Answer:
1 - 3/10 = 7/10 of the distance left
(3/7)(7/10) = 3/10 of the total distance
Zachary's family traveled [tex]\( \frac{51}{70} \)[/tex] of the total distance to his aunt's house.
To find the fraction of the total distance traveled to Zachary's aunt's house, we need to combine the distances traveled and express it as a fraction of the total distance.
Given:
1. Zachary's family traveled [tex]\( \frac{3}{10} \)[/tex] of the total distance to his aunt's house.
2. Then, they traveled [tex]\( \frac{3}{7} \)[/tex] of the remaining distance.
Step 1: Calculate the total distance traveled by combining the two distances.
[tex]\[ \text{Total distance traveled} = \frac{3}{10} + \frac{3}{7} \][/tex]
Step 2: Find a common denominator for [tex]\( \frac{3}{10} \) and \( \frac{3}{7} \).[/tex] The least common multiple (LCM) of 10 and 7 is 70.
Step 3: Rewrite the fractions with the common denominator of 70.
[tex]\[ \frac{3}{10} = \frac{3 \times 7}{10 \times 7} = \frac{21}{70} \][/tex]
[tex]\[ \frac{3}{7} = \frac{3 \times 10}{7 \times 10} = \frac{30}{70} \][/tex]
Step 4: Add the fractions:
[tex]\[ \frac{21}{70} + \frac{30}{70} = \frac{21 + 30}{70} = \frac{51}{70} \][/tex]
Therefore, Zachary's family traveled [tex]\( \frac{51}{70} \)[/tex] of the total distance to his aunt's house.
what is the second smallest number that has 1,2,3,4,5 as factors
Solve the system of equations. y = 6x - 27 y = 4x - 17 a. ( -5, 3) c. ( 5, 3) b. ( -3, -5) d. No solution Please select the best answer from the choices provided A B C D
Answer:
c. ( 5, 3)
Step-by-step explanation:
6x-27=4x-17
6x-27-4x=4x-17-4x
2x-27=-17
2x-27+27=-17+27
2x=10
x=10/2
x=5
y=6(5)-27
y=30-27
y=3
Which graph represents viable values for y = 5.5x, where x is the number of cans of tomato paste and y is the total weight of the sealed cans in ounces?
On a coordinate plane, x-axis is numbered negative 5 to positive 5 in increments of 1, and the y-axis is numbered negative 27.5 to 27.5 in increments of 5.5. A straight line with a positive slope begins at point (0, 0) and ends at point (5, 27.5)
On a coordinate plane, x-axis is numbered negative 5 to positive 5 in increments of 1, and the y-axis is numbered negative 27.5 to 27.5 in increments of 5.5. Solid circles appear at points (0, 0), (1, 5.5), (2, 11), (3, 16.5), (4, 22), (5, 27.5)
On a coordinate plane, x-axis is numbered negative 5 to 5 in increments of 1, and the y-axis is numbered negative 27.5 to 27.5 in increments of 5.5. A straight line with a positive slope begins at point (negative 5, negative 27.5) and ends at point (5, 27.5).
On a coordinate plane, x-axis is numbered negative 5 to 5 in increments of 1, and the y-axis is numbered negative 27.5 to 27.5 in increments of 5.5. Solid circles appear at points (negative 5, negative 27.5), (negative 4, negative 22), negative 3, negative 16.5), (negative 2, negative 11), (negative 1, negative 5.5), (0, 0), (1, 5.5), (2, 11), (3, 16.5), (4, 22), (5, 27.5)
Answer:
the answer is the first graph
Step-by-step explanation:
because the negative points are not viable
The graph of the equation y = 5.5x is shown in the picture and the slope of the line is positive, which is 5.5 option first is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have a linear equation in the form of slope:
y = 5.5x
Slope of the line m = 5.5
Slope is positive, which means the line goes down to up.
We can plot the graph of the equation y = 5.5x
Option first On a coordinate plane, x-axis is numbered negative 5 to positive 5 in increments of 1, and the y-axis is numbered negative 27.5 to 27.5 in increments of 5.5. A straight line with a positive slope begins at point (0, 0) and ends at point (5, 27.5) is correct.
Thus, the graph of the equation y = 5.5x is shown in the picture and the slope of the line is positive, which is 5.5 option first is correct.
Learn more about the straight line here:
brainly.com/question/3493733
#SPJ2
Is this right? If not someone explain to me why it’s not. :)
Answer:
x= 14√3
y= 28√3
Step-by-step explanation:
Please see attached picture for full solution.
(tan30° and cos30° are special angles so there's an exact value to it in which we can memorise.)
In this case, by Pythagoras's Theorem, you should ensure that:
[tex] {y}^{2} = 42^{2} + {x}^{2} [/tex]
✓ Let's check:
[tex]{y}^{2} = (28 \sqrt{3} )^{2} \\ y^{2} = 2352 \\ {x}^{2} + {42}^{2} = ( 14\sqrt{3})^{2} + 1764 = 2352[/tex]
This satisfies Pythagoras' Theorem :)
For this kind of questions, first label the adjacent side, opposite side and the hypotenuse side of the triangle.
Cosine angle= adjacent/ hypotenuse
Sine angle= opposite/ hypotenuse
tangent angle= opposite/ adjacent
Then substitute the known side and angle to find the unknown side.
Find the slope for the following pair of points:
(10,4) and (-2, 17)
Final answer:
The slope of the line passing through the points (10,4) and (-2, 17) is calculated using the slope formula and is approximately -1.08.
Explanation:
To find the slope for the line passing through the two points (10,4) and (-2, 17), we use the slope formula which is (change in y)/(change in x) or (y2 - y1) / (x2 - x1). Applying this formula to our points:
m = (17 - 4) / (-2 - 10)
m = 13 / -12
m = -1.0833...
So, the slope of the line that passes through the points (10,4) and (-2, 17) is approximately -1.08.
100 points for the first five people!!!!!
Answer:
cj sjx soiebxidhevdi hi
Answer: hi
Step-by-step explanation:
Lol
question and answer choices in the attachment
The additive inverse is the idea of adding a negative number, which is the same as subtraction. Example: 2 + (-3) = 2-3
Based on the example above, if we start off with 3 and add on its additive inverse -3, then 3 + (-3) = 3-3 = 0. In general, x + (-x) = x-x = 0. So adding any number with its additive inverse gets you 0 every time.
-----------------------------------------------
Extra info:
Choice A is ruled out because the commutative property of multiplication is the idea that we can multiply two numbers in any order we want. Eg: 7*8 = 56 and 8*7 = 56, so 7*8 = 8*7Choice B is ruled out as well. The commutative property of addition is similar to the rule mentioned in choice A. But now we're adding. This rule says we can add two numbers in any order. Eg: 4+5 = 5+4 = 9Choice D is ruled out also. The multiplicative inverse of x is 1/x. Multiplying the two together gets you 1. Keep in mind that x cannot be zero. Example: The multiplicative inverse of 99 is 1/99, since 99*(1/99) = 99/99 = 1.What is the answer for 25% of 450
Answer:
112.5
Step-by-step explanation:
112.5 ÷ 450 =
0.25 =
0.25 × 100/100 =
0.25 × 100% =
(0.25 × 100)% =
25%
or
25% × 450 =
(25 ÷ 100) × 450 =
(25 × 450) ÷ 100 =
11,250 ÷ 100 =
112.5
Answer:
112.5
Step-by-step explanation:
First you would divide 450÷100=4.5. Then you would multiply 4.5×25=112.5.
this would give you 25% of 450
400÷100=4.5
4.5×25=112.5
The awnser choices are in the second photonplz awnser asap their are
3 questions plz help
Answer:
Part A : [tex]1621\frac{1}{3}\pi[/tex] cubic meters.
Part B : 540π cubic cm.
Part C : [tex]V = \frac{4}{3}\pi r^{3}[/tex]
Step-by-step explanation:
Part A :
The volume of the silo includes the volume of a hemisphere and a cylinder.
So, the total volume
[tex]V = \frac{2}{3}\pi r^{3} + \pi r^{2}h[/tex]
⇒ [tex]V = \frac{2}{3} \times \pi (8)^{3} + \pi (8)^{2} (20)[/tex]
⇒ [tex]V = \frac{1024}{3}\pi + 1280\pi = 1621\frac{1}{3}\pi[/tex] cubic meters. (Answer)
Part B :
The volume of the cylindrical cup with height 15 cm and base radius 6 cm is given by
[tex]V = \pi r^{2}h = \pi (6)^{2} (15) = 540\pi[/tex] cubic cm.
Therefore, Mary can put 540π cubic cm of water in the cup with out it overflowing. (Answer)
Part C :
A basketball is of a spherical shape.
So, the formula of its volume is given by [tex]V = \frac{4}{3}\pi r^{3}[/tex]. (Answer)
Tony believes that x = -9 is a root of the polynomial x^2 + 13x + 36. Erika, however, believes that x = 4 is a root of the same polynomial. Who is correct?
Tony is correct.
Step-by-step explanation:
Given polynomial is;
[tex]x^2+13x+36=0[/tex]
Tony's answer is x = -9
We will put x = -9 in given polynomial.
[tex](-9)^2+13(-9)+36=0\\81-117+36=0\\0 = 0[/tex]
Tony's solution satisfies the equation.
Erika's answer is x = 4
We will put x = 4 in given polynomial.
[tex](4)^2+13(4)+36=0\\16+52+36=0\\104\neq 0[/tex]
Erika's solution does not satisfy the equation, therefore
Tony is correct.
Keywords: polynomial, roots
Learn more about polynomials at:
brainly.com/question/11258952brainly.com/question/11343416#LearnwithBrainly
Which equation uses the distributive property to show 6 × 78 = 468? A) 6 + (70 × 8) = 468 B) 6 × (70 + 8) = 468 C) 6 + (70 + 8) = 468 D) 6 × (70 × 8) = 468
Answer:
b
Step-by-step explanation:
you can break the 78 into 70 and 8, and multiply them separately by 6 and then add the two answers to get 468
Answer:
B
Step-by-step explanation:
literally the only equivalent equation
a syrup is made by dissolving 2 cups of sugar to 2/3 cups of boiling water. how many cups of sugar should be used for 2 cups of boiling water
Answer:
6 cups
Step-by-step explanation:
did the math
For two cups of boiling water, 6 cups of sugar would be needed
The first step is to determine how many cups of sugar that would be needed for one cup of boiling water
The number of cups of sugar needed for a cup of boiling water = cups of sugar / cups of boiling water
2 ÷ [tex]\frac{2}{3}[/tex]
2 x [tex]\frac{3}{2}[/tex] = 3 cups
The second step is to determine the number of cups of sugar that would be needed with two cups of boiling water
Cups of sugar needed for 2 cups of water = cups of sugar needed for one cups of boiling water x 2
3 cups x 2 cups = 6 cups
In order to determine the cups of sugar needed for two cups of boiling water, first determine the number of cups of sugar needed for a cup of boiling water. Use the figure determined to find the cups of sugar needed for 2 cups of water
A similar question was solved here: https://brainly.com/question/16614723?referrer=searchResults
Let f(x)=2x^2+3x-15 and g(x)=x-1. Perform the function operation and then find the domain.
(F+G)(X)=
Answer:
[tex](F+G)x=2x^2+4x-16[/tex]
[tex]Domain[/tex] [tex]=(-\infty,\infty)[/tex]
Step-by-step explanation:
Given that
[tex]F(x)=2x^2+3x-15[/tex]
and [tex]G(x)=x-1[/tex]
then [tex](F+G)x = F(x)+G(x)[/tex]
[tex]=(2x^2+3x-15)+(x-1)\\=2x^2+3x-15+x-1\\\\(F+G)x=2x^2+4x-16[/tex]
Domain
since it is a polynomial of degree [tex]2[/tex], the domain will be whole real line
[tex]domain[/tex] [tex]=(-\infty,\infty)[/tex]
Final answer:
To perform the function operation (F+G)(X), add the functions f(x) and g(x) together to get (F+G)(X) = 2x² + 4x - 16. The domain of this function is all real numbers.
Explanation:
To perform the function operation (F+G)(X), where f(x) is given as 2x² + 3x - 15 and g(x) is x - 1, we simply add the two functions together:
(F+G)(X) = f(x) + g(x)
(F+G)(X) = (2x² + 3x - 15) + (x - 1)
This simplifies to:
(F+G)(X) = 2x² + (3x + x) - (15 + 1)
(F+G)(X) = 2x² + 4x - 16
The domain for this new function is all real numbers, since there are no restrictions such as division by zero or taking the square root of a negative number that would limit the values that x can take.
Simplify the expression.
Answer:
The answer is (t4)-7
Step-by-step explanation:
First you simplify the like terms so t add the 2s together and you get t4 then add the negative numbers and it equals -7.
Answer:(t4)-7
Step-by-step explanation:
Please help me asap i will mark branlist please explain
Answer:
195in^2 is the correct answer.
Step-by-step explanation:
WILL GIVE BRAINIEST!!!
Dominic collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected: Favorite Sport Swimming Running Volleyball Row totals Grade 8 0.24 0.17 0.05 0.46 Grade 9 0.18 0.14 0.22 0.54 Column totals 0.42 0.31 0.27 1 Based on the data, which statement is most likely correct? In Grade 8, 14 students liked swimming. In Grade 8, 17% of students liked running. In Grade 9, 31% of students liked volleyball. In Grade 9, 22 students liked volleyball.
Answer:
The only correct statement is ii) In Grade 8, 17% of the students liked
running.
Step-by-step explanation:
Favorite Sports
Swimming Running Volleyball Total
Grade 8 0.24 0.17 0.05 0.46
Grade 9 0.18 0.14 0.22 0.54
Total 0.42 0.31 0.27 1
i.) In Grade 8 14 students liked swimming.
This cannot be said with accuracy as the total number of students is not
known.
ii) In Grade 8, 17% of the students liked running.
This statement is TRUE.
iii) In Grade 9, 31% of students liked volleyball.
This statement is NOT TRUE. In Grade 9, 22% of the students liked
volleyball.
iv) In Grade 9, 22 students liked volleyball.
This cannot be said with accuracy as the total number of students is not
known.
The only correct statement is ii) In Grade 8, 17% of the students liked
running.
Answer:
In Grade 8, 17% of the students liked running.
find the sum of the product of 10 and 36 and the product of 12 and 51
Answer:
972
Step-by-step explanation:
10 x 36= 360
12 x 51= 612
360+612= 972
Brainliest please :)
Answer:
972
Step-by-step explanation:
Product = Multiplication
Sum = Addition
10 * 36 + 12 * 51
Multiply first
360 + 612
Add
972
Hope this helps :)
can some one plz help me with this question
Solve the equation.
6(2x - 3) + 4 = 16 - (-18)
Answer:
x=4.16
Step-by-step explanation:
12x -18 +4 = 16+18
12x-16= 16+18
12x-16=34
+16 +16
12x=50
50/12
4.16
points (0,12) and (1,3) in linear function
Answer:
y = -9x + 12
Step-by-step explanation:
first find the slope
m= 3 - 12
1 - 0
m = -9
y = mx + b
y = -9x + 12
(the 12 is the y intercept and is given in the question so there is no need to solve for it)
the solution to 5 - 3x> 35 is either x>-10 or -10> x. which solution is correct
The area of the right triangle shown is 24 square feet.
Which equations can be used to find the lengths of the
legs of the triangle? Select three options.
3 0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x - 24 = 0
10 ft
(x + 2) ft
* x2 + 2x - 48 = 0
* x2 + (x + 2)2 = 100
xft
Not drawn to scale
The equations used to find the length of leg of triangle are:
[tex]0.5x(x+2) = 24\\\\x^2+2x-48=0\\\\x^2+(x+2)^2 = 100[/tex]
Solution:
From given,
Area of right triangle = 24 square feet
Also from given figure in question (attached below )
base = x and height = x + 2
The area of triangle is given by formula:
[tex]Area = \frac{1}{2} \times base \times height[/tex]
Substituting the values we get,
[tex]24 = \frac{1}{2} \times x \times (x+2)\\\\24 = 0.5x(x + 2)\\\\48 = x(x+2)\\\\x^2 + 2x - 48 = 0\\\\[/tex]
Also, the above equation can be written as,
[tex]x^2 + (x+2)^2 =100[/tex]
Thus the equations used to find the length of leg of triangle are:
[tex]0.5x(x+2) = 24\\\\x^2+2x-48=0\\\\x^2+(x+2)^2 = 100[/tex]
Answer:
A, D, E
Step-by-step explanation:
From the answer above, but the letters to make it easier :)
John is 3 years younger than twice Monica's age. If m represents Monica's age, which equation can be used to find j, John's age?
A. j = 2m-3
B. m = 2j-3
C. j = 3-2m
D. m = 3-2
Answer:
J =2m -3
Step-by-step explanation:
2m is twice Monica's age
-3 represents 3 years younger
if you know abc=def can you state bc=ef
Answer:
CPCTC
Step-by-step explanation:
If abc=def is given,
then using the cpctc rule. (corresponding parts of congruent triangles are congruent) should state this answer.
Calculate the mean of 12, 15, 6, 4, and 3.
Answer:
8
Step-by-step explanation:
12+15=27 27+3=30 30+6+4=40 40/5=8
Answer:
the answer is 8
Step-by-step explanation:
12+15+6+4+3 / 5 = 8
Please help! How do I simplify -16(0.47)^2?
I know the answer, I'm just not sure of the steps.
Step-by-step explanation:
We have,
[tex]-16(0.47)^2[/tex]
To find, the value of [tex]-16(0.47)^2[/tex] = ?
∴ [tex]-16(0.47)^2[/tex]
= [tex]-16(\dfrac{47}{100} )^2[/tex]
= [tex]-16\times \dfrac{47}{100}\times \dfrac{47}{100}[/tex]
= [tex]-4\times \dfrac{47}{25}\times \dfrac{47}{100}[/tex]
= [tex]- \dfrac{47}{25}\times \dfrac{47}{25}[/tex]
=[tex]- \dfrac{2209}{625}[/tex]
= - 3.5344
∴ The value of [tex]-16(0.47)^2[/tex] = - 3.5344
Thus, the value of [tex]-16(0.47)^2[/tex] is equal to - 3.5344.
Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked
from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the
total distance Courtney walked was 8 kilometers,
Let 6 be the number of hours it took Courtney to walk from her house to the beach, and p the number of hours
it took her to walk from the beach to the park.
Which system of equations represents this situation?
Question:
Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.
Let b be the number of hours it took Courtney to walk from her house to the beach, and p the number of hours it took her to walk from the beach to the park.
Which system of equations represents this situation?
Answer:
CORRECT (SELECTED)
⎪b+p=2
⎨4b+5p=8
Simplify 3(1/6+2/9) + (-2)
Answer:96
Step-by-step explanation:
Answer:
-5/6
Step-by-step explanation:
3(1/6+2/9)+(-2)
1/6+2/9= 7/18
3*7/18 = 21/18 = 1 1/6
1 1/6 - 2 = -5/6
The hypotenuse of a right triangle is 14 centimeters long. One of the legs of the
triangle is 6 centimeters. What is the length of the triangle's other leg?
6. Find the value of x.
19x - 36
6x + 31
Final answer:
To find the value of x, set the expressions equal to each other and solve for x.
Explanation:
To find the value of x in the given equation, we need to set the two expressions equal to each other and solve for x. So, we have:
19x - 36 = 6x + 31
Subtracting 6x from both sides, we get:
13x - 36 = 31
Adding 36 to both sides, we get:
13x = 67
Dividing both sides by 13, we get:
x = 67/13
So the value of x is approximately 5.15.
The ratio of men to women working for a company is 4 to 7. If there are 105 women working for the company, what is the total number of employees? (Help please)
Answer:
165 people
Step-by-step explanation:
If there are 105 woman then there are going to be 60 men because 105/7=14, so you multiply 4*15 and get 60. 60 + 105= 165. So the total employees will be 165.
The total number of employees is the sum of men and women, which is 105 (women) + 60 (men) = 165 employees.
To find the total number of employees, calculate the number of men from the given ratio 4:7 and the number of women (105), and then add the number of men to the number of women to get the total.
The question is about finding the total number of employees in a company given the ratio of men to women and the number of women.
Let's use the provided ratio of men to women, which is 4 to 7, to calculate the number of men.
Since there are 105 women, and the ratio dictates that for every 7 women there are 4 men, we divide 105 by 7 to find the number of units that represent women, which is 15.
We then multiply this by 4 (the number of men) to find the number of men, which is 60.
105 + 60 = 165