Using the segment addition postulate, which is true?
AB + BC = AD
AB + BC = CD
BC + CD = AD
BC + CD = BD
Answer: The answer is (d) BC + CD = BD.
Step-by-step explanation: We are given the number line and four points A, B, C and D on the line with co-ordinate -6, -1, 2 and 8 respectively.
We are to select the correct statement out of the given four.
(a) L.H.S. = AB + BC = 5 + 3 = 8,
R.H.S = AD = 14 ≠ 8.
So, this option is incorrect.
(b) L.H.S. = AB + BC = 5 + 3 = 8,
R.H.S = CD = 6 ≠ 8.
So, this option is incorrect.
(c) L.H.S. = BC + CD = 3 + 6 = 9,
R.H.S = AD = 14 ≠ 9.
So, this option is incorrect.
(d) L.H.S. = BC + CD = 3 + 6 = 9,
R.H.S = BD = 9.
So, this option is correct.
Thus, the correct option is (d).
which answer describes the polynomial?
3x^3 + 4x^2 - 7
A) Quartic Trinomial
B) Cubic Trinomial
C) Quadratic Trinomial
D) Cubic Binomial
A car travel at an average speed of 48 miles per hour. how many miles does it travel in 4 hours and 15 minutes
M(1,7) is the midpoint of PQ. The coordinates of point P are (-8,3)
What are the coordinates of point Q
Please only answer if you have the answer.
To find the coordinates of point Q when M(1,7) is the midpoint of PQ, and P(-8,3), we use the midpoint formula to get Q's coordinates as (10, 11).
Explanation:The question asks for the coordinates of point Q given that M(1,7) is the midpoint of PQ and the coordinates of point P are (-8,3). To find the coordinates of Q, we can use the midpoint formula which is (x1 + x2)/2, (y1 + y2)/2 where (x1, y1) are the coordinates of P and (x2, y2) are the coordinates of Q. Since M is the midpoint, its coordinates (1,7) equal these averages.
For x: (-8 + x2)/2 = 1For y: (3 + y2)/2 = 7Solving these equations for x2 and y2, we find the coordinates of Q to be (10, 11).
What the opposite of 30 degrees North latitude
Which of the following is a fundamental quantity?
A) Volume
B) Density
C) Area
D) Mass
E) Acceleration
When fractions share the same number on the bottom what is it called?
Step-by-step explanation: When fractions have the same bottom number, they're called like fractions. When adding and subtracting fractions, our goal is to get like fractions or fractions that have the same denominator.
Also, it's easy to compare like fractions because you just have to look at the numerators of each of the fractions you are givemn.
Bettina’s age is three times Melvina’s age. If 20 is added to Melvina’s age and 20 is subtracted from Bettina’s age, their ages will be equal. How old is each now?
A bakery packages 868 cupcakes into 31 boxes. The same number of cupcakes are pput into each box. How many cupcakes are in each box?
if the federal reserve decreases the reserve rate from 5% to 2.5% how does this affect the amount of money that would result because of fractional reserve banking from an initial deposit into a bank of $35000
It increases the amount by 700,000
The function g(x) is a continuous quadratic function defined for all real numbers, with some of its values given by the table below.The quadratic function ƒ(x) is represented by the parabola below. x g(x) -3 0 -2 5 0 9 2 5 3 0 Select all the statements that are true. The function ƒ(x) has a maximum value at x = 4.5. The function g(x) has a minimum value of 0. The maximum value of g(x) is twice the maximum value of ƒ(x). Neither function has a minimum value.
The function g(x) has a minimum value of 0, but we cannot determine the maximum value of g(x) or compare it to the maximum value of f(x). The statements about the maximum value of ƒ(x) and the lack of minimum value for both functions are not supported by the given information.
Explanation:The function g(x) is a continuous quadratic function that can be represented by a parabola. From the given table, we can observe that the minimum value of g(x) is 0 and it occurs when x = -3 or x = 3. Therefore, the statement 'The function g(x) has a minimum value of 0' is true.
To determine the maximum value of g(x), we need to find the vertex of the parabola representing g(x). Since the function is continuous and quadratic, the vertex occurs at the axis of symmetry. The axis of symmetry is given by x = -b/2a, where a and b are the coefficients of the quadratic function. In this case, the equation representing g(x) is not given, so we cannot determine the exact maximum value of g(x) or compare it to the maximum value of f(x).
Based on the given information, we cannot determine whether the function f(x) has a maximum value at x = 4.5 or if the maximum value of g(x) is twice the maximum value of f(x). Therefore, the statements 'The function ƒ(x) has a maximum value at x = 4.5' and 'The maximum value of g(x) is twice the maximum value of ƒ(x)' are false.
Regarding the statement 'Neither function has a minimum value,' it is not accurate based on the given information. We already established that g(x) has a minimum value of 0.
Which is greater 300 kelvins or 34 degrees Celsius ? Show your work
To answer this item, we are to convert one of the unit to the other. The approach to answering is to convert the 34 degrees Celsius to kelvin by the equation,
T = C + 273.15
Substituting the known value,
T = (34) + 273.15 = 307.15 K
Since 307.15K is greater than 300K then, the greater value is 34 degrees C.
ANSWER: 34 degrees C
Find the value of x that makes m ∥ n, m ∥ n.
The value of x that will make m parallel to n is: 40.
Recall:According to the Converse of Corresponding Angles Theorem, the two lines cut across by a transversal line are parallel to each other if the two corresponding angles formed are congruent.
Therefore, let's find the value of x that will make m parallel to n.
Thus,[tex]3x^{\circ} = 120^{\circ}[/tex] (corresponding angles)
Solve for x. Divide both sides by 3[tex]x = 40[/tex]
Therefore, the value of x that will make lines m and n to be parallel to each other is 40.
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Cameron estimates that the math class will sell 200 calendars. what will the total cost be'
Which quadratic equation is equivalent to (x + 2)2 + 5(x + 2) – 6 = 0?
(u + 2)2 + 5(u + 2) – 6 = 0 where u = (x – 2) u2 + 4 + 5u – 6 = 0 where u = (x – 2) u2 + 5u – 6 = 0 where u = (x + 2) u2 + u – 6 = 0 where u = (x + 2)
we have
[tex](x+2)^{2} +5(x+2)-6=0[/tex]
Let
[tex]u=(x+2)[/tex]
Substitute in the expression
[tex](u)^{2} +5(u)-6=0[/tex]
therefore
the answer is
[tex](u)^{2} +5(u)-6=0[/tex] is equivalent to [tex](x+2)^{2} +5(x+2)-6=0[/tex]
Answer: C
Step-by-step explanation:
Took the test
A pattern for 1 1 uniform uses 12 12 yards of material. Boleslaw wants to know how many yards are needed for 8 8 uniforms. Chantal wants to know how many yards she will need to make 15 15 uniforms.
To find the amount of material needed for a certain number of uniforms, we can use a proportion and multiply the amount of material needed for 1 uniform by the desired number of uniforms.
Explanation:To find out how many yards are needed for 8 uniforms, we can set up a proportional relationship between the number of uniforms and the amount of material needed. We can do this by dividing the amount of material needed for 1 uniform by the number of uniforms, and then multiplying by the desired number of uniforms. The formula for this is (Amount of material needed for 1 uniform / Number of uniforms) * Desired number of uniforms. Using this formula, we can determine that 8 uniforms would require (12 yards / 1 uniform) * 8 uniforms = 96 yards of material.
To find out how many yards are needed for 15 uniforms, we can use the same formula. (12 yards / 1 uniform) * 15 uniforms = 180 yards of material.
Therefore, 8 uniforms require 96 yards of material, and 15 uniforms require 180 yards of material.
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If angle A and angle B are complementary then the measure of angle A is 45, find a counterexample
The measure of a angle B is 45°.
Given that, angle A and angle B are complementary and ∠A=45°.
What are complementary angles?In geometry, complementary angles are defined as two angles whose sum is 90 degrees.
Now, ∠A + ∠B = 90°
⇒ 45° + ∠B = 90°
⇒ ∠B = 45°
Counter example: If angle A is 90°, then the angle A and angle B are not complementary angles.
Therefore, the measure of a angle B is 45°.
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the sum of two numbers is 8, and the sum of their squares is 34. what is the smaller number?
5 +3 = 8
3^2 = 9
5^2 = 25
25 +9 = 34
smaller number is 3
What is the graph of the equation 4x – 5y = 15?
Describe how to graph the solution of
y ≤ −x2 + 2x.
We are given a inequality as:
[tex]y\leq -x^2+2x[/tex]
We know that the graph of this inequality will be a solid parabola ( since the inequality is with equality sign) .The parabola will be downward parabola ( Since for any general equation of parabola as y=ax^2+bx+c if a<0 then the parabola is downward and if a>0 then the parabola is upward)Also the roots of the parabola are the points where y=0.( The roots are: -x(x-2)=0
x=0 and x=2 are the roots of the parabola)
Also the region inside the parabola is shaded.(This could be checked by taking different points)
To graph the solution of y ≤ -x² + 2x, follow these steps: graph the equation y = -x² + 2x, determine the boundary line, and shade the appropriate region based on a test point.
Explanation:To graph the solution of the inequality y ≤ -x² + 2x, we can follow these steps:
Start by graphing the equation y = -x² + 2x as a parabola.Next, determine the boundary line which separates the region where y is less than or equal to the parabola from the region where y is greater than the parabola. In this case, the boundary line is the actual graph of the equation y = -x² + 2x.Then, choose a test point that is not on the boundary line and substitute its coordinates into the inequality to check if it is true. If it is true, shade the region that includes the test point. If it is false, shade the other region.By following these steps, you will be able to graph the solution of the inequality y ≤ -x² + 2x.
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An item costs $410 before tax, and the sales tax is $20.50 . find the sales tax rate. write your answer as a percentage.
The percentage of sales tax is 5%.
Given that, an item costs $410 before tax, and the sales tax is $20.50.
What is the sales tax?Calculating the sales tax applied to a purchase is a matter of simply multiplying the tax rate by the purchase price using the equation sales tax = purchase price × sales tax rate. Adding the sales tax to the original purchase price gives the total price paid with tax.
Let x% be the sales tax.
Now, x% of 410 = 20.50
0.01x ×410 = 20.50
⇒ 4.1x=20.50
⇒ x=20.50/4.1
⇒ x=5
Therefore, the percentage of sales tax is 5%.
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what is the decimal equivalent to 15 1/4
The equivalent decimal number will be 15.25.
What is Decimal number?
A decimal number is a number that consists of a whole and a fractional part.
Given that;
The number is,
⇒ 15 1/4
⇒ 61 / 4
Now,
Solve the number in decimal form as;
The number is,
⇒ 15 1/4
⇒ 61 / 4
⇒ 61 ÷ 4
After divide we get;
⇒ 61 ÷ 4 = 15.25
Thus, The equivalent decimal number will be 15.25.
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a bag contains 42 cups of dog food. your dog eats 2 1 3 cups of dog food each day how many days does the bag of dog food last
divide 42 by 2 1/3
2 1/3 = 7/3
42 / 7/3 =
42 * 3/7 =
126/7 = 18
it will last 18 days
The number of days it will take the dog to consume the 42 cup of food will be 18 days.
Total cups of dog food = 42 cups Amount of cups consumed per day = [tex] 2 \frac{1}{3} \: cups [/tex]To obtain the number of days it will take to consume the entire food :
Divide the total amount of food by the amount consumed per dayHence,
(42 ÷ (7/3))
Take the reciprocal of 7/3 and change the operation sign to multiplication
42 × 3/7 = (42 × 3) / 7 = 126 / 7 = 18 days
Therefore, it will take the dog 18 days to finish up the 42 cups of food.
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Find the derivative of y = sin2 (4x) cos (3x) with respect to x.
A. 8 sin (4x) cos (4x) cos (3x) - 3 sin2 (4x) sin (3x)
B. 8 sin (4x) cos (3x) - 3 sin2 (4x) sin (3x)
C. 8 sin (4x) cos (4x) cos (3x) - 3 sin2 (4x) sin (3x) cos (3x)
D. 8 cos (4x) cos (3x) - 3 sin2 (4x) sin (3x)
Find the sum and express it in scientific notation. 0.00348 + (6.2 x 10^-2) A) 2.176 x 10^-4 B) 6.2348 x 10^-2 C) 6.2348 x 10^-1 D) 6.548 x 10^-2
23 POINTS PLZ HELP
The sum of the expression in scientific notation is given by option D) 6.548 × 10⁻².
Given expression is,
0.00348 + (6.2 x 10⁻²)
We have to first find the sum.
For that, rewrite the number in the scientific form in the normal form.
Since the exponent of 10 is -2, the decimal point is shifted 2 units to the left.
6.2 x 10⁻² = 0.062
0.00348 + (6.2 x 10⁻²) = 0.00348 + (0.062)
= 0.06548
Now, we have to write this in scientific notation as the power of 10.
After shifting the decimal point to the right up to 2 units, 0.06548 becomes = 6.548.
So, 0.06548 = 6.548 × 10⁻²
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Need help on answer I’m not so sure what to do
Ms. Rao buys a computer, a printer, and a scanner for $2,543. The computer costs $1,502 more than the printer. The printer costs $123 more than the scanner. How much does Ms. Rao pay for the computer?
How did you get the answer? I got the answer of $1808. Please explain...
All scatter plots show either a positive or a negative trend.
True
False
Solve for x: −2x − 4 > 8 (1 point)
x < −6
x > −6
x < −2
x > −2
Option A : x < -6 is the correct choice.
We have a inequality -
−2x − 4 > 8
We have solve and find the solutions to this inequality.
What is an Inequality in mathematics ?An inequality compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.
According to the question, we have -
−2x − 4 > 8
Add 4 on both sides -
-2x - 4 + 4 > 8 + 4
-2x > 12
Multiply both sides by -1, we get -
2x < - 12
Divide by 2 on both sides -
x < -6
Hence, x < -6 represents the solution of the inequality.
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Jose drives a truck for a soft drink company. His truck is filled with
15-ounce cans and 70-ounce bottles. Let c be the number of 15-ounce cans the truck is carrying, and let b be the number of 70-ounce bottles.Suppose the truck can carry at most 6000 pounds (96,000 ounces).
Using the values and variables given, write an inequality describing this.
PLEASE HELP! I'm struggling so much
Answer : 15c+70b<96,000
Step-by-step explanation: