Answer:
it
should be something along the lines of math
a pizza shop delivered 8 pepperoni pizzas to a college on the first night of final exams. the total cost of the pizzas was $56. a small pizza costs $3 and contains 4 ounces of pepperoni. a medium pizza costs $5 and contains 9 ounces of pepperoni. a large pizza cost $11 and contains 12 ounces of pepperoni. the owner of the pizza shop used 4 pounds 12 ounces of pepperoni in making the pizzas. how many pizzas of each size were delivered to the college?
From the word problem given, the number of pizzas each that were delivered are:
1 small7 medium; and2 large.Step I
Let a = number of small pizzas delivered
Let b = number of medium pizzas delivered
Let c = number of large pizzas delivered
Step 2 - Creating relevant expressions based on number and type ordered, we have:
a + b + c = 8.............................1
3a + 5b + 11c = 56..................2
4a + 9b + 12C = 4 * 8 + 12.....3a
We can rewrite (3) as
4a + 9b + 12C = 44 ....3b
Step 3
Multiply both sides of (1) by 4
We have
4a +4b +4c = 32
If we remove (1) from (3) we have-
4a +4b +4c = 32
5b +8C = 12......................(4)
Multiply both sides of (1) by 3 and subtract from (2), and we have:
3a + 3b + 3c = 24, removing this from (2) we have
3a + 5b + 11c = 56
-
3a + 3b + 3c = 24
2b + 8c = 32.....................(5)
Step 4 - Subtract (4) from (5)
2b + 8c = 32
-
5b + 8c = 12
-3b = 20
b = - 20/3
= - 6.67
Since we cannot have negative values, we work with absolute value to get:
b [tex]\approx[/tex] 7
Since b = 7
2(7) + 8c = 32
8c = 32 - 14
c = 18/8
c [tex]\approx[/tex] 2
Plug in that back into a we have
a + b + c = 8
a + 7 + 2 = 8
a = 8-9
a = -1 (recall we must have absolute values)
a therefore = 1.
Hence the number of pizzas that were ordered are:
1 small
7 medium; and
2 large.
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16. If a = 5, b = 4, and c = 7, find the value for 3(b + a) - c.
O 20
O 15
O 34
O 10
A stack of recyclable newspaper 36 inches high will save one tree. The number of trees saved by recycling is directly proportional to the height of a stack of recyclable newspapers. How many trees would be saved from a stack of newspapers 24 feet high?
The number of trees that would be saved from a stack of newspapers 24 feet high given the by ratio of trees saved from a stack of recyclable newspaper is 8 trees
How many trees would be saved from a stack of newspapers 24 feet high?Stack of recyclable newspaper that will save one tree = 36 inches highConvert feet to inches
1 feet = 12 inches24 feet = 288 inchesNumber of trees that would be saved from a stack of newspapers that is 24 feet high = xEquate the ratio of Stack of recyclable newspaper needed to save a tree to number of treesQuantity of recyclable newspaper needed : number of trees
36 : 1 = 288 : x
36/1 = 288/x
cross product36 × x = 1 × 288
36x = 288
divide both sides by 36x = 288 / 36
x = 8 trees
In conclusion, the trees that would be saved from a stack of newspapers 24 feet high is 8 trees
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Find the sum of the AP: 2,7,12 to 10 terms.
Answer:
Clearly, the given sequence is an AP with first term a=2, common difference d=5 and n=10.
Now,
s10 = 10/2 (2a + 10-1d)
=5(2x2+9x5)
=245
Step-by-step explanation:
Answer:
S₁₀ = 245
Step-by-step explanation:
the sum to n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = 2 and d = a₂ - a₁ = 7 - 2 = 5 , then
S₁₀ = [tex]\frac{10}{2}[/tex] [ (2 × 2) + (9 × 5) ]
= 5(4 + 45)
= 5 × 49
= 245
Find the values of p and q if x-1 is a common factor of f(x)=x⁴-px³ +7qx+1, and g(x)=x²-4x² + px² +qx-3,
The values of p and q if x-1 is a common factor of f(x)=x⁴-px³ +7qx+1, and g(x)=x²-4x² + px² +qx-3,are 13/2 and -1/2 respectively.
What is a factor?In Mathematics, factors are positive integers that can divide a number evenly. Suppose we multiply two numbers to get product. The number that is multiplied are the factors of the product. Each number is factor of itself. Factors have many real-life examples, such as arranging sweets in box, arranging numbers in pattern, distributing chocolates among children, etc. To find the factors of number, we need to use the multiplication or division method.
Factors are numbers that can divide a number exactly. Hence, after the division, there is no remainder left. Factors are numbers you multiply together to get the another number. Thus, factor is the divisor of another number.
f(x)=[tex]x^{4}-px^{3}+7qx+1[/tex]
= 1-p+7q+1
= p-7q=2---------1
g(x)= [tex]-3x^{2} +px^{2} +qx-3[/tex]
= -3+p+q-3
=p+q= 6----------2
p-7q=2
p+q=6
-----------------
By subtracting 2 from 1
-8q=4
q=-1/2
putting value of q in equation 2 we get,
p+(-1/2)=6
p=6+[tex]\frac{1}{2}[/tex]
p=13/2
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Determina el valor de un número negativo tal que la suma de
ese número y su cuadrado es 42.
The value of a negative number such that the sum of that number and its square is 42 is -7.
What are negative numbers?A negative number is one that always has a value lower than zero and is denoted by the minus (-) symbol. On a number line, negative numbers are displayed to the left of zero. Negative numbers include -6 and -15 as examples.Let the negative number be -x.
According to the question, the sum of the negative number and its square is 42.
So, we form an equation
- x + (-x)² = 42
x² - x - 42 = 0
Solving the quadratic equation,
x² - 7x + 6x - 42 = 0
x(x - 7) + 6(x - 7) = 0
(x - 7)(x + 6) = 0
x = -6 and x = 7
We have taken the number -x to be negative.
So, -x = -6 and -x = 7
x = 6 and x = -7
Hence, the value of the negative number is -7.
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The correct question is: "Determine the value of a negative number such that the sum of that number and its square is 42."
Which numbers are in order form least to greatest?
Answer:
B
Step-by-step explanation:
Please help me! I will give 50 points! I have a test tomorrow and don't understand how to do this! Please explain step by step
1) [tex]\angle A \cong \angle D, \angle C \cong \angle E, \overline{AB} \cong \overline{DF}[/tex] (given)
2) [tex]\triangle ABC \cong \triangle DFE[/tex] (AAS)
3) [tex]\angle ACB \cong \angle DEF[/tex] (CPCTC)
Given that f(x)=x2-7 and g(x) = 2x + 9, find (g-f)(-2), if it exists.
By solving using given linear equation f(x)=x2-7 and g(x) = 2x + 9 we get the desired value as ( g - f )(-2) = 32 .
What is linear equation?An equation is deemed to be linear when the maximum power of the variable is consistently 1. It is also known as a one-degree equation. A linear equation with one variable usually has the form Ax + B = 0. In this scenario, the variables x and A are variables, whereas B is a constant.
What are Linear Equations in two Variables?A linear equation in two variables is of the form Ax + By + C = 0, in which A and B are the coefficients, C is a constant term, and x and y are the two variables, each with a degree of 1.
For example, 7x + 9y + 4 = 0 is a linear equation in two variables. If we consider two such linear equations, they are called simultaneous linear equations.
Simplification:
f(x) = x2 - 7
g(x) = 2x + 9
( g - f )(-2) = (2x-7-2x -9)(-2)
= -16 * -2
= 32 .
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Write an algebraic expression to represent each statement.
the number, b, divided by thirty-six
Write an algebraic expression to represent each statement.
the number, b, divided by thirty-six
b/36
Determine whether the graph represents a function.
Help me I’m so confused I don’t understand how to do this problem…
a) The problem is in the second step, the square root can't be distributed under sum.
b) 10*√41
How to simplify the numeric expression?a) The incorrect step is the second one, the square root can't be distributed like that.
Here we have the numeric expression:
5*√164
And we want to simplify it.
We can write:
5 = √25
Then:
5*√164 = √25*√164 = √(164*25) = √4,010
Now we can decompose this as a product of square numbers:
4,010 = 4*1,025 = 4*25*41
Then we rewrite:
√4,010 = √4*√25*√41 = 2*5*√41 = 10*√41
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Simplify
(x + 3)
(x + 3)
Answer:
1. X+3x8=24
2.X+3x5=15
Step-by-step explanation:
Hello! So...
We are given the following to simplify:
[tex]\frac{(x+3)^8}{(x+3)^5}[/tex]
_______________________________
1. Apply the exponent rule ([tex]a^b^+^c=a^b * a^c[/tex]).
[tex](x+3)^8=(x+3)^5(x+3)^3[/tex]
=[tex]\frac{(x+3)^5(x+3)^3}{(x+3)^5}[/tex]
________________
2. Cancel out the common factor, given us our solution: [tex](x+3)^5[/tex].
________________________________________________________
Hope this helps! If so, please lmk! Thanks and good luck!
this dude has a farm and 1/8 were pigs, 2/3 were horses, and the rest were chickens. there are 10 chickens, how many animals are on the farm?
The number of animals that are on the farm is 48.
How many animals are on the farm?A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 2/3.
The first step is to determine the fraction of the animals that are chickens.
Fraction that are chickens = 1 - fraction that are pigs and horses.
[tex]\frac{1}{8} + \frac{2}{3}[/tex]
[tex]\frac{3 + 16}{24}[/tex] = [tex]\frac{19}{24}[/tex]
Fraction that are chickens = 1 - 19/24 = 5/24
The next step is to divide the number of chickens by the fraction of the chickens.
Number of animals = number of chickens ÷ fraction of chickens
10 ÷ 5/24
10 x 24/ 5 = 48
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What is the sum of the 8th square
number and the 5th cube number?
8 square = 64
5 cube = 125
Step-by-step explanation:
=8² + 5³
=64 + 125
=189
What are square and cube ?
The square of a number is the multiplication by itself. That means, for any integer, we can obtain the square by multiplying the integer itself. For example, the square of an integer 4 will be: 4 × 4 = 16, i.e., the square of 4 is equal to 16.
The cube of a number is the multiplication by itself thrice. That means, for any integer, we can obtain the cube by multiplying the integer by its square. For example, the cube of an integer 5 will be: 52 × 5 or 5 × 5 × 5, i.e., the cube of 5 is equal to 125.
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what is the line that passes through the point -1, four and is parallel to the line 2
X plus Y equals one
The line that passes through the point -1, four and is parallel to the line 2 X plus Y equals one is y + 2x = 2.
What is a slope?Slope is measure of steepness of a line.
The Equation of line is y = mx + c
where,
m is slope
c is y intercept
To find equation of the parallel line we must first find the slope of the original line
The original line is 2x + y = 1
We must first write equation in the general form above
That's
y = - 2x + 1
Comparing with general equation above
Slope = - 2
Since lines are parallel their slope are also same
Slope of parallel line = - 2
So the equation of line using point
( - 1 , 4) and the slope - 2 is
y-4= -2(x+1)
y-4= 2x-2
y+2x= -2+4
We have final answer as
y + 2x = 2
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Use the figure below to answer questions #1-3.
What is the special angle pair relationship between 1 and 23?
m
2/7
3/6
4/5
at
1/8
The special angle pair relationship between the given angles are:
1. Corresponding angles
2. Alternate exterior angles
3. Consecutive
What are Some Special Angle Pair Relationship?The following are some special angle pair relationships:
Corresponding Angles: These are pairs of angles that lie on relative position to each other on the two parallel lines that are intercepted by a transversal. They are congruent to each other.Alternate Exterior Angles: These are exterior angles that are on each parallel lines that are crossed by a transversal and lie alternate to each other. They are congruent to each other also.Consecutive Interior Angles: These are angles on the same side of a transversal but lie each on the parallel lines that the transversal cuts across. They are supplementary.1. Angles 1 and 3 form a special angle pair relationship known as: corresponding angles.
2. Angles 8 and 4 form a special angle pair relationship known as: alternate exterior angles.
3. Angles 2 and 3 both lie on the same side of the given transversal, therefore, the special angle pair relationship between angle 2 and angle 3 is: consecutive interior angles.
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Multiplicative inverses or ______, is a number that when multiplied by the ___________ gives the product as 1.
Answer: Multiplicative inverses or reciprocal, is a number that when multiplied by the given number gives the product as 1.
Step-by-step explanation:
HELPPP PLLZZZZ
54 ÷ 9 = 6, therefore 54 ÷ 0.9 = 0.6.
True
False
Answer:
False.
Step-by-step explanation:
That answer would be true if, it was 54 ÷ 9 = 6
54 ÷ 0.9 = 60.
Hope this helps!
Answer:
False
Step-by-step explanation:
hope it helps and have a nice day! :)
Kyle played four rounds of golf. His scores were
72, 75, 68, and 84. If he would like an exact mean
of 74 for five rounds, what must he score on the
next round?
71
72
73
74
Answer:
71
Step-by-step explanation:
Mean is Average
You can Find the Mean of a set of numbers by adding them all up and then dividing that number by the amount of numbers in the set.
72 + 75 + 68 + 84 = 231
231 / 4 = 57.75
This is his current mean.
Let's add his next score.
72 + 75 + 68 + 84 + 71 = 370
Divide by 5 instead of 4 because we added another number to the data set.
370 / 5 = 74
the hypotenuse of a right triangle measures 16 cm and one of its legs measures 5 cm. Find the measure of the other leg.
Step-by-step explanation:
Use the Pythagorean Theorem.
a^2+b^2=c^2
a^2 + 5^2 = 16^2
a^2 + 25 = 256
a^2 = 231
a = square root of 231
a= 15.20
Answer:15.20
Step-by-step explanation:
you have three purple chips and two green chips in a bag. you draw one chip, and then without replacing it, you draw another chip. (a) what is the probability that the second chip drawn is green?
Answer: 8
Step-by-step explanation:
5-1
3 out of 4 = 1/4
Name three different angles in the diagram.
<HMN, <HMK, <KMN
using the graph
s=1/2pl+b solve for l
[tex]s=(\frac{1}{2} p)(l)[/tex]
Flip equation:
[tex]\frac{1}{2} lp=s[/tex]
Divide both sides by p/2:
[tex]\frac{1/2lp}{p/2} =\frac{s}{p/2}[/tex]
[tex]l=\frac{2s}{p}[/tex]
PLEASE HELP
1. Check whether the following is closure under multiplication : 7×12 = 72
2. The sum of two integers is -38,one of them is -22.Find the other.
3. In a competitive exam, Gopi gets 4 marks for each correct answer and -2 for each wrong answer. If he gives 32 correct answers and 8 wrong answers, what will be his total score?
7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.
1)
Closure property of multiplication:
It states that if two real numbers a and b are multiplied, then the product will be a real number as well.
We have 7 × 12 = 72
7, 12 and 72 all are real numbers.
So, it is a closure property under multiplication.
2)
Sum = - 38
a = - 22
We need to find b
a + b = - 38
- 22 + b = - 38
b = - 38 + 22
b = - 16
3)
1 correct answer = 4 marks
1 incorrect answer = - 2 marks
Number of correct answers = 32
Number of incorrect answers = 8
Total score = 32 × 4 + (- 2) × 8
= 128 - 16
= 112 marks.
Therefore, we get that, 7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.
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estimate using a rate per 100 24% of 289
The estimate of 24% of 289 is 69.36
Estimating percentagesFrom the question, we are to determine the estimate the given rate
The given rate is
24% of 289
This can be expressed as
24% × 289
Now, we will evaluate the percentage
To evaluate the percentage, we will divide the number by 100.
That is,
24% = 24/100
Thus,
The expression can further be expressed as
24/100 × 289
= 0.24 × 289
= 69.36
Hence, the estimate is 69.36
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a family decides to have children until it has three chil- dren of the same gender. assuming p(b) 5 p(g) 5 .5, what is the pmf of x 5 the number of children in the family?
one is the pmf or probability mass function of X = number of children in the family
The Probability Mass Function (PMF) is also called a probability function or frequency function which characterizes the distribution of a discrete random variable.
X takes values: { 3, 4, 5 }
where: P ( X = 3 ) + P ( X = 4 ) + P ( X = 5 ) = 1
For X = 3 we have : BBB or GGG.
P ( X = 3 ) = ( 1/2 * 1/2 * 1/2 ) * 2 = 1/8 * 2 = 2 / 8 = 1/4
P ( X = 4 ) = ( 1/2 * 1/2 * 1/2 * 1/2 ) * 6 = 6 /16 = 3/8
P ( X = 5 ) = ( 1/2 * 1/2 * 1/2 * 1/2 * 1/2 ) * 12 = 12 / 32 = 3/8
1 / 4 + 3 / 8 + 3 / 8 = 8 / 8 = 1
the complete question is
A family decides to have children until it has three kids of the same gender. Assuming P(B) = P(G) = 0.5, what is the pmf of X = number of children in the family?
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A line has a slope of – 3 and includes the points (5, – 6) and (s, – 3). What is the value of s?
Answer:
[tex]{ \tt{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ \\ { \tt{ - 3 = \frac{ - 3 - ( - 6)}{s - 5} }} \\ \\ { \tt{ - 3(s - 5) = 3}} \\ \\ { \tt{s - 5 = - 1}} \\ \\ { \tt{s = 4}}[/tex]
7:8:9=__:12:__:
please help me
Answer:
10.5:12:13.5
Step-by-step explanation:
The only two values you know and can compare are 8 and 12, so you have to find the relationship between them. 12/8 = 1.5. To get the two unknown values, you multiply 1.5 by the ones you do know.
7 * 1.5 = 10.5
9 * 1.5 = 13.5
So, you get 10.5:12:13.5
If someone could help me with these questions would be nice!
( will mark brainliest if correct! )
1. The value of t in the triangle is 50°
2. The value of x in the triangle is 107°
How to illustrate the information?It should be noted that the total sum of the angles that are in a triangle is 180°.
Therefore, the calculation of the angles will be illustrated thus:
1. 2t + 12 + t + 18 = 180°
3t + 30 = 180°
Collect like terms
3t = 180° - 30°
3t = 150°
Divide through by 3
3t/3 = 150° / 3
t = 50°
2. x + 30° + 43° = 180°
x + 73° = 180°
Collect like terms
x = 180° - 73°
x = 107°
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