Answer:
ITS C: Multiplying by 15 is the same as multiplying by 20%
Step-by-step explanation:
The solution is Option C.
The equation of multiplying by 1/5 is the same as multiplying by 20%
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Cara has driven one-fifth of the total distance, d, to her destination
So , the distance traveled by Cara S = ( 1/5 )d
And , the distance traveled by Cara S = 0.2d
On simplifying the equation , we get
The value of ( 1/5 )d = d/5
The value of 0.2d = ( 20/100 )d
The value of 0.2d = 20 % of d
Therefore , the value of ( 1/5 )d = value of 0.2d
Hence , the equations are same
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The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 2 multiplied by 1.5 to the power of x. The straight line f of x joins ordered pairs 3, 1 and 2, minus 1 and is extended on both sides. The straight line p of x joins the ordered pairs 1, 3 and 3, 1 and is extended on both sides. Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points) Part B: Write any two solutions for f(x). (3 points) Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)
A) (3, 1)
B) (3, 1), (2, -1)
C) (1, 3)
Step-by-step explanation:A) The problem statement tells you the point (3, 1) is on both lines.
B) The problem statement tells you the line goes through points ...
... (3, 1) and (2, -1).
C) The problem statement tells you point (1, 3) is a solution to p(x). It also happens that g(1) = 2·1.5¹ = 3, so (1, 3) is also a solution to g(x).
(1, 3) is a solution to p(x) = g(x) because p(1) = 3 = g(1).
What is the fraction in decimal form?
21/6
Enter your answer in the box
Answer: Your answer would come out to be 3.5
Step-by-step explanation: it would be 3.5 due to the fact that you have to break these numbers down to the smallest one possible meaning simplify which would result in this equation 7 over 2
7 over 2 = 3 1 over 2 this equals 3.5
please help!!!
A,B,C and D are four towns.
B is 30km due East of A
C is 30km due North of A
D is 45km due South of A
calculate the bearing of D from B
Answer:
213.7°
Step-by-step explanation:
The bearing of B from D is angle ADB, which is ...
... ∠ADB = arctan(30/45) ≈ 33.7°
The bearing of D from B is that angle plus 180°, so is ...
... 180° +33.7° = 213.7°
_____
We use angle ADB because the reference direction for bearings is North.
The tangent of an angle (ADB) is the ratio of its opposite side (AB) to its adjacent side (AD).
Which chart shows that the price of a slice of sausage pizza is greater than the price of a slice of mushroom pizza?
The formula for the area A of a trapezoid is A=1/2(b1+b2)h, where b1 and b2 represents the lengths of the bases and h represents the height. Which equation can be used to find the height of a trapezoid?
A. h=2A-b1-b2
B. h=2A/b1+b2
C. h=A(b1+b2)/2
D. h=A-2/b1-b2
Answer:
B. h=2A/(b1+b2) . . . . parentheses are needed
Step-by-step explanation:
Multiply the equation by the inverse of the coefficient of h. That coefficient is (b1 +b2)/2, so its inverse is 2/(b1 +b2). Parentheses are needed.
... 2A/(b1 +b2) = h
_____
Comment on the answer choices
As written, none of them are correct. The denominator can only be written without parentheses if the division bar is horizontal, and so serves also as a grouping symbol.
On Sunday, a local hamburger shop sold a combined total of 405 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Sunday?
Answer:
135
Step-by-step explanation:
1 of every 1+2 = 3 items sold was a hamburger.
# of hamburgers = (1/3)·405 = 135
To solve the problem, we first create and solve an algebraic equation. The equation shows that the hamburger shop sold 135 hamburgers on Sunday.
Explanation:The given problem is a classic example of algebraic equations. We know that the total number of hamburgers and cheeseburgers sold was 405. And we know that the number of cheeseburgers sold was two times the number of hamburgers. Let's denote the number of hamburgers sold as H, and the number of cheeseburgers as C. From the information provided, we have two equations:
C = 2HH + C = 405Now, we can substitute the first equation into the second, replacing C with 2H:
H + 2H = 405This simplifies to:
3H = 405Finally, to find H, we divide both sides of this equation by 3:
H = 405 / 3Therefore, 135 hamburgers were sold on Sunday.
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lauren decided to see how many jumping jakes she could do in 10 seconds. She told her mom that she could do 20. she was acually able to complete 15 jumping jacks when the timer went off. what was her percent error.
Answer:
Her error was overestimating by 33.3%
Step-by-step explanation:
To calculate a relative error (or percent error), we need to identify the absolute error first. In this case, the absolute error is the difference between Lauren's estimate and the actual outcome: 15 jacks - 20 estimated jacks = -5. The fact that this error is negative is only to indicate that Lauren overestimated (as opposed to underestimated). Usually, the absolute value is taken.
As next step, the absolute error is made to a relative one by dividing by the ground truth, which is the actual outcome of 15 jumping jacks. The relative error = |-5|/15 = 1/3. Expressed in percent: 33.3%. Lauren made an error of 33.3% (overestimate).
please hurry thank you
Answer:
7.9 ft
Step-by-step explanation:
The hypotenuse is the side opposite of the right angle, hence the hypotenuse for this triangle is 11 ft.
Side [tex]x[/tex] is adjacent to the angle given. So we need adjacent and we have hypotenuse. Which trigonometric ratio relates adjacent and hypotenuse? It is COSINE.
Thus, we can write:
[tex]cos(A)=\frac{adjacent}{hypotenuse}\\cos(44)=\frac{x}{11}[/tex]
Cross multiplying, we can solve for [tex]x[/tex]:
[tex]cos(44)=\frac{x}{11}\\x=cos(44)*11\\x=7.91[/tex]
Rounding to nearest tenth, we have [tex]x=7.9[/tex] ft.
Camacho is buying a monster truck. The price of the truck is xx dollars, and he also has to pay a 13\%13% monster truck tax.
how much Camacho pays in total for the truck?
Answer:
[tex]1.13x[/tex]
Step-by-step explanation:
We have been given that Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13% monster truck tax. We are asked to find the total amount paid by Camacho for the monster truck.
The total cost of monster truck would be x plus 13% of x.
[tex]\text{The total cost of monster truck}=x+\frac{13}{100}x[/tex]
[tex]\text{The total cost of monster truck}=x+0.13x[/tex]
[tex]\text{The total cost of monster truck}=1.13x[/tex]
Therefore, Camacho paid [tex]1.13x[/tex] dollars in total for the truck.
Final answer:
To find the total cost of the monster truck, convert the 13\% tax to decimal form (0.13), multiply it by the price of the truck (xx dollars), then add the result to the original price to get the total cost, which is 1.13xx.
Explanation:
To determine the total amount Camacho will pay for the monster truck, we need to calculate the sales tax and add it to the original price of the truck. The sales tax is 13\%, which can be converted to a decimal for calculation purposes. First, convert 13\% to a decimal by dividing by 100, which gives us 0.13. Then multiply 0.13 by the price of the truck (xx dollars) to find the amount of tax Camacho will have to pay.
After calculating the tax, you can find the total cost by adding the tax to the original price of the truck.
Step 1: Convert 13\% to a decimal = 0.13
Step 2: Multiply the price of the truck (xx dollars) by 0.13 to find the tax = 0.13 * xx
Step 3: Add the tax to the original price to find the total cost: xx + (0.13 * xx).
Total cost = xx + 0.13xx = 1.13xx
If m ABC is 53 degrees then m EDF is ?
Answer:
74°
Step-by-step explanation:
The triangle is isosceles and the congruent base angles are 53°. The sum of angles in a triangle is 180°, so the apex angle (∠EDF) will be ...
... 180° - 2×53° = 74°
Answer:
74* is the answer
Step-by-step explanation:
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The lunch platter at one restaurant cost $7. Write an equation that shows the total cost, c, of p people buying the lunch platter?
I’m am not sure how to factor the variables into the equation.
Answer:
c = 7p
Step-by-step explanation:
If 1 person buys the platter, the bill is c = 1 × $7.
If 2 people buy the platter, the bill is c = 2 × $7.
If 3 people buy the platter, the bill is c = 3 × $7.
(Do you see the pattern yet?)
If "p" people buy the platter, the bill is c = p × $7.
We ususally say "c is in dollars" and drop the "$" sign from the equation. When p is multiplied by 7, we conventionally write it as 7p.
... c = 7p
Suppose a fair six-sided is rolled three times in a row. The probability of rolling a number less than 3 three times in a row is __________ . Express the probability as a fraction.
Answer:
1/27
Step-by-step explanation:
The probabaility of rolling a number less than 3 is 2/6 = 1/3, since only two of the six numbers are less than 3.
Assuming the die rolls are independent, the probability of doing this 3 times is the product of the probabilities of doing it each time:
... (1/3)^3 = 1/27
(2.)are NOT opposite reciprocals
(1.)are NOT equal
(2.) are NOT opposite reciprocals
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The slope of AB is ...
... slope = (change in y)/(change in x) = (-6-(-3))/(8-2) = -3/6 = -1/2
The slope of AD is ...
... slope = (change in y)/(change in x) = (0 -(-3))/(8 -2) = 3/6 = 1/2
We note that the differences have the same magnitudes in both cases (y changes by 6; x changes by 3). This tells us the line segments are the same length. (Each side of the figure is equivalent to the hypotenuse of a right triangle with legs 3 and 6.)
The opposite reciprocal of a number is found by dividing -1 by that number. Thus the opposite reciprocal of the slope of AB is ...
... -1/(-1/2) = (-1/1)·(-2/1) = 2
This value is not the same as the slope of AD, so the slopes are NOT opposite reciprocals.
_____
Plotting the points, we see that we have a rhombus, not a rectangle (or square).
After all of the start-up costs, a company starts with $100 and makes $0.75 on each unit sold. Write a linear equation in slope-intercept form that models this situation using p for profit and n for number of units sold.
Answer:
y=.75x+100
Step-by-step explanation:
y=mx+b
m=slope (rate)
b=y-intercept (starting point)
y=.75x+100
The linear equation that models this situation, using 'p' for profit and 'n' for number of units sold, is p = 0.75n + 100.
Explanation:The situation described is one of a linear relationship between the number of units sold (n) and the profit (p). In this case, we are given the initial profit (the y-intercept) of $100 (a = 100) and the profit per unit sold (the slope) of $0.75 (b = 0.75). Therefore, the linear equation modeling this situation in slope-intercept form would be p = 0.75n + 100.
In this equation, n represents the number of units sold and p represents the profit. For every unit sold (increase in n by 1), the profit (p) increases by $0.75. The $100 represents the initial profit, or the starting point of sales, which in this case is after covering the start-up costs.
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please help me asap!
please help me asap!
7. Law of cosines
a² = b² + c² - 2bc cos A
where a is the side opposite to ∠A and b and c are adjacent sides to ∠A.
Here, a=BC= 3.8
b=CA =4.8
c = AB = 3.2
Substituting the values in the formula,
3.8² = 4.8² + 3.2² - 2(4.8)(3.2) cos A
30.72 cos A =23.04 + 10.24 -14.44=18.84
cos A = 18.84/30.72 = 0.6133
∴ cos A =0.6133
8. It is a right angled triangle.
Pythagoras theorem
hypotenuse² = Perpendicular² + base²
Here, hypotenuse = 6.7, base = 5.4
Perpendicular² = 6.7² -5.4²=44.89 - 29.16 =15.73
Perpendicular = √15.73 = 3.966 = 3.97
∴ The length of the missing side is 3.97.
9. Given: Side of new cube = 5 * Side of original cube
Let the side of the original cube measure 1 unit.
So, volume of original cube = side³ = 1
The side of new cube = 5 * 1 =5 units
So, volume of new cube = side³ = 5³ =125
The volume of the bigger cube is 125 times larger than the original cube.
10. Given : Height of the cone = 7 in
Radius of the base of the cone = 2 in
Volume of cone = (1/3) πr²h
=(1/3)π(2²)(7)
=29.32 cubic inches
∴ Volume of the cone is 29.32 cubic inches.
11. The given equation is:
x² -18x +10 =0
(x² -18x + 9²) +10 -9² =0
(x-9)²-71 =0
(x-9)² =71
x-9 =√71
x = 9 + √71
∴ x = 9+√71
The sum of the measures of the angles shown is 63° . Which choice is the measure of angle y ?
Answer:
63
Step-by-step explanation:
Answer:
25 degrees.
Step-by-step If one of the angles is 38 degrees then in order for the sum to be 63, the answer is 25
Write and solve a polynomial equation for the situation described.
A rectangular two-story horse barn is
being designed for a farm. The upper floor will be used
for storing hay, and the lower floor will have horse stalls
that extend 5 feet from both of the longer walls. The barn’s
length is twice the barn’s width, and the lower floor’s
ceiling height is 6 feet less than the barn’s width. What
should the dimensions of the lower floor be if the space
not used for stalls is to have a volume of 1920 cubic feet?
We can let x represent the width of the barn in feet. Then the length of the barn is 2x. The portion of width not used for stalls is (x-10). The height of that is (x-6).
So, the product of length, width not used for stalls, and height must be 1920 ft³. The equation for that is ...
... 2x(x -10)(x -6) = 1920 . . . . the equation
Solution
I generally find it convenient to use a graphing calculator to find the solutions to higher-order equations. Rearranging this so we're looking for a zero, it becomes ...
... 2x(x -10)(x -6) -1920 = 0
The graph shows one real root, at x = 16.
The dimensions of the lower floor should be 16 feet wide, 32 feet long, and a ceiling height of 10 feet.
_____
Alternate solution
Dividing by 2, we have
... x(x-6)(x-10) = 960
If we look at the factors of 960, we find that it is the product of 16, 10, and 6, which would let us assign x=16.
___
There are 28 divisors of 960. According to the Rational Root theorem, any of them might be a solution. There are arguments that can be made regarding reasonable dimensions that suggest x will be more than 12 (6 ft ceiling, 2 ft aisle). So, the number of trial-and-error possibilities is reduced somewhat.
The dimensions of the lower barn floor should be a width of 8 feet, a length of 16 feet, and a height of 2 feet, determined by setting up and solving a polynomial equation based on the given parameters.
Explanation:The problem can be solved using polynomial equations. First, let's denote the width of the lower barn floor as x. Given that the length of the barn is twice the width, the length is 2x. The height of the lower barn floor is 6 feet less than the width of the barn, so it's x - 6 feet.
The volume of a rectangular solid is given by length times width times height. So according to the information provided, we can set up the following polynomial equation: 2x * x * (x - 6) = 1920.
By simplifying the equation, we get 2x^3 - 12x^2 - 1920 = 0.
This equation can be solved using various methods such as the rational root theorem, synthetic division, or factoring. After solving, we find that the root x = 8 is the only physically meaningful solution (length width and height must be positive). Therefore, the width of the lower floor should be 8 feet, the length should be 2 * 8 = 16 feet, and the height should be 8 - 6 = 2 feet.
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1/3(y+7)=(y-1) y= what?
Answer:
y=5
Step-by-step explanation:
1/3(y+7)=(y-1)
I will multiply by 3 on each side to get rid of the fractions
3*1/3(y+7)=(y-1)*3
y+7 = 3*(y-1)
Distribute the 3
y+7 = 3y -3
Subtract y from each side
y-y+7 = 3y-y-3
7 = 2y-3
Add 3 to each side
7+3 = 2y-3+3
10=2y
Divide each side by 2
10/2 = 2y/2
5 =y
I need help fast if you can PLEASE HELP
Answer:
333°
Step-by-step explanation:
Minor arc ST is the difference between minor arc RT and minor arc RS:
... 153° -126° = 27°
Major arc SPT is the remainder of the circle:
... 360° -27° = 333°
Please help if you can
Step-by-step explanation:
sqrt of 81 is 9 so rational
Sqrt of 89 is irrational
Sqrt of 121 is 11 so rational
Sqrt of 131 is irrational.
Given the following figure, what is the measure of angle B?
Answer:
132°
Step-by-step explanation:
Sum of the interior angles of a polygon is given by the formula:
[tex](n-2)*180[/tex]
Where [tex]n[/tex] is the number of sides of the polygon.
The figure shows a 5 sided polygon (aka Pentagon). So the sum of all the angles is:
Sum = [tex](5-2)*180\\=3*180\\=540[/tex]
If we add up all the expressions/angles given and equate to 540, we can figure out [tex]x[/tex]. So:
[tex]84+13x+6+9x-16+92+12x=540\\34x+166=540\\34x=540-166\\34x=374\\x=\frac{374}{34}=11[/tex]
But angle B measures [tex]12x[/tex], so plugging in [tex]x=11[/tex], we have:
Angle B = [tex]12x=12(11)=132[/tex]°
Second answer is right.
Ben has $5. In order to have money for a new tablet computer, Ben is going to sell his collection of stamps for $3 per stamp. Ben has decided to graph a line showing the relationship between the number of stamps he sells and the total amount of money he has. Which will be the y-intercept of Ben's graph?
Answer:
5
Step-by-step explanation:
It is 5 because no matter how many stamps he sells, he has $5.
Answer:
The y-intercept of Ben's graph is [tex]y = 5[/tex].
Step-by-step explanation:
The function for Ben's amount of money y, depending on the number of stamps sold x, is as follows:
[tex]y = ax + b[/tex]
In which a is the price of each stamp and b is his initial money.
Building the function:
Ben has $5. This means that if he sells no stamps, he is still going to have $5. So [tex]b = 5[/tex].
For each stamp sold, he gains $3. So if sells 1 stamp, he will have $8, if he sells 2, he will have $11. So [tex]a = 3[/tex].
The function is:
[tex]y = 3x + 5[/tex]
Which will be the y-intercept of Ben's graph?
This is the value of y when x = 0.
So
[tex]y = 3*0 + 5 = 5[/tex]
The y-intercept of Ben's graph is [tex]y = 5[/tex].
Colin bought a Nissan Sentra that's 3¾ times as expensive as the car his parents bought. If his parents paid $8,000 for theirs, what's the cost of Colin's car?
A. $30,000
B. $28,000
C. $26,000
D. $29,000
A. $30,000
Step-by-step explanation:Let c represent the cost of Colin's car. Then ...
... c = (3 3/4) × $8000 = (3 × $8000) + ((3/4) × $8000)
... = $24000 + 6000
... c = $30,000
The cost of Colin's car is $30,000.
Answer:
A. $30,000
Step-by-step explanation:
To solve this you just have to do a simple rule of three, where in one side has the price of the car that his parents bought for 8,000 dollars and calculate the money that colin´s car costed in the other side:
[tex]\frac{8000}{1}= \frac{x}{3\frac{3}{4} } \\x=\frac{3,75*8000}{1}\\ x=30000[/tex]
So now we know that the car that Colin bought was 3.75 times as expensive as his parents 8,000 dollar car, that means it costed 30,000 dollars.
What is the apparent solution to the system of equations?
y=12x+2y=2x−1
y=12x+2y=2x−1
Graph the system of equations using the Line tool. Plot a point at the apparent solution to the system using the Point tool.
Answer:
(x, y) = (-0.3, -1.6)
Step-by-step explanation:
The graph below shows these equations graphed. Their point of intersection is (-0.3, -1.6).
_____
Analytical solution
You can equate the expressions for y to get ...
... 12x +2 = 2x -1
... 10x = -3 . . . . subtract (2x+2)
... x = -0.3 . . . . . divide by 10
... y = 2(-.3)-1 = -1.6 . . . . use the 2nd equation to find y.
Find the value of the polynomial:
4x^6y^3–3x^6y^3+2x^2y^2–x^6y^3–x^2y^2+y
x = −2, y = −1
Answer:
3
Step-by-step explanation:
Terms combine to simplify the expression somewhat.
... = x^6y^3·(4 -3 -1) +x^2y^2·(2 -1) +y
... = x^2y^2 +y
... = (xy)^2 +y
For your given values, this is ...
... ((-2)(-1))^2 +(-1)
... = 2^2 -1 = 3
Which postulate or theorem proves ∆MNQ ≅ ∆PNQ ?
SSS Congruence Postulate
AAS Congruence Postulate
ASA Congruence Postulate
AAS Congruence Postulate proves that ∆MNQ ≅ ∆PNQ
What is congruency?When two triangles have shape and sizes then the triangles are said to be congruent.There are 5 types of congruencies. They are SAS, AAS, ASA , SSS , RHS.How to know which postulate or theorem proves ∆MNQ ≅ ∆PNQ ?Considering ΔMNQ and ΔPNQ
∠QMN = ∠QPN (given)
∠QNM = ∠ QNP ( both are right angles)
Side NQ is common
∴ ΔMNQ and ΔPNQ are congruent by AAS congruency since two angles and a side are considered to prove the congruency.
The side is not included between the angles and hence ASA congruency is not the answer.The correct answer is option B. AAS congruency postulates.
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GUYS HELP PLEASE!!!! I NEED THIS ASAP!!!!!!!
Answer:
slope = .4
She ran .4 laps per min.
She ran 12 laps in 30 minutes
Step-by-step explanation:
The slope is the rate of change. It can be found by using the formula
slope = (y2-y1)/(x2-x1)
The given points are (11, 4.4) (5.5 ,2.2)
slope = (2.2-4.4(/ (5.5-11)
= -2.2/-5.5
.4
The slope represents .4 laps per min since y is in laps and x is in minutes.
If she ran 30 minutes, we multiply the time by the slope to calculate the laps.
30 * .4 = 12
She ran 12 laps.
A) The slope is the change in Y over the change in X.
Using the 2 points given on the graph (11,4.4) and (5.5, 2.2)
The first number in the parenthesis are the X value and the 2nd numbers are the Y values.
Slope = (4.4 - 2.2) / (11-5.5)
= 2.2 / 5.5
= 0.4
B) From the slope, she ran 0.4 laps per minute.
C) To find the total laps, multiple laps per minute by total minutes:
30 minutes x 0.4 laps per minute = 12 laps.
A number is doubled and then 1 is added to it. The answer is divided by 5 and then increased by 16. The final result is 18.
A)Develop an equation that shows the step above
Equation:___________________
B) Solve the equation to determine the value of the number.
Solve the equation. Show your work
Answer: The number is___________
So let's break down this sentence (Let n = unknown number):
"A number is doubled and then 1 is added to it"; Remember that double means multiplied by 2. With this sentence, we can determine that "2n + 1" is a part of the equation."The answer is divided by 5, and then increased by 16"; The "answer" they refer to is "2n + 1" from the prior sentence. Since this is divided by 5 and then added by 16, we can determine that [tex]\frac{2n+1}{5}+16[/tex] is a part of our equation."The final result is 18"; This means that the prior part of the equation is equal (=) to 18. With this info, our full equation is [tex]\frac{2n+1}{5}+16=18[/tex]B.Now, let's solve our prior equation found in A. To solve for the unknown number, n, we need to isolate the variable onto 1 side of the equation. Firstly subtract both sides by 16 to cancel out the + 16 on the left side:
[tex]\frac{2n+1}{5}=2[/tex]
Next, multiply both sides by 5 to cancel out the division on the left side:
[tex]2n+1=10[/tex]
Next, subtract both sides by 1 to cancel out the + 1:
[tex]2n=9[/tex]
Lastly, divide both sides by 2 to cancel out the multiplication:
[tex]n=\frac{9}{2}\ \textsf{OR}\ 4.5[/tex]
In short, the number is 9/2 or 4.5.
Solve each of these systems using the substitution method. Make sure to check your answers !
2x + 3y = -4
x − 2y = 5
a. x = 1, y = -2
b. x = -1, y = 2
c. x = 1, y = 2
d. x = -2, y = -1
Answer:
a. x = 1, y = -2
Step-by-step explanation:
The given equations are 2x + 3y = -4 -------------(1)
x - 2y = 5 -----------------(2)
From the second equation, we get x = 2y + 5
Now plug in x = 2y + 5 in the first equation, we get
2(2y + 5) + 3y = - 4
4y + 10 + 3y = -4
7y + 10 = -4
7y = -14
y = -2
Now plug in y = -2 in x = 2y + 5 to find the x value.
x = 2(-2) + 5
x = -4 + 5
x = 1
Therefore, x = 1, y = -2
Thank you.