The present age of father is 35 and daughter is 7.
Step-by-step explanation:
Let,
Age of father = x
Age of daughter = y
According to given statement;
A man is 5 times older than his daughter.
x = 5y Eqn 1
In 7 years, the man is 3 times as old as his daughter.
x+7 = 3(y+7)
[tex]x+7=3y+21\\x=3y+21-7\\x=3y+14\ \ \ Eqn\ 2[/tex]
Putting value of x from Eqn 2 in Eqn 1
[tex]3y+14=5y\\14=5y-3y\\14=2y\\2y=14[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{14}{2}\\y=7[/tex]
Putting y=7 in Eqn 1
[tex]x=5(7)\\x=35[/tex]
The present age of father is 35 and daughter is 7.
Keywords: linear equation, substitution method
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Final answer:
The present ages of the man and his daughter are 35 years and 7 years, respectively.
Explanation:
The question asks us to find the current ages of a man and his daughter, given that the man is currently five times older than his daughter and that after 7 years, he will be three times as old as her. To solve this, we can set up two equations based on the information provided:
Let D be the daughter's current age, the man's current age is 5D (since he is five times older).In 7 years, the daughter's age will be D+7 and the man's age will be 5D+7. At that time, the man will be three times as old as his daughter, so we have 5D+7 = 3(D+7).Now, we solve the equation from step 2 to find the daughter's age:
5D + 7 = 3(D + 7)5D + 7 = 3D + 215D - 3D = 21 - 72D = 14D = 7So, the daughter is currently 7 years old. To find the man's age, we multiply the daughter's age by 5:
Man's age = 5 x 7 = 35 years old
Therefore, the man is currently 35 years old and the daughter is 7 years old.
7 X 7 X 5 X 5 in exponential form
Answer:
7^2*5^2
Step-by-step explanation:
The equation contains two 7's and two 5's. 7 squared and 5 squared can be written like this, so the answer is 7^2*5^2
How can I use fractions tiles to help divide a whole number by a unit fraction
Final answer:
To divide a whole number by a unit fraction using fraction tiles, treat the division as multiplication by the reciprocal of the unit fraction and then split the whole number tiles accordingly.
Explanation:
To use fraction tiles to help divide a whole number by a unit fraction, you can follow these steps:
Understand that dividing by a unit fraction is the same as multiplying by its reciprocal. For example, dividing by 1/2 is the same as multiplying by 2, since 2 is the reciprocal of 1/2.Start with fraction tiles that represent the whole number you want to divide. For instance, if the whole number is 6 and you're dividing by 1/2, use 6 whole tiles.Since you're multiplying by the reciprocal of the unit fraction, convert the action of dividing into multiplication. Each whole tile would be split into the number of pieces that are equivalent to the denominator of the unit fraction. If dividing by 1/2, split each whole into 2 pieces.Count all the new pieces. The result is the number of pieces you have after dividing by the unit fraction. In our example with 6 whole tiles and dividing by 1/2, you'd end up with 12 pieces since each whole tile is split into 2 pieces.What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1?
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
–8
–5
0
6
Answer: 0 on edge
Step-by-step explanation:
got it correct
Answer: C
Step-by-step explanation:
took quiz
Help help help help
The missing length [tex]x=\frac{12}{5}[/tex].
Solution:
The image of the answer is attached below.
In figure ABCD, AB = 4, BC = 10
In figure PQRS, PQ = x, RS = 6
Given figures are similar.
If two figures are similar, then the sides are proportionate to each other.
⇒ [tex]\frac{AB}{BC}= \frac{PQ}{QR}[/tex]
⇒ [tex]\frac{4}{10}= \frac{x}{6}[/tex]
Do cross multiply.
⇒ [tex]4 \times 6 = x \times 10[/tex]
⇒ [tex]24 = 10x[/tex]
⇒ [tex]x=\frac{24}{10}[/tex]
To reduce the length, divide both numerator and denominator by 2.
⇒ [tex]x=\frac{12}{5}[/tex]
Hence, the missing length [tex]x=\frac{12}{5}[/tex].
Can some one help me please and explain it
Answer:
c= -2
Step-by-step explanation:
Perpendicular lines imply that the product of the gradient of the two lines is -1.
So let's find the gradient of each lines.
[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]
Gradient of 1st line
= 1-(-4)/ -3-2
= 5/-5
= -1
(gradient of 1st line)(gradient if 2nd line)= -1
(-1)(gradient of 2nd line)= -1
gradient of 2nd line= -1 ÷ (-1) =1
Now make use of the gradient formula to find an expression of the gradient of the second line.
Gradient of 2nd line= c-1/ -2-1
subst. gradient of second line and simplify:
1= c-1/-3
c-1= -3 (multiply by -3 on both sides)
c= -3+1 (add 1 on both sides)
c= -2
Simplify (p squared) to the power of 5
Answer:
p^10.
Step-by-step explanation:
(p^2)^5
= p^(2*5)
= p^10.
Answer:
Step-by-step explanation:
(P²)^5 = P^(2×5) = P^10
What are the like terms in this expression?
9a - 3b + 4ab
Answer:
There are no like terms for all 3 variables for 9a-3b+4ab
What is the value of n?
Answer:
What is n?
Step-by-step explanation:
ASAP
Of 450 lunches sold at school on Thursday, 40% were hamburgers
and the rest were pizza. How many more pizza lunches were sold than
hamburgers? Explain how you found your answer.
Answer: 90
Step-by-step explanation:
Total number of lunches sold = 450
Number of hamburgers = 40% of the total , that is
number of hamburgers = 40/100 x 450 = 180
number of pizza = 450 - 180 = 270
Therefore , the number of pizza lunches sold more than hamburgers will be
270 - 180 = 90
Therefore : 90 more pizza lunches were sold than hamburgers.
The friends now To go on the loop D loop and the roller coaster. Explain why only 1 of the friends can go on both of these rides
Are there any more instructions or information?
Due to requirements such as height and ride capacity, only one friend can go on both the loop and the roller coaster at the same time.
Explanation:In order to go on the loop and the roller coaster, the friends need to meet certain requirements. For example, they need to be tall enough to ride the roller coaster and meet any age restrictions. Additionally, the roller coaster may have a limited number of seats or ride capacity. Due to these factors, it's possible that only one friend can go on both of these rides at the same time.
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Is 1/8+1/6 greater than 16/63
Answer:
yes
Step-by-step explanation:
Write as a product of two polynomials (y–5)–y(5–y)
pls answer asap I will post free coins
The product of the two binomials is (y + 1)(y - 5)
Step-by-step explanation:
To write a polynomial as a product of two binomials
At first simplify the polynomialAdd the like terms if necessaryFactorize it using any type of factorization to get a product of two binomials∵ The polynomial is (y - 5) - y(5 - y)
- Multiply y by the bracket (5 - y)
∵ y(5 - y) = y(5) - y(y)
∴ y(5 - y) = 5y - y²
- Substitute 5(5 - y) by (5y - y²)
∴ (y - 5) - y(5 - y) = (y - 5) - (5y - y²)
- Multiply (-) by the bracket (5y - y²)
∵ (-)(5y) = -5y
∵ (-)(-y²) = y²
∴ (y - 5) - y(5 - y) = y - 5 - 5y + y²
- Add the like terms
∴ (y - 5) - y(5 - y) = -4y - 5 + y²
- Arrange the terms from greatest power of y
∴ (y - 5) - y(5 - y) = y² - 4y - 5
Now let us factorize y² - 4y - 5 into two factors
∵ y² = y × y
∵ -5 = -5 × 1
- Multiply y by 1 and y by -5, then add the product the sum
must be equal the middle term of the polynomial above
∵ y(1) + y(-5) = y - 5y = -4y ⇒ as the middle term
- Now write the two bracts
∴ y² - 4y - 5 = (y + 1)(y - 5)
The product of the two binomials is (y + 1)(y - 5)
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Common factor and HCF of 10m squared,15mk
Answer:
Step-by-step explanation:
10m^2 and 15mk
common factor is 5m
HCF is 5m
Factor each expression.
17. 5x -25
Hii!
_________________________________________________________
Answer:
5(x-5)
Step-by-step explanation:
Both terms, 5x and -25, have something in common. This "something" is called the greatest common factor, or g.c.f.
The g.c.f. of 5x and -25 is 5, so we factor 5 out by dividing 5x and -25 by 5. Upon doing this we obtain
x-5
Now we need to put parentheses around x-5.
(x-5)
Next, we put 5 outside the parentheses.
5(x-5)
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Hope that this helped! Best wishes.
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Solve using elimination.
10x + 6y = –2
2x + 6y = –10
Answer:
(1, - 2 )
Step-by-step explanation:
Given the 2 equations
10x + 6y = - 2 → (1)
2x + 6y = - 10 → (2)
Multiplying (2) by - 1 and adding to (1) will eliminate the y- term
- 2x - 6y = 10 → (3)
Add (1) and (3) term by term
(10x - 2x) + (6y - 6y) = (- 2 + 10), that is
8x = 8 ( divide both sides by 8 )
x = 1
Substitute x = 1 into either of the 2 equations.
Substituting x = 1 into (1)
10(1) + 6y = - 2
10 + 6y = - 2 ( subtract 10 from both sides )
6y = - 12 ( divide both sides by 6 )
y = - 2
Solution is (1, - 2 )
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which is a true statement about the diagram?
m∠5 + m∠6 = m∠1
m∠3 + m∠4 + m∠5 = 180°
m∠1 + m∠2 = 180°
m∠2 + m∠3 = m∠5
i need it to be correct please help<3
Final answer:
The correct statement regarding the interior and exterior angles of the triangle is 'm∠3 + m∠4 + m∠5 = 180°'. Option b
Explanation:
When considering the properties of interior and exterior angles in a triangle, several theorems are useful to determine the correct statement among the choices provided.
Specifically, one important theorem to recall is: The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Additionally, the sum of all interior angles in a triangle is always 180 degrees.
With these principles in mind, we can examine the provided statements:
m∠5 + m∠6 = m∠1 - Incorrect. The exterior angle at a vertex of a triangle is the sum of the two opposite interior angles, not an addition of an interior and its adjacent exterior angle.
m∠3 + m∠4 + m∠5 = 180° - Correct. This is true because m∠4, being an exterior angle, is equal to m∠2 + m∠5, and since the sum of the interior angles of a triangle is 180 degrees, m∠2 + m∠3 + m∠5 = 180 degrees. Replacing m∠2 + m∠5 with m∠4 gives us the correct equation.
m∠1 + m∠2 = 180° - Incorrect. This statement would imply that angle 1 and angle 2 are on a straight line, which is not the case in a triangle's exterior and interior angles.
m∠2 + m∠3 = m∠5 - Incorrect. There is no direct theorem that supports this statement as a relationship between these angles in a triangle.
The correct statement, based on the theorems regarding triangle angles, is m∠3 + m∠4 + m∠5 = 180°.
ASAP PLEASE !!!!!
Two trains leave a station on different tracks. The tracks make an angle of 130°, with the station as a vertex. The first train
travels 100 km and makes its first stop at point A, while the second train travels 200 km and makes it first stop at point B.
How far apart are the trains when both are at their first stop? Round the answer to the nearest integer.
The trains are 275 km apart when both are at their first stop
Solution:
The tracks make an angle of 130°, with the station as a vertex
Therefore, from given figure in question,
Angle at station = 130 degree
Let "c" be the point at station
The first train travels 100 km and makes its first stop at point A
Distance between A and station c = 100 km
Let a = 100 km
The second train travels 200 km and makes it first stop at point B
Distance between B and station c = 200 km
Let b = 200 km
We have to find the value of "d"
We can use the law of cosine
The square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.
From given figure in question,
Side opposite "d" to 130 degree is equal to sum of square of other sides a and b minus twice the product of those sides and the cosine of the angle between them which is 130 degrees
Therefore,
[tex]d^2 = a^2 + b^2 - 2ab\ cos\ d[/tex]
[tex]d^2 = 100^2 + 200^2 - 2(100)(200)cos 130\\\\d^2 = 10000 + 40000 - 40000cos 130\\\\d^2 = 50000 - 40000 \times -0.6427\\\\d^2 = 50000 + 25711.5\\\\d^2 = 75711.5\\\\\text{Take square root on both sides }\\\\d = 275.15 \approx 275[/tex]
Thus trains are 275 km apart when both are at their first stop
Answer:
D. 275 km
Step-by-step explanation:
Simplify.
Remove all perfect squares from inside the square root. Assume yyy is positive.
\sqrt{39y^9}=
39y
9
Answer:
[tex]y^4\sqrt{39y}[/tex]
Step-by-step explanation:
[tex]\displaystyle\sqrt{39y^9}=\sqrt{39y(y^4)^2}=y^4\sqrt{39y}[/tex]
To simplify √(39y¹¹), rewrite y¹¹ as (y²)·(y²)·(y²) and take out the perfect square. The simplified expression is 3y√(39y).
Explanation:To simplify the expression √(39y¹¹), we need to remove the perfect square from inside the square root. Since y is raised to the power of 9 and is positive, it is a perfect square. We can rewrite y¹¹ as (y²)·(y²)·(y²).
Therefore, √(39y¹¹) = √(39(y²)·(y²)·(y²)) = √(39)·(y²)√(y²)√(y²) = √(39)·y²·y²·y² = √(39)·y¹ = 3y√(39y).
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Solve by using substitution. Express your answer as an ordered pair.
3x+y=10
Y=x+2
A.) 8,10
B.) 8/3,2
C.) 2,4
D.) 4,2
Answer:
c. 2,4
Step-by-step explanation:
elizabeth can run 5 mils in 24 1/2 minutes Dez can run 8 miles in 32 1/3 minutes. who can run faster?
Equivalent ratio 1:
Equivalent ratio 2:
Answer:
Des can run faster than Elizabeth.
Des can run 1 mile in 4.037 minutes while Elizabeth can run 1 Mile in 4.9 minutes
Step-by-step explanation:
If Elizabeth can run 5 miles in 24.5 minutes. Elizabeth will run 1 mile in 24.5/5=4.9 minutes.
If Dez can run 8 miles in 32 1/3 minutes. Then Dez will run 1 mile in 32.3/8=4.037 minutes
Therefore if Dez can run 1 mile in 4.037 minutes and Elizabeth can run 1 mile in 4.9 minutes then Dez can run faster than Elizabeth.
Ben drove his car 467 kilometer in 5 hours while he was on vacation in Italy. He was trying to estimate how far he could drive in 7 hours the next day, so he set up the following proportion: . Is his proportion correct? Or, incorrect? Explain your choice and support with appropriate mathematical terminology.
Answer:653.8
Step-by-step explanation:
467 /5=93.4 miles in five hours. 93.4 *7 =653.8
If sin A is negative and cos A is positive, what
is the number of the quadrant in which angle A
terminates?
Answer:
Quadrant 4
Step-by-step explanation:
sinA < 0 in quadrants 3 and 4
cosA > 0 in quadrants 1 and 4
Thus sinA < 0 and cosA > 0 in quadrant 4
What is 3 5/8 ÷14 please answer this
Answer:
29/112
Step-by-step explanation:
3 5/8=29/8
(29/8)/14
(29/8)(1/14)=29/112
Michelle sets up a lemonade stand to make some extra money.She spends $4.75 purchasing supplies.She earns $16.50 selling lemonade.How much money does she make after she subtracts her expenses?
3,562,185 What is the value of 3?
Answer: 3 millions
Explanation: To determine what the digit "3" means in 3,562,185, if we put 3,562,185 into the place value chart, we can see that the 3 appears in the units column of the millions period so in this problem 3 refers to 3 millions.
Desmond's Desserts made a batch of fresh scones with 2/3 of a pound of butter and 1/2 of a
pound of sugar. How much more butter than sugar was used?
Write your answer as a fraction or as a whole or mixed number.
pounds
[tex]\frac{1}{6}[/tex] or 0.167 pounds more butter was used than sugar
Solution:
Given that, Desmond's Desserts made a batch of fresh scones with 2/3 of a pound of butter and 1/2 of a pound of sugar
To find: Amount of butter used than sugar
From given information,
[tex]\text{Butter used} = \frac{2}{3} \text{ pound }[/tex]
[tex]\text{Sugar used } = \frac{1}{2} \text{ pound }[/tex]
To find how much butter is used than sugar, find the difference between them
[tex]Difference = Butter\ used - Sugar\ used[/tex]
[tex]Difference = \frac{2}{3} - \frac{1}{2}\\\\Difference = \frac{2 \times 2-1 \times 3}{3 \times 2}\\\\Difference =\frac{4-3}{6}\\\\Difference =\frac{1}{6} = 0.167\\\\[/tex]
Thus [tex]\frac{1}{6}[/tex] or 0.167 pounds more butter was used than sugar
Sammy is taking a test. Each correct question gives him 5 points and each incorrect question causes him to lose a point. He answers all 20 questions and gets a score of 64. How many questions did he answer correctly?
Answer:14
Step-by-step explanation:
figure out 5x20,, which gives you 100 points
use trial and error is my method :)
if he answered 10 correct, he would get 50 points and lose 10. this gives 40 points. its an error
we now know its between 11 right and 19 right
we continue to do this till we get it right
14 x 5 = 68. - 4 makes 64.
Sammy answered 14 questions correctly on his test, as determined by setting up and solving the equation 5x - (20 - x) = 64, where x represents the number of correct answers.
Sammy is taking a test where each correct question awards him 5 points and each incorrect one deducts a point. With 20 questions in total and a score of 64, we can set up an equation to find out how many questions he answered correctly. Let x represent the number of correct answers. Then, the number of incorrect answers would be 20-x. The scoring system gives us the following equation:
5x - (20 - x) = 64
By solving this equation, we can find out how many questions Sammy answered correctly:
Combine like terms: 5x - 20 + x = 64
Simplify: 6x - 20 = 64
Add 20 to both sides: 6x = 84
Divide both sides by 6: x = 14
Thus, Sammy answered 14 questions correctly on his test.
A figure is translated using the mapping (x, y) → (x + a, y + b). If the value of a is negative and the value of b is negative, which best describes the translation? The figure moves left and up. The figure moves left and down. The figure moves right and up. The figure moves right and down.
The translation is The figure moves left and down.
Option:B.
Step-by-step explanation:
The given coordinate (x,y) is mapped and it gets translated using mapping (x+a,y+b).
Also, we are given with information that the value of a and also value of b is negative (-a,-b).
⇒the mapping coordinate = (x+(-a),y+(-b)).
The mapping coordinate = ( x-a, y-b).
The coordinate points will be decreasing in x and y axis. So it will move towards the left and downside of the graph.
For example,
Consider that a= -3 and b= -2.
∴The translating coordinate will be (x-3,y-2).
Choose a coordinate point ( 2,2) initially.
Substitute the x,y coordinate in the translating coordinate.
⇒ (x-3,y-2) = (2-3,2-2).
=(-1,0).
After translation the points will be (-1,0).
∴The figure will move towards left and downwards.
Answer:
b} The figure moves left and down
Step-by-step explanation:
i took the test
it took Bob 55 minutes to clean the garbage. How many seconds did it take bob?there are 60 seconds in one minute please help me .
Answer:
3,300 sec
Step-by-step explanation:
Angle 1 and angle 2 are vertical angles.
Angle 2 has a measure of 93°
What is the measure of angle 1 ?
Enter your answer in the box
Answer:
<1 = 93 (vertical opposite angle are equal)
Step-by-step explanation:
Answer: I can confirm, Josshyaby is correct I took the test
Step-by-step explanation: