Answer:
The answer to this problem is x = 3 and y = -2.
Step-by-step explanation:
To solve this problem, we first have to remember how to solve problems using substitution. We first solve one equation completely in terms of another variable. In this case, this has already been done for us - the first equation is in the form y = f(x). Next, we should substitute this "value" or function for y into the other equation. This process is modeled below:
y = -4x + 10
y = -6x + 16
If we substitute, we get:
-4x + 10 = -6x + 16
Now this is a simple one variable equation that we can solve easily. First, we should add 6x to both sides, giving us:
2x + 10 = 16
Then, we should subtract 10 from both sides, yielding:
2x = 6
Finally, we can divide both sides by 2 to get:
x = 3
Now, we must plug in this value for x into one of our original equations (it doesn't matter which one we choose) to solve for the other variable, y.
y = -4x + 10
y = -4(3) + 10
y = -12 + 10
y = -2
Therefore, the answer to this problem is x = 3 and y = -2.
Hope this helps!
Answer:
x = 3
y = -2
Step-by-step explanation:
y = -4x + 10 first equation
y = -6x + 16 second equation
from the second equation:
6x = -y + 16
x = (-y + 16) / 6 third equation
substituying the value of the third equation into the first equation:
y = -4(-y+16)/6 + 10
y - 10 = -4(-y+16(/6
6(y-10) = -4(-y+16)
6*y + 6*-10 = -4*-y -4*16
6y - 60 = 4y - 64
6y - 4y = 60 - 64
2y = -4
y = -4/2
y = -2
from the third equation:
x = (-y + 16) / 6
x = (-(-2) + 16) / 6
x = (2+16)/6
x = 18/6
x = 3
Check:
from the first equation:
y = -4x + 10
-2 = -4*3 + 10
-2 = -12 + 10
PLEASE PLEASE PLEASE HELP ME!
Answer: 50 Minutes = 309 gal
Step-by-step explanation: Every 10 minutes the amount of water goes up by 18, so after 50 minutes the water would be equivalent to 309 gallons.
Answer:
[tex]y=1.8x+219[/tex]
309 gallons
Step-by-step explanation:
So to find the linear equation, we can use the data from the table.
First, use the data from the table to find the slope. Pick any two points. I'm going to use (10,237) and (20,255).
Let (10,237) be x₁ and y₁ and let (20,255) be x₂ and y₂.
The formula for slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\frac{255-237}{20-10}[/tex]
Simplify:
[tex]m=18/10=1.8[/tex]
Thus, the slope is 1.8. This means that 1.8 gallons of water flow into the tank every minute.
Now, let's find the slope-intercept. To do this, we can use the point-slope form. The point-slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
Let's use (10,237) for consistency. Plug in 237 for y₁ and 10 for x₁. Also use 1.8 for m. Thus:
[tex]y-237=1.8(x-10)[/tex]
Distribute:
[tex]y-237=1.8x-18[/tex]
Add 237 to both sides:
[tex]y=1.8x+219[/tex]
What this means is that there is initially 219 gallons of water in the tank already. Every minute, 1.8 gallons is added further.
And that's our linear equation :)
So, to find the amount of gallons after 50 minutes, plug in 50 for x and solve:
[tex]y=1.8(50)+219\\y=90+219=309[/tex]
After 50 minutes, there will be 309 gallons of water.
Which equation can be used to solve for b? Triangle A B C is shown. Angle A C B is 90 degrees and angle C B A is 30 degrees. The length of side B C is 8 feet, the length of B A is c, and the length of C A is b.
Answer:
b = 8tan30°
Step-by-step explanation:
Find the diagram of the triangle in the attachment. Using SOH CAH TOA to find the side AC which is b. Side AC will be the opposite of the triangle since it is facing the acute angle 30° and side BC will be adjacent.
Using TOA;
Tan<CBA = CA/BC
Given <CBA = 30°, BC = 8feet
CA = BCtan<CBA
CA = 8tan30° = b
Hence the equation that can be used to solve for b is 8tan30°
Answer:
B
Step-by-step explanation:
Adam would like to build a deck thatbis 60,feet long by 8 feet hiw much wood would he need
Answer:
136 ft of woods
Step-by-step explanation:
1. Let us assume that we are solving for the frame of the deck alone
2. And also from the given parameters the deck has a rectangular shape
we know that the total amount of woods to be used is same as the perimeter of the rectangle.
Given that
length l= 60 ft
width w= 8 ft
The formula for the perimeter of a rectangle is given as
Perimeter= 2l+2w
perimeter= 2*60+ 2*8
perimeter= 120+16
perimeter= 136 ft
Hence in other to construct the frame of the deck Adam needs a total of 136 ft of woods
11. Listed below are the temperature in °C for 10 days.
-6.-8. 0. 3. 2. 0. 1, 5, 4, 4
What is the range of the data?
Answer:13
Step-by-step explanation: range is the biggest value - the smallest value, in this case, the biggest value= 5 and the smallest value= -8 so, 5--8= 5+8 ( when it is a minus minus it is automatically changed to a plus)= 13.
1. Describe the figure using precise mathematical language
please help
17. Tonya's mother is 1.5 times as tall as
Tonya was when she was 6. How tall
is Tonya's mother? Use the correct
number of significant digits.
The question is incomplete:
17. Tonya's mother is 1.5 times as tall as Tonya was when she was 6. How tall is Tonya's mother? Use the correct number of significant digits.
The image with the information about Tonya's height is attached.
Answer:
68 in.
Step-by-step explanation:
According to the information given, you can write the following expression:
x=1.5y
x=Tonya's mother height
y= Tony's height when she was 6
Also, you know from the table that Tonya's height when she was 6 was 45 in. and you can replace this value in the formula:
x=1.5*45
x=67.5
Because of this, the answer is that Tonya's mother height is 68 in.
What is 8.61×10−8 in decimal form?
0.000000861
0.0000000861
8,610,000
861,000,000
Answer:
0.000000861
Step-by-step explanation:
Answer:
0.0000000861
Step-by-step explanation:
I took the test. Hope this helps!
Write 2.3181818... as a mixed number.
What is the minimum value of the function g(x) = x2 - 6x – 12?
-21
3-21
3
3+21
Answer:
- 21
Step-by-step explanation:
The minimum value occurs at the vertex of the function
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
Given
f(x) = x² - 6x - 12
add/ subtract ( half the coefficient of the x- term)² to x² - 6x
f(x) = x² + 2(- 3)x + 9 - 9 - 12
= (x - 3)² - 21
with vertex = (3, - 21 )
The minimum is the value of k, that is minimum value = - 21
Which list shows the numbers in order from least value to greatest value?
Solve for a: 2.2a + 3.4 b = 1.2a + 2.6
What is the value of a when b = 2? b =
1.5?
Answer:
when b=2 , a = -4.2
when b=1.5 , b=-2.5
Step-by-step explanation:
When b = 1.5
[tex]2.2a + 3.4b = 1.2a + 2.6 \\ a = \\ b = 1.5 \\ 2.2a + 3.4(1.5) = 1.2a + 2.6 \\ 2.2a + 5.1 = 1.2a + 2.6[/tex]
[tex]2.2a - 1.2a = 2.6 - 5.1 \\ a = - 2.5[/tex]
When b = 2
[tex]2.2a + 3.4(2) = 1.2a + 2.6 \\ 2.2a + 6.8 = 1.2a + 2.6[/tex]
Collect like terms and simplify
[tex]2.2a - 1.2a = 2.6 - 6.8 \\ a = - 4.2[/tex]
Whats the quotient or -42/-7
Answer: 6
Step-by-step explanation: when you divide two negative numbers, the answer will always be positive .
Hello! I need some help figuring out what 12 x 6,012 is. Ty!
Answer:
12 times 6012 u can type in calculator is 72144
Answer:
72144 is the answer.
Hope this helps
8 + 56/-7 х -4
-24
-40
0
40
Answer:
0
Step-by-step explanation:
8+56/-7x-4
8+(-8)x-4
0x-4
0
Hope this helps ;) ❤❤❤
Find the value of x/y if (3/5)^4*(15/10)^4=x/y^4
Answer:
9/10
Step-by-step explanation:
3^4/5^4 × 15^4/10^4=x^4/y^4
81/625 × 50625/10000= x^4/y^4
multiply
4100625/6250000=x^4/y^4
break it down by dividing it by 5
820125/1250000
divide by 5
164025/250000
divide by 5
32805/50000
divide by 5
6561/10000 = x^4/y^4
4√6561/4√10000=x/y
9/10= x/y
A veterinarian is visited by many pets and their owners each day. Before the doctor attends to each pet, an assistant
records information including the type, age, weight, and height of each pet. Which of the variables is a categorical
variable?
The correct answer is Type
Explanation:
Categorical variables differ from other types of variables because these involve categories or defined groups. For example, sex is a categorical variable because in a population individuals are either classified as females or males (categories). This concept applies to types of pets because this variable involves categories or defined groups such as dogs, cats, hamsters, turtles, etc. Also, other variables such as age, weight, or height are not naturally categorical because these can be understood using numbers rather than categories.
Answer: The answer is definitely TYPE
Step-by-step explanation: For example the brand of a car is a category. You could have a Toyota. Toyota is a category of a car. Therefore, this can be applied in this problem; the Type of a pet is a category. The pet could be a dog or a cat e.t.c.
f(x)= 2x+5, g(x)=x+10, f-g (x)
Answer:
x -5
Step-by-step explanation:
f(x)= 2x+5, g(x)=x+10,
f-g (x) = 2x+5 - (x+10)
Distribute the minus sign
= 2x+5 - x-10
=2x-x +5-10
Combine like terms
x -5
Megan purchased 12 square yards of flooring for a total of $432. What was the price of this
flooring per square foot
Answer:
$5184
Step-by-step explanation:
1 per square foot =$432/1
12 square =12×$432/1
$5184
This set has me absolutely confused. Can anyone help with the first problem?
Answer:
The other endpoint is ( -1,15)
Step-by-step explanation:
21.
The x coordinate of the midpoint is the sum of the x coordinate of the endpoints divided by 2
(-5 +x)/2 = -3
Multiply each side by 2
-5+x = -6
Add 5 to each side
-5+x+5 = -6+5
x = -1
The y coordinate of the midpoint is the sum of the y coordinate of the endpoints divided by 2
(-1 +y)/2 = -8
Multiply each side by 2
-1+y = -16
Add 1 to each side
-1+y+1 = -16+1
y = -15
The other endpoint is ( -1,15)
let f(x) = 12/4x+2. find f(-1)
What is the exact area of a circle with a diameter of 20 cm?
Answer:
314 cm^2
Step-by-step explanation:
pi(r^2)
r= d/2
pi= 3.14
3.14(10^2)
3.14(100)
314
Answer:
100π cm^2
Step-by-step explanation:
The area of a circle is given by the formula ...
A = πr^2
where r represents the radius, which is half the diameter. For a circle of radius 10 cm, the area is ...
A = π(10 cm)^2 = 100π cm^2
please answer!!! I really need this
Answer:
A
Step-by-step explanation:
a would be the correct answer to create a rectangle
The sum of one-third of a number and 27
Answer:
a/3 + 27
Step-by-step explanation:
One third is: 1/3
then:
, the expressipn is:
a/3 + 27
The required expression, that is the sum of one-third of a number, and 27 is x / 3 + 7.
Given that,
To determine the arithmetic, the sum of one-third of a number and 27.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Let the number be x,
one-third of the number is = x/3,
Now according to the question,
Applying arithmetic operations,
Sum = x / 3 + 27
Thus, the required expression, that is the sum of one-third of a number and 27 is x / 3 + 7.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
which of the following is equivalent to complex number i6 ?
A 1
B i
C -1
D -i
Answer:
-1
Step-by-step explanation:
What is 0.895 repeating simplified in a fraction
Answer:
[tex]\dfrac{887}{990}[/tex]
Step-by-step explanation:
Multiply by 100, subtract the original and divide the result by 99.
[tex]x=0.8\overline{95}\\100x=89.5\overline{95}\\100x-x=89.5\overline{95}-0.8\overline{95}=88.7\\99x=88.7\\\\x=\dfrac{88.7}{99}=\boxed{\dfrac{887}{990}}[/tex]
Describe how to draw a tape diagram to represent and answer 3÷3/5=? 3 ÷ 3/5 = ? for a friend who was absent.
Answer:
The numerical answer is 5
Please see the tape diagram evolution in the attached image
Step-by-step explanation:
Start by drawing three unit tapes, and divide each one of them in 5 equal parts since we need to be dividing the quantity 3 by 3/5 (denominator 5)
In the second step, join the three tapes in one long one maintaining the original divisions.
In the third step, select groups of 3 divisions (recall you need to divide by 3/5) which will identify in your tape how many of these 3/5 groups you have.
Finally count the number of 3/5 groups you found in the collection of the three original tapes placed together. You should count a total of 5 of these 3/5 groups.
5 then tells you what is the quotient of 3 divided in 3/5
What is the slope m of a line that is perpendicular to the line represented by x = 8? (If an answer is undefined, enter UNDEFINED.)
Answer:
slope = 0
Step-by-step explanation:
x = 8 is a vertical line parallel to the y- axis
A line perpendicular to it is a horizontal line parallel to the x- axis.
The x- axis has a slope of zero thus the line perpendicular to x = 8 is zero
The slope of a line is simply the ratio of a change in the vertical axis to the horizontal axis. The line perpendicular to [tex]x = 8[/tex] has a slope of 0
Given that
[tex]x = 8[/tex]
See attachment for the line of [tex]x = 8[/tex]
First, we determine the slope of [tex]x = 8[/tex]
The slope of a line (m) is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]x = 8[/tex] means that, the value of x is always 8; irrespective of the y-value.
So:
[tex]x_2 = x_1 = 8[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes
[tex]m = \frac{y_2 - y_1}{8-8}[/tex]
[tex]m = \frac{y_2 - y_1}{0}[/tex]
Assume the slope of the line perpendicular to [tex]x = 8[/tex] is [tex]m_2[/tex].
[tex]m_2[/tex] is calculated as follows:
[tex]m_2 = -\frac{1}{m}[/tex]
Substitute [tex]m = \frac{y_2 - y_1}{0}[/tex]
[tex]m_2 = -\frac{1}{(y_2 - y_1)/0}[/tex]
This gives
[tex]m_2 = -\frac{1\times 0}{y_2 - y_1}[/tex]
[tex]m_2 = -\frac{0}{y_2 - y_1}[/tex]
[tex]m_2 = -0[/tex]
[tex]m_2 = 0[/tex]
The slope of the line perpendicular to [tex]x = 8[/tex] is 0.
Read more about slopes at
https://brainly.com/question/3605446
How far will Danny travel in12 hours at a speed of 99 kilometers per hour?
Answer: 1,188 km
Step-by-step explanation:
99 x 12 = 1,188
42 divided by (14-6)
Answer:
5 r 2
Step-by-step explanation:
Which equation does not represent y as a function of x? Group of answer choices A. 5x2 + 5y = 3 B. 2x = 8y C. –4y = –8 D. 3x + 6y = –5 E. 7y2 + 8x = 9 Please Post the explanation!! I want to understand it.
Answer:
The correct option is (C).
Step-by-step explanation:
We need to find the correct option that does not represent y as a function of x.
In options A, B, D and E, both x and y are involved. It means we can represent y as a fucntion of x.
But in option (c), it has only y as a variable i.e.
-4y=-8
y=(8/4)
y = 2
So, this option does not represent y as a function of x.