1a) This equation is written using the Distributive Property of Multiplication.
b) Both factors in this equation are negative.
c) The product will be positive.
2a) This equation is written using the Additive inverses of Multiplication.
b) The product of this equation is 0.
c) This is because the sum of (-8+8) is equal to 0.
3a) This equation is written using the Commutative Property of Multiplication.
b) The products of the commutative multiplications do not change.
c) This is because changing the order of factors does not affect the solution.
What are the properties of multiplication?The properties of multiplication are:
Identity Property of Multiplication (product of 1 and another factor remains the factor.)Associative Property of Multiplication (grouping order of factors does not change the product.)Distributive Property of MultiplicationCommutative Property of Multiplication (the order of factors does not change the product.)For the distributive property, multiplying the sum of two numbers by another number gives the same result as distributing the first number to both other numbers and multiplying them separately and adding.
1) -3(-12) = -12(-3)
= 36 = 36
2) -7 (-8+8) = [-7 (-8)] + [-7 (8)]
= -7(0) = [56 + - 56
0 = 0
3. (5 (-9))-6 = -5 ((-9) +6)
(-45)-6 = -5(-54)
270 = 270
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Question Completion:2) -7 (-8+8) = [-7 (-8)] + [-7 (8)]
3. (5 (-9))-6 = -5 ((-9) +6)
Please help I was sick today and I don’t understand
Answer:
This is a 30 60 90 triangle. They are saying the hypotenuse is 3x + 6 and the shortest side is 8x - 4. In a 30 60 90 triangle, the hypotenuse is 2 times the short side meaning that/
3x + 6 = 16x - 4
Now we can solve...
10 = 13x
x= [tex]\frac{10}{13}[/tex]
A map of a park has no scale. The distance between the campground and the entrance station on the map is 2 inches. The actual distance between them is 8 miles. On the map, the distance between the campground and the lake is 12 inch.
What is the actual distance in miles between the campground and the lake?
The distance between the lake and campground is 48 miles.
Given
The distance between the campground and the entrance is 2
The actual distance between them is 8 miles
Hence the scale is 2 for 8 miles
Also, Distance on the map between campground and lake is 12 inch.
Let us say actual distance is x
There fore we can form equation as
2x = 12x18
2x = 216
x=48
Hence the actual distance between campground and lake is 48 miles.
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Use the rule for the order of operations to simplify: 8+6(6-2(5-4))
Given the expression below
[tex]8+6(6-2(5-4))[/tex]Step 1: Using PEMDAS rule
P=> Parenthesis
E=>Exponent
M=>Multiplication
D=>Division
A=>Addition
S=> Subtraction
From the rule above, we will start our simplification with the parenthesis
Step 1: simplify (5-4)
[tex]\begin{gathered} 8+6(6-2(5-4) \\ 8+6(6-2(1)) \end{gathered}[/tex]Step 2: Expand 2(1)=> 2x1, then simplify (6-2(1))
[tex]8+6(6-2(1))\Rightarrow8+6(6-2)\Rightarrow\cdot=8+6(4)[/tex]Step 3: Expand 6(4)=>6 x 4
[tex]8+6(4)\Rightarrow8+6\times4\Rightarrow8+24[/tex]Step 4: Add 8 and 24
[tex]8+24=32[/tex]Hence, the final answer is 32
Answer: your answer would be 32
Step-by-step explanation:
using PEMDAS we would first go by parentheses and use the order by each step.
What does it mean by non collinear points and another name for angle ABD?
a) Point = could be any point A to D = for example A
b) Line : AD
Could be any line named by the endpoints.
c) Segment: Fragment of a line
AB
d) Ray: part of a line that has a fixed star but no end:
BE
e) Angle : Could be any angle, the middle letter is where the angle rests.
f) 3 collinear points: A,B,C
3 points that are in the same line
g)Opposite rays: same end point but opposite directions
BE and BC
h) Plane: infinite set of points forming a connected flat surface.
ABDC
i) 3 non collinear points: AEC
Three points that aren't on the same line
j) another name for m
2(q + 4) = 10
Solve for q
Answer:
q=1
Step-by-step explanation:
2(q+4)=10
q+4=5
q=1
:]
Answer:
3
Step-by-step explanation:
2 x 3 6 4 10
(b) Use the function to predict the average price per square foot in 2032 .
Answer:
1187.49
Step-by-step explanation:
[tex]P(40)=0.023(40)^3-0.289(40)^2+3.068(40)+55.170=1187.49[/tex]
7. Select all the equations that have the same solution as 3x - 6 = 18.
a. 3x = 12
b. 3x = 24
f.
c. 3(x - 2) = 18
d. 6x 12 = 36
e. 3x 12 = 36
18 = 5 - 3x
The equation which satisfied the given expression after simplification are (a) 3x = 24 and (c) 3(x - 2) = 18.
How simplification method work?
In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.
According to the question, the given equation can be simplified by using simplification method and it is written below:
The given equation is: 3x - 6 = 18
3x = 18 + 6 = 24 ⇒ 3x = 24
Similarly, 3x - 6 = 18
3(x - 2) = 18
Hence, the equation which satisfied the given expression after simplification are (a) 3x = 24 and (c) 3(x - 2) = 18.
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The graph below shows the number of bushels of soybeans a farmer harvested from his field.NUMBER OF ACRES HARVESTEDwhich set of ordered pairs could have been used to make the graph?A. (3, 125), (4, 200), (5, 225)B. (50, 1), (200, 4), (300, 6)C. (100, 2), (250, 5), (350, 7)D. (2, 100), (3, 150), (5, 250)And don't worry this is just a practice :)
From the graph, we can see that the set of ordered pairs which belongs to the line are
D). (2, 100), (3, 150), (5, 250)
Because x-axis is the first coordinate and y-axis is the second coordinate. In options B and C, they are
arranged in the wrong place. In option A, point (3,125) doesn´t belong to the line.
The amount of water a bag of salt can treat is known in cubic feet.
Given:
There is a rectangular prism shape water tank given with 23yd 15yd anf 4yd measurements
Required:
A) We need to find the volume of tank in cubic ft
B) 18.8 cubic ft need 1 salt bag then we need to find to total needed salt bag
C) $4.65 per bag then find total cost
Explanation:
first pf all we need to convert given measures in feet from yd
[tex]\begin{gathered} 1yd=3ft \\ 23yd=69ft \\ 15yd=45ft \\ 4yd=12ft \end{gathered}[/tex]A)
Volume
[tex]V=lwh=69*45*15=37260ft^3[/tex]B)
18.8 cubic ft need 1 bag
then
37260 cubic ft need x
[tex]x=\frac{37260}{18.8}=1981.9\approx1982\text{ bags}[/tex]C)
Cost for 1 bag is $4.65
then
cost for 1982 bags is y
[tex]y=1982*4.65=9216.3[/tex]Final answer:
A) volume of tank in cubic ft is 37260
B) 18.8 cubic ft need 1 salt bag then we need total 1982 needed salt bags
C) $4.65 per bag then total cost is $9216.3
Classify the triangle with the following angle measure: 20^, 50^, 110^
An acute triangle is a triangle with three acute angles, whereas an obtuse triangle is a triangle with one obtuse angle and two acute angles.
An obtuse angle is a angle which is more than 90°.
In our problem, the triangle has a 110° angle, and 110°>90°; therefore, the answer is obtuse triangle
Let f(x) = 9x - 8. Find (f o f)(1).
Let f(x) = 9x - 8. Find (f o f)(1).
we know that
(f o f)(1).=f(f(1))
step 1
find f(1)
f(1)=9(1)-8
f(1)=1
substitute
f(f(1))=f(1)=1
therefore
the answer is 1
Find the distance between the points P (3, 5) and Q (8,7).
Answer:
The distance between two points (x₁,y₁) and (x₂,y₂) on the coordinate plane is d=√((x₂-x₁)²+(y₂-y₁)²)
√(8 - 3)² + (7 - 5)² = √29 ≈ 5.3851648071345
Define a variable, write an inequality, and solve: A number decreased by 7 is at least 15
Inequality: [tex]x-7\ge 15[/tex]
Solution: [tex]x\ge 22[/tex]
Inequality is a mathematical statement which depicts the relation between two or more mathematical variable or quantities which involves in relation which is not equal or inequal.
Given the statement is "A number decreased by 7 is at least 15"
Let the number be the variable x.
Now decreased by 7 = x-7
Suitable inequality sign for at least statement is [tex]\ge[/tex]
So the required inequality is given by,
[tex]x-7\ge15[/tex]
Solving the same we get,
[tex]x-7+7\ge 15+7[/tex]
[tex]x\ge 22[/tex]
Thus the number is [tex]x\ge 22[/tex]
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Use the drawing tool(s) to form the correct answer on the provided graph.The graph of function f is shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.g(x) = -1/2f(x + 2)
Given:
The graph of the function f is given and the function g is as:
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]Required:
To graph the function g.
Explanation:
The graph of the function f(x+2), shift the graph f(x) left 2 units by subtracting 2 from the x-coordinates of the points on the graph of f.
The graph of the function
[tex]\frac{1}{2}f(x+2)[/tex]here
[tex]a=\frac{1}{2}[/tex]So the graph of g has undergone a vertical shrinking by a factor of
[tex]\frac{1}{2}[/tex]The graph of the function
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]reflect the graph of
[tex]\frac{1}{2}f(x+2)[/tex]across the x-axis by multiplying the y coordinate of the points on the graph of
[tex]\frac{1}{2}f(x+2)[/tex]by -1.
Thus the graph of the function
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]is as:
Final Answer:
The graph of the function g is attached in the explanation part.
.5t + .1 < 10t + .05
Answer: t> -4/95
Step-by-step explanation: times both sides by 10(just make the calculation easier, no need to do that)
5t+1<100t+5
-95t<4
t > -4/95
he table shows the gallons of water in a pool over time. A two column table with six rows. The first column, Time in minutes, has the entries, 0, 1, 2, 3, 4, 5. The second column, Water in Pool in gallons, has the entries, 50, 44, 38, 32, 26, 20. Choose the term that describes the slope of the line of a graph representing the data in the table. The slope of a line graphed to represent the volume of water in a pool over time would be described as .
The slope of the line to represent the volume of water in a pool over time would described as -10
From the given table we have to choose points to find the slope of the line
The domain is defined as the set of possible inputs of the function.
The range is defined as the set of all possible outputs of the function.
The slope of the line is the change in y coordinate with respect to the change in y coordinates
Slope of the line m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Where m is the slope of the line
[tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] are the coordinates of the two points
We have to choose two points
The two points (2,44) and (4,26)
m = [tex]\frac{26-46}{4-2}[/tex]
m = -20/2
m = -10
Hence, the slope of the line to represent the volume of water in a pool over time would described as -10
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Rodger biked 30 miles in 2 hours. Write this rate as a unit rate.
Rodger biked 30 miles in 2 hours. Write this rate as a unit rate.
__________________________________
30 miles / 2 hours = 15 miles/hour
_________________________________________
Answer
15 miles/hour
Integers greater than -6 and less than 2
IN OTHER WORDS WE ARE LOOKING FOR WHOLE NUMBERS BETWEEN -6 AND 2
[tex] - 5 \\ - 4 \\ - 3 \\ - 2 \\ - 1 \\ 0 \\ 1[/tex]
ATTACHED IS THE SOLUTION
Answer:
1,0,-1,-2,-3,-4,-5
Step-by-step explanation:
can someone help me please ?
The most appropriate choice for HCF of two numbers will be given by -
Maximum number of performers in each row so that all the rows are equal in length = 8
What is HCF?
HCF means Highest Common Factor. HCF of two numbers a and b is the largest number that is divides both a and b.
Number of instruments = 24
Number of flag bearers = 16
Maximum number of performers in each row so that all the rows are equal in length = HCF of 24 , 16
[tex]24 = 2^3 \times 3\\16 = 2^4[/tex]
HCF = [tex]2^3[/tex] = 8
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what is the value of f(x)=2(0.75)^x when x=3
Answer: f(3) = 0.84375
Step-by-step explanation:
f(3) is asking for the value of the function when x = 3, not multiplying f by 3. (f(x) is basically the output, y)
So we just plug in 3 for x and simplify (use PEMDAS)
f(3) = 2(0.75)^3
f(3) = 2(0.421875)
f(3) = 0.84375
Answer:
[tex]\frac{27}{32}[/tex]
Step-by-step explanation:
It may be a bit easier to represent 0.75 as a fraction, since we can use the following property of exponents: [tex](\frac{a}{b})^x = \frac{a^x}{b^x}[/tex]
We can represent 0.75 as: [tex]\frac{3}{4}[/tex]
And substituting this into the function we get: [tex]f(x)=2(\frac{3}{4})^x[/tex]
calculating the value when x=3, we get: [tex]f(3)=2(\frac{3}{4})^3[/tex]
using the property previously stated we get: [tex]f(3)=2(\frac{3^3}{4^3})[/tex]
Raising each value to the exponent we get: [tex]f(3)=2(\frac{27}{64})[/tex]
When we multiply by two, we can simplify by splitting up 64, into two factors: 2 and 32, to get: [tex]\frac{2*27}{32*2}[/tex]
From here it's easy to see that we can cancel out the values 2, to get: [tex]\frac{27}{32}[/tex]
Which is our answer!
Classify the four angles of the quadrilateral. С 750 B 1050 90° 90-
Anlges A and D are right angles becuase they measure 90
Angle C is Acute because it is smaller than 90
Angle B is Obtuse because it is grather than 90
Complete sheet given
Answer:
good jb
Step-by-step explanation:
Homework 4: Trigonometry:Finding Sides and Angle** This is a 2-page document! **x=7.3Directions: Solve for x. Round to the nearest tenth.
Using trigonometric ratio. SOHCAHTOA
[tex]\begin{gathered} \cos 63^{\circ}=\frac{adjacent}{\text{hypotenus}} \\ \cos 63^{\circ}=\frac{x}{16} \\ x=16\cos 63^{\circ} \\ x=16\times0.45399049974 \\ x=7.26384799583 \\ x\approx7.3 \end{gathered}[/tex]PLEASE HELP WILL MARK BRANLIEST!!!
What is the equation of a line that is parallel to y = x + 2 and passes through the point (5,7)?
Enter your answer with no spaces.
Answer:
See below
Step-by-step explanation:
Slope of given line is 1 y = (1) x + 2
parallel line has same slope
so it will start to look like this y = (1) x + b
sub in the point 5,7 to find b = 2
final answer y=x+2
At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph?
A) approximately 16%
B) at most 34%
C) at most 2.5%
D) at most 13.5%
The percentage of players serves were between 115 mph and 145 mph is approximately 16%.
Given :
The statistician reported that the mean serve speed was 100 miles per hour
the standard deviation of the serve speeds was 15 mph
Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric
To find :
What percentage of the player's serves were between 115 mph and 145 mph?
Solution :
μ =100
σ = 15
P ( 115 < x <145)
= P ( [tex]\frac{115-100}{15}[/tex] < x-μ /6 <[tex]\frac{145-100}{15}[/tex] )
= P ( [tex]\frac{15}{15}[/tex] < z < [tex]\frac{15}{15}[/tex] )
= p ( 1<z<3)
= p( z<3)-p(z-1)
=0.9987-0.8413
=0.1574
p ( 115<xx<145)= 15.74 %
p( 115<x<145)= approximately 16%
The percentage of players serves were between 115 mph and 145 mph is approximately 16%.
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Where ya got 12 from ?
Answer:
12 is the number that comes after 11 and before 13. 12 represents the number between 11 and 13. 12 is a composite number.
Step-by-step explanation:
12 is the number that comes after 11 and before 13.
12 represents the number between 11 and 13. 12 is a composite number.
The following expression gives an approximate value of the total average credit card debt in a U.S. household (in dollars)
t
years after 1995.
420
t
+
5750
Use this expression to predict what the total average credit card debt was or will be in the year 2006.
Answer: In the year 2006, the total average credit card debt for a U.S. household will be (or was)
dollars.
In the year 2006, the total average credit card debt for a U.S. household was 10370 dollars.
How to solve Exponential functions?
We are given the expression that gives an approximate value of the total average credit card debt in a U.S. household (in dollars), t years after 1995 as;
420t + 5750
where t represents number of years after the year 1995. Thus, for the year 2006, the value of t is;
t = 2006 - 1995
t = 11 years
Thus;
f(11) = 420(11) + 5750
f(11) = 10370 dollars
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Figures 1 and 2 are shown in the coordinate grid. Which is a true statement?
As per given by the question,
There are given two figure on coordinate grid, figures 1 and 2.
Now,
From concept of similar figure:
Similar figure means, that have the same shape and exactly the same in every way, on the other hand;
The similar figure means they are same shape but not the same size, then these figure is also called similar figure.
Now,
From concept of the congruent figure:
The congruent means, that two figure exactly the same that means, we can say that they are congruent, when both figure have same shape and same size.
So,
According to both concept, similar and congruent;
The given figure 1 and 2 is simililar, because of same shape. But due to different size, both figure have not congruent.
So, the given figures 1 and 2 is similar, but not congruent.
Hence, the option first is correct.
differentiate y = (x²-7x)^5 (3x^5-5x)
The given expression is
y = (x²-7x)^5 (3x^5-5x)
To differentiate, we would apply the product rule which is expressed as
(fg)' = f'g + fg'
Let f = (x²-7x)^5 and g = (3x^5-5x)
f' = 5(2x - 7)(x²-7x)^4
g' = 15x^4 - 5
By applying the product rule, it becomes
y' = 5(2x - 7)(3x^5-5x)(x²-7x)^4 + (15x^4 - 5)(x²-7x)^5
3. Using the diagram below, answer the following questions. Remember, you must
show your work for credit.
LA = 6y+42
ZC
ZD
A. Solve for y. (2 points)
ZA=
y=
I
B. Find the measure of angles A, C and D showing all work. (2 points)
ZC=
LB = 66
ZD =
Using vertical angles, it is found that:
A. The solution for y is of y = 4.
B. The angle measures are given as follows:
<A = 66º.<C = 114º.<D = 114º.Vertical AnglesIf two angles are opposite by the same vertex in crossing segments, these angles are called vertical angles, and they are congruent, that is, they have the same measure.
In the context of this problem, the angles of 6y + 42 and of 66 are vertical, hence the value of y is calculated as follows:
6y + 42 = 66
6y = 24
y = 24/6
y = 4.
Angles A and C are supplementary, meaning that the sum of their measures is of 180º, hence:
<C + 66º = 180º
<C = 180º - 66º
<C = 114º.
Angles C and D are vertical, hence the measure of angle D is calculated as follows:
<D = 114º.
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