p = 32
Solution:
Given p represents the amount of air pressure in a tire.
t represents the time it takes for the tire to go flat and t = –8.
To find the value of p, if [tex]\frac{p}{t}=-4[/tex].
⇒ [tex]\frac{p}{t}=-4[/tex]
Substitute t = –8 in the above equation.
⇒ [tex]\frac{p}{-8}=-4[/tex]
Do cross multiply, we get
⇒ p = (–8) × (– 4)
⇒ p = 32
Hence, the value of p is 32 if the quotient [tex]\frac{p}{t}[/tex] is –4.
The number of banks in a country for the years 1935 through 2009 is given by the following function.
81.8x + 12,361 if x < 90
f(x) = 3
where x is the number of years after 1900
- 376.4x + 48,685 if x 290
Complete parts (a) (b)
a) What does this model give as the number of banks in 1970? 1990? 2010?
The number of banks in 1970 is
Answer:
1990
Step-by-step explanation:
The number of banks in 1970 is 18,137, in 1990 is 3, and in 2010 is 7,250.
(a) Since 1970 is 70 years after 1900,
use the function f(x) = 81.8x + 12,361 for the years before 1990 (when x < 90).
f(70) = 81.8 * 70 + 12,361
= 5776 + 12,361
= 18,137
The number of banks in 1970 is 18,137.
(b) Since 1990 is exactly 90 years after 1900,
use the other part of the function f(x) = 3 for the years between 1990 and 2010.
f(90) = 3
The number of banks in 1990 is 3.
(c) Since 2010 is 110 years after 1900, use the function
f(x) = -376.4x + 48,685 for the years after 290 (when x > 290).
f(110) = -376.4 * 110 + 48,685
= -41404 + 48,685
= 7250
The number of banks in 2010 is 7,250.
So, the number of banks are 18,137, 3 and 7,250.
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789
Bernie, Eddy and Gery share £450
Bernie gets twice as much as Eddy who gets three times as much as Gery.
Work out how much they each get.
Answer:
Gery will get 45 £,Eddy will get 135 £ and Bernie will get 270 £ of the total share.
Step-by-step explanation:
Given:
Bernie, Eddy and Gery share £450.
Bernie gets twice as much as Eddy.
Eddy gets three times as much as Gery.
So,
Let Gery gets 'x' share of the amount.
Then,
Eddy's share will be '[tex]3x[/tex]'
and
Bernie's share will be [tex]2\times 3x=6x[/tex]
According to the question.
Total share summation of total share = [tex]450[/tex]
⇒ [tex]x+3x+6x=450[/tex]
⇒ [tex]10x=450[/tex]
⇒ [tex]x=\frac{450}{10}=45[/tex]
So Gery's share = 'x' [tex]= 45[/tex]
Eddy's share = [tex]3x=3\times 45=135[/tex]
Bernie's share = [tex]6x=6\times 45=270[/tex]
Gery will get 45 £,Eddy will get 135 £ and Bernie will get 270 £ of the total share.
1.428571429 rounded to the nearest tenth
Answer: 1.428571429 rounded to the nearest tenth is 1.4.
Step-by-step explanation: The answer is 1.4 because the number you were using to round was lower than five.
Final answer:
The number 1.428571429 rounded to the nearest tenth is 1.4, as the hundredth's place digit is less than 5.
Explanation:
To round the number 1.428571429 to the nearest tenth, we look at the first digit after the tenth's place, which is the hundredth's place. If this digit is 5 or greater, we round up. If it's less than 5, we do not round up. In this case, the hundredth's digit is 2, which is less than 5. Therefore, the number 1.428571429 rounded to the nearest tenth is 1.4. This process of rounding to the nearest tenth simplifies numbers while maintaining their approximate value, aiding in concise representation and easier comprehension of numerical data in various contexts.
Show that DEFG is a rectangle.
Answer:
opposite sides that are parallel,
opposite angles that are congruent,
opposite sides that are congruent,
consecutive angles that are supplementary, and
diagonals that bisect each other.
Step-by-step explanation:
not sure if this is the kind of answer you're looking for so i'm sorry if this didn't help
Answer:
in the steps
Step-by-step explanation:
D(-2,3) E(4,-1) F(2,-4) G(-4,0)
slope DG: (0-3)/(-4+2) = -3/-2 = 3/2
slope EF: (-4+1)/(2-4) = -3/-2 = 3/2
DG // EF
slope DE: (-1-3)/(4+2) = -4/6 = -2/3
slope GF: (-4-0)/(2+4) = -4/6 = -2/3
DE // GF
slope DG = - 1/slope DE
DG ⊥ DE
The same reason
DG ⊥ GF
DE ⊥ EF
EF ⊥ GF
∴ DEFG is a parallelogram with four 90° interior angles, it's a rectangle
Eight less than a number is 18
Answer:
x-8=18
Step-by-step explanation:
A number is our variable, so we will use X. 8 less than a number would be 8-x and that equals 18 so x-8=18.
Pleas help anyone please
NEED HELP PLEASE AND THANK YOu !
Answer:
3
Step-by-step explanation:
we know there is 18 total. so we subtract the other numbers from 18.
18-5=13
13-10=3
hope this helps!
Points D and E are midpoints of the sides of triangle ABC. The perimeter of the triangle is 48 units.
Q: what’s the value of t?
a) 2
b) 3
c) 6
d) 8
The value of t = 2. Option a) 2 is the correct answer.
Step-by-step explanation:
Perimeter is the sum of three sides of a triangle.
Given that, the points D and E are midpoints of the sides.
Therefore,
side AB= AD+DB
AB= 3t + 3t = 6t
side BC= BE+EC
BC= 4t + 4t = 8t
side AC= 7t+6
Perimeter of the triangle= sum of (side AB+side BC+side AC)
48 = 6t+8t+7t+6
48 = 21t+6
t= 42/21
t= 2
The inequality 9 - 4x< 3x - 5 is equivalent to:
A. x> -2
B. x> 2
c. x <2
D.x< -2
Answer:
B
Step-by-step explanation:
move x to one side and numbers on another side.
9+5<3x+4x. --» 14<7x. --»/7--» x>2
Final answer:
The inequality 9 - 4x < 3x - 5 simplifies to x > 2 after collecting like terms and performing basic algebraic operations. Therefore, the correct answer is B. x > 2.
Explanation:
To solve the inequality 9 - 4x < 3x - 5, we need first to collect like terms on one side. This step involves moving all the x terms to one side of the inequality and the constant terms to the other side.
Let's do this now:
Add 4x to each side: 9 - 4x + 4x < 3x - 5 + 4x, which simplifies to 9 < 7x - 5.Next, add 5 to each side: 9 + 5 < 7x - 5 + 5, which simplifies to 14 < 7x.Finally, divide each side by 7: 14/7 < 7x/7, which simplifies to 2 < x.The answer is x > 2, which corresponds to option B.
Find the distance between
(-12,1) and (12,-1)
ANSWER: Exact Form: 2[tex]\sqrt{145}[/tex]
Decimal Form: 24.08318915
STEP-BY-STEP EXPLANATION:
(-12,1) (12,-1)
Use the distance formula to determine the distance between the two points.
Distance = [tex]\sqrt{(X2-X1)^{2 }+ (Y2-Y1)^{2} }[/tex]
Substitute the actual values of the points into the distance formula.
[tex]\sqrt{(12-(-12))^{2 }+ ((-1)-1)^{2} }[/tex]
Multiply -1 BY -12
[tex]\sqrt{(12+12)^{2 }+ ((-1)-1)^{2} }[/tex]
Add 12 and 12
[tex]\sqrt{24^{2} +((-1)-1)^{2} }[/tex]
Raise 24 to the power of 2
[tex]\sqrt{576 +((-1)-1)^{2} }[/tex]
[tex]\sqrt{576+4}[/tex]
[tex]\sqrt{580}[/tex]
Rewrite 580 as [tex]2^{2}[/tex]·145
Factor 4 out of 580
[tex]\sqrt{4(145)}[/tex]
Rewrite 4 as [tex]2^{2}[/tex]
[tex]\sqrt{2^{2}(145) }[/tex]
Pull terms out from under the radical.
2[tex]\sqrt{145}[/tex]
The result can be shown in multiple forms.
Exact Form: 2[tex]\sqrt{145}[/tex]
Decimal Form: 24.08318915
The distance between the points will be "24.08 units".
Given points:
[tex](x_1,y_1) = (-12,1)[/tex][tex](x_2,y_2) = (12,-1)[/tex]As we know the formula,
→ [tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
By substituting the values, we get
[tex]= \sqrt{(12-(-12))^2+(-1-1)^2}[/tex]
[tex]= \sqrt{(24)^2+(-2)^2}[/tex]
[tex]= \sqrt{576+4}[/tex]
[tex]= \sqrt{580}[/tex]
[tex]= 24.08 \ units[/tex]
Thus the above answer is correct.
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Answer this question please.
Answer:
see explanation
Step-by-step explanation:
The side of the square = x + 2, thus area is equal to
(x + 2)² ← expand using FOIL
= x² + 4x + 4
Given area = 7 then
x² + 4x + 4 = 7 ( subtract 4 from both sides )
x² + 4x = 3 ← as required
Answer:
the area of the square ABCD = 7
on the other hand, the area of the square ABCD = (2+x)² = x² + 4x + 4
then x² + 4x + 4 = 7
then x² + 4x + 4 = 4 + 3
then x² + 4x = 3
Step-by-step explanation:
In scoop county 16.8% of residents have diabetes. If 12,914 scioto county residents have diabetes, what is the population of the county
The population of the county is 76,869.
Step-by-step explanation:
Given,
Number of people with Diabetes = 12914
Percent of people with Diabetes = 16.8%
Let,
x be the number of people in county.
16.8% of x = 12914
[tex]\frac{16.8}{100}x=12914\\0.168x=12914[/tex]
Dividing both sides by 0.168
[tex]\frac{0.168x}{0.168}=\frac{12914}{0.168}\\x=76869.04[/tex]
Rounding off to nearest whole number
x = 76,869
The population of the county is 76,869.
Keywords: division, percentage
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Answer:
i got it for the team sooo
1. 10.1
2. 16.5
3. 58.9
4. 41.1
it gave me the right answers this is edg 2020
Determining Relative Frequencies as Percentages
Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 440 miles on 20 gallons of gas. How far could you drive on 60 gallons o gas? What is the car’s gas mileage?
Answer:
Step-by-step explanation:
20 : 440 = 60:x
Product of means = 440*60
Product of extremes = 20*x
20*x = 440*60
x = 440*60/20 = 440*3
x = 1320 miles
Here’s another one thank u all for helping me. I really appreciate it!
Answer:
100(2)(3.14) = about 628 feet
Marys watch keeps perfect time and Bills watch loses 4 minutes a day.
Both watches are set at midnight on January 1. How many times a year will they match?
Bill's and Mary's watches will match once a year on a non-leap year and twice a year on a leap year since Bill's watch loses 4 minutes per day. After 360 days, Bill's watch will be exactly 24 hours behind Mary's.
You asked how many times a year Mary's watch (which keeps perfect time) and Bill's watch (which loses 4 minutes a day) would match if they were both set at midnight on January 1. This is a mathematical problem involving the concept of elapsed time.
Since Bill's watch loses 4 minutes per day, after 1 day, there will be a 4-minute difference between the two watches. As this pattern continues, we calculate how many days it will take for Bill's watch to lose an entire 24-hour cycle (1440 minutes) since 1440 minutes divided by 4 minutes/day equals 360 days. Therefore, Bill's watch would match Mary's watch exactly one more time, 361 days after both watches were set, which would be on the next New Year's Eve, just before both watches hit midnight.
However, this scenario would only occur in a non-leap year. During a leap year, Bill's watch would be 4 minutes slow on December 30th instead of on December 31st, so Bill's watch would match Mary's watch two times in a leap year, once on January 1st and again on December 30th. In conclusion, Bill's and Mary's watches match once a year during a non-leap year and twice during a leap year.
x (rooms) y (towels)
5 25
6 30
7 35
9 40
Tim works as a housekeeper at the Woodwind Hotel. The table shows the number of rooms occupied, x, and the number of towels Tim needs to supply, y. What is the unit rate of towels per room?
A. 3
B. 4
C. 5
D. 7
Answer:
Step-by-step explanation:
the answer is 5
The Answer is (5) :D Hope this helps
A cheetah runs 108 meters in 4 seconds. How far can the cheetah run in 9 seconds?
Answer:
Step-by-step explanation:
It moves 108m in 4sec
Than in 1sec it moves 108/4m= 27m
And in 9sec it will move 27×9m
= 243m
Can someone please help me this is due in 10 mins
George finished 1/4 of a level on his computer games in 1/3 of an hour at this rate. How many hours will it take to complete on level?
Answer:
1 hour 20 minutes
Step-by-step explanation:
It takes twenty minutes to finish a quarter of one level. Which indicates that it would take one hour and twenty minutes to finish said level by simply multiplying twenty by four.
George will complete a level on his computer games in 1 1/3 of the hours.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
We have been given that he finished 1/4 of a level on his computer games in 1/3 of an hour at this rate.
Let x the number of hours will it take to complete on a level
According to the given question, we can write the ratio would be as:
1/4 of a level : 1/3 of an hour = 1 level : x hour
⇒ (1/4) / (1/3) = 1/x
Apply the cross-multiplication operation,
⇒ x = (1/3) × 4
⇒ x = 4/3
⇒ x = 1 1/3
Therefore, there will be 1 1/3 of the hours it takes to complete a level.
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{-8, 0, 5, 11} which elements are greater than 5
Answer:
Therefore elements greater than 5 is only 11.
Step-by-step explanation:
Set:
A set in mathematics is a collection of well defined and distinct objects, also consist of a collection of elements.
Example:
Let A be the set for {-8, 0, 5, 11}
∴ A = {-8, 0, 5, 11}
This is the set ' A 'consists of elements as a number -8, 0, 5, 11.
Therefore elements greater than 5 is only 11. ( 5 will not come as it is mentioned greater than 5 )
-8, 0 are less then 5
How much greater is the area of a circle with a radius of 6.2 inches than the area of a square with a side length of 4 inches?
Answer:
7.54 times greater.
Step-by-step explanation:
The square with a side length of 4 inches has a 4×4=16 inches squared area. The area of a cirkel is calculated with the formula \pi×r^2. Using the 6.2 inch radius given, we get \pi×6.2^2=120.76 inches squared. 120.76/16=7.54 times greater.
Final answer:
Calculate the difference in area between a circle and a square given their respective dimensions.
Explanation:
To find the area of a circle with a radius of 6.2 inches:
Calculate the area using the formula A = πr², where r = 6.2 inches.Area of circle = π x (6.2)² = 38.48 square inches.To find the area of a square with a side length of 4 inches:
Calculate the area of the square using the formula A = s², where s = 4 inches.Area of square = 4 x 4 = 16 square inches.Subtract the area of the square from the area of the circle to find the difference:
Difference = 38.48 - 16 = 22.48 square inches.
how do I solve 14x+5=105
Answer:7.14
Don’t rely on me I tried. Might be wrong but there’s an app called photo math and it’ll help with equations just like this.
Step-by-step explanation:subtract 5 from 5 and subtract 5 from 105 because you want to get X by itself. There for 14x equals 100. Then divide both by 14. 14 cancels out and you get your answer.
(05.03)
What is the rate of change and initial value for the linear relation that includes the points shown in the table? (4 points)
x y
1 10
2 8
3 6
4 4
Group of answer choices
Initial value: 12, rate of change: -2
Initial value: 8, rate of change: 2
Initial value: 12, rate of change: 2
Initial value 8, rate of change: -2
Answer:
Initial value: 12, rate of change: -2
Step-by-step explanation:
The rate of change is given by change in the y-values over change in x-values.
There is a constant change of -2 in y-values.
There is also a constant change of 1 in the x-values.
The rate of change is -2
The initial value is when x=0,
So we go back one step, and that will give us (0,12)
Therefore the initial value is 12.
Answer:
The answer is A, "Initial value: 12, rate of change: -2."
Step-by-step explanation:
I just completed the test and got it correct.
Julie and her brother go to Atlanta to ride the SkyView Ferris wheel. It measures 200 feet in diameter.
A)I want to know the distance around the Ferris Wheel. Would I use Circumference or Area?
B)What is the formula needed to solve this problem?Look in your notes!
C)What is the distance traveled in one rotation? Explain how you used the formula to solve the problem.
Answer:
628.32 feet
Step-by-step explanation:
The SkyView Ferris wheel is 200 feet in diameter.
A) The distance around the Ferris wheel would be the Circumference of
the Ferris Wheel.
B) The formula for circumference is given by
circumference = [tex]\pi[/tex] × diameter
C) the distance traveled in one rotation is the length of the circumference
given by circumference = [tex]\pi[/tex] × diameter
∴ circumference = 3.14159 × 200 feet = 628.32 feet.
A circle is cut from a square piece of cloth, as shown: width is 45
How many square inches of cloth would the circle create?
(π = 3.14)
Group of answer choices
1,808.64 in^2
192.00 in^2
1,152.00 in^2
150.72 in^2
The circle will create 1808.64 square inches.
Step-by-step explanation:
Given,
Width of square cloth = 48 inches
This will be the diameter of circle.
Therefore,
Diameter = 48 inches
Radius = [tex]\frac{Diameter}{2}=\frac{48}{2}=24\ inches\\[/tex]
Area of circle = πr²
Area of circle = [tex]3.14*(24)^2[/tex]
Area of circle = 3.14 * 576
Area of circle = 1808.64 square inches
The circle will create 1808.64 square inches.
Keywords: radius, circle
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Steve made 9 3/6 cups of pancake batter on a weekend camping trip. He used 3 4/6 cios of batter for breakfast on Saturday. Write each mixed number as a fraction greater than one.
Answer:
9 3/6 ⇒ 19/2
3 4/6 ⇒ 11/3
Step-by-step explanation:
A fraction greater than one is an improper fraction.
[tex]9\frac{3}{6}[/tex] when converted into an improper fraction is
[tex]9\frac{3}{6} =9+\frac{3}{6} \\\\=\frac{9*6}{6}+ \frac{3}{6}\\\\ =\frac{54}{6}+ \frac{3}{6}=\frac{57}{6}\\\\ =\boxed{\frac{19}{2}. }[/tex]
[tex]3\frac{4}{6}[/tex] when converted to a fraction is
[tex]3\frac{4}{6}=3+\frac{4}{6}\\\\=\frac{3*6}{6}+ \frac{4}{\\\\6}\\\\=\frac{18}{6}+\frac{4}{6}=\frac{22}{6}\\\\=\boxed{\frac{11}{3}. }[/tex]
Thus fractions [tex]9\frac{3}{6}[/tex] and [tex]3\frac{4}{6}[/tex] when converted to fractions greater than one are [tex]\frac{19}{2}[/tex] and [tex]\frac{11}{3}[/tex] respectively.
9 3/6 cups of pancake batter is [tex]\( \frac{19}{2} \)[/tex]and 3 4/6 cups is [tex]\( \frac{11}{3} \)[/tex].
Step 1:
Convert the mixed number 9 3/6 to an improper fraction:
[tex]\[ 9 \frac{3}{6} = \frac{(9 \times 6) + 3}{6} = \frac{54 + 3}{6} = \frac{57}{6} \][/tex]
Step 2:
Simplify the fraction:
[tex]\[ \frac{57}{6} = \frac{19 \times 3}{2 \times 3} = \frac{19}{2} \][/tex]
So, 9 3/6 cups of pancake batter is equivalent to the improper fraction [tex]\( \frac{19}{2} \).[/tex]
Step 3:
Now, convert the mixed number 3 4/6 to an improper fraction:
[tex]\[ 3 \frac{4}{6} = \frac{(3 \times 6) + 4}{6} = \frac{18 + 4}{6} = \frac{22}{6} \][/tex]
Step 4:
Simplify the fraction:
[tex]\[ \frac{22}{6} = \frac{11 \times 2}{3 \times 2} = \frac{11}{3} \][/tex]
So, 3 4/6 cups of pancake batter is equivalent to the improper fraction [tex]\( \frac{11}{3} \).[/tex]
Therefore, each mixed number, when expressed as a fraction greater than one, is [tex]\( \frac{19}{2} \)[/tex] and [tex]\( \frac{11}{3} \)[/tex], respectively.
solve 15x+20-10x-9=25x+8-21x-7
Answer:
X=-10
Step-by-step explanation:
Answer:
Step-by-step explanation:
15x+20-10x-9=25x+8-21x-7
5x + 11 = 4x + 1
Collecting like terms
5x - 4x = 1 - 11
x = -10
Solve the system of equations.
\begin{aligned} & -10y+9x = -9 \\\\ &10y+5x = -5 \end{aligned}
−10y+9x=−9
10y+5x=−5
Can I get the correct answer for this please.
Answer:
c
Step-by-step explanation:
Answer:
Y i hhad this question before but you need too show the questions as well
Step-by-step explanation:
What two numbers multiple to get -12 and add to -5
Original question: What two numbers multiply to get -12 and add to -5.
Answer:
Pairs of numbers (1.772, -6.772) and (-6.772, 1.772).
Step-by-step explanation:
Let [tex]x[/tex] and [tex]y[/tex] be the two numbers, the we know that
(1). [tex]xy=-12[/tex]
and
(2). [tex]x+y=-5[/tex]
We solve for [tex]y[/tex] in equation(2) and substitute this into equation(1)
[tex]y=-(5+x)[/tex]
[tex]xy=-x(x+5)=-12[/tex]
[tex]x^2+5x-12=0[/tex]
This is a quadratic equation, and its solutions are
[tex]x=1.772\\\\x=-6.772[/tex]
we substitute these two solutions into equation(1) and find the corresponding [tex]y[/tex] values:
[tex](1.772)y=-12\: \therefore y=-6.772[/tex]
[tex](-6.772)y=-12 \: \therefore y=1.772[/tex]
Thus we have two pairs of numbers which multiply to give -12 and add to give -5
[tex](1.772, -6.772)[/tex] and [tex](-6.772, 1.772).[/tex]