Answer:
Let the height be represented as x
width = 14 + x
Length of diagonal = 34 inches.
Taking one diagonal of the rectangle to form a triangle.
using the Pythagoras theorem.
34² = (14 + x)² + x²
1156 = 196 + 28x + x² + x²
2x² + 28x - 960 = 0
divide through by 2
x² + 14x - 480 = 0
x² + 30x - 16x - 480 = 0
x(x + 30) - 16 (x + 30) = 0
(x - 16) = 0 or (x + 30) = 0
x = 16 or x = - 30
since the length can't be negative
therefore 16 inches is correct
3. A carpet company uses the following formula for
estimating the number of square feet, A, of carpeting
needed for a room x feet by y feet containing a stairway w
feet by z feet with n stairs:
A=xy+w[z(2n−1)+2n]
To estimate the number of square feet of carpeting needed for a room with dimensions x, y, w, z, and n, we can use the formula A = xy + w[z(2n - 1) + 2n].
What are the dimensions?
The given formula for estimating the number of square feet, A, of carpeting needed for a room x feet by y feet containing a stairway w feet by z feet with n stairs is:
A = xy + w[z(2n - 1) + 2n]
Let's break down this formula to understand the different parts:
xy represents the area of the main part of the room, which is a rectangle with length x and width y.w represents the width of the stairway.z represents the depth of each stair.n represents the number of stairs.The expression z(2n - 1) represents the total vertical distance covered by all the stairs, including the top and bottom levels.The expression 2n represents the total horizontal distance covered by all the stairs.The term w[z(2n - 1) + 2n] represents the additional area needed to cover the stairway. We add this to the area of the main part of the room, xy, to get the total area of carpeting needed, A.
So to estimate the number of square feet of carpeting needed for a room with dimensions x, y, w, z, and n, we can use the formula A = xy + w[z(2n - 1) + 2n].
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The marked price of a DVD player is $320. if a 15% discount is offered, find the actual selling price of the DVD player
The selling price of the DVD player after a 15% discount is applied can be found as follows:
Discount = 15% of the marked price = (15/100)*$320 = $48
Selling price = Marked price - Discount = $320 - $48 = $272
Therefore, the actual selling price of the DVD player after a 15% discount is $272.
Answer:
$272
Step-by-step explanation:
Formula:
Selling price = Marked price - Discount
We first find the discount by taking 15% off of $320 which is $48
We then insert the Maked price and the Discount into the formula which is:
Selling price = $320 - $48
Selling price = $272
To find the surface area of a refrigerator, what units will be used; check all that applies
Group of answer choices
square feet (sq ft)
meters (m)
square inches (sq in)
millimeters (mm)
surface area of a refrigerator,
square feet (sq ft)
square inches (sq in)
What is surface area ?the total area or the solid that the surface of the solid occupies.
we know that refrigerator have cuboid shape so,
surface area of cuboid =2(lb+bh+hl)
where l is length ,b is breath ,and h is height of cuboid .
The units generally used to measure the surface area of a refrigerator are:
square feet (sq ft)
square inches (sq in)
Therefore, the options are square feet (sq ft) and square inches (sq in) correct.
Meters (m) and millimeters (mm) are typically not used for measuring the surface area of a refrigerator.
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Find the area of the shape below. Use NUMBERS ONLY in the blank. NO units.
30 ft
60 ft
60 ft
60 ft
60 ft
30 ft
The shape is like a plus sign
The area of the shape, given the dimensions of the various parts of the shape, can be found to be 8, 100 ft ².
How to find the area ?You can divide the shape into other shapes. Then you can find the areas of these shapes and then sum them up.
The area of the composite shapes would therefore be :
= ( 30 x 60 ) + ( 30 x 60 ) + ( ( 60 + 30 + 60) x 30 )
= ( 30 x 60 ) + ( 30 x 60 ) + ( 150 x 30 )
= 1, 800 + 1, 800 + 4, 500
= 8, 100 ft ²
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What value of x will make this proportion true/ 14/x=1/2 7, or 18, or 24, or 28, show the problem worked.
Answer:
378
Step-by-step explanation:
[tex]\frac{14}{x}[/tex] = [tex]\frac{1}{27}[/tex] Cross multiply and solve for x
x = (14)(27)
x = 378
Helping in the name of Jesus.
A pole that is 3.2 m tall casts a shadow that is 1.59 m long. At the same time, a nearby building casts a shadow that is 44.25 m long. How tall is the building? Round your answer to the nearest meter.
The building is 89 m tall.
What is proportional?
A comparison of two numbers is called a proportion. Two sets of supplied numbers are said to be directly proportional to one another in terms of proportion if they increase or decrease in the same ratio between them.
height of pole : 3.2 m
shadow of pole : 1.59 m
shadow of building : 44.25 m
let the height of building : x m
Now, according to the question:
height of pole/shadow of pole = height of building/shadow of building
Putting values into the equation.
we get, 3.2 / 1.59 = x / 44.25
3.2 × 44.25 = 1.59x
141.6 = 1.59x
∴ x = 141.6/1.59
= 89 m
hence, height of the building is 89 m.
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The figure below shows a satellite orbiting Earth. The satellite passes directly over two tracking stations A and B, which are 68 miles apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be 83.9 degrees and 86.2 degrees respectively. How far is the satellite from station
A and how high is the satellite above the ground? Round answers to the nearest whole mile.
Step-by-step explanation:
let the third vertex=C
180-86.2=93.8°
angle near the satellite=180-(83.9+93.8)=180-177.7°=2.3°
angles of triangle are 83.9°,93.8°,2.3°
by sine formula
[tex]\frac{AC}{Sin~93.8} =\frac{AB}{Sin 2.3} \\\frac{AC}{Sin(180-93.8)} =\frac{68}{Sin~2.3} \\\frac{AC}{Sin~86.2} =\frac{68}{Sin~2.3} \\AC=\frac{Sin~86.2}{Sin~2.3} \times~68\\AC \approx 1690.69\\AC\approx1691~mile[/tex]
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500. Mark this and return
The answer is failed to estimate number of rock songs on his MP3 player.
What is a MP3 player and how does it work?
It's a compressed digital audio file. A player stores these files on a memory chip so that you can play it back at your leisure. Contains a miniature hard disk drive, which can store huge quantities of data. MP3s usually contain music, but the format is also used for general audio files such as audiobooks and podcasts.
The statements that are true about Josiah's solution are:
He set up a proportion correctly using the information given.
He correctly solved for x, the number of rock songs on his MP3 player.
Therefore, he did not find the average of the number of rock songs in the sample to estimate the number of rock songs on his MP3 player.
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give me a furmula a triangle
Answer:
The formula for finding the area of a triangle is:
Area = 1/2 x base x height
where "base" is the length of one of the sides of the triangle, and "height" is the distance from that side to the opposite vertex.
If the profit region is shaded in blue, which of the following graphs corresponds to the given situation?
The prοfit exceeds the cοst as y > 1000 + 15x. Sο, οptiοn 4 is cοrrect.
What is profit?Gaining anything is knοwn as prοfit. When the Selling price ( SP ) οf the prοduct is mοre than the cοst price ( CP ) οf the prοduct, we gain prοfit. Oppοsite tο the prοfit is lοss i.e. lοsing anything is called lοss. When the Selling price ( SP ) οf the prοduct is less than the cοst price ( CP ) οf the prοduct, we get a lοss.
Prοfit can be calculated by the fοrmula,
Prοfit = Selling Price - Cοst price
P = SP - CP
Lοss can be calculated by the fοrmula,
Lοss = Cοst price - Selling price
L = CP - SP
As per the questiοn,
x = number οf units prοduced
expressiοn = 1000 + 15x
⇒ When y > 1000 + 15x, then prοfit exceeds cοst:
x = 50 & y = 1750
x = 100 & y = 2500
x = 150 & y = 3250
x = 200 & y = 4000
x = 0 & y = 1000
Therefοre, the graph in the 1st οptiοn is cοrrect as the prοfit exceeds the cοst.
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Complete question:
The cost of a small business is given by the expression 1000 + 15x, where x is the number of units produced. the business will be profitable whenever its profit y exceeds its cost. if the profit region is shaded in blue, which of the following graphs corresponds to the given situation?
Emily is selling t-shirts for $7 each. If she earns a total of $126, how many t-shirts did she sell? Write and solve an equation to solve this problem. (Hint. You need to identify a variable AND embed it in the equation.)
Answer:
7x = 126 is the equation
She sold 18 t-shirts.
Step-by-step explanation:
Since she sold t-shirts for 7 each, we need to find how many T-shirts she sold. 126 dollars is how much she made, so we need to divide.
126/7 = 18.
The equation would be:
7x = 126.
A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 5 cm more than the shorter leg and the hypotenuse 10 cm more than the shorter leg. How long should the sides of the triangle be?
The sides of the right triangle are 15 cm, 20 cm, and 25 cm.
What is triangle?
A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.
Let x be the length of the shorter leg of the right triangle.
Then, according to the problem statement, the longer leg is 5 cm more than the shorter leg, which means its length is x + 5 cm.
The hypotenuse is 10 cm more than the shorter leg, so its length is x + 10 cm.
By the Pythagorean theorem, we have:
x² + (x+5)² = (x+10)²
Expanding the squares and simplifying, we get:
x² + x² + 10x + 25 = x² + 20x + 100
Subtracting x² and simplifying further, we get:
x² - 10x - 75 = 0
Factorizing the left-hand side, we get:
(x - 15)(x + 5) = 0
Therefore, the possible solutions are x = 15 and x = -5, but x cannot be negative in this context, so we take x = 15 cm.
Then, the longer leg is x + 5 = 20 cm, and the hypotenuse is x + 10 = 25 cm.
Therefore, the sides of the right triangle are 15 cm, 20 cm, and 25 cm.
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helpp!!!!11!1!1 !!!:(
The number of books that each kid in Mr. Johnson's sixth-grade class read during the summer was recorded. 5 books have been read on average by Mr. Johnson's students.
There are six students in Mr. Johnson's sixth-grade class, and their number of books read is 0, 2, 4, 6, 8, and 10.
To find the median, we need to find the middle value in the list of numbers. If there is an odd number of values, then the median is the middle number. If there is an even number of values, then the median is the average of the two middle numbers.
In this case, there are six numbers, which is an even number, so we need to find the average of the two middle numbers, which are 4 and 6.
The average of 4 and 6 is (4 + 6)/2 = 5.
Therefore, the median number of books read by Mr. Johnson's students is 5.
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A pizza parlor in Tallahassee sells a pizza with a 16-inch diameter. A pizza parlor in Jaco, Costa Rica, sells a pizza with a 27.8-centimeter diameter.
Part A: How many square inches of pizza is the pizza from Tallahassee? Show every step of your work. (1 point)
Part B: How many square centimeters of pizza is the pizza from Jaco, Costa Rica? Show every step of your work. (1 point)
Part C: If 1 in. = 2.54 cm, which pizza has the larger area? Show every step of your work. (1 point)
Part D: Using the diameter of each pizza, determine the scale factor relationship between the pizzas. (1 point)
A) 64π inches² B) 94.15π inches² C) the pizza from Tallahassee is larger. D) The scale factor relationship between the pizzas is: 1.462
Part A: The diameter of the pizza from Tallahassee is 16 inches, so the radius is 8 inches. The area of the pizza is:
A = πr²
= π(8)²
= 64π inches²
Part B: The diameter of the pizza from Jaco, Costa Rica is 27.8 centimeters. Converting this to inches, we get:
27.8 cm ÷ 2.54 cm/inch = 10.94 inches
The radius is 5.47 inches, so the area of the pizza is:
A = πr²
= π(5.47)²
= 94.15π inches²
Part C: Converting the area of the pizza from Tallahassee to square centimeters, we get:
64π inches² × (2.54 cm/inch)² = 1648.89 centimeters²
The area of the pizza from Jaco, Costa Rica is 94.15π inches² × (2.54 cm/inch)² = 594.85π centimeters². Therefore, the pizza from Tallahassee is larger.
Part D: The scale factor relationship between the pizzas is:
16 inches ÷ 27.8 cm × 2.54 cm/inch = 1.462
This means that the diameter of the pizza from Tallahassee is 1.462 times larger than the diameter of the pizza from Jaco, Costa Rica. Since area is proportional to the square of the diameter (or radius), the area of the pizza from Tallahassee is (1.462)² = 2.14 times larger than the area of the pizza from Jaco, Costa Rica.
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find the intersection (2,2) (2,4) (8,4) (8,2)
The intersection (2,2) (2,4) (8,4) (8,2) is (5,3).
On the coordinate plane, the four points that are given together form a rectangle. We must first locate the midway of both diagonals in order to determine where the diagonals will connect.
The midpoint of the diagonal that passes through the points (2,2) and (8,4) is ((2+8)/2, (2+4)/2). (5,3).
The midpoint of the diagonal that passes through the points (2,4) and (8,2) is ((2+8)/2, (4+2)/2). (5,3).
Consequently, the diagonals' point of intersection is (5,3).
Due to the fact that a rectangle's two diagonals meet here in the middle, this location also serves as the rectangle's centre.
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What is the average cost per unit?
Using calculations based on a perpetual inventory system, the inventory balance that Altira Corporation would report in its August 31, 2024, balance sheet and the cost of goods sold it would report in the income statement, using the Average Cost Method are as follows:
Ending inventory = $39,860Cost of Goods Sold = $71,540.What is the average cost method under the perpetual inventory system?The average cost method or the weighted-average cost method under the perpetual inventory system adds up all the cost of goods available for sale at each sales point and divides by the number of units available for sale in determining the average cost to be applied to the cost of goods sold.
Principally, the perpetual inventory system ensures that each inventory movement is separately recognized and the cost of goods sold determined, unlike the periodic inventory system.
Cost of Goods Sold:August 14 for Sales of 6,000 units:
Average cost per unit = $5.46 ($54,600 ÷ 10,000)
Cost of goods sold = $32,760 ($5.46 x 6,000)
August 25 for Sales of 7,000 units:
Average cost per unit = $5.54 ($21,840 + $33,600 ÷ 10,000)
Cost of goods sold = $38,780 ($5.54 x 7,000)
Total cost of goods sold = $71,540 ($32,760 + $38,780)
Total cost of goods available for sale = $111,400 ($10,600 + $44,000 + $33,600 + $23,200)
Ending Inventory = $39,860 ($111,400 - $71,540)
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pls help lol it’s due tomorrow
The measure of angle D is 100°
What is sum of angle in a Triangle?A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°.
Since the the sum of angle in a triangle is 180°, then to get the value of angle D will subtract the sum of the known angles from 180.
Therefore,
angle D = 180-( 40+40)
= 180-80
= 100°
therefore the measure of angle D Is 180°
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what's the linear relationship for this im stuck
Answer:
slope = 15
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (2, 21) ← 2 ordered pairs from the table
m = [tex]\frac{21-6}{2-1}[/tex] = [tex]\frac{15}{1}[/tex] = 15
the linear relationship is then of the form
y = mx + c ( m is the slope and c the y- intercept )
from the table the point (0, - 9 ) crosses the y- axis at - 9 ⇒ c = - 9
y = 15x - 9 ← linear relationship
Mona had 32 math problems for homework. She completed 3/4 of them before dinner and the remaining 1/4 after dinner. How many problems did she complete before dinner?
Step-by-step explanation:
Mona had = 32 math problems.
Let math problems shw completed be x.
Before dinner: 3/4x maths.
remaining maths = x- 3/4x
= 4x-3x/4 = 1/3x.
2. Write an equation that represents the following situation
Starting value = 200
Rate = 2.5% decay per year
Years = 5 years
Answer:
The equation that represents the situation is: A = 200(1-0.025)^5 where A is the amount remaining after 5 years, 200 is the starting value, 0.025 is the decimal equivalent of the decay rate of 2.5%, and 5 is the number of years.
Need help for this question.
The measure of the angle x is 41.41° in the given triangle.
What is a triangle?Triangle is a clοsed twο-dimensiοnal shape. It is a three-sided pοlygοn. All sides are made οf straight lines. The pοint where twο straight lines jοin is the vertex. Hence, the triangle has three vertices. Each vertex fοrms an angle.
Given that cos θ = side adjacent to angle x/hypotensive
Here, side adjacent to angle x = 6
hypotensive = 8
cos x = 6/8
x = arccos 6/8
x = 41.41°
Thus, the measure of the angle x is 41.41° in the given triangle.
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Pythagorean theorem find the length of the leg in the triangle 45, 51
Answer:
68.01
Step-by-step explanation:
let the unknown be y
opposite is 45
adjacent is 51
hypotenuse is ?
=y^2=45^2+51^2
y^2=2025+2601
y^2=4626
y=68.01
What is the axis of symmetry for the function f(x)=7-4x+x^2
the axis of symmetry for the function f(x) = 7 - 4x + x²2 is x = 2.
Why it is and what does symmetry mean?
To find the axis of symmetry of the quadratic function f(x) = 7 - 4x + x²2, we can use the formula:
x = -b / 2a
where a and b are the coefficients of the x²2 and x terms, respectively, in the quadratic equation ax²2 + bx + c = 0.
In the given function, a = 1 and b = -4. Substituting these values into the formula, we get:
x = -(-4) / 2(1) = 2
Therefore, the axis of symmetry for the function f(x) = 7 - 4x + x²2 is x = 2.
Symmetry is a property that describes a balanced and consistent arrangement of parts or elements that are similar in size, shape, and position. In mathematics, symmetry refers to the idea that a geometric object, function, or equation remains unchanged after some transformation, such as a reflection, rotation, or translation.
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please help with this
Option b (2x−1)(3x+4) and d 2(3x² −4x) only matches the polynomial given.
What is a polynomial?A pοlynοmial is a mathematical expressiοn cοnsisting οf variables, cοefficients, and the οperatiοns οf additiοn, subtractiοn, multiplicatiοn, and nοn-negative integer expοnents.
Pοlynοmials are an impοrtant part οf the "language" οf mathematics and algebra. They are used in nearly every field οf mathematics tο express numbers as a result οf mathematical οperatiοns. Pοlynοmials are alsο "building blοcks" in οther types οf mathematical expressiοns, such as ratiοnal expressiοns.
We have:
6x² − 8x
= 2(3x² −4x)
Then,
6x² - 3x + 8x -4
= 6x² +8x−3x−4
= 2x(3x+4) −3x −4
= 2x(3x+4)−(3x+4)
= (2x−1)(3x+4)
Thus, option b (2x−1)(3x+4) and d 2(3x² −4x) only matches the polynomial given.
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A letter of the alphabet is chosen, then a digit from 1-9 is chosen. Find the probability of getting X, then a prime number.
Answer:
There are 26 letters in the alphabet, and 9 digits from 1 to 9.
The probability of choosing X as the letter is 1/26, since there is only one X in the alphabet.
The probability of choosing a prime number digit is 4/9, since there are 4 prime numbers among the digits 1-9 (2, 3, 5, and 7) and 9 total digits.
Therefore, the probability of choosing X followed by a prime number digit is:
P(X and prime) = P(X) × P(prime) = (1/26) × (4/9) = 4/234
So the probability of getting X followed by a prime number is 4/234, or approximately 0.017 or 1.7%.
an 800 deposit for 2 years months earned 200$ in interest
The measures of the angles of abc are given by the expression in the table
Answer:
∠A=125° and ∠B=35°
Step-by-step explanation:
We know that, by angle sum property of triangles,
∠A +∠B+∠C=180°
⇒ (6x−1)° +20° +(x + 14)°=180°
⇒ 6x−1 +20 +x + 14=180 [Open parenthesis]
⇒7x+33=180
⇒7x=180-33 [Subtracting 33 from both sides]
⇒7x=147
⇒x=21 [Divide 7 from both sides]
Now substitute value of x in the expressions of ∠A and ∠B.
Therefore, ∠A=(6(21)-1)°=(126-1)°=125°
∠B=(21+14)°=35°
stick of butter weight a quarter of a pound how much do 13 sticks of butter weight
The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate r.
P = 4500 $, A = 4561.88 $, t = 3 months
The loan's simple interest rate is 5.232% per quarter.
What is the formula for the future value of a loan with simple interest?
A = P(1 + rt)
where A is the future value, P is the principal, r is the simple interest rate per period, and t is the number of periods.
In this case, we have:
P = 4500
A = 4561.88
t = 3 months = 3/12 year =0.25 year
Substituting these values into the formula,
[tex]4561.88 = 4500(1 + 0.25r)[/tex]
Dividing both sides by 4500,
[tex]1.01308 = 1 + 0.25r[/tex]
Subtracting 1 from both sides,
[tex]0.01308 = 0.25r[/tex]
Dividing both sides by 0.25,
[tex]r = 0.05232 \: or \: 5.232\%[/tex]
Therefore, the loan's simple interest rate is 5.232% per quarter.
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need help on this question :p
Answer:
d= 90 Degrees
e= 97 Degrees
f = 83
Answer:
see belowStep-by-step explanation:
To find:-
The values of e , f and d .Answer:-
We can see that angles e and 97° are vertically opposite angles. So they will be equal as vertically opposite angles are equal .
Hence here ,
→ e = 97°
Secondly e and f form linear pair , and the sum of linear pair is 180° . Hence here ,
→ e + f = 180°
→ 97° + f = 180°
→ f = (180-97)°
→ f = 83°
Same goes with d and 90° . They both form linear pair. So that ,
→ 90° + d = 180°
→ d = 180°-90°
→ d = 90°
These are the required values of the unknown angles.