Answer:
The approximate distance between the points is 38.2
Step-by-step explanation:
The distance between these two points is a diagonal line. In order to solve this problem, you need to plot your points and form a right triangle. The overall distance from one point to another on the x-axis is 26 (12-(-14)), and the overall distance from one point to another on the y-axis is 28 (20-(-8)). These two distances will form a right angle at (-14,-8). The distances on the x and y axis are the 'legs' of the triangle and the distance between the given points in the problem represents the hypotenuse. Using the pythagorean theorem (a^2 +b^2 = c^2), we can substitute in our values of 'a' and 'b' to get 28^2 + 26^2 = c^2, or 784 + 676= 1460, therefor the square root of 1460 is approximately 38.2.
So to find the distance between these two points, we are going to be plugging them into the Distance Formula and solving as such:
[tex]D=\sqrt{(12-(-14))^2+(-8-20)^2}\\D=\sqrt{(26)^2+(-28)^2}\\D=\sqrt{676+784}\\D=\sqrt{1460}[/tex]
Now, with this radical we can simplify it using the product rule of radicals (√ab = √a × √b) as such:
[tex]\sqrt{1460}=\sqrt{10*146}=\sqrt{5*2*2*73}=2*\sqrt{73*5}=2\sqrt{365}[/tex]
Answer:In short:
Exact distance: √1460 or 2√365 unitsApproximate Distance (rounded to the hundreths): 38.21 unitsAllison is rolling her hula hoop on the playground. The radius of her hula hoop is 35 cm.
Answer:
The hula hoop rolls 879 \text{ cm}879 cm.
Step-by-step explanation:
A 12-ounce bottle of soda costs $3.60. If the unit price remains the same how much would a 20-ounce bottle of soda cost?
A) $3.00
B) $5.50
C) $6.00
D) $6.50
For this, simply set up a proportion. If 12 oz. costs $3.60, then this means $3.60 per oz, or [tex]\frac{3.6}{12}[/tex]. Now letś make a proportion for 20 oz. Itś asking for how much it would cost if the unit price was the same, which means that the two should have a similar ratio. Because we don´t know how much it costs yet, this means x dollars for a 20 oz. bottle, or [tex]\frac{x}{20}[/tex]. I´ve already mentioned that they two are proportional, so write [tex]\frac{3.6}{12} = \frac{x}{20}[/tex].
To solve, cross multiply.
⇒[tex]12*x=3.6*20[/tex]
⇒[tex]12x=72[/tex]
Isolate variable x.
⇒[tex]\frac{12x}{12} = \frac{72}{12}[/tex]
⇒ x = 6: $6.00 for 20 ounces of soda.
Checking your work:
3.6/12 = 0.3
6/20 = 0.3
This means that theyŕe proportional, and that your answer is correct. Hope this was helpful.
3 pounds of peaches cost $6. how many pounds of peaches could be bought for $24. find the algebraic equation
Answer:
Step-by-step explanation:The algebraic equation is 24/6*3 which will give you 12 pounds
Answer:
Equation
2x = 24
Step-by-step explanation:
3 pounds of peaches cost $6
so each pound = $6/3 = $2
so if you have $24 then $24/ 2 = 12 pounds
Let x = # of pounds of peaches
Equation
2x = 24
The slope of the line below is 2. Write a point-slope equation of the line using the coordinates of the labeled point( 3,10)
Answer:
Point slope form of the line is [tex]y-10=2(x-3)[/tex]
Step-by-step explanation:
The point-slope form of a line is given as:
[tex]y-y_1=m(x-x_1)[/tex]
Where,
[tex]m[/tex] is the slope, and [tex](x_1,y_1)[/tex] is the x point and y point respectivelyThe question tells us the slope is 2, hence [tex]m=2[/tex] and the point given is (3,10) which means [tex]x_1=3[/tex] and [tex]y_1=10[/tex]. Substituting these values into the point slope form of a line gives us:
[tex]y-(10)=2(x-(3))\\y-10=2(x-3)[/tex]
Hence, point slope form of the line is [tex]y-10=2(x-3)[/tex]
Which equation could have been used to create this graph
a. y = 4x
b. y = x + 4
c. y = 2x
d.y = x + 2
Answer:
The answer is A
Hoped it helped <3 tell me if I am wrong
Step-by-step explanation:
The Girls’ Scouts are sponsoring a cookie sale. If their goal is to raise at least $500.00, how many cookies must they sell at $5.50 each in order to meet that goal? Write and solve an inequality.
Answer:
91 boxes
hope it helps
Step-by-step explanation:
you will divide $500.00 by $5.50 to find you how many cookies need to be sold
500 ÷ 5.50 = 90.9
so they need to sell about 91 boxes in order meet their goal
To check your work you can multiply
5.50 x 91 = $500.50
Using the divison operation, the number of cookies that must be sold in other to meet their target is 91
Target amount to be raised = $500Cost per cookie = $5.50The Number of cookies that must be sold to meet their target can be obtained using the divison operation thus :
Target amount ÷ cost per cookieHence,
Number of cookies to be sold = $500 ÷ 5.50 = 90.90 = 91(nearest whole number)
Therefore, the Number of cookies that must be sold to meet their target is 91.
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What is the equation of this line
A) y=2x-3
B) y=-1/2x-3
C) y=-2x-3
D) y= 1/2x-3
Answer:
A) y=2x-3
Step-by-step explanation:
I looked at the first 2 points that were perfectly on the x and y axis, so (3,3) and (5,7). I then put the numbers into their correct spots. When they were plugged in, both of the answers came back correct, so that is the correct equation.
Answer:
A. y=2x-3
Step-by-step explanation:
Since we have it in slope intercept form y=mx+b. B is our y intercet which we know is -3. Next we can find the slope which rise over run. This gives up 2 and our answer.
if i √ 1 what is the value of i 2
Answer:
I is the √-1 so it would be √-2 as your answer
Step-by-step explanation:
If the value of i = [tex]\sqrt{1}[/tex] then value of i² = 1.
What are surds and indices ?When we raise numbers to powers they are either called surds when we raise powers which are greater than zero but less than 1 in fraction from.
We call indices when we raise powers to which are greater than 1.
Indices make the base larger after simplification and surds make the bases smaller after simplification.
According to the given question i = [tex]\sqrt{1}[/tex].
∴ The value of i² is i×i = [tex]\sqrt{1}[/tex] × [tex]\sqrt{1}[/tex] = [tex]1^\frac{1}{2}[/tex] × [tex]1^\frac{1}{2}[/tex] = [tex]1^[\frac{1}{2}+\frac{1}{2}][/tex] = 1¹ = 1.
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4x=100 the answer on alegebra 1
Answer:
Its C. 25
Step-by-step explanation:
I just divided 100 by 4
4x = 100 divide both sides by 4
x = 25 → c.
--------------------------
5x = 25 divide both sides by 5
x = 5 → c.
---------------------------
3x + 5 = 17 subtract 5 from both sides
3x = 12 divide both sides by 3
x = 4 → a.
--------------------------
3x + 14 = 11 subtract 14 from both sides
3x = -3 divide both sides by 3
x = -1 → b.
A bookcase in a classroom contains textbooks that weigh 0.8 pound each. The bookcase alone weighs 22.2 pounds. If the total weight of the books and the bookcase is 31.8 pounds, how many books are in the bookcase?
Answer:
It should be 12 because:
31.8 - 22.2 = 9.6
9.6 ÷ 0.8 = 12
A creative group of students produces a reality television show that features various aspects of college and dorm life. Once the show begins airing on the university's public access cable channel, the function shown below represents the number of weeks that pass until x percent of the campus is watching the show. Compute w(50) to one decimal place, and interpret the result in the context of this problem.
w(x)=(x+125)^1/3
A. It will be about 6 weeks until 50 percent of the campus is watching the show.
B. It will be about 5.7 weeks until 60 percent of the campus is watching the show.
C. It will be about 5.6 weeks until 50 percent of the campus is watching the show.
D. It will be about 5.5 weeks until 50 percent of the campus is watching the show.
Answer:
Option c is correct option
it will be about 5.6 weeks until 50 percent of the campus is watching the show
Step-by-step explanation:
we are given
w(x)=[tex]x+125^{\frac{1}{3} }[/tex]
w(50)=[tex]50+125^{\frac{1}{3} }[/tex]
w(50)=[tex]175^{\frac{1}{3} }[/tex]
w(50)=[tex]\sqrt[3]{175}[/tex]
w(50)=5.59
we have to convert it into one decimal form
5.59=5.6
hence option c is correct option.
Computing w(50) using the provided function yields a value of approximately 5.6, which means it will take about 5.6 weeks for 50 percent of the campus to start watching the student-produced reality show. Thus, the correct answer to the student's question is option (C).
To compute w(50) based on the given function [tex]w(x)=(x+125)^{(1/3)}[/tex], we substitute x with 50:
[tex]w(50) = (50+125)^{(1/3)}[/tex]
Calculate the value inside the parenthesis:
[tex]175^{(1/3)}[/tex]
Taking the cube root of 175 gives us approximately:
5.6
Thus, w(50) ≈ 5.6, and we can interpret this in context by stating:
It will be about 5.6 weeks until 50 percent of the campus is watching the show.
This means the correct answer from the provided options is C. It takes approximately 5.6 weeks for the reality television show produced by the students to reach a viewership of 50 percent of the campus.
2. Dan and Bob went to the carnival. Dan bought 3 ticket refills and a lunch for $10.35. Bob bought 2 ticket refills and the lunch for $8.35. SHOW YOUR WORK (a) Write a system of equations. Use t for tickets and l for lunch. (b) Graph the equations in the system. (c) Use your graph to estimate how much each item cost.
Answer:
Let t represents for ticket and l represents for lunch.
As per the given statement: Dan bought 3 ticket refills and a lunch for $10.35
then, we have
[tex]3t + l = \$10.35[/tex]
Also, it is given that Bob bought 2 ticket refills and the lunch for $8.35.
⇒[tex]2t + l = \$8.35[/tex]
(a)
System of an equations are:
[tex]3t + l = \$10.35[/tex]
[tex]2t + l = \$8.35[/tex]
(b)
Let x-coordinate represents ticket refills and y-coordinates represents lunch
You can see the graph of the given equation as shown below in the attachment.
(c)
To find the cost of each items;
Using graph to estimate the cost of each items;
then;
Cost of ticket refills(t) = $2
and
Cost of lunch(l) = $4.35
how do i prove am + am = AB
Statement 1: AM is the midpoint of AB
Reason 1: Given
=====================================
Statement 2: AM+MB = AB
Reason 2: Segment Addition Postulate
Further explanation: Basically this idea is where you can break up the line segment into smaller pieces, or glue smaller segments to form a larger segment.
=====================================
Statement 3: AM = MB
Reason 3: Definition of midpoint
Further explanation: The midpoint cuts a line segment in half. The two smaller pieces AM and MB are congruent (ie equal in length)
=====================================
Statement 4: AM + AM = AB
Reason 4: Substitution
Further explanation: We replace the MB in statement 2 with AM. This replacement is possible because of the equation AM = MB in statement 3.
This concludes the proof.
cc has 3/4 gallons of chocolate ice cream left from her birthday party .she ate 1/2 of the chocolate ice cream while watching tv .how much ive crea does she have left?
Answer:
3/8 gallons left
Step-by-step explanation:
she has 0.75 of a gallon
she eats 0.5(0.75) while watching TV
multiply 0.5 by 0.75 to get half of 3/4 of a gallon
0.375 of a gallon is what she has left
or 3/8 of a gallon
Write the expression in complete factored form 3c(c+3)-4(c+3)
3c(c+3)-4(c+3)=3c^2+9c-4c-12=3c^2+5c-12
The expression in complete factored form is (3c - 4)(c + 3)
What is a complete factored form expression ?A complete factored form is a form of expressing a complex polynomial expression as the products of factors of the polynomial. If we equate the complete factored expression with zero, we get the solutions of the polynomial expression.
Solving the given expression in complete factored form -The expression given is [tex]3c(c + 3) - 4(c + 3)[/tex]
Expanding the given expression [tex]3c^{2} + 9c - 4c - 12[/tex]
= [tex]3c^{2} + 5c - 12[/tex]
= [tex]3c^{2} + 9c - 4c - 12[/tex]
= [tex]3c(c + 3) - 4(c + 3)[/tex]
= [tex](3c - 4)(c + 3)[/tex]
Thus the expression in complete factored form is (3c - 4)(c + 3)
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the ages of three men are in the ratio 3:4:5.if the difference between the age of the oldest and the youngest is 18years, fine d the sum of the age of the three men
Answer:
108
Step-by-step explanation:
Givens
let the oldest one = 5xLet the youngest one = 3xLet the middle one = 4xEquation
3x + 18 = 5xSolution
3x + 18 = 5x Subtract 3x from both sides3x - 3x + 18 = 5x - 3x Combine18 = 2x Divide by 218/2 = 2x/2 Dividex = 9Answer
3x = 3*9 = 275x = 5*9 = 454x = 4*9 = 36The sum is 108Comment
This is a very tricky problem. It is not the usual way that 3 part ratios are handled. Thanks for posting.
Mr. Willis is building a new dock at his lake house that will be 35 feet long. If the blueprints show the dock as 16 inches long, what scale was used to create the blueprint?
Answer:
1:26.25
Step-by-step explanation:
Scale = 16 in:35 ft
Convert 35 ft to inches
1 ft = 12 in
35 × 12/1 = 420 in
Scale = 16 in:420 in Divide each term by 16
Scale = 1:26.25
The scale used to create the blueprint for Mr. Willis's dock is 1:26.25, meaning that each inch on the blueprint represents 26.25 inches of the actual dock.
The actual dock is 35 feet long, and there are 12 inches in a foot, so the dock is 35 feet × 12 inches/foot = 420 inches long. The blueprint shows the dock as 16 inches long. Therefore, we use the scale factor formula:
scale factor = blueprint length / actual length
The scale factor is 16 inches / 420 inches, which simplifies to 1/26.25. Thus, the blueprint is drawn at a scale of 1:26.25, meaning that 1 inch on the blueprint represents 26.25 inches in the actual size.
Given: m∠1 = 140°, find m∠6.
A) 40°
B) 50°
C) 90°
D) 140°
Answer:
The answer is A
Step-by-step explanation:
When two parallel lines are crossed by another line the angle of 1 will be equal to 4, 5, and 8. The angle 2 will be equal to 3, 6, and 7. Since a straight line has a degree of 180, the subtracted degree of 180-140=40 which would mean 2=40 which 2=6 so 6=40.
Answer:
40°, A
Step-by-step explanation:
What are we going to do to figure out measure 6?
First of all, we know that measure 5 and measure 6 are equal to 180 degrees.
Second of all, we know that measure 1 and measure five are corresponding angles, which means they are congruent. If measure one is 140 degrees, measure 5 would also be 140 degrees.
So we know that measure 5 and measure 6 are equal to 180 degrees. We can now make an equation...
Let x = measure 6
140° + x = 180° x = 40°Complete the synthetic division below.
Answer:
The quotient is (x+7)
Step-by-step explanation:
Given the synthetic division problem
2|1 5 -14
we have to complete the synthetic division to find the quotient.
The steps are
Step 1: Set up the synthetic division
Step 2: Bring down the leading coefficient to the last row.
Step 3: Multiply the value which is written on the top left by the value just written on the bottom row.
Step 4: Add the column created in above step.
Step 5: continue until we reached last column.
The synthetic division is shown in attachment.
The quotient is (x+7)
Option D is correct
You and some friends rent a limousine for a formal reception. The bill for the evening is $65.00. A tax of 7% will be added to your total, and you want to tip the chauffeur for his excellent driving. You decide to leave him a tip that is 20% of the bill before tax is added. How much will be paid in total?
A. 92.00
B.91.00
C. 85.50
D. 82.55
Answer:
D YEET
Step-by-step explanation:
Which equation represents a circle that is concentric with the circle shown but has a radius that is twice as large ?
Answer:
the awnser is c
Step-by-step explanation:
the c
Answer:
Its C
Step-by-step explanation:
I got a 100% on the test
Using the number 234.58937 what is the sum of the hundreds digit and the hundredths digit? A) 12 B) 11 C) 10 D) 9 E) 8
Answer:
b
Step-by-step explanation:
add 3 and 8 = 11
Sooo.... I need some help with my math someone plz help
Answer:
The total area of the two triangles is 100 inches²
Step-by-step explanation:
To solve for the area of a triangle we use the formula [tex]\frac{1}{2} bh[/tex]
(or base*height divided by 2)
First I solved for the area of the blue triangle.
The base is 12 inches and the height is 10 inches.
[tex]\frac{1}{2}[/tex] * 12 * 10 equals 60 inches².
For the orange triangle the base is 8 inches and the height is 10 inches.
[tex]\frac{1}{2}[/tex] * 8 * 10 equals 40 inches².
60in² + 40in² = 100in²
If 100 dollars in one year gain 3 1/2 dollars interest, what sum will gain $38.50 cents in a year and a quarter
Answer:
10,300?
Step-by-step explanation:
Chole wants to build a storage container in the shape of a cube to hold 15.625 cubic meters of hay for her horse. Slove the equation 15.625 =s3 find the length of oneside of the container
Answer:
The length of each side is 2.5 m
Step-by-step explanation:
A cube has a volume of 15.625 m^3 of hay
We want to find the length of one side
V= s^3 where s is the length of one side
15.625 = s^3
Take the cube root of each side
15.625 ^ (1/3) = s^3 ^(1/3)
15.625 ^ (1/3) = s
2.5 = s
The length of each side is 2.5 m
a) 120 is what percentage of 30
b) 30 is 120% of what number
c) what number is 30%of 120
WHOEVER GIVES ME THE RIGHT ANSWER AND A STEP BY STEP EXPLANATION GETS POINTS AND BRAINLIST************************************************************************************************
Answer:
a ) 400 percent
b ) n = 25
c) n= 36
Step-by-step explanation:
Is means equals, of means multiply and percents need to be changed to decimals.
a) 120 is what percentage of 30
120 = P * 30
Divide each side by 30
120/30 =P* 30/30
4 = P
Multiply by 100 to give the percentage
4 * 100
400 percent
b) 30 is 120% of what number
30 = 1.2 * n
Divide each side by 1.2
30/1.2 = 1.2n/1.2
25 = n
c) what number is 30%of 120
n = .3 * 120
n =36
I hope its bigger so u can seeeeeeeeeee!!!
Answers:
Gabe needs 30 liters of the 50% solution
Gabe needs 30 liters of the 70% solution
Both answers are 30
==================================
Explanation:
We have two beakers, each of which we don't know how much is inside. Let's call this x and y
x = amount of liquid in the first beaker (water+acid)
y = amount of liquid in the second beaker (water+acid)
We're told that the beakers have a 50% solution and a 70% solution of acid. This means that the first beaker has 0.5*x liters of pure acid, and the second beaker has 0.7*y liters of pure acid. In total, there is 0.5x+0.7y liters of pure acid when we combine the two beakers. This is out of x+y = 60 liters total, which we can solve for y to get y = 60-x. We will use y = 60-x later on when it comes to the substitution step
We can divide the total amount of pure acid (0.5x+0.7y liters) over the total amount of solution (x+y = 60) to get the following
(0.5x+0.7y)/(x+y) = (0.5x+0.7y)/60
We want this to be equal to 0.6 because Gabe wants a 60% solution when everything is said and done, so
(0.5x+0.7y)/60 = 0.60
0.5x+0.7y = 0.60*60 .... multiply both sides by 60
0.5x+0.7y = 36
0.5x+0.7( y ) = 36
0.5x+0.7(60-x) = 36 ........ replace y with 60-x (substitution step)
0.5x+0.7(60)+0.7(-x) = 36 .... distribute
0.5x+42-0.7x = 36
-0.2x+42 = 36
-0.2x = 36-42 .... subtract 42 from both sides
-0.2x = -6
x = -6/(-0.2) .... divide both sides by -0.2
x = 30
He needs 30 liters of the 50% solution
Use this x value to find y
y = 60-x
y = 60-30
y = 30
So he needs 30 liters of the 70% solution
On a scale model of a building, 1 4 inch represents 3 8 foot. What length on the model represents 1 foot? 3 32 in. 2 3 in. 1 1 1 in. 10 2 3 in.
Answer:
2/3 in
Step-by-step explanation:
We can use ratios to solve this problem.
1/4 inch x inches
-------------- = ---------------------
3 /8 ft 1 ft
Using cross products
1/4 * 1 = 3/8 * x
Multiply each side by 8/3 to isolate x
1/4 * 8/3 = 3/8*8/3 x
2/3 = x
What’s the answer please
Answer:
Step-by-step explanation:
Answer:
(x, y ) = (5, 4 )
Step-by-step explanation:
given the 2 equations
3x - 2y = 7 → (1)
- 3x + 5y = 5 → (2)
adding the 2 equations term by term will eliminate x
(3x - 3x) + (- 2y + 5y ) = (7 + 5 )
0 + 3y = 12
3y = 12 ( divide both sides by 3 )
y = 4
substitute y = 4 in either of the 2 equations and solve for x
(1 ) : 3x - 8 = 7 ( add 8 to both sides )
3x = 15 ( divide both sides by 3 )
x = 5
solution is (5 , 4 )
In a right triangle the length of a hypotenuse is c and the length of one leg is a. Find the length of the other leg b, if:
c=6, a=5
34 points to the first one who gets it correct
Answer:
b = sqrt(11)
Step-by-step explanation:
Using the Pythagorean theorem
a^2 + b^2 = c^2
and substituting what we know
5^2 + b^2= 6^2
25 + b^2 = 36
Subtract 25 from each side
25-25 + b^2 = 36-25
b^2 = 11
Take the square root of each side.
sqrt(b^2) = sqrt(11)
b = sqrt(11)
We only take the positive because length must be positive.
Use the Pythagorean theorem
[tex]a^2+b^2=c^2[/tex]
a,b - legs
c - hypotenuse
We have c = 6 and a = 5. Substitute:
[tex]5^2+b^2=6^2[/tex]
[tex]25+b^2=36[/tex] subtract 25 from both sides
[tex]b^2=11\to \boxed{b=\sqrt{11}}[/tex]