7. Angela bought some sugar and strawberries to make strawberry jam.Sugar costs $1.80 per pound, and strawberries cost $2.50 per pound.Angela spent a total of $19.40. Which point on the coordinate plane couldrepresent the pounds of sugar and strawberries that Angela used to makejam?
Answers
Equation of the Line
Let's use the following variables:
x = pounds of sugar
y = pounds of strawberries
Angela spent a total of $19.40 to make strawberry jam, thus:
1.80x + 2.50y = 19.40
The equation of the line represents the relationship between x and y. Any point that solves the problem must lie in the line.
The image shows the graph of a line, but we need to be sure it represents the equation above. A small checkup will be done as follows:
For x = 0, solve for y:
1.80*(0) + 2.50y = 19.40
y = 19.4 / 2.5 = 7.76
This point corresponds to the y-intercept (0, 7.76). It can be correctly found on the graph.
For y = 0, solve for x:
1.80x + 2.50*(0) = 19.40
x = 19.40 / 1.8 = 10.78
This point corresponds to the x-intercept at (10.78, 0). It can also be found on the graph.
Now we are sure the line is the representation of our equation, the only point that lies on that line is B(8, 2).
If we substitute x = 8, y = 2:
1.80*(8) + 2.50*(2) = 19.40
14.4 + 5 = 19.40
19.40 = 19.40
The equation is satisfied, thus, the answer is:
Point B
Related Questions
Classify the slope as upward downward vertical or horizontal. m = -7
Answers
Answer:
downward
Explanation:
A negative slope decreases from left to right.
a line with a negative slope can be thought of as a downward side of a hill. Therefore we classify negative slopes as downward (because our idea of 'upward' is something that increases from left to right).
Therefore, the slope m = - 7 since it is negative is classified as downward.
The upward slope is
a vertical slope is
a horizontal slope is
I need help answering it I don’t know howTo do it
Answers
Okay, here we have this:
Considering the provided graph we obtain that:
Recall that the slope is undefined when lines are vertical. So in this case we can see that this description is fulfilled, therefore, finally we obtain that the Type of slope is Undefined
The triangle has the sides AB = 4cm BC = 6cm AC = 8cmCalculate the triangles Area
Answers
Given: A triangle ABC with sides AB=4cm, BC=6cm and AC=8cm
Required: To find out the area of the given triangle.
Explanation: Area of the triangle by Heron's formula is given by,
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]where, a,b,c are the sides of triangle and s is the semi-perimeter given by,
[tex]s=\frac{(a+b+c)}{2}[/tex]Now, let a=4, b=6 and c=8. Hence the semi perimeter s is-
[tex]s=\frac{4+6+8}{2}[/tex][tex]s=9\text{ cm}[/tex]Now, putting these values of s, a, b, and c in Heron's formula we get,
[tex]A=\sqrt{9(9-4)(9-6)(9-8)}[/tex][tex]A=\sqrt{9\times5\times3\times1}[/tex][tex]A=3\sqrt{15}\text{ }cm^2[/tex][tex]A=11.61\text{ }cm^2[/tex]Final Answer: Area of triangle is 11.61 sq cm.
Gloria, an experienced bungee jumper, leaps from a tall bridge and falls toward the river below. The bridge is 200 feet above the water and Gloria's bungee cord is 130 feet long unstretched. When will Gloria's cord begin to stretch? Round your answer to two decimal places.
Answers
We are given that Gloria jumps from a bridge using a bungee cord. The quadratic expression that models an object falling freely is the following:
[tex]h=h_0+v_0t-\frac{1}{2}gt^2[/tex]Where:
[tex]\begin{gathered} h_0=\text{initial height} \\ v_0=\text{initial velocity} \\ g=\text{acceleration of gravity} \\ t\text{ = time} \end{gathered}[/tex]A representation of the problem is the following:
If we assume that the initial velocity is zero, we get the following values:
[tex]\begin{gathered} h_0=200 \\ h=200-130 \\ g=32 \\ \end{gathered}[/tex]The height is equivalent to the total height of the bridge minus the longitude of the cord. The value for "g" is a constant equivalent to 32 feet per second.
Replacing we get:
[tex]200-130=200-\frac{1}{2}(32)t^2[/tex]Now we solve for "t", first by subtracting 200 to both sides:
[tex]-130=-\frac{1}{2}(32)t^2[/tex]Solving the operation:
[tex]-130=-\frac{1}{2}(32)t^2[/tex]Multiplying both sides by -2:
[tex]260=32t^2[/tex]Dividing both sides by 32:
[tex]\frac{260}{32}=t^2[/tex]Taking square root on both sides of the equation:
[tex]\sqrt[]{\frac{260}{32}}=\sqrt{t^2}[/tex]Solving the operations:
[tex]2.85=t[/tex]Therefore, the cord starts stretching at 2.85 seconds.
Triangle 1 is a scale drawing of Triangle 2 as shown below. Based on the information shown in these triangles, what is the length of the side x? A. 9 B. 15.75 c. 7
Answers
x = 7
Explanations:Since triangle 1 is a scale drawing of triangle 2, the ratio of corresponding sides will be the same.
Therefore:
[tex]\frac{4}{6}=\text{ }\frac{x}{10.5}[/tex]Cross multiply:
4(10.5) = 6x
42 = 6x
6x = 42
x = 42/6
x = 7
Find the given equation of the line through (8,-7) which is perpendicular to the line y= x/2-9
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
By comapring the given equation,
slope, m = 1/2
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Thus,
slope of line passing through (8, - 7) = - 2/1 = - 2
We would find the y intercept of the line passing through (8, - 7) by substituting x = 8, y = - 7 and m = - 2 into the slope intercept equation. We have
- 7 = - 2 * 8 + c
- 7 = - 16 + c
c = - 7 + 16 = 9
The equation of the line is
y = - 2x + 9
which conversion factors are used to multiply to 12m/s to get kilometers per minute A. 1000m over 1kmB. 60S Over 1 minC.1 km over 1000mD.1min over 60s
Answers
To convert 12 meter per seconds to kilometer per minute
We need kilometer in the denominator and minute in the denomiator
But 1 km = 1000 m and 60 seconds = 1 minute
12m / s x 60s / 1 min x 1km / 1000m
Hence the correct option is;
B and C
George runs hurdles he clears the hurdles 90% of the time which of the following statements applyGeorge clears the hurdles 9/9George clears the 9/100George clears the hurdles 90 /100George clears the hurdles 90/1000
Answers
90% = 90/100
answer is the third one
Label the sides of the right triangle.*2 pointsCaptionless ImageA) Hypotenuse = 8 m, Adjacent = 15 m, Opposite = 17 mB) Hypotenuse = 17 m, Adjacent = 8 m, Opposite = 15 mC) Hypotenuse = 15 m, Adjacent = 17 m, Opposite = 8 mD) Hypotenuse = 17 m, Adjacent = 15 m, Opposite = 8 m
Answers
Given:
There are given that the right angle triangle, UVW.
Where,
[tex]\begin{gathered} UV=8m \\ VW=15m \\ UW=17m \end{gathered}[/tex]Explanation:
According to the concept:
The hypotenuse is defined as the longest side in the right-angle triangle.
The perpendicular side is defined by the perpendicular base angle.
And,
The adjacent side is defined by the leg of the right-angle triangle.
Final answer:
Hence, the correct option is D.
Karlo has $7,300 saved for a down payment towards the $26,700 car he wants to buy. He needs to have adown payment of at least 40% in order to get the lowest interest rate. How much more money would he need tosave?
Answers
The Solution:
Given:
The cost of car Karlo wants to buy is $26,700.
Karlo has saved = $7,300
We are required to find how much Karlo need to save more for the car.
Step 1:
Down payment of 40% of the total cost of the car is:
[tex]Down\text{ payment amount}=\frac{40}{100}\times26700=40\times267=\text{\$}10680[/tex]Step 2:
Subtract $10680 from $26700.
[tex]Amount\text{ to save more }=26700-10680=\text{\$}16,020[/tex]Therefore, the correct answer is $16,020.
Part 2: Consider this word problem: "Professor has several tarantulas and frogs. She counts 104 legs and 80 eyes in the room (not including her own). How many of each creature does she have?" Answer the question in a paragraph form. Answer the following: • What bits of information are not explicitly stated in the problem that would help us figure out the answer? Do you need to look anything up orpull some information from the back of your head?• Which mathematical concept(s) that we've gone over so far would be helpful for solving this problem?• Now, solve the problem and explain your solution. (It's OK if your answer isn't completely right. We're here to learn!)
Answers
Okay, here we have this:
Considering the provided information we are going to calculate how many of each creature does she have, so we obtain the following:
• What bits of information are not explicitly stated in the problem that would help us figure out the answer? Do you need to look anything up or
pull some information from the back of your head?:
The missing information of the exercise is the amount of legs and eyes of each type of animal
• Which mathematical concept(s) that we've gone over so far would be helpful for solving this problem?:
The mathematical concept that we apply to solve this exercise will be the systems of equations of two equations by two incognites.
• Now, solve the problem and explain your solution. (It's OK if your answer isn't completely right. We're here to learn!):
According to the given information we obtain the following systems of equations:
8x+4y=104 (Equation of the legs)
8x+2y=80 (Eye equation)
"X" corresponds to the number of tarantulas and "y" to the number of frogs.
Solving:
We will clear x in the second equation:
8x+2y=80
8x=80-2y
x=(80-2y)/8
x=10-2y/8
Replacing in the first equation:
8x+4y=104
8(10-2y/8)+4y=104
80-2y+4y=104
80+2y=104
2y=24
y=24/2
y=12
Using this value of y in the equation of x:
x=10-2y/8
x=10-2(12)/8
x=10-24/8
x=10-3
x=7
Finally we obtain that she has 7 tarantulas and 12 frogs.
The table below shows data for a class's mid-term and final exams:
Mid-TermFinal
96 100
95 85
92 85
90 83
87 83
86 82
82 81
81 78
80 78
78 78
73 75
Which data set has the smallest IQR? (1 point)
Group of answer choices
They have the same IQR
Mid-term exams
Final exams
There is not enough information
Answers
The interquartile range is a measure of where the “middle fifty” is in a data set, where the bulk of the values lies.
The interquartile range formula is the first quartile subtracted from the third quartile:
[tex]IQR=Q_3-Q_1[/tex]IQR of the Mid-Term
Step 1: Arrange the numbers in order
[tex]73,78,80,81,82,86,87,90,92,95,96[/tex]Step 2: Find the median
[tex]Median\Rightarrow86[/tex]Step 3: Find Q1 and Q3
Q1 and Q3 are the median of the numbers before and after the median of the data set. Therefore, Q1 is the median of the first 5 numbers:
[tex]Q_1=80[/tex]Q3 is the median of the last 5 numbers:
[tex]Q_3=92[/tex]Step 4: Calculate the IQR
[tex]IQR=92-80=12[/tex]IQR of the Final
Step 1: Arrange the numbers in order
[tex]75,78,78,78,81,82,83,83,85,85,100[/tex]Step 2: Find the median
[tex]Median\Rightarrow82[/tex]Step 3: Find Q1 and Q3
Q1 and Q3 are the median of the numbers before and after the median of the data set. Therefore, Q1 is the median of the first 5 numbers:
[tex]Q_1=78[/tex]Q3 is the median of the last 5 numbers:
[tex]Q_3=85[/tex]Step 4: Calculate the IQR
[tex]IQR=85-78=7[/tex]ANSWER
The data with the smallest IQR is the FINAL.
WHAT IS THE MEASURE OF
Answers
The measure of the angle ∠XYZ = 76°
What is an angle?Angles are formed when two lines intersect at a point. The measure of the 'opening' between these two rays is called an 'angle'. It is represented by the symbol ∠. Angles are usually measured in degrees and radians
∠XYZ = ∠WXY + ∠XWY( exterior angle of a triangle is equal to the sum of the two interior angle)
substituting their values,
12x - 20 = 3x + 11 + 5x + 1
collecting like terms we have
12x -3x - 5x = 20 + 1 + 11
4x = 32
x = 32/4
x = 8
recall ∠XYZ = 12x - 20
substitute x = 8 into the above equation
∠XYZ = 12(8) - 20
∠XYZ = 96 - 20
∠XYZ = 76°
In conclusion, the value of ∠XYZ = 76°
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Which inequality is true when the value of c is −11?−c−4≤−3c-4≥3-c-4≤3c-4≤3
Answers
In order to find which inequality is true, let's use the value of c in each one and check if they are true or false:
[tex]\begin{gathered} -c-4\le-3 \\ 11-4\le3 \\ 7\le-3\text{ (false)} \\ \\ c-4\ge3 \\ -11-4\ge3 \\ -15\ge3\text{ (false)} \\ \\ -c-4\le3 \\ 11-4\le3 \\ 7\le3\text{ (false)} \\ \\ c-4\le3 \\ -11-4\le3 \\ -15\le3\text{ (true)} \end{gathered}[/tex]Therefore the correct option is the fourth one.
Use the diagram below to answer the next 4 questions that follow. Lines L1 1 pointand L2 are parallel. Point N is the midpoint of segment GH. If the measureof IHM is 125°, what is the measure of ZIHU? *M3N687
Answers
180 - 125 = 55
angle IHJ = 55
IHM + IHJ = 180
Since IHM = 125
What is mZS? Q 108° P R S m2S = O
Answers
First, we find arc RSP
[tex]\begin{gathered} 108=\frac{1}{2}\cdot RSP \\ \text{RSP}=2\cdot108=216 \end{gathered}[/tex]Arc RSP measures 216°.
Then,
[tex]\begin{gathered} 216+RQP=360 \\ \text{RQP}=360-216=144 \end{gathered}[/tex]Now, we find angle S
[tex]m\angle S=\frac{1}{2}\cdot144=72[/tex]Hence, angle S measures 72°.i need help with this problem its a two step equation -17= -9- 8m
Answers
The table below shows the birth months for all 25 students in Mr. Battistini's class.Student Birth MonthsWhat is the probability of selecting a student at random from this class who was NOT bornin June?А. 4%B. 16%C.21%D.84%
Answers
Given data:
The given table.
The probability that the student not born in june is,
[tex]\begin{gathered} P(J^{\prime})=1-\frac{4}{25} \\ =\frac{21}{25} \\ =0.84 \\ =84\text{ percent} \end{gathered}[/tex]Thus, the option (D) is correct.
Find the next 3 terms of the arithmetic sequence 5, 9, 13, 17
Answers
You have the following arithmetic sequence:
5, 9, 13, 17
due to the it is an arithmetic sequence, difference between consecutive numbers is constant.
In fact, when you calculate the difference between consecutive numbers you have:
9 - 5 = 4
13 - 9 = 4
17 - 13 = 4
To determine the next three terms it is necessary to sum 4 (the previous result) to each previous term, just as follow:
17 + 4 = 21
21 + 4 = 25
25 + 4 = 29
Hence, 21, 25 and 29 are the next three terms
What is the area, in square inches, of the shape below? 8.4 in 9.7 in
Answers
Problem:
The area of the triangle is
[tex]A\text{ = }\frac{bxh}{2}[/tex]here, b is the base of the triangle and the variable h is its height so :
[tex]A\text{ = }\frac{bxh}{2}\text{ = }\frac{9.7\text{ in x 8.4 in}}{2}\text{ = }\frac{81.48in^2}{2}=40.74in^2[/tex]We can conclude that the area of the shape is 40.74 in^2
The temperature fell by 3°F every hour during a 6-hour period. What
was the overall change in temperature during the 6-hour period?
PLS HELP THIS IS DUE TMR
Answers
Answer:
it decreased 18°F over 6 hours
Step-by-step explanation:
if it fell 3°F every hour for 6 hours just times it by 6
3x6=18
it decreased 18°F over 6 hours
Find the area and perimeter of each polygon:
6
5
4
8
Area:
unit2
Perimeter:
unit2
OK
Answers
Part a
The area of the figure is equal to the area of two rectangles
Area of the top rectangle
A=(6)*(5)=30 unit2
Area of the bottom rectangle
A=(8)*(4)=32 unit2
therefore
The total area is
A=30+32
A=62 unit2Part b
Find out the perimeter
To find out the perimeter adds all the length sides
so
P=8+4+(8-6)+5+6+5+4
P=34 unitsA growing company has been hiring employees at a steady rate of 1 new hire per month. The company started with 2 employees. The growth of the company can be modeled by the function g (2) = 2 + 2, where x represents the number of months, and g(x) represents the number of employees. Evaluate the function over the domain {3,4, 18, 24}.
Answers
The function that represents the number of employees by the number of months is:
[tex]g(x)\text{ = 2+x}[/tex]For x = 3:
[tex]\begin{gathered} g(3)\text{ = 2+3} \\ g(3)\text{ = 5} \end{gathered}[/tex]For x=6:
[tex]\begin{gathered} g(6)=2+6 \\ g(6)\text{ = 8} \end{gathered}[/tex]For 18:
[tex]\begin{gathered} g(18)\text{ = 2+18} \\ g(18)\text{ = 20} \end{gathered}[/tex]For 24:
[tex]\begin{gathered} g(24)=24+2 \\ g(24)=26 \end{gathered}[/tex]the table shows how many gummies a candy-maker can make in a certain number of hours
15 =1,500
25= 2,500
50= 5,000
what is the constant of proportionality? show your equation, work, and correct lables.
Answers
The constant of proportionality will be 100.
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The table shows how many gummies a candy-maker can make in a certain number of hours;
15 =1,500
25= 2,500
50= 5,000
Now,
We know that;
Th expression is,
⇒ y = kx
Where, K is constant of proportionality.
Here, By the first condition;
k = 1500/15
k = 100
By the second condition;
k = 2500/25
k = 100
By the third condition,
k = 5000/50
k = 100
Thus, The constant of proportionality will be 100.
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Find the value of the variable that is not given: V=I w h; Given V = 90,1 = 10, h = 3 (Round the answer to 2 decimal places if necessary)
Answers
V= l*w*h
V=90
l=10
h=3
Replace the values in the expression and clear w
V= l*w*h
90=10*w*3
90=30w
w=3
jacobs school is selling tickets to a fall musical. On the first day of ticket sales the school sold 2 senior citizens tickets and 6 child tickets for a total of $26. The school took in $54 on the second day by selling 12 senior citizen tickets and 2 child tickets. Find the price of senior citizen ticket and the price of a child ticket.
Answers
Let s and c represent the prices of the senior citizen and the child tickets respectively
Then the problem can be modelled as follows:
[tex]\begin{gathered} 2s+6c=26--------------------(1) \\ 12s+2c=54--------------------(2) \\ We\text{ will now solve the simultaneous equation by elimination method} \\ \text{equation (1) }\times6\colon \\ 12s+36c=156---------------------(3) \\ 12s+2c=54-----------------------(2) \\ ---------------------------------------- \\ \text{equation (3) - equation (2):} \\ 34c=102 \\ \Rightarrow c=\frac{102}{34}=3 \\ \text{Substituting the value of c into equation (1), we have:} \\ 2s+6(3)=26 \\ 2s+18=26 \\ \Rightarrow2s=26-18=8 \\ \Rightarrow s=\frac{8}{2}=4 \end{gathered}[/tex]During 5/8 of the 72 physical education classes, Ethan played games involving running. During how many of this years physical education classes did Ethan have to run?
Answers
Ethan has to run in 45 classes
Here, we want to get the number of games that involved running
Mathematically, what we have to do here is to calculate the number in the fraction
We have this as;
[tex]\frac{5}{8}\text{ of 72 = }\frac{5}{8}\times\text{ 72 = 45}[/tex]Mrs. Nolan hired a painter to paint the exterior of her house. It took the painter 3 days to paint her house. The painter agreed to a rate of $23 per hour with a 12-hour unpaid lunch break each day. The table shows when the painter clocked in and out each day.Before taxes, how much money did the painter make
Answers
Given that the painter took three days to paint the exterior of the house in the following timings.
Thursday 7.30 am to 5.15 pm = 9 hours 45 minutes
Friday 7.00 am to 4.40 pm = 9 hours 40 minutes
Saturday 8.30 am to 4.30 pm = 8 hours
Also, it is given that the rate 23 $ per hour, and there is a rest of 1/2 hour lunch break each day.
So total lunch break = 3 x 1/2 hours = 3/2 hours = 1.5 hours = 1 hour 30 minutes
Total working time = 9 hours 45 minutes + 9 hours 40 minutes + 8 hours
= 27 hours 25 minutes
For 1 hour the rate is $ 23
1 hour = $ 23
60 minutes = $ 23
1 minute = $ 23/60
Now we have to subtract the lunchtime from the total time.
Then,
Time for which he was paid = 27 hours 25 minutes - 1 hour 30 minutes
= 25 hours 55 minutes
So,
25 hours = $ 25 x 23 = $ 575
55 minutes = $ 55 x 23/60 = $ 21.08
Hence, the total money he was paid is = $ 575 + $ 21.08 = $ 596.08
Therefore the required answer is $ 596.08
3. From a boat on the lake, the angle of elevation to the top of a cliff is 25.2°. If the base of the cliff is 1384 ft from the boat, how high is the cliff? Round results to an appropriate number of significant digits.
Answers
Using trig function Tan to get the height of the cliff;
[tex]\begin{gathered} \tan25.2=\frac{h}{1384} \\ h=tan25.2\times1384 \\ =0.471\times1384 \\ =651.26096 \end{gathered}[/tex]ANSWER
[tex]651.26ft[/tex]The Fancy Marble Company makes one type of spherical marble with a radius of 2 cm. The maximum error in measurement is 0.1 cm for the radius. Which of the following is closest to the minimum .volume of one of these marbles? A 7.95 cm B. 8.79 cm C. 28.72 cm D. 38.77 cm
Answers
hello
to solve this question, we need to find the volume of a sphere
the formula is given as
[tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ r=2\pm0.1 \\ \pi=3.14 \end{gathered}[/tex]the minimum volume of the sphere is would be as a result in reduction of the radius of the sphere
[tex]\begin{gathered} R=r-0.1 \\ R=2.0-0.1 \\ R=1.9\operatorname{cm} \end{gathered}[/tex]we can use this radius to calculate the volume of the sphere
[tex]\begin{gathered} v=\frac{4}{3}\pi R^3 \\ v=\frac{4}{3}\times3.14\times1.9^3 \\ v=28.716\cong28.72\operatorname{cm}^3 \end{gathered}[/tex]from the calculations above, the minimum volume of the sphere is 28.72cm^3 which corresponds to option C