Answer:
x = 4, y = 12 → (4, 12)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}10x+2y=64&\text{multiply both sides by 2}\\3x-4y=-36\end{array}\right\\\underline{+\left\{\begin{array}{ccc}20x+4y=128\\3x-4y=-36\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad23x=92\qquad\text{divide both sides by 2}\\.\qquad x=4\\\\\text{put the value of x to the first equation:}\\\\10(4)+2y=64\\40+2y=64\qquad\text{subtract 40 from both sides}\\2y=24\qquad\text{divide both sides by 2}\\y=12[/tex]
What are axioms in algebra called in geometry
Answer:
Sometimes they are called algebraic postulates.
Step-by-step explanation:
Please mark brainliest and have a great day!
Which of the following interpretation for the given sentence is correct?
What is the area of the kite?
135 m2
108 m2
90 m2
Answer:
Step-by-step explanation:
135 m2
The triangles are similar. The area of the larger triangle is 1200 cm?
What is the area of the smaller triangle?
Answer:
75 cm^2
Step-by-step explanation:
We have the lengths of two corresponding sides. The scale factor from the large triangle to the small triangle is 16/64 = 1/4. Each side of the smaller triangle is 1/4 times the length of the corresponding side of the large triangle.
For the areas, the scale factor is the square of the scale factor of the lengths. Area scale factor = 1/4^2 = 1/16.
The area of the small triangle is 1/16 the area of the large triangle.
area of small triangle = (area of large triangle) * (area scale factor)
area of small triangle = 1200 cm^2 * 1/6 = 1200 cm^2/16
area of small triangle = (1200 cm^2)/16 = 75 cm^2
Answer:
I would say 75cm^2.
Can someone please explain to me how to use sin, cos, and tan for triangle calculations? Feel free to use whatever example. I just want to understand how use the trigonometric ratios. Thanks!
Answer:
Hi there!
A way to remember how to do each way is: Soh Cah Toa
Sin- opposite over hypotenuse Cos- Adjacent over hypotenuse Tan- opposite over adjacent.
Hypotenuse is the longest the side of the triangle
and the adjacent side is the side laying near the symbol theta.
The table represents a linear function. The rate of change between the points (–5, 10) and (–4, 5) is –5. What is the rate of change between the points (–3, 0) and (–2, –5)? x y –5 10 –4 5 –3 0 –2 –5
Answer:
=-5
Step-by-step explanation:
The rate of change, the slope, can be found by using the formula for calculating the slope given two points on the line directly.... However what I like to do is just like up the points and subtract then put 2nd difference over first difference.
(-3 , 0)
-(-2 , -5)
------------
-1 5
So the slope is 5/-1 which is just -5
Answer:
the anser is -5
Step-by-step explanation:
you better get 100 now good luck
What is the mode for the set of data shown below?
34, 75, 26, 81, 65, 38, 49, 73, 58, 12, 31, 25, 75, 86, 47, 99
Answer:
75
Step-by-step explanation:
Mode means the number that occurs the most. There can be more than 1 mode also no mode at all.
Looking at the number set closely, we see that "75" occurs twice and every number occurs once. Hence 75 is the mode.
Hello There!
The "MODE" is the numbers that occur most often in a set of numbers.
In this scenario, 75 would be the mode because it occurs twice, No other numbers in this data set repeat except 75.
WILL MARK BRAINLIEST
Answer:
The correct answer is second option
380 square feet
Step-by-step explanation:
Area of composite solid = Base area + area of side rectangles + area of triangles
To find the area of base
Base area = length * width
= 10 * 10 = 100 ft²
To find the area of side rectangle
There are 4 rectangles with length 10 ft and width 6 ft
Area = 4 * area of one rectangle
= 4 * (10 * 6)
= 240 ft²
To find the area of triangle
Here base of triangle = 10 ft and height = 7 ft
Area of 4 triangles =4 * area of single triangle = 4 * (bh)/2
= 4 *(10 * 7)/2 = 140 ft²
To find the total area = Base area + area of side rectangles + area of triangles
= 100 + 240 + 140
= 380 square feet
The correct answer is second option
380 square feet
Answer:
380
Step-by-step explanation:
(-3, 4) is one of many solutions to the inequality:
2x + y > -2.
True or false
Answer:
False
Step-by-step explanation:
Let's check whether (-3, 4) satisfies the given inequality 2x + y > -2.
Replacing x with -3 and y with 4 yields 2(-3) + (4) > - 2
or:
-6 + 4 > -2, or -2 > -2. This end result is false, and so (-3, 4) is NOT a solution of the given inequality 2x + y > -2.
Answer:false
Step-by-step explanation:
A number is equal to twice a smaller number plus 3. The same number is equal to twuce the sum of the smaller number and 1. How many solutions are possible for this situation
Answer:
No solution
Step-by-step explanation:
Suppose the number is [tex]y[/tex] so ([tex]y = ...[/tex]).
Now [tex]y[/tex] is equal to twice a smaller number plus 3. Assuming the smaller number as [tex]x[/tex], we can write it as:
[tex]y = 2x + 3[/tex] --- (1)
Also, the same number [tex]y[/tex] is equal to twice the sum of smaller number and 1:
[tex]y=2x+1[/tex] --- (2)
Now for both of these equations, we need to find a point which satisfies them.
For example, for equation 1, take [tex]y=5[/tex] which means [tex]2(1) + 3[/tex] so the solution will be (1, 3).
Substituting the same value of y here in equation 2:
[tex]5=2(2)+1[/tex] so the solution for this will be (2, 5).
It means that there is no such point which can satisfy both the equations. Hence, there is no solution possible for these two equations.
Answer: The system of equations HAS NO SOLUTION.
Step-by-step explanation:
Let be "y" the first number and "x" the smaller number.
Since the first number is equal to twice a smaller number plus 3, then:
[tex]y=2x+3[/tex] (Equation 1)
Since the same number is equal to twice the sum of the smaller number and 1, then:
[tex]y=2(x+1)[/tex]
[tex]y=2x+2[/tex] (Equation 2)
We need to remember that the equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
You can observe in the Equation 1 that the slope of this line is 2 and you can notice in the Equation 2 that the slope of that line is also 2. Therefore, the lines are parallel and the system of equations has no solution.
PLEASE HELP, IT WOULD BE AWESOME IF YOU COULD!!!!!!!
Joseph is conducting a survey to determine the blood types of 100 people who have come to give blood at a blood donor clinic. Which of the following questions is an appropriate statistical question for this survey? How many people at the clinic have blood type AB? Which blood type does the least number of people have? What is the blood type of each person at the clinic? What is the average age of people with the most common blood type?
Answer: What is the blood type of each person at the clinic?
A rectangular gym has an area of 4x^2ft^2. The school decides to add a new
weight room. The total area of the gym and the weight room is (4x^2+480)ft^2.
What does the constant term represent in terms of this problem?
Answer:
The constant term is the area of weight room.
Step-by-step explanation:
A rectangular gym has an area of [tex]4x^2[/tex] square feet
The school decides to add a new weight room.
The total area of the gym and the weight room is [tex](4x^2+480)[/tex] ft^2.
Here, 480 is the area of the weight room because [tex]4x^2[/tex] is the area of gym and the total area will be addition of both the areas.
Hence, the constant term is the area of weight room.
The area of the weight room is 480 square ft and the constant term 480 represents the area of the weight room.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
We have:
The area of the rectangular gym = 4x² square ft
The total area of the gym and the weight room = (4x² + 480) square ft
Let A be the area of the weight room:
Total area = area of gym + area of weight room
4x² + 480 = 4x² + A
A = 480 square ft
Thus, the area of the weight room is 480 square ft and the constant term represents the area of the weight room.
Learn more about the rectangle here:
https://brainly.com/question/15019502
#SPJ5
What is the name of a polygon that has four congruent sides and theses angle measures 60,120,60,120?
Answer:
The correct answer for this is: rhombus.
Step-by-step explanation:
The name of a polygon that has four congruent sides with the angles measuring 60°, 120°, 60° and 120° is rhombus.
According to the properties of a rhombus, the opposite angles are equal and opposite sides are parallel.
However, the adjacent angles of rhombus are supplementary which means that they add up to 180°.
For example:
60° + 120° = 180°
Answer:
Rhombus
Step-by-step explanation:
A rhombus has 4 congruent sides and the opposite angle s are congruent. I will throw in something extra a rhombus has perpendicular bisectors
3 (x+2)= 6 (x-1) +3
Answer:
x = 3
Step-by-step explanation:
3(x + 2) = 6(x - 1) + 3
Divide both sides by 3.
x + 2 = 2(x - 1) + 1
Distribute the 2 on the right side.
x + 2 = 2x - 2 + 1
Combine like terms on the right side.
x + 2 = 2x - 1
Add 1 to both sides. Subtract x from both sides.
3 = x
x = 3
9 cubic yard 113 cubic inches - 4 cubic feet 129 cubic inches
Answer: 8 yds³ 22ft³ 1712 in³
Step-by-step explanation:
9 yds³ + 113 in³ - (4 ft³ + 129 in³)
Understand that you need to "borrow" 1 yd³ and convert it into ft³ and then "borrow" 1 ft³ and convert it into in³
Conversions:
[tex]1 yd^3\times \bigg(\dfrac{3ft}{1yd}\bigg)^3=\large\boxed{27ft^3}\\\\\\1ft\times\bigg(\dfrac{12in}{1ft}\bigg)^3=\large\boxed{1728in^3}[/tex]
The given equation:
9 yds³ + 0 ft³ + 113 in³
- 4 ft³ - 129 in³
Borrow 1 yd³ to create 27 ft³:
= 8 yds³ + 27 ft³ + 113 in³
- 4 ft³ - 129 in³
Borrow 1 ft³ to create 1728 in³:
= 8 yds³ + 26 ft³ + 1841 in³
- 4 ft³ - 129 in³
= 8 yds³ + 22 ft³ + 1712 in³
For the given system of equations, identify the type of system, a system of equations with the same solution, and the estimated solution of the
systems. Select one response for each column of the table.
...
Type of System
System with the Same Solution
Estimated
Solution
inconsistent
-31x - 19y=95
-14x + 19 y = 76
(3.8, -1.2)
(-3.8, -1.2)
consistent-dependent
31x - 19y=95
14x + 19 = 76
consistent-independent
(-3.8, 1.2)
31x + 19 = 95
14x - 19y = 76
Answer:
Part 1)
-31x - 19y=95
-14x + 19 y = 76
The solution is the point (-3.8,1.2)
The system is consistent independent
Part 2)
31x - 19y=95
14x + 19y = 76
The solution is the point (3.8,1.2)
The system is consistent independent
Part 3)
31x + 19y = 95
14x - 19y = 76
The solution is the point (3.8,-1.2)
The system is consistent independent
Step-by-step explanation:
Part 1) we have
-31x-19y=95 -----> equation A
-14x+19y=76 ---> equation B
Solve the system of equations by elimination
Adds equation A and equation B
-31x-14x=95+76
-45x=171
x=-3.8
Find the value of y
-14(-3.8)+19y=76
19y=76-53.2
y=22.8/19=1.2
The solution is the point (-3.8,1.2)
The system has only one solution
therefore
The system is consistent independent
Part 2) we have
31x-19y=95 -----> equation A
14x+19y=76 ---> equation B
Solve the system of equations by elimination
Adds equation A and equation B
31x+14x=95+76
45x=171
x=3.8
Find the value of y
14(3.8)+19y=76
19y=76-53.2
y=22.8/19=1.2
The solution is the point (3.8,1.2)
The system has only one solution
therefore
The system is consistent independent
Part 3) we have
31x+19y=95 -----> equation A
14x-19y=76 ---> equation B
Solve the system of equations by elimination
Adds equation A and equation B
31x+14x=95+76
45x=171
x=3.8
Find the value of y
14(3.8)-19y=76
-19y=76-53.2
y=-22.8/19=-1.2
The solution is the point (3.8,-1.2)
The system has only one solution
therefore
The system is consistent independent
To determine the type of system, we need to look at the coefficients of the variables and the constants. For the system of linear equations:
```
31x - 19y = 95
-14x + 19y = 76
```
Let's perform the steps to find the solution:
1. We will use elimination or substitution to solve for the variables x and y.
2. We will verify the resulting solution to ensure that it solves both equations.
**Step 1: Elimination**
By adding the two equations together, the y terms will eliminate each other:
```
31x - 19y = 95
-14x + 19y = 76
-----------------
(31x - 14x) + (-19y + 19y) = 95 + 76
17x = 171
```
Divide both sides by 17 to solve for x:
```
x = 171 / 17
x = 10
```
**Step 2: Substitution**
Now that we have x, let's substitute it into one of the original equations to find y. We can use the first equation:
```
31(10) - 19y = 95
310 - 19y = 95
``
Subtract 310 from both sides:
```
-19y = 95 - 310
-19y = -215
```
Divide both sides by -19 to solve for y:
```
y = -215 / -19
y = 11.3158
```
The estimated values of x and y are (10, 11.3158). Since these are not exact values from the multiple choices, it seems there might be a rounding or calculation error. Let's recheck:
```
y = -215 / -19
y = 11.3158...
```
Given the options, the rounded value would be y = 11.3.
**Type of System:**
Given that we were able to find unique values for x and y, the system is "consistent-independent" because it has one solution.
**System with the Same Solution:**
A system with the same solution will have the same coefficients for the variables or will be multiples of one another.
**Estimated Solution:**
As worked out above, x = 10 and y ≈ 11.3. Since this isn't precisely written in the choices, we have to consider rounding for y, which would be approximately 11.3.
With these considerations, the answer to fill the table is:
- Type of System: consistent-independent
- System with the Same Solution: Not provided precisely, but typically it would have proportional coefficients.
- Estimated Solution: (10, 11.3 - considering the second decimal place)
Please note that since we're manually calculating the solution, there may be some approximation in the final values. If exact arithmetic were applied, you should expect to find a precise value for y that matches one of the options more closely.
a line has the equation y=1/4x-1. find the equation if a parallel line through (8,5)
Answer:
y = [tex]\frac{1}{4}[/tex] x + 3
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 )
y = [tex]\frac{1}{4}[/tex] x - 1 ← is in this form
with slope m = [tex]\frac{1}{4}[/tex]
• Parallel lines have equal slopes, thus
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the parallel line
To find c substitute (8, 5) into the partial equation
5 = 2 + c ⇒ c = 5 - 2 = 3
y = [tex]\frac{1}{4}[/tex] x + 3 ← equation of parallel line
A six-sided number cube is rolled twice.
What is the probability that the first roll is an even numbe and the second roll is a number greater than 4?
[tex]|\Omega|=6^2=36\\|A|=3\cdot2=8\\\\P(A)=\dfrac{8}{36}=\dfrac{2}{9}[/tex]
HELP PLEASE !
for a moving object, the force acting on the object varies directly with the objects acceleration. When a force of 90 N acts on a certain object, the acceleration of the object is 10 m/s2. If the force is changed to 72 N, what will be the acceleration of the object?
Answer:
8 m/s^2
Step-by-step explanation:
F=kA
F=force
k=constant you will use for each F=kA relation
A=acceleration
Second sentence says F=90 while A=10 (plug in and find k)
90=k(10) so k=9
We have for any (A,F) that F=9A
Last sentence F=72, what is A?
So 72=9A which means A=8 m/s^2
An account pays 7% per year simple interest. In year 1, the amount in the
account is $950. How much is in the account in year 6?
Answer: $1349
Step-by-step explanation:
SI = prt / 100
= (950 * 7 * 6) / 100
= 399
Amount in the account
950 + 399 = 1349
help please.........................................
Answer:
x =-2 and z =-4
Step-by-step explanation:
We need to solve the following systems of equation
-3x-2y+4z = -16 eq(1)
10x+10y-5z = 30 eq(2)
5x+7y+8z = -21 eq(3)
Multiply eq(1) with 10 and eq(2) with 3
-30x-20y+40z = -160
30x+30y-15z = 90
__________________
10y+25z = -70
Divide by 10
2y+5z = -14 eq(4)
Multiply eq(1) with 10 and eq(3) with 6
-30x-20y+40z = -160
30x+42y+48z = -126
__________________
22y+88z = -286
Divide by 11
2y+8z = -26 eq(5)
Subtract eq(4) and eq(5)
2y+5z = -14
2y+8z = -26
- - +
__________
-3z = 12
z = 12/-3
z = -4
Putting value of z in eq(4)
2y+5z = -14
2y +5(-4) = -14
2y = -14 +20
2y = 6
y = 3
Putting value of z and y in eq(1)
-3x-2y+4z = -16
-3x-2(3)+4(-4) = -16
-3x -6 -16 = -16
-3x = -16+16+6
-3x = 6
x = 6/-3
x = -2
Solve for x.
5/6 x = 10/3
x = 4/3
x = 2
x = 25/9
x = 4
For this case we must solve the following equation:
[tex]\frac {5} {6} x = \frac {10} {3}[/tex]
Multiplying by "6" on both sides of the equation we have:
[tex]5x = \frac {10 * 6} {3}\\5x = \frac {60} {3}\\5x = 20[/tex]
Dividing between 5 on both sides of the equation we have:
[tex]x = \frac {20} {5}\\x = 4[/tex]
So, the solution is [tex]x = 4[/tex]
Answer:
Option D
Answer: LAST OPTION.
Step-by-step explanation:
In order to solve for the variable "x" from the expression [tex]\frac{5}{6}x=\frac{10}{3}[/tex], you need to follow these steps:
1) You need to multiply both sides of the equation by 3:
[tex]3(\frac{5}{6}x)=(\frac{10}{3})(3)\\\\\frac{15}{6}x=10[/tex]
2) You need to multiply both sides of the equation by 6:
[tex](6)(\frac{15}{6}x)=(10)(6)\\\\15x=60[/tex]
3) Finally, you can divide both sides of the equation by 15:
[tex]\frac{15x}{15}=\frac{60}{15}\\\\x=4[/tex]
If the discriminant if a qudratic equation is 4, which statement describes the roots?
Answer:
see explanation
Step-by-step explanation:
The value of the discriminant determines the nature of the roots
• If b² - 4ac > 0 then roots are real and distinct
• If b² - 4ac = 0 then roots are real and equal
• If b² - 4ac < 0 then roots are not real
Here b² - 4ac = 4 > 0
Hence roots are real and distinct
The sum of the squares of two numbers is 8 . The product of the two numbers is 4. Find the numbers.
To find the two numbers, we can set up a system of equations using the given information. Solving this system of equations, we find that the two numbers are 2 and 2, or -2 and -2.
Explanation:To solve this problem, we can use the given information to set up a system of equations. Let's assume the two numbers are x and y. From the problem, we know that
[tex]x^2 + y^2[/tex] = 8 and xy = 4.
We can solve this system of equations by substituting the value of y from the second equation into the first equation. This gives us [tex]x^2 + (4/x)^2[/tex] = 8. Multiplying both sides by [tex]x^2[/tex] gives us [tex]x^4 + 16 = 8x^2[/tex]. Rearranging the equation and factoring, we get [tex]x^4 - 8x^2[/tex] + 16 = 0.
This equation can be factored as [tex](x^2 - 4)(x^2 - 4)[/tex] = 0. Taking the square root of both sides, we find that [tex]x^2[/tex] = 4. Solving for x, we get x = ±2. Substituting these values back into the second equation, we find that the two numbers are 2 and 2, or -2 and -2.
The expression 5^-8 * 7^-9 is equal to which of the following?
A. 1/5(35)^8
B. 1/7(35)^8
Answer:
Your answer is wrong.... M
Final answer:
The expression[tex]5^-8 * 7^-9[/tex]simplifies to 1 / [tex]5^8 * 1 / 7^9[/tex], which can be rearranged to 1 / [tex](35^8 * 7),[/tex] hence the correct answer is option B:[tex]1 / (7 * 35^8).[/tex]
Explanation:
The expression [tex]5^-8 * 7^-9[/tex] simplifies to:
([tex]1/5^8) * (1/7^9)[/tex]
[tex]1 / (5^8 * 7^9)[/tex]
We notice that [tex]5^8 * 7^9[/tex] can be rearranged to [tex](5*7)^8 * 7[/tex]
[tex]1 / (35^8 * 7)[/tex]
Finally, we get [tex]1 / (7 * 35^8)[/tex]which is option B.
Evaluate the following expression. you should do this without a calculator log4 256
Answer:
4
Step-by-step explanation:
Using the rule of logarithms
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
let [tex]log_{4}[/tex] 256 = n, then
256 = [tex]4^{n}[/tex]
Note that 256 = [tex]4^{4}[/tex], hence
[tex]4^{4}[/tex] = [tex]4^{n}[/tex]
Since the bases are equal ( both 4) equate the exponents, hence
n = 4
The mass of a piece of aluminum is 250 grams. The density of aluminum is 2.7 g/mL. What is the volume of the piece of aluminum?
The volume of a given piece of aluminum is 92.6 mL.
What is Density?It is defined as the ratio of mass to volume.It is an extensive property of any substance.
Given: A piece of Aluminum.
Mass = 250 g
Density = 2.7 g/mL
We need to find the volume.
We know, density is given by:
⇒ Density = Mass / Volume
⇒ Volume = Mass / Density
⇒ Volume = 250/2.7
⇒ Volume = 92.6 mL
Therefore, the volume of the piece of aluminum is 92.6 mL.
Learn more about the Density here: https://brainly.com/question/14517477
#SPJ2
A car is purchased for a downpayment of $3,000 with an additional monthly payment of $400 for 36 months. The
formula for the amount spent on the car is S = 3000 + 400 M, where S is the current amount of money that has been
spent and M is the number of months of payments that have been made.
i) How much money will have been spent after a year?
ii) What will be the final cost of the car?
Answer:
$3400 after one year
$17400 after the 36 months
Step-by-step explanation:
3000+400*1=3400
3000+400*36=17400
After a year, $7,800 will have been spent on the car. The final cost of the car will be $16,800.
Explanation:i) To find out how much money will have been spent after a year, we need to substitute the value of M with 12 (since there are 12 months in a year) in the formula S = 3000 + 400M. Therefore, S = 3000 + 400 × 12 = $7,800.
ii) The final cost of the car can be found by substituting the value of M with 36 (since there are 36 months of payments) in the same formula. Therefore, S = 3000 + 400 ×36 = $16,800.
Learn more about Purchase cost of a car here:https://brainly.com/question/15272640
#SPJ2
A circumscribed circle will touch every vertex of a regular polygon ,true or false
Answer:
True
Step-by-step explanation:
we know that
A circle can be circumscribed about any regular polygon
A circumscribed circle surrounds a regular polygon, touching every vertex
What is the following product? Assume x>0.
Oxx
o 12,5
o 6
Answer:
the answer would be the 3rd one :)
Step-by-step explanation: