The linear equation that passes through the two given points is:
y = (-1/4)*x - 2/4
Which is the equation of the line?A general linear equation is written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of the line is:
m = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (-1, -1/4) and (1, -3/4)
Then the slope is:
m = (-3/4 + 1/4)/(1 + 1)
m = (-2/4)/2 = -2/8 = -1/4
the line is:
y = (-1/4)*x + b
To find the value of v we can replace the point (1, -3/4) so we get:
-3/4 = (-1/4)*1 + b
-3/4 + 1/4 = b
-2/4 = b
The linear equation is:
y = (-1/4)*x - 2/4
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The equation of line p is y + 5 = -10(x + 2). Line q is perpendicular to line p and passes
through (-1, -1). What is the equation of line q?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
ojo
Submit
Work it out
Not feeling ready vet? These can help:
Ver en
The equation of line q is y = x/10 - 9/10.
What is equation of straight line?
A line that does not curl or bend is said to be straight. A line has length but no width, making it a one-dimensional figure. A line consists of points that extend infinitely in opposite directions. Two points in a 2D plane determine it. A, B, and C are real-based constants in the formula Ax + By + C = 0, A, B 0. The geometric representation of the equation is always a straight line.
Here the given line P,
=> y+5=-10(x+2)
=> y+5=-10x-20
=> y = -10x-25
Here in the given line y=mx+c , where m=slope. Then,
=> Slope of line P = -10.
Here line P is perpendicular to line q.
Then, slope of line q = -1/ slope of line p = -1/-10 = 1/10
Now the line passes through the point [tex](x_1,y_1)=(-1,-1)[/tex] then,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y+1 = 1/10 (x+1)
=> 10y+10 = x+1
=> 10y=x-9
=> y = x/10 - 9/10.
Hence the equation of the line q is y = x/10 - 9/10.
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A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is 24-ft by 26-ft rectangle, and the pavers measure 6 inches across the flats, how many pavers are needed?To surface a driveway about _ pavers are needed
The number of pavers required is 961.
The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.
Given data
A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is a 24-by-26-foot rectangle with pavers 6 inches wide across the flats.
We have to determine how many pavers are needed
We know that area of a regular hexagon
A = (3√3)/2 a^2
= (3√3)/2 〖(6)〗^2
= (3 x 1.732)/2 x 36
= 93.528 sq.inches
Now area of rectangle
= l x w
= 24 x 26 x (12)2 (1feet = 12 inches)
= 89856 sq.inches
Now pavers required
= 89856/93.528
= 960.73
= 961
Therefore the number of pavers required is 961.
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What is the reason for each step in the solution of the equation?
−6x=−2(x+12)
Drag and drop the reasons into the boxes to correctly complete the table.
Answer:
Given
Distributive Property
Addition Property of Equality
Division Property of Equality
Step-by-step explanation:
Frist you distribute the -2 by multiplying it to everything in the parentheses. Next, you add 2x to both sides of the equation and lastly you divide both sides of the equation by -4
At Happy Tails Animal Boarding, cat food and dog food is purchased weekly, Last week, Karen purchased 6 bags of cat food and 9 bags of dog food for a total of 117$. This week, she purchased 4 bags of cat food and 7 bags of dog food for a total of 87$.
Assuming the prices for cat and dog food have not changed over the past two weeks, find and solve the system of equations which can be used to determine the cost of a bag of cat food, c, and the cost of a bag of dog food, d.
c=cost of a bag of cat food
d=cost of a bag of dog food
Write Two Equation
?
?
One bag of cat food costs $6 and one bag of dog food costs $9.
What is system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
The problem states that c equals the cost of bag of cat food and d equals the cost of bag of dog food.
Last week she paid $117 for 6 bags of cat food and 9 bags of dog food.
Therefore, the equation becomes,
6c + 9d = 117 ..(1)
This week she paid $87 for 4 bags of cat food and 7 bags of dog food.
Therefore, the equation becomes,
4c + 7d = 87 ..(2)
Now to solve the system of equations
To solve the first equation for c.
6c + 9d = 117
6c = 117 - 9d
[tex]c = \frac{117}{6}-\frac{9d}{6}[/tex]
Plug value of c in equation (2).
[tex]4(\frac{117}{6}-\frac{9d}{6}) +7d = 87\\78 - 6d + 7d = 87\\d = 87-78\\d = 9[/tex]
Plug d = 9 in equation (1)
6c + 9(d) = 117
6c + 9(9) = 117
6c + 81 = 117
6c = 117 - 81
6c = 36
c = 6
Hence, one bag of cat food costs $6 and one bag of dog food costs $9.
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Hello, please answer this correctly and you will get 5 stars and 20 points.
Answer:
Step-by-step explanation:
90
Colton made a scale drawing of a city park. In real life, the soccer field is 90 meters long.
It is 18 millimeters long in the drawing. What scale did Colton use?
By using unitary method it is obtained that -
Scale used my Colton = 1 : 500
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here unitary method is used
18 mm long field in the drawing is equivalent to 9000 mm long field in real
1 mm long field in the drawing is equivalent to [tex]\frac{9000}{18}[/tex] mm long field in real
1 mm long field in the drawing is equivalent to 500 mm long field in real
Scale used by Colton 1 : 500
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(6, y) and (-8, 4); slope: 1/7
For the given points (6, y) and (-8, 4) having slope = 1/7 the value of y = 10.
What is the slope of a line?
A line's slope, also known as its gradient, is defined as the value of a line's steepness or direction in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.
If P(a, b) and Q(c, d) are two given points on a coordinate plane, then the slope of line PQ can be computed using the formula
[tex]Slope(m)=\frac{d - b}{ c - a}[/tex]
The given points are (6, y) and (-8, 4).
and the slope of the line is given as m = 7.
By using the slope of a line formula, we get
[tex]m = \frac{8-y}{-8-7}\\\\ \frac{1}{7}= \frac{8-y}{-8-7}\\\\\frac{1}{7}= \frac{8-y}{-14}\\\\\\8-y=-2\\y=8+2\\y=10[/tex]
Hence, the value of y is 10.
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what did i do wrong? how do i do y-int?
In 2012, 1,664,479 students took the SAT exam. The distribution
of scores in the verbal section of the SAT had a mean μ = 496 and a
standard deviation of o= 114.
Let X = a SAT exam verbal score section for 2012.
Then X-N (496, 114)
Find the z-scores for x1 = 325 and x2= 366.21.
Interpret each z-score.
What can you say about the x1= 325 and the x2= 366.21?
By using normal distribution of probability, it can be inferred that
For [tex]x_1 = 325[/tex], z = -1.5
This means 325 is 1.5 standard deviation below the mean.
For [tex]x_2 = 366.21[/tex], z = -1.1385
This means 366.21 is 1.1385 standard deviation below the mean.
[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.
[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.
What is normal distribution of probability?
Normal distribution of probability is a continuous type probability distribution whose probability density function is given by-
[tex]f(x) = \frac{1}{\sigma \sqrt{2\pi}}}e^{-\frac{z^2}{2}[/tex]
where [tex]z = \frac{x - \mu}{\sigma}[/tex], [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
For [tex]x_1 = 325[/tex]
[tex]z = \frac{325 - 496}{114} = -1.5[/tex]
This means 325 is 1.5 standard deviation below the mean.
For [tex]x_2 = 366.21[/tex]
[tex]z = \frac{366.21 - 496}{114}[/tex] = -1.1385
This means 366.21 is 1.1385 standard deviation below the mean.
[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.
[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.
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48 - (3 c+4)=4(c+5)+3 c=???
Answer in multiple forms depending on what needed
Answer:
c = 3
Step-by-step explanation:
48- (3c+4)=4(c+5)+3
48-3c-4=4(c+5)+3 Distributed the - sign
48 -3c -4= 4c+20 +3 Distributed the 4
44-3c =4c+23 Combined like terms
21-3c=4c Subtract 23 from both sides
21=7c Add 3c to both sides
3=c
Factor of 14a–35? Pls Ty
I NEED HEEEEELP!!
There are 5 cockroaches crawling on each square meter of the front of this building. How many cockroaches are crawling on the front of the building?
Please, show your work and explain. TYSM!! ^^
There are 855 cockroaches crawling on the front of the building
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
The population density is given as:
Population density = total animals / area occupied
Given that, the population density of the cockroaches is 5 cockroaches per square meter.
The area of the building = area of triangle + area of square
Area of building = (1/2) * (24 - 9)(12) + (9 * 9) = 90 + 81 = 171 m²
Population density = total animals / area occupied
5 cockroaches per square meter = Total cockroaches / 171 m²
Total cockroaches = 855
There are 855 cockroaches
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The laundry room at a hotel sent 160 bath
towels and 64 washcloths to the most rooms
they could so that each room received the
same number of each type of towel. How
many bath towels and how many washcloths
went to each room?
Answer:
5 bath towels
2 washcloths
Step-by-step explanation:
160 = 2⁵ × 5
64 = 2⁶
HCF= 2⁵ = 32
160 ÷ 32 = 5
64 ÷ 32 = 2
Mr. Carson drove 1,027 miles in April. He drove 988 miles in May. Mr. Carson used the expression below to find how many more miles he drove in April than in May -> 1,027 - 988. How many more miles did Mr. Carson drive in April than in May?
Answer:
Mr. Carson drove 39 more miles in April than in May
Step-by-step explanation:
1027-988=39
winner gets brainiest | Don't type in any bs Actually answer the question please
Find domain and range of this linear graph
Answer:
Domain: {0 \leq x} Range {0 \leq y}
Step-by-step explanation:
btw \leq means less than or equal to
4. Angle X in the triangle below is a right angle.
W
15
X
T
h
-25-
2
20
R
9²4625
9+ 25²..
= 20²
400
-625-625
19² √225
15
(a) What is the measure of angle W?
450
(b) What is the height, h, of the triangle?
15.
/2 pts)
a ) The required measure of x = 90°
b ) The height of the right angled triangle = = [tex]\sqrt{244}[/tex]
Given is a triangle with measure 15, 20 and 25
a ) Since a perpendicular is dropped from above
the two angles of x are equal because the angle is bisected by an angle bisector
So to check whether the angle x is a right angled or not
we can use the pythagoras theorem and check if the LHS = RHS or not
LHS = 15² + 20² = 225 + 400 = 625
and RHS = 25² = 625
Since LHS = RHS thus the angle is 90 degrees
b ) The height of the right triangle ;
by using the Pythagoras theorem again
12.5² + h² = 20² { side 25 is bisected = 12.5 }
h² = 400 - 156.25
h = [tex]\sqrt{244}[/tex]
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Critical thinking questions:
Write a system of equations with the solution (4, -3).
Answer: (4,-3)
Step-by-step explanation:
4x+5y=1 (1)
3x-2y=18 (2)
Multiply both parts of equation (1) by 2 and both parts of equation (2) by 5:
8x+10y=2
15x-10y=90
Sum these equations:
23x=92
Divide both parts of the equation by 23:
x=4
Substitute the value of x=4 into equation (1):
4(4)+5y=1
16+5y=1
16+5y-16=1-16
5y=-15
Divide both parts of the equation by 5:
y=-3
Thus, (4,-3)
Evaluate the exponential functions
I hope this helps. Have a great rest of your day!
50. WATER HOSES A water hose can spray water at an
initial velocity of 40 feet per second. Use the formula
h(t) = vot – 16t², where h(t) is the height of the water
in feet, vo is the initial velocity in feet per second, and
t is the time in seconds.
-
a. How long will it take the water to hit the
nozzle on the way down?
b. Assuming the nozzle is 5 feet up, what is
the maximum height of the water?
It will take 2.5 seconds for the water to hit the nozzle on the way down if the initial velocity is 40 feet per second. The maximum height of the water is 30 feet if the nozzle is 5 feet up.
a) Given equation
h(t) = v₀t - 16t^2
Substitute v₀ = 40, h(t) = 0 in the given equation
40t - 16t^2 = 0
Solve for t
⇒ 16t^2 = 40t
⇒ 16t = 40
⇒ t = 40/16
⇒ t = 2.5 seconds
Hence, water will take 2.5 seconds to hit the nozzle on the way down.
b) The function that represents the given condition
h(t) = -16t^2 + 40t + 5
The maximum value of the function is the y-coordinate of the vertex.
The x-coordinate of the vertex
= -40/2(-16) = 5/4
Find the y-coordinate of the vertex by substituting t = 5/4
⇒ h(5/4) = -16(5/4)^2 + 40(5/4) + 5
⇒ h(5/4) = -25 + 50 + 5
⇒ h(5/4) = 30
Hence, the maximum height of the water is 30 ft.
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4. Enrique collected 152 recyclable bottles, and
Latasha collected brecyclable bottles. Write
an expression for the number of bottles they
collected altogether.
The required expression is Total = 152+x .
What is expression ?
Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.
Here,
The number of bottles Enrique collected = 152
Let us take number of bottles collected by Latasha as x. Then,
Total number of bottles collected by the is ,
=> Total = Number of bottles collected + Number of bottle collected
by Enrique By Latasha.
=> Total = 152+x
Hence the required expression is Total = 152+x.
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Which of the quotients is equivalent to -5/8? Select all that apply.
The equivalent quotient to -5/8 are; -5/8 and .5/-8.
The correct answer options are options A and C
How to find equivalent quotient?A quotient is the number resulting from the division of one number by another. For instance, the quotient of 12 divided by 4 is 3.
A divisor number or expression that another is to be divided by. For instance, in "42 ÷ 3" the divisor is the 3.
Dividend is a number or expression that is to be divided by another. For instance, In "42 ÷ 3" the dividend is the 42.
Complete question:
Given options:
A. -5/8
True
B. 5/8
False
C.5/-8
True
D. -(5/-8)
False
E. -5/-8
False
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A Starbucks gift card has a balance of $75. Assume that the person who owns the gift card only uses it to purchase Frappuccino drinks that cost $4.65 apiece.
A submarine was 400 meters below sea level it then moved to 583 meters below sea level. How many meters did the submarine descend? how did you get the answer?
Answer:
Step-by-step explanation:
You subtract 583 from 400 (400-583)
Then you get 183
Given that €1 = £0.75
a) How much is €530 in £?
b) What is the £ to €-exchange rate?
Answer: a.) 397.5 b.) 1.3333
Step-by-step explanation:
1 cent = £0.75
530 x 0.75 = 397.5
530 / 397.5 = 1.3333
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Find the circumference and the area of a circle with diameter 7 cm.
The circumference of the circle is 21.98cm and the area of the circle is 38.465 square cm.
Circumference of the circle:
The Circumference (also known as) perimeter of circle = 2πR
where,
R is the radius of the circle
π is the mathematical constant with an approximate value is 3.14.
Area of circle:
The formula to find the area of the circle is;
A = πr²
Where r represents the radius of the circle.
Given,
The diameter of the circle is 7 cm.
Here we need to find the circumference and the area of a circle.
Here we have the value of diameter, in order to find the circumference we have to find the value of radius that can be derived by dividing the diameter by 2.
So, the radius is
=> 7/2 = 3.5
Now the circumference of the circle is calculated as,
C = 2 x π x 3.5
When the value of π = 3.14
Therefore, the circumference of the given circle is,
=> C = 2 x 3.14 x 3.5
=> C = 21.98
Now, the area of the circle is,
=> A = π x (3.5)²
=> A = 3.14 x 12.25
=> 38.465
Therefore, the area of the circle is 38.465 square cm.
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what is 20 x4 please i need a answer quickly
What is the sale price including tax to the nearest cent? $595 refrigerator, 20% discount; 9.25% tax
The sale price including tax for the refrigerator is $520.
How to calculate the price?From the information, the following can be deduced:
Refrigerator = $595
Discount = 20%
Tax = 9.25%
The sales price will be:
= Refrigerator price + Tax - Discount
= $595 + (9.25% × $595) - (20% × 650)
= $595 + $55 - $130
= $520
The price is $520.
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f: x → x + 5 9: x→ 8x What is the value of fg(4.5)?
The mapping of the function f of g(x) will result to 41
What is a functionA function in mathematics is a rule that defines a relationship between one variable. This is a mapping whose codomain is the set of real numbers.
By mapping of the functions f and g defined as;
f : x » x + 5 and g : x » 8x
then;
f of g(x) = f of 8(4.5)
f of g(x) = f of 36
f of g(x) = 36 + 5
f of g(x) = 41
Hence, with proper mapping of the defined functions of f and g, the correct value for f of g(x) is 41.
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The second and fifth terms of a geometric sequence are 750 and -6 respectively. Find the
common ratio and first term of the sequence.
Step-by-step explanation:
T2= -6
T5=750
ar=-6
ar4=750
both a's cancel each other
we have;
r=-6
r4=750
r4-1(The law of indices) =750
r3=750
r=3√750
r=9.1
Consider the equation and the following ordered pairs: (6,y) and (x,1).
y=−2x+5
The values of x and y are 2 and -7 respectively, this forms an ordered pair of (6,-7) and (2,1).
What are the the values of x and y to complete the given ordered pair?Given the equation and ordered pair the question;
y = -2x + 5Point: (6,y) Point; (x,1)To determine, the y-value, plug the x-value into the equation and solve for y.
y = -2x + 5
Plug in x = 6
y = -2( 6 ) + 5
y = -12 + 5
y = -7
Determine the x-value by plunging in the y-value into the equation and solve for x.
y = -2x + 5
Plug in y = 1
1 = -2x + 5
1 + 2x = 5
2x = 5 - 1
2x = 4
x = 4/2
x = 2.
Therefore, the ordered pair are (6,-7) and (2,1).
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