Answer: The equations are as follows;
5p + 4d = 43.25 ————(1) and
3p + 2d = 24.25 ————(2)
Also a bag of popcorn costs $5.25
Step-by-step explanation: We start by assigning letters to the unknown variables. Let a bag of popcorn be p and let one drink be d. The clues given in the question include the cost of buying five bags of popcorn and four drinks which is a total of $43.25. This can be expressed as
5p + 4d = 43.25 ————(1)
Another clue is that three bags of popcorn and two drinks cost $24.25. This also can be expressed as
3p + 2d = 24.25 ————(2)
Now we have a pair of simultaneous equations as follows
5p + 4d = 43.25 ————(1)
3p + 2d = 24.25 ————(2)
We shall use the elimination method since all the unknowns have coefficients greater than 1. Multiply equation one by 3, and multiply equation two by 5 (so as to eliminate ‘p’)
5p + 4d = 43.25 ——— x3
3p + 2d = 24.25 ——— x5
15p + 12d = 129.75 ———(3)
15p + 10d = 121.25 ———(4)
Subtract equation (4) from equation (3) and we have
2d = 8.5
Divide both sides of the equation by 2
d = 4.25.
That means each drink costs $4.25
We can now substitute for the value of d into equation (2)
3p + 2d = 24.25
When d = 4.25
3p + 2(4.25) = 24.25
3p + 8.5 = 24.25
Subtract 8.5 from both sides of the equation
3p = 15.75
Divide both sides of the equation by 3
p = 5.25. This means a bag of popcorn costs $5.25
Find the GCF of 21, 30
Answer:
The GCF of 21 and 30 is 3.
Step-by-step explanation:
Find the prime factorization of 21
21 = 3 × 7
Find the prime factorization of 30
30 = 2 × 3 × 5
To find the gcf, multiply all the prime factors common to both numbers:
Therefore, GCF = 3
Answer:
3
Step-by-step explanation:
Factors of 21: 1, 3, 7, 21
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The GCF is the largest factor they both have.
GCF = 3
A partial
hubcap is shown. Copy and complete the
figure so that the completed hubcap has
rotational symmetry of 90°, 180°, and 270°.
Answer:
just complete the whole drawing
Step-by-step explanation:
Four laps around the track equals one mile. How many miles does sixteen laps equal?
Answer:
It equals 4 miles
Solve for 18. will give brainliest to first answer
Answer:
v > -1
Step-by-step explanation:
1/3(v-2) < v
Multiply both sides by 3(from 1/3) to equalize both sides.
This is equal to:
v-2 < 3v
Simplify equation:
v-2 < 3v =
-2 < 3v - v =
-2 < 2v
-1 < v
Swap sides:
v > -1
Therefore v is greater than -1.
Answer:
v > -1
Step-by-step explanation:
Simplify the left side.
Apply the distributive property.
13v+13⋅−2<v
Combine 13 and v
v3+13⋅−2<v
Combine 13 and −2
v3+−23<v
Move the negative in front of the fraction.
v3−23<v
Move all terms containing v to the left side of the inequality.
Subtract v from both sides of the inequality.
v3−23−v<0
Simplify the left side of the inequality.
−2(v+1)3<0
Multiply each term in −2(v+1)3<0 by −1
2(v+1)3>0
Multiply both sides of the equation by 3
2(v+1)>0⋅(3)
and again Simplify the left side.
Apply the distributive property.
2v+2⋅1>0⋅(3)
Multiply 2 by 1
2v+2>0⋅(3)
Multiply 0 by 3
2v+2>0
Subtract 2 from both sides of the inequality.
2v>−2
Divide each term by 2 and simplify.
Getting the conclusion where V is greater than 1
v>−1
Hope this helps
0.44, 4/9, 0.4445, 44.5 on a number line please
Ben goes to the grocery store at a rate of 7 times a week. How many times would he be expected to
go to the grocery store in 17 weeks?
times
Translate to a proportion:
V
weeks
weeks
times in 17 weeks
Answer:
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Step-by-step explanation:
bfyhh a ryagdh a child with hai tu ki baat nahin hota ha ha bol de mon iPhone and I will send you a Raha tha u y ok bye uy y ok bye y ok Sharjah United Arab and I have written to occur
Final answer:
Ben goes to the grocery store at a rate of 7 times a week. To find out how many times he goes in 17 weeks, you multiply 7 by 17, which equals 119. Therefore, Ben is expected to go to the grocery store 119 times in 17 weeks.
Explanation:
To calculate how many times Ben goes to the grocery store in 17 weeks, given that he goes at a rate of 7 times a week, we need to multiply the number of weeks by the frequency of his visits per week. The calculation is as follows:
Multiply the number of visits per week by the number of weeks: 7 visits/week imes 17 weeks. Perform the multiplication: 7 imes 17 = 119. Therefore, Ben is expected to go to the grocery store 119 times in 17 weeks.
As a proportion, this can be represented as:
V
--- =
weeks
7 times/week
-------------- =
1 week
Which can be scaled up to represent the 17 weeks:
119 times
--------------
17 weeks
3 Fred is making a fruit salad. The ratio
of cups of peaches to cups of cherries
is 2 to 3. How many cups of peaches
will Fred need to make 60 cups of
fruit salad?
Answer: 24 cups.
Step-by-step explanation:
Let be "x" the amount of cups of peaches that Fred will need to make 60 cups of fruit salad.
According to the information given in the exercise, you know that the ratio of cups of peaches to cups of cherries is the one shown below:
[tex]2:3[/tex]
Which can also be written as a fraction:
[tex]\frac{2}{3}[/tex]
Then, if he uses 2 cups of peaches and 3 cups of cherries, he will get 5 cups of fruit salad.
Knowing the above, you can set up the following proportion:
[tex]\frac{2}{5}=\frac{x}{60}[/tex]
Now you must solve for "x" in order to find its value. This is:
[tex](60)(\frac{2}{5})=x\\\\x=24[/tex]
a card is randomly chosen from a standard deck of cards. Find each probability.
Answer: The probability is 1/52 or .0192.
Step-by-step explanation:
A standard deck of cards has 52 so the probability of picking 1 card would be 1/52.
(a) The probability of drawing a spade is 1/4.
(b) The probability of drawing a face card (jack, queen, or king) is 3/13.
(c) The probability of drawing a red card is 1/2.
(d) The probability of drawing a card that is not an ace is 12/13.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
(a) The probability of drawing a spade.
There are 13 spades in a standard deck of 52 cards, so the probability of drawing a spade is:
P(spade) = 13/52 = 1/4
(b) The probability of drawing a face card (jack, queen, or king).
There are 12 face cards (4 jacks, 4 queens, and 4 kings) in a standard deck of 52 cards, so the probability of drawing a face card is:
P(face card) = 12/52 = 3/13
(c) The probability of drawing a red card.
There are 26 red cards (13 hearts and 13 diamonds) in a standard deck of 52 cards, so the probability of drawing a red card is:
P(red card) = 26/52 = 1/2
(d) The probability of drawing a card that is not an ace.
There are 48 cards that are not aces in a standard deck of 52 cards (there are 4 aces), so the probability of drawing a card that is not an ace is:
P(not ace) = 48/52 = 12/13
Thus,
(a) The probability of drawing a spade is 1/4.
(b) The probability of drawing a face card (jack, queen, or king) is 3/13.
(c) The probability of drawing a red card is 1/2.
(d) The probability of drawing a card that is not an ace is 12/13.
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The complete question:
A card is randomly chosen from a standard deck of cards. Find each probability.
(a) The probability of drawing a spade.
(b) The probability of drawing a face card (jack, queen, or king).
(d) The probability of drawing a card that is not an ace.
Jenna takes a survey of students in her class to determine how many hours they studied for their Math exam. The mean of the responses is 5.6 hours. Which conclusion MUST be true?
A) No one in the class studied more than 5 hours.
B) Every member of the class studied for the exam.
C) At least one person in the class studied 1 hour.
D) At least one person in the class studied more than 5 hours.
A) No one in the class studied more then 5 hours
Answer:
d
Step-by-step explanation:
trust me
y = -8x2 + 665x – 5754
Answer:
Is the -8x2 a -8x squared? Because the answer of this problem can be different.
Step-by-step explanation:
Determine whether the following statement is true or false. Explain.
All spheres are similar
Answer:
Below.
Step-by-step explanation:
They are all the same shape.
Also, the only parameter of a sphere that can vary is the radius, so they are all similar.
quinn rolled a regular number cube 42 times. how many times would you predict he rolled a 6?
Answer:
1/7 so around 7
Step-by-step explanation:
becuase there are 6 numbers and there is a 1/6 chance to get each number and 42/6 is seven so there is a 1/7 chance to get each number.
Answer:
1/7 or 7
Step-by-step explanation:
There are 6 numbers on a number cube and when you divide 42/6 you get 7, so 1/7 should be your answer.
What is the slope of the line that passes through point (3,2)
(
3
,
2
)
and point (6,11)
(
6
,
11
)
?
Answer:
Slope=3
Step-by-step explanation:
Slope=Rise/Run=(11-2)/(6-3)=9/3=3
Answer:
The slope is 3.
Step-by-step explanation:
Use the slope formula.
[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
We use the y-coordinates of the two points as y2 and y1.
We use the x-coordinates of the two points as x2 and x1. x2 goes with y2. x1 goes with y1.
[tex] slope = m = \dfrac{11 - 2}{6 - 3} = \dfrac{9}{3} = 3[/tex]
The slope is 3.
5.4 - 6 - 2 = x
A. (5.4)-6= 2 = x
B. 5.(4-6-2) = x
5.4—(6= 2)= x
5.(4-6)= 2 = x
00
Answer:
[tex]x=-2.6[/tex]
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
if the cost of goods sold was $42,000 the income from sales was $86,000 and the expenses were $12,000 find gross profit and net profit
Gross profit is $44,000 and Net profit is $32,000
Step-by-step explanation:
Given :
cost of goods sold = $42,000The income or revenue = $86,000expenses = $12,000Gross profit :
Gross Profit = Total income - Cost of goods sold
⇒ $86,000 - $42,000
⇒ $44,000
⇒ Gross profit is $44,000
Net profit :
Net profit = Gross profit – Total Expenses
⇒ $44,000 - $12,000
⇒ $32,000
⇒ Net profit is $32,000
solve for x: (x-5)^2 = 49
Answer: [tex]x=12, -2[/tex]
Step-by-step explanation:
[tex](x-5)^{2}=49[/tex]
F.O.I.L the binomial
[tex]x^2-10x+25=49[/tex]
Set to 0
[tex]x^2-10x+25_{-49} =49_{-49}[/tex]
[tex]x^2-10x-24=0[/tex]
Factor the polynomial
[tex](x-12)(x+2)[/tex]
Set to 0 and Inverse operations
[tex](x-12)=0\\x=12[/tex]
Set to 0 and Inverse operations
[tex](x+2)=0\\x=-2[/tex]
Answer:
[tex]x=12, -2[/tex]
Which item has a unit rate of $6.50?
O caps: 4 for $25.00
o posters: 3 for $20.25
o tote bag: 4 for $30.00
O T-shirts: 5 for $32.50
Answer:
T-shirts
Step-by-step explanation:
First, find the unit price for caps. Divide 25 by 4, which equals $6.25. Then, divide 20.25 by 3, which equals $6.75. Next, divide 30 by 4, which equals $7.50. Finally, divide 32.50 by 5, which equals $6.50. To t-shirts have a unit rate of $6.50
i think the answer is t-shirts , hope this helps
can 3,4,7 make a possible right triangle?
Let's see by using the Pythagorean theorem.
3 and 4 are legs. 3 is the shortest leg.
7 is the hypotenuse.
The theorem states that:
a² + b² = c²
a = 3
b = 4
c = 7
3² + 4² = 7²
9 + 16 = 49
25 = 49 (Incorrect)
So it is not possible for 3,4,7 to be a right triangle.
The numbers 3, 4, and 7 do not satisfy the Pythagorean theorem, as the sum of the squares of 3 and 4 is 25, which does not equal the square of 7 (49). Hence, these numbers cannot form a right triangle.
To determine if the numbers 3, 4, and 7 can form the sides of a right triangle, we use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we would expect the square of the longest side (7) to be equal to the sum of the squares of the other two sides (3 and 4).
Calculating, we have:
32 + 42 = 9 + 16 = 25.
The square of the longest side is 72 = 49.
Since 25 does not equal 49, the sides 3, 4, and 7 do not satisfy the Pythagorean theorem and therefore cannot form a right triangle.
The quotient of d minus 16 and 3 is 4 . Which equation shows this ?
Answer: d-16/3=4
Step-by-step explanation: thats the equation!
hope it helps please mark brainliest
Final answer:
The equation representing the statement "The quotient of d minus 16 and 3 is 4" is (d - 16) / 3 = 4. By solving the equation, we find that d = 28.
Explanation:
The question asks to find the equation that represents the statement: "The quotient of d minus 16 and 3 is 4." This translates to a mathematical equation by dividing the difference of d and 16 by 3, which equals 4. The equation that shows this relationship is (d - 16) / 3 = 4.
To solve this equation for d, you can follow these steps:
Multiply both sides of the equation by 3 to eliminate the denominator: (d - 16) = 12.
Add 16 to both sides of the equation to solve for d: d = 12 + 16.
This gives you d = 28 as the solution.
Therefore, the equation that accurately represents the given statement is (d - 16) / 3 = 4, and the value of d that satisfies this equation is 28.
2•2•2•3•3 in exponent form
Answer:
2^3 * 3^2
Step-by-step explanation:
Step 1: Convert into exponent form
2 * 2 * 2 * 3 * 3
2^3 * 3^2
Answer: 2^3 * 3^2
find the equation of a line that passes through (-2,4) and (1,-2)
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-2)}}}\implies \cfrac{-6}{1+2}\implies \cfrac{-6}{3}\implies -2[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-2}[x-\stackrel{x_1}{(-2)}]\implies y-4=-2(x+2) \\\\\\ y-4=-2x-4\implies y = -2x[/tex]
If |OQ| = 9.4 units, |OQ’| = 17.1 units, and |P’Q’| = 17.1 units, determine |PQ|. Round your answer to the tenths place, if necessary.
Answer:
9.4 units.
Step-by-step explanation:
Given information: |OQ| = 9.4 units, |OQ’| = 17.1 units, and |P’Q’| = 17.1 units.
Dilated figure is similar to the original figure. It means the corresponding sides are proportional.
[tex]\dfrac{|OQ|}{|OQ'|}=\dfrac{|PQ|}{|P'Q'|}[/tex]
Substitute the given values.
[tex]\dfrac{9.4}{17.1}=\dfrac{|PQ|}{17.1}[/tex]
Multiply both sides by 17.1.
[tex]\dfrac{9.4}{17.1}\times 17.1=\dfrac{|PQ|}{17.1}\times 17.1[/tex]
[tex]9.4=|PQ|[/tex]
Hence, the measure of |PQ| is 9.4 units.
Ariana and two friends decide to split a pizza and garlic bread. If the total cost for the food is $15.33, how much should each person pay?
Answer: $7.665 each, approximately $7.67 each
Step-by-step explanation:
If cost is $15.33
To be sharedby two friends will be the cost/2
15.33/2= $7.665 each
Each person should pay $5.11 to equally split the total cost of the pizza and garlic bread, which is $15.33.
The student is asking how to divide the total cost of a pizza and garlic bread, which is $15.33, evenly among three people. To calculate this, we can use simple division.
Here is the step-by-step calculation:
First, identify the total cost of the food: $15.33.
Next, determine the number of people sharing the cost, which is three.
Divide the total cost by the number of people: $15.33 ÷ 3 = $5.11.
Therefore, each person should pay $5.11 to equally split the cost of the pizza and garlic bread.
1/3 x 1/2
PLS PSL eellelele
Step-by-step explanation:
1/3 x 1/2
3 x 2=6
so ∴1/3 x 1/2=1/6
Which choices are equivalent to the quotient below? Check all that apply. √12/√6
The expression (√12) / (√6) simplifies to √2 by combining square roots and simplifying the fraction. The final simplified form is √2. Here option A is correct.
Given Expression:
(√12) / (√6)
Step 1: Write as Quotient of Square Roots
(√12) / (√6) can be expressed as √(12/6)
We express the division of square roots as the square root of the division of the radicands.
Step 2: Simplify the Quotient Under the Radical
√(12/6)
To simplify the fraction under the square root, divide the numerator by the denominator:
√(12/6) = √2
Step 3: Write the Answer in Simplified Form
√2
Therefore, the given expression (√12) / (√6) simplifies to √2.
We simplified the expression by combining the two square roots into one using the rule for dividing square roots and then simplified the fraction under the square root to arrive at the final answer, which is √2. Here option A is correct.
The correct option is A and C.
The equivalent choices to the given quotient [tex]\(\frac{\sqrt{12}}{\sqrt{6}}\)[/tex] are A [tex](\(\sqrt{2}\))[/tex] and C [tex](\(\frac{\sqrt{4}}{\sqrt{2}}\))[/tex].
The question shows a math problem asking which choices are equivalent to the given quotient:
[tex]\[ \frac{\sqrt{12}}{\sqrt{6}} \][/tex]
We'll solve this step by step:
1. Simplify the square roots by factoring out squares:
[tex]\[ \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \][/tex]
[tex]\[ \sqrt{6} = \sqrt{2 \cdot 3} = \sqrt{2} \cdot \sqrt{3} \][/tex]
2. Write the original quotient with the simplified square roots:
[tex]\[ \frac{\sqrt{12}}{\sqrt{6}} = \frac{2\sqrt{3}}{\sqrt{2} \cdot \sqrt{3}} \][/tex]
3. Cancel out the common terms:
[tex]\[ \frac{2\sqrt{3}}{\sqrt{2} \cdot \sqrt{3}} = \frac{2}{\sqrt{2}} \][/tex]
4. Rationalize the denominator by multiplying the numerator and denominator by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ \frac{2}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{2} \][/tex]
5. Simplify the fraction:
[tex]\[ \frac{2\sqrt{2}}{2} = \sqrt{2} \][/tex]
So the simplified quotient is [tex]\(\sqrt{2}\)[/tex]. Now let's check the options in the image to see which ones are equivalent to [tex]\(\sqrt{2}\)[/tex]:
A. [tex]\(\sqrt{2}\)[/tex] - This is the correct simplified form of the given quotient.
B. [tex]\(2\)[/tex] - This is incorrect because it is not the square root of 2.
C. [tex]\(\frac{\sqrt{4}}{\sqrt{2}}\)[/tex] - Since [tex]\(\sqrt{4} = 2\)[/tex], this simplifies to [tex]\(\frac{2}{\sqrt{2}}\)[/tex], which after rationalization becomes [tex]\(\sqrt{2}\)[/tex], so this is also correct.
D. [tex]\(\frac{2}{\sqrt{3}}\)[/tex] - This is incorrect because it does not simplify to [tex]\(\sqrt{2}\)[/tex].
E. [tex]\(\frac{\sqrt{6}}{\sqrt{2}}\)[/tex] - Since [tex]\(\sqrt{6} = \sqrt{2 \cdot 3}\)[/tex], this simplifies to [tex]\(\sqrt{3}\)[/tex], which is incorrect.
F. [tex]\(\frac{\sqrt{6}}{2}\)[/tex] - This does not simplify to [tex]\(\sqrt{2}\)[/tex] and is therefore incorrect.
The correct answer choices are A and C, which are both equivalent to [tex]\(\sqrt{2}\)[/tex].
The complete question is here:
Given the parent function, y=2^x, write an equation for a function that has a vertical shift down 5 units.
Answer:
y=2^x - 5
Step-by-step explanation:
"- 5" demonstrates a verical shift 5 units down
If a line has a slope of 3/4, what is the
slope of the line perpendicular to the
line?
The perpendicular of the line is -4/3.
What is perpendicular?Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular sign ⊥ , can be used to visually depict the state of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.
Given a line has a slope of 3/4.
So the slope of the line perpendicular will have the opposite reciprocal as a slope,
That means perpendicular of a line = - reciprocal of slope of the line
perpendicular of a line = - (4/3)
Therefore the perpendicular of the line is -4/3.
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Find a linear function that models the data in the table.
f(x)= *blank* x + *blank*
The linear function that models the data in the table is [tex]\( f(x) = 2x + 3 \)[/tex].
Explanation:To find the linear function, we need two key pieces of information: the slope mn and the y-intercept b. In the given function f(x) = 2x + 3, the coefficient of x (2) represents the slope, and the constant term (3) represents the y-intercept.
The slope m indicates the rate at which the function is changing, and in this case, it is 2. This means that for every unit increase in x, y increases by 2 units. The y-intercept b is the value of y when x is zero, which is 3 in this case. Therefore, the linear function f(x) = 2x + 3 accurately models the relationship between x and y in the given dat x in a linear manner.
In summary, the general form of a linear function is [tex]\(f(x) = mx + b\)[/tex], where m is the slope and b is the y-intercept. The values of m and b can be determined from the data or information provided.
The linear function that models the data in the table is [tex]\(f(x) = \frac{13}{7}x + 1\)[/tex], where x represents the input and f(x) the output.
To find a linear function that models the data in the table, we can use the slope-intercept form of a linear equation: f(x) = mx + b, where m is the slope and b is the y-intercept.
Let's find the slope (m) first using the given data points (-4, -6) and (3, 7):
[tex]\[m = \frac{\text{change in } y}{\text{change in } x} = \frac{7 - (-6)}{3 - (-4)} = \frac{13}{7}.\][/tex]
Now that we have the slope, we can use any point from the table to find the y-intercept (b). Let's use the point (0, 1):
[tex]\[1 = m(0) + b \implies b = 1.\][/tex]
Now, we can write the linear function:
[tex]\[f(x) = \frac{13}{7}x + 1.\][/tex]
So, the linear function that models the data in the table is [tex]\(f(x) = \frac{13}{7}x + 1\)[/tex].
A physician prescribes one 0.7 mg tablet of a medication to be taken twice a day for 15 days.
How many total mcg of the medication will the patient have taken after 15 days?
Answer:
21 mg
Step-by-step explanation:
0.7 × 2 × 15 = 21
Which number line represents all of the values of x for the equation x2 = 25?
Answer:
x = 5 and x = -5
Step-by-step explanation:
Given x^2 = 25, we take the square root of both sides. The two solutions are x = 5 and x = -5
The values for x in the equation x2 = 25 are 5 and -5. These solutions are represented on a number line at points 5 and -5.
Explanation:The equation x2 = 25 can be solved by taking the square root of both sides of the equation. When we take the square root of a number, we get two possibilities: a positive and a negative value, since squaring a number always results in a positive number. Therefore, the values for x in the given equation would be x = 5 and x = -5.
On a number line, these points would be represented at the 5 and -5 positions. Therefore the number line that represents all the values of x for the equation x2 = 25 is the one that includes both -5 and 5. Keep in mind that no other numbers would satisfy the equation x2 = 25.
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