The postulate that is illustrated for the real numbers 2(x + 3) = 2x + 6 is The Distributive postulate , the correct option is (E) The Distributive postulate .
The Distributive Postulate states that for any three numbers a,b and c ,
a(b+c) = a*b + a*c
For Example : 5(6+1) = 5*6 + 5*1
5*7 = 30+5
35=35
In the question ,
it is given that
2(x + 3) = 2x + 6
On applying Distributive postulate in 2(x + 3)
we get
= 2*x + 2*3
= 2x + 6
hence Distributive postulate is applied in 2(x + 3) = 2x + 6 .
Therefore , the postulate that is illustrated for the real numbers 2(x + 3) = 2x + 6 is The Distributive postulate , the correct option is (E) The Distributive postulate .
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how do I know where which choices below go into the correct blanks for number 1-4?
For 1, we have the following triangle:
Using the cosine function to get the hypotenuse we get:
[tex]\begin{gathered} \cos (45)=\frac{7}{h} \\ \Rightarrow h=\frac{7}{\cos(45)}=\frac{7}{\frac{1}{\sqrt[]{2}}}=7\cdot\sqrt[]{2} \\ h=7\cdot\sqrt[]{2} \end{gathered}[/tex]Now that we have the hypotenuse, we can find the remaining side using the pythagorean theorem:
[tex]\begin{gathered} h^2=7^2+x^2 \\ \Rightarrow x^2=h^2-7^2=(7\cdot\sqrt[]{2})^2-7^2=49\cdot2-49=49 \\ \Rightarrow x^2=49 \\ x=7 \end{gathered}[/tex]Therefore, the value of the remaining side is 7.
In the figure below, BAC~QPR. Use this information and the diagram below to name the corresponding parts of the similar triangles
a.
∠A is the right angle of the triangle ABC, so the corresponding angle is ∠P, which is the right angle of the triangle PQR.
b.
BC is the hypotenuse of the triangle ABC, so the corresponding side is QR, which is the hypotenuse of the triangle PQR.
c.
∠C is the smaller angle of the triangle ABC, so the corresponding angle is ∠R.
d.
∠Q is the bigger angle of the triangle PQR, so the corresponding angle is ∠B.
e.
PQ is the smaller leg of the triangle PQR, so the corresponding side is AB.
The diagonal of a rectangle is 25 inches. The width is 15 inches. What is the area of the rectangle?
Answer:
300 in²
Step-by-step explanation:
Hello!
Because the diagonal forms right triangles, we can use the Pythagorean Theorem to find the missing length of the rectangle.
a² + b² = c²
a = legb = legc = hypotenuseIn this case, 25 is c, and 15 is a. We can solve for b using the formula.
Solve for ba² + b² = c²15² + b² = 25²225 + b² = 625b² = 400b = 20So the missing length of the rectangle is 20. We can find the area by multiplying 15 and 20
15 * 20 = A300 = AThe area is 300 in².
Write an equation of the line containing the given point and parallel to the given line.
(9,−6); 4x−3y=2
Answer:
y=4/3x-18
Step-by-step explanation:
4x-2=3y
y=4/3x-2/3
to parallel slope has to be the same
-6=9*(4/3)+b
b=-18
y=4/3x-18
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?
c = price of a slice of Cheese pizza
m= price of a slice of mushroom pizza
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50
3c + 4 m = 12.50
Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50.
3c + 2m = 8.50
We have the system of equations:
3c + 4 m = 12.50 (a)
3c + 2m = 8.50 (b)
Subtract (b) to (a) to eliminate c
3c + 4m = 12.50
-
3c + 2m = 8.50
_____________
2m = 4
Solve for m:
m = 4/2
m=2
The cost of one slice of mushroom pizza is $2
estimate 328 divided by 11=?
Answer:
30
Step-by-step explanation:
It takes chuck 24 minutes to type and spell check 14 pages. Find how many pages he can type and spell check in 1.5 hours. Remember to convert 1.5 hours to minutes
In order to find how many pages can be typed, first let's convert 1.5 hours to minutes:
[tex]\begin{gathered} 1\text{ hour}\to60\text{ minutes} \\ 1.5\text{ hour}\to x\text{ minutes} \\ \\ \frac{1}{1.5}=\frac{60}{x} \\ x=60\cdot1.5 \\ x=90 \end{gathered}[/tex]Then, to find the number of pages, let's do the following rule of three:
[tex]\begin{gathered} 14\text{ pages}\to24\text{ minutes} \\ x\text{ pages}\to90\text{ minutes} \\ \\ \frac{14}{x}=\frac{24}{90} \\ 24x=14\cdot90 \\ x=\frac{14\cdot90}{24}=52.5 \end{gathered}[/tex]Therefore Chuck can type and spell check 52.5 pages in 1.5 hours.
10 Zara writes a sequence of five numbers. The first number is 2. The last number is 18. Her rule is to add the same amount each time. Write the missing numbers. 2,____ ,_____,______, 18
If the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that, the first number is 2 and the last number is 18,
a = 2
L=18
n=5
a₅=5
a₅=a+(5-1)d
18=2+4d
4d = 18-2
4d = 16
d= 16 / 4
d=4
The terms of the sequence are,
a₁=2
a₂=2+4=6
a₃=6+4=10
a₄=10+4=14
a₅=14+4=18
Thus, if the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
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Are the two triangles similar? If so, state the reason and the similarity statement
Two sides are in same proportion and the included angle is common as per SAS. Therefore, both the triangles are similar.
Triangle:
A triangle is the three-sided polygon, which has three vertices. The three sides are interconnected with each other end to end at a point, which forms the angles of the triangle.
Here there are two triangles KLP and KMN. And the sum of all three angles of the two triangle is equal to 180 degrees.
Given,
Here we have the two triangle and we need to find that they are similar or not.
For that we have to calculate the total length of the sides of the triangle,
That,
KM = KL + LM
KM = 8 + 2 = 10
Similarly,
KN = KP + PN
KN = 12 + 3 = 15
In triangles KLP & KMN,
KL/KP = 8/12 = 2/3
Similarly, for the triangle KMN,
KM/KN = 2/3
Here the angles have the same values so they are parallel. Which states that, Angle O is common in both the triangles.
Therefore, the two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.
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Frankenstein was in charge of bringing punch to the Halloween party. He brought 36 liters of his famous eyeball punch. How many gallons was this?
Answer: 9.5112
Step-by-step explanation:
There are 0.2642 gallons in a liter. So, in 36 liters, there are [tex]36(0.2642)=9.5112 \text{ gal }[/tex]
Converting between metric units of volume and capacityA water tower has a volume of 874 m³.Find how many liters of water it would take to completely fill thewater tower. Use the table of conversion facts, as needed.LXS?Conversion facts for volume and capacity1 cubic centimeter (cm³) = 1 milliliter (mL)1 cubic decimeter (dm³) = 1 liter (L)1 cubic meter (m³) = 1 kiloliter (KL) I need help with this math problem
Given: A water tower has a volume of 874 m³
To Determine: How many liters of water it would take to completely fill the
water tower
Solution
Please note that 1 cubic meter (m³) = 1 kiloliter (KL)
Therefore
[tex]\begin{gathered} 1m^3=1KL \\ 874m^3=xKL \\ Cross-multiply \\ x=874KL \end{gathered}[/tex]Also note that Kilo means 1000
Therefore
[tex]\begin{gathered} 874KL=874\times1000L \\ =874000L \end{gathered}[/tex]Hence, the water tower will be completely fill with 874000 liters(L)
Rounded to three decimal places, the value of the irrational number e is .A.3.142B.3.615C.2.718D.2.947
REQUIRED:
Round to 3 decimal placed the value of the irrational number e.
Step-by-step solution/explanation;
The letter e in mathematics is also known as the Eular's number and is a mathematical constant used in many calculations especially natural logarithms of numbers.
The value of the Eular's number is approximately;
[tex]e\approx2.71828182846...[/tex]It can continue till infinity, however approximations of this number is always used to avoid unnecessary complications.
Therefore, rounded to 3 decimal places, the value of e is now;
ANSWER:
[tex]e\approx2.718[/tex]Note that we take 3 digits aftre the decimal and then if the fourth digit after the decimal is 5 or greater than 5, we make it 1 and add that 1 to the third digit after the decimal. Otherwise we simply make it zero and cancel it along with all other digits after it.
The digit that follows 8 (third digit) is less than 5, therefore, we write it off along with all other digits after it, and we are left with the decimal point and then ...718.
Option C is the correct answer.
how do I determine the hypotenuse, opposite, and adjacent angles when I'm only given sides and no angles?
[tex]\angle J = 90^{\circ}\\\\\cos (\angle K)=\frac{5}{23} \implies \angle K=\arccos(5/23)\\\\\sin (\angle I)=\frac{5}{23} \implies \angle I=\arcsin(5/23)[/tex]
27. Ava surveys teachers for how long it takes them to drive to school eachmorning. She records each response in the dot plot shown.5 10 15 20 25 30 35 40 45 50 55 60Length of Drive (minutes)Ava considers drives of 55 minutes or more as not typical. Given this,which measure of the entire data set represents the most typicaldriving time?meanrangemedianmean absolute deviation
EXPLANATION
The measure that represent the most typical driving time is the mean.
A company has been forced to reduce its number of employees. Today the company has 29% fewer employees than it did a year ago. If there are currently355 employees, how many employees did the company have a year agoemployees?
to solve this, question, we would have to convert the percentage to fractions or decimals.
Let x represent the numbers of employees the had a year ago
[tex]\begin{gathered} \frac{29}{100}\times x=355 \\ 0.29x=355 \\ \text{divide both sides by the coefficient of x} \\ \frac{0.29x}{0.29}=\frac{355}{0.29} \\ x=1224.127 \\ x\approx1224 \end{gathered}[/tex]a year ago, the company had 1224 empolyees
Question 8 Let h(t) = –1612 +64 + 80 represent the height of an object
To find the time it takes the object to reach the maximum height we need to remember that this happens in the axis of symmetry of the parabola described by the function:
[tex]h(t)=at^2+bt+c[/tex]The axis of symmetry is given as:
[tex]t=-\frac{b}{2a}[/tex]in this case we have that a=-16 and b=64, then we have:
[tex]t=-\frac{64}{2(-16)}=\frac{-64}{-32}=2[/tex]Therefore it takes 2 seconds to the object to reach its maximum height.
Now, to find the maximum height we plug this value of t in the equation, then we have:
[tex]\begin{gathered} h(2)=-16(2)^2+64(2)+80 \\ =-16(4)+128+80 \\ =-64+128+80 \\ =144 \end{gathered}[/tex]therefore the maximum height is 144 ft.
4. Martin was asked to solve the following system of equations. Hegraphed the two equations below, and decided that the answer was"infinitely many solutions". Do you agree with Martin? Why or why not? Ifyou disagree, what should the answer be?*y=-x-3y=-***+3
Types of solutions in a system of equations:
Based on this image, we can see that when they are parallel lines (same slope), there is no solution because the lines never touch.
The type of solution Martin was describing is when the lines are the same (letter b in the image) and it looks like one line when graphed.
Answer: We disagree with Martin because the lines never touch, meaning that the system has no solutions.
which transformation occurred to create the graph shown below from square root parent function?
Solution:
Given the function:
[tex]f(x)=\sqrt{x+4}[/tex]whose graph is shown below:
Suppose that the parent function is expressed as
[tex]f(x)=\sqrt{x}[/tex]This implies that the parent function is transformed by a horizontal shift to the left by four spaces.
The correct option is
Find the distance between the pair of points. (16,0) and (1, -7) The distance is. (Round to the nearest thousandth as needed.)
Solution
For this case we can use the formula for the distance between two points:
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]and replacing we got:
[tex]d=\sqrt[]{(-7-0)^2+(1-16)^2}=\sqrt[]{274}[/tex]And the correct answer after round would be:
16.553
Write an explicit formula that represents the sequence defined by the following recursive formula: a1=7 and an=2a_n-1
Answer:
[tex]a_n=7(2^{n-1})[/tex]Explanation:
Given the sequence with the recursive formula:
[tex]\begin{gathered} a_1=7 \\ a_n=2a_{n-1} \end{gathered}[/tex]First, we determine the first three terms in the sequence.
[tex]\begin{gathered} a_2=2a_{2-1}=2a_1=2\times7=14 \\ a_3=2a_{3-1}=2a_2=2\times14=28 \end{gathered}[/tex]Therefore, the first three terms of the sequence are: 7, 14 and 28.
This is a geometric sequence where:
• The first term, a=7
,• The common ratio, r =14/7 = 2
We use the formula for the nth term of a GP.
[tex]\begin{gathered} a_n=ar^{n-1} \\ a_n=7\times2^{n-1} \end{gathered}[/tex]The explicit formula for the sequence is:
[tex]a_n=7(2^{n-1})[/tex]1/2+1/9Please help me
If the fraction whose denominator are equal then they will add up
In the given fraction 1/2 +1/9, the denominator of both the fraction 1/2 & 1/9 is not same
so, to make the base same we take the LCM of the 2 & 9
[tex]\begin{gathered} \text{LCM of 2 \& 9 is 18} \\ Si,\text{ the fraction will be :} \\ \frac{1}{2}+\frac{1}{9}=\frac{9+2}{18} \\ \frac{1}{2}+\frac{1}{9}=\frac{11}{18} \end{gathered}[/tex]Answer : 11/18
I need help with part b, c ii, and d
Recall that:
[tex]\text{average speed=}\frac{total\text{ distance}}{total\text{ time}}.[/tex](b) Since Marcos traveled for 2 hours and 17 minutes a distance of 155 miles, then Marco's average speed for the 155 miles trip is:
[tex]\frac{155mi}{(2+\frac{17}{60})h}=\frac{155mi}{\frac{137}{60}h}=\frac{9300}{137}miles\text{ per hour}\approx67.89miles\text{ per hour.}[/tex](c ii) Since Devon also traveled the 155 miles in 2hours and 17 minutes but at a constant speed, then the constant speed at which he traveled is equal to his average speed, which is equal to:
[tex]\frac{155mi}{(2+\frac{17}{60})h}=\frac{155mi}{\frac{137}{60}h}=\frac{9300}{137}miles\text{ per hour}\approx67.89miles\text{ per hour.}[/tex](d) Marco needs to drive 2 miles in 5 minutes to be able to complete the 155 miles trip in 2 hours and 17 minutes, then he must drive at a constant speed of:
[tex]\frac{2mi}{5\min }=\frac{2mi}{\frac{5}{60}h}=\frac{120mi}{5h}=24\text{miles per hour.}[/tex]Answer:
(b) 67.89 miles per hour.
(c ii) 67.89 miles per hour.
(d) 24 miles per hour.
Question 19 of 25Which of the following equations is an example of inverse variation betweenthe variables x and y?O A. y -O B. y = 8xO C. y -OD. y=x+8SUBMIT
Where 8 is the constant
The Final answerOption CThe number of milligrams D (h) of a certain drug that is in a patients bloodstream h hours after the drug is injected is given by the following function. D (h)=40e ^0.2h When the number of milligrams reaches 9, the drug has to be injected again. How much time is needed between injections? Round your answer to the nearest tenth, and do not round any intermediate computations.
we need to find the value of h when D is 9, so we need to replace D by 9 and find h:
andrew went to the store to buy some walnuts. the price pee walnut is $4 per pound and he has a coupon for $1 off the final amount. with the coupon, how much would andrew have to pay to buy 4 pounds of walnuts? what is the expression for the cost to buy p pounds of walnuts , assuming at least one pound is purchased.
The amount Andrew have to pay to buy 4 pounds of walnuts = $19
The expression for the cost to buy p pounds of walnuts= 4p - 1
Explanation:
Amount per pound of walnut = $4
Amount of coupon = $1
The cost of 4 pounds of walnuts:
[tex]\text{Cost = 4 }\times5=\text{ \$20}[/tex]The amount Andrew have to pay to buy 4 pounds of walnuts:
Amount = cost - coupon
Amount = $20 - $1
The amount Andrew have to pay to buy 4 pounds of walnuts = $19
The expression for the cost to buy p pounds of walnuts:
let number of pounds = p
Cost for p pounds of walnut = Amount per walnut * number of walnut
Cost for p pounds of walnut = $4 * p
= $4p
The expression for the cost to buy p pounds of walnuts= cost for p - coupon
= 4p - 1
Without needing to graph determined the number of solutions for this system
Given the system of equations:
[tex]\text{ x + y = 6}[/tex][tex]\text{ y = -x + 6}[/tex]The two equations appear to be just the same, thus, we are only given one system of equations.
Therefore, the answer is letter B. It has infinite solutions because the two equations are just the same line.
Please help me on #1 Please show your work so I can follow and understand
Answer:
Between markers 3 and 4.
Explanation:
We know that each student runs 2 / 11 miles. Given this, how many miles do the first two students run?
The answer is
[tex]\frac{2}{11}\cdot2=\frac{4}{11}\text{miles}[/tex]Now, we know that the course has markers every 0.1 miles. How many markers are ther in 4 /11 miles?
The answer is
[tex]\frac{2}{11}\text{miles}\times\frac{1\text{marker}}{0.1\; miles}[/tex][tex]=3.6\text{ markers}[/tex]This is between markers 3 and 4. Meaning that the second student finishes between markers 3 and 4.
cuántos cifras tiene el cociente de 900÷25
Given the expression
3) There are 24 applicants for three jobs: computer programmer, software tester, and manager. How many ways can this be done?
this is a combination, so
[tex]24C3=\frac{24\cdot23\cdot22}{3\cdot2\cdot1}=2024[/tex]answer: 2024 ways
Which of these steps will eliminate a variable in this system?3x-3y=66x+9y=3OA. Multiply the first equation by 3. Then subtract the second equationfrom the first.B. Multiply the first equation by 2. Then add the equations.C. Multiply the first equation by 2. Then subtract the second equationfrom the first.OD. Multiply the second equation by 2. Then subtract the secondequation from the first.
The given system of equation is:
[tex]\begin{gathered} 3x-3y=6 \\ 6x+9y=3 \end{gathered}[/tex]Multiply through the first equation by 2:
[tex]\begin{gathered} 6x-6y=12 \\ 6x+9y=3 \end{gathered}[/tex]Subtract the second equation from the first equation to get:
[tex]-15y=9[/tex]Therefore, the steps that will eliminate the variable x are:
Multiply the first equation by 2. Then subtract the second equation from the first.
Choice C