Final answer:
The area of the trapezoid can be found by decomposing it into a rectangle and two triangles. Using the given dimensions, x = 4 units, y = 5 units, and h = 7 units, the calculated area of the trapezoid is 35 square units.
Explanation:
To find the area of the trapezoid using decomposition, we can break it down into simpler shapes whose area we can calculate more easily. Here, we will break the trapezoid into a rectangle and two triangles.
Let's identify the dimensions of the trapezoid: the top base (x), the bottom base (y), and the height (h). The student has provided that x = 4 units, y = 5 units, and h = 7 units.
The area of the rectangle that forms part of the trapezoid is the product of its base (x) and height (h):
Area of Rectangle = x * h = 4 units * 7 units = 28 square units
Next, we have two right triangles with one of the legs being the difference in the length of the bases (y - x) and the other leg equal to the height (h). The area of one triangle will be:
Area of Triangle = 0.5 * (y - x) * h = 0.5 * (5 units - 4 units) * 7 units = 3.5 square units
Since there are two identical triangles, we double this value:
Total Area of Triangles = 2 * 3.5 square units = 7 square units
Now we can sum the area of the rectangle and the total area of the triangles:
Total Area of Trapezoid = Area of Rectangle + Total Area of Triangles = 28 square units + 7 square units = 35 square units
Therefore, the area of the trapezoid is 35 square units.
Final answer:
The area of the trapezoid can be calculated by decomposing it into simpler shapes and using the formula A = ½(h)(b1 + b2), resulting in 31.5 units² for the given measurements.
Explanation:
To find the area of the trapezoid using decomposition, given that x = 4 units, y = 5 units, and h = 7 units, we need to decompose the trapezoid into simpler shapes like rectangles and triangles.
The area of a trapezoid can be found using the formula A = ½(h)(b1 + b2), where h is the height and b1 and b2 are the lengths of the two parallel bases. As there is no visual provided, and we are given three measurements, we must assume these represent the height and the bases of the trapezoid. The area is then calculated as follows:
Area of Trapezoid = ½(7)(4 + 5) = ½(7)(9) = ½(63) = 31.5 units².
one year, super bowl commercial time sold for 4 million for 30 seconds of air time. What was the price per second? Round to the nearest cent
Final answer:
To calculate the cost per second for a $4 million Super Bowl ad that runs for 30 seconds, divide the total cost by the number of seconds, yielding a cost of approximately $133,333.33 per second.
Explanation:
The question asks us to calculate the cost per second for Super Bowl commercial air time when 30 seconds of air time sold for $4 million. To find the price per second, we divide the total cost by the total number of seconds.
Price per second = Total cost ÷ Number of seconds
Price per second = $4,000,000 ÷ 30 seconds
Price per second = $133,333.33 (rounded to the nearest cent)
Therefore, the price per second for Super Bowl commercial air time was approximately $133,333.33.
Write the numbers in order from greatest to least.
-5, 1 1⁄5, -5 3⁄4, 5⁄12
Answer:
-5 3/4, -5, 5/12, 1 1/5
Step-by-step explanation:
Negatives are opposite of positives when least to greatest
Mara spent 3/5 of her vacation in British Columbia. While in that province, she spent 1/2 of her time in Vancouver. What fraction of her vacation did Michaela spend in Vancouver? If her vacation lasted 20 days, how many days did she spend in Vancouver?
Answer:
6 days
Step-by-step explanation:
Data given:
Vancouver is in the British Columbia
3/5 of the vacation was spent in British Columbia
1/2 of the time spent in British Columbia was spent in Vancouver.
The whole vacation was 20 days long
total days spent in British Columbia = 3/5 *20
total days spent in British Columbia = 12
Since the 1/2 of the time in British Columbia was spent in Vancouver then
time spent in Vancouver = 1/2 * 12
time spent in Vancouver =6 days
Mara spent [tex]\(\frac{3}{10}\)[/tex] of her vacation in Vancouver. If her vacation lasted 20 days, she spent 6 days in Vancouver.
Mara spent [tex]\(\frac{3}{10}\)[/tex]of her vacation in British Columbia. While in British Columbia, she spent [tex]\(\frac{1}{2}\)[/tex] of her time in Vancouver.
To find the fraction of her entire vacation that Mara spent in Vancouver, we multiply the two fractions:
[tex]\[ \text{Fraction of vacation in Vancouver} = \frac{3}{5} \times \frac{1}{2} = \frac{3 \times 1}{5 \times 2} = \frac{3}{10} \][/tex]
So, Mara spent [tex]\(\frac{3}{10}\)[/tex] of her vacation in Vancouver.
Next, to find out how many days she spent in Vancouver, we take the total number of days of her vacation, which is 20 days, and multiply it by the fraction of the vacation spent in Vancouver:
[tex]\[ \text{Days in Vancouver} = 20 \times \frac{3}{10} \][/tex]
[tex]\[ \text{Days in Vancouver} = 6 \][/tex]
Therefore, Mara spent 6 days in Vancouver.
What is the quotient 212,960\1000
The quotient of 212,960 divided by 1,000 is 212.960, achieved by moving the decimal point to the left by three places, reflecting the three zeros in 1,000.
Explanation:The question asks to find the quotient when 212,960 is divided by 1,000. To find the quotient, you essentially move the decimal point three places to the left. When dividing by powers of 10, each power of 10 represents the number of places you move the decimal to the left. Therefore, 212,960 divided by 1,000 gives us 212.960. This methodology is similar to the examples provided in the reference where dividing by 10, 100, and 1000 shifts the decimal point to the left by one, two, and three places respectively.
Remember that when multiplying or dividing by powers of 10, the decimal point is moved rather than actually performing the multiplication or division action. This is one of the reasons why working with decimals and powers of 10 is simpler compared to other numbers.
please answer both with work,please use a paper and picture, thanks
⚠️ANSWER FAST⚠️
ITS U.R.G.E.N.T
thanks
Answer:
a. [tex]$ \frac{\textbf{17}}{\textbf{4}} $[/tex]
b. [tex]$ \frac{\textbf{3}}{\textbf{8}} $[/tex]
Step-by-step explanation:
a. [tex]$ \textbf{3} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{1}\frac{\textbf{1}}{\textbf{4}} $[/tex]
A mixed fraction of the form [tex]$ a\frac{x}{y} = a + \frac{x}{y} $[/tex]
[tex]$ \therefore 3 + 1\frac{1}{4} = 3 + 1 + \frac{1}{4} $[/tex]
[tex]$ = 4 + \frac{1}{4} $[/tex]
[tex]$ = \frac{\textbf{17}}{\textbf{4}} $[/tex]
b. [tex]$ \textbf{2} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{1}\frac{\textbf{5}}{\textbf{8}} $[/tex]
A mixed fraction of the form [tex]$ -c\frac{a}{b} = - c - \frac{a}{b} $[/tex]
[tex]$ \therefore 2 - 1\frac{5}{8} = 2 - 1 - \frac{5}{8} $[/tex]
[tex]$ = 1 - \frac{5}{8} $[/tex]
[tex]$ = \frac{8 - 5}{8} $[/tex]
[tex]$ = \frac{\textbf{3}}{\textbf{8}} $[/tex]
Hence, the answer.
Can someone please help first answer gets brainlist
Answer:
3/5
Step-by-step explanation:
0.6 is actually 6/10 as a fraction. You divide bot the 6 and the 10 by 2 to get 3/5
what is x+3y=15 and 4×2y=30
Answer:
For the first one, x is 9 and y is 2. 9 + 3(2) = 15. The second is y = 3.75
4 friends share 5 medium pizzas equally once a week after school when they study for their math quiz. James wants to know how much pizza he’s eaten this year. If they’ve been meeting for 14 weeks, how much pizza had James eaten while at his study group? Show your work.
Answer:
17 pies and one half pie
Step-by-step explanation:
x+13/2=4 what x equal
Step-by-step explanation:
x+13÷2×2=4×2
x+13=8
x+13-13=8-13
x=8-13
x=-5
Answer:-2.5
Step-by-step explanation:
13/2=6.5. 4-6.5 =-2.5
Find the missing side length, m.
Answer:
m=5
Step-by-step explanation:
Since we know that triangle ABC is similar to QRS, we know that the side lengths will be proportional to one another. As such, we should take a ratio to determine the side length of m.
Choose whole numbers to make the division easier
[tex]\frac{QR}{AB} = \frac{QS}{AC} \\\frac{10}{6} = \frac{m}{3} \\\frac{10*3}{6} =m\\m=10*3/6 = 5[/tex]
The missing side length, [tex]$m$[/tex], is [tex]$\boxed{5}$[/tex].
The missing side length, [tex]$m$[/tex], can be found using the fact that triangles [tex]$ABC$[/tex] and[tex]$QRS$[/tex] are similar. This means that their corresponding side lengths are proportional. We can set up a proportion like this:
(m)/(3)=(10)/(6)
Cross-multiplying, we get:
[tex]$$6m[/tex] =[tex]30$$[/tex]
Solving for [tex]$m$[/tex], we get:
[tex]$$m[/tex] =[tex]5$$[/tex]
Therefore, the missing side length, [tex]$m$[/tex], is [tex]$\boxed{5}$[/tex].
i need help on 1 & 2
Answer:
1 - Avenue A is perpendicular to South St.
2 - 70°
Step-by-step explanation:
1 - North, Center, and South St. are parallel lines. Therefore Ave A will be perpendicular to the three lines.
2 - Ave B and Center street forms a 70° angle. Since Center and South St. are parallel lines, they have corresponding angles. Therefore, Ave B and South St also form a 70° angle. The same is true for Ave B and North St.
oakwood has a mass of 2.85 kilograms and a volume of 4100 cubic centimeters. determine the density of oak in grams per cubic centimeter.
Answer:
The density of oak is 0.695 grams per cubic centimeter.
Step-by-step explanation:
Given:
Oakwood has a mass of 2.85 kilograms and a volume of 4100 cubic centimeters.
Now, to find the density of oak in grams per cubic centimeter.
Mass (m) = 2.85 kilograms.
So, using conversion factor we convert into grams:
[tex]2.85\times 1000=2850\ grams.[/tex]
Volume (v) = 4100 cubic centimeters.
Now, to get the density by using formula:
[tex]Density=\frac{mass}{volume} \\Density=\frac{m}{v}[/tex]
[tex]Density=\frac{2850}{4100}[/tex]
[tex]Density=0.695\ grams\ per\ cubic\ centimeter.[/tex]
Therefore, the density of oak is 0.695 in grams per cubic centimeter.
the table shows the distance a small motor scooter can travel using one gallon of gasoline comeplete the table to find the number of miles the scooter can travel for other amounts of gasoline
By using the information that the scooter can travel 118 miles with 1 gallon of gasoline as a reference, we calculate that it can travel 11.8 miles with 0.1 gallons and 1180 miles with 10 gallons.
To complete the table and find the number of miles the scooter can travel for other amounts of gasoline, we can use the given information that the scooter can travel 118 miles with 1 gallon of gasoline as a reference point. We can calculate the mileage for different amounts of gasoline using this information.
Here's how we can complete the table:
Gallon 0.1:
We can calculate the distance for 0.1 gallons by taking 10% of the mileage for 1 gallon:
0.1 * 118 miles = 11.8 miles
Gallon 10:
Similarly, we can calculate the distance for 10 gallons by multiplying the mileage for 1 gallon by 10:
10 * 118 miles = 1180 miles
So, the completed table would look like this:
Gallon 0.1: 11.8 miles
Gallon 1: 118 miles
Gallon 10: 1180 miles
This table provides the number of miles the scooter can travel for different amounts of gasoline, including 0.1 gallons, 1 gallon, and 10 gallons.
For more such information on: miles
https://brainly.com/question/29806974
#SPJ2
18. You run along a path at a constant speed of 5.5 miles per hour. How far do you travel in 1.5 hours? in 3.8 hours?
Answer:
the travel of only 1.5 hours:8.25
The travel in 3.8 hours:20.9
Step-by-step explanation:
1.5(5.5)
1.5(3.8)
What percent of 140 is 50.4?
Answer:
36
Step-by-step explanation:
X/100% x 140 = 50.4
X x 140 = 50.4 x 100
X x 140 = 5040
X = 5040/140
X = 36
A business woman invests $41,500 into two accounts: one that returns 8% annual interest and one that returns 15% annual interest. After 1 year, she earns $5490. How much did she invest in each account?
$10,500 in the 8% interest account, $31,000 in the 15% interest account.
$11,500 in the 8% interest account, $30,000 in the 15% interest account.
$9,500 in the 8% interest account, $32,000 in the 15% interest account.
$32,000 in the 8% interest account, $9,500 in the 15% interest account.
Answer:
$10,500 in the 8% interest account,
$31,000 in the 15% interest account
Step-by-step explanation:
Let
x ---> the amount invested in the 8% interest account
41,500-x ----> the amount invested in the 15% interest account
we know that
The amount invested in the 8% interest account multiplied by the interest in decimal form plus the amount invested in the 15% interest account multiplied by the interest in decimal form, must be equal to $5,490
so
The linear equation that represent this problem is
[tex]0.08x+0.15(41,500-x)=5,490[/tex]
solve for x
[tex]0.08x+6,225-0.15x=5,490\\0.15x-0.08x=6,225-5,490\\0.07x=735\\x=\$10,500[/tex]
so
[tex]41,500-x=41,500-10,500=\$31,000[/tex]
therefore
$10,500 in the 8% interest account,
$31,000 in the 15% interest account
the sum of 4 numbers is 771. the ratio of the first to second number is 2:3. the ratio of the second to third is 5:4. the ratio of the third to the fourth is 5:6. find the value of the second number
Answer:
The second number is 225.
Step-by-step explanation:
Consider the provided information.
Let the first number is x.
Second number
[tex]\dfrac{x}{\text{Second number}} =\dfrac{2}{3}\\\\\text{Second number}=\dfrac{3}{2}x[/tex]
Third number is:
[tex]\dfrac{\text{Second number}}{\text{Third number}} =\dfrac{5}{4}\\\\\text{Third number}=\dfrac{3}{2}x\times\dfrac{4}{5}=\dfrac{6}{5}x[/tex]
Fourth number is:
[tex]\dfrac{\text{Third number}}{\text{Fourth number}} =\dfrac{5}{6}\\\\\text{Fourth number}=\dfrac{6}{5}x\times\dfrac{6}{5}=\dfrac{36}{25}x[/tex]
The sum of 4 numbers is 771.
[tex]x+\dfrac{3}{2}x+\dfrac{6}{5}x+\dfrac{36}{25}x=771[/tex]
[tex]50x+75x+60x+72x=38550[/tex]
[tex]257x=38550\\x=150[/tex]
First number is 150.
[tex]\text{Second number}=\dfrac{3}{2}\times150=225[/tex]
Hence, the second number is 225.
The value of the second number is 165.21.
Step 1: Understand the problem.
We have four numbers whose sum is 771. The ratios between consecutive numbers are given. We need to find the value of the second number.
Step 2: Construct equations using the provided ratios.
Let the four numbers be represented as 2x, 3x, 4x, and 5x respectively (using the smallest common multiple of the ratios).
Step 3: Create an equation using the total of the numbers.
2x + 3x + 4x + 5x = 771
Step 4: Solve for x.
[tex]\(2x + 3x + 4x + 5x = 771\)[/tex]
[tex]\(14x = 771\)[/tex]
[tex]\(x = \frac{771}{14}\)[/tex]
[tex]\(x = 55.07\)[/tex]
Step 5: Find the value of the second number.
The second number is 3x.
[tex]\(3x = 3 \times 55.07 = 165.21\)[/tex]
So, the value of the second number is 165.21.
Name the property the equation illustrates.
(ab)3 = a (63)
Accociative Property of addition
Name the property the equation illustrates
(ab)3 = a(b3)
A. Commutative property of addition
B. Associative property of Multiplication
C. Associative Property of Addition
D. Inverse Property of Multiplication
Answer:Associative property of Multiplication
Solution:From given equation
(ab)3 = a(b3)
We have to find the property used here
We find the brackets are interchanged
So here, given is a multiplication equation
Therefore, Associative property of Multiplication is used
Associative property of Multiplication:This property says that when we are multiplying it does not matter where you put the parenthesis
The result will be same wherever we put the parenthesis in multiplying two or more numbers
Which means,
[tex]a \times (b \times c) = (a \times b) \times c[/tex]
Therefore, from given,
[tex]a \times (b \times 3) = (a \times b) \times 3[/tex]
Thus associative property of multiplication is used
What does -8/3 simplify to ?
Answer:
exact form: -8/3
decimal form: -2.6666666
mixed number: -2 2/3
Step-by-step explanation:
Solve each inequality
X + 15 > 3
Answer:
It can be anything
Step-by-step explanation:
It just has to be grater.
which question represents a line that passes through (2,-1/2) and has a slope of 3?
Answer:
y=3x-13/2
Step-by-step explanation:
y-y1=m(x-x1)
y-(-1/2)=3(x-2)
y+1/2=3x-6
y=3x-6-1/2
y=3x-12/2-1/2
y=3x-13/2
What’s the distributive property of 12(x+5)?
Answer:
12x+60
Step-by-step explanation:
12 gets multiplied with x
12 gets multiplied with 5
Which gives 12x + 60
A cyclist traveled 9 kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel 45 kilometers, the skater had gone 30 kilometers. What’s the speed of the skater?
Final answer:
The speed of the skater is 18 km/h.
Explanation:
To find the speed of the skater, we can set up a proportion using the information given. Let's let the speed of the skater be x km/h. Since the cyclist traveled 9 km/h faster than the skater, the speed of the cyclist would be x + 9 km/h. Now, we can set up the proportion:
(x + 9 km/h)/(45 km) = x km/h)/(30 km).
To solve this proportion, we can cross-multiply and solve for x:
(x + 9 km/h)(30 km) = (x km/h)(45 km)
30x + 270 = 45x
270 = 45x - 30x
270 = 15x
x = 18
Therefore, the speed of the skater is 18 km/h.
What is the answer to
10x+4=6x+9
Answer:
x = 5/4 or 1.25.
Step-by-step explanation:
10x + 4 = 6x + 9
10x - 6x = 9 - 4
4x = 5
x = 5/4.
Answer: x = 5/4 or 1.25 or 1 1/4
Step-by-step explanation:
Step 1: Subtract 6x from both sides.
10x+4−6x=6x+9−6x
4x+4=9
Step 2: Subtract 4 from both sides.
4x+4−4=9−4
4x=5
Step 3: Divide both sides by 4.
4x/4 = 5/4
Write 80/100 as tenths in fraction form and decimal form
Answer:
0.8
Step-by-step explanation:
A + 6 equals 3 a - 8
Answer:
7
Step-by-step explanation:
Let's solve your equation step-by-step.
a+6=3a−8
Step 1: Subtract 3a from both sides.
a+6−3a=3a−8−3a
−2a+6=−8
Step 2: Subtract 6 from both sides.
−2a+6−6=−8−6
−2a=−14
Step 3: Divide both sides by -2.
−2a
−2
=
−14
−2
a=7
Answer:
a=7
The president of a company creates a graph of the price of the company’s stock over one year. He describes the graph as follows: • The price of the stock rose to about $17 before falling to about $3. • There have only been two periods during which the price of the stock decreased. • The price of the stock is expected to increase in the long run. Which graph correctly shows the price of the stock?
Answer:
Option D
Just took test on ed2020 it is the last graph. Option D
Step-by-step explanation:
Answer: D
Step-by-step explanation:
2. A sweater costs $35. Find the total cost of the
sweater if the sales tax is 5%.
The total cost of the sweater will be $36.75.
What is Percentage?Percentage is a number or ratio which is a fraction of hundred.
Given,
Cost price of sweater =$35.
Sales tax= 5%.
The total cost of the sweater can be calculated as,
Total cost price = CP of sweater + sales tax
= 35 + (5/35)*100
=$36.75
Hence, The total cost price of sweater would be $36.75.
Learn about Percentages:
https://brainly.com/question/29306119
#SPJ5
What is the slope intercept form of 6x+2y=8
Answer: y = -3x + 4
Step-by-step explanation:
subtract the 6x on both sides (2y = -6x + 8)
divide on both sides by 2 to isolate y ( y = -3x + 4)
Done :)
I really need help can ya'll please help. ://
Thank you
a) Wayne's savings before he spent $28 is $30
b) Stef's savings after she spent $28 is $8
Step-by-step explanation:
step 1 :
let,
Wayne's savings = 5x
Stef's savings = 6x
step 2 :
After spending $28 each of them, The ratio becomes 1/4.
⇒ (28 - 5x) / (28 - 6x) = 1/4
⇒ 4(28 - 5x) = 1 (28 - 6x)
⇒ 112 - 20x = 28 - 6x
⇒ 112 - 28 = 20x - 6x
⇒ 84 = 14 x
x = 84/4 = 6
step 3 :
a) Wayne's savings before he spent $28 = 5x
substitute x=6,
Wayne's savings = 5(6) = $30
step 4 :
b) Stef's savings after she spent $28 = Total savings - $28
= 6x - 28
= 6(6) - 28
∴ Stef's savings after she spent $28 = 36 - 28 =$8
(a) Wayne's savings before he spent $28 is $30.
(b) Stef's savings after she spent $28 is $8.
Solution:
Ratio of Wayne's savings to Stef's savings = 5 : 6
Let x be the common amount they have.
After spending $28 each, the ratio becomes 1 : 4.
5x – 28 : 6x – 28 = 1 : 4
This can be written in a fraction form.
[tex]$\Rightarrow\frac{5x-28}{6x-28}=\frac{1}{4}[/tex]
Do cross multiplication.
[tex]$\Rightarrow 4(5x-28)}=1({6x-28})[/tex]
[tex]$\Rightarrow 20x-112=6x-28[/tex]
Arrange like term one side.
[tex]$\Rightarrow 20x-6x=112-28[/tex]
[tex]$\Rightarrow 14x=84[/tex]
⇒ x = 6
(a) Wayne's savings before he spent $28 = 5x = 5(6) = $30
(b) To find stef's savings after spent $28:
Stef's savings before she spent $28 = 6x = 6(6) = $36
Stef's savings after she spent $28 = $36 – $28 = $8
Hence Wayne's savings before he spent $28 is $30
Stef's savings after she spent $28 is $8.