A system of equations to represent the situation with Sparkles the Clown is: 2p + 2g = 12 for Jenny's party and 4p + 5g = 27 for Roger's party. We can use substitution or elimination methods to solve for 'p' and 'g' to determine the number of balloons needed for each animal.
Explanation:To write a system of equations based on the given situation with Sparkles the Clown, we will let 'p' represent the number of balloons needed for a poodle and 'g' represent the number of balloons needed for a giraffe. From Jenny's party, we know that 2 poodles plus 2 giraffes used a total of 12 balloons. From Roger’s party, we learn that 4 poodles plus 5 giraffes used a total of 27 balloons. Therefore, our system of equations to represent this situation is:
2p + 2g = 12 (Jenny's party)4p + 5g = 27 (Roger's party)To solve this system of equations, we could use methods such as substitution or elimination to find the values of 'p' and 'g' which would tell us how many balloons are required for each balloon animal.
Final answer:
To find out how many balloons are required for each balloon animal, we set up a system of equations with p representing the number of balloons for a poodle, and g for a giraffe. The system is based on the balloon usage at two parties, resulting in the equations 2p + 2g = 12 and 4p + 5g = 27.
Explanation:
To solve the problem of how many balloons Sparkles the Clown needs for each type of balloon animal, we need to set up a system of linear equations based on the given information. We will let p represent the number of balloons needed for a poodle, and g represent the number for a giraffe.
From Jenny's party, we have the first equation:
2p + 2g = 12
From Roger's party, we have the second equation:
4p + 5g = 27
Now, we have established our system of equations:
1) 2p + 2g = 12
2) 4p + 5g = 27
Solving this system will give us the number of balloons needed to make each type of balloon animal.
Given the figure below find the values of x and z.
1a.) Write an expression that represents the area of a circle with a radius of 7 units? (1 point)
b. Using your expression, solve for the area of a circle with a radius of 7 units. (1 point) PLEASE HELP PLEASE WILL MARK BRAINLIEST AND GIVE POINTS
Final answer:
To find the area of a circle with a radius of 7 units, use the formula A = πr². Substitute 7 for r to get A = π(7²), which calculates to approximately 153.93804 square units. We round it to 150 square units, to match the significant figures of the radius.
Explanation:
The expression representing the area of a circle with a radius of 7 units is A = πr², where 'A' is the area and 'r' is the radius of the circle. To solve for the area with a radius of 7 units:
Substitute the radius (7 units) into the expression: A = π(7²).
Square the radius: 7² = 49.
Multiply by π (approximately 3.14159): A = π(49) or A ≈ 3.14159 × 49.
Calculate the area, which gives approximately 153.93804 square units.
Since the radius is given in two significant figures, you should express the area in two significant figures: A ≈ 150 square units.
Irwin purchased a $195,000 home with a 30-year mortgage at
5.55%. If makes a $1500 monthly mortgage payment, how
many months early will he pay off his mortgage?
A. 224 months
B. 127 months
C. 136 months
D. 160 months
What is the answer for the question
Answer:
200.52 m²
Step-by-step explanation:
A = 12² + π·6²/2
= 144 + 36π/2
= 144 + 18×3.14
= 144 + 56.52
= 200.52 m²
What is the answer plz help-thank you
Answer:
14.1cm (3s.f.)
Step-by-step explanation:
Please see attached picture for full solution.
sine angle= opp/hyp
cosine angle= adj/hyp
What is 78 1/3 as a fraction
Answer:235/3
Step-by-step explanation:
Two hundred and thirty five over three as an imperfections fraction
Answer:
235/3
Step-by-step explanation:
78 * 3 from denominator which equals 234 + 1 from the numerator.
Question 4:
Gregory is x years old. Daisy is 2 years older than Gregory. The sum of their ages is 40.
(a) Form an equation in terms of x.
(b) Solve the equation and work out Gregory's and Daisy's ages.
gregory is 19 years old and daisy is 21 because 21 is two more that 19 but 19 +21=40
The correct answer is:
Gregory is 19 years old and daisy is 21
Applying linear equation
Let,
Age of Gregory = x years
Age of Daisy = (x+2) years
An equation in term of x
x + (x+2) = 40
2x + 2 = 40
2x = 40 - 2
x = [tex]\frac{38}{2}[/tex]
x = 19
∵ 19+21=40
⇒ Gregory is 19 years old
⇒ daisy is 21 years old
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(ab + 3)(ab - 3)
2262 +9
o alb2-6ab-9
o 2²2²-9
Answer:
a^2b^2 - 3ab + 3ab - 9
a^2b^2 - 9
Step-by-step explanation:
Which nation has a command economy?
O Cuba
O Norway
South Korea
o the United States
Answer:
Cuba
Step-by-step explanation:
Paulina gets on an elevator. At the first stop, 4 people get off and 3 get on. At the second stop, 5 people get off and one gets on. At the the third stop, Paulina gets off. If 4 people are still on the elevator when Paulina gets off, how many people were on the elevator when she got on?
Answer:
look down + pls give me brainiest
Step-by-step explanation:
Let x = number of people when she got on.
x -4+3 -5+1 -1 = 4
x -6 = 4
Solve for x to get x=10.
So there were 10 people when Paulina got on (including herself).
Suppose point P(4, -9) is translated according to the rule (x,y)→(x+3,y-2). What are the coordinates of P'? Explain.
The coordinates of P' is [tex](7,-11)[/tex]
Explanation:
The coordinates of Point P is [tex](4,-9)[/tex]
It is given that the point P is translated according to the rule,
[tex]$(x, y) \implies(x+3, y-2)$[/tex]
Now, substituting, the values for x and y, we get,
[tex](4,-9)\implies(4+3,-9-2)[/tex]
Adding the values, we get,
[tex](7,-11)[/tex]
Thus, the coordinates of P' is [tex](7,-11)[/tex]
4x-y=1 slope intercept form
Answer:
y=4x-1
Step-by-step explanation:
4x-y=1
4x=y+1 then negative Y becomes positive after going to the other side of the equal sign.
4x-1=y the positive 1 becomes negative after going to the other side of the equal sign.
Answer:
y = 4x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c
Given
4x - y = 1 ( subtract 4x from both sides )
- y = - 4x + 1 ( multiply through by - 1 )
y = 4x - 1 ← in slope- intercept form
Solve by elimination -2x+2y=6 and 4x×2y=-5
Answer:
x=-11/6, y=7/6. (-11/6, 7/6).
Step-by-step explanation:
-2x+2y=6
4x+2y=-5
-----------------
2(-2x+2y)=2(6)
4x+2y=-5
----------------------
-4x+4y=12
4x+2y=-5
----------------
6y=7
y=7/6
4x+2(7/6)=-5
4x+14/6=-5
4x=-5-14/6
4x=-30/6-14/6
4x=-44/6
x=(-44/6)/4
x=(-44/6)(1/4)
x=-44/24
simplify
x=-11/6
D={[x, f(x)]: (-1,3), (0, 2), (1, 3), (2, 6), (3, 11)]
Write the rule for f(x).
Answer:
f(x) = x² +2
Step-by-step explanation:
x-values are evenly spaced, and y-values decrease to a minimum of 2, then increase again. First differences are -1, 1, 3, 5, and second differences are constant at 2. This means that a 2nd degree polynomial can be used for the rule.
The minimum of f(x) occurs at x=0, so there is no horizontal shift of the vertex of the quadratic function. f(1) -f(0) = 1, so the vertical scale factor for the quadratic is 1.
The quadratic with a vertex of (0, 2) and a vertical scale factor of 1 is ...
f(x) = 1·(x -0)² +2
f(x) = x² +2 . . . . . . simplified
_____
Comment on differences
"First differences" are the differences between successive "y" values when the "x" values are evenly spaced. Here, they are 2-3 = -1, 3-2 = 1, 6-3 = 3, 11-6 = 5. These are not constant, so the function is not a linear function.
"Second differences" are the differences between successive first differences. Here, they are 1-(-1) = 2, 3-1 = 2, 5-3 = 2. These are constant, so the function is a quadratic (2nd-degree). When n-th differences are constant, the sequence can be modeled by a polynomial of degree n.
__
Comment on determining the rule
Once you know the rule is 2nd-degree, there are a number of ways you can find out what it is. One way is to write it as ...
f(x) = ax^2 + bx + c
and fill in three different values for x and f(x). This will give you three linear equations in a, b, and c, which can be solved by any of the usual means for solving systems of linear equations.
Fortunately, this set of data includes the vertex of the function, making it easy to start with the vertex form:
f(x) = a(x -h)^2 +k
where (h, k) is the vertex (minimum, in this case), and "a" is the vertical scale factor. The value of "a" is easily determined as being the difference between f(h+1) and f(h). Here, h=0, so that is f(1) -f(0) = 3-2 = 1.
Answer:
x² +2
Step-by-step explanation:
Which set of integers is NOT a Pythagorean triple and are NOT the side lengths of a right triangle?
A.) 12 ,16 ,20
B.)10 ,24 ,26
C.)14, 48, 50
D.)27, 32, 45
The set of integers 27, 32, 45 is NOT a Pythagorean triple and are NOT the side lengths of a right triangle ⇒ D
Step-by-step explanation:
The Pythagorean triple is:
The sum of the squares of the least two numbers is equal to the square of the greatest numbera, b and c are three integers where c is the greatest one,then if a² + b² = c², then a, b and c are Pythagorean triplePythagorean triple can form side lengths of a right triangleA. 12, 16, 20
∵ 20 is the greatest number
∵ (12)² + (16)² = 144 + 256 = 400
∵ (20)² = 400
∴ (20)² = (12)² + (16)²
∴ The set of integers 12, 16, 20 is a Pythagorean triple
∴ 12, 16, 20 are the side lengths of a right triangle
B. 10, 24, 26
∵ 26 is the greatest number
∵ (10)² + (24)² = 100 + 576 = 676
∵ (26)² = 676
∴ (26)² = (10)² + (24)²
∴ The set of integers 10, 24, 26 is a Pythagorean triple
∴ 10, 24, 26 are the side lengths of a right triangle
C. 14, 48, 50
∵ 50 is the greatest number
∵ (14)² + (48)² = 196 + 2304 = 2500
∵ (50)² = 2500
∴ (50)² = (14)² + (48)²
∴ The set of integers 14, 48, 50 is a Pythagorean triple
∴ 14, 48, 50 are the side lengths of a right triangle
D. 27, 32, 45
∵ 45 is the greatest number
∵ (27)² + (32)² = 729 + 1024 = 1753
∵ (45)² = 2025
∴ (45)² ≠ (27)² + (32)²
∴ The set of integers 27, 32, 45 is NOT a Pythagorean triple
∴ 27, 32, 45 are NOT the side lengths of a right triangle
The set of integers 27, 32, 45 is NOT a Pythagorean triple and are NOT the side lengths of a right triangle
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If 5(3-2y)+4y=8 what is y
Answer:
7/6 (= 1 1/6)
Step-by-step explanation:
5(3-2y)+4y=8 (by PEDMAS, expand distribute parenthesis first)
3(5) -2y(5) + 4y = 8
15 - 10y + 4y = 8
15 - 6y = 8 (subtract 15 from both sides)
-6y = 8 - 15
-6y = -7 (divide both sides by -6)
y = -7 / -6 = 7/6 = 1 1/6
Answer:
y = 10.5
Step-by-step explanation:
5 x (3 - 2y) + 4y = 8
5 x (3 + -2y) + 4y = 8
15 + -10y + 4y = 8
15 + -6y = 8
(15/6) (-6y/+6)
2.5 Y
-Y + 2.5 = 8
10.5 - 2.5 = 8
Simplify 24-4.57+(-4.62
Final answer:
To simplify the expression 24 - 4.57 + (-4.62), add the negative numbers together and then subtract the sum from the positive number, resulting in a simplified answer of 14.81.
Explanation:
The question involves simplifying an expression, which is a basic arithmetic operation in mathematics. We are given the expression 24 - 4.57 + (-4.62). To simplify, we need to combine like terms and perform the addition and subtraction.
First, let's combine the positive and negative numbers separately:
Positive number: 24
Negative numbers: -4.57 and -4.62
We add the negative numbers together: -4.57 + (-4.62) = -9.19
Now, we subtract this sum from the positive number:
24 - 9.19 = 14.81
Therefore, the simplified result of the expression 24 - 4.57 + (-4.62) is 14.81.
number 24 please help
Answer:
is 24 a b c and d?
Step-by-step explanation:
Which of the following is equivalent to (7x + 3y)(8x + 5y)?
To find the product of (7x + 3y)(8x + 5y), you can use the distributive property of multiplication. The equivalent expression is 56x^2 + 59xy + 15y^2.
Explanation:To find the product of (7x + 3y)(8x + 5y), you can use the distributive property of multiplication over addition.
This means that each term in the first expression is multiplied by each term in the second expression.
Here are the steps:
Apply the distributive property to multiply 7x by each term in the second expression: 7x * 8x + 7x * 5y
Apply the distributive property to multiply 3y by each term in the second expression: 3y * 8x + 3y * 5y
Simplify each term: 56x^2 + 35xy + 24xy + 15y^2
Combine like terms: 56x^2 + 59xy + 15y^2
Therefore, the expression (7x + 3y)(8x + 5y) is equivalent to 56x^2 + 59xy + 15y^2.
Which expression has a positive quotient? Negative three-fourths divided by Negative two-thirds Negative StartFraction 1 over 8 EndFraction divided by 3 and one-fifth 2 and StartFraction 2 over 7 EndFraction divided by negative one-fifth Negative 6 divided by Five-thirds
Answer:
The correct answer is 1 and 1/2
Trust Me
Answer:
The correct option is A
Step-by-step explanation:
quiz
It cost $6 to join an online DVD club and $2.50 to rent a DVD. Write an equation for the relationship that gives the total cost y in dollars for renting x DVD. Then complete the table.
DVD rented 3, 4, 5.
Answer:
store A
Step-by-step explanation:
Find the reciprocal of -1 1/12
Answer:
-12/13
Step-by-step explanation:
When solving the equation 2y2 – 16y = 6 by completing the square, what is your first step?
Question 6 options:
Divide –16 by 2 and square the result.
Divide each side of the equation by 2.
Take the square root of 6.
Subtract 6 from each side of the equation.
Answer:
Divide each side of the equation by 2.
Step-by-step explanation:
(I took the test so i know its right) Basically, when doing the this by completing the square we need y^2 by itself, so we divide 2y^2-16y=6 by two first.
Answer:
Divide each side of the equation by 2.
Step-by-step explanation:
2y² – 16y = 6
Divide both sides by 2
y² - 8y = 3
3/8s of the students in Ms Mull’s class ride the bus. If there are 24 students in the class how many students ride the bus?
Answer:
9 students ride the bus.
Step-by-step explanation:
First you take the amount of students which is 24 and divide the denominator which is 8. then you would get 3, meaning 1/8 = 3 students. Now you would multiply the 3 students making one 8 by three ( because there are 3/8 students taking the bus, and you would get 9 students.
Final answer:
To find how many students ride the bus in Ms Mull's class, multiply the fraction of bus riders (3/8) by the total number of students (24), resulting in 9 students who ride the bus.
Explanation:
The question asks to determine how many students in Ms Mull’s class ride the bus, given that 3/8 of the students use the bus and there are 24 students in total. To find the number of students who ride the bus, multiply the total number of students by the fraction that represents the bus riders.
Identify the total number of students: 24.
Calculate 3/8 of 24:
(3/8) × 24.
Multiply: 3 × 3 = 9 (since 24/8 = 3).
Conclude that 9 students in Ms Mull’s class ride the bus.
What is the answer to 2(x+2)+2(x+4)=28 ?
Answer:
x=4
Step-by-step explanation:
2(x+2)+2(x+4)=28
Simplify the equation
2x+4+2x+8=28
4x+12=28
4x=16
x=4
Write f(x)=8x^2-4x+11 in vertex form
Answer:
[tex]f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}[/tex]
or
[tex]f(x)=8(x-0.25)^{2}+10.5[/tex]
Step-by-step explanation:
we have
[tex]f(x)=8x^{2}-4x+11[/tex]
This is a vertical parabola open upward (because the leading coefficient is positive)
The vertex is a minimum
Convert to vertex form
Factor the leading coefficient
[tex]f(x)=8(x^{2}-\frac{1}{2}x)+11[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+11-\frac{1}{2}[/tex]
[tex]f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+\frac{21}{2}[/tex]
Rewrite as perfect squares
[tex]f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}[/tex] ----> equation in vertex form
or
[tex]f(x)=8(x-0.25)^{2}+10.5[/tex]
The vertex is the point (0.25,10.5)
Simplify the radical 80
15. The volume of a refrigerator is x3-3x2-16x-12. Its height is x + 2. What
are the other two dimensions?
A. x + 6 and x - 1
B. x-3 and x + 2
C. x-2 and x + 3
D. x-6 and x + 1
Final answer:
The volume of the refrigerator is factored by dividing with the given height, resulting in a quadratic polynomial that provides the other two dimensions. Upon factoring, we discover that the other dimensions are x - 6 and x + 1, corresponding to option D.
Explanation:
The volume of the refrigerator is given by the polynomial [tex]x^3 - 3x^2 - 16x - 12[/tex]. To find the other two dimensions of the refrigerator, we need to factor this polynomial using the given height of the refrigerator, which is x + 2. The goal is to divide the volume polynomial by the height polynomial to get the product of the remaining two dimensions.
We proceed with polynomial division or factoring:
Divide the volume polynomial by x + 2 using synthetic division or long division.
The result should be a quadratic polynomial that further factors into the product of two linear factors corresponding to the unknown dimensions.
Factor the quadratic polynomial to find the two missing dimensions.
In this case, the volume polynomial [tex]x^3 - 3x^2 - 16x - 12[/tex] can be divided by x + 2 to yield [tex]x^2 - 5x - 6[/tex], which can then be factored into (x - 6)(x + 1). Hence, the other two dimensions are x - 6 and x + 1, making option D correct.
Which of the following numbers are greater than -0.33?
Choose all that apply:
A.-0.3
B. -3/9
C. 1/6
Answer:
A: -0.3 and C: 1/6
Step-by-step explanation:
Step 1. Since 1/6 is positive it is greater than all negative numbers including -0.33
Step 2. -0.33 and -0.3 have the same numbers they are both negative but in -0.33 there are more hundred.
-0.3 >- 0.33
Step 3. -3/9= 0.33333..... -0.33 and -3/9 have the same number of units, tenths and hundredths and both are negative but, -3/9 has more thousandths, so it's farther below 0.
-3/9 < -0.33
Final Step 4. -0.3 and 1/6 are greater than-0.33
The correct options are A.-0.3 and C. 1/6
What is a number line in mathematics?In mathematics, an interval can be defined as a set of real numbers that contains all real numbers lying within any two specific numbers of the set R.
Given here: -0.33 which is equivalent to -1/3
The numbers greater than -1/3 lie in the interval (-1/3, ∞)
Clearly out of the given options only -0.3 and 1/6 lie in this interval.
Hence, The correct options are A.-0.3 and C. 1/6
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Please answer !!!!!!!!!
Answer:
answer is b
Step-by-step explanation:
look at the picture
Yo sup??
slope=y2-y1/x2-x1
just take any value of x1 x2 y1 and y2
let x1,y1=2,1
and
x2,y2=4,-2
plugging in the values
slope=-2-1/4-2
=-3/2
therefore your answer is option 2
Hope this helps