The perimeter of the rectangle ABCD in the coordinate plane is 8 units
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
The distance between two points in the coordinate plane is given by:
[tex]Distance=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
The vertices of the rectangle is A(-6, -4), B(-4, -4), C(-4, -2) and D(-6, -2). Hence:
[tex]AB=\sqrt{(-4-(-4))^2+(-4-(-6))^2}=2\ units \\\\BC=\sqrt{(-2-(-4))^2+(-4-(-4))^2}=2\ units[/tex]
Perimeter of ABCD = 2(AB + BC) = 2(2 + 2) = 8 units
The perimeter is 8 units
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The package of tissues has 180 pieces of tissues. We know that 10% of tissues are blue, 25% of the package are pink tissues, and the rest are white. How many pieces were blue and how many were pink tissue in the package?
write the equation of a vertical line that goes through the point (8,4).
Answer: A vertical line has an undefined slope, so we cannot use the slope-intercept form (y = mx + b) to write the equation of the line. Instead, we can use the point-slope form (y - y1 = m(x - x1)) where the slope m is undefined and we have a point (x1,y1) on the line.
Since the line goes through the point (8,4), we can use the point (8,4) in the point-slope form:
y - 4 = undefined(x - 8)
We can simplify this equation by dropping the undefined slope and replacing it with a variable:
y = kx + b
Where k is the slope and b is the y-intercept.
The equation of the vertical line that goes through the point (8,4) is x = 8
It's worth noting that the x-coordinate of a vertical line doesn't change, thus it's equal to a constant value and the equation for a vertical line is of the form x=k where k is a constant.
Step-by-step explanation:
Answer:
x = 8
Step-by-step explanation:
The equation of a vertical line is in the form:
x = anumber
You were given the point (8,4) which is in the form (x,y). So x is 8 and y is 4.
x is 8
x = 8
Combine like terms to create an equivalent expression. 1.3 b 7.8 − 3.2 b
The equivalent expression is -1.9b + 7.8.
What is an equivalent phrase?There is a concept known as an analogous expression, which is an expression that has the same value as another expression but has a different appearance.
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
Combine similar phrases now:
The definition of like words is the terms that have the same variable raised to the same power. Only the numerical coefficients can change in algebra.
When we combine the term b's coefficient, we get
1.3b + 7.8–3.2b
= (1.3−3.2)⋅b + 7.8
By condensing the equation, we obtain
= (- 1.9) +b + 7.8
= −1.9b + 7.8
There is a condensed equivalent formula of -1.9b + 7.8.
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Can someone solve this please I really need the answer and your help
The cost of Adult ticket is $ 4 and Cost of Children ticket is $ 3.
What is System of Linear Equation ?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the standard form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.
The cost of adult ticket be x and child ticket be y respectively.
Now as per sum ,
(i) 5x + 13y = 59 and,
(ii) 5x + 9y = 47
Subtracting equation (ii) from (i) we get,
13y - 9y = 59 - 47
⇒ 4y = 12
⇒ y = 3
putting y = 3 in equation (ii) we get
5x + 9*3 = 47 ⇒ x = 20/5 = 4
The cost of Adult ticket is $ 4 and Cost of Children ticket is $ 3.
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Calculate the monthly payment for a loan of $7,500 with an 11% interest rate compounded monthly over a period of 5 years. a. $128.46 b. $163.07 c. $858.18 d. $1541.50 please select the best answer from the choices provided a b c d
Option b is correct monthly payment = $163.07
A loan of $7,500 with an 11% interest rate compounded monthly over a time period of 5 years.
Monthly Payment = Amount / Discount factor
Discount factor [tex]D = \frac{1-(1+i)^{n} }{i}[/tex]
where,
Amount = $7500
Rate= 11%=0.11
[tex]i = \frac{0.11}{12} = 0.0091[/tex] ( by using division)
Time = 5 years
Time (n) = 5 × 12 = 60
Now, put i and n in the Discount factor,
[tex]D = \frac{1-(1+i)^{n} }{i}[/tex]
[tex]D = \frac{1-(1+0.009)^{-60} }{0.009}[/tex]
[tex]D = \frac{1-(1.009)^{-60} }{0.009}[/tex]
[tex]D = \frac{0.421 }{0.009}[/tex]
D = 46.77
Monthly payment (M),
[tex]M = \frac{Amount}{Discout factor} = \frac{A}{D}[/tex]
[tex]M = \frac{7500}{46.77}[/tex] ( by using division)
Monthly payment = 163.07
Therefore, Option b is the correct monthly payment = $163.07.
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Greta has two pet lizards, Draco and Lizzy. For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets. Last week, Greta fed Draco 77 crickets.
How many crickets did Greta feed Lizzy?
How many crickets did Greta feed Lizzy?
Answer:
56
Step-by-step explanation:
For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.
Since Gretta fed Draco 77 crickets just do:
77 ÷ 11
= 7
Then:
8 x 7
= 56
You're welcome
Type the correct answer in the box. Round your answer to the nearest whole number.
The mass of Venus is 4.87 × 1024 kilograms, and the mass of Jupiter is 1,898 × 1024 kilograms.
The mass of Jupiter is about _____ times the mass of Venus.
Answer:
The mass of Jupiter is about 11.8 times the mass of Venus.
Step-by-step explanation:
what is 5 divided by 2/3 as a fraction
Answer: 7 and 1/2
Step-by-step explanation:
When dividing a fraction by a whole number you could turn the whole number into a fraction:
5 = 5/1
Once you turn the whole number into a fraction you then do the keep, change, flip, method
you would keep 5/1 as it is and change the divide sign to the multiplication sign the flip 2/3 to 3/2:
5/1 x 3/2
then you just multiply across
5/1 x 3/2 = 15/2
and 15/2 could be simplified to 7 and 1/2
15/12 is the right representation of 5 divided by 2/3 as a fraction.
To divide a number by a fraction, you can multiply the number by the reciprocal of the fraction. In this case, to divide 5 by 2/3, you can multiply 5 by the reciprocal of 2/3.
Reciprocal of 2/3 = 3/2
So, 5 divided by 2/3 can be written as:
5 * (3/2)
To simplify this, you multiply the numerators together and the denominators together:
(5 * 3) / (2 * 1) = 15/2
Therefore, 5 divided by 2/3 is equal to 15/2 as a fraction.
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What are some examples of exponential relationships?
An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form
f(x) = [tex]a^x[/tex]
Where a>0 and a is not equal to 1.
x is any real number.
If the variable is negative, the function is undefined for -1 < x < 1.
Here,
“x” is a variable
“a” is a constant, which is the base of the function.
The examples of exponential functions are:
f(x) = [tex]2^x[/tex]
f(x) = 1/ [tex]2^x[/tex] = [tex]2^-x[/tex]
f(x) =[tex]2^(x+3)[/tex]
f(x) = [tex]0.5^x[/tex]
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If the m<1 = (6x-20), and the m<8 (4x-30), what is the m<7?
The angle m∠7 corresponds to angle m∠3 which is vertically opposite the angle m∠1, and so the measure of the angle m∠7 = 118°
How to evaluate for the angle m∠7angles m∠1 and m∠3 are vertically opposite angles and are said to be equal so;
m∠1 = m∠3 = 6x - 20
angles m∠3 and m∠7 are corresponding angles and are said to be equal so;
m∠3 = m∠7 = 6x - 20
angles m∠7 and m∠8 lie on a straight line so;
6x - 20 + 4x - 30 = 180°
10x - 50° = 180°
10x = 180° + 50° {collect like terms}
10x = 230°
x = 230°/10 {divide through by 10}
x = 23
Therefore since the value of x is 23, then the measure of the angle m∠7 = 6(23) - 20, which result to 118°
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6. Ali and Steve share some sweets in the ratio 2:7
Steve gets 30 more sweets than Ali.
Work out how many sweets Steve gets.
The required amount of sweets Steve will get is 42.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
here,
Ali and Steve share some sweets in a ratio of 2:7 Steve gets 30 more sweets than Ali.
Let the amount of sweet Ali and steve be x and y,
According to the question,
x / y = 2/7
x = 2y/7 - - - - (1)
And
y = 30 + x
From equation 1
y = 30 + 2y / 7
5y = 30 × 7
y = 42
Now,
x = 2 × 42 /7
x = 12
Thus, the required amount of sweets Steve will get is 42.
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What would be the order of these quadratic functions when they are
arranged from the narrowest graph to the widest graph?
f(x) = -5x²
g(x) = 0.5x²
h(x) = 3x²
(1) f(x), g(x), h(x)
(2) g(x), h(x), f(x)
(3) h(x), f(x), g(x)
(4) f(x), h(x), g(x)
please help ASAP
Therefore , the solution to the given problem of function comes out to be f(x)=0.5x² is the narrowest graph.
What does the word function mean?A relationship that explains how two variables relate to one another is represented by the word "functions," which is frequently used in mathematics. There are three: a variable, which can be any type of input, and predictor variables, which are the results of the function or equation.
Here,
A quadratic function's "width" can be calculated using the coefficient before the variable.
The graph will be narrower than the parent graph if the coefficient is more than one (f(x)=x2), and
wider if the coefficient is less than one. Thus, from widest to narrowest:
f(x)=0.5x²
f(x)=3x²
f(x)=-5x²
Therefore , the solution to the given problem of function comes out to be f(x)=0.5x² is the narrowest graph.
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SOMEONE HELP ASAP. THIS IS DUE IN A FEW HOURS AND THE LAST QUESTION I NEED.
It will be much appreciated, and I will add rewards
Ignore the 18/15=1.2, I am in a rush
Assumption 1: [tex]\triangle ABE \sim \triangle ACD/tex]
[tex]\frac{x}{10}=\frac{3}{15} \implies x=2[/tex]
Assumption 2: [tex]\triangle ABE \sim \triangle ADC[/tex]
[tex]\frac{x}{15}=\frac{3}{10} \implies x=4.5[/tex]
Find the total surface area for the rectangular prism.
The rectangular prism shown is 8 inches by 7.5 inches by
6 inches.
Use the formula:
Now, substitute
B.
1.5
for P,
for h and
Rewrite the formula with the numbers:
The total surface area is:
Next find just the lateral surface area
Use the formula:
Now, substitute
for P and for h.
The lateral surface area is:
Rewrite the formula with the numbers:
for
When the length, breadth, and height are provided as 8 inches, 7.5 inches, and 6 inches, respectively, the rectangular prism's total surface area is 360 inches2.
what is surface area ?Surface area is a measure of how much space an object's surface takes up overall. The total area of a three-dimensional shape's surroundings is its surface area. Surface area refers to the total surface area of a three-dimensional shape. You may compute the surface area of a cuboid with six rectangular faces by adding together their individual areas. Alternatively, you can use the following formula to name the box's dimensions: Surface (SA) = 2lh plus 2lw plus 2hw. A three-dimensional shape's surface area is calculated as the total amount of space it occupies (a three-dimensional shape is a shape that has height, width, and depth).
given
rectangle prism has a length of 8 inches and a width of 7.5 inches.
6 inches is the rectangular prism's height.
SA equals two square units of (lh + wh + lw).
A=360 inches2
When the length, breadth, and height are provided as 8 inches, 7.5 inches, and 6 inches, respectively, the rectangular prism's total surface area is 360 inches2.
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x + 4.25=7.50 what is the value on the x in the equation?
Answer:
x = 3.25
Step-by-step explanation:
Answer:
Just subtract the answer to what your adding:
7.50 - 4.25 = 3.25
Step-by-step explanation:
Hope it helps! =D
URGENT HELP! PICTURES ATTACHED.
The perimeter of the rectangle, given that the rectangle has an area of 40 ft² and a length of 8 ft is 26 ft
How do I determine the perimeter of the rectangle?We'll begin by obtaining the width of the rectangle. The width of the rectangle can be obtained as follow:
Area = 40 ft²Length = 8 ftWidth =?Area = Length × Width
40 = 8 × Width
Divide both sides by 8
Width = 40 / 8
Width = 5 ft
Finally, we shall determine the perimeter of the rectangle. Details below:
Length = 8 ftWidth = 5 ft Perimeter =?Perimeter = 2(Lenght + Width)
Perimeter = 2(8 + 5)
Perimeter = 2(13)
Perimeter = 26 ft
Thus, we can conclude that the perimeter is 26 ft
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Solve for the missing variable. Round to the nearest hundredth.
X
8
20
Answer:
656
Step-by-step explanation:
What is R1 and R2 in lens maker formula?
In the lens maker's formula, R1 and R2 represent the radii of curvature
The lens maker's method specifies the association among the focal length, refractive index, and curvature radii of a lens's two surfaces. It's a method that lens makers employ to make lenses with a particular power out of the glass with a particular refractive index.
R1 and R2 in the lens manufacturer's formula stand for the radii of curvature of the two surfaces of a lens. R1 and R2 are the radiuses of the surfaces that face the item being imaged and the surface that faces the image, respectively. A lens's focal length is calculated using a formula based on the lens's surface curvature and the material's refractive index.
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If a man work for 8 hour a day, he can finih a job in 12 day. How many hour per day mut he work to complete it in 10 day?
He must work for 10 hours a day to complete the job in 10 days. 10 hours per day is the optimal amount of time to finish the job in 10 days
1. Begin by setting up an equation. Let x be the number of hours worked.
2. 8 hours x 12 days = 96 hours
3. We want to finish the job in 10 days, so 10x = 96
4. Solve for x. 10x = 96, x = 9.6
5. Since we can't work partial hours, round up to 10 hours. Therefore, the man must work 10 hours a day to complete the job in 10 days.
To finish the job in 10 days, the man must work for a total of 100 hours. This means he must work for 10 hours a day to complete the job in the allotted time. Working 8 hours a day would take 12 days, and working 9 hours a day would take 11.11 days. Therefore, 10 hours per day is the optimal amount of time to finish the job in 10 days.
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What triangle has 70?
A triangle with two equal side lengths is known as an isosceles triangle. The angle of an isosceles triangle is 70 degrees.
A triangle is a three-sided geometry shape with 3 vertices. The internal angle of the triangle, which is 180 degrees, is built. It means that a triangle's internal angles sum to 180 degrees.
A triangle with two equal side lengths is known as an isosceles triangle. The vertex angle is the leftover angle that results from subtracting the two specified angles from 180 degrees. The two angles between it base and equal sides are identical in magnitude.
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Mc Graw Hill < 3-8 Slope and Equations of Lines Question 10 of 12 ✓ Question 10 X = D Find the value of x that satisfies the given conditions. Then graph the line on a separate sheet of paper. The line containing (4, -2) and (x,-6) is perpendicular to the line containing (-2,-9) and (3,-4).
To solve the problem, we must first find the slope of the line containing (4, -2) and (x, -6). The slope of a line is calculated as the change in y-coordinates divided by the change in x-coordinates, or (y2 - y1) / (x2 - x1). In this case, the slope of the line containing (4, -2) and (x, -6) is (-6 - (-2)) / (x - 4) = -4 / (x - 4)
Since the line containing (4, -2) and (x,-6) is perpendicular to the line containing (-2,-9) and (3,-4), we know that the product of the slopes of these two lines is -1. We can use that information to find the slope of the second line: -1 = (-4 / (x - 4)) * m, where m is the slope of the second line. Solving for m, we get m = -1 / (-4 / (x - 4)) = (x - 4) / 4.
We can now use the point-slope form of a linear equation to find the equation of the line containing (-2,-9) and (3,-4). The point-slope form is y - y1 = m(x - x1). In this case, we can use (-2,-9) as (x1, y1) and (x - 4) / 4 as m:
y - (-9) = (x - 4) / 4 * (x + 2)
Simplifying we get y = (x-4)/4 + (-9) = (x-4)/4 - 9
Now we can substitute x = -2 and y = -9 to check if it belongs to this line:
-9 = (-2 - 4)/4 - 9
-9 = -2/4 - 9
-9 = -0.5 - 9
-9 = -9.5
It match so this line is the correct one.
The value of x that satisfies the given conditions is x = -2
You can graph this line on a separate sheet of paper by plotting the point (-2, -9) and using the slope (x-4)/4 to find additional points on the line.
The measure of <1 is 125 degrees . Find the measure of <4.
Answer:
55°
Step-by-step explanation:
so the total should be 360, so if 2 angles are 125 (360-250=110) then the leftover 110 has to be split into 2 angles, which is 55
Bianca deposits $3,000
in a savings account earning 4.25%
simple interest per year.
How much interest will Bianca earn for a period of 3
years?
Bianca will earn interest of $382.5 for a period of 3years.
What is simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same.
Simple interest is calculated with the following formula:
S.I. = P × R × T,
where P = Principal, R = Rate of Interest in % per annum, and T = Time
Given,
Principal P = $3000
Rate of interest R = 4.25% = 4.25/100 = 0.0425
Time T = 3 years
Simple interest S.I. = P × R × T
= 3000 × 0.0425 × 3
= 127.5 × 3
S.I. = $382.5
Hence, Interest Bianca will earn in 3 years = $382.5
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How do you find the values of a function?
f(x)=mx+b. The function's value is f(x). The line's slope is m. When x is equal to 0, the function's value is equal to b.
what is function ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
iven
f(x)=mx+b. The function's value is f(x). The line's slope is m.
When x is equal to 0, the function's value is equal to b, which is also the coordinate at where the line in the coordinate plane crosses the y-axis.
The x-value coordinate's is given by x.
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Jaylen ha a fun-ize bag SweetTart. Inide the bag are 4 pink, 1 blue, 2 yellow, 3 purple and 2 green SweetTart. What i the probability of drawing a yellow SweetTart three time in a row if each SweetTart elected i eaten before the next SweetTart i drawn?
The probability of drawing a yellow SweetTart three times in a row is (2/15) x (1/14) x (2/13) = 0.0002692.
1. There are a total of 15 SweetTarts in the bag (4 pink, 1 blue, 2 yellow, 3 purple and 2 green SweetTarts).
2. The probability of drawing a yellow SweetTart first is 2/15.
3. The probability of drawing a yellow SweetTart second is 1/14 (since one yellow SweetTart has already been drawn).
4. The probability of drawing a yellow SweetTart third is 2/13 (since two yellow SweetTarts have already been drawn).
5. The overall probability of drawing a yellow SweetTart three times in a row is (2/15) x (1/14) x (2/13) = 0.0002692.
The probability of drawing a yellow SweetTart three times in a row is (2/15) x (1/14) x (2/13) = 0.0002692.
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I really need help besties what is 67=-7x-10
Answer:
x = 11
Step-by-step explanation:
We'll have to get X alone by doing the opposite of what the current equation is showing
67 = 7x-10. I usually turn the numbers around cause it looks better...
7x-10 = 67
We see it's subtracting 10, so we'll add 10 on both sides
7x = 67 + 10
7x = 77
Since 7x is being multiplied, we'll divide on both sides
x = 77/7
x = 11
Answer: -11
Step-by-step explanation:
rearrange it so it's -7x-10=67
add 10 to itself and 67
then you get -7x=77
then divide 77 by -7
and you get -11
i hope this was right :)
A drama club is building a wooden stage in the shape of a trapezoidal prism. The height of the
stage is 2 feet. Some measurements of the stage are shown here. What is the area of all the
faces of the stage, excluding the bottom? Show your reasoning. If you get stuck, consider
drawing a net of the prism.
Two triangles will be better than one half times five times thirteen. We'll also have a single rectangular piece. It measures 12 by 10. 20 times 2 equals 40. 13 divided by 2 divided by 2 is equal to 4. I am capable of 44 times two times two. 13 is 52 One is equal to 10 x 2 x 1/2. 12 times 10 is 120, and 5 times 13 is 65. Consequently, the area is 297 square feet (40 plus 52 plus 20 plus 65 plus 120).
What is prism?A prism is a solid shape that is bound on all its sides by plane faces. There are two types of faces in a prism. The top and bottom faces are identical and are called bases. A prism is named after the shape of these bases. For example, if a prism has a triangular base it is called a triangular prism.The faces other than the top and bottom of a prism are called its lateral faces. All the lateral faces are also identical to each other and belong to the class of parallelograms. This means that the lateral faces can either be parallelograms, rectangles, or even squares since all of them have their opposite sides parallel to each other. One of the most common examples of a prism is a cuboid. It has a rectangular base and is called a rectangular prism.To learn more about rectangular prism refer to:
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Answer: 297 ft.2
Step-by-step explanation:
The quotient of five times x and fifteen
Answer:
the answer to your question is 3.
Determine whether the ytem ha no olution, one olution, or infinitely many olution. If the ytem ha one olution, name it. Xy= 5
3x5y=15
The solution of the given system of equation x + y = 5 , 3x + 5y = 15 represents it has one solution given by intersecting lines at point
(x, y ) = ( 5, 0).
As given in the question,
Given system of equation is :
x + y = 5 __(1)
3x + 5y = 15 ___(2)
The standard rule to get the solution of the system of equation is given by :
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂= 0
One solution :
a₁ / a₂ ≠ b₁ / b₂
No solution :
a₁ / a₂ = b₁ / b₂ ≠ c₁/c₂
Infinitely many solution :
a₁ / a₂ = b₁ / b₂ = c₁/c₂
Here in the given system of equation:
1/3 ≠ 1/5
One solution exist.
Solve by elimination method.
Multiply (1) by 3 and subtract from (2) we get,
3x + 5y = 15
3x + 3y = 15
2y = 0
⇒y =0
Substitute y =0 in (1) we get,
x = 5
It represents both the lines intersect at point ( x, y) = ( 5,0)
Therefore , the given system of equation has one solution equal to
intersecting point ( x, y) = ( 5,0).
The above question is incomplete , the complete question is :
Determine whether the system of equation has no solution, one solution, or infinitely many solution. If the system of equation has one solution, name it.
x + y = 5
3x + 5y = 15
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The number of feet in a yard can be represented by a graph. Circle the graphs) that could
be used to represent the number of feet, y, in x yards.
Answer: graph a and d
Step-by-step explanation: