Answer:
a. y= -1/5x+1
Step-by-step explanation:
If we have 2 points , we can find the slope using the formula
m = (y2-y1)/(x2-x1)
= (-1-2)/(10--5)
=(-1-2)/(10+5)
= -3/15
= -1/5
The slope if -1/5
We can use the point slope form of a line to write an equation
y-y1= m(x-x1)
y-2 = -1/5(x--5)
y-2 =-1/5(x+5)
Distribute the -1/5
y-2=-1/5x -1
Add 2 to each side
y-2+2 = -1/5x -1+2
y = -1/5x+1
Step-by-step explanation:
Use this formula: Y2 - Y1
X2 -X1
Then, use point slope form: y - Y1 = m (x - X1)
m is the slopeY1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineFinally, it'll reveal your answer!!! :)
help me understand this question
Answer:
m∡J = 110°, m∡L = 45°, m∡K = 25°
Step-by-step explanation:
Similar means they have the same angles. F corresponds with K, G with J, and E with L.
m∡J = 110° because it corresponds with m∡G.
m∡L = 45° because it corresponds with m∡E.
To get m∡K, we have to remember all triangles add to 180. Add J and L together, and subtract that sum from 180° to get m∡F, which is equal to m∡K.
110 + 45 = 155
180 - 155 = 25
m∡K = 25°
Solve for p:
3 + p < 10
Answer:
p < 7
Step-by-step explanation:
To isolate the p, subtract 3 from both sides to get p < 7.
The correct answer is p < 7
Explanation:
To get your answer you need to first set out you equation, 3 + p < 10. Next, you need to subtract 3 from both sides of the equation, 3 + p - 3 < 10 - 3 = p < 7. Finally, we have our answer of p < 7.
Hope This Helps!!!
-AnimeDabGirl
mrs. barney earns $80 for tutoring for 2 hours. If she gets a 10% raise, how much does she now earn per hour.
please show work
Answer:$88
Step-by-step explanation:
multiply 80 dollars by 10% then add that answer to 80 dollars and that gives you 88 dollars
Find the perimeter and area of the polygon shown below. The polygon is a trapezoid made up of a rectangle and a right triangle. The rectangle is 20 feet long and 15 feet wide. The right triangle joins the rectangle at a side that is 15 feet wide, and this is the height of the triangle. The base of the triangle is 8 feet and the hypotenuse is 17 feet.
The perimeter of the polygon is 110 feet and the area is 360 square feet.
Explanation:The polygon consists of a rectangle and a right triangle. To find the perimeter, we add the lengths of all sides. The length of the rectangle is 20 feet and its width is 15 feet, so the perimeter of the rectangle is 2 * (20 + 15) = 70 feet. The length of the base of the right triangle is 8 feet and the hypotenuse is 17 feet. The other side of the triangle is the height, which is given as 15 feet. Therefore, the perimeter of the polygon is 70 + 8 + 15 + 17 = 110 feet.
To find the area, we calculate the area of the rectangle and the triangle separately and then add them together. The area of the rectangle is length * width = 20 * 15 = 300 square feet. The area of the right triangle is 0.5 * base * height = 0.5 * 8 * 15 = 60 square feet. Therefore, the area of the polygon is 300 + 60 = 360 square feet.
Shelly types 301 words in 3 1/2 minutes what is the rate at which Shelly types in words per minute?
Answer: " 86 words per minute "
______________________________________________
Step-by-step explanation:
______________________________________________
We are looking for the "unit rate" ; or "rate per [single] unit" ;
in this case, "words per [single} minute" ; that is "words per minute"
Given: "301 words per 3.5 minutes" ;
or: " 301 words / 3.5 min. " ;
= " (301 / 3.5) words/ min.
= " 86 words / min. "
_______________________________________________
The answer is: " 86 words per minute " .
_______________________________________________
Hope this helps!
Best wishes!
_______________________________________________
The points with coordinates (x, -1), (2,2), and (4,3) lie on the same line. What is the value of x?
Find the slope of the line passing throught the points (2, 2) and (4, 3).
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\dfrac{3-2}{4-2}=\dfrac{1}{2}[/tex]
If the point (x, -1) lie on the same line, then the slope of line passing through the points (2, 2) and (x, -1) the same:
Substitute:
[tex]m=\dfrac{-1-2}{x-2}=\dfrac{-3}{x-2}[/tex]
We have the equation:
[tex]\dfrac{-3}{x-2}=\dfrac{1}{2}[/tex] cross multiply
[tex](1)(x-2)=(-3)(2)[/tex]
[tex]x-2=-6[/tex] add 2 to both sides
[tex]x=-4[/tex]
Answer: x = -4.In each family of functions, the function is the most basic function in the family
Answer:
I think it would be linear because its really easy?!
Step-by-step explanation:
write the standard form of the equation of the line through the given point with the given slope THROUGH:(1,2), slope =7, 50 POINTS
The equation of line passes through the point (1, 2) will be;
⇒ y = 7x - 5
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (1, 2).
And, The slope is,
⇒ m = 7
Now,
Since, The equation of line passes through the point (1, 2).
And, Slope of the line is,
⇒ m = 7
Thus, The equation of line with slope 7 is,
⇒ y - 2 = 7 (x - 1)
⇒ y - 2 = 7x - 7
⇒ y = 7x - 7 + 2
⇒ y = 7x - 5
Therefore, The equation of line passes through the point (1, 2) will be;
⇒ y = 7x - 5
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Rachel is driving from New York to Dayton Florida a distance of 1034 miles. How Much Time Is Saved By Doing The Trip At An Average Speed Of 60mph as compared with 55 mph? Round to the nearest half hour
By increasing her speed from 55 mph to 60 mph, Rachel can save approximately 1.5 hours on her 1034-mile trip from New York to Dayton, Florida.
Explanation:The subject of this question is Mathematics, specifically dealing with the concept of speed, distance, and time. To answer your question, we need to calculate how long the trip would take at each speed and then find the difference.
First, we calculate the time taken when the average speed is 55 mph. The formula to calculate time is distance divided by speed. So, 1034 miles divided by 55 mph equals about 18.8 hours.
Next, we do the same for 60 mph. 1034 miles divided by 60 mph equals about 17.2 hours.
The difference between the two times will give the time saved by increasing the speed to 60 mph from 55 mph. So, 18.8 hours - 17.2 hours equals 1.6 hours, which is approximately 1.5 hours when rounded to the nearest half hour.
Therefore, Rachel can save about 1.5 hours driving at an average speed of 60 mph compared to 55 mph over the distance of 1034 miles.
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The following graph depicts the total cost of purchasing blueberries at Blue Basket Farm at certain price per pound.
The graph is: A) linear. B) nonlinear.
The graph represents a: A) discrete function
B) continuous function
Answer:
A.) Linear
B.) Continuous function
Step-by-step explanation:
Its linear because it is not all over the place and continuous because it does not stop it will keep going because it is a ray
Answer: The graph is A) Linear
The graph represents a B) Continuous function.
Step-by-step explanation:
Since we have given a figure which depicts the total cost of purchasing blueberries at Blue Basket Farm at certain price per pound.
Since the graph is linear .
As we can write it as :
At x = 1, y = 4
At x = 2 , y = 8
At x = 3, y = 12
So, it will become
[tex]y=kx[/tex], where k = 4 units.
So, it is linear graph.
The graph is continuous function as it does not break any where and it is unbroken line.
hence, the graph is A) Linear
The graph represents a B) Continuous function.
Factor -8x^3-2x^2-12x-3
[tex]-8x^3-2x^2-12x-3\\\\=-2x^2(4x+1)-3(4x+1)\\\\=(4x+1)(-2x^2-3)\\\\=\boxed{-(4x+1)(2x^2+3)}[/tex]
Darious is training for the marathon and he usually runs a mile in 8.5 minutes how long will it take him to run the marathon which is 26.2 miles long
Answer:
222.7 minutes
Step-by-step explanation:
You multiply 26.2 by 8.5
Answer:9.5 is the anser
Step-by-step explanation:
A positive real number is 6 less than another. If the sum of the square of the two numbers is 38, then finds the numbers.
Answer:
There seems to be a typo error but still this has solution.
Let the number be = x
A positive real number is 6 less than another. Means the second will be [tex](x+6)[/tex]
The sum of the square of the two numbers is 38.
[tex]x^{2} +(x+6)^{2} =38[/tex]
=> [tex]x^{2} +36+12x+x^{2} =38[/tex]
=> [tex]2x^{2}+12x+36 =38[/tex]
=> [tex]2x^{2}+12x=2[/tex]
=> [tex]2x^{2}+12x-2=0[/tex]
Taking out 2 common;
=> [tex]x^{2}+6x-1=0[/tex]
Solving this quadratic equation, we get;
[tex]x=-3+\sqrt{10}[/tex] and [tex]x=-3-\sqrt{10}[/tex]
As positive number is needed, we have [tex]-3+\sqrt{10}[/tex]
or x = [tex]\sqrt{10}-3[/tex]
x = 0.162277
And other number is 6.162277.
Given:
A positive real number is 6 less than another. The sum of the square of the two numbers is 38.Question:
Find out the numbers.
Problem-solving:
Let us use [tex]\boxed{ \ x \ }[/tex] to represent the positive real number.
This positive real number is 6 less than another. The other number is [tex]\boxed{ \ x + 6 \ }[/tex]
The sum of the square of the two numbers is 38, i.e., [tex]\boxed{ \ x^2 + (x + 6)^2 = 38 \ }[/tex]
Let us work on expanding it.
[tex]\boxed{ \ x^2 + (x + 6)^2 = 38 \ }[/tex]
Recall that [tex]\boxed{ \ (a + b)^2 = a^2 + 2ab + b^2 \ }[/tex]
[tex]\boxed{ \ x^2 + x^2 + 12x + 36 = 38 \ }[/tex]
[tex]\boxed{ \ 2x^2 + 12x + 36 - 38 = 0 \ }[/tex]
[tex]\boxed{ \ 2x^2 + 12x - 2 = 0 \ }[/tex]
Both sides are divided by two.
[tex]\boxed{ \ x^2 + 6x - 1 = 0 \ }[/tex]
Let us solve the equation by using the quadratic formula.
[tex]\boxed{ \ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ }[/tex]
a = 1b = 6c = -1[tex]\boxed{ \ x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-1)}}{2(1)} \ }[/tex]
[tex]\boxed{ \ x = \frac{-6 \pm \sqrt{36 + 4}}{2} \ }[/tex]
[tex]\boxed{ \ x = \frac{-6 \pm \sqrt{40}}{2} \ }[/tex]
[tex]\boxed{ \ x = \frac{-6 \pm 2\sqrt{10}}{2} \ }[/tex]
[tex]\boxed{ \ x = \frac{-6}{2} \pm \frac{2\sqrt{10}}{2} \ }[/tex]
[tex]\boxed{ \ x = -3 \pm \sqrt{10} \ }[/tex]
[tex]\boxed{ \ x_1 = -3 + \sqrt{10} \ . \ . \ . \ x_1 > 10 \ }[/tex] this is fulfilled.
[tex]\boxed{ \ x_2 = -3 - \sqrt{10} \ . \ . \ . \ x_2 < 10 \ }[/tex]
Thus, the positive real number is [tex]\boxed{ \ x = -3 + \sqrt{10} \ }[/tex]The other number is [tex]\boxed{ \ (-3 + \sqrt{10}) + 6 \rightarrow \boxed{ \ 3 + \sqrt{10} \ }}[/tex][tex]\boxed{ \sqrt {10} = 3.162 \ }[/tex]
Therefore [tex]\boxed{ \ x = -3 + 3.162 \rightarrow \boxed{ \ 0.162 \ }}[/tex]And the other number is [tex]\boxed{ \ 0.162 + 6 \rightarrow \boxed{ \ 6.162 \ }}[/tex]Notes:
[tex]\boxed{ \ ax^2 + bx + c = 0, \ \ \ \ \ a \neq 0 \ }[/tex] is a quadratic equation in standard form.
x is a variable a, b, and c are real number coefficientsMethods of solving quadratic equations include:
Factoring and using the zero product property: [tex]\boxed{ \ (x - a)(x - b) = 0 \ } \ if \ and \ only \ if \ \boxed{ \ (x - a) = 0 \ or \ (x - b) = 0 \ }[/tex]Using the square root property: [tex]\boxed{ \ x^2 = a, \ then \ x = \pm \sqrt{a} \ }[/tex]Completing the square: [tex]\boxed{ \ x^2 + bx + \bigg({\frac{b}{2}} \bigg)^2 = \bigg( x + \frac{b}{2} \bigg)^2 \ }[/tex]Using the quadratic formula: [tex]\boxed{ \ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ }[/tex]Learn moreFactoring methods https://brainly.com/question/2568692What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? https://brainly.com/question/1332667What are the coordinates of the vertex of the graph? https://brainly.com/question/1286775Keywords: a positive real number is 6, less than another, if the sum of the square, 38, then finds, quadratic equation, methods, factoring, the zero product property, the square root, completing, the quadratic formula
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What is the equation of the line –3x–2y=30 in slope-intercept form? y = mx + b is slope-intercept form Enter your answer in the box.
Answer:
y = -3/2 x -15
Step-by-step explanation:
–3x–2y=30
To get the equation is slope intercept form y=mx+b, we need to solve for y
Add 3x to each side
–3x+3x–2y=3x+30
-2y = 3x+30
Divide by -2
-2y/-2 = 3x/-2 + 30 /-2
y = -3/2 x -15
The slope is -3/2 and the y interceot us -15
witch ordered pair is the solution to the system of equations
{-5x-3y=12
{y=x-12
[tex]\left\{\begin{array}{ccc}-5x-3y=12&(**)\\y=x-12&(*)\end{array}\right\\\\\text{Substitute}\ (*)\ \text{to}\ (**):\\\\-5x-3(x-12)=12\qquad\text{use distributive property}\\-5x+(-3)(x)+(-3)(-12)=12\\-5x-3x+36=12\qquad\text{subtract 36 from both sides}\\-8x=-24\qquad\text{divide both sides by (-8)}\\\boxed{x=3}\\\\\text{Put the value of x to}\ (**):\\\\y=3-12\\\boxed{y=-9}\\\\Answer:\ \boxed{x=3\ and\ y=-9\to(3,\ -9)}[/tex]
can√(a²+b²) be written as √(a+b)?????
Answer:
It can be written that way, but the functions are not the same. The numbers the would be plugged in would not produce the same answer.
The local market is selling fresh fruit in baskets. The weights and amounts charged are shown below. For fruit weighing greater than or equal to 0.01 pounds and less than or equal to 0.5 pounds, the amount charged is $2.00. For fruit weighing greater than 0.5 pounds and less than or equal to 1.0 pounds, the amount charged is $3.50. For fruit weighing greater than 1.0 pounds and less than or equal to 1.5 pounds, the amount charged is $5.00. For fruit weighing greater than 1.5 pounds and less than or equal to 2.0 pounds, the amount charged is $6.50. For fruit weighing greater than 2.0 pounds and less than or equal to 2.5 pounds, the amount charged is $8.00. Which graph represents the function described?
Answer:
The graph is shown below.
Step-by-step explanation:
Let x be the weight of fruit in pounds and P(x) be the price of fruit.
For fruit weighing greater than or equal to 0.01 pounds and less than or equal to 0.5 pounds, the amount charged is $2.00.
P(x) = $2.00 for 0.01 ≤ x ≤ 0.5
For fruit weighing greater than 0.5 pounds and less than or equal to 1.0 pounds, the amount charged is $3.50.
P(x) = $3.50 for 0.5 < x ≤ 1.0
For fruit weighing greater than 1.0 pounds and less than or equal to 1.5 pounds, the amount charged is $5.00.
P(x) = $5.00 for 1.0 < x ≤ 1.5
For fruit weighing greater than 1.5 pounds and less than or equal to 2.0 pounds, the amount charged is $6.50.
P(x) = $6.50 for 1.5 < x ≤ 2.0
For fruit weighing greater than 2.0 pounds and less than or equal to 2.5 pounds, the amount charged is $8.00.
P(x) = $8.00 for 2.0 < x ≤ 2.5
It is a piecewise floor function. We have open circle on left side of each floor except first floor because the sign of inequality in all other is < .
We have closed circle on right side of each floor because the sign of inequality is ≤ .
The graph is shown below.
How much is 0.324 divided by 0.27
Answer:
The answer is 1.2
Step-by-step explanation:
Answer:
1.2
Step-by-step explanation:
You can use a calculator... Or you can ask google this, "What is 0.324 divided by 0.27?"
0.324 divided by 0.27 is 1.2
PLEASE SHOW WORK
Solve using substitution
x=y+6
y=x+4
Answer:
no solution
Step-by-step explanation:
1. Substitute the value of into the equation. y = y + 6 + 4
2. Solve. the system has no solution because y = y.
PLEASE I BEG YOU TOO HELP ME OR ELSE IM GOING TK FAIL MY CLASS
Explanation: For questions 4-11, plug in the values of the variables into the equations. Ex no. 8: 7.8 + 3.5(w) where w=6.8. Plug 6.8 into the equation: 7.8 + 3.5(6.8) = 7.8 + 23.8 = 31.6 is the answer.
For questions 12-15, the order of operations is Please Excuse My Dear Aunt Sally: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. In other words, solve each equation according to the arrangement of the operations. Ex no. 15: y² - 10 ÷ 5 + x where x = 2.5 and y = 4. Plug these numbers into the equation: 4² - 10 ÷ 5 + 2.5. The order of operations says that parenthesis should be solved first. Since there are no parenthesis, we can skip this operation. The next operation is exponents. 4² has an exponent of 2, which means that we multiply 4 by itself 2 times to get 16 (4 x 4 = 16). We now have 16 - 10 ÷ 5 + 2.5. The next operation is multiplication. There is no multiplication in this equation, so we skip this operation. Next is division. We can divide -10 by 5 to get -2. We now have 16 - 2 + 2.5 (Do not change an addition sign unless you are dividing a negative number by a positive number). The next operation is addition. We can add -2 and 2.5 to get 0.5. Lastly, we can also add 16 by 0.5: 16 + 0.5 = 16.5 is the answer.
Walking on his own, the distance, D, in feet, that Roberto can cover in M, minutes is given by the function D(m)=264m. When he walks on the moving sidewalk at the airport, the distance, A, in feet, that he can cover in m m minutes is given by the function A(m)=440m. Let B be the distance, in feet, that Roberto would travel on the moving sidewalk in m m minutes if he were standing still. Write a formula for B(m) in terms of D(m) and A(m).
Answer:
B(m)=A(m)-D(m)
B(m)=176m
Step-by-step explanation:
we are given
Walking on his own, the distance, D, in feet, that Roberto can cover in M, minutes is given by the function
D(m)=264m
When he walks on the moving sidewalk at the airport, the distance, A, in feet, that he can cover in m m minutes is given by the function
A(m)=440m
B is the distance, in feet, that Roberto would travel on the moving sidewalk in m minutes if he were standing still
moving sidewalk distance = standstill distance + walking distance
A(m)=D(m)+B(m)
so, we get
B(m)=A(m)-D(m)
now, we can plug values
B(m)=440m-264m
B(m)=176m
Final answer:
To find the distance B(m) that Roberto would travel on a moving sidewalk in m minutes if he stood still, one must subtract the function for walking alone D(m) from the function for walking on a moving sidewalk A(m). Thus, B(m) is calculated as B(m) = A(m) - D(m), resulting in B(m) = 176m.
Explanation:
The student needs to find the formula for the distance B(m) that Roberto would travel on the moving sidewalk in m minutes if he stands still, in terms of the functions D(m) and A(m). The function D(m) = 264m represents the distance Roberto covers by walking on his own in m minutes, and A(m) = 440m represents the distance covered while walking on a moving sidewalk.
Since A(m) represents the combined effect of walking and the moving sidewalk, and D(m) represents just walking, the difference A(m) - D(m) will give us the contribution of the moving sidewalk alone, while Roberto stands still. Thus, the formula for B(m) is:
B(m) = A(m) - D(m)
B(m) = 440m - 264m
B(m) = 176m
The formula B(m) indicates the distance Roberto would cover on the moving sidewalk if he did not walk and just stood still.
Two triangles have altitudes of equal length. if the areas of these triangles have a ratio of 3:4 then the bases of the triangles have the ration of what?
show work pleaseeee
Final answer:
The bases of the triangles have a ratio of 3:4.
Explanation:
The areas of two triangles with equal altitudes have a ratio of 3:4. We can set up the equation:
A₁/A₂ = 3/4
Let's denote the bases of the triangles as b₁ and b₂. The formula for the area of a triangle is A = (1/2) * base * height. Since the altitudes are equal, we can write:
A₁ = (1/2) * b₁ * h
A₂ = (1/2) * b₂ * h
Substituting these equations into the ratio, we get:
(1/2) * b₁ * h / (1/2) * b₂ * h = 3/4
Cancelling out the height and simplifying, we find:
b₁ / b₂ = 3/4
Therefore, the bases of the triangles have a ratio of 3:4.
I WILL GIVE BRAINLYEST TO FIRST 7 PEOPLE TO ANSWER IN THE NEXT 10 MINUTES
last year austin texas received 23.5 inches of rainfall. this year , austin recieved 21.2 inches of rainfall find the percent of decrease in the number of inches of rainfall. round your answer to the nearest tenth of a percent, if necessary
Answer:
9.8 percent decrease
Step-by-step explanation:
To find the percent decrease, we take the original value and subtract the new value and divide by the original value.
percent decrease = (original - new)/ original
= (23.5 - 21.2)/ 23.5
=2.3/23.5
=.09787234
This is in decimal form. Multiply by 100 to put it in percent form
9.787234 percent
Round to the nearest tenth so we look at the 8 and round up.
9.8 percent decrease
Answer:
The answer is 9.8%
Step-by-step explanation:
Also, only two people can answer a question.
Write an equation of the line that passes through the points (1,1) (5,9)
Answer:
y = 2x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
To find m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (1, 1) and (x₂, y₂ ) = (5, 9)
m = [tex]\frac{9-1}{5-1}[/tex] = [tex]\frac{8}{4}[/tex] = 2
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
using (1, 1 ), then
1 = 2 + c ⇒ c = 1 - 2 = - 1
y = 2x - 1 ← equation of line
Daniel worked for 2/13 hours and earned $18.20.
How much would he make if he worked for 5 1/4 hours?
624.75
first get the numeric values simplified
2/13h=0.153h
so 18.20÷0.153=119
meaning he earned 119 dollars every hour
now you can multipy this number with 5.25 to get the answer which is 624.75 dollars
Please help!! What is the value of the following expression when x=3 and y= -2?
Answer:
20 is the answer.
Step-by-step explanation:
Substitute 3 in for x and -2 in for y.
4(3) - (-2 to the third power)
12 - -8 = 12 + 8
The answer is 20
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The graph shows the function f(x).
What is the function's average rate of change from x = 9 to x = 15?
Enter your answer in the box.
Answer:
3/2
Step-by-step explanation:
To find the rate of change
f(x2) - f(x1)
------------------ = rate of change
x2-x1
Looking at the graph
f(15) = 12
f(9) = 3
Substituting this into the equation
12-3
---------
15-9
9
------
6
3/2
The rate of change is 3/2
The average rate of change of a function from x = 9 to x = 15 is calculated by the slope of the secant line, which is (f(15) - f(9)) / (15 - 9). Specific function values are needed to perform this calculation.
Explanation:To calculate the function's average rate of change from x = 9 to x = 15, you can use the formula for the slope of the secant line between these two points on the graph of the function. This is given by the difference in the function values at these points divided by the difference in x-values:
Average Rate of Change = (f(15) - f(9)) / (15 - 9).
You would need the specific function values f(15) and f(9) in order to calculate this. If the function is linear, like the one represented by f(x) = 7x, you would substitute these x-values into the function to get f(15) = 7*15 and f(9) = 7*9, and then perform the calculation. However, without the actual function values, we cannot complete this calculation.
In a recent international sport competition, the top three countrieslong dash—Country A, Country B, and Country Clong dash—won a total of 119119 medals. Country B won 1111 more medals than Country C. Country A won 3737 more medals than the total amount won by the other two. How many medals did each of the top three countries win?
Answer:
Country A won 78 medals
Country B won 26 medals
Country C won 15 medals
Step-by-step explanation:
We have been given with :-
A+B+C=119 _____equation(1)
B=C+11 ____equation(2)
A=B+C+37 ____equation(3)
1) Starting with the 3rd equation,
A=B+C+37
2) Subtract 37 from both sides
A-37=B+C+37-37
3) Cancelling out +37 and -37 from the right side we get,
A-37 = B+C
or
B+C = A-37
4) Plugin B+C= A-37 in the equation 1,
A+B+C = 119
=> A+(A-37) = 119
=> 2A-37 = 119
5) Add 37 to both sides
2A-37+37=119+37
6) Cancelling out -37 and +37 from the left side, we get
2A = 156
7) Divide both sides by 2
[tex]\frac{2A}{2} =\frac{156}{2}[/tex]
8) Cancelling out the 2's on the left side, we get
A = 78
9) Now, we plugin A=78 in the equation 1
A+B+C=119
=> 78+B+C=119
10) Subtract 78 from both sides
78+B+C-78 = 119 -78
11) Cancelling out +78 and -78 from the left side, we get
B+C= 41 ____let it be equation (4)
12) Subtracting C from both the sides of the equation 2, we get
B=C+11
=> B-C = C+11 - C
13) Cancelling out +C and -C from the right side, we get
B-C= 11 _____let it be equation (5)
14) Adding the equations 4 and 5, we get
B+C+B-C=41+11
15) Cancelling out the +C and -C, we get
2B = 52
16) Divide both sides by 2
[tex]\frac{2B}{2}=\frac{52}{2}[/tex]
17) Cancelling out the 2's on the left, we get
B = 26
18) Substituting A= 78 and B= 26 in the equation (1), we get
A+B+C=119
=> 78+26+C=119
=> 104+C=119
19) Subtracting 104 from both the sides, we get
104 + C - 104 = 119 -104
20) Cancelling out +104 and -104 from the left side, we get
C = 15
The problem is a basic algebra problem where we assign variables to the number of medals each country won. We then use given equations related to these variables to solve for each unknown.
Explanation:In this problem, we are trying to solve for the number of medals each country won, so let's start by assigning variables for the number of medals for each country. Let's say, Country A = A, Country B = B, and Country C = C.
According to the problem, we know that Country A won 37 more medals than the sum of the other two countries, that's expressed by this equation: A = B + C + 37.
It's also stated that Country B won 11 more medals than Country C, so we have this equation: B = C + 11.
Further, we know that the total number of medals is 119, so we have this equation: A + B + C = 119.
Now, solve these equations systematically. First, substitute the value of A and B from first and second equation into the third equation and solve the variable C, then substitute the obtained value of C in second equation to find B and finally substitute the obtained values of B and C in first equation to find A.
This is a basic algebraic problem-solving situation. It involves the use of equations and variables to find the solution.
Learn more about Algebra problem-solving here:https://brainly.com/question/11315620
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Jayla ate 75% of the jelly beans in the bag. If she ate 24 jelly beans how many were in the bag?
Answer:
32 jelly beans were in the bag
Step-by-step explanation:
We know 75% is 3/4 and that she ate 24, so divide 24 by 3 then multiply it by 4:
24/3= 8
8 x 4 = 32
Final answer:
By dividing the number of jelly beans Jayla ate (24) by 75% and scaling it up to 100%, we determine that the bag initially contained 32 jelly beans.
Explanation:
Jayla ate 75% of the jelly beans in the bag, which equaled 24 jelly beans. To find out how many jelly beans were in the bag originally, we need to find what amount corresponds to 100% if 75% is 24 jelly beans. We perform this calculation by dividing the amount eaten (24 jelly beans) by the percentage she ate (75%), and then multiplying by 100% to scale it up to the total amount.
The calculation goes as follows: (24 / 0.75) = 32. This means there were originally 32 jelly beans in the bag before Jayla ate any.
Triangle ABC is similar to triangle XYZ. Side AB measures 2, side BC measures x + 5, side CA measures x + 7, side XY measures 4 and side ZX measures 4x – 2. Find the value of x.
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
In similar triangles, corresponding sides' ratio are equal.
Side AB corresponds to Side XYSide BC corresponds to Side YZSide CA corresponds to Side ZXWe can set up a ratio of [tex]\frac{SideAB}{Side XY}=\frac{SideCA}{Side ZX}[/tex]
Hence, we can write (and solve):
[tex]\frac{Side AB}{Side XY}=\frac{Side CA}{SideZX}\\\frac{2}{4}=\frac{x+7}{4x-2}\\2(4x-2)=4(x+7)\\8x-4=4x+28\\8x-4x=28+4\\4x=32\\x=\frac{32}{4}=8[/tex]
So, x = 8