $200 that has been reduced by 20% if the tax rate is 6.5%.
The slope of the line passing through the points (0,0) and (2,3) is
Explain how you can tell without calculating whether the sum of a postitive number and a negative number will be positive, negative or zero.
If sin theta = 12/13 and theta is an acute angle find cot theta
Answer:
cot θ = [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
If sin θ = [tex]\frac{12}{13}[/tex] and 'θ' is an acute angle then we have to find the value of cotθ
From the figure attached.
y² + 12² = 13² [ by Pythagoras Theorem ]
y + 144 = 169
y² = 169 - 144 = 25
y = 5
Now cot θ = [tex]\frac{base}{Height}[/tex]
= [tex]\frac{y}{12}[/tex]
= [tex]\frac{5}{12}[/tex]
Therefore, cot θ =[tex]\frac{5}{12}[/tex] is the answer.
You are going to bake an over-sized sheet cake. The recipe calls for 2 cups of sugar for every 3 cups of flour. How many cups of flour are needed if you use 18 cups of sugar?
Answer:27
Step-by-step explanation:
Sara has 16 red flowers and 24 yellow flowers. She wants to make a bouquet with the same number of each color flowers in each bouquet. How many red flowers will be in each bouquet.
In the diagram shown below, ∠K=18º and ∠H=18º.
Prove KJ=13.75. Justify your steps in a paragraph proof.
If function f is defined by f x( ) = 3x2 − 5x + 4, what is f x( − 4) ?
How to find the sum of the squares of the roots of an equation?
Final answer:
To calculate the sum of the squares of the roots of a quadratic equation, apply Vieta's formulas to find the sum and product of the roots and use them in the identity (α + β)² - 2αβ to avoid directly solving for the roots.
Explanation:
To find the sum of the squares of the roots of an equation, especially for a quadratic equation of the form ax²+bx+c=0, we use the relationship between the coefficients and the roots provided by Vieta's formulas.
The sum of the roots, denoted as α and β, is given by -b/a, and the product of the roots is c/a. To find the sum of the squares of the roots (α² + β²), you can use the identity (α + β)² = α² + 2αβ + β², or α² + β² = (α + β)² - 2αβ.
By substituting the sum and product of the roots from Vieta's formulas, you can calculate the sum of the squares without actually solving for the roots. This approach is especially useful in equilibrium problems or other situations where you might encounter square roots or higher powers and wish to simplify calculations.
A store sells a floor lamp for 73.99. The store is having a sale that reduces the lamps price by 35%.How much does the lamp cost during sale?
73.99 * 0.30 = 22.197 = $22.20
73.99 - 22.20 = 51.79
Lamp is $51.79