An apple pie requires 7 apples and an apple tart requires 4 apples
How to write a system of equations to describe a situation?To set up this problem, we can let p represent the number of apples needed for one pie and t represents the number of apples needed for one tart.
We can then set up the following system of equations to represent the information given in the problem:
2p + 6t = 38
2p + 8t = 46
To solve this system, we can subtract the first equation from the second to eliminate the p terms:
2p + 8t - 2p - 6t = 46 - 38
2t = 8
t = 4
Substituting this value back into the first equation, we get:
2p + 6(4) = 38
2p = 14
p = 7
Thus, an apple pie requires 7 apples and an apple tart requires 4 apples.
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In right triangle ABC, point D is on side BC, as shown. If BC= 5 x BD and the area of Triangle ABD is 8 in2, what is the area of Triangle ABC?
Answer: 40 in2
Step-by-step explanation:
Area of a triangle = 1/2 (base)(height)
Side AB is common to both triangles
BC = 5(BD)
Area ABD = 8, therefore Area ABC = 5(8) = 40
HELP PLEASE
Researchers are conducting clinical trials for a new medication to treat people suffering from asthma, a respiratory disease.
They selected 100 asthma patients from a national hospitals database in these age groups: under 15 years, 15 to 60 years,
and over 60 years. In each group, half the subjects received the new medication, and the other half received a placebo. The
subjects were not informed whether they received the medication or the placebo.
Which statements about this study are true?
Answer:
1. This study uses blocking to reduce variability from known factors.
2. This study uses random sampling.
Step-by-step explanation:
Hope it helps!
A tate government borrow $2,000,000 at imple annual interet. Some of the money i borrowed at 6%, ome at 7. 5%, and ome at 8. 5%. Ue a ytem of linear equation to determine how much (in dollar) i borrowed at each rate given that the total annual interet i $137,000 and the amount borrowed at 7. 5% i four time the amount borrowed at 8. 5%. Solve the ytem of linear equation uing matrice
By solving the linear matrices we got the values X = 1000000 , Y = 800000 , Z = 200000
What is an equation ?According to algebra, an equation is a statement that shows the equality of two mathematical expressions. For instance, the equation 4x + 5 = 15 consists of the two equations 4x + 5 and 15, which are separated by the 'equal' sign.
According to the given information
X + Y + Z = 2000000
0.07X + 0.085Y + 0.095Z = 157000
Y = 4Z
Y = 4Z is substituted into the first and second equations as follows:
X + 5Z = 2000000
0.07X + 0.085 (4Z) + 0.095Z = 157000
X = 2000000 - 5Z
0.07X + 0.435Z = 157000
0.07 (2000000 - 5Z) + 0.435Z = 157000
140000 - 0.35Z + 0.435Z = 157000
0.085Z + 140000 = 157000
0.085Z = 17000
Z = 200000
Y = 800000
X = 1000000
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A publisher used 10 boxes to send 375 books to a local book retailer. The
small boxes hold 30 books and each large box holds 55 books. Determine
the number of small and the number of large boxes used.
Answer: Number of small boxes = 7, Number of large boxes =3
Step-by-step explanation:
Let x= Number of small boxes , y = Number of large boxes.
As per given , 30x+55y=375 (i)
x+y=10 (ii)
Multiply (ii) by 30, we get
30x+30y=300 (iii)
Eliminate (iii) from (i), we get
25y=75
⇒ y= 3 [Divide both sides by 25]
Put y=3 in (ii), we get
x+3=10 ⇒ x=7
Hence, Number of small boxes = 7, Number of large boxes =3
Hope this helps!!! :)
15% of $28 =
20% of $74 =
18% of $128 =
The value of the given expression is 15% of $28 = (15×28)/100 = $4.2, 20% of $74 = (20×74)/100 = $14.8, 18% of $128 = (18×128)/100 = $23.04
What is an expression?
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
Here, we have
Given the following expression and we have to find the values of given expressions.
15% of $28 = (15×28)/100 = $4.2
20% of $74 = (20×74)/100 = $14.8
18% of $128 = (18×128)/100 = $23.04
Hence, the value of the given expression is 15% of $28 = (15×28)/100 = $4.2, 20% of $74 = (20×74)/100 = $14.8, 18% of $128 = (18×128)/100 = $23.04
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Input (a): a number
Output (y): 8 less than 3 times x
The output will be if Input (x) = a number is y = 3x - 8, so option D is correct.
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given:
Input (x) = a number,
Output (y) = 8 less than 3 times x.
Assume a number x which is an input,
3 times of x = 3x,
8 less than 3 times of x = 3x - 8
Therefore, the output will be if Input (x) = a number is y = 3x - 8.
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Answer:
Hope this help :)
Step-by-step explanation:
If x = 5, find the value of
a) x2
b) (x + 3)2
Answer:
25
64
Step-by-step explanation:
x^2
5^2
25
(X+3)^2
(5+3)^2
8^2
64
Hopes this helps please mark brainliest
Answer:
a) x = 25
b) 16
Step-by-step explanation:
a) x^2 = 5^2 = 25
b) (x + 3)2 = (5 + 3)2= (8)2 = 16
Sam wants to purchase birthday gifts for his two sisters that share the same birthday. One sister likes daisies which cost $2 per stem and the other likes tulips which cost $3 per stem. 1). If he has $12 to spend, how many of each could he buy?
You must write an inequality.
2). Graph your solution
The inequality which represents is 2x + 3y ≤ 12 where x is the number of daisies and y is the number of tulips.
What is inequality?A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
Suppose the cost of one daisy is x while the cost of one tulip is y.
2x + 3y will be totally spent and it can be almost $12.
2x + 3y ≤ 12
Hence "The inequality which represents is 2x + 3y ≤ 12 where x is the number of daisies and y is the number of tulips.".
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8.2 end of unit assessment Triangle ABC and DEF are similar
The Assessment Triangle and the Domains and Dimensions of the Assessment Framework.
How to Find the Perimeter of Similar Triangles?If two triangles are similar to each other, and the perimeter of one is A with a side length of a, and the perimeter of the other is B with a side length of b, then, the following below is the ratio of their perimeters are intended as a reminder to professionals undertaking the assessment and to be given to parents to help them understand the areas the worker will want to explore.The PAT was originally developed in 1996 by Dr s. Ronald Dickman, Dena Brownstein and Marianne Gausche-Hill as a novel tool to standardize the initial assessment of infants and children for all levels of health care providers.Background The Paediatric Assessment Triangle (PAT) has been proven to be effective in the general impression of the health status of the child and can interlink the potential underlying pathophysiology so to alert the clinician into how critically ill/ injured the child might bePerimeter of A/perimeter of B = a/b
Given that triangles ABC and DEF are similar triangles, we have the following:
Perimeter of triangle ABC = x
One side length of triangle ABC = 4 cm
Perimeter of triangle DEF = 12 + 6 + 9 = 27 cm
One side length of triangle DEF = 6 cm
Therefore:
x/27 = 4/6
Cross multiply
6x = (27)(4)
6x = 108
6x/6 = 108/6
x = 18
Thus, the perimeter of tr8angle DEF that is similar to triangle ABC is: 18 cm.
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Patrick walk 9/10 to the gym. How far ha he walked when he ha covered 2/3 of the ditance to the gym
In linear equation, The number of miles that he walked when he was covered and 2/3 of the distance to the gym will be 7/30 miles.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Patrick walks 9/10 miles to the gym.
Then the number of miles that he walked when he was covered 2/3 of the distance to the gym will be
⇒ 9 / 10 - 2 / 3
⇒ (27 - 20) / 30
⇒ 7 / 30
The number of miles that he walked when he was covered and 2/3 of the distance to the gym will be 7/30 miles.
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Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x) = 2x, where x is the length. Explain how he can convert this equation to a logarithmic function when strength is 8 Pascals.
x = ㏑₂8 in the logarithmic function.
What is a logarithmic function?A logarithmic function is the inverse of an exponential function.
Given function if f(x) = [tex]2^{x}[/tex],
When strength is equal to 8 pascals, f(x) = 8
Therefore, 8 = [tex]2^{x}[/tex]
Taking log on both sides:
ln8 = ln[tex]2^{x}[/tex]
ln8 = xln2
or x = ln8/ln2
x = ㏑₂8
Hence, the required function is x = ㏑₂8.
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When solving a system of linear equations by substitution, how do you decide which variable to solve for in step 1?.
When solving a system of linear equations by substitution, normally, we want to try to solve for the easiest one to get to or we choose a variable with unit coefficient.
What you mean by a variable?A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.
What a coefficient means?A constant component of a word as opposed to a variable. a measurement of some property or characteristic using a number (as of a substance, device, or process)
There are many factors, it is all a matter of preference, normally, we want to try to solve for the easiest one to get to
example;
if we have
(x-3)^2+y=9
we would solve for y because it is less tricky or we choose a variable with unit coefficient.
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Folgers coffee is priced at 12.88$ for 80 cups of coffee, and Seattle's best is priced at 9.00$ for 50 cups. Which brand of coffee is the better value for each cup
what is
2/4 + 2/4 - 4/7
Answer: 3/7
Step-by-step explanation:
1. We know that 2/4 + 2/4 is 1.
2. 1 can also be expressed as 7/7, because its easier to subtract 7/7 and 4/7 because they have the same denominator
3. 7/7-4/7=3/7
Answer:
3/7
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!!!!
Answer:
C
Step-by-step explanation:
x² + 6x - 7 = 0 ( add 7 to both sides )
x² + 6x = 7
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(3)x + 9 = 7 + 9
(x + 3)² = 16
list five requirements that a person should know about their pet before owning one
The five requirements that a person should know about their pet before owning one are shown below.
What is pet?An animal that you keep as a pet in your home is for your entertainment and company.
There are 5 requirements that a person should know about their pet before owning one.
Freedom from thirst and hunger All canines and felines have to have quick access to food and clean water.
Liberation from discomfort.
Freedom from discomfort, harm, or illness.
Having the ability to act normally.
Freedom from anxiety and pain.
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Last year at a certain high school, there were 60 boys on the honor roll and 100 girls on the honor roll. This year, the number of boys on the honor roll increased by 20% and the number of girls on the honor roll increased by 3%. By what percentage did the total number of students on the honor roll increase? round your answer to the nearest tenth (if necessary).
The percent increase in the total number of students on the honor roll is 9.4% .
In the question,
it is given that ,
last year , the number of boys in the honor roll is = 60 boys ,
the number of girls in the honor roll is = 100 girls ,
total number of students last year = 160
percent increase in the number of boys in the honor roll is = 20% ,
so , number of boys become = 60 + (0.20*60) = 72 boys ,
percent increase in the number of girls in the honor roll is = 3% ,
so , number of girls become = 100 + (0.03*100) = 103 girls ,
total number of students this year = 103 + 72 = 175 .
increase in number of students = 175 - 160 = 15
So , percent increase is = (15/160) × 100
= 0.09375 × 100
= 9.375 %
≈ 9.4%
Therefore , the percent increase is 9.4% .
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I'LL GIVE BRAINLIEST!! ANSWER THE QUESTION!!!
Part a
This represents a translation of 2 units to the right. So, the points are [tex](6, -3), (0,0), (8, -15)[/tex].
Part b
This represents a translation of 9 units up. So, the points are [tex](4,6), (-2,9), (-10,-6)[/tex].
Part c
This represents a translation of 3 units left and 1 unit down. So, the points are [tex](1, -4), (-5, -1), (-13, -16)[/tex].
−5 5 6 x1 1 2=? Type an integer, proper fraction, or mixed number.
Multiplying Rational Numbers Problem Solving
Answer:
-62272
Step-by-step explanation:
Multiplication on a piece of paper also a positive multiplied by a negative is negative so -556 * 112 = -66272.
simple q help pls due tomorrow
Answer:
(1/2x+3)(1/2x+3)
OR
[tex](1/2x+3)^{2}[/tex]
4d +7e =68
-4d-6e = -72
Answer:
d=24
Step-by-step explanation:
(2/5)x2x100 divided by 2/3 +(2x4 divide by (13-5)
Answer: The answer is 121
See screenshot below
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The roster form of the set P is; {-2, -1, 0, 1}
The builder notation of the set P is; {x : x ∈ I, −2 < x ≤ 1}
How to write set builder notations?We are told that P is the set of integers that are greater than -3 and less than or equal to 1.
Roster form of sets is done by listing the elements of the set, separated by commas, inside a set of curly brackets.
Since P is the set of integers that are greater than -3 and less than or equal to 1, then the possible numbers are; (-2, -1, 0, 1)
The roster form is; {-2, -1, 0, 1}
The builder notation of this set is;
{x : x ∈ I, −2 < x ≤ 1}
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Which number corresponds to the number in scientific notation? 3. 21 × 104 kg = kg 2. 0 × 10-5 l = l
Number is the equivalent of the one written in scientific notation is
3. 21 × 104 kg = kg 2. 0 × 10-5 l = l
Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It can also be referred to as standard form in the UK, standard index form, or scientific form.
Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 108 in scientific notation.
we have the number,
[tex]$0.000013$we know that$0.000013=\frac{13}{1000,000}=\frac{13}{10^6}=13 * 10^{-6}=1.3 * 10^{-5}$[/tex]
[tex]thereforethe answer is$1.3 * 10^{-5}$[/tex]
Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It can also be referred to as standard form in the UK, standard index form, or scientific form.
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Why do you divide to find unit rate?
Please help!!! For what value of why must LMNP be a parallelogram?
Answer:
107 degrees
Step-by-step explanation:
The four angles of a parallelogram add up to 360 degrees. Any two adjacent angles of a parallelogram add up to 180 degrees. So y is equal to 180 degrees minus 73 degrees, which is equal to 107 degrees.
Who said that "his life was
worth no more than other, and
his liberty as dear to him"
which gave Nat confidence in
his determination to help?
A. Sam
B. Will
C. Henry
D. Hark
Answer: Sam
Step-by-step explanation: I am pretty sure. Hope you find it helpful!
Help solve this please:
Adam has saved £2 less than Dan.
Write and expression for the amount that Dan saved.
I think of a number and add 3. The answer is 18
Answer: 15
Step-by-step explanation:
15+3=18
Which equation choice could represent the graph shown below?
The function representing the graph is f(x) = (x + 5)²(x - 3)². The correct option is (a).
What is a function?A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.
The given graph of the function cuts x axis at (-5,0) and (3,0) and y axis at (0,225) respectively.
Since the zeros of a function is the point at which it cuts the x-axis, the zeros at of the given functions are -5 and 3.
Which implies that the factors are (x + 5) and (x - 3) respectively.
The given factors are valid for options (a) and (d).
Now, at x = 0 f(x) should be 225.
It can be checked for both the options as follows,
(a) f(x) = (x + 5)²(x - 3)²
=> f(0) = (0 + 5)²(0 - 3)²
= 5² × -3²
= 225
Hence, the function that represents the given graph is f(x) = (x + 5)²(x - 3)².
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