Here, we want to use a model to solve the multiplication
We have this as follows;
Mathematically;
[tex]\frac{2}{3}\times6\text{ = 4}[/tex][tex](3x^{2} -x+1)-(6x^{2} -x+2)[/tex]
Answer:
−3x2−1
Step-by-step explanation:
−3x2−1 Is the answer to this equatiom
Janelle alternates between running and walking. She begins by walking for a short period, and then runsfor the same amount of time. She takes a break before beginning to walk again. Consider the four graphsbelow. Which graph best represents the given situation?
the answer is letter C
letter C best represents a situation in which Janelle starts walking and then running.
We can know this by the slope of the lines.
a bakery typically sells its cupcakes for $24 per box for the first week of school they have a sale of $10 off of each box of cupcakes how much will a box of cupcakes cost during the first week of school
cupcakes = $24/box
If they sold each box $10 off, the sold each box for only 24 - 10 = $14
Each box was sold for $14.00
You have a bank account in which your balance increases annually at a rate of 4%. If your initial investment was $100. Write an equation that represents your balance.
Initial investment = $100
The balance increases annually at a rate = 4%
The increased amount = 4% of $100
This gives
[tex]\frac{4}{100}\times\text{\$}100=\text{\$}4[/tex]Hence the investment increase annually by $4 yearly
In the second year the investment will increase by 2 x $4 = $8
In the third year the investment will increase by 3 x $4 = $$12
This implies that
In n years
The investment will increase by n × $4 = $4n
The balance at n years is given as
Balance = Investment + year increment
This is as shown below
[tex]\text{Balnace }=\text{ \$100 }+\text{ \$4n}[/tex]с C' B' A B D' D The distance from A to B is 10 and the distance from A to B'is 2. What is the scale factor? 1/5 4 5 1/4
In this problem, we have that
the center of the dilation is pointed A ----> because the intersection segments c
so
the scale factor is equal to
scale factor=AB'/AB
substitute given values
scale=2/10
scale =1/5Which is an equation of the line perpendicular to y+5X=7and passes through (10,-4)[A] y = 1/5x +7[B] y = 5x + 25/4[C] y = 1/5x - 6[D] y = 5x + 7
Given the equation:
[tex]y+5x=7[/tex]we can find its slope if we write it in the y=mx+b form:
[tex]\begin{gathered} y+5x=7 \\ \Rightarrow y=-5x+7 \end{gathered}[/tex]Now, we know as a general rule, that the slope of the perpendicular of the line that has slope m, is -1/m, more clearly:
[tex]\begin{gathered} \text{if m is the slope of the line} \\ \Rightarrow m_p=-\frac{1}{m}\text{ is the slope of the perpendicular line} \end{gathered}[/tex]So, in this case we have:
[tex]\begin{gathered} m=-5 \\ \Rightarrow m_p=-\frac{1}{m}=-\frac{1}{-5}=\frac{1}{5} \\ m_p=\frac{1}{5} \end{gathered}[/tex]now we use the slope-point formula to find the equation of the perpendicular line:
[tex]\begin{gathered} (x_0,y_0)=(10,-4) \\ m_p=\frac{1}{5}_{} \\ y-y_0=m(x-x_0)_{} \\ \Rightarrow y-(-4)=\frac{1}{5}(x-10) \\ \Rightarrow y+4=\frac{1}{5}x-\frac{10}{5} \\ \Rightarrow y=\frac{1}{5}x-2-4=\frac{1}{5}x-6 \\ y=\frac{1}{5}x-6 \end{gathered}[/tex]therefore, the line perpendicular to y+5x=7 that passes through (10,-4) is y=1/5x-6
The table shows coffee preference from a survey. …If a person is chosen at random in the survey what is P (regular or creamer)?
The formula we will use to calculate the probability is given to be:
[tex]P(A\text{ or }B)=P(A)+P(B)-P(A\cap B)[/tex]Let A represent regular and B represent creamer.
We have the following parameters:
[tex]\begin{gathered} P(A)=0.78 \\ P(B)=0.41 \\ P(A\cap B)=0.32 \end{gathered}[/tex]Therefore, we can calculate the probability to be:
[tex]\begin{gathered} P(A\text{ or }B)=0.78+0.41-0.32 \\ P(A\text{ or }B)=0.87 \end{gathered}[/tex]The FOURTH OPTION is correct.
If f(x) = 2x2 + x - 3, which equation can be used to determine the zeros of the function?
Given the function:
[tex]f(x)=2x^2+x-3[/tex]to find the zeros of the function, we have to solve the equation f(x) = 0, this means the following:
[tex]\begin{gathered} f(x)=0 \\ \Rightarrow2x^2+x-3=0 \end{gathered}[/tex]solving for 'x', we get the zeros of the function, if there are any.
In the parallelogram ABCD, MLA = 2x + 50 and m C = 3x + 40. The measure of LA is
The measure of angle m∠A will be 70°,for the parallelogram ABCD
Parallelogram and its Properties:
Parallelogram is a special kind of quadrilateral, in which opposite sides are equal and parallel to each other.
Properties:
1. Opposite sides are parallel to each other.
2. Length of opposite sides are equal.
3.Diagonally opposite angles are equal.
4. Diagonals bisects each other.
5. Sum of any two adjacent angle is 180°
From figure,
ABCD is a parallelogram
m∠A = 2x + 50
m∠ C = 3x + 40
In a parallelogram ABCD we know opposite angles are equal to each other,
m∠A = m∠C
2x + 50 = 3x + 40
3x - 2x = 50 - 40
x = 10
Hence,
m∠A = 2x + 50
put the value of x we get,
m∠A = 2 * 10 + 50
= 20 + 50
= 70°
m∠A = 70°
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Solve Each System by Elimination:-3x-5y=14-5x+7y=8
(-3, -1)
1) Solving this system by Elimination method:
Let's eliminate the x variables firstly:
-3x-5y=14 x -5 Multiply by the factor that yields the LCM (3,5) =15
-5x+7y=8 x 3 Multiply by the factor that yields the LCM (3,5) =15
15x +25y =-70
-15x +21y =24 Add both equations simultaneously
-----------------------
46y= -46 Divide both sides by 46
y= -1
2) Plug y=-1, into the smaller coefficients equation, just for convenience
-3x -5y = 14
-3x -5(-1) = 14
-3x +5=14 Subtract 5 from both sides
-3x = 9
x= -3
3) So the answer to this Linear System is (-3, -1)
Transformation (x + 2, y - 3) is applied to triangle ABC.What are the coordinates of B’ (the transformation of point B)?A) (-5, 3)B) (2, - 1)C) (0, - 2)D) (2, - 3)
Transformation:
[tex](x+2,y-3)[/tex]The coordinate of B in (x, y) we can get from the graph, which is (-2, 1):
Thus, the transformation based on the information given is:
[tex](-2+2,1-3)[/tex]Simplifying:
[tex](0,-2)[/tex]Answer: C) (0, -2)
Joanie believes that you cannot use cross products to solve the proportion 50 / 3 equals 75 over x 4x she says that if you multiply both sides of the equation by X you get 50 x / 3 equals 75 then if you multiply both sides of the equation by 3 you get 50 x equals 75 which is a different equation then you would get if you cross multiply what mistake did Yuri make in her reasoning?
The proportion is shown below and we cross multiply, do algebra, to solve it.
[tex]\begin{gathered} \frac{50}{3}=\frac{75}{x} \\ 50x=3\cdot75 \\ 50x=225 \\ x=\frac{225}{50} \\ x=\frac{9}{2} \end{gathered}[/tex]If you read the question, so will see this part:
if you multiply both sides of the equation by 3 you get 50 x equals 75
This is the part where there is a problem. You did say to multiply by 3 (both sides). But don't multiply the right hand side of "75" mistakenly.
The last part of this line should be "equals 75 times 3"
This is the mistake.
The graph of a function f is given. Use the graph to estimate the following. (Enter your answers using interval notation) PLEASE HELP!! confused on whole problem
From the graph
Domain = [ -1 , 4]
Range = [ -1 , 3 ]
b) When you look at the graph, the function f
Increasing = [ -1, 1 ] , [ 2, 4 ]
Decreasing = [ 1 , 2 ]
Hi can you help me with this question it is timed i just need an quick answer please and thank you .
ANSWER
EXPLANATION
When triangle DEF is reflected over the y-axis, its vertices are mapped to,
Then, after the translation down 4 units and right 3 units, D' is mapped to S, E' is mapped to R, and F' is mapped to U.
Hence, the congruency statement that describes the two triangles is ΔDEF
PLEASE HELP!! ALGEBRA 1 HW I WILL GIVE BRAINLYEST
Answer:
answer Is -5/2 becouse if the line Is horizontal his equation Is y=k and in this case k= -5/2
1.) A.) Name the 'item' on which point L exists.B.) If ML= 6x - 4, LH = 10x+1 and MH = 29, find the length of ML.
Now for the point A), L is in the middle of M and H, and the interval will be:
[tex](M,H)[/tex]For the second point, We need to put the value of the segments in the draw...
From the draw, we can deduce that:
[tex]ML+LH=MH[/tex]We replace with values:
[tex]\begin{gathered} ML+LH=MH \\ 6x-4+(10x+1)=29 \end{gathered}[/tex]We solve to x:
[tex]\begin{gathered} 6x-4+(10x+1)=29 \\ 6x\text{ -4 +10x +1=29 ; we agroup the values with x} \\ (6x+10x)-4+1=29 \\ 16x-3=29 \\ 16x=29+3 \\ 16x=32 \\ x=\frac{32}{16}=2 \\ x=2 \end{gathered}[/tex]Finally, if the value of x = 2, then whi can replace in:
[tex]\begin{gathered} ML=6x-4 \\ ML=6(2)-4 \\ ML=12-4 \\ ML=8 \end{gathered}[/tex]Your answer of point B) is ML=8.
Nanny using using an app that shows him how many kilometers he has to run to prepare for a Marathon. The app says here an 8.0 45 kilometer who wants to Post online how many miles away Danny ran blank miles.(one mile = 1.609 km)
The conversion for distance in kilometer to miles is as,
[tex]\begin{gathered} 1\text{ mile=1.609 km} \\ 1\text{ km=}\frac{1}{1.609}\text{ miles} \end{gathered}[/tex]Determine the number of miles in 8.045 km.
[tex]\begin{gathered} 8.045\text{ km=8.045}\cdot\frac{1}{1.609}\text{ miles} \\ =5\text{ miles} \end{gathered}[/tex]So Nanny ran 5 miles.
what is 7/8 - 3 1/5? i cant firgure it out
Answer:
-93/40 or -2 13/40
Step-by-step explanation:
7/8 - 16/5
Adjust based on the LCM
35/40 - 128/40
35-128/40
The freezing point of water is 0 °C. Imanis refrigerator is set at 4°C and her freezer is set at -19°C. which change in temperature would bring imanis refrigerator or her freezer to the same temperature as the freezing point of water?A: +23°CB: +15°CC: -19°CD: -4°C
The freezing point of water is 0 °C
The tempreature of Imanis refrigerator = 4degree C
and the freezer is -19 degreeC
So, the net tenpreature of refrigerator is 4+(-19)
The net tempreature = (-15) degreeC
We want
Find the measure of base of the following parallelogram shown below.Area =10.92 cm?2.6 cmAnswer:cm
The area of a paralllelogram can be found by multiplying its base with its height. In this problem we were given the area and the height, therefore we can solve for the base as shown below.
[tex]\begin{gathered} Area=base\cdot height \\ ase=\frac{Area}{height} \\ base=\frac{10.92}{2.6} \\ base=4.2\text{ cm} \end{gathered}[/tex]The base of the parallelogram is 4.2 cm
Find the area ofa cirde with a circumference of 50.24 units,
Step 1
Find radius r , from circumference
circumference = 50.24
[tex]\begin{gathered} \text{Circumference = 2 }\pi\text{ r} \\ \pi\text{ = 3.142} \\ 50.24\text{ = 2 x 3.142r} \\ 50.24\text{ = 6.284r} \\ r\text{ = }\frac{50.24}{6.284} \\ r\text{ = 7.99} \end{gathered}[/tex][tex]\begin{gathered} \text{Area = }\pi r^2 \\ =3.142\text{ x 7.99 x 7.99} \\ =\text{ 200.58} \end{gathered}[/tex]Please see attached photo for question
For the function g(x), the graph is shown and the domain of that function is set of all integer numbers.
Domain of a function is all possible input values for that function.
Here, the domain of g(x) is set of all integers numbers
The x intercept of g(x)
The x intercept is when the value of y is zero, analysing the graph the x intercept can be interpreted as -5 and 1
The y intercept is when the value of x is zero, analysing the graph the y intercept can be interpreted as 1
From the graph,
g(4) is 1
Therefore, For the function g(x), the graph is shown and the domain of that function is set of all integer numbers.
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simplify the following giving the answer with a positive exponent 2n^4*2n^3÷4
so the answer is n^7
Question 8 of 10The diagonal of a TV is 30 inches long. Assuming that this diagonal forms apair of 30-60-90 right triangles, what are the exact length and width of the TV?A. 60 inches by 60/3 inchesB. 15 inches by 15/5 inchesC. 60/2 inches by 600/2 inchesO D. 15.2 inches by 15.2 inches
The diagram of the triangle formed is shown below
The length is BC and the width is AB
To find BC, we would apply the cosine trigonometric ratio which is expressed as
Cos# = adjacent side /hypotenuse
hypotenuse = AC = 30
adjacent side = BC
# = 30
Thus, we have
[tex]\begin{gathered} \text{Cos}30\text{ = }\frac{BC}{30} \\ \text{Note, Cos30 = }\frac{\sqrt[]{3}}{2} \\ We\text{ have} \\ \frac{\sqrt[]{3}}{2}=\text{ }\frac{BC}{30} \\ 2BC\text{ = 30}\sqrt[]{3} \\ BC\text{ = }\frac{30\sqrt[]{3}}{2} \\ BC\text{ = 15}\sqrt[]{3} \end{gathered}[/tex]To find AB, we would apply the sine trigonometric ratio which is expressed as
Sin# = opposite side /hypotenuse
hypotenuse = AC = 30
opposite side = AB
# = 30
Thus, we have
Sin30 = AB/30
Recall, sin30 = 0.5
Thus,
0.5 = AB/30
AB = 30 * 0,5
AB = 15
Thus, the correct option is B
James and Susan wish to have $10,000 available for their wedding in 2 years.
How much money should they set aside now at 6% compounded monthly in
order to reach their financial goal?
They need to set aside $8871.86
10 Natalie uses a 15% off coupon when she buys a camera. The original price of the camera is $45.00. How much money does Natalie save by using the coupon.?
Given data:
The given discount through coupon is d=15%.
The original price of camera is c=$45.00.
The discount on the given amount is,
[tex]\begin{gathered} d=(\frac{15}{100})(45) \\ =6.75 \end{gathered}[/tex]Thus, the amount saved is $6.75.
Hi can you please help me with this problem?The shape is shown below What is the area of the triangle below (in square units)?
ANSWER:
28 square inches
STEP-BY-STEP EXPLANATION:
Given:
Base = 7 inches
Height = 8 inches
We can calculate the area with the help of the triangle area formula, which is as follows:
[tex]A=\frac{1}{2}b\cdot h[/tex]We replacing:
[tex]\begin{gathered} A=\frac{1}{2}\cdot7\cdot8 \\ A=28 \end{gathered}[/tex]The area is 28 square inches.
Dustin boat traveled 36 miles downstream in three hours. The same boat traveled 30 miles upstream in five hours. What is the speed of the boat and the speed of the current
Answer:
The speed of the boat is 9 miles/hour and the speed of the current is 3 miles/hour
Explanation:
Let's call x the speed of the boat and y the speed of the current.
The distance traveled is equal to the speed times the time, so the boat traveled 36 miles in three hours and we can write the following equation
(x + y)3 = 36
3(x + y) = 36
because when the boat traveled downstream, the total speed is the sum of x and y.
On the other hand, the boat traveled 30 miles upstream in 5 hours, so
(x - y)5 = 30
5(x - y) = 30
Therefore, the system of equations is
3(x + y) = 36
5(x - y) = 30
Solving the first equation for x, we get
[tex]\begin{gathered} 3(x+y)=36 \\ \\ \frac{3(x+y)}{3}=\frac{36}{3} \\ \\ x+y=12 \\ x+y-y=12-y \\ x=12-y \end{gathered}[/tex]Now, we can replace this expression on the second equation as follows
[tex]\begin{gathered} 5(x-y)=30 \\ \\ {\frac{5(x-y)}{5}}=\frac{30}{5} \\ \\ x-y=6 \\ \\ \text{ Replacing x = 12 - y} \\ 12-y-y=6 \\ 12-2y=6 \\ 12-2y-12=6-12 \\ -2y=-6 \\ \\ \frac{-2y}{-2}=\frac{-6}{-2} \\ \\ y=3 \end{gathered}[/tex]Then, the value of x is
x = 12 - y
x = 12 - 3
x = 9
So, the speed of the boat is 9 miles/hour and the speed of the current is 3 miles/hour
You spin the spinner twice.678What is the probability of landing on an odd number and then landing on a 6?Simplify your answer and write it as a fraction or whole number.
We are asked to determine the probability of landing on an odd number and then landing on a 6.
To do that we will use the product rule of probabilities:
[tex]P(AandB)=P(A)P(B)[/tex]Where:
[tex]\begin{gathered} A=\text{ landing on an odd number} \\ B=\text{ landing on a 6} \end{gathered}[/tex]To determine the value of the probability of A we need to have into account that there is only 1 odd number (7) out of 3 possible numbers, therefore, the probability is:
[tex]P(A)=\frac{1}{3}[/tex]Now, to determine the value of the probability of "B" we need to have into account that there is only one number 6 out of 3 numbers therefore, we have:
[tex]P(B)=\frac{1}{3}[/tex]Now, we substitute the values:
[tex]P(AandB)=(\frac{1}{3})(\frac{1}{3})[/tex]Now, we solve the operations:
[tex]P(AandB)=\frac{1}{9}[/tex]Therefore, the probability is 1/9
There are 3 consecutive odd integers that sum to –9. What is the least of these integers?
let the three consecutive numbers are,
a , a+ 1 , a+2
sum of the numbers = -9
a + a +1 + a + 2 = -9
3a + 3 = -9
3a = -9 - 3
3a = -12
a = -12/3
a = -4
so the least number is a = -4
thus the answer is -4.
