“Jesse bought 10 more pencils than erasers” means P = 10 + E
“A pencil costs $0.15” means that $0.15*P was spent on pencils
“an eraser costs $.22” means that $0.22*E was spent on erasers
“He paid a total of $4.46” means that $0.15*P + $0.22*E = $4.46
15*(10+E) + 22*E = 446
150 + 37E = 446
37E = 296
E = 8 Jesse bought 8 erasers
Jesse bought 8 erasers. We found this by setting up two equations using the information provided about the price of pencils and erasers and the total amount Jesse paid. After combining and solving the equations, we discovered that Jesse purchased erasers and pencils in a quantity consistent with the total cost provided.
Explanation:To determine how many erasers Jesse bought, we need to set up a system of equations based on the given information:
Let e be the number of erasers Jesse bought. Then he bought e + 10 pencils.A pencil costs $0.15 and an eraser costs $0.22.The total amount paid for pencils and erasers is $4.46.We can express this as two equations:
0.15(e + 10) + 0.22e = 4.46 (Total cost equation)e + 10 (Number of pencils bought)Solving for e (number of erasers):
0.15e + 1.5 + 0.22e = 4.46(0.15 + 0.22)e = 4.46 - 1.50.37e = 2.96e = 2.96 / 0.37e = 8Jesse bought 8 erasers.
how many pennies would be on the square labled H?
square A: 1 penny 2^0
square B: 2 pennies 2^1
square c: 4 pennies 2^2
[tex]\bf \begin{array}{|lllllllll|ll} \cline{1-9} label&A&B&C&D&E&F&G&H\\ &&&&&&&&&\\ pennies&2^0&2^1&2^2&2^3&2^4&2^5&2^6&2^7\implies 128\\ \cline{1-9} \end{array}[/tex]
Answer: part 2: 2n-1
Step-by-step explanation:
The point (−3, 1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
ANSWER
See below
EXPLANATION
The given point (-3,1) lies in the second quadrant.
In this quadrant only sine is positive.
The length of the hypotenuse formed by the right angle triangle is
[tex] {h}^{2} = {3}^{2} + {1}^{2} [/tex]
[tex] {h}^{2} = 9 + 1[/tex]
[tex]{h}^{2} = 10[/tex]
[tex]h = \sqrt{10} [/tex]
The side opposite to θ, is 1 units.
The adjacent side is 3 units.
[tex] \sin( \theta) = \frac{opposite}{hypotenuse} [/tex]
[tex]\sin( \theta) = \frac{1}{ \sqrt{10} } = \frac{ \sqrt{10} }{10} [/tex]
[tex]\cos( \theta) = - \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos( \theta) = - \frac{3}{ \sqrt{10} } = - \frac{3 \sqrt{10} }{10} [/tex]
[tex] \tan( \theta) = - \frac{opposite}{adjacent} [/tex]
[tex]\tan( \theta) = - \frac{1}{3} [/tex]
The values of sine, cosine and tangent of θ are; 1/√10, -3/√10 and -1/3 respectively.
Sine, Cosine and Tangent of anglesFrom the task content, it follows from Pythagoras theorem that;
hypothenuse = √((-3)²+1²)hypothenuse = √10On this note;
Sin θ = 1/√10Cos θ = (-3)/√10Tan θ = -1/3Read more on Trigonometric identities;
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select the items that would be best measured in grams.
mark all that apply.
A=watermelon
B=lettuce leaf
C=grape
D=onion
Final answer:
Grams are best used to measure small, lightweight items. Therefore, a lettuce leaf, a grape, and an onion are the items from the provided list that would be best measured in grams. A watermelon, being larger, is typically measured in kilograms.
Explanation:
Selecting Items Best Measured in Grams
To answer the question regarding which items would be best measured in grams, let's start by understanding what grams are used for. Grams are a unit of mass commonly used to measure smaller, lightweight items. Considering the options given, let's evaluate each one:
A watermelon: While it has a significant amount of mass, a watermelon is generally better measured in kilograms due to its larger size.
B lettuce leaf: This is lightweight and would be best measured in grams, fitting the use of grams for small items.
C grape: Grapes are small and light, making grams the appropriate measure for their mass.
D onion: Typically, an onion is not too heavy and is suitably measured in grams, although if it's a particularly large onion, kilograms might be considered.
So, the items from the list that would be best measured in grams - considering they are small enough to fall into the range that the gram unit typically covers - would be a lettuce leaf, a grape, and an onion.
Solve the equation 5|b+8|=30
Answer:
b = -2 or b = -14Step-by-step explanation:
[tex]5|b+8|=30\qquad\text{divide both sides by 5}\\\\|b+8|=6\iff b+8=6\ or\ b+8=-6\qquad\text{subtract 8 from both sides}\\\\b=-2\ or\ b=-14[/tex]
To solve the equation 5|b+8|=30, we first isolate the absolute value by dividing by 5, then set up two separate equations for b + 8 = 6 and b + 8 = -6. Solving each gives us the solutions b = -2 and b = -14.
Explanation:To solve the equation 5|b+8|=30, we will first divide both sides of the equation by 5 to isolate the absolute value expression.
So moving from the equation 5|b+8|=30, we get |b+8| = 6. This means that the expression inside the absolute value can be either positive 6 or negative 6.
We then write two separate equations to solve for the variable b:
b + 8 = 6b + 8 = -6Solving the first equation, we subtract 8 from both sides to find that b = -2. Solving the second equation, we subtract 8 from both sides to find that b = -14.
Thus, the solution for the equation 5|b+8|=30 is b = -2 or b = -14.
what is 2 3/2 equal to?
A) Two times the square root of 8
B) three times the square root of 8
C) Three times the square root of 16
D) Two times the square root of 16
The expression '2 3/2' is a mixed number. Converting this to an improper fraction results in 7/2, which simplifies to 3.5. This does not match any of the provided options.
Explanation:The expression '2 3/2' implies that we are dealing with mixed numbers, meaning you have a whole number and a fraction combined. When you see this, you should convert the mixed number into an improper fraction. The way to do this is to multiply the whole number by the denominator of the fraction and then add the numerator to this product. In this case that would be (2*2) + 3 which equals 7. Your new fraction would be 7/2 which equals 3.5 when simplified to a decimal. This does not correspond to any of the provided options (A, B, C, D), signifying that the original question may have been misinterpreted or contains a typographical error.
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2 3/2 is equal to 7/2 or D) Two times the square root of 16.
Explanation:When we have a whole number followed by a fraction, we can convert it to an improper fraction.
To do this, we multiply the whole number by the denominator of the fraction and add the numerator.
So in this case, 2 x 2 + 3 = 7.
Therefore, 2 3/2 is equal to 7/2 or D) Two times the square root of 16.
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what is the sum of an 8-term geometric series if the first term is -11, the last term is 180, 224, and the common ratio is -4
Answer:
The sum is [tex]144,177[/tex]
Step-by-step explanation:
we know that
The formula of the sum in a geometric sequence is equal to
[tex]S=a1[\frac{1-r^{n}}{1-r}][/tex]
where
a1 is the first term
r is the common ratio
n is the number of terms
we have
a1=-11
r=-4
n=8
substitute the values
[tex]S=(-11)[\frac{1-(-4)^{8}}{1-(-4)}][/tex]
[tex]S=(-11)[\frac{1-(65.536)}{5}][/tex]
[tex]S=144,177[/tex]
Which verbal description, when graphed has the same slope as y= -2x+6
A. Teo has read 6 books. He reads 2 per day, X is the number of days and y is the total number of books read
B. Caroline is 6 miles from home. She walks towards home at 2 miles per hour, X is the number of hours and Y is the number of miles from Home
C. Ned deposits $6 per week into his saving account, which already has $2 in it, X is the number of weeks and Y is the total of dollars
Answer: i say its A but i could be wrong
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Find the slope of the line through (2, -3) and (-4, 3).
-1
0
1
ANSWER
-1
EXPLANATION
The slope formula is given by
[tex]m = \frac{y_1-y_2}{x_1-x_2} [/tex]
The slope of the line through (2, -3) and (-4, 3) is found by substituting the points into the above formula;
[tex]m = \frac{ - 3 - 3}{2 - - 4} [/tex]
This simplifies to
[tex]m = \frac{ - 6}{ 6} = - 1[/tex]
The slope is -1
Answer:
-1
Step-by-step explanation:
The slope of a line is the ratio of its change in rise to its change in run. In the -xy-plane, this is the same as the ratio of the change in y coordinate to the change in x coordinate. In notation, we write this as
[tex]\frac{\Delta y}{\Delta x}[/tex]
and calculate it by finding the difference between y coordinates and dividing it by the difference between x coordinates. Here, our y coordinates are 3 and -3, and our x coordinates are -4 and 2, so our slope would be
[tex]\frac{3-(-3)}{-4-2}=\frac{3+3}{-6}=\frac{6}{-6}=-1[/tex]
simplify the expression -7/9 - 5/10
We can sum two fractions if they have the same denominator, so we have to rewrite both fractions so that they'll have the same denominator.
We can generate equivalent fractions by multiplying both numerator and denominator by the same number.
So, we have
[tex]-\dfrac{7}{9} = -\dfrac{7\cdot 10}{9\cdot 10} = -\dfrac{70}{90}[/tex]
Similarly, we have
[tex]-\dfrac{5}{10} = -\dfrac{5\cdot 9}{10\cdot 9} = -\dfrac{45}{90}[/tex]
Now we can sum the fractions:
[tex]-\dfrac{7}{9}-\dfrac{5}{10} = -\dfrac{70}{90}-\dfrac{45}{90} = \dfrac{-70-45}{90} = -\dfrac{115}{90} = -\dfrac{23}{18}[/tex]
To simplify the expression -7/9 - 5/10, find a common denominator, which is 90, convert and add the fractions to get -115/90, which is the simplified form of the expression.
The question asks to simplify the expression -7/9 - 5/10. To do this, we need to find a common denominator to combine these fractions. The least common denominator (LCD) for 9 and 10 is 90.
First, convert both fractions:
-7/9 = (-7*10)/(9*10) = -70/90-5/10 = (-5*9)/(10*9) = -45/90Then, add the fractions:
-70/90 - 45/90 = -115/90
Finally, it is usually a good practice to simplify the fraction, but in this case, -115 and 90 do not have any common factors other than 1, so the simplified expression is -115/90.
What is the point-slope form of a line that has a slope of 3 and passes through point (1, 4)?
Answer: [tex](y-4)=3(x-1)[/tex]
Step-by-step explanation:
We know that the point slope form of a line that has a slope m and passing through point (a,b) is given by :-
[tex](y-b)=m(x-a)[/tex]
Given: Slope of a line: m = 3
Point through which line is passing : (1, 4)
The point slope form of a line that has a slope 3 and passing through point (1, 4) is given by :-
[tex](y-4)=3(x-1)[/tex]
– 4 = 3[(x – (–1)]
Step-by-step explanation:
if you spin the spinner twice what is the probability that it will land on an even number both times
The answer would be [tex]\frac{1}{4}[/tex] because half the chance of landing on an even number divided by 2 (2 times landing on the even number).
The probability that the spinner will land on an even number both times when spun twice is 1/4 or 25%.
To find the probability of two independent events occurring together, we multiply their individual probabilities. First, let's determine the probability of landing on an even number in a single spin. There are two even numbers (2 and 4) out of the four possible outcomes, so the probability of landing on an even number in one spin is 2/4 or 1/2.
Since we're spinning the spinner twice, the events are independent. This means that the outcome of the first spin does not affect the outcome of the second spin. Therefore, the probability of landing on an even number in both spins is the product of the individual probabilities. So, the probability of landing on an even number both times is:
Probability of landing on an even number in one spin = 1/2
Probability of landing on an even number twice = (1/2) * (1/2) = 1/4
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A French class has a total of
42
students. The number of males is
8
more than the number of females. How many males and how many females are in the class?
Their are 34 females in the class.
If 42 is the total amount of French students; subtract the amount of males(8) from the whole class to receive how many females their are in the class. Which is 34.
Which statement is true about the solution to √2x-1==1
Answer:
There are no real number solutions to this question.
The statement which is true for the equation[tex]\sqrt{2x-1} =-1[/tex] is option C which is that x=1.
What is an equation?It is a relationship between variables and it can be in the form of one variable also.
How to solve the problem?We have been given [tex]\sqrt{2x-1} =-1[/tex]
squaring both sides we get
2x-1=1
2x=1+1
2x=2
x=1
Hence the solution of the equation is x=1.
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tell whether the angles are complementary or supplementary. then find the value of x
Hello,
In Q5. Being a straight line the angles are supplementary to each other.
And x = 70°
In Q6.
The angles sum up to 90° , so 25x + 30° = 90
25x = 60°
x= 60°/25 = 2.4°
Hope this helps.
Answer:
see explanation
Step-by-step explanation:
5
x and 110 form a straight angle and are supplementary, thus
x + 110 = 180 ( subtract 110 from both sides )
x = 70
6.
25x and 30 form a right angle and are complementary, thus
25x + 30 = 90 ( subtract 30 from both sides )
25x = 60 ( divide both sides by 25 )
x = [tex]\frac{60}{25}[/tex] = [tex]\frac{12}{5}[/tex]
15% of 20 is
Ο 30
Ο 300
Answer:
3
Step-by-step explanation:
Is means equals and of means multiply
15% * 20 = ?
Change to decimal form
.15 * 20 = ?
3 = ?
15% of 20 is 3
Simplify the variable expression by evaluating its numerical parts and enter your answer m - 22 + 37 - 8
7 is the answer dddddddddddddddd
Answer:
M+7
Step-by-step explanation:
hoped it heped ^v^Solve the inequality n/-3+ 8 > 6.
A.) n > -6
B.)n > 42
C.)n < 6
D.)n > -42
Answer:
C.) n < 6
Step-by-step explanation:
Subtract 8:
n/-3 > -2
Multiply by -3. The negative multiplier requires the comparison be reversed:
n < 6
To solve the inequality n/-3 + 8 > 6, we first subtract 8 from both sides of the inequality and then multiply by -3. This reveals that n < 6, which corresponds to option C.
Explanation:To solve the inequality n/-3 + 8 > 6, we first isolate the term containing n by subtracting 8 from both sides of the inequality:
n/-3 + 8 - 8 > 6 - 8
n/-3 > -2
Now, we can multiply both sides of the inequality by -3 to find the value of n. Remember, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign:
n/-3 × -3 < -2 × -3
n < 6
Thus, the correct answer to the inequality n/-3 + 8 > 6 is n < 6, which corresponds to option C.
a submarine is at a depth of 2 1/3 km below sea level and if it starts ascending at the rate of 800m/h.then find its position after 2 hours?
Answer:
66 ⅔ m
Step-by-step explanation:
2 ⅓ km can be written in improper form as 5/3 km.
There's 1000 m in 1 km, so we can convert this:
5/3 km × (1000 m / km) = 5000/3 m
The submarine rises at 800 m/h. So after 2 hours:
distance = rate × time
d = 800 m/h × 2 h
d = 1600 m
So the new position is:
5000/3 m − 1600 m
5000/3 m − 4800/3 m
200/3 m
66 ⅔ m
Final answer:
After ascending at a rate of 800 meters per hour for 2 hours from a depth of 2 1/3 kilometers, the position of the submarine would be 733.3 meters below sea level.
Explanation:
The student has asked to find the position of a submarine after it ascends from a depth of 2 1/3 km below sea level at a rate of 800 m/h for 2 hours.
Firstly, we convert the depth of the submarine from kilometers to meters to match the ascent rate's unit. There are 1,000 meters in a kilometer, so 2 1/3 km is equivalent to 2,333.3 meters (since 2 km = 2000 m and 1/3 km = 333.3 m).
The submarine ascends at a rate of 800 meters per hour. After 2 hours, the total ascent will be 800 m/h * 2 h = 1,600 meters.
To find the new position, we subtract the ascent distance from the original depth: 2,333.3 m - 1,600 m = 733.3 meters below sea level.
Therefore, after 2 hours, the position of the submarine would be 733.3 meters below sea level.
Which fact would help you to solve for x in the diagram shown?
A) Angles in an equilateral triangle are congruent.
B) The sum of the interior angles in a quadrilateral is 360°.
C) Alternate interior angles formed by a transversal and parallel lines are congruent.
D) The exterior angle of a triangle is equal to the sum of the two remote interior angles.
The answer is A, Angles in an equilateral triangle are congruent.
Which fact would help you to solve for x in the diagram shown?
A) Angles in an equilateral triangle are congruent.
The admission fee at an amusement park is $4.50 for children and $13 for adults. On a certain day, 249 people enter the park, and the admission fees collected totaled $2,013.00 how many children and how many adults were admitted?
Answer:
154 adults 94kids
Step-by-step explanation:
What graph represents a reflection of abc over the line x=0
Answer: D
Step-by-step explanation: APEX
Answer:
The correct option is D)
Step-by-step explanation:
line x = 0 is y-axis (vertical line)
When graph is reflected along y-axis so, it will be in second quadrant.
so, the graph which satisfying these condition is only option D)
in which c ordinate are A has (-1,1) ,B has (-4,1) and C has (-3,3)
Hence, the correct option is D)
13 divide 32,708 what is the answer
Answer:
0.00039745627
13 / 32708 is 0.004
I got this answer by using Long Division.
Hope this helps
Which of the following could be folded to produce the object above?
Answer:
answer is Z
Step-by-step explanation:
Find the exact value. cos150°
ANSWER
[tex]\cos(150 \degree) = - \frac{ \sqrt{3} }{2} [/tex]
EXPLANATION
We want to find the exact value of cos(150°).
150° makes an angle of 30° with the positive direction of the x-axis and it is also in the second quadrant.
The cosine ratio is negative in the second quadrant.
Using the unit circle,
[tex] \cos(150 \degree) = - \cos(30 \degree) = - \frac{ \sqrt{3} }{2} [/tex]
Answer:
-√3/2
Step-by-step explanation:
Cos 150° can also be rewritten as shown;
Cos 150° = cos(90°+60°)
According to trigonometry identity
Cos(A+B) = cosAcosB - sinAsinB
Therefore;
Cos(90°+60°) = cos90cos60-sin90sin60
Cos(90°+60°) = 0(1/2) - 1(√3/2)
Cos(90°+60°) = 0-√3/2
Cos(90°+60°) = -√3/2
Cos 150° = -√3/2
what is y+5=7(x-8) written in standard form
Answer:
7x-y=61
Step-by-step explanation:
The standard form is Ax+By=C.
Let's simplify the equation first.
1. Distribute: y+5=7x-56
2. Subtract 5: y=7x-61
3. Arrange into standard form: 7x-y=61
Answer
-7x+y=-61
Its the same as 7x-y=61, but in a different form
Can someone please help me out
Answer:
D
Step-by-step explanation:
Look at where the two functions intersect.
[tex](-3,-3)[/tex] and [tex](0,6)[/tex].
Those are the solutions.
If I had $33,50 last month and this month I got a raise and brought back $45,70 how much more did I bring back
You brought back 12.2
hope that helped
what is the best next step in the construction of a line that passes through B and is perpendicular to line A?
A. set the compass to be equal to CD
B. set the co pass to be wider than it was when placed at point B to draw the arc that passes through C and D
C. set the compass to be greater than CD
D. keep the compass setting the same width as when it was placed at point B to draw the arc that passes through C and D
Answer:The answe is D
Step-by-step explanation:
The correct next step is to keep the compass at the same width used at point B to draw an arc through points C and D, enabling the construction of a perpendicular line. Hence correct option D.
The best next step in the construction of a line that passes through point B and is perpendicular to line A is to keep the compass setting the same width as when it was placed at point B to draw the arc that passes through points C and D. This ensures that the arcs intersect the line A at points that are equidistant from B, which is essential in establishing a perpendicular line.
Find the number of even-numbered subsets that have only even numbers from the set (1,2,3,4,5,6...100)
I would greatly appreciate a quick answer
Answer:
Step-by-step explanation:
You could use the 'brute force' method, which would be to simply write out all the possible subsets. We could avoid repetition within the subsets.
{2} would be the first subset; it contains one even number.
Next would be {2, 4}, next {2, 4, 6} ... {2, 4, 6, ... 94, 96, 98, 100}. Provided that we correctly understand what this problem is asking for, writing out and then counting all these subsets should answer the question.
does the equation y = 4.2 x represent a proportional relationship
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=\stackrel{\stackrel{k}{\downarrow }}{4.2}x~~\checkmark~\hfill[/tex]
Answer: its proportional,
bud
Step-by-step explanation: