Answer:
1/3
Step-by-step explanation:
to find the slope of two points the formula is (y2-y1)/(x2-x1) so if you plug in the numbers given into that formula you get (3-4)/(7-10), then simplifying that you get (-1)/(-3) and the negatives cancle out so you get 1/3
The slope is the inclination of a line and can be calculated by the ratio of the difference of y's coordinate to x's coordinate thus the slope of the line passing through points (10,4)and (7,3) is 1/3.
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines . The slope could be positive or negative.
The slope of the lines passing through points (x₁, y₁) and (x₂, y₂) is,
⇒ (y₂ - y₁)/(x₂ - x₁)
As per the given points (10,4)and (7,3)
Slope = (3 - 4)/(7 - 10)
Slope = -1/-3 = 1/3
Hence "The slope is the inclination of a line thus the slope of the line passing through points (10,4)and (7,3) is 1/3".
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solve the following equation for x
4x - 6y=20
Answer:
x = [tex]\frac{3}{2}[/tex]y + 20
[Given]
4x - 6y = 20
[Add 6y to both sides of the equation]
4x = 6y + 20
[Divide both sides of the equation by 4]
x = [tex]\frac{6}{4}[/tex]y + 20
[Simplify [tex]\frac{6}{4}[/tex], both 6 and 4 are divisible by 2]
x = [tex]\frac{3}{2}[/tex]y + 20
Question 3
Thank youuu
Answer:
45⁰
Step-by-step explanation:
We need to find n first.
we are given that GQH is 90⁰ which means that the sum of GQL and LQK should 90⁰ because these are angles on a straight line which adds up to 180⁰.
so,
(4n-15) + 3n = 90⁰
Take the -15 to the other side after opening the brackets.
4n + 3n = 90⁰ + 15
7n = 105⁰
Divide it by 7 for both sides.
n = 15⁰
Now substitute n=15⁰ in you LQK equation.
4n -15
(4×15) -15
60⁰ - 15
45⁰
g(n) = f(n)
f(n) = 2n² + 6
g(2) = ?
»f(n) = 2n² + 6
so, g(n) = 2n² + 6
»g(2) = 2(2)² + 6
»g(2) = 2(4) + 6
»g(2) = 8 + 6
»g(2) = 14✅
As
[tex]\\ \rm\Rrightarrow g(n)=f(n)[/tex]
[tex]\\ \rm\Rrightarrow g(2)=f(2)=14[/tex]
Are 9/21 and 6/14 equivalent fractions
Answer:
Yes
Step-by-step explanation:
9/21 SIMPLIFIED= 3/7
6/14 SIMPLIFIED= 3/7
A rectangular goat pen has a perimeter of 20 meters and an area of 24 square meters. What
are the dimensions of the pen?
Answer:
4m and 6m
Step-by-step explanation:
factors of 24: 2, 3, 4, 6, 8, 12
now just go through each and find one that fits the description
Which operation should you perform first when you simplify 63 − (2 + 54 multiply 6) ÷ 5?
Answer:
Multiply 54 by 6
Step-by-step explanation:
Remember the Order of Operations:
Parentheses
Exponents
Multiplication/Division (Whichever comes first)
Addition/Subtraction (Whichever comes first)
In this case, we can start by looking inside of the parentheses.
There are two signs; addition and multiplication.
Now we look back to the order of operations (PEMDAS), and see that multiplication comes before addition, therefore you should first multiply 54 by 6.
A shoe store uses a %60 markup for all of the shoes it sells. What would be the selling price of a pair of shoes that has a wholesale cost of $51?
Answer:
81.60 is your selling price
Step-by-step explanation:
60% = 0.60
0.60 x 51 = 30.60
51 + 30.60 = 81.60
How do you solve friendly numbers 71+18+9=
Answer:
98
Step-by-step explanation:
71 + 9 + 18 = ( 71 + 9 ) + 18 Group numbers that add to 10 to make it easier
= 80 + 18
= 98
If you have any questions, you can ask them in the comments section of this answer. If you could mark this answer as brainliest, I would greatly appreciate it.
Can someone simplify the following product, 6 x 4x²?
Answer:
24x²
Step-by-step explanation:
6 x 4x² = 24(x)(x) = 24x²
write an equation for the nth term of the sequence 8,32,128,512
Answer:
8*(4^n)
where n is the nth number
equation ar^n
where a is first term
r common ratio.
I dont know how to do this will someone help me
Answer: A
Step-by-step explanation:
The change in the y coordinates is 0, but the change in the x coordinates is 8.
HELP ME OUT PLS!!!!
All postcards at a store cost the same amount. It costs $0.50 more to buy 8 postcards than it does to buy 6 postcards.
Which equation can be used to find x, the cost of each postcard in dollars?
Answer:
I'm pretty sure it's D) 8x = 6x + 0.50
Nolan has 4 sets of water colors. Each set has 8 colors. How
many total colors would he have if he bought 2 more sets?
Answer:
He would have 48
Step-by-step explanation:
1 set: 8
2 sets: 16
3 sets: 24
4 sets: 32
5 sets: 40
5 sets: 48
OR
{4(8)} + 2(8)
32 + 2(8)
32 + 16
48
Have an amazing day!!
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Answers
48
Steps
4+2=6
8 times 6= 48
09. Find the rate A sum of money doubled itself in 15 years. In how many years will it become 8 times of itself?
Answer:
45 years
Step-by-step explanation:
Let the sum be x and CI=2x
We know that
CI=P(1+100R)T
2x=x(1+100R) ^15
(1+100R)^15=2
Let m be the number of years.
Therefore,
x(1+100R)m=8x
(1+100R)m=23
(1+100R)m=[(1+100R)^15]3
From eqn(1)
(1+100R)m=(1+100R)45
On comparing both power, we get
m=45 years
Use the relationship between the angles in the figure to answer the question.
Which equation can be used to find the value of x?
x = 52
x + 52 = 180
x + 52 = 90
52 + 38 = x
Two lines intersecting with the top right angle of fifty two degrees and a bottom left angle of labeled X degrees
Answer:
it is letter B and then it is letter a
For the following exercises, evaluate the function f(x) =-3x: + 2x at the given input.
3 f(-2)
4 f(a)
5. show that the function f(x) =ー2(x-1): + 3 is not one to one
Answer:
We use a variety of different notations to express the derivative of a function. In (Figure) we showed that if f(x)=x^2-2x, then f^{\prime}(x)=2x-2. If we had expressed this function in the form y=x^2-2x, we could have expressed the derivative as y^{\prime}=2x-2 or \frac{dy}{dx}=2x-2. We could have conveyed the same information by writing \frac{d}{dx}(x^2-2x)=2x-2. Thus, for the function y=f(x), each of the following notations represents the derivative of f(x):
f^{\prime}(x), \, \frac{dy}{dx}, \, y^{\prime}, \, \frac{d}{dx}(f(x)).
In place of f^{\prime}(a) we may also use \frac{dy}{dx}\Big|_{x=a} Use of the \frac{dy}{dx} notation (called Leibniz notation) is quite common in engineering and physics. To understand this notation better, recall that the derivative of a function at a point is the limit of the slopes of secant lines as the secant lines approach the tangent line. The slopes of these secant lines are often expressed in the form \frac{\Delta y}{\Delta x} where \Delta y is the difference in the y values corresponding to the difference in the x values, which are expressed as \Delta x ((Figure)). Thus the derivative, which can be thought of as the instantaneous rate of change of y with respect to x, is expressed as
\frac{dy}{dx}=\underset{\Delta x\to 0}{\lim}\frac{\Delta y}{\Delta x}.
Step-by-step explanation:
C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 3 ± 0.05 inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 3.001 inches with a standard deviation of 0.030 inch.
Long ago, in some town, a phone number consisted of a letter followed by 3 digits (e.g. K651). How many
possible phone numbers could there be?
Answer:
25978
Step-by-step explanation:
There are 26 letters in the alphabet and 999 numbers with 3 digits so I multiplied and got the answer
Please mark Brainlest if I helped
A public parking garage charges $5 plus an additional $2 per hour. Write the equation for the line in slope-intercept form.
A restaurant offers a dinner special that lets you choose from 3 entrees, 6 side dishes, and 4 desserts. You can choose one entree, two sides dishes, and one dessert. How many different meals are possible?
Step-by-step explanation:
Two meals are the different
Answer:
5*3*4 = 60, so 60 different main meals could be ordered.
An airplane is traveling at 625 miles per hour. At this rate, about how long will it take the plane to travel 3,250 miles?
Answer:
5.2 hours
Step-by-step explanation:
divide the total distance by how fast
td/speed
3250/625=5.2hrs
In a recipe mike uses 4 cups of brown sugar for every 3 cups of flower. What is ratio of flour to brown sugar SIMPLEST FORM.
Answer:
3:12 = 1:4
Step-by-step explanation:
3 cups of flour = 4 cups brown sugar
4 x 3 = 12
3:12 = 1:4 (simplest form)
Find the measure of the missing ANGLE.
46 degrees
52 degrees
65 degrees
83 degrees
Answer:
83°
Step-by-step explanation:
? = (1/2)[m(arc)DE + m(arc)RF]
? = (1/2)[106° + 60°]
? = 83°
Find a polynomial f(x) of degree 5 that has the following zeros.
2,9,-4 (multiplicity 2 ), -5
leave your answer in factored form
F(x) =?
Answer:
Step-by-step explanation:
F(x) = (x - 2)(x - 9)(x + 4)²(x + 5)
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on square 15? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)
Answer:
Square 15: 16,384
Sum of all grains up to and including square 15: 32,767
Total weight up to and including square 15: 4.681 lb
Step-by-step explanation:
Square 1: 1 = 2^0
Square 2: 2 = 2^1
Square 3: 4 = 2^2
Square 4: 8 = 2^3
Notice that the exponent of the 2 is 1 less than the number of the square, so for square n, the number of grains is 2^(n - 1)
Square n: 2^(n - 1)
Square 15: 2^(15 - 1) = 2^14 = 16,384
Now let's look at the sums.
Square 1 sum: 1
Square 2 sum: 1 + 2 = 3
Square 3 sum: 3 + 4 = 7
Square 4 sum: 7 + 8 = 15
Notice that each sum is one grain less than 2 raised to the number of the square.
Square 1 sum: 1 = 2^1 - 1
Square 2 sum: 1 + 2 = 3 = 2^2 - 1
Square 3 sum: 3 + 4 = 7 = 2^3 - 1
Square 4 sum: 7 + 8 = 15 = 2^4 - 1
Square n sum: 2^n - 1
Square 15 sum: 2^15 - 1 = 32,767
Weight:
32,767 × 1/7000 lb = 4.681 lb
Evaluate (6 + 2i) / (3 –i ).
5/4 + 6/4i
8/5 + 6/5i
20/8 + 12/8i
16/9 + 12/9i
We are given with a complex no. and need to simplify it , so let's start !!!
Let's assume that :
[tex]{:\implies \quad z=\sf \dfrac{6+2\iota}{3-\iota}}[/tex]
Now , Rationalizing the denominator or in other words multiplying and dividing [tex]{z}[/tex] by the conjugate of the denominator
[tex]{:\implies \quad z=\sf \dfrac{6+2\iota}{3-\iota}\times \dfrac{3+\iota}{3+\iota}}[/tex]
[tex]{:\implies \quad z=\sf \dfrac{(6+2\iota)(3+\iota)}{(3-\iota)(3+\iota)}}[/tex]
[tex]{:\implies \quad z=\sf \dfrac{6(3+\iota)+2\iota (3+\iota)}{(3)^{2}-(\iota)^{2}}\quad \qquad \{\because (a-b)(a+b)=a^{2}-b^{2}\}}[/tex]
[tex]{:\implies \quad z=\sf \dfrac{18+6\iota +6\iota +2(\iota)^{2}}{9-(-1)}\quad \qquad \{\because (\iota)^{2}=-1\}}[/tex]
[tex]{:\implies \quad z=\sf \dfrac{18+12\iota -2}{10}}[/tex]
[tex]{:\implies \quad z=\sf \dfrac{16+12\iota}{10}}[/tex]
[tex]{:\implies \quad z=\sf \dfrac{16}{10}+\dfrac{12\iota}{10}}[/tex]
[tex]{:\implies \quad {\bf \therefore}\quad \underline{\underline{z=\bf \dfrac{8}{5}+\dfrac{6}{5}\iota}}}[/tex]
Hence , Option B) (8/5) + (6/5)i is correct :D
Answer: 8/5+6/4i
Proof of validity is shown below.
calculate the length of the diagonal for the given rectangular prism. Round to the nearest tenth
Length = 10cm
Width = 4cm
Height = 10cm
The length of the diagonal of the rectangular prism is 14.7 feet to the nearest tenth.
What is a prism?In a three-dimensional space prism is a polyhedron where two ends are similar.
Given:
The dimensions of the right rectangular prism:
Length l = 10cm
Width w = 4cm
Height h = 10cm
The length of the diagonal of the rectangular prism,
= √(l² + w² + h)
= √{(10)² + (4)² + (10)²}
= 14.69
= 14.7 feet.
Therefore, the length of the diagonal is 14.7 feet.
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A trapezoidal prism undergoes a dilation. The surface area of the pre-image is 49 mm². The surface area of the image is 784 mm². The height of the pre-image is 6.1 mm.
What is the height of the image?
Enter your answer as a decimal in the box.
mm
The term "dilation" refers to a transformation. The height of the pre-image is 24.4 mm.
What is the dilation factor?The term "dilation" refers to a transformation that is used to downsize an item. Dilation is a technique for making items appear bigger or smaller. The picture produced by this transformation is identical to the original shape.
Let the dilation factor of the trapezoid be x.
Now, if we write the area of the pre-image trapezoid, it can be written as,
[tex]\text{Area of trapezoid} = \dfrac{(a+b)}{2}h = 49\rm\ mm^2[/tex]
As we know the dilation is applicable to dimensions, therefore, the area of the trapezoid which is the image can be written as,
[tex]\text{Area of Image trapezoid} = \dfrac{(ax+bx)}{2}hx[/tex]
[tex]= \dfrac{x(a+b)}{2}hx\\\\=\dfrac{(a+b)}{2}h\cdot x^2\\\\=49\cdot x^2[/tex]
Now, if we calculate the scale factor(x) of the dilation we will get,
[tex]{\text{Area of trapezoid}}={\text{Area of Image trapezoid}}\\\\x^2 \cdot 49 = 784\\\\x = 4[/tex]
Further, the scale factor applied to the height of the image can be written as,
The height of the Image = 4 × Height of pre-image
= 4 × 6.1 = 24.4 mm
Hence, the height of the pre-image is 24.4 mm.
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Answer:
24.4 mn
Step-by-step explanation: I took the quiz
help please , thank you
Answer:
Graph 1 (big) shows that it has the biggest number which means that graph 1 (big) is the correct answer!
Step-by-step explanation:
Simplify the expression:
3x4-8d+1
Answer:
-8d+13
Step-by-step explanation:
Add and Multiply all of the numbers without variables:
3x4+1
Use PEMDAS to solve (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction):
3x4=12
12+1=13
Now you have your answer:
-8d+13
Answer:
-8d+13
Step-by-step explanation:
Multiply first:
3x4=12
Add:
12+1=13
Add equations:
-8d+13
The correct answer is -8d+13
