Answer:
3x-5y
Step-by-step explanation:
Combine like terms
To simplify the expression 13x + 2y - 10x - 7y, combine the like terms together. The simplified expression is 3x - 5y.
Explanation:To simplify the expression 13x + 2y - 10x - 7y, combine the like terms together. Start by combining the x terms and then combine the y terms.
13x - 10x = 3x
2y - 7y = -5y
Therefore, the simplified expression is "3x - 5y."
Learn more about Combining like terms here:https://brainly.com/question/17359085
#SPJ2
the sum of two numbers is 158.if we add 25 to each one of them,then the first becomes the triple of the other.what are these numbers
Answer:
Why is 90 the sum of all factors of 40, including 40? The factors of the number 40 are: 1, 2, 4, 5, 8, 10, 20, 40. If you add them up, you will get the total of 90.
Step-by-step explanation:
2. Given the points A, B, C, D, calculate:
(a) the angle B of the triangle ABC
(b) the area of the triangle ABC
(c) the median BE of the triangle ABC
(d) the height AH of the triangle ABC
(e) the volume of tetrahedron ABCD
(f) the point E so that ABCE is a parallelogram.
A(-1, 2, -3), B(4, -1, 0), C(2, 1, -2), D( 3,4,5)
Dudley Greene's charge account statement shows an unpaid balance of $376.00. The monthly finance charge
is 1.85 percent of the unpaid balance. What is the finance charge?
Answer:
The finance charge is $6.96.
Step-by-step explanation:
Given:
Dudley Greene's charge account statement shows an unpaid balance of $376.00.
The monthly finance charge is 1.85 percent of the unpaid balance.
Now, to find the finance charge.
Unpaid balance = $376.00.
Finance charge = 1.85% of unpaid balance.
So, to get the finance charge:
1.85% of $376.00.
[tex]=\frac{1.85}{100} \times 376.00[/tex]
[tex]=0.0185\times 376.00[/tex]
[tex]=\$6.96.[/tex]
Therefore, the finance charge is $6.96.
A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues, what will be the population of moose after 12 years?
years=x population =y
0,40
1,62
2,96
3,149
4,231
The population of the moose after 12 years is 7692
Step-by-step explanation:
The form of the exponential growth function is [tex]y=a(b)^{x}[/tex] , where
a is the initial valueb is the growth factorThe table:
→ x : y
→ 0 : 40
→ 1 : 62
→ 2 : 96
→ 3 : 149
→ 4 : 231
To find the value of a , b in the equation use the data in the table
∵ At x = 0 , y = 40
- Substitute them in the form of the equation above
∵ [tex]40=a(b)^{0}[/tex]
- Remember any number to the power of zero is 1 (except 0)
∴ 40 = a(1)
∴ a = 40
- Substitute the value of a in the equation
∴ [tex]y=40(b)^{x}[/tex]
∵ At x = 1 , y = 62
- Substitute them in the form of the equation above
∵ [tex]62=40(b)^{1}[/tex]
∴ 62 = 40 b
- Divide both sides by 40
∴ 1.55 ≅ b
∴ The growth factor is about 1.55
- Substitute its value in the equation
∴ The equation of the population is [tex]y=40(1.55)^{x}[/tex]
To find the population of moose after 12 years substitute x by 12 in the equation
∵ [tex]y=40(1.55)^{12}[/tex]
∴ y ≅ 7692
The population of the moose after 12 years is 7692
Learn more:
You can learn more about the logarithmic functions in brainly.com/question/11921476
#LearnwithBrainly
A line has a slope of -3/4 and has a y intercept of 3. What is the x intercept of the line
Answer:
The x-intercept is 4
Step-by-step explanation:
We are given;
The slope of a line as -3/4
y-intercept is 3
We are supposed to determine the x-intercept;
We need to know that;
The slope of a line is given by the ratio of the change in y to the change in x
The coordinates of y-intercept are (0, 3)
Taking the x-intercept as a, then the coordinates of x-intercept is (a, 0)
But;
slope = Δ in y ÷ Δ in x
Therefore;
[tex]\frac{0-3}{a-0}= \frac{-3}{4}[/tex]
Solving for a
[tex]-3a = -12 \\ a =4[/tex]
Therefore, the x-intercept is 4
- 1/3 square root-90
Answer: [tex]-i\sqrt{10}[/tex]
Step-by-step explanation:
Assuming that you need to simplify the expression, below is the explanation to do it.
Given the following expression:
[tex]-\frac{1}{3}\sqrt{-90}[/tex]
You need to decompose the radicand (The number inside the square root) into its prime factors:
[tex]90=2*3*3*5=2*3^2*5[/tex]
Knowing that, you can rewrite the expression in this form:
[tex]=-\frac{(1)(\sqrt{-2*3^2*5})}{3}=-\frac{\sqrt{-2*3^2*5}}{3}[/tex]
Since [tex]\sqrt{-1}=i[/tex], you must substitute it into the expression:
[tex]=-\frac{i\sqrt{2*3^2*5}}{3}[/tex]
Now you need to remember the following property:
[tex]\sqrt[n]{a^n}=a^{\frac{n}{n}}=a[/tex]
Then, applying that property, you get:i:
[tex]=-\frac{3i\sqrt{2*5}}{3}=-\frac{3i\sqrt{10}}{3}[/tex]
Finally, you must divide the numerator and the denominator by 3. So, you get:
[tex]=-\frac{i\sqrt{10}}{1}=-i\sqrt{10}[/tex]
Lisa’s pet shop has 2 fish tanks. Tank A contains smaller fish who are fed 1 gram of food each per day. Tank B contains larger fish who are fed 2 grams of food each per day. If tank B contains 2/3 (fraction) the number fo fish thank Tank A contains, will Lisa ever feed both tanks the same amount of food?
Answer:
No, lisa will not be able to feed both the tanks same amount of food.
Step-by-step explanation:
No, lisa will never be able to feed both tanks the same amount of food.Let tank A contains x number of fish then according to the information given Tank B contains 2/3x number of fishLisa feds 1 gm of food in tank A that means Lisa feds 2 gm of food in tank B that means we have to tell whether lisa will ever feed both tanks the same amount it will be possible if which is not possibleTherefore, lisa will not be able to feed both the tanks same amount of food.
The actual length of a soccer field is 500 feet. A broken measuring instrument shows the length to be 493 feet. Find the percent error for the length of the soccer field.
Answer:
Percent error for the length of the soccer field is 1.4 %
Step-by-step explanation:
The actual length of the soccer field = 500 ft
The measured length of he field = 493 ft
ERROR in the measurement = ACTUAL LENGTH - MEASURED LENGTH
= 500 ft - 493 ft = 7 ft
So, there is an error of 7 ft in measuring the length of the field.
[tex]\textrm{ERROR PERCENTAGE} = \frac{\textrm{Error}}{\textrm{Actual Measuement}} \times 100\\= \frac{7}{500} \times 100 = 1.4[/tex]
Hence, percent error for the length of the soccer field is 1.4 %
The percent error for the length of the soccer field is 1.4%.
We are asked to find the percent error for the length of a soccer field when the actual length is 500 feet, but a broken measuring instrument shows it to be 493 feet.
Calculating percent error:
Find the absolute difference: |493 - 500| = 7 feet.
Calculate percent error: (7/500) x 100%
Percent error = 1.4%.
Where in the world may a person walk one mile west, and then one mile north and arrive back at the starting point
Answer:
North Pole
Step-by-step explanation:
Answer:
So your walk of 1 mile West is a complete circle. You then walk 1 mile North, which brings you back to your starting point, (1 + 1/(2pi)) miles from the South Pole. The obvious answer is the North Pole. You're either on the North Pole, or somewhere very near (about 840 feet or less) the South Pole.-step explanation:
The cost, C, in dollars, of playing g games at an arcade game
center is modeled by the linear function C = 0.5g + 2.
Determine the rate of change of the function and explain
what this value means in terms of the context.
Determine the initial value of the function and explain what
this value means in terms of the context.
The rate of change is 0.5 which means that each game cost .50 cents
The initial value is 2 which means that you must initially pay $2.00
The rate of change of the function C = 0.5g + 2 is 0.5, indicating a cost increase of $0.50 per game. The initial value is 2, representing the fixed entry fee at the arcade.
Explanation:The rate of change of the function C = 0.5g + 2, which represents the cost, C, in dollars, of playing g games at an arcade game center, is the coefficient of g, whic h is 0.5. Thisvalue means that for each additional game played, the cost increases by $0.50. The initial value of the function is the constant term, which is 2. This represents the starting fee or fixed cost at the arcade game center before any games are played.
Learn more about Linear Function here:https://brainly.com/question/40461731
#SPJ2
What is the solution set of the system of inequalities 5x<8+4y and 2y≤6?
Answer:
See the explanation and the image.Step-by-step explanation:
The inequality [tex]2y \leq 6[/tex] means [tex]y \leq 3[/tex].
y = 0, satisfies the above inequality, so the arrows will be towards the x axis.
Now, we need to draw 5x < 8 + 4y.
First, lets draw the equation of 5x = 8 + 4y.
y = 1 gives x = 2.4 & y = 0 gives x = 1.6.
Hence, the above equation passes through (2.4, 1) and (1.6, 0).
The point (0, 0) satisfies the inequality 5x < 8 + 4y. Hence, the arrows will be towards the origin.
The solution will be the area of APQ except any point on PQ, as PQ is nothing but the line 5x = 8 + 4y.
prince is 6n years old. jordan is (3n + 10) years older than prince
a) find jordans age
b) find the total age of prince and jordan
c) kimberly is 9 yrs younger than prince. find kimberlys age
d) find the total age of three people
e) if n = 4 find the total age of the three people
#13 Kayla is 4 years
younger than her sister.
Write an algebraic
expression that represents
the situation.
Step-by-step explanation:
Let us suppose that her sister age is x,we have given that Kayla is 4 years younger than her sister .
this the age of Kayla would be 4 less than x,
So the algebraic expressions is :
x - 4. ans.The scale of a room in a blueprint is 6in : 13ft. A wall in the same blueprint is 9 inches. How long is the actual wall?
Answer:
Step-by-step explanation:
6 in to 13 ft = 9 in to x ft
6 / 13 = 9 / x.....cross multiply because this is a proportion
(6)(x) = (13)(9)
6x = 117
x = 117/6
x = 19.5 (or 19 1/2) ft <====
The Garcia family wants to paint their house. They have found a painter who will pain
their house for $25 per hour, plus the cost of the paint. They need 10 cans of paint whic
cost $15 per can. Write an equation which can be used to find c, the cost of painting the
house in terms of h, the amount of hours the painter paints?
AC = 25h +150
e c = 25h +15
C<= 150h + 25
D C = 25h +10
Answer:
If the painter will paint for $25 per hour, then the amount of dollars for h number of hours is $25h , if the cost of paint is $15 per can, 10 cans will be $150. The cost C of painting the house is
C= 25h +150
The amount of hours the painter paints is make h the subject of the formula
h= (C - 150)/25
The equation to find the cost of painting the house in terms of the hours worked by the painter is C = 25h + 150
Explanation:The equation that can be used to find the cost of painting the house in terms of the amount of hours the painter paints is C = 25h + 150. This equation represents the cost of the labor ($25 per hour) plus the cost of the paint (10 cans at $15 per can, which equals $150). The variable h represents the number of hours the painter works.
Learn more about Cost of painting a house here:https://brainly.com/question/31074930
#SPJ11
What is the formula for the volume of a cylinder
Answer:
V=πr2h
Step-by-step explanation:
Answer:
V=πr2h
That's the formula for the volume of a cylinder
In the next 10 months Colin wants to save $900 for his vacation. He plans to save $75 each for the first eight months. How much must he save each of the last two months in order to meet his goal if he saves the same amount each month
He must save $150 each of the last two months in order to meet his goal.
Step-by-step explanation:
Given,
Amount Colin wants to save = $900
Amount saved each month for 8 months = $75
Amount saved in 8 months = 75*8 = $600
Let,
x be the amount saved each month for remaining two months.
Therefore;
Number of months * Amount saved + Amount saved in 8 months = Total amount to save
[tex]2x+600=900\\2x=900-600\\2x=300[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{300}{2}\\x=150[/tex]
He must save $150 each of the last two months in order to meet his goal.
Keywords: subtraction, division
Learn more about division at:
brainly.com/question/10015690brainly.com/question/10048445#LearnwithBrainly
What is the area of this shape
The given shapes area is found to be 132 square feet.
Step-by-step explanation:
Step 1; To determine the area of an indefinite shape we must divide it into the shapes that we know. The shape that is given can be split into a rectangle with a triangle on top of it.
Step 2; To determine the area occupied by a different shape, we must sum the areas of the triangle and the rectangle. The given rectangle measures a length of 11 feet and a width of 9 feet. The area of any given rectangle is the multiplication of its length and width. Area of Rectangle = Length * Width = 11 feet * 9 feet = 99 square feet.
Any given triangles area is half the multiplication of its base value and its height value. In the given diagram, the base of the triangle measures a length of 11 feet (same as the rectangle's length) and the length from base to top is 6 feet (Entire shape's height which is 15 feet - the calculated value of the rectangle's width which is 9).
Area of Triangle = [tex]\frac{1}{2}[/tex]* base * height = [tex]\frac{1}{2}[/tex] * 11 feet * 6 feet = 33 square feet.
Step 3; To find the total area of the shape we must add the areas of the rectangle and the triangle.
Area of given shape = Area of rectangle + Area of Triangle
Area of given shape = 99 square feet + 33 square feet = 132 square feet.
What is 4 1/2 + 3 1/4
Add the whole numbers 4 + 3 = 7
Add the fractions 1/2 + 1/4
Rewrite 1/2 to have a common denominator with 1/4
1/2 = 2/4
Now add 2/4 + 1/4 = 3/4
The answer would be 7 3/4
What are the values of x and y?
Answer:
[tex]x=70^o[/tex]
[tex]y=110^o[/tex]
Step-by-step explanation:
we know that
In a parallelogram, opposite angles are congruent and consecutive angles are supplementary
In this problem the quadrilateral ABCD is a parallelogram
so
[tex]x=70^o[/tex] -----> by opposite angles in a parallelogram
[tex]x+y=180^o[/tex] ---> by consecutive angles in a parallelogram
substitute the value of x
[tex]70^o+y=180^o[/tex]
[tex]y=180^o-70^o=110^o[/tex]
According to the graph, what is the solution (ordered pair) of this system of equations?
Answer:
(2, -1)
Step-by-step explanation:
When line 1 intercepts with line 2, they meet at (2, -1). Therefore that's the solution.
A committee consisting of 2 faculty members and 3 students is to be formed. Every committee position has the same duties and voting rights. There are 9 faculty members and 14 students eligible to serve on the committee. In how many ways can the committee be formed?
Answer:
13104
Step-by-step explanation:
9C2 x 14C3 = 36 x 364
= 13104
What is the slope of a line that passes through (5,-5) and (-6, -4)
Answer: m = [tex]\frac{-1}{11}[/tex]
Step-by-step explanation:
The slope of a line is calculated by :
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = 5
[tex]x_{2}[/tex] = -6
[tex]y_{1}[/tex] = -5
[tex]y_{2}[/tex] = -4
substituting the values , we have :
m = [tex]\frac{-4-(-5)}{-6-5}[/tex]
m = [tex]\frac{-4+5}{-11}[/tex]
Therefore :
slope = [tex]\frac{-1}{11}[/tex]
A pentagon the Measures of four of its angle are shown bellow: what is the value of x?
Answer:
See below.
Step-by-step explanation:
The sum of the measures of the interior angles of an n-sided polygon is
(n - 2)180
A pentagon has 5 sides, so for a pentagon, n = 5.
(n - 2)180 = (5 - 2)180 = 3(180) = 540
The sum of the measures of the angles of a pentagon is 540.
You don't show the measures of the 4 angles that are known, so to answer the question, add the 4 given measures and subtract the sum from 540.
PLEASE HELP ASAP :>
John deposited $13 in his bank account on Monday. Then, on Friday he withdrew $15. How much money is in John's bank account now?
$2
$28
-$28
-$2
Answer:
-2
Step-by-step explanation:
Answer:
-2 is 100% correct !
Step-by-step explanation:
Which pair of adjacent angles is complementary?
Answer:
Option C
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
In this problem we have
Option C
One angle measure 35 degrees and the other angle measure 55 degrees (90-35=55)
so
[tex]35^o+55^o=90^o[/tex]
therefore
The pair of angles are complementary
Answer:
C.)
Step-by-step explanation:
In Tampa, Florida the sun shines about 66% of the year about how many days does the sun shine in Tampa
Answer: 241 days a year
Step-by-step explanation: 365*0.66=240.9 and then you round up to 241
The total number of days in a year the sun shines in Tampa will be equal to 241 days.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the instructions given in the question,
The total number of days in a year is 365 days.
Then, 66% of the total number of days in a year will be,
365 × 66/100 = 240.9 or,
The number of days of sunshine will be 241 days after rounding up the value.
To know more about Percentage:
https://brainly.com/question/29306119
#SPJ2
PLS HELP!!!!!
What is the value of tanC in this triangle
A)24/25
B)7/24
C)7/25
D)24/7
Answer:
d. 24/7 i belive
Step-by-step explanation:
Final answer:
To find the value of tanC in the triangle, calculate the angles A, B, and C using the cosine rule and understanding the relationship between these angles.
Explanation:
The value of tanC in the triangle can be calculated using the given information.
Calculate angle A using the cosine rule: 16 = 25 + 36.Calculate angle C by the cosine rule: 36 = 16 + 25. Since cos(2A) = 2cos²(A) - 1, it implies that C = 2A.The external angle at B is 3A.Arman, Babken, and Cecilia decided to compete in a 100m run. When Arman crossed the finish line, Babken was 10m behind him. When Babken crossed the finish line, Cecilia was 10m behind him. How far was Cecilia behind Arman when he crossed the finish line?
Answer:
19 meters
Step-by-step explanation:
When Arman finished, Babken is 10 meters behind. So, Babken has 10 meters left.
Ex: Babken has 10 meters left, Cecilia is 9 meters behind.
So, the answer is 10+9=19.
19 meters.
Cecilia's position is 19 m behind when Arman is at the finish line.
Arman, Babken, and Cecilia 3 decided to compete in a 100m run.
What is the distance?Distance is defined as the difference in position.
Here,
Cecilia covers 90% of Babken's covered distance. Babken Covered 90% of Arman distance. So distance covered by Cecilia is.
= 90/100 * 90/100 x 100
= 81m
Now, distance between Cecilia and Arman when he crossed the finish line,
= 100m-81m
=19m
Thus, Cecilia's position is 19 m behind when Arman is at the finish line.
Get more information about distance here:
https://brainly.com/question/18651046
#SPJ2
What is the value of x?
(3x - 14)
X
[4(X-9)
Enter your answer in the box.
Answer:
12x^2 - 164x + 504
Step-by-step explanation:
(3x-14)(4(x-9)) equals this, as I used an algebra calculator.
Solve the system:
2/x - 3/y =-5; 4/x + 6\y =14
The solution is [tex]x = 2 \text{ and } y = \frac{1}{2}[/tex]
Solution:
Let us assume,
[tex]a = \frac{1}{x}\\\\b = \frac{1}{y}[/tex]
Given system of equations are:
[tex]\frac{2}{x} - \frac{3}{y} = -5[/tex]
[tex]\frac{4}{x} + \frac{6}{y} = 14[/tex]
Rewrite the equation using "a" and "b"
2a - 3b = -5 ------------ eqn 1
4a + 6b = 14 -------------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 1 by 2
2(2a - 3b = -5)
4a - 6b = -10 ------------- eqn 3
Add eqn 2 and eqn 3
4a + 6b = 14
4a - 6b = -10
( - ) --------------------
8a = 4
[tex]a = \frac{4}{8}\\\\a = \frac{1}{2}[/tex]
Substitute a = 1/2 in eqn 1
[tex]2(\frac{1}{2}) -3b = -5\\\\1 - 3b = -5\\\\3b = 6\\\\b = 2[/tex]
Now let us go back to our assumed values
Substitute a = 1/2 in assumed values
[tex]a = \frac{1}{x}\\\\\frac{1}{2} = \frac{1}{x}\\\\x = 2[/tex]
Substitute b = 2 in assumed value
[tex]b = \frac{1}{y}\\\\2 = \frac{1}{y}\\\\y = \frac{1}{2}[/tex]
Thus the solution is [tex]x = 2 \text{ and } y = \frac{1}{2}[/tex]