*30 points* Consider the figure shown on the coordinate plane. What are the coordinates of the midpoint of line segment AC?
A) -2, -1
B) 4, 0
C) -1, 1
D) -1, -1
Answers
Midpoint of AC = (–1, –1)
Solution:
In the given graph we can find the coordinates of A and C.
Coordinates of A = (–4, 2)
Coordinates of C = (2, –4)
Here, [tex]x_1=-4,x_2=2,y_1=2,y_2=-4[/tex]
Let us find the midpoint of the segment AC.
Midpoint formula:
[tex]$\text{Midpoint} =\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)[/tex]
[tex]$=\left(\frac{-4+2}{2}, \frac{2-4}{2}\right)[/tex]
[tex]$=\left(\frac{-2}{2}, \frac{-2}{2}\right)[/tex]
[tex]$=(-1, -1)[/tex]
Midpoint of AC = (–1, –1)
Option D is the correct answer.
Hence the coordinates of the midpoint of the line segment AC is (–1, –1).
Related Questions
Keisha drinks 15 quarts of water in 12 days what is the average amount of water that she drinks per day
Answers
Keisha drinks 1.25 quarts of water per day
Solution:
Given that,
Keisha drinks 15 quarts of water in 12 days
To find: Average amount of water that she drinks per day
Average amount of water that she drinks per day is found by dividing 15 quarts by 12 days
The formula used is:
[tex]Amount\ of\ water\ drank\ per\ day = \frac{\text{15 quarts of water}}{12\ days}[/tex]
Therefore,
[tex]Amount\ of\ water\ drank\ per\ day = \frac{15}{12}\\\\Amount\ of\ water\ drank\ per\ day = 1.25[/tex]
Thus she drinks 1.25 quarts of water per day
If y = 7x - 5, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?
{(-5, 0), (9, 2), (-26, -3)}
{(2, 7), (1, 6), (3, 13)
{(0, -5), (2, 9), (-3, -26)}
{(1,3), (6, 18), (8, 15)}
Answers
Answer:
C is correct
Step-by-step explanation:
If you plug in the ordered pairs from C, they always work.
Expand 64 and then solve.
Answers
answer will be 6400tftfftfttfft
[tex]\text{Hey there!}[/tex]
[tex]\text{Expanded formed would be the number expanded into an addition equation}[/tex]
[tex]\text{Here is a(n) example: 699 would be expanded as 600 + 90 + 09 = 699}[/tex]
[tex]\text{Now we know what expanded is and what it should look like similar, to}\\\text{we can answer your question}[/tex]
[tex]\boxed{\bf{\underline{60 + 04}}}\leftarrow\bf which\ would\ be\ converted\ to\ 64}[/tex]
[tex]\boxed{\boxed{\mathsf{Answer: 60 +04}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Annie got 7 flowers and gave 2 to Karen how many does she have left
Answers
Answer:
5 flowers
Step-by-step explanation:
To get the answer you do 7-2
so she has 5 flowers left.
7-2=5
what is 7/10+1/4 in simplest form
Answers
Answer: 19/20
Step-by-step explanation:
7/10 turns into 14/20
1/4 turns into 5/20
14/20 + 5/20
14 + 5 over 20
= 19/20
19/20 is in simplest form.
[tex]\text{Hey there!}[/tex]
[tex]\mathsf{What\ is\ \dfrac{7}{10}+\dfrac{1}{4}\ in\ simplest\ form?}[/tex]
[tex]\text{First, look for the lowest common denominator (LCD) of the fractions.}\\\text{If you did the calculations correctly, you should've came up with 20 as}\\\text{your LCD}[/tex]
[tex]\mathsf{Here\ is\ how so: \dfrac{7\times2}{10\times2}+\dfrac{1\times5}{4\times5} = \ ?}[/tex]
[tex]\mathsf{7\times2=14\leftarrow first\ numerator}\\\mathsf{10\times2=20\leftarrow first\ denominator}[/tex]
[tex]\mathsf{1\times5=5\leftarrow second\ numerator}\\\mathsf{4\times5=20\leftarrow second\ denominator}[/tex]
[tex]\mathsf{Your\ new\ equation\ SHOULD\ look\ like\ this: \dfrac{14}{20}+\dfrac{5}{20}}[/tex]
[tex]\text{Since, your DENOMINATORS are ALIKE we can KEEP IT}[/tex]
[tex]\mathsf{Which\ leaves\ us\ with\ the\ last\ step\ of\ the\ problem}[/tex]
[tex]\mathsf{ \dfrac{14+5}{20}}}[/tex]
[tex]\mathsf{14+5=19\leftarrow your\ new\ numerator}\\\\\mathsf{20 = 20\leftarrow your\ new\ denominator}[/tex]
[tex]\boxed{\boxed{\bf{Answer: \mathsf{\dfrac{19}{20}}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
The polynomial equation x4 - 6x3 + 10x2 + 2x - 15 = 0 has solution set _____.
{2 + i, 2 - i, -3, -1}
{2 + i, 2 - i, 3, -1}
{3 + i, 2 - i, 3, -1}
{3 + i, 3 - i, 3, -1}
Answers
Final answer:
The solution set of the polynomial equation can be found by testing the given sets of roots and verifying which set satisfies the polynomial equation.
Explanation:
To find the solution set of the polynomial equation x4 - 6x3 + 10x2 + 2x - 15 = 0, we need to factor the polynomial or use numerical methods to find roots. Polynomial equations of higher degrees such as quartics can often be simplified into quadratic equations or factored based on known roots or rational root theorem. Once a root is found, it can be used for polynomial division to reduce the degree of the polynomial and find other roots. One simple numerical method to guess and check roots would be to use synthetic division with possible rational roots.
However, since the question provides the sets of the roots, we only need to verify which set of roots satisfy the equation. We can use these sets as potential solutions and substitute the roots back into the equation to see if it satisfies the equation. Since complex roots always come in conjugate pairs for polynomials with real coefficients the only possible sets of roots that can be correct are {2 + i, 2 - i, -3, -1} or {2 + i, 2 - i, 3, -1}. Now we can substitute these roots into the original polynomial to determine which set is the actual solution
If x = 4 units, y = 5 units, and h = 7 units, find the area of the trapezoid shown above using decomposition.
Answers
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.
Determine whether the number could be the probability of an event. Explain your reasoning. − 0 . 25
Answers
Answer:
So the answer is NO, the probability of an event cannot be -0.25.
Step-by-step explanation:
i) The probability or likelihood of an event cannot be negative or less than zero.
ii) The probability of an event cannot be greater than 1.
iii) If the probability of an event is 0 then the event did not or does not happen
iv) If the probability of an event is one then the event did or does happen with 100% certainty.
v) If the probability is between 0 and 1 then the event occurs wit a certainty that is less than 100%.
vi) So the answer is NO, the probability of an event cannot be -0.25.
Final answer:
The number -0.25 cannot represent the probability of an event because probability values must be between 0 and 1, and negative values are not within this range.
Explanation:
The number -0.25 cannot be the probability of an event. In probability theory, the value assigned to the likelihood of an event occurring must be within a certain range, specifically between 0 and 1, inclusive.
A probability of 0 denotes an impossible event, whereas a probability of 1 represents an event that is certain to occur. Since -0.25 is a negative number, it falls outside of this acceptable range, therefore it cannot represent the probability of an event occurring in any valid probability distribution.
$8000 principal earning 5% compounded annually, after 6 years
Answers
Answer:
The final balance is $10,792.14.
The total compound interest is $2,792.14.
Step-by-step explanation:
Final answer:
Explanation on calculating the amount of $8000 principal at 5% compounded annually after 6 years using compound interest formula.
Explanation:
The question: $8000 principal earning 5% compounded annually after 6 years.
Step-by-step explanation:
Use the compound interest formula: A = P(1 + r/n)^(nt) where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the time in years.
Plug in the values: P = $8000, r = 0.05, n = 1 (compounded annually), t = 6.
Calculate: A = $8000(1 + 0.05/1)^(1*6)
A = $10,720.77.
Juan paid 59.99 tor a jacket that originially sold for 85.50. about what percent of the originial price did he pay for the jacket?
Answers
Juan paid 70.16 % of the original price of the jacket.
Step-by-step explanation:
Step 1:
Given details, Original Selling Price of the jacket = 85.50
New Selling Price of the jacket = 59.99
Step 2:
To determine what percentage of the old price is the new price, we have to use percentage calculation.
[tex]x/100\times 85.50 = 59.99[/tex]
Step 3:
Substitute in the formula, the given values
x = [tex](59.99/85.50) \times 100[/tex]
= [tex](0.7016) \times 100[/tex]
= [tex]70.16[/tex]
Therefore, percentage paid is 70.16%
Multiply.
6x^2 - 4x-5
2x^2 + 3x
A. 12x^4 + 18x^3 - 22x^2 - 15x
B. 12x^4 + 10x^3 – 22x^2 - 15x
c. 12x^4 + 18x^3 - 12x^2 - 15x
D. 12^4 + 10x^3 - 12x^2 - 15x
Answers
Answer:
its B
Step-by-step explanation:
i took the test the answer is B
please give me brainly
(6x² - 4x - 5)(2x² + 3x)
= 12x⁴ + 18x³ - 8x³ - 12x² - 10x² - 15x
= 12x⁴ + 10x³ - 22x² - 15x
so the answer is B
What is the solution to the equation x−23=−13 ? Enter your answer in the box.
Answers
Answer:
Step-by-step explanation: so u are going to put it like this x- -6 =5
Next u subtract -6 from both sides
x=11
Answer:
x=10
Step-by-step explanation:
Need some help with the answer to the question
Answers
Answer:
(- 4, 27 )
Step-by-step explanation:
Equate the right sides of both equations, that is
x² - 2x + 3 = - 2x + 19 ← subtract - 2x + 19 from both sides
x² - 16 = 0 ← in standard form
(x - 4)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 4 = 0 ⇒ x = - 4
Substitute these values into f(x) = - 2x + 19
f(4) = - 2(4) + 19 = - 8 + 19 = 11 ⇒ (4, 11 )
f(- 4) = - 2(- 4) + 19 = 8 + 19 = 27 ⇒ (- 4, 27 )
pls help thx
A bag contains 1 red, 2 blue, and 3 green marbles. Two marbles are drawn from the bag without replacement.
Based on the tree diagram, what is the probability that a GREEN marble and then a RED marble is drawn? (in simplest fraction form)
A)
1
5
B)
1
10
C)
3
10
D)
4
11
Answers
Answer:
Step-by-step explanation:
so you have 1 red, 2 blue, and 3 red. Together that would be 6 marbles. However it apears that with each draw you gain two marbles. therefore there are 12 possibilities. The likely hood that you will get a green marble then a red marble should be 2/12. In simplified form it is 1/6.
Answer:the answer is 1/5 the other guy got it wrong
Step-by-step explanation:
Help! Asap! Explain why dividing by a fraction results in the same answer as multiplying by its reciprocal.
Answers
Answer:
Hey "Dixie" heres why: That's why you're being told to flip the second fraction. You're recognizing that dividing by a number is the same as multiplying by the reciprocal. ... Now to multiply fractions, we simply multiply the numerators to get the new numerator and multiply the denominators to get the new denominator.
Hope it helped!
Dividing by a fraction and multiplying by its reciprocal, b/a, yield the same result as division and multiplication interact in such a way. The reciprocal (or flip) of a fraction makes it easier to perform mathematical operations like multiplication and division.
Explanation:In mathematics, dividing by a fraction a/b is indeed equivalent to multiplying by its reciprocal, which is b/a. This is because of the way division and multiplication operations work.
Here's an example: If you have 4 ÷ (1/2), this can also be seen as 4 multiplied by the reciprocal of 1/2, which is 2/1, or 2. In both cases, the answer would be 8. This shows that dividing by a fraction is the same as multiplying by its reciprocal.
Therefore, when you have any number divided by a fraction, you can simplify the operation by turning it into multiplication by performing the flip (reciprocal) on the fraction you're dividing by.
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I REALLY NEED HELP!!! I WILL MARK BRAINLIEST TO WHOEVER GETS IT FIRST!!!
You make 3 quarts of tomato sauce from two baskets of tomatoes. How much tomato sauce can you make from five baskets of tomatoes
Answers
Answer:
7.5 quarts
Step-by-step explanation:
2 baskets ------> make 3 quarts
1 basket ---------> makes 3/2 quarts
5 baskets -------> makes 3/2 x 5 = 15/2 = 7.5 quarts
The problem involves calculating ratios or proportional relationships. We find from a known ratio that 2 baskets yield 3 quarts of tomato sauce, and using cross-multiplication, we determine that 5 baskets would produce 7.5 quarts of tomato sauce.
Explanation:This is a ratio problem. Here, we see that 2 baskets of tomatoes yield 3 quarts of tomato sauce. Hence, the ratio of baskets to quarts is 2:3. Likewise, if we increase the number of baskets to 5, the amount of tomato sauce will also increase according to the ratio. To determine how much sauce that would be, use the principle of equivalent ratios, also known as cross-multiplication.
So, (2 baskets / 3 quarts) = (5 baskets / x quarts), where x is the quantity of sauce from 5 baskets. By cross-multiplying and simplifying, you get x = (5 baskets * 3 quarts) / 2 baskets, which simplifies to x = 7.5 quarts.
So, you can make 7.5 quarts of tomato sauce from 5 baskets of tomatoes.
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If 22,000 pounds of soybeans were harvested from 10 acres, how many bushels per acre we
harvested? (Note: 60 lb = 1 bu)
Answers
Answer:
36.66 bushels per acre
Step-by-step explanation:
First divide 22,000 by 10 to get pounds per acre
2200 lbs/acre
But the question asks how many pounds per bushel. So now we will divide 2200 by 60
36.66 bushels per acre
Answer:
36.67bu per acre
Step-by-step explanation:
Find Pound per acre
22,000/10 = 2200 lb per acre
Find bushels per acre
60lb = 1 bu
2200/60 = 36.67bu per acre
if x equals 10 what 5x-10
Answers
Answer:
40
Step-by-step explanation:
x = 10
Substitute 10 for x
5 (10) -10
Multiply 5 by 10
50 - 10
= 40
Mark Brainliest
Answer:40
Step-by-step explanation:
the list shows how much yarn mary has= 1/3 red yarn, 2/9 white yarn, 2/6 blue yarn what is the total amount of yarn mary has?
Answers
The total amount of yarn Mary has is [tex]\frac{8}{9}[/tex].
Step-by-step explanation:
Mary has;
Red yarn = [tex]\frac{1}{3}[/tex]
White yarn = [tex]\frac{2}{9}[/tex]
Blue yarn = [tex]\frac{2}{6}[/tex]
Total yarn = Red + White + Blue
Total yarn = [tex]\frac{1}{3}+\frac{2}{9}+\frac{2}{6}\\[/tex]
Taking LCM = 18
Total yarn = [tex]\frac{6+4+6}{18}[/tex]
Total yarn = [tex]\frac{16}{18}=\frac{8}{9}[/tex]
The total amount of yarn Mary has is [tex]\frac{8}{9}[/tex].
Keywords: fraction, addition
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The total amount of yarn that Mary has is the sum of the fractions representing each color of yarn. After converting all fractions to like terms with denominator 9, we find that Mary has 8/9 in total.
Explanation:To calculate the total amount of yarn Mary has, you should add all the given fractions together. We have:
1/3 red yarn,
2/9 white yarn, and
2/6 (which can be simplified to 1/3) blue yarn.
To add these fractions, they need to have a common denominator. The lowest common denominator of 3 and 9 is 9. So, we get:
3/9 red yarn + 2/9 white yarn + 3/9 blue yarn = 8/9.
Therefore, the total amount of yarn Mary has is 8/9.
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Determine which line the point (2, -1) lies on. y = 2x + 1 y = x + 5 y = 2x - 5 y = x - 2
Answers
To determine which line the point lies on, you can just plug in one of the numbers into the equations to see if it equals out.
(2, -1) I will use the 2 and plug it in for x in the equation.
y = 2x + 1
y = 2(2) + 1
y = 5 The point does not lie on this line because when x = 2, y = 5 (2, 5)
y = x + 5
y = 2 + 5
y = 7 The point does not lie on this line because when x = 2, y = 7 (2, 7)
y = 2x - 5
y = 2(2) - 5
y = 4 - 5
y = -1 The point does lie on this line because when x = 2, y = -1 (2, -1)
y = x - 2
y = 2 - 2
y = 0 The point does not lie on this line because when x = 2, y = 0 (2, 0)
In the figure below, the segments cd and ce are tangent to the circle centered at o. Given that od= 4.8 and oc= 7.3, find ce
Answers
Answer:
[tex]CE=5.5\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
we know that
According to the Perpendicular Tangent Theorem, tangent lines are always perpendicular to a circle's radius at the point of intersection
That means ----> Triangles ODC and OEC are right triangles
In the right triangle OEC
we have
[tex]OE=OD=4.8\ units[/tex] ----> radius of the circle
[tex]OC=7.3\ units[/tex]
Applying the Pythagorean Theorem
[tex]OC^2=OE^2+CE^2[/tex]
substitute the given values
[tex]7.3^2=4.8^2+CE^2[/tex]
[tex]CE^2=7.3^2-4.8^2\\CE^2=30.25\\CE=5.5\ units[/tex]
Final answer:
The length of the segment CE, which is a tangent to a circle, can be found using the properties of tangents and the Pythagorean theorem. Given OD = 4.8 and OC = 7.3, the length of CE is calculated to be approximately 5.5 units.
Explanation:
The question involves finding the length of segment CE in a configuration where segments CD and CE are tangents to a circle centered at O. Given that OD = 4.8 and OC = 7.3, to find CE, one can use the properties of tangents to a circle. Tangents drawn from the same external point to a circle are congruent. Therefore, the lengths of CD and CE are equal. Since OD and OC form a right triangle with CD (considering triangle OCD), applying the Pythagorean theorem gives us the length of CE directly.
To calculate, let CD = CE = x, hence:
[tex]OD^2 + CD^2 = OC^2[/tex][tex]4.8^2 + x^2 = 7.3^2[/tex][tex]x^2 = 7.3^2 - 4.8^2[/tex]x = [tex]\sqrt{(7.3^2 - 4.8^2)[/tex]After calculation:
x ≈ 5.5Therefore, the length of CE is approximately 5.5 units.
A ruler is 12 inches long. What is the of this ruler
Answers
Can you please clarify what you want to ask? Thanks!
50 pounds to 35 pounds
Answers
Step-by-step explanation:
I think that you are interested in finding the ratio between given quantities. If yes then let us find.
[tex]50 \: pound : 35 \: pound \\ = \frac{50}{35} \\ = \frac{5 \times 10}{5 \times 7} \\ = \frac{10}{7} \\ = 10 : 7[/tex]
The membership dues at an exclusive club are $1,750 annually. After every year of membership, the dues are lowered by $75. Choose the equation below that gives the dues of members, Dn, in their 7th year of membership.
A.
Dn = $1,750 - $75·n ; D7 = $1,300
B.
Dn = $1,750 - $75·(n - 1) ; D7 = $1,225
C.
Dn = $1,750 - $75·(n - 1) ; D7 = $1,300
D.
Dn = $1,750 - $75·n ; D7 = $1,225
Answers
Answer:
C.
Dn = $1,750 - $75·(n - 1) ; D7 = $1,300
Step-by-step explanation:
"n" represents each year of membership. The first year that you are a member (n = 1), the fee is $1,750.
In year 2, (n = 2), the fee is $1,750 - $75, which is 75·1. If n=1, and 75 is multiplied by 1, then the formula will use (n - 1).
At this point, the answer will be either B. or C.
Substitute n = 7 into the formula to find the cost in the 7th year.
Dn = $1,750 - $75·(n - 1)
D7 = $1,750 - $75·(7 - 1) Solve inside the brackets first.
D7 = $1,750 - $75·6 Multiply first, then subtract the product from 1750.
D7 = $1,300 Answer
Therefore the answer is C.
How many times does 33 go into 264?
Answers
Answer:
IT GOES 8 TIMES
Answer: 8 times
Step-by-step explanation:
solve each inequality, graph the solution, and write the solution in interval notation
5 ≤ 4x− 1 < 7
Answers
The compound inequality 5 \u2264 4x - 1 < 7 results in the solution set [1.5, 2) when solved and graphed. In interval notation, it is expressed as [1.5, 2).
Explanation:To solve the compound inequality 5 \<= 4x - 1 < 7, we split it into two separate inequalities and solve them individually:
Add 1 to all parts of the inequality: 6 \<= 4x < 8.Divide all parts by 4:\(\frac{6}{4} \<= x < \frac{8}{4}\).Simplify the fractions:1.5 \<= x < 2.The solution set is the interval [1.5, 2). To graph this solution, plot a closed circle at 1.5 and an open circle at 2, and shade the region in between. In interval notation, the solution set is represented as [1.5, 2).
Jack and Jill live 345 miles apart from one another. They want to meet for lunch and agree to leave the
same time, drive toward each other, and meet somewhere along the route. lack's average rates 60 pland
Hill's average rate is 55mph How long will it take them to meet? Give your wet in bo and sites
Answers
It will take them 3 hours to meet
Step-by-step explanation:
The given is:
Jack and Jill live 345 miles apart from one anotherThey want to meet for lunch and agree to leave the same time, drive toward each other, and meet somewhere along the routeJack's average rates 60 mphJill's average rate is 55 mphWe need to find how long it will take them to meet
Distance = Speed × Time
∵ They will drive toward each other at the same time and meet
each other somewhere
- That means they will drive for the same time
∵ Jack's average rates 60 mph for t hours
∴ Jack will drive a distance = 60 × t = 60 t miles
∵ Jill's average rate is 55 mph for t hours
∴ Jill will drive a distance = 55 × t = 55 t miles
∵ The distance between Jack and Jill is 345 miles apart
- Add their distance above and equate the sum by 345
∴ 60 t + 55 t = 345
∴ 115 t = 345
- Divide both sides by 115
∴ t = 3 hours
It will take them 3 hours to meet
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Can someone please help me
Answers
Answer:
(I did both because I'm not sure which problem you are referring to.)
Left: 3.5 miles per hour
Right: *equation- 12.5+2.5x=27.5*
6 pairs of socks
Step-by-step explanation:
Left:
First, make a ratio of 0.875 miles/15 minutes. (I converted to decimal form) Next, I made another ratio of x miles/60 minutes. This tells me how many miles she ran in an hour.
Then, to get from 15 minutes to 60 minutes(1 hour), I divided 60 by 15, and got 4. Since to get from 15 to 60 is to multiply by 4 in the denominator, you will also have to multiply 0.875 by 4 in the numerator. By doing that, you will find that x is equal to 3.5 miles.
Right:
First, I made an equation 12.5+2.5x=27.5.
12.5 represents the cost of one shirt.
2.5 represents the cost of a pair of socks
x represents the unknown amount of socks.
27.5 represents the total amount of money she spent.
Next, my goal is to figure out what x is, so I substracted 12.5 from both sides in order to get x to be alone. *Result: 2.50x=15
Then, I divided 2.50 from both sides, and got x=6
I hope this helped!
Use substitution to solve 1-2.
3x – 3y = 9
x= 7 – 3y
Answers
Answer:
Solutions are x =4 and y = 1
Step-by-step explanation:
[tex]3x-3y =9[/tex]
In this equation substitute [tex]x=7-3y[/tex], we get
[tex]3(7-3y) -3y=9\\21-9y-3y=9\\-12y= 9-21\\-12y= -12\\y=1[/tex]
now substitute y =1 in x equation,
[tex]x=7-3(1)\\x=7-3\\x=4[/tex]
Solutions are x =4 and y = 1
Use the Side-Splitting Theorem to find the value of x.
A. 10
B. 15
C. 8.5
D. 9.6
Answers
Step-by-step explanation:
In given figure,
AD = x, DB = 12, BE = 8 and EC = 10
To find, the value of x = ?
Use the Side-Splitting Theorem,
We know that,
[tex]\dfrac{AD}{DB} =\dfrac{BE}{EC}[/tex]
⇒ [tex]\dfrac{x}{12} =\dfrac{8}{10}[/tex]
⇒ x =[tex]\dfrac{8 \times 12}{10}[/tex]
⇒ x = [tex]\dfrac{96}{10}[/tex]
⇒ x = 9.6
∴ The value of x = 9.6
Thus, the required "option D. 9.6" is correct.