Use properties of operations to write equivalent expressions
WRITING EQUIVALENT EXPRESSIONS USING PROPERTIES
Commutative Property of Addition :
When adding, changing the order of the numbers does not change the sum. ...
Commutative Property of Multiplication : ...
Associative Property of Addition : ...
Associative Property of Multiplication : ...
Distributive Property :
2.8 w + 5.6
= 2.8 ( w + 2 ) ----------- OPTION B
The population of the state of Colorado was about 5,846,000 people in 2020.
Which number best approximates the population as a single digit times a
power of 10?
OA. 6x 10-6
OB. 6 x 106
C. 5 × 105
D. 5 x 106
Answer: [tex]6 \times 10^6[/tex] which is choice B
==========================================
Method 1
5,846,000 rounds to 6,000,000 aka "6 million".
This converts to the scientific notation [tex]6 \times 10^6[/tex]
The first 6 is from "6 million", while the 6 as the exponent tells us to move the decimal point that many places to the right to go from 6.0 to 6,000,000
---------------
Method 2
Place a decimal point between the first two digits of 5,846,000 and erase the zeros at the end.
So we get 5.846
We must move the decimal point 6 spaces to the right to go from 5.846 back to 5,846,000 again
Therefore, [tex]5,846,000 = 5.846 \times 10^6[/tex]
Then the 5.846 rounds to 6.0 or simply 6 when rounding to the nearest whole number. This leads to [tex]6 \times 10^6[/tex]
Find the area of the prism in the figure shown.
TherWe are asked to determine the area of the triangular prism. To do that we will add the area of the surfaces of the prism and add them together.
we have that the front and back areas are the areas of a triangle which is given by the following formula:
[tex]A_t=\frac{bh}{2}[/tex]Where:
[tex]\begin{gathered} b=\text{ length of the base} \\ h=\text{ height of the triangle} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} b=3 \\ h=4 \end{gathered}[/tex]Substituting the values we get:
[tex]A_t=\frac{\left(3\right)\lparen4)}{2}[/tex]Solving the operations:
[tex]A_t=6[/tex]Since the front and back faces are the same triangle we can multiply the result by 2:
[tex]A_t=2\times6=12[/tex]Therefore, the areas of the front and back faces add up to 12.
Now, we determine the area of the right side. This is the area of a rectangle and is given by the following formula:
[tex]A_r=lh[/tex]Where:
[tex]\begin{gathered} l=\text{ length of the rectangle} \\ h=\text{ height of the rectangle} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} l=5 \\ h=4 \end{gathered}[/tex]Substituting the values we get:
[tex]A_r=\left(5\right)\left(4\right)[/tex]Solving the operation:
[tex]A_r=20[/tex]Now, we determine the area of the left face which is also a rectangle with the following dimensions:
[tex]\begin{gathered} h=5 \\ l=5 \end{gathered}[/tex]Substituting we get:
[tex]A_l=\left(5\right)\left(5\right)=25[/tex]Therefore, the area of the left side is 25.
The area of the bottom face is also a rectangle with the following dimensions:
[tex]\begin{gathered} h=5 \\ l=3 \end{gathered}[/tex]Substituting we get:
[tex]A_b=\left(5\right)\left(3\right)=15[/tex]Now, the total surface area is the sum of the areas of each of the faces:
[tex]A=A_t+A_r+A_l+A_b[/tex]Substituting the values we get:
[tex]A=12+20+25+15[/tex]Solving the operations:
[tex]A=72[/tex]Therefore, the surface area is 72.
what is the answer and how do i solve it?
EXPLANATION
Since we have the expression:
[tex]\frac{x}{x^2+x-6}-\frac{2}{x+3}[/tex]First, we need to find the least common multiplier as follows:
Least common multiplier of x^2 + x - 6, x+3: (x-2)(x+3)
Ajust fractions based on the LCM:
[tex]=\frac{x}{\left(x-2\right)\left(x+3\right)}-\frac{2\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}[/tex][tex]\mathrm{Apply\: the\: fraction\: rule}\colon\quad \frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex][tex]=\frac{x-2\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}[/tex][tex]Expand\text{ x-2(x-2)}[/tex][tex]=\frac{-x+4}{\left(x-2\right)\left(x+3\right)}[/tex]The final expression is as follows:
[tex]=\frac{-x+4}{(x-2)(x+3)}[/tex]
Mai works as a tutor for $12 an hour and as a waitress for $7 an hour. This month,she worked a combined total of 85 hours at her two jobs. Let t be the number of hours Mai worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.total earned (in dollars) = ?
Solution:
Let t be the number of hours Mai works as a tutor.
Given that She earns $12 a hour as a tutor, this implies that for t number of hours, she will earn
[tex]\begin{gathered} \$12\times t \\ =\$\text{ 12t} \end{gathered}[/tex]For the month, she worked a combined total of 85 hours. This implies that
[tex]\begin{gathered} 85=t\text{ + (number of hours worked as a waitress) } \\ \Rightarrow nu\text{mber of hours worked as a waitress = (85-t) hours} \end{gathered}[/tex]Her total eranings for the month is expressed as
[tex]\text{Total earnings = 12(number of hours worked as a tutor)+7(number of hours worked as a waitress)}[/tex]Recall that she earnes $7 an hour while working as a waitress.
Thus, we have her combined total amount in dollars expressed as
[tex]\text{Total earned (in dollars)=12t+7(85-t)}[/tex]Hence, the expression is
[tex]\begin{gathered} \text{12t+7(85-t) } \\ \text{open parentheses} \\ \Rightarrow12t+595-7t \\ \text{collect like terms.} \\ \text{thus, the expression is simplied to be} \\ 5t+595 \end{gathered}[/tex]-Fractions-My sister needs help with this, and I totally forgot how to do fractions Mind helping out?
Because we have the same denominator we can do the subtraction
[tex]\frac{12}{10}-\frac{3}{10}=\frac{12-3}{10}=\frac{9}{10}[/tex]Paul did well the representation of the fractions in the diagram, but the operation that he made as we can see is wrong because the result is 9/10
18
If p percent of an adult's daily allowance of
potassium is provided by x servings of Crunchy
Grain cereal per day, which of the following
expresses p in terms of x ?
Express p in terms of x : p = 5x
What is Percent?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.
If 5% of an adult's daily potassium requirement is provided by each serving of Crunchy Grain cereal, then x servings will offer x times 5%.
Five times as many servings, or p, of potassium are required for an adult's daily requirement.
As a result,
p = 5x can be used to describe the proportion of potassium in an adult's daily allotment.
To learn more about Percent click on the link
https://brainly.com/question/24304697
#SPJ13
Drag each number to the correct location on the statements. Not all numbers will be used. Consider the sequence below. --3, -12, -48, -192, ... Complete the recursively-defined function to describe this sequence. f(1) =...... f(n) = f(n-1) × .....for n = 2, 3, 4... 3, 2, 3, 4, 12, -4
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following sequence:
[tex]-3,-12,-48,-192...[/tex]f(1), is the first term of the sequence, therefore, it would be:
[tex]f(1)=-3[/tex]Now, we calculate the common ratio, just like this:
[tex]\begin{gathered} r=\frac{-192}{-48}=4 \\ \\ r=\frac{-48}{-12}=4 \\ \\ r=\frac{-12}{-3}=4 \end{gathered}[/tex]So the sequence would be:
[tex]f(n)=f(n-1)\cdot4[/tex]Professor Torres is stucked in a burning building. He is leaning to the window on the 5th floor which is 60feets above the ground. For stability, the firefighter have to place the bottom of their ladder 15feet from the wall of the building. How long does the ladder needs to be to reach the window on the 5th floor and save professor Torres? round to 2 decimal place
The situation forms the right triangle above:
Where x is the length of the ladder.
Apply the Pythagorean theorem:
c^2 = a^2 +b^1
where:
c = hypotenuse = longest side = x
A &b = the other 2 legs of the triangle
Replacing:
x^2 = 60^2 + 15^2
Solve for x
x^2 = 3,600 + 225
x^2 = 3,825
x =√3,825
x = 61.85 ft
ocupo encontrar la x con procedimiento
les regalare coronas!!!!
La variable x asociada al sistema geométrico con dos ángulos alternos externos es igual a 23.
¿Cómo determinar la variable asociada a dos ángulos alternos externos?
En esta pregunta tenemos un sistema geométrico conformado por dos líneas paralelas atravesadas por una tercera línea. Este conjunto incluye dos ángulos alternos externos, que guardan la siguiente relación según la geometría euclídea:
6 · x - 28 = 4 · x + 18
A continuación, despejamos la variable x:
6 · x - 4 · x = 28 + 18
2 · x = 46
x = 23
El valor de la variable x es 23.
ObservaciónNo existen preguntas en español sobre ángulos alternos externos, por lo que se añade una pregunta en inglés.
Para aprender más sobre ángulos alternos externos: https://brainly.com/question/28380652
#SPJ1
help me pleaseeeeeeeee
The value of the car after 5 years is $13,500 and the value of the car after 9 years is $10,500.
According to the question,
We have the following information:
The value of the car is given by V(x) where x is the number of years.
V(x) = -1500x + 21,000
(a) Now, to find the value of car after 5 years, we will put 5 in place of x in the given expression:
V(5) = -1500*5+21000
V(5) = -7500+21000
V(5) = $13,500
(b) Now, to find the value of car after 9 years, we will put 9 in place of x in the given expression:
V(9) = -1500*9+21000
V(9) = -10500+21000
V(9) = $10,500
(c) When V(12) = 3000 then it means that the value of the car after 12 years is $3000.
Hence, the value of car after 5 years and 9 years is $13,500 and $10,500 respectively.
To know more about value here
https://brainly.com/question/20593631
#SPJ1
A bucket can hold 26 litres of water when it is 8/9 full. How many litres can it hold when it is full?
Answer:
[tex]29.25\text{ liters}[/tex]Explanation:
Here, we want to know the amount of water the bucket can hold when full
Let us have the volume as x liters
Mathematically:
[tex]\begin{gathered} \frac{8}{9}\times x\text{ = 26} \\ \\ 8x\text{ = 9 }\times\text{ 26} \\ x=\text{ }\frac{9\times26}{8} \\ \\ x\text{ = 29.25 liters} \end{gathered}[/tex]Find the length to the nearest whole number of the diagonal (hypotenuse) of a square with 30 cm on a side. Round answers to the nearest tenth if necessary. Your answer
Notice that we can draw a triangle in the square , and that the length of the square's diagonal is the same as the length of the triangle's hypotenuse. The triangle is a right triangle therefore it satisfies the Phytagorean Theorem. To calculate for it's hypotenuse , we will use:
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse, and a, b are the other legs of the triangle.
[tex]\begin{gathered} c^2=30^2+30^2 \\ c^2=1800 \\ c=\sqrt[]{1800} \\ c=42.43 \end{gathered}[/tex]Since the hypotenuse of the triangle is 42.43 cm. Therefore, the square's diagonal is also 42.43 cm
Answer:
The square's diagonal is 42.43 cm
Which of the following actions will best help her find out whether the two equations in the system are in fact parallel
Check to see whether the slope of both lines are the same (option A)
Explanation:[tex]\begin{gathered} \text{Given} \\ y\text{ - x = }21 \\ 2y\text{ = 2x + 16} \end{gathered}[/tex]When two system of equations do not intersect, the lines are said to be parallel lines.
This means there is no solution.
To determine if the lines are trully parallel, the slope of each equation need to be determined.
For parallel lines, the slope will be the same
The best action to help her find out whether the two equations are inded parallel, Check to see whether the slope of both lines are the same (option A)
Solve for y.
|6y + 12| = -18
Answer: y=-5
Step-by-step explanation:
12-12=0
-18-12=-30
6y=-30
y=-5
Plot ( 0 -5/8) on the coordinate axes. Where is it located? State the axis or the quadrant.
We need to plot the coordinate (0, -5/8).
An ordered pair (x, y) represents the location of the point in the coordinate plane. Based on the given, we have x = 0 and y = -5/8. No movement will happen around the x-axis since we have x = 0. Since y is a negative number, we will go down on the y axis from the origin depending on the value of y.
We see that our y value is equal to -5/8. What we can do first is to represent each grid to be equal to 2/8. There are 4 grids that we will encounter before going to -1. At the second grid, the value is (2/8)*2 = 4/8. At the third grid, we have (2/8)*3 = 6/8. The middle term for these two fractions is equal to 5/8, hence, the plot of (0, -5/8) will be around:
Based on the plot above, the coo
In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11. What is the probability that the mixture will test positive?
From the information available, the mixture will test negative if all 6 samples are negative.
The probability of each is independent of the other for all 6 samples.
The probability of a sample testing positive is 0.11. That means the probability of a sample testing negative would be
[tex]\begin{gathered} P\lbrack neg\rbrack=1-P\lbrack pos\rbrack \\ P\lbrack\text{neg\rbrack}=1-0.11 \\ P\lbrack\text{neg\rbrack}=0.89 \end{gathered}[/tex]However, for all 6 samples, the probability of having a negative result would be a product of probabilities, that is;
[tex]\begin{gathered} P\lbrack tests\text{ negative}\rbrack=0.89\times0.89\times0.89\times0.89\times0.89\times0.89 \\ P\lbrack\text{tests negative}\rbrack=0.89^6 \\ P\lbrack\text{tests negative\rbrack}=0.4969 \end{gathered}[/tex]Therefore if we have the probability of the mixture testing negative as
[tex]P_{\text{neg}}=0.4969[/tex]The probability of the mixture testing positive would be;
[tex]\begin{gathered} P_{\text{pos}}=1-P_{\text{neg}} \\ P_{\text{pos}}=1-0.4969 \\ P_{\text{pos}}=0.5031 \end{gathered}[/tex]ANSWER:
The probability that the mixture will test positive is 0.5031
Rounded to 2 decimal places,
[tex]P_{\text{pos}}=0.50[/tex]resents "three lessWrite the expression -- 5x(4 + 3x) using words,the sum of negative five times a number andfour minus three times the numberthe product of negative five times a numberand the quantity four plus three times thenumberthe product of three times a number plus thequantity four and five times the numberpresents "thetwo less than theDONE
Given:
[tex]=-5x(3x+4)[/tex]Sol:.
The product of negative five times a number and the quantity four plus three times the number.
Which inequality is represented by the graph?
Answer:
it's option c ............
In a data set, the median is less than the mean. What does that indicate about the data?A.It is skewed to the right.B.It is skewed to the left.C.It is symmetric.D.It is bell-shaped.
SOLUTION:
Step 1:
In this question, we are given the following:
In a data set, the median is less than the mean. What does that indicate about the data?
A. It is skewed to the right.
B. It is skewed to the left.
C. It is symmetric.
D. It is bell-shaped.
Step 2:
The diagram that explains the question above is:
A left-skewed distribution has a long left tail. Left-skewed distributions are also called negatively-skewed distributions. That’s because there is a long tail in the negative direction on the number line. The mean is also to the left of the peak.
A right-skewed distribution has a long right tail. Right-skewed distributions are also called positive-skew distributions. That’s because there is a long tail in the positive direction on the number line. The mean is also to the right of the peak.
Back to the question, in a data set, the median is less than the mean
It indicates that:
It is skewed to the right ( OPTION A )
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.
To know more about Triangle here.
https://brainly.com/question/2773823
#SPJ1
Identify the rate, base, and portion.
21% of what number is 57?
Question content area bottom
Which values are given? Select the correct choice below and fill in any answer boxes in your choice. (Type an integer or a decimal. Do not perform the calculation.)
A.The base is (enter your response here) and the portion is (enter your response here). The rate is not given.
B.The rate is (enter your response here % ) and the portion is (enter your response here). The base is not given.
C. The rate is (enter your response here %) and the base is (enter your response here).
Given:
21% of what number is 57
Let the number = x
So, 21% of x = 57
so, the rate = 21%
and the base = x
and the portion = 57
So, the base is not given
so, the answer will be option B
B) the rate is 21% and the portion is 57. the base is not given.
Find the slope and the x- & y-intercepts of x + 2y = 6(5 pts) (Show work for finding X- & y-intercepts)
First, we need to write our equation in standard form — the y should be on the left- hand - side and the x should be on the right- hand side.
The first step is to subtract x from both sides, doing this we get:
[tex]2y=6-x[/tex]Now we divide both sides of the equation by 2 (this isolates the y on LHS), doing this gives us:
[tex]y\text{ = }\frac{6-x}{2}[/tex]which can also be written as
[tex]y=\frac{-x}{2}+3[/tex]The y-intercept is the point at which the line described by our equation intersects the y-axis. This intersection happens when x = 0; therefore, the y-intercept is
[tex]y=\frac{-0}{2}+\text{ 3}[/tex][tex]y=0\text{.}[/tex]The x-intercept is the point at which the line intersects the x-axis. This happens when y =0; therefore, the x-intercept is
[tex]0=\frac{-x}{2}+3[/tex][tex]-3\text{ = }\frac{-x}{2}[/tex][tex]x\text{ = 6.}[/tex]Now we see that the slope of the equation is -1/2 (the coefficient of x ). The y-intercept is y = 3 and the x-intercept is 6.
Solve for y: 5 left parenthesis 3 y plus 4 right parenthesis equals 6 open parentheses 2 y minus 2 over 3 close parentheses The solution is Y = _______
ANSWER:
-8
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]5\cdot\mleft(3y+4\mright)=6\cdot\mleft(2y-\frac{2}{3}\mright)[/tex]Solving for y:
[tex]\begin{gathered} 15y+20=12y-4 \\ 15y-12y=-4-20 \\ 3y=-24 \\ y=-\frac{24}{3} \\ y=-8 \end{gathered}[/tex]The solution of y is equal to -8
simplify 5(3c-4d)-8c
Answer:
7c - 20d
Step-by-step explanation:
5(3c - 4d) - 8c ← distribute parenthesis by 5
= 15c - 20d - 8c ← collect like terms
= 7c - 20d
f(x)=3x-4g(x)=-x^2+2x-5h(x)2x)^2+1j(x)=6x^2-8xk(x)=-x+7calculate (g+j)(x)
To calculate (g+j)(x) we need the function:
[tex]\begin{gathered} g(x)=-x^2+2x-5 \\ j(x)=6x^2-8x \end{gathered}[/tex]and we can made the addition so:
[tex]\begin{gathered} (g+j)(x)=g(x)+j(x) \\ (g+j)(x)=-x^2+2x-5+6x^2-8x \end{gathered}[/tex]and we can simplify
[tex](g+j)(x)=5x^2-6x-5[/tex]What is the equation for this? I don't understand which piece of information is irrelevant.
It is given that she produce print of her photos at a cost of 4 dollar per print and a setup cost of 45 dollar per run.
Let the number of photos produced be x.
Then the equation formed is
[tex]C(x)=4x+45[/tex]The sellling cost given is the unnecessary data given in the question.
The total cost is determined by only the setup cost and cost produce per prints.
The graph formed for the total cost and number of photos produced is
X-axis represent the number of photos produced and Y-axis represent the total cost.
Find the midpoint M of the line segment joining the points R = (-5. -9) and S = (1. -1).
Answer:
(-2,-5)
Step-by-step explanation:
(-5+1÷2, -9+(-1)÷2)
=(-4÷2, -10÷2)
=(-2,-5)
Someone help me please
Approximately 5 meters long.
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)
Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answerbox. Also, specify any restrictions on the variable.a²-3a-4/a² + 5a + 4Rational expression in lowest terms:Variable restrictions for the original expression: a
Factorize both quadratic polynomials, as shown below
[tex]\begin{gathered} a^2-3a-4=0 \\ \Rightarrow a=\frac{3\pm\sqrt{9+16}}{2}=\frac{3\pm\sqrt{25}}{2}=\frac{3\pm5}{2}\Rightarrow a=-1,4 \\ \Rightarrow a^2-3a-4=(a+1)(a-4) \\ \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} a^2+5a+4=0 \\ \Rightarrow a=\frac{-5\pm\sqrt{25-16}}{2}=\frac{-5\pm3}{2}\Rightarrow a=-1,-4 \\ \Rightarrow a^2+5a+4=(a+1)(a+4) \end{gathered}[/tex]Thus,
[tex]\Rightarrow\frac{a^2-3a-4}{a^2+5a+4}=\frac{(a+1)(a-4)}{(a+1)(a+4)}[/tex]Therefore, since the denominator cannot be equal to zero.
The variable restrictions for the original expression are a≠-1,-4Then, provided that a is different than -1,
[tex]\Rightarrow\frac{a^2-3a-4}{a^2+5a+4}=\frac{x-4}{x+4}[/tex]The rational expression in the lowest terms is (x-4)/(x+4)