Question 14 a certain drug is made from only two ingredients: compound a and compound
b. there are 3 milliliters of compound a used for every 4 milliliters of compound
b. if a chemist wants to make 497 milliliters of the drug, how many milliliters of compound b are needed?
Solve the inequality
5x < 16 + x.
A.) x < 1/4
B.) x > 1/4
C.) x < 4
D.) x > 4
Suppose that y varies inversely with x. Use the information to find k, and then choose the equation of variation. x = 2.5 when y = 100.
Answer:
constant of variation(k) is, 250.
[tex]y = \frac{250}{x}[/tex]
Step-by-step explanation:
The inverse variation says that:
[tex]y \propto \frac{1}{x}[/tex]
then, the equation is in the form of :
[tex]y = \frac{k}{x}[/tex] ....[1] where, k is the constant of variation
As per the statement:
Suppose that y varies inversely with x.
then,
by definition of inverse variation we have;
[tex]y = \frac{k}{x}[/tex]
When x = 2.5 and y = 100 then
Substitute these in [1] we have;
[tex]100 = \frac{k}{2.5}[/tex]
Multiply 2.5 both sides we have;
[tex]250 = k[/tex]
or
k = 250
⇒[tex]y = \frac{250}{x}[/tex]
Therefore, the constant of variation is, 250 and the equation we get [tex]y = \frac{250}{x}[/tex]
Which angle in triangle XYZ has the largest measure?
Answer:
A. [tex]\angle x[/tex]
Step-by-step explanation:
We have been given measure of three sides of a triangle. We are asked to determine, which angle has the largest measure.
We know that the side of triangle corresponds to its opposite angle. The angle opposite to smallest side will have smallest measure and angle opposite to largest side will have largest measure.
We can see that the measure of largest side of our given triangle is 9 and it is opposite to angle x, therefore, [tex]\angle x[/tex] has the largest measure and option A is the correct choice.
Someone help with number 11 please!! Thank you
In the diagram, JG = 5 cm and GE = 10 cm. Based on this information, can G be a centroid of triangle HJK? Point G cannot be a centroid because JG does not equal GE. Point G cannot be a centroid because JG is shorter than GE. Point G can be a centroid because GE and JG are in the ratio 2:1. Point G can be a centroid because JG + GE = JE.
in short terms it's b lol
Five more than three times a number q is written as
Answer:
Step-by-step explanation:
5+(3q) I think
HELP PLEASE!!
Graph the system of linear equations.
-1/2y=1/2x+5 and y=2x+2
The solution to the system is ( _ , _ )
the correct answer is -4, -6
In space, the intersection of a line and a plane is
A) not possible.
B) a point or a line.
C) a line or a plane.
D) a point or a plane.
Two radical expressions with the same degree and the same _____ are called like terms.
Answer:
Two radical expressions with the same degree and the same radicand are called like terms.
Step-by-step explanation:
All the terms that have same power and vari ables are called like terms.
For example: 3x²y and 5x²y are like terms, 2x³ and 7x³ are like terms, etc.
The number under the root is known as radicand.
Two radical expressions are like terms if
1. They have same degree.
2. They have same radicand.
Therefore the two radical expressions with the same degree and the same radicand are called like terms.
Two radical expressions are called like terms if they have the same degree and the same:
E. radicand
Two radical expressions are called like terms if they have the same degree and the same radicand. The radicand is the number or expression inside the radical symbol. For example, in the radical expression [tex]\(\sqrt{5}\)[/tex], the radicand is 5. For two radical expressions to be like terms, they must not only have the same index (degree) of the radical but also the same radicand.
Consider the expressions [tex]\(\sqrt{3}\) and \(2\sqrt{3}\)[/tex]. These are like terms because they both have the same degree (square root, which is an index of 2) and the same radicand (3). Similarly, [tex]\(\sqrt[3]{7}\) and \(4\sqrt[3]{7}\)[/tex] are like terms because both are cube roots with a radicand of 7.
However, [tex]\(\sqrt{2}\) and \(\sqrt{3}\)[/tex] are not like terms because their radicands differ. Likewise, [tex]\(\sqrt[4]{5}\) and \(\sqrt{5}\)[/tex] are not like terms because their degrees (indices) differ. Therefore, for radical expressions to be like terms, matching radicands and degrees are essential.
The correct question is:
Two radical expressions are called like terms if they have the same degree and the same
A. denominator
B. radical
C. term
D. number
E. radicand
In which number is the digit 8 ten times larger than it is in the number 18? A) 108 B) 387 C) 801 D) 1,840 E) 8,205
what fractions is 0.75 equal to
At day camp, hiking began at 8:30 a.m. and lasted 2 hours and 42 minutes. What time did hiking end? A. 9:02 a.m. B. 10:12 a.m. C. 11:12 a.m. D. 12:02 p.m.
Plz help ppl
HEEEEEEEEEEEEEEEEEEEEEEELPLLLLPLPLPLPLPLPLPLPLPLPLPLPLPL
Natalie recorded her exercise for a week. She ran 16 miles, swam 3 miles, biked 22 miles, and rollerbladed 7 miles. What part of her total distance during the week did she run?
Expand the logarithm. log₅ 5x⁻⁵
PLS HELP!
Help me please i will award
Miranda wants to buy as many collectible dolls as possible, for $2.50 each. If she has $45.00 to spend, how many dolls can she buy?
Which equation BEST represents this situation?
A) 45x = 2.5
B) 2.5x = 45
C) x + 2.5 = 45
D) x + 45 = 2.5
Solve the following equation. Then place the correct number in the box provided. 2x - 1 ≤ x + 5
Answer:
The solution for the inequality is [tex]x \leq 6[/tex].
Step-by-step explanation:
Consider the provided inequality.
[tex]2x - 1 \leq x + 5[/tex]
Subtract x from both the sides.
[tex]2x -x- 1 \leq x-x + 5[/tex]
[tex]x- 1 \leq 5[/tex]
Add 1 to both the sides.
[tex]x- 1+1 \leq 5+1[/tex]
[tex]x \leq 6[/tex]
Hence the solution for the inequality is [tex]x \leq 6[/tex].
The number of State Parks in California is 36 more than one third the number of State Parks in Florida. There are 85 State Parks in California. Which of the following equations would you use to find the number of State Parks in Florida? Note: f represents the number of state parks in Florida. 3(f − 36) = 85 1 over 3f + 36 = 85 Quantity f minus 36 all over 3 equals 85 Quantity f plus 36 all over 3 equals 85 Question 3(Mu
the greatest wind speed ever recorded on earth's surface is 231 miles per hour. what is the speed in kilometers per hour
To convert 231 miles per hour to kilometers per hour, multiply by the conversion factor of 1.60934, resulting in approximately 371.76 km/h.
The greatest wind speed ever recorded on Earth's surface is 231 miles per hour (mph). To convert this speed into kilometers per hour (km/h), we use the conversion factor that 1 mile is approximately 1.60934 kilometers. Therefore, the speed in kilometers per hour is given by multiplying the speed in miles per hour by this conversion factor.
Here is the calculation:
231 mph x 1.60934 = 371.75774 km/h.
Approximately, the wind speed would be 371.76 km/h after converting from miles per hour.
what percent is 608 million of 845 million
Express the complex number -3i in trigonometric form.
Type an equation of the horizontal line that passes through the point (-2,5)
The equation of the horizontal line that passes through the point ( -2 , 5 ) is
y = 5
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , let the point be A ( x₁ , y₁ )
The value of A ( x₁ , y₁ ) = A ( -2 , 5 )
Now , the slope of the line m is given by
Since , the line is a horizontal line , the slope of the line m = 0
Slope m = 0
Now , the equation of line is given by the equation
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 5 = 0 ( x + 2 )
y - 5 = 0
Adding 5 on both sides of the equation, we get
y = 5
Therefore, the value of A is y = 5
Hence ,
The equation of the horizontal line that passes through the point ( -2 , 5 ) is y = 5
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Which are the possible side lengths of a triangle?
A.3 cm, 5 cm, 9 cm
B.4 cm, 8 cm, 10 cm
C.6 cm, 9 cm, 17 cm
D.8 cm, 10 cm, 18 cm
Final answer:
The possible side lengths of a triangle, according to the Triangle Inequality Theorem, must adhere to the principle that the sum of any two sides must be greater than the third side. Option B, with side lengths of 4 cm, 8 cm, and 10 cm, fulfills this requirement and forms a valid triangle.
Explanation:
The question asks which set of side lengths can form a triangle. In order to determine the possible side lengths of a triangle, we must use the Triangle Inequality Theorem. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Now, let's evaluate the options provided:
A. 3 cm, 5 cm, 9 cm: Here, 3 + 5 is not greater than 9, so these sides do not satisfy the theorem.
B. 4 cm, 8 cm, 10 cm: In this case, 4 + 8 is greater than 10, 8 + 10 is greater than 4, and 4 + 10 is greater than 8, satisfying the inequality.
C. 6 cm, 9 cm, 17 cm: For these measurements, 6 + 9 is less than 17, failing to meet the criteria.
D. 8 cm, 10 cm, 18 cm: Here too, 8 + 10 is less than 18, thus not compliant.
Hence, the correct answer is B. 4 cm, 8 cm, 10 cm, as these are the only side lengths that satisfy the Triangle Inequality Theorem and can form a triangle.
Tommy is twice as old as his younger sister.The sum of the siblings' ages is 21. Which equation can be used to determine the age of Tommy's younger sister? A. x-2=21 B. x+2x=21 C. 2x=21 or D. x/2=21
find the center and radius for the circle, given the equation: x2+16x+y2-6y=-24
Anna lives 2.5 miles to the east of her school, and Ben lives 2 miles to the west of the same school. Anna draws a map with a number line connecting her house to Ben’s house. On the number line, the school is at 0 and her house is at the point +2.5. On the map, Ben’s house is at the point
Answer:
Ben's house is at point -2
Step-by-step explanation:
Given that Anna lives 2.5 miles to the east of her school, and Ben lives 2 miles to the west of the same school
When Anna draws a map with a number line connecting her house to Ben’s house, with school marked as 0 then to the east would be +2.5
Since Ben lives 2 miles to the west, Ben would be marked as negative -2.
(West denotes negative in number line)
So answer is Ben's house is at point -2
Ben's house is at the point -2 on the map of number line.
What is Number line?A number line is pictorially represented as a horizontal straight line where numbers are placed at equal distance. Usually integers are placed in the number line with negative numbers placed to the left of 0 and positive numbers placed to the right of 0.
Number lines are used in performing basic operations in mathematics such as addition, multiplication, subtraction and division.
Here, it is given that Anna lives 2.5 miles to the east of her school and Ben lives 2 miles to the west of the same school.
So school is a common point here with respect to which both of their distance to house are marked.
On the number line school is at 0.
Anna's and Ben's house lies two opposite sides from the school.
So if one of their houses is at the positive side, the house of other one's will be at the negative side.
Given that, Anna's house is at positive side at the point +2.5.
Then clearly Ben's house will be at the negative side and the point will be -2 since it is 2 miles away from the school.
Hence, Ben's house will be at the negative side of the number line at point -2.
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Multiply (2x2 + 3x − 6)(x − 1).
help in math ...........................................
Solve by completing the square
X^2+12x-13=0
To solve the quadratic equation x^2 + 12x - 13 = 0 by completing the square, follow these steps. The solutions to the equation are x = 1 or x = -13.
Explanation:To solve the quadratic equation x^2 + 12x - 13 = 0 by completing the square, follow these steps:
Move the constant term to the other side of the equation:x^2 + 12x = 13Take half of the coefficient of the x-term and square it:(12/2)^2 = 36Add this value to both sides of the equation:x^2 + 12x + 36 = 13 + 36Factor the left side of the equation, which should be a perfect square:(x + 6)^2 = 49Take the square root of both sides and solve for x:x + 6 = ±√49x + 6 = ±7x = -6 ± 7Therefore, the solutions to the equation are x = 1 or x = -13.