If after using the salt, 2/5 of the salt remains, it means that Anna used 3/5 of the salt in the bag.
A bag contains 6 1/2 pounds of salt, convert this to a fractional number:
[tex]6\frac{1}{2}=6+\frac{1}{2}=\frac{13}{2}[/tex]To find how many pounds of salt she used, multiply 3/5 by the total amount of salt in the bag, this is:
[tex]\frac{3}{5}\cdot\frac{13}{2}=\frac{39}{10}[/tex]She used 39/10 pounds of salt.
Find the X intercept and coordinate of the vertex for the parabola Y=X^2+ 4X -21 ,if there is more than one Y intercept separate them with commas.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
y = x² + 4x - 21
Step 02:
parabola equation:
y = x² + 4x - 21
a = 1
b = 4
c = -21
x-intercepts:
x² + 4x - 21 = 0
(x + 7)(x - 3) = 0
x1 = - 7
x2 = 3
(-7 , 0)
(3 , 0)
vertex:
[tex]xv\text{ = }\frac{-b}{2a}=\frac{-4}{2\cdot1}=-2[/tex][tex]\begin{gathered} yv=xv^2+4xv\text{ -21} \\ yv=(-2)^2+4(-2)\text{ - 21 = - 25} \end{gathered}[/tex](xv , yv)
(- 2, -25)
The answer is:
x-intercepts:
(-7 , 0)
(3 , 0)
vertex:
(- 2, -25)
how many terms are there in each of the following sequences?:
a) The given sequence is expressed as
52, 53, 54, 55, .......252
The first step is to determine the type of sequence by comparing the consecutive terms. We can see that there is a common difference, d between the consecutive terms.
d = 53 - 52 = 54 - 53 = 1
This means that it is an arithmetic sequence. The formula for determining the nth term of an arithmetic sequence is expressed as
an = a1 + (n - 1)d
where
an is the nth term of the sequence
n is the number of terms in the sequence
d is the common difference
a1 is the first term
From the information given,
a1 = 52, d = 1, an = 252
thus, we have
252 = 52 + (n - 1)1
252 = 52 + n - 1
252 = 52 - 1 + n = 51 + n
n = 252 - 51
n = 201
There are 201 terms in the sequence
A Place from this table is chosen at random. Let event A= The place is a city. what is P(Ac)?
Okay, here we have this:
How The probability of an event is a ratio that compares the number of calculating favorable outcomes with the number of possible outcomes. We obtain:
[tex]P(A^C)=\frac{numberof\text{cities}}{numberofplaces}=\frac{4}{7}[/tex]Finally we obtain that the correct answer is the option B.
Order each set of numbers from least to greatest. numbers are in the photo
Answer:
Explanation:
Given the below set of numbers;
[tex]\lbrace2.8,-2\frac{3}{4},3\frac{1}{8},-\bar{2.2}\rbrace[/tex]Let's go ahead and reduce the mixed fractions to improper fractions;
[tex]undefined[/tex]If x varies inversely as y and x=16 when y=5, find x when y=20.
Since x varies inversely as y, then it can be represented as the expression below:
[tex]y=\frac{1}{a}\cdot x[/tex]Where a is the proportionality constant. We need to find a to determine the value of x when y is 20. For that we will use the two values given as shown below:
[tex]\begin{gathered} 5=\frac{1}{a}\cdot16 \\ 5\cdot a=16 \\ a=\frac{16}{5}=3.2 \end{gathered}[/tex]The expression is:
[tex]y=\frac{1}{3.2}\cdot x[/tex]If y is 20, then x must be:
[tex]\begin{gathered} 20=\frac{1}{3.2}\cdot x \\ x=3.2\cdot20 \\ x=64 \end{gathered}[/tex]The value of x must be 64.
The drawing below represents the frame for an isosceles triangle-shaped roof. The height of the roof is 4 feet. What is the distance from Point A to Point B in feet? B 41 3 feet 8v 6 feet 8V3 feet 8 feet
We can make a drawing to see better:
In the picture above, we can see the sides AC and BC are equals because triangle ABC is isosceles, and also the segments AD and DB are equals for the same reason.
We can calculate the lenght of segment AD as:
[tex]\begin{gathered} \tan (30)=\frac{CD}{AD} \\ AD=\frac{CD}{\tan (30)}=\frac{4}{\frac{1}{\sqrt[]{3}}} \\ AD=4\cdot\sqrt[]{3} \end{gathered}[/tex]With the lenght of segment AD we can calculate the lenght of AB as:
[tex]AB=2\cdot AD=8\cdot\sqrt[]{3}[/tex]The correct answer is in yellow.
Bonnie is searching online for airline tickets two weeks ago the cost to fly from Orlando to Denver was $200 .now the cost is $345. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with with the new ticket price?
Answer:457
Step-by-step explanation:
Please Help! I will give brainliest! Need the correct answer!
Answer:
HL
Step-by-step explanation:
The two triangles are rectangle and have a congruent hypotenuse and a congruent leg
7. (-/5 Points]DETAILSMY NOTESASMaurice is traveling to Mexico and needs to exchange $390 into Mexican pesos. If each dollar is worth 12.29 pesos, how many pesos will he get for his trip?pesos
Let's apply Rule of 3
1 dollar ---------------- 12.29 Mexican pesos
390 dollars----------- x
x= 390 . 12.29 = 4793.1 Mexican pesos
Instructions: Use the given information to answer the questions and interpret key features. Use any method of graphing or solving. Round to one decimal place, if necessary.
SOLUTION
The given equation is:
[tex]h(x)=-x^2+10x+9.5[/tex]The graph of the function is shown.
The irrigation system is positioned 9.5 feet above the ground to start
The spray reaches maximum height of 34.5 feet at a horizontal distance of 5 feet away from the sprinkler head.
The spray reaches all the way to the ground about 10.874 feet away.
find the average rates of change of each function for each 1-hour interval from t=0 to t=6
Step 1
Given;
[tex]Organization\text{ A, B and C}[/tex]Required; To determine the type of function representing each company
Step 2
Determine the type of function for company A
[tex]Since\text{ the number of donations quadruples each hour company A has an exponential}[/tex]An exponential function represents the number of donations collected by organization A
Determine the type of function for company B
[tex]Rate\text{ of change=}\frac{8-4}{2-1}=\frac{12-8}{3-2}=\frac{4}{1}=4[/tex]Since the rise and the run measured at points on the table are the same a linear function represents the number of donations collected by organization B.
Determine the type of function for company C
A quadratic function represents the number of donations collected by organization C
Step 3
Fill the chart.
Average rate of change for company A
[tex]undefined[/tex]4x - 4y = 20y = -5Solve the system of linear equations by graphing
The given system of equation:
4x - 4y = 20
y = -5
Plot the equation in the graph
the point at which both the lines meet is the solution of the system of equation:
the graph is :
The lines intersect at (0,-5) i.e x = 0, y = -5
So, the solution of the system of equation is x = 0 & y = -5
Answer:
x = 0
y = -5
How many pounds of candy that sells for $0.87 per lb must be mixed with candy that sells for $1.22 per lb to obtain 9 lb of a mixture that should sell for $0.91 per lb?$0.87-per-lb candy: _____lb$1.22-per-lb candy: _____lb(Type an integer or decimal rounded to two decimal places as needed.)
Let x and y be the candy pounds that sells for $0.87 and $1.22 , respectively. Since they both must add up to 9 lb, we have
[tex]x+y=9...(A)[/tex]On the other hand, the mixture should sell for $0.91 per lib, so we can write,
[tex]0.87x+1.22y=9\times0.91[/tex]Or euivalently,
[tex]\begin{gathered} \frac{0.87}{0.91}x+\frac{1.22}{0.91}y=9 \\ that\text{ is, } \\ 0.95604x+1.340659y=9...(B) \end{gathered}[/tex]Then, we need to solve the following system of equations:
[tex]\begin{gathered} x+y=9...(A) \\ 0.95604x+1.340659y=9 \end{gathered}[/tex]Solving by elimination method.
In order to eliminate variable x, we can to multiply equation (A) by -0.95604 and get an equivalent system of equations:
[tex]\begin{gathered} -0.95604x-0.95604y=-8.60439 \\ 0.95604x+1.340659y=9 \end{gathered}[/tex]Then, by adding both equations, we get
[tex]0.384619y=0.39561[/tex]Then, y is given by
[tex]\begin{gathered} y=\frac{0.39561}{0.384619} \\ y=1.02857 \end{gathered}[/tex]Once we have obtained the result for y, we can substitute in into equation (A), that is,
[tex]x+1.02857=9[/tex]then, x is given as
[tex]\begin{gathered} x=9-1.02857 \\ x=7.9714 \end{gathered}[/tex]Therefore, by rounding to two decimal places, the answer is:
$ 0.87 per lb of candy: 7.97 lb
$1.22-per-lb of candy: 1.03 lb
Translate the sentence into an inequality.Twice the difference of a number and 2 is at least - 29.Use the variable y for the unknown number.
We will start translating the phrase "the difference of a number and 2", using y as the unknown number:
[tex]y-2[/tex]Next, using that expression, we translate the phrase "twice the difference of a number and 2", in this step, we multiply the whole previous expression by 2:
[tex]2(y-2)[/tex]To continue we consider the phrase "is at least -29", this means that the previous expression 2(y-2) has to be at least -29 or it can be greater than -29. This is represented in the following expression:
[tex]2(y-2)\ge-29[/tex]Where the symbol ≥ means greater or equal to.
Answer:
[tex]2(y-2)\ge-29[/tex]Which equation represents the line that is perpendicular to y = 3/4x+ 1 and passes through (-5,11)A.y=-4/3x+13/3B.y=-4/3x+29/3C.y=3/4x+59/4D.y=3/4x-53/4
Answer:
A.y=-4/3x+13/3
Step-by-step explanation:
The equation of a line has the following format:
y = ax + b
In which a is the slope.
Perpendicular to y = 3/4x+ 1:
Two lines are perpendicular if the multiplication of their slopes is -1.
Here the slope is 3/4.
In the answer to this exercise, the slope is a.
So
[tex]\frac{3}{4}\ast a=-1[/tex][tex]\frac{3a}{4}=-1[/tex]Now, cross multiplication
3a = -4
a = -4/3
So, for now, the equation is:
y = (-4/3)x + b
Passes through (-5,11):
This means that when x = -5, y = 11. So
11 = (-4/3)*(-5) + b
11 = (20/3) + b
b = 11 - (20/3)
[tex]11-\frac{20}{3}=\frac{\frac{3}{1}\ast11-\frac{3}{3}\ast20}{3}=\frac{33-20}{3}=\frac{13}{3}[/tex]So the correct answer is:
A.y=-4/3x+13/3
Generate ordered pairs for y = x^2 - 9 using x = -4,-2,0,2 and 4. Identify the corresponding graph.
Given,
The equation is y=x^2-9.
The values of x are -4, -2, 0, 2, 4.
The odered pair are,
At x= - 4,
The value of y is,
[tex]y=(-4)^2-9=7[/tex]The ordered pair is (-4, 7).
At x= - 2,
The value of y is,
[tex]y=(-2)^2-9=-5[/tex]The ordered pair is (-2, -5).
At x= 0,
The value of y is,
[tex]y=(0)^2-9=-9[/tex]The ordered pair is (0, -9).
At x= 2,
The value of y is,
[tex]y=(2)^2-9=-5[/tex]The ordered pair is (2, -5).
At x= 4,
The value of y is,
[tex]y=(4)^2-9=7[/tex]The ordered pair is (4, 7).
The corresponding graph is,
it wants me to solve for the other leg and for the hypotenuse of the 45-45-90 triangle
Given:
In the given 45-45-90 triangle,
Use the tan ratio,
[tex]\begin{gathered} \tan 45^{\circ}=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan 45^{\circ}=\frac{v}{7} \\ 1=\frac{v}{7} \\ v=7 \end{gathered}[/tex]Use the cosine ratio,
[tex]\begin{gathered} \cos 45^{\circ}=\frac{adjacent\text{ side}}{\text{hypotenuse}} \\ \cos 45^{\circ}=\frac{7}{u} \\ \frac{1}{\sqrt[]{2}}=\frac{7}{u} \\ u=\frac{7}{\sqrt[]{2}} \\ u=7\sqrt[]{2} \end{gathered}[/tex]Answer: option a)
[tex]u=7\sqrt[]{2},v=7[/tex]Orang has worked as a nurse at Springfield general hospital for 5 years longer than her friend Bill. Two years ago she had been at the hospital for twice as long. How long has each been at the hospital?
Answer:
• Bill = 3 years
,• Hoang = 8 years.
Explanation:
Let the time Bill had worked in the hospital = b years.
Hoang has worked for 5 years longer than her friend Bill, therefore:
• The time ,Hoang, had worked in the hospital = (b+5) years.
Two years ago:
• Bill's Time = (b-2) years
,• Hoang's Time = (b+5-2) years
Two years ago she had been at the hospital for twice as long as Bill.
[tex]\implies b+5-2=2b[/tex]Solve the equation for b:
[tex]\begin{gathered} b+5-2=2b \\ b+3=2b \\ 2b-b=3 \\ b=3 \end{gathered}[/tex]Hoang has been at the hospital for 8 years and Bill has been there 3 years.
Select the correct answer. A pyramid is placed inside a rectangular prism with height h. Area of the base of the pyramid and the prism is B. A pyramid is placed inside a prism as shown. The pyramid has the same base area, B, as the prism but half the height, h, of the prism. Which expression gives the volume of the pyramid? A. V = 2 3 B h B. V = 1 4 B h C. V = 2 B h D.
An expression which gives the volume of this pyramid is D. V = 1/6 Bh.
How to calculate the volume of a pyramid?Mathematically, the volume of a pyramid can be calculated by using this formula:
V = 1/3 × B × h
Where:
V represents the volume of a pyramid.h represents the height of a pyramid.B represents the base area of a pyramid.Since the pyramid has the same base area (B) as the prism but half (1/2) the height (h) of the prism, the new volume of this pyramid can be derived as follows:
New height, h = h/2
Substituting the parameters into the formula, we have:
Volume, V = 1/3 × B × (h/2)
Volume, V = 1/6 Bh
Read more on volume of a pyramid here: https://brainly.com/question/1388738
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Complete Question:
A pyramid is placed inside a prism as shown. The pyramid has the same base area, B, as the prism but half the height, h, of the prism. Which expression gives the volume of the pyramid?
A. V = 2/3 Bh
B. V = 1/4 Bh
C. V = 2 Bh
D. V = 1/6 Bh
Solve the equation 4x2 + 8x + 1 = 0 by completing the square.
Let's compare the given equation with the notable product below:
[tex](a+b)^2=a^2+2ab+b^2[/tex]Since the first term is 4x², we have a = 2x.
Then, the second term is 8x, so since a = 2x, we have b = 2, this way 2ab = 8x
Now, since b = 2, we have b² = 4.
The constant term is just 1, so we need to add 3 units:
[tex]\begin{gathered} 4x^2+8x+1+3-3=0 \\ 4x^2_{}+8x+4-3=0 \\ (2x+2)^2=3 \\ 2x+2=\pm\sqrt[]{3} \\ 2x=-2\pm\sqrt[]{3} \\ x=\frac{-2\pm\sqrt[]{3}}{2} \end{gathered}[/tex]Therefore the correct option is the third one.
To find the angle of rotation θ between the previous x and y axes and the new x′ and y′ axes, we use the formula: cotangent of 2 theta equals A minus C all over B , where 2θ lies on the interval (0°, 180°).TrueFalse
The equation is the given one:
[tex]\cot 2\theta=\frac{A-C}{B}[/tex]Which is the same as:
[tex]\tan 2\theta=\frac{B}{A-C}[/tex]And the interval of the angle θ must be (0°,90°) so, 2θ must be (0°,180°).
So the statement is True.
we have to write the equation of the line using y=mx+b passing through the points (6,2) and (2,4)
The general equation of line passes through point (x_1,y_1) and (x_2,y_2) is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Determine the equation of line passes through point (6,2) and (2,4).
[tex]\begin{gathered} y-2=\frac{4-2}{2-6}(x-6) \\ y-2=\frac{2}{-4}(x-6) \\ y=-\frac{1}{2}x+3+2 \\ =-\frac{1}{2}x+5 \end{gathered}[/tex]So equation of line is y = -1/2x + 5.
12 in.4 inShoe Box2 inWhat is the volume of the shoebox shown above in cubic inches?18 cubic inches48 cubic inches*96 cubic inches114 cubic inches
We have a shoebox with 3 dimensions, we are asked to find the volume of this shoebox
To do this we use the following volume formulation
[tex]V=l\cdot w\cdot h[/tex]Where the length is l=12, the width is w=2 and the height is h=4, now we replace a solve this
[tex]V=12\cdot2\cdot4V=96[/tex]In conclusion, the shoebox is 96 cubic inches
The monthly rents for five apartments advertised in a newspaper were $650, $650, $750, $1650, and $850.the mean, median, and mode of the rents to answer the question. Which value best describes the monthlyrents?
SOLUTION
Given the question in the image, the following are the solution steps to get the correct answer
Step 1: Write the monthly rents
[tex]\text{\$}650,\text{\$}650,\text{\$}750,\text{\$}1650,\text{\$}850[/tex]We need to calculate the mean, median and moce of these data to allow us choose the best answer
Step 2: Calculate the mean
a
[tex]\begin{gathered} \text{\$}650,\text{\$}650,\text{\$}750,\text{\$}1650,\text{\$}850 \\ \operatorname{mean}=\frac{sum\text{ of monthly rents}}{number\text{ of monthly rents}} \\ \operatorname{mean}=\frac{\text{\$}650+\text{\$}650+\text{\$}750+\text{\$}1650+\text{\$}850}{5}=\frac{4550}{5}=\text{\$}910 \end{gathered}[/tex]Step 3: Calculate the median
The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number.
[tex]\begin{gathered} By\text{ rearrangement},\text{ we have} \\ \text{\$}650,\text{\$}650,\text{\$}750,\text{\$}850,\text{\$}1650 \\ \operatorname{median}=\text{\$}750 \end{gathered}[/tex]Step 4: Calculate the mode
The mode is the number in a data set that occurs most frequently.
[tex]\begin{gathered} \text{data}=\text{\$}650,\text{\$}650,\text{\$}750,\text{\$}850,\text{\$}1650 \\ \mod e=\text{\$}650 \end{gathered}[/tex]Hence, the value that best describe the rents is mean because $910 is the average rent
Option A
Juan has already run 6 miles this month. He plans to run an additional 2 miles per day. At this rate, how long will it take Juan to run 40 miles?Hint: Write and solve a 2-step equation
ANSWER
[tex]17\text{ days}[/tex]EXPLANATION
We want to find how long it will take Juan to run 40 miles.
To do this, we have to set up an equation that describes the situation.
We have that Juan has already run 6 miles and he wants to run an additional 2 miles per day.
This implies that after d days, he would have run:
[tex]6+2d[/tex]For Juan to run 40 miles, it implies that:
[tex]6+2d=40[/tex]Solve that for d:
[tex]\begin{gathered} 2d=40-6=34 \\ d=\frac{34}{2} \\ d=17\text{ days} \end{gathered}[/tex]That is how long it will take Juan to run 40 miles.
Melody has a monthly commission plan under which she receives 2% on the first $40,000 ofsales during the month and 3% on sales above $40,000. If Melody has sales of $73,000 during amonth, computer her commission for that month.
Melody sales is above $40, 000
For sales above $40, 000, she gets 3%
So Melody commission for that month is 3% of $73,000
= 3/100 x $73000
= 3 x $730
=$2190
Right to sleep as a fraction by the Y intercept as well
Given:
The points (0,3) and (2,0) lie on the line.
Required:
We need to find the slope and y-intercept of the given line.
Explanation:
The y-intercept is the point where the line crosses the y-axis.
The given line crosses the y-axis at 3.
y-intercept=(0,3).
Consider the slope formula,
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Substitu\text{te }y_2=0,y_1=3,x_2=2\text{ , and }x_1=0\text{ in the formula.}[/tex][tex]slope=\frac{0-3}{2-0}[/tex][tex]slope=\frac{-3}{2}[/tex]Final answer:
[tex]slope=\frac{-3}{2}[/tex]y-intercept=(0,3).
Solve. Write in scientific notation. 1.44 x 108 1.2 x 105
1.44 x 1081.2 x 105 =
what is 6 / 1/5 helppppp
We have the following:
[tex]6\div\frac{1}{5}[/tex]we carry out the operation, in a division, a cross multiplication is made, like this
[tex]\frac{6}{1}\div\frac{1}{5}=\frac{30}{1}=30[/tex]Therefore, the answer is 30
Lynn had an opening balance of $179.30 in her checking account.She made deposits of $432 and had bank charges of $5.35. If herclosing balance was $353.82, how much did she write in checks?a. $625.89b. $258.05c. $262.83d. $252.13
Given:
Opening balance $179.30 then she deposits $432 and had bank charges $5.35
Closing balance is $353.82
[tex]\text{Amount written in the check = 179.30+432-5.35-353.82}[/tex][tex]\text{Amount written in the check = \$}252.13[/tex]Therefore, Option d is the correct answer.