State the equation of the line which has the y-intercept :
a) 2 and slope 7 .
b) -1 and is parallel to y= 5x - 7.
c) 2 and is inclined at 45 degree to the x- axis.
Answer:
A general line is written as:
y = a*x + b
where:
a is the slope
b is the y-intercept.
a) y-intercept = 2 and slope = 7.
This line is:
y = 7*x + 2
b) y-intercept = -1 and is parallel to y= 5x - 7.
Now, if two linear equations are parallel if they have the same slope and different y-intercept. Then if we want a line parallel to y= 5x - 7, this means that the slope of this line must also be equal to 5.
y = 5*x + (-1)
c) y-intercept 2 and is inclined at 45° to the x- axis.
When we have an inclination of A degrees from the x-axis, the slope of the equation is given by: a = Tan(A)
In this case, we have A = 45°
Then the slope is a = Tan(45°) = 1
Then the equation of this line is:
y = 1*x + 2
The first term of a geometric sequence is 6 and the common ratio is -8. Find the 6th term.
9514 1404 393
Answer:
a6 = -196,608
Step-by-step explanation:
The general term of a geometric sequence with first term a1 and common ratio r is given by ...
an = a1·r^(n-1)
For a1 = 6, r = -8, and n = 6, we find the 6th term to be ...
a6 = 6·(-8)^(6-1)
a6 = -196,608
Solve log x=4
x=4
x=40
x=1000
x=10000
Answer:10000
Step-by-step explanation:
Remember that log x and 10^x are inverse functions.
If you have log x = 4 and want the value of x, write this out:
log x 4
10 = 10
This simplifies to:
x = 10^4, and so the fourth answer choice is the correct one.
Aiko stands 5 m from a tree. At that distance, the angle of elevation from the ground to the top of the tree is 80°.
Approximately how tall is the tree?
Answer:
[tex]\boxed {\boxed {\sf About \ 28.36 \ meters }}[/tex]
Step-by-step explanation:
Assuming the tree is perpendicular to the ground, we can use the right triangle trigonometric ratios to find the tree's height.
sin(θ)= opposite/hypotenuse cos(θ)= adjacent/hypotenuse tan(θ)= opposite/adjacentNow, let's draw a diagram. We know Aiko is 5 meters from the base of the tree. From there, the angle to the top of the tree is 80 degrees. We are looking for x, the tree's height. The diagram attached is not to scale.
We base the sides off of the angle. x is opposite of 80 degrees and 5 is adjacent. Therefore we must use tangent.
[tex]tan(\Theta)=\frac{opposite}{adjacent}[/tex]
opposite=x adjacent=5 mθ=80Substitute in the known variables.
[tex]tan(80)=\frac{x}{5 \ m }[/tex]
We want to find x, the height of the tree. Therefore we need to isolate that variable.
x is being divided and the inverse operation is multiplication. Multiply both sides of the equation by 5 meters.
[tex]5 \ m* tan(80)=\frac{x}{5 \ m }* 5 \ m[/tex]
[tex]5 \ m* tan(80)=x[/tex]
[tex]5 \ m *5.67128182=x[/tex]
[tex]28.3564091 \ m = x[/tex]
The question asks for an approximation, so let's round to the nearest hundredth.
The 6 in the thousandth place tells us to round the 5 to a 6.
[tex]28.36 \ m \approx x[/tex]
The tree is about 28.36 meters tall.
The surface area for a rectangular prism is given by the formula SA = 2ab + 2bc + 2ac, where a, b, and c are the lengths of the prism. If the surface area of a rectangular prism with side c measuring 12 meters is 434 square meters and length of side a measuring the same length as side b, then what is the length of side a of the rectangular prism?
Answer:
We are given
We are also given and , which allows us to rewrite the equation as
(I substituted every "b" with "a" and every "c" with "9").
The solutions to this quadratic equation are -25 and 7. We discard -25 because a side with negative length would make no sense.
The required measure of side a of the rectangular prism is a = 9.3 meters.
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
Here,
SA = 2ab + 2bc + 2ac
434 = 2a² + 14a + 14a
434 = 2a² + 28a
2a² + 28a - 434 = 0
a² + 14a - 217 = 0
a² + 14a + 49 - 49 - 217 = 0
(a + 7)² = 266
a = 9.3 or a = -23.3
Since the negative measure of length can be neglected.
a = 9.3 = b
Thus, the required measure of side a of the rectangular prism is a = 9.3 meters.
Learn more about the surface area here: https://brainly.com/question/2835293
#SPJ5
Graph the following equation
2y-4x=8
1 Rewrite in slope intercept form
Help please- I’m about to stress the heck out djhdhd
-x / 8 = 5
a local restaurant purchased 10 pounds of flour at a total cost of $40. what is the cost for one pound of flour?
Answer:
4 dollars a pound
Step-by-step explanation:
4x 10 = 40
all of the following proportions can be used to solve for m except
Answer:
abcdefghijklmnopqrstuvwxyz
Which line on the graph below has an undefined slope?
P
Q
R
S
Answer:
Q
Step-by-step explanation:
X has constant value
x'-x = 0
m =(y'-y)/(x'-x) --> undefined
Answer:
R
Step-by-step explanation:
A vertical line has a slope that is "undefined". Line R is the vertical line on your graph
___________
The slope of a vertical line is "undefined" because of the way slope is defined. Slope is the vertical change divided by the horizontal change. When the line is vertical, there is no horizontal change, so the computation of slope involves division by zero. The result of division by zero is "undefined."
please help me please will give brainliest to
Solve the system of equations by using the substitution method. 4x - 5y = 25 y=x-6
Answer:
x=5
Step-by-step explanation:
substitute y to the first expression
4x-5(x-6)=25
4x-5x+30=25
-x=25-30
-x=-5
times left and right hand side with minus youll get
x=5
help me nowwwww!!!!!!
Answer:
its the second one
Step-by-step explanation:
it's the only one where the x number dosent repeat
3kg of meat costs £54
Nina buys 2 kg of the meat.
Work out how much Nina pays
Answer:
£36
Step-by-step explanation:
3kg = 54
÷ 3
1kg = 18
18 × 2 = 36
hope this helps...
What is the measure of JGK shown in the diagram below?
A. 56
B. 112
C. 138
D. 69
Answer:
B.56
Step-by-step explanation:
HELP URGENT 40 POINTS
Answer:
Step-by-step explanation:
Do you mind telling me what grade you are in? Oh and can you take a better picture?
WILL GIVE BRAINLIEST
3. Determine the amount of an investment of $500.00 is invested at an interest rate of 4.75% compounded quarterly for 20 years.
Step-by-step explanation:
Use the compound interest formula:
A = P( 1 + r/n)^nt
A is the amount at the end
P is the principal or original amount.
R is annual rate as a decimal (you have to convert)
N is the # of compounding periods in a year (quarterly means 4)
T is time in years
A = 500( 1 + 0.0475/4)^(4×20)
This would be $1285.64 when fully computed.
Select all figures for which there exists a direction such that all cross sections taken at that direction are congruent.
O triangular pyramid
O square pyramid
O rectangular prism
O cube
O cone
O cylinder
O sphere
Answer:
Rectangular PrismCube CylinderStep-by-step explanation:
I know because I just did it on an assignement and it said these were the right answers.
In this exercise we have to use knowledge of direction and congruent lines to identify which objects have these characteristics, so we can say that:
Rectangular Prism
Cube
Cylinder
Triangular pyramid
First we have to remember the definition of congruent lines, such as:
having the same size and shape. equal angles.From this we can now identify these figures as:
Rectangular PrismCubeCylinderTriangular pyramidSee more about congruent at brainly.com/question/24887947
What value of x makes the equation -4+12x=8 true?
Answer:
1
Step-by-step explanation:
50 points and brainiest if correct.
Answer:
2
Step-by-step explanation:
2
Answer:
28 gallons.
Step-by-step explanation:
1/5 is 20% of the container's full capatcity.
7/10 is 70% of the container's full capatcity.
20% - 70% = 50%
By adding 14 gallons of water, the container's water went up by 50%.
If we multiply 14 by 2, we will know what the container can hold at 100% capatcity.
14 x 2 = 28
what is 7/5minus 5 equal?
answer:
- 3 3/5
7/5-5/1 = 18/5
18/5 = - 3 3/5
HELP DUE in 20 MIN
m∠16 =
9514 1404 393
Answer:
∠16 = 47°
Step-by-step explanation:
Vertical and corresponding angles are congruent. The remainder are supplementary to those.
∠1≅∠4≅∠5≅∠7≅∠10≅∠12≅∠13≅∠15 = 133°
∠2≅∠3≅∠6≅∠8≅∠9≅∠11≅∠14≅∠16 = 47°
PLEASE HELP HELP ASAP ASAP PLEASE HELP
Which two grids can be combined to represent 140%?
JA
В
C
O A and B
O A and C
OB and D
O C and D
Answer:
0A and C
Step-by-step explanation:
Please mark me brainlist
pls help i need it asap
Answer:
down below
Step-by-step explanation:
k) 1 and 22/48
l)124/26
m)68/20
n)2 and 5/10
o)2 and 18/19
please give me brainliest!!!<3
1. S(–4, –4), P(4, –2), A(6, 6) and Z(–2, 4) a) Apply the distance formula for each side to determine whether SPAZ is equilateral. b) Apply the slope formula to determine whether the diagonals are perpendicular. c) Apply the midpoint formula to each diagonal to determine whether the diagonals bisect each other.
Answer:
a) SPAZ is equilateral.
b) Diagonals SA and PZ are perpendicular to each other.
c) Diagonals SA and PZ bisect each other.
Step-by-step explanation:
At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.
a) If figure is equilateral, then SP = PA = AZ = ZS:
[tex]SP = \sqrt{[4-(-4)]^{2}+[(-2)-(-4)]^{2}}[/tex]
[tex]SP \approx 8.246[/tex]
[tex]PA = \sqrt{(6-4)^{2}+[6-(-2)]^{2}}[/tex]
[tex]PA \approx 8.246[/tex]
[tex]AZ =\sqrt{(-2-6)^{2}+(4-6)^{2}}[/tex]
[tex]AZ \approx 8.246[/tex]
[tex]ZS = \sqrt{[-4-(-2)]^{2}+(-4-4)^{2}}[/tex]
[tex]ZS \approx 8.246[/tex]
Therefore, SPAZ is equilateral.
b) We use the slope formula to determine the inclination of diagonals SA and PZ:
[tex]m_{SA} = \frac{6-(-4)}{6-(-4)}[/tex]
[tex]m_{SA} = 1[/tex]
[tex]m_{PZ} = \frac{4-(-2)}{-2-4}[/tex]
[tex]m_{PZ} = -1[/tex]
Since [tex]m_{SA}\cdot m_{PZ} = -1[/tex], diagonals SA and PZ are perpendicular to each other.
c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:
[tex]M_{SA} = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot A(x,y)[/tex]
[tex]M_{SA} = \frac{1}{2}\cdot (-4,-4)+\frac{1}{2}\cdot (6,6)[/tex]
[tex]M_{SA} = (-2,-2)+(3,3)[/tex]
[tex]M_{SA} = (1,1)[/tex]
[tex]M_{PZ} = \frac{1}{2}\cdot P(x,y) + \frac{1}{2}\cdot Z(x,y)[/tex]
[tex]M_{PZ} = \frac{1}{2}\cdot (4,-2)+\frac{1}{2}\cdot (-2,4)[/tex]
[tex]M_{PZ} = (2,-1)+(-1,2)[/tex]
[tex]M_{PZ} = (1,1)[/tex]
Then, the diagonals SA and PZ bisect each other.
What is the probability of drawing a face card from a standard deck of cards and rolling a 3 or more on a 20-sided dice?
Write your answer in percent format but do not include the symbol.
Write and round your answer to the nearest hundredth
Answer: 20.77%
Step-by-step explanation:
There are 52 cards in a standard deck. Out of these cards, there are 12 face cards. Thus, the probability of drawing a face is 12/52.
On a 20-sided dice, there are 20 options of numbers to roll. Out of these 20 numbers, 18 of the numbers are greater than or equal to 3, making the probability 18/20, or 9/10.
To find the probability of two events, you need to multiply the probabilities together. Thus, you need to multiply 12/52 by 9/10.
(12/52) * (9/10) = 27/130
27/130 is about equal to 0.2077, or a 20.77% probability.
Can somebody simply these matrixs for me please I will give out brainlist to first correct answer
Answer:
I think it's D:)
Step-by-step explanation:
Is a circles area proportional to its radius? Is a circles circumference proportional to its diameter?
If a figure is dilated by a factor of 6 the area of the figure will change by a factor of?
find the slope of the lines
Answer:
m = 1
Step-by-step explanation:
We can use the x & y intercepts.
Rise = 2
Run = 2
m = Rise/Run = 2/2 = 1