17. The area of the rectangle shown exceeds the area of the square by
2 cm². Find x.
y
X
x-1
18. The area of the square exceeds the area of the rectangle by 13 m².
Find y.
X
x + 2
y
X
y + 1
19. The area of the square is half the area of the rectangle. Find x.
y-3
2(x + 4)
(x - 2)
Answers
The values of the missing variables from the areas of rectangle and square are;
17) x = 4
18) y = 5
19) x = 4
What is the area of the rectangle and square?17) The formula for area of rectangle is;
A = Length * Width
Formula for area of square is;
A = side * side
Thus;
A_rect = (x - 1)(x + 2) = x² + x - 2
A_sq = x²
The area of the rectangle shown exceeds the area of the square by
2 cm². Thus;
x² + x - 2 - x² = 2
x - 2 = 2
x = 4
18) Area of the square; A_sq = y²
Area of the rectangle; A_rect = (y - 3)(y + 1) = y² - 2y - 3
The area of the square exceeds the area of the rectangle by 13 m². Thus;
y² - y² + 2y + 3 = 13
2y = 10
y = 5
19) The area of the square is half the area of the rectangle. Thus;
x² = ¹/₂(2(x² + 2x - 8))
x² = x² + 2x - 8
2x - 8 = 0
x = 4
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Related Questions
oh so Sorry about that Here it is
Answers
Answer:
y = 1/4x + 1
1/4 is the slope and 1 is the y-intercept
1) Draw a graph that:
a. Has a x-intercept of (1,0)
b. Has a y - intercept of (0,3)
c. Is continuous
d. Is a 1:1 function
e. Is linear
Answers
Answer:
the answer is c
Step-by-step explanation:
Find the area of the figure. (Sides meet at right angles.)
3 m
8 m
5 m
5 m
10 m
Answers
3 x 5 x 5 x 8 x 10 = 6,000
3 x 5 = 15, 15 x 5 = 75.
8 x 10 = 80.
75 x 80 = 6,000
What is a good job for people with dyslexia, but also love mathamatics?
Answers
Lawyer or judge
Professor
Social media manager
These are a few that would still involve math but are good jobs for people with dyslexia
A school wants to create a census to identify the favorite subject of students. Which description describes who they should ask?
all students their favorite subject in school
all sophomores their favorite subject in school
all staff their favorite subject in school
all male students their favorite subject in school
Answers
Answer:
all students their favorite subject in school
This morning, the owner of Sam's Spaghetti House withdrew $180 from the restaurant's bank account to pay for an oven repair. This afternoon, he deposited $430 from lunch sales.
What is the total change in the restaurant's bank account relative to where it started
Answers
Answer:
The restaurant is at a profit of $250
name one ray?
i’m not sure which is a ray .. lol
Answers
Answer: Ray BA and Ray BC
Explanation:
A ray starts at at a fixed point and moves forever in one direction. If we break line AC into two parts BA and BC, then we can form two opposite rays. Another ray points to the right but the letter marked for this isn't clear, so I'm not sure what to write for that ray. Same goes for the dashed ray that points to the left.
BD is a segment because both endpoints are fixed. We don't have either side extending forever in that direction.
A ticket for the train costs $6.23. If Barbara has $32, does she have enough money to buy 5 tickets? Explain your reasoning.
Answers
6.23•5=31.15
32 is more then 31.15
So yes, she has enough money!
55 is the difference of Chrissy's height and 21.
Use the variable to represent Chrissy's height.
Answers
The value of Chrissy's height from the problem is 76
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Let x represent Chrissy's height. 55 is the difference of Chrissy's height and 21. Hence:
x - 21 = 55
x = 76
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Simplify the expression.
3(−6+2 ÷ 4) - 72²
Answers
Does(3, 1)make the inequality 3x + 10y ≥ 20 true?
Answers
Answer:
See below
Step-by-step explanation:
Plug in x = 3 And y = 1 to see
3(3) + 10(1) >= 20 ?
9 + 10 >= 20?
19 >= 20 Not true ....the point does not make the inequality true
9. Solve
x(c- b) = g solve for x
Answers
Step-by-step explanation:
x(c - b) = g
divide through by (c - b)
x(c - b) = g
(c - b) (c - b)
x = g/ (c - b)
a whole number is more than 50. if this number is divided by 3, the remainder is 2. if it divided by 4, the remainder is 3. what is the smallest such whole number
Answers
The smallest such whole number is 11 which is, Which is divided by 3, the remainder is 2, f it, divided by 4, the remainder is 3
Let the number be x
Here we have to find the whole number which is Divided by 3,4 the remainder is 2,3 respectively,
x+(3–2)= x +1 is multiple of 3
Div by 4 remainder is
3x+(4–3) = x+1 is multiple of 4
So LCM of 3,4 is 3×4 = 12
Hence,x=12 –1 =11
The smallest such whole number is 11 which is divided by 3, the remainder is 2, if it divided by 4, the remainder is 3.
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josie took a total of 24 quizzes over the course of 6 weeks. after attending 10 weeks of school this quarter, how many quizzes will josie have taken in total? solve using unit rates.
Answers
In linear equation, 42 units quizzes will josie have taken in total.
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y.When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.josie took a total = 24 quizzes
the course = 6 weeks
quizzes will josie have taken = 24/6 = 4
after attending 10 weeks of school this quarter = 10 * 4 = 40 units
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A stack of 30 science flashcards includes a review card for each of the following 10 insects, eight trees eight flowers, 4 birds. What is the probability of randomly selecting a TREE or a FLOWER?
Answers
From the statement, we know that stack of 30 science flashcards has:
• 10 with insects,
,• 8 with trees,
,• 8 with flowers,
,• 4 with birds.
The probability of selecting a tree or a flower is given by:
[tex]P(\text{tree or flower})=\frac{\text{\# of trees + \# of flowers}}{\text{total \# of cards}}=\frac{8+8}{30}=\frac{16}{30}=\frac{4}{15}.[/tex]Answer4/15
i need help fast pls be correct
Answers
1) The rule of transformation is described as; A: A rotation 90° clockwise about the origin
2) The value of x is; 2
3) The value of x is 10
4) The slope of the line is; 2
How to Interpret rule of transformation?
1) The rule of transformation for When the point M (h, k) is rotated through 90° clockwise about the origin, the point M (h, k) takes the image M' (k, -h). Thus, that is the rule here.
2) From the given image, we can tell that the angles 50° and 26x - 2 are corresponding angles. Thus, they are congruent and we have;
26x - 2 = 50
26x = 52
x = 2
3) From the given image, we can see that the given angles are supplementary and as such they add up to 180 degrees. Thus;
9x + 15 + 6x + 15 = 180
15x + 30 = 180
15x = 150
x = 10
4) Slope is;
m = (y2 - y1)/(x2 - x1)
m = (1 - (-3))/(1 - (-1))
m = 4/2
m = 2
5) Same question as the first one.
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86,794 magazines/day = magazines/week
Answers
86,794(7) = 607,558 magazines/week
A hot utensil kept away from the flame and cools down. Name and define the process of heat transfer invloved in given example
Answers
Help me with this please thanks
Answers
Answer: the function only intersects the y axis
Step-by-step explanation:
Answer:
The function only intersects the y axis.
Step-by-step explanation:
See the attached worksheet.
Using the figure below, Maggie used the definition of vertical angles to help her solve for x. Since vertical angles are congruent, she set the two given expressions equal to each other. After solving for x, her teacher said she got the wrong value for x. Explain where Maggie made her mistake when solving for x.
Answers
Maggie's mistake on the solution of the expression for x was when she subtracted 7x to both sides, the result should have been -3x and not 3x.
What is the solution for the equation?The equation is given as follows, as the angles are congruent, that is, they have the same measure:
4x + 2 = 7x - 25.
First, we isolate x on the left side of the equality, subtracting 7x from both sides, hence:
4x + 2 - 7x = 7x - 25 - 7x
Then the correct expression is:
-3x + 2 = -25
Which is where Maggie's mistake happened, on the subtraction of 4x and 7x.
Then, isolating x, we subtract 2 from both sides of the equality, to remove the +2 term on the left side of the equality.
-3x = -27
3x = 27
x = 27/3
x = 9.
The correct solution is x = 9.
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Henry and his children went into a restaurant that sells drinks for $2 each and tacos for $4 each. Henry has $40 to spend and must buy at least 14 drinks and tacos altogether. If x represents the number of drinks purchased and y represents the number of tacos purchased, write and solve a system of inequalities graphically and determine one possible solution.
Answers
One possible solution for the system of inequalities that models the situation is: (5,7), when he purchases 5 drinks and 7 tacos.
What is a system of inequalities?A system of inequalities is when multiple variables are related in a context, and then inequalities are built to find the numeric range of values that each variable can assume, according to the constraints in this problem.
For this problem, the variables are defined as follows, as stated in the text:
Variable x: number of drinks purchased.Variable y: number of tacos purchased.Both amounts cannot assume negative values, hence the first constraints are:
x ≥ 0.y ≥ 0.He must buy at least 14 drinks, hence:
x + y ≥ 14.
He must spend at most $40, hence, considering the price of each item, the constraint is given by:
2x + 4y ≤ 40.
The graphic solution to the inequality is given at the end of the answer. One possible solution is of (5,7), meaning that he buys 5 drinks and 7 tacos.
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How would you solve this problem?
The mass of Earth is 5.97 X 10^24 kilograms while the mass of Jupiter is 1.9 x 10^27 kilograms. Approximately how many times greater is the mass of Jupiter compared to Earth? Give your answer in scientific notation.
Answers
Provided the figures we have that describe the mass of Earth and the mass of Jupiter, we can conclude that Jupiter is 318 times greater than the mass of Earth.
How do we arrive at the planet with the greater mass?From the figures we have, we can see that the mass of Jupiter is greater than the mass of Earth because it has more zeros.
So, we have to divide the value of the mass of Jupiter by the mass of the earth as follows:
1.9 x 10^27
5.97 X 10^24
=1. 9 ÷ 5.97 × 10^27 - 10^24
= 0.318... ×10³
= 318
Do note that when we have to divide figures that are raised to some figures, the rule will be to subtract the figures as we find in the fact that 27 - 24 is equal to 3. And when we multiply, we arrive at the stated figure.
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Miranda has the following income and expenses:
$550 bi-weekly paychecks
$60 cell phone
$85 car insurance
●
$195 car payment
• $55 HULU
• $575 rent
How much are Miranda's total monthly expenses?
Answers
The amount of Miranda's total monthly expense is $970.
What is the meaning of an expenses?Basically, an expense refers to any cost of operations that a company incurs to generate revenue. It also means the cost that one is required to spend on obtaining something.
In a typical firm, the common expenses include a payment to suppliers, employee wages, factory leases, equipment depreciation etc.
in the question context, the expenses are:
$60 cell phone$85 car insurance$195 car payment$55 HULU$575 rentTotal monthly expenses = $60 + $85 + $195 + $55 + $575
Total monthly expenses = $970.
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Three-fourths of students in your classroom like chocolate chip cookie dough ice cream. One-half of these same students also like mint-flavored ice cream. What fraction of students in your classroom like both flavors?
ANSWER FOR 100 POINTS
Answers
The fraction of the students in the classroom that like both flavors is 1/4.
How to calculate the fraction?From the information, three-fourths of students in the classroom like chocolate chip cookie dough ice cream and one-half of these same students also like mint-flavored ice cream.
The fraction of the students in the classroom that like both flavors will be the addition of both flavors subtracted from 1. This will be illustrated as:
= (3/4 + 1/2) - 1
= 3/4 + 2/4 - 1
= 5/4 - 1
= 1/4
The fraction is 1/4.
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5. Which number is the smallest?
2.2458103 x 10^-6
2x10^-5
3.215 × 10^-7
3x10⁰
HELP
Answers
Answer: 3.215 × 10^-7
Step-by-step explanation:
The exponent is smaller than all of the others, so it's the smallest.
How many 1 3/5-inch-thick books can fit on a 1 4/12-inch-long bookshelf?
You can fit ? books on the bookshelf.
Answers
Using division we can calculate that 8 books can fit in the 14 inch long bookshelf .
Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number. Multiplication, addition, and subtraction make up the remaining operations.
One way to understand the division of two natural numbers is to tally the occasions in which one number is included within another. This number doesn't have to be an integer. For instance, each individual will receive 5 apples if 20 apples are spread evenly among 4 people.Both types of division are applied to various algebraic structures, or means of describing mathematical structure. These contain polynomial rings in a single indeterminate and are known as Euclidean domains. These are the cases where a defined Euclidean division (with remainder) exists.length of book shelf = 14 inch
length of each book = 1 3/5 inch = 1.6 inches
Number of books = 14 ÷ 1.6 = 8.75 books
Hence by division we get that 8 book can be put in the bookshelf.
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I need help ASAP 15 points
Answers
The value of x is 9 and the mistake that Maggie made is that she did use the proper operation sign when rearranging the numbers.
How to find vertical opposite angles?When any two straight lines intersect each other, then four angles are formed. The angles that are directly opposite to each other are known as opposite angles. They are also called vertical angles or vertically opposite angles.
Now, from the image attached, we see that the two given angles are opposite angles and as such they are congruent. Thus, we have;
4x + 2 = 7x - 25
Rearrange to collect like terms on same side to get;
7x - 4x = 25 + 2
3x = 27
x = 27/3
x = 9
The mistake that Maggie made is that she did use the proper operation sign when rearranging the numbers.
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Enter the inverse function of f(x) = 15x - 14.
Answers
replace 'x' with 'y'
15y - 14 = x; solve for y
15y = x + 14
y = (x+14)/15
Shen invested in a savings bond for 6 years and was paid simple interest at an annual rate of 3% . the total interest that he earned was $1620 . how much did he invest?
Answers
The principal amount invested by Shen in the saving bond is $9,000.
What is explained as the simple interest?Simple interest is a simple and fast method to calculate the interest on a loan. Simple interest is calculated by multiplying this same daily interest rate even by principal multiplied by the amount of days between payments.As per the given question;
The formula for simple interest is-
SI = PRT/100
Principal be 'P'Simple Interest SI = $1620.Time t = 6 yearsRate of interest R = 3%.Put the values;
SI = PRT/100, write the formula in the terms of P
P = 100×SI/RT
P = 100×1620 / (3×6)
On simplification;
P = 9,000
Thus, the amount invested by Shen in the saving bond is $9,000.
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Help on these please
Answers
Answer:
a)16777216
b)279936
c)32768
d)49
Plss mark as brainliest
Answer:
ok!
a) 4^9 ×4^3=4^9+3=4^12
b) 6^5 ×6^2=6^5+2=6^7
c) 8^6 ÷8=8^6-1 =8^5
d) 7^8÷7^6=7^8-6=7^2
Pls mark me as brainliest.
I answered first.
Step-by-step explanation:
It's simple!
If there is multiplication, add the powers.
If there is division, subtract the powers.