Answer:
The result of [tex]\tt{}3 \sqrt{5} - 2 \sqrt{7} + \sqrt{45} - \sqrt{28} [/tex] is [tex]\tt{}6\sqrt{ 5} - 4 \sqrt{7}. [/tex]
Step-by-step explanation:
[tex]\tt{}3 \sqrt{5} - 2 \sqrt{7} + \sqrt{45} - \sqrt{28} [/tex]
[tex]\tt{}3 \sqrt{5} - 2 \sqrt{7} + 3\sqrt{5} -2 \sqrt{7}[/tex]
[tex]\tt{}6\sqrt{5} - 4 \sqrt{7}[/tex]
what is the slope to the perpendicular line to y=7/8x-9
Select the correct answer. The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation: 2n + 1 = 157. What is the first number?
Answer:
78
Step-by-step explanation:
2n + 1 = 157
2n = 157 - 1
2n = 156
n = 156 ÷ 2
n = 78
What is the density for an unknown liquid with a mass of 6 grams and a volume of 12 mL?.
1) Considering that
[tex]undefined[/tex]Sara, Jenna, and Julia are going on a trip and want to combine their income over the next few months to pay for it. Jenna and Julia both make $450 per week and Sara makes $750 per week. Jenna and Julia also receive a $100 bonus from their bosses. Which expression represents how much money all three women make together, given they work the same number of weeks?
The expression which represents how much money all three women make together, given they work the same number of weeks is (1,650w + 200)
Algebraic expressionNumber of weeks = wAmount Jenna make per week = $450Amount Julia make per week = $450Bonus Jenna receives = $100Bonus Julia receives = $100Amount Sara makes per week = $750Total mount Jenna makes = 450w + 100Total mount Julia makes = 450w + 100Total mount Sara makes = 750wTotal amount all three women make together = (450w + 100) + (450w + 100) + (750w)
= 450w + 100 + 450w + 100 + 750w
= 1,650w + 200
So therefore, the total amount made by the three women is given by the expression 1,650w + 200
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Is this graph a function?
Answer:
It is a function
Step-by-step explanation:
To know whether a graph is a function or not we practice vertical line test.
If the vertical line drawed touches the graph only at one point then we can confirm it's a function.
Solve p3 = −512.
answers are
p = ±8
p = −8
p = ±23
p = −23
Option b) p = -8 is correct, when p³ = 518.
Define cube root.A integer y such that y3 = x is known as the cube root of a number x in mathematics. All nonzero complex numbers have three different complex cube roots, while all nonzero real numbers have exactly one real cube root and two complex conjugate cube roots. We are aware that adding three times to any number yields the cube of that number. Additionally, the inverse action of cubing a number is known as the cube root of a number. For instance, 63 has a cube value of 216. In that case, 216's cube root is equal to 6.
Given,
Equation
p³ = -518
Multiplying cube root each side
p = -∛518
p = -8
Option b) p = -8 is correct, when p³ = 518.
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The hypotenuse of a right-angled triangle is 1 cm longer than twice the shorter side and is 2 cm longer than the other side.
Find the perimeter of the triangle.
Answer:
The perimeter is 40 cmStep-by-step explanation:
Let the sides be:
Hypotenuse = a,Short leg = b,Long leg = c.According to question are given:
a = 2b + 1 ⇒ b = (a - 1)/2,a = c + 2 ⇒ c = a - 2.Use Pythagorean to find the length of hypotenuse:
a² = b² + c²a² = [(a - 1)/2]² + (a - 2)²a² = (a² - 2a + 1)/4 + a² - 4a + 40 = (a² - 2a + 1)/4 - 4a + 4a² - 2a + 1 - 16a + 16 = 0a² - 18a + 17 = 0a² - a - 17a + 17 = 0a(a - 1) - 17(a - 1) = 0(a - 1)(a - 17) = 0a - 1 = 0 and a - 17 = 0a = 1 and a = 17The first option is discarded, as all sides should be positive. With a = 1 we get negative value for c.
So a = 17 cm.
Find the other sides:
b = (17 - 1)/2 = 8 cmc = 17 - 2 = 15 cmFind the perimeter:
P = a + b + c = 17 + 8 + 15 = 40 cmAnswer:
40 cm
Step-by-step explanation:
Pythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right triangle.c is the hypotenuse of the right triangle.Let a be the shorter leg.
If the hypotenuse is 1 cm longer than twice the shorter side then:
[tex]\implies c = 2a + 1[/tex]
If the hypotenuse is 2 cm longer than the other side then:
[tex]\implies c = b + 2[/tex]
Equate the two expressions for c and solve for b:
[tex]\implies b+2=2a+1[/tex]
[tex]\implies b=2a-1[/tex]
Substitute the expression for c involving a, and the expression for b involving a, into Pythagoras Theorem and solve for a:
[tex]\implies a^2+(2a-1)^2=(2a+1)^2[/tex]
[tex]\implies a^2+4a^2-4a+1=4a^2+4a+1[/tex]
[tex]\implies a^2-4a=4a[/tex]
[tex]\implies a^2-8a=0[/tex]
[tex]\implies a(a-8)=0[/tex]
[tex]\implies a=0, \quad a=8[/tex]
Since the length of a side cannot be zero, a = 8.
The perimeter of a two-dimensional shape is the distance around the outside. Therefore, the perimeter of the triangle is the sum of its sides:
[tex]\begin{aligned} \implies \textsf{Perimeter}&=a+b+c\\&=a+(2a-1)+(2a+1)\\&=5a\end{aligned}[/tex]
Substitute the found value of a into the expression for the perimeter:
[tex]\begin{aligned} \implies \textsf{Perimeter}&=5(8)\\&=40\sf \; cm\end{aligned}[/tex]
Therefore, the perimeter of the triangle is 40 cm.
What is the quotient of 1.232 x 10⁸ and 3.85 x 10 expressed in scientific notation?
Answer:
3.2 x 10⁶
Explanation:
Given the quotient:
[tex]\frac{1.232\times10^8}{3.85\times10}[/tex]We can rewrite the expression by removing the decimals as follows:
[tex]=\frac{1232\times10^{-3}\times10^8}{385\times10^{-2}\times10}[/tex]Next, we rewrite the powers of 10 so we can cancel out common terms.
[tex]\begin{gathered} =\frac{1232}{385}\times\frac{(10^{-2}\times10^{-1})\times(10\times10^7)}{10^{-2}\times10} \\ \frac{1232}{385}\times10^{-1}\times10^7 \end{gathered}[/tex]Next, express the first fraction in the lowest possible form:
[tex]\begin{gathered} =\frac{16\times77}{5\times77}\times10^{-1}\times10^7 \\ =\frac{16}{5}\times10^{-1}\times10^7 \\ =3.2\times10^{-1+7} \\ =3.2\times10^6 \end{gathered}[/tex]The quotient expressed in scientific notation is 3.2 x 10⁶.
interior and exterior triangle angles
Answer:
∠ GHI = 17°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ HIJ is an exterior angle of the triangle , then
∠ HJI = ∠ GHI + ∠ IGH , that is
7x - 18 = 2x - 3 + 2x + 15
7x - 18 = 4x + 12 ( subtract 4x from both sides )
3x - 18 = 12 ( add 18 to both sides )
3x = 30 ( divide both sides by 3 )
x = 10
Then
∠ GHI = 2x - 3 = 2(10) - 3 = 20 - 3 = 17°
What is the graph of 5y- 15x =30
A graph of this linear function (y = 3x + 6) is shown in the image attached below.
What is a graph?A graph can be defined as a type of chart that is commonly used for the graphical representation of data on both the horizontal line (x-axis) and vertical line (y-axis) of a cartesian coordinate.
Next, we would simplify the given linear function by dividing all through by 5 as follows:
5y - 15x = 30
5y/5 - 15x/5 = 30/5
y - 3x = 6
Rearranging the linear function, we have:
y = 3x + 6
In this context, we can reasonably and logically deduce that only the graph of a proportional relationship such as a linear function is always characterized by a straight line with all of the data points passing through the origin (0, 0).
In conclusion, a graph which represents the given linear function does not show a proportional relationship between the value of x and y.
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17/20= t + ( - 13/20) t = ?
Answer:
t = 3/2
Step-by-step explanation:
You want to know the value of t that satisfies 17/20= t + ( - 13/20).
SolutionAdd 13/20 to both sides of the equation.
17/20 +13/20 = t -13/20 +13/20
30/20 = t . . . . . simplify
3/2 = t . . . . . . . reduce the fraction
The solution is t = 3/2.
Hello! I need some assistance with this homework question, pleaseQ7
You have the following function:
[tex]f(x)=x^2+8[/tex]In order to calculate
[tex]\frac{f(x+h)-f(x)}{h}[/tex]Consider that f(x + h) is given by:
[tex]f(x+h)=(x+h)^2+8=x^2+2xh+h^2[/tex]Then, by replacing f(x) and f(x+h) into the difference quotient and by simplifying, you get:
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{x^2+2xh+h^2+8-x^2-8}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{2xh+h^2}{h}=\frac{h(2x+h)}{h}=2x+h \end{gathered}[/tex]Hence, the result to the quotient difference is 2x + h
Please help asap it's going to go overdue if I don't get an answer ):
use the data in attend for this exercise. (i) in the model of example 6.3, argue that dstndfnl/dprigpa < b2 1 2b4 prigpa 1 b6atndrte. use equation (6.19) to estimate the partial effect when prigpa 5 2.59 and atndrte 5 82. interpret your estimate
These are the coefficients of x1 and x2 respectively, and helps us to know the the significance of the independent variable in predicting the independent variable.
We are given the following information:
The estimate regression equation for a model involving two independent variables and 10 observations follows:
y= 29.1270+0.5906x1+0.4980x2
where x1 and x2 are the two independent variable and y is the dependent variable.
a) The regression line is of the form:
y=b0+b1 x1+b2 x2
where b0 is the y intercept and b1 , b2 are the coefficients of x1 and x2
Comparing, we get,
b1 = 0.5906
b2= 0.4980
These are the coefficients of x1 and x2 respectively, and helps us to know the the significance of the independent variable in predicting the independent variable.
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HURRY- WILL GIVE B-RAINLIEST! 30 POINTS!
Selina had been renting for six months when there was a flood. The total cost to replace her damaged belongings was $1,760.00. What percent would Selina have saved if she had a renters' insurance policy at a monthly cost of $19.00? Round to the nearest tenth. (2 points)
10.7%
14.4%
89.2%
93.5%
The percent Selina would have saved if she had a renters' insurance policy at a monthly cost of $19.00 is 93. 5%
What is percentage?A percentage can be defined as a ratio or number that is expressed as a fraction of 100.
It is represented with the symbol "%"
Based on the information given, we have that;
The total cost to replace her damaged belongings was $1,760.00She's renting for six monthsTo determine the percent she saved for an insurance policy at a monthly cost of $19.00
We take the following steps;
Total cost - 6(insurance policy)/total cost × 100/1
Substitute the values
$1760 - 6(19.00)/1760 × 100/1
Subtract the numerators
1646/1760 × 100/1
Find the quotient
0. 935 × 100/1
Multiply through
93. 5%
Hence, the value is 93. 5%
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Find each missing measure
10−(−9) exponent 2 for the nine in parentheses
Well, I hope this helps.
10-(9²) = 91
Help me! The average car on the highway can go 240 miles in 4 hours.
At this rate, how long would it take the average car to drive 1,200 miles?
A. 2 hours
B.20 hours
C. 200 hours
D. 2,000 hours
An orca is swimming at the surface of the water and dives below the surface 25.5 feet. Then the orca swims up 1214feet. What is the location of the orca relative to the surface of the water?
i
If an orca is swimming at the surface of the water and dives below the surface 25.5 feet. Then the orca swims up [tex]12\frac{1}{4}[/tex] , then the location of the orca relative to the surface of the water is 13.25 feet below the surface of water
The depth he dives below the surface = 25.5 feet
The the orca swims up [tex]12\frac{1}{4}[/tex] feet
Convert the mixed fraction to simple fraction
[tex]12\frac{1}{4}[/tex] feet = 49/4 feet
Convert the simple fraction to the decimal number
49/4 feet = 12.25 feet
The distance orca dives below will consider as negative and the distance swims up will considered as positive
Then the position of orca = -25.5+12.25
= -13.25
Hence, if an orca is swimming at the surface of the water and dives below the surface 25.5 feet. Then the orca swims up [tex]12\frac{1}{4}[/tex] , then the location of the orca relative to the surface of the water is 13.25 feet below the surface of water
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Write an equation of the line that passes through the pair of points (-4,-6) (5,-6)
The equation of the line passing through (-4,-6), (5,-6) will be y = -6
In the given question, it is stated that the line passes through points (-4,-6), and (5,-6). We need to find out an equation of the line that satisfies the given condition.
Firstly, we will need to find out the slope of the line. We can find the slope by using the point-slope form which is represented by:
=> [tex]m = \frac{y_{2}-y_{1} }{x_{2} - x_{1} }[/tex]
Putting values (x₁, y₁) = (-4,-6) and (x₂, y₂) = (5,-6) we get:
=> [tex]m = \frac{-6+ 6 }{5+ 4 }[/tex]
=> m = 0
We get slope m = 0. Now, putting the value of slope into the point-slope form and taking (x₁, y₁) = (-4,-6), we get values:
=> y - y₁ = m(x - x₁)
=> y + 6 = 0(x + 4)
=> y = -6
Hence, we get the equation of line y = -6
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Driver A and B have two different routes. Driver A's route is 80km, and driver B's route is 100km. Driver B travels 10km/h faster than driver A and finishes 10 minutes earlier. What are the speeds of each driver?
Speed of Driver A is 30 km/h.
Speed of Driver B is 40 km/h
Define speed.The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
Given Data
Driver A and B have two different routes. Driver A's route is 80km, and driver B's route is 100km. Driver B travels 10km/h faster than driver A and finishes 10 minutes earlier.
Distance = Speed (Time)
Distance for Driver A: 80 kilometers
Consider Driver A's speed to be A km/h.
Driver A's time was [tex]\frac{80}{A}[/tex] hours.
Distance for Driver B is 100 kilometers
Speed of Driver B: A + 10 km/h
Driver B's time was equal to 100/(A + 10) hours.
Arrived 10 minutes early, or [tex]\frac{10}{60}[/tex], or [tex]\frac{1}{6}[/tex]hour.
100/(A + 10) = [tex]\frac{80}{A}[/tex] - [tex]\frac{1}{6}[/tex]
600A = 480(A + 10) - A(A + 10)
600A = 480A + 4800 - A² - 10A
A² +130A - 4800 = 0
A² + 160A - 30A - 4800 = 0
A(A + 160) - 30(A + 160) = 0
(A - 30)(A + 160) = 0
A = 30 since speed cannot be negative.
Speed of Driver A is 30 km/h.
Speed of Driver B: 40 km/h
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2x7(2•2)^2 14-9
what is the answer
Answer:
3127Step-by-step explanation:
2x7(2•2)^2 14-9
what is the answer
2*7(2*2)^2 14-9 = (remember PEMDAS)
2*7*16*14-9=
14 * 16 * 14 -9=
224*14 -9=
3136 -9=
3127
in the computer game world of warcraft, some of the strikes are critical strikes, which do more damage. assume that the probability of a critical strike is the same for every attack, and that attacks are independent. during a particular fight, a character has 243 critical strikes out of 534 attacks.
Answer: whats the question?
Step-by-step explanation:
In a sale, normal prices are reduced by 10%.
David bought a pair of trainers in the sale for £36.
What was the original price of the trainers?
In a sale, if the normal prices are reduced by 10% and David bought a pair of trainers in the sale for £36 then the marked price of these trainers was £40.
What is original price?Original price is said to be as the price that was fixed by the MSRP (i.e said to be the Manufacturer’s Suggested Retail Price).
In most of the case scenario, the original price would taken to be as always lower than the current price and then also in some other cases, original price and current price can be taken as the same.
How do you calculate the original price?First you have to convert the total percent discount to a decimal by dividing by 100% . Step 2: Set up the equation P=(1−d)x P = ( 1 – d ) x to find the original price of the item where P is the sale price, d is the discount as a decimal, and x is the original price of the item.
The selling price, may be that of a product or a service, is said to be as the customer or client’s final price
How do you find the original price from a discounted price calculator?To calculate the exact original price of a selected item, you have to divide the sale price by the value of 1 minus the entire value of the percentage off and then divided by 100.
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You are flying in an airplane on vacation. You have been told that there are
less molecules in a cubic meter of air the higher in altitude you go.
a. There are 1025 molecules in a cubic meter of air at sea level and 1023
molecules at an altitude of 33 km. How many more molecules are there at
sea level?
b. How many more molecules would there be if you went to an altitude of 50 km
where there are 1020 molecules?
2 more molecules are there at sea level compared to at an altitude of 33Km and 5 more molecules are there at sea level compared to at an altitude of 50Km.
We have been told that there are less molecules in a cubic meter of air the higher in altitude we will go.
Part : A
Number of molecules at sea level = 1025 molecules
Number of molecules at an altitude of 33 km = 1023 molecules
Difference between number of molecules at sea level and number of molecules at an altitude of 33 km = 1025 - 1023 = 2 molecules
Part : B
Number of molecules at sea level = 1025 molecules
Number of molecules at an altitude of 50 km = 1020 molecules
Difference between number of molecules at sea level and number of molecules at an altitude of 50 km = 1025 - 1020 = 5 molecules.
So, we can conclude that 2 molecules are more at sea level compared to at an altitude of 33Km and 5 molecules are more at sea level compared to at an altitude of 50Km.
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the area A of a rectangle is represented by the formula A=lw where l is the length and w is the width. write an equation that makes it easy to find the width of the rectangle if we know the area and the length
Answer:
See below
Step-by-step explanation:
A = l w looking for w...... divide both sides of the equation by ' l '
A/l = w Done.
Cole drove from Los Angeles to San Francisco to visit friends.
Cole drove the speed limit which was 70 miles/hour. If Cole's
driving time for the trip was 6 hours, how many miles did Cole
drive?
Answer:
420 miles
Step-by-step explanation:
GivensWe are given that Cole drove a distance at a speed of 70 miles/hour. We are also shown that the driving time was 6 hours.
We are asked to find how many miles Cole drove.
SolveRealize that since the speed is constant, it can be multiplied by the driving time to find the mileage.
Therefore, multiply the speed limit by the driving time:
[tex]\text{70 miles/hour} \times \text{6 hours} = \text{420 miles}[/tex]
Final AnswerTherefore, Cole drove 420 miles.
Answer:
420 miles
Step-by-step explanation:
Is known:
70 miles / hour
Question:
how many miles will it cover in 6 hours?
70mil/jam × 6 hour
= 420 miles
StudyForEducation.
If
F(x)=3x-2
and
G(x)=x−5
, what is
F(x)⋅g(x)
The composite function f(x). g(x) is represented as 3x² - 17x + 10
How to find composite function?The composite function can be solved as follows:
f(x) = 3x - 2
g(x) = x - 5
Therefore, the composite function f(x). g(x) is as follows:
f(x). g(x) = f(x) × g(x)
Hence,
f(x) × g(x) = (3x - 2)(x - 5)
f(x) × g(x) = 3x² - 15x - 2x + 10
f(x) × g(x) = 3x² - 17x + 10
Therefore, the function f(x) × g(x) = 3x² - 17x + 10
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i need help please its kinda difficult for me tbh
The equation that would represent the gold medals won by the United States is 1 + 4F = 7 + F.
The gold medals won by France is 2.
The gold medals won by the United State is 9.
How many gold medals were won by each country?The equation that would represent the gold medals won by the United States would be a linear function. A linear function is a function that has a single variable that is raised to the power of one. A linear equation is a straight line that slopes either upward or downward when drawn on a coordinate plane.
The equation that represents the gold medals won by the United States is:
1 + ( 4 x F) = 7 + F
1 + 4F = 7 + F
In order to determine the value of F, take the following steps:
Combine similar terms together: 4F - F = 7 - 1
Add similar terms: 3F = 6
Divide both sides of the equation by 3 : F = 6 / 3
F = 2
The gold medals won by the United states
7 + 2 = 9
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Picture kansnaiks snaijskxkxkks
Answer:
I said right foot creep looking in that heat make sure it stay low make sure they don't see the devil under your feet your on the way to see em
this question don't make sense