Final answer:
The correct method to find Wilson's and Mary's ages with the given equations is to solve the equation m + 6 = 5m - 10 by substitution, which will give you the value of Mary's age (m). After finding m, you can then solve for Wilson's age (w).
Explanation:
Among the provided methods to find Wilson's and Mary's ages based on the given equations w = m + 6 and w = 5m - 10, the correct approach is to solve m + 6 = 5m - 10 to find the value of m, Mary's age. This is due to the fact that by substituting the expression for w from the first equation into the second, we isolate m and solve for it directly. Here is how you'd solve it step by step:
First, substitute w from the first equation into the second equation, resulting in m + 6 = 5m - 10.
Next, rearrange the terms to get all the m terms on one side: 5m - m = 10 + 6.
Then, simplify to find that 4m = 16.
Last, divide both sides by 4 to get m = 4.
Once you have m, substitute it back into either of the original equations to find w. In this case, w = 4 + 6 = 10.
Graphical solutions involving the x or y axis do not apply directly to solving the system of equations and are therefore not correct methods for this particular problem.
What is -9-x when x= 4.3
Answer:
-9-x=13.3
Step-by-step explanation:
x=4.3
-9-x=
-9-4.3=-13.3
Simplify the expression Square root of 63
Answer:
[tex]3\sqrt{7}[/tex]
Step-by-step explanation:
Step 1: Simplify
[tex]\sqrt{63}[/tex]
[tex]\sqrt{3^2 * 7}[/tex]
[tex]3\sqrt{7}[/tex]
Answer: [tex]3\sqrt{7}[/tex]
Answer:
7.94 0r 3 square root of 7
Step-by-step explanation:
The square root of 63 is 7.9372539331937717715048472609178. If you round it to two places it is 7.94. In radical form it is 3 square root of 7.
Consider the graph that represents the following quadratic equation.
y=-1/3(x+2)^2+5
--the graph opens:
-downward
-upward
--the vertex of the graph is:
-(2,5)
-(-2,-5)
-(-2,5)
--the axis of symmetry of the graph is:
-x=2
-x=-2
Answer:
Part 1) The graphs open downward
Part 2) The vertex is the point (-2,5)
Part 3) The axis of symmetry is x=-2
Step-by-step explanation:
step 1
we have
[tex]y=-\frac{1}{3}(x+2)^2+5[/tex]
This is a vertical parabola open downward (because the leading coefficient is negative)
The vertex is a maximum
step 2
The quadratic equation is written in vertex form
[tex]y=a(x-h)^2+k[/tex]
where
(h,k) is the vertex
so
In this problem
The vertex is the point (-2,5)
step 3
The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
The x-coordinate of the vertex is -2
therefore
The axis of symmetry is x=-2
what is 25x10^9 in standard form
[tex]25*10^9=25*100000000=2500000000[/tex]
NEED HELP ASAP A survey was conducted with high school students in
each grade to see how many prefer math or science.
Some of the data are shown below.
Which statement is true about the joint frequencies in
this table?
40
11 | 12 |
Total
O Twenty-three 9th graders and fifteen 11th graders
prefer math.
O Fourteen 11th graders prefer math and eight 10th
graders prefer science.
O Thirty-five 12th graders prefer math and nine 10th
graders prefer science.
Twenty-three 9th graders and thirty-two 12th
graders prefer math.
Math
18
90
Science 40
15
95
Total
63
26
29
67
185
Question:
a. Twenty-three ninth graders and fifteen eleventh graders prefer math.
b. Fourteen eleventh graders prefer math and eight tenth graders prefer English.
c. Thirty-five twelfth graders prefer math and nine tenth graders prefer English.
d. Twenty-three ninth graders and thirty-five twelfth graders prefer math.
e. Eighteen tenth graders prefer English and fourteen eleventh graders prefer math.
Answer:
Therefore, the correct options are;
b. and d.
Step-by-step explanation:
Here we have a table with blank boxes and totals from which we can fill the boxes;
For the 12th graders, we have a total of 67 pupils with 32 preferring English, therefore the number of the 12th graders that prefer math is 67 - 32 = 35 pupils
Similarly for the 11th graders we have total pupils = 29 with 15 preferring English, therefore the number of the 11th graders that prefer math is 29 - 15 = 14 pupils
Also for the 10th graders we have total pupils = 26 with 18 preferring math, therefore the number of the 11th graders that prefer English is 26 - 18 = 8 pupils
Finally for the 9th graders, we have a total of 63 pupils with 40 preferring English, therefore the number of the 9th graders that prefer math is 63 - 40 = 23 pupils
From the above, the correct option is
Answer:
b only
Step-by-step explanation:
Solve the equation
[tex] {x}^{2} = 196[/tex]
Show your work and explain your steps.
In a class of 18 children, 13 have pet dogs at home, 11 have pet cats, and 8 have both. How many kids do not have four-legged pets at home?
Answer:
2 people
Step-by-step explanation:
8 have both that means that of the 11 people that have cats 3 have only cats and of the 13 that have dogs 5 only have dogs therefore 2 people don't have four-legged animals at home
Answer:
2
Step-by-step explanation:
it starts out with 18 students, 24 pets in total. -16 for the dogs and cats, to lead up to 8, and 10 students left after subtracting 8 for how many students don't have a pet at home. So 2 students shouldn't have four legged pets left after subtracting the rest. (this is my answer, it's probably wrong, i think you should wait for more,)
17. a) Ula jest dwa razy młodsza od Oli i o 4 lata starsza od Ali. Razem te trzy
dziewczynki mają 24 lata. Ile lat ma każda z nich?
b) Tata Zosi jest od niej 3 razy starszy, a Zosia jest od niego młodsza o 30 lat.
Ile lat ma Zosia?
c) Julek i Asia są w sumie o 6 lat starsi od Michała, ale każde z nich z osobna
jest od niego młodsze: Julek o 7 lat, Asia o 2 lata. Ile lat mają wszyscy razem?
Daje Naj za odpowiedź daną za godzinę maks
Answer:
Part 17)
Ula's age is 7 years
Ola's age is 14 years
Ali's age is 3 years
Part 18) Zosia's age is 15 years
Part 19) All together are 36 years old
Step-by-step explanation:
The question in English is
17. Ula is twice as young as Ola and four years older than Ali. Together these three girls are 24 years old. How old is each of them?
18. Zosia's father is 3 times older than her and Zosia is 30 years younger than him.
How old is Zosia?
19. Julek and Asia are 6 years older than Michael, but each of them separately is younger than him: Julek by 7 years, Asia by 2 years. How old are they all together?
Part 17)
Let
x ----> Ula's age
y ---> Ola's age
z ---> Ali's age
we know that
Ula is twice as young as Ola
[tex]y=2x[/tex] ----> equation A
Ula is four years older than Ali
[tex]x=z+4[/tex]
[tex]z=x-4[/tex]----> equation B
Together these three girls are 24 years old.
so
[tex]x+y+z=24[/tex] -----> equation C
substitute equation A and equation B in equation C
[tex]x+2x+(x-4)=24[/tex]
solve for x
[tex]4x=24+4\\4x=28\\x=7[/tex]
Find the value of y
[tex]y=2(7)=14[/tex]
Find the value of z
[tex]z=7-4=3[/tex]
therefore
Ula's age is 7 years
Ola's age is 14 years
Ali's age is 3 years
Part 18)
Let
x ----> Zosia's father's age
y ----> Zosia's age
we know that
Zosia's father is 3 times older than Zosia.
so
[tex]x=3y[/tex] ----> equation A
Zosia is 30 years younger than him.
so
[tex]y=x-30[/tex] ----> equation B
substitute equation A in equation B
[tex]y=3y-30[/tex]
solve for y
[tex]3y-y=30\\2y=30\\y=15[/tex]
therefore
Zosia's age is 15 years
Part 19)
Let
x ----> Julek's age
y ----> Asia's age
z ----> Michael's age
we know that
Julek and Asia are 6 years older than Michael
so
[tex]x+y=z+6[/tex] ----> equation A
Julek is 7 years younger than Michael
[tex]x=z-7[/tex] ----> equation B
Asia is 2 years younger than Michael
so
[tex]y=z-2[/tex] -----> equation C
substitute equation B and equation C in equation A
[tex](z-7)+(z-2)=z+6[/tex]
solve for z
[tex]2z-z=6+9\\z=15[/tex]
Find the value of x
[tex]x=15-7=8[/tex]
Find the value of y
[tex]y=15-2=13[/tex]
Adds the ages
[tex]x+y+z=8+13+15=36\ years[/tex]
therefore
All together are 36 years old
I need to find the line of the slope that passes through the points (-2,3) and (-14,-5) answer in simplest form
Hope this will help u....:)
y varies directly with x. If x=6 when y=30, determine y when x=8.
Answer:
Y=40
Explanation:
Due to the nature of both X and Y varying directly, you can view the problem as a proportion. If x=6 and y=30, that must mean that when x=8 y must equal 40.
6:30 = 8:40
or
30/6= 5
Y/8= 5
Because they vary directly they are equivalent, and so multiply 8 by 5 and get 40.
Answer:40
Step-by-step explanation:
6 times 5 is 30
so 8 times 5 = 40
Find a number that is not a solution to 3x-1>8 or 7-x>3
Answer:
All of the numbers are solutions.
Step-by-step explanation:
Step 1: Solve for x in the first equation
[tex]3x - 1 + 1 > 8 + 1[/tex]
[tex]3x / 3 > 9 / 3[/tex]
[tex]x > 3[/tex]
Step 2: Solve for x in the second equation
[tex]7 - x - 7 > 3 - 7[/tex]
[tex]-x / -1 > -4 / -1[/tex]
Since you divided by a negative, you must flip the sign.
[tex]x < 4[/tex]
Step 3: Find the number
x > 3 and x < 4
Answer: All of the numbers are solutions.
The function f(x) = 2* is translated left 3 units and down 2 units. Which is the equation of the translated function?
g(x) = 2x-3-2
g(x) = 2x -2-3
g(x) = 2x - 2 + 3
g(x) = 2x + 3-2
Answer:
g(x) = 2^(x+3) -2
Step-by-step explanation:
To translate a function f(x) right h units and up k units, it becomes ...
g(x) = f(x -h) +k
Here, your translation is (h, k) = (-3, -2), so the function becomes ...
g(x) = f(x +3) -2
g(x) = 2^(x+3) -2 . . . . matches the last choice
Answer:
D.
Step-by-step explanation:
An aeroplane is flying horizontally, directly towards the city of Melbourne at an altitude of 400 metres. At a given time the pilot views the city lights of Melbourne at an angle of depression of 1.5°. Two minutes later the angle of depression of the city lights is 5°. Find the speed of the aeroplane in km/h, correct to one decimal place.
Please include a diagram
A diagram and review of the basic trig functions will show that the distance d flown by the plane between observations is
d = 400 cot 1.5° - 400 cot 5° = 10700m = 10.7km
10.7km/2min * 60min/hr = 321 km/hr
Hope this helps
Use Appropriate Tools
1) A group of students were
on a school bus. At the last
stop, the bus picked up 16
more students. The bus
arrived at school with a
total of 25 students. How
many students were on the
bus before the last stop?
Solve this problem any way
you choose.
Answer:
9
Step-by-step explanation:
just subtract 16 from 25
will give brainiest to the first person who answers correctly!!!!
Answer:
Option B
Step-by-step explanation:
Its the same because its basically just like stacking the same shape over and over to make a prism
Answer:
answer is B your welcome:)
Step-by-step explanation:
Mr abbot mowed1/4 of his lawn .his son mowed 3/7 of it who mowed most of the lawn how much of the lawn still needs to be mowed
Mr Abbot's son mowed more of the lawn. In total, they mowed 19/28 or approximately 68% of the lawn. Hence, approximately 32% or 9/28 of the lawn still has to be mowed.
Explanation:To find out who mowed more lawn and how much of the lawn is still left to be mowed, we need to compare the fractions and then add them together.
Mr. Abbot mowed 1/4 of his lawn and his son mowed 3/7 of it. To compare these fractions, you can turn them into decimals or percent by dividing the numerator (the top number) by the denominator (the bottom number). Doing that, we find Mr. Abbot mowed 0.25 (or 25%) of the lawn and his son mowed approximately 0.43 (or 43%) of the lawn. Therefore, the son has mowed more lawn.
To figure out how much lawn is still left to be mowed, we add up the fractions of the lawn that Mr. Abbot and his son mowed: [tex]1/4 + 3/7 = 7/28 + 12/28 = 19/28[/tex]. Thus, 19/28 of the lawn have been mowed, and to figure out what fraction is left, we subtract this number from 1 since 1 represents the whole or 100% of the lawn: [tex]1 - 19/28 = 9/28[/tex]. So, 9/28 of the lawn still needs to be mowed.
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What is the positive solution of x2 – 36 = 5x?
Answer:
x² - 5x - 36 = 0
(x - 9)(x + 4) = 0
x = 9 is the positive solution.
From the equation, find the axis of symmetry of the parabola.
y = 3x2 - 12x+11
a. x = -2
b. x = 2
c. x = 1
d. x = -1
Answer:
B. x=2
Step-by-step explanation:
The formula to find the axis of symmetry is -b/2a.
So, in this case, we find our b and a, which are 3 and -12.
Plug them into the formula.
-(-12)/2(3)
The negative sign times another negative makes it into a positive, now we have a positive 12 and then 2 multiplied by 3 equals 6.
Our new equation is 12/6.
Then, simply solve it, 12 divided by 6 equals 2.
Therefore, B would be your answer, x=2.
The axis of symmetry of the parabola defined by the equation y = 3x^2 - 12x + 11 is x = 2.
Explanation:To find the axis of symmetry of the parabola defined by the equation y = 3x2 - 12x + 11,
we can use the formula for the axis of symmetry for a parabola in standard form which is x = -b/2a.
In this equation, a is the coefficient of x2, which is 3, and b is the coefficient of x, which is -12.
Plugging the values into the formula, we get x = -(-12)/(2*3) = 12/6 = 2.
Therefore, the axis of symmetry of the given parabola is x = 2.
Joan has a cafe. Each day, she bakes 24 muffins. She gives away 3 and sells the rest. Each day, she also bakes 36 bagels. she gives away 4 and sells the rest. Write an expression to represent the total number of muffins and bagels Joan sells in 5 days. Then evaluate the expression to find the total amount of muffins and bagels Joan sells in 5 days.
Answer:
(24+36)×5 First you do whatever is in the parentheses first which would be 60. Next you would multiply it by 5 which is 5 days. It is 500. Joan sells 500 muffins and bagels in a day.
The stem-and-lear plot lists the scores earned
by students on a science test.
Stem | Leaf
40
How many students earned a core of 85 or
greater?
5 57
610
7 00 78
Enter your answer in the box.
8 2 2 2 556
9111455
40
Key: 410 means 40.
Answer: I'm sure it is 33
−3x−4y=4
−5x+y=2
Is (2,10)left parenthesis, 2, comma, 10, right parenthesis a solution of the system?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes
(Choice B)
B
No
Substituting the solution (2,10) into both equations of the system shows that it does not satisfy either equation, hence it is not a valid solution.(Choice B.No)
Explanation:To verify the solution of the system of equations, we can substitute the ordered pair (2,10) into both equations. Let's do this:
In the first equation, -3x - 4y = 4, we substitute x = 2 and y = 10. This gives us -3*2 - 4*10 = -6 - 40 = -46, which is not equal to 4.In the second equation, -5x + y = 2, we substitute x = 2 and y = 10. This gives us -5*2 + 10 = -10 + 10 = 0, which is not equal to 2.Since the ordered pair (2,10) does not satisfy either of the two given equations, we can say that (2,10) is not a solution of the system of the equations.
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The point (2,10) is not a solution to the system of equations -3x - 4y = 4 and -5x + y = 2, as it does not satisfy either equation when substituted.
To determine if the point (2,10) is a solution of the given system of equations:
-3x - 4y = 4
-5x + y = 2
we need to substitute x=2 and y=10 into each equation to see if the left-hand side equals the right-hand side.
For the first equation:
-3(2) - 4(10) = -6 - 40 = -46
which does not equal 4, therefore the point (2,10) is not a solution to this equation.
For the second equation:
-5(2) + (10) = -10 + 10 = 0
which does not equal 2, so (2,10) is also not a solution to the second equation.
Since (2,10) does not satisfy either equation, we can conclude that:
(Choice B)
No, (2,10) is not a solution to the system of equations.
An large pizza has a diameter of 14 inches and is cut into 6 equal pieces . Find the area of 2 pieces , rounded to the nearest hundredth
Answer
51.312in^2
hope this helps...
Please help free Brainliest to correct answer!!!!!!!!!!!!
Answer:
D
Step-by-step explanation:
[tex]\frac{5}{6}[/tex]÷[tex]\frac{1}{5}[/tex]
Keep, change, flip.
So, [tex]\frac{5}{6}[/tex] stays the same.
The division sign changes to multiplication.
[tex]\frac{1}{5}[/tex] changes to 5.
So now you have
[tex]\frac{5}{6}[/tex]×[tex]\frac{5}{1}[/tex]= [tex]\frac{25}{6}[/tex]
6·4=24
25-24=1
D= [tex]4\frac{1}{6}[/tex]
Answer:
The correct answer is D. Brainliest plz. I am trying to level up and only have 2 out of the 5 needed. Thanks! Have a good day
Find the slope of the line through (-9,-10) and (-2,-5).
A. -5/7
B. 7/5
C. 5/7
D.-7/5
Just need help with this thank you.
Hope this will help u...:)
Look at the attached picture...!!
76.98 divided by 45.2
Answer:
1.7030973451327434
Step-by-step explanation:
Answer:1.7039735
Step-by-step explanation:
a child should no longer play in the kid zone area when they reach 4'4" tall joe is 54" tall is he allowed to play in the kid zone area
Answer: No.
Step-by-step explanation: Joe is 4'6" tall. Convert 54" to feet by dividing by 12. 54/12=4.5. Half of a foot is 6 inches.
Joe is 54 inches tall, which is taller than the kid zone's maximum allowed height of 52 inches (4 feet 4 inches). Therefore, he is not allowed to play in the kid zone area.
To determine if Joe is allowed to play in the kid zone area, we must compare his height to the maximum height allowed for the kid zone. The maximum height for the kid zone is 4 feet 4 inches, which needs to be converted to inches to compare easily with Joe's height.
First, we know that 1 foot equals 12 inches. So, 4 feet is equal to 4 x 12 inches, which is 48 inches. Adding the extra 4 inches from the height limit gives us 48 + 4 inches, which is 52 inches. This is the maximum height allowed for the kid zone.
Since Joe is 54 inches tall, which is greater than the maximum 52 inches, it means he is too tall to play in the kid zone. Therefore, he is not allowed to play there according to the height restriction.
Some of the students at Kahlo Middle School like to ride their bikes to and from school. They always ride unless it rains. Let d be the distance in miles from a student's home to the school. Write two different expressions that represent how far a student travels by bike in a four week period if there is one rainy day each week.
Answer:
32d
Step-by-step explanation:
-The students ride their bikes to and from school every day. The distance is thus;
[tex]d_t=2d[/tex]
-Taking that there are 5 school days per week and that it rains in one per week. the total number of days is:
[tex]Days=Days \ per \ week \times \ number \ of \ weeks\\\\=(5-1)\times 4\\\\=16\ days[/tex]
Now, we multiply the distance per day by the total number of days:
[tex]Distance, D=2d\times 16\\\\=32d[/tex]
Hence, the total distance in a 4-week period is expressed as 32d ( where d is the distance from home to school).
Find the area of a regular hexagon with an apothem of 15cm
Final answer:
The area of a regular hexagon with an apothem of 15 cm is approximately 1166.55 cm².
Explanation:
The area of a regular hexagon can be found by using the formula:
Area = (3 x apothem x side length) / 2
In this case, the apothem is given as 15 cm. We need to find the side length to calculate the area. The side length can be found using the formula:
side length = 2 x apothem / tan(180° / 6)
Using a calculator, we can find that the side length is approximately 25.98 cm. Plugging in the values into the area formula, we get:
Area = (3 x 15 cm x 25.98 cm) / 2 = 1166.55 cm²
PLEASE ANSWER QUICK! A police officer is estimating the distance from one side of a street to the other. The actual distance is 13.8. The police officer's estimate is 14. Find the absolute error and the percent error of the police officer's estimate. If necessary, round your answers to the nearest tenth
Answer:
The absolute error is 0.2
The percent error is 1.45
Step-by-step explanation:
Please kindly check the attached for explanation
The absolute error of the police officer's estimate is 0.2, and the percent error is approximately 1.5%
Explanation:In Mathematics, absolute error is determined by the absolute value of the difference between the estimated value and the actual value. Therefore, the absolute error in this case is |14 - 13.8| = 0.2.
Percent error, on the other hand, is calculated by first finding the absolute error, then dividing the absolute error by the actual measurement, and finally multiplying the result by 100% to turn it into a percentage. So in this case, the percent error is given by (0.2 / 13.8) * 100 = 1.45%. Since we should round it off to the nearest tenths, the percent error will be roughly 1.5%.
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Given that there are four Cups in a quart and 4 quarts in a gallon which quantity below is equal to 16 quarts?
16 gallons
16 cups
64 cups
126 cups
Answer:
64 cups
Step-by-step explanation:
16 quarts ; 1 quart = 4 cups ; 16*4=64
Answer:
1 quart = 4 cups
Therefore 16 quarts = 16 * 4 cups or
64 cups.
Step-by-step explanation: