keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]5x+4y=16\implies 4y=-5x+16\implies y=\cfrac{-5x+16}{4} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{4}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is -5/4 and it passes through (8 , -7)
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{8}) \implies y +7= -\cfrac{5}{4} (x -8) \\\\\\ y+7=-\cfrac{5}{4}x+10\implies {\Large \begin{array}{llll} y=-\cfrac{5}{4}x+3 \end{array}}[/tex]
what is pie over 2 pls this is needed now
big reward
HELP ASAP PLS
Find the volume
Answer:
637 in^3
Step-by-step explanation:
V=(BxH)/2
V=((13x7) x 14)/2
V=(91x14)/2
V=1274/2
V=637 in^3
Use the distributive property to simplify 5( x + 3).
(A). 8 x
(B). 5 x + 3
(C). 5 x + 8
(D). 5 x + 15
Answer:
D) 5x+15
Step-by-step explanation:
5×x+5×3
5x+15
plz mark as brainliest
A Cone and Cylinder have the same radius and height. If the Cylinder’s volume is 363 cm3 . What is the Cone’s volume?
ok um 213=89Step-by-step explanation:ummmmmmmmmm
23x² + 6x + 7 please help
Answer:
the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.
Step-by-step explanation:
The expression 23x² + 6x + 7 is in the form of a quadratic equation. A quadratic equation is an equation in the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. In this case, the coefficients of the x², x, and the constant term are a = 23, b = 6, c = 7.
One way to factor a quadratic equation is by using the factoring by grouping method, where we group the terms in pairs and factor out the greatest common factor (GCF) from each group.
Here is one way to factor this equation:
23x² + 6x + 7 = (23x² + 6x) + 7
= (23x² + 6x) + 7
= (23x² + 6x + 6x) + 7
= (23x² + 12x) + 7
= (23x(x) + 3x(4)) + 7
= (23x(x+4) + 7)
= (x+4)(23x + 7)
So the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.
It's important to note that the above expression factors into a product of two binomials and not two factors of 23x² + 6x + 7
You can also use Quadratic formula to solve the above expression if this method seems confusing.
solve for the missing side length in this triangle
Answer:
10 and 24units
Step-by-step explanation:
Pythagoras' TheoremPythagoras' Theorem applies to right angle triangles with the formula:
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
where c is the longest side, with a and b the shorter ones (interchangable)
SolutionWith the parameters given from the question and the formula given as well, we can find the value of x and therefore the side lengths.
By Pythagoras' Theorem,
[tex] {26}^{2} = ( {5x)}^{2} + ( {12x)}^{2} \\ 676 = 25 {x}^{2} + 144 {x}^{2} \\ 169 {x}^{2} = 676 \\ {x}^{2} = 676 \div 169 \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ = 2[/tex]
Now we can find the side lengths.
[tex]5x = 5(2) = 10units \\ 12x = 12(2) = 24units[/tex]
Therefore the side lengths are 10 and 24 units.
Find the interet and total amount due on 1200 after 1 year 5 month at a rate
of interet of 4% p. A
Total interest earned = 68
Total amount collected = 1268
What is simple Interest ?Simple interest is a way to figure out how much interest will be paid on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the following year's principal to compute interest, the principal amount under simple interest remains constant.
Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the initial principle amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of several forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest.
Since nothiong mentioned the interest is considered simple
Total amount = 1200 (principal)
Time = 1 year 5 month = [tex]1\frac{5}{12} = \frac{17}{12}[/tex]
rate = 4 %
Total interest earned = [tex]\frac{1200 * 4 * \frac{17}{12} }{100}[/tex] = 68
Total amount generated = 1200 + 68 = 1268.
To learn more about Simple interest refer to :
https://brainly.com/question/29709325
#SPJ4
Find the area of the front face of the shed. Please help asap.
Answer:
8.25cm²
Step-by-step explanation:
the area of the triangle = (half x base x height )=
(1.5x3)÷2= 2.25cm²
the area of the rectangle= length x width = 3x2= 6cm²
total = 2.25+6= 8.25cm²
PLEASE HELP !! WILL MARK BRAINLIEST
Answer:
(8,-2)
Step-by-step explanation:
What are ideal and real solutions?
Solutions refers to the answer to the problem, Real Solutions are realistic and practical whereas ideal solutions are the best cases for the solutions.
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
Ideal Solutions - Best cases, Usually not possible.
Real Solutions - Practical and possible to attain.
To learn more about solutions visit:
https://brainly.com/question/30109489
#SPJ4
solve -2.3 - (4.5-3.5)
Answer:
-3.3
Step-by-step explanation:
-2.3 - (4.5-3.5)
-2.3 - (1.)
-3.3
How do you solve 2 polynomial equations?
The steps to solve two polynomial equations are given below.
What is polynomial?
A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
x^2 + 4x + 7 is an illustration of a polynomial with a single indeterminate x.
Apply the Zero Factor Property to an Equation Solving.
ZERO. FACTOR, write the equation with one side equal to zero. the expression by a factor.
PROPERTY. Solve the equation by setting each factor to zero.
Check by adding substitutes to the initial equation.
Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero once it has reached zero. The original equations' solutions are the solutions to the resulting equations. Factoring cannot always be used to solve polynomial equations.
To know more about polynomial, click on the link
https://brainly.com/question/2833285
#SPJ4
If you know the answer to this question please help!! 7th grade math
Answer: obtuse
Step-by-step explanation:
need help fast Geometry
Answer:
D. 29°
Step-by-step explanation:
Triangle ACB is an isosceles triangle so the two base angles are the same(61° and 61°). A triangle's angles must add up to 180, so take 180-61-61.
180-61-61 = 58
Divide by 2 to find angle ACB:
58/2 = 29
Answer:
Option D; 29°
Step-by-step explanation:
ΔAOB is isosceles triangle: so ∠B = ∠A, ∠A = 61, therefore:
∠O = 180 - (61 + 61)
∠O = 58
and ∠C = 58 / 2
∠C = 29
Hope this helps!
Which government tax policy is most likely to result in an increase in consumer demand? A - an increase in personal income tax B - a decrease in corporate tax C - a decrease in personal income tax D - an increase in corporate tax
The correct answer is "C" - a decrease in personal income tax is most likely to result in an increase in consumer demand.
Define Tax.Taxes are compulsory payments made by a government organization, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools.
What is VAT?A value-added tax, often referred to as a goods and services tax in some nations, is a kind of tax that is imposed gradually. At every stage of manufacture, distribution, or sale to the final customer, it is added to the cost of a good or service.
There is an increase in consumer demand when personal income taxes are cut because people have more money that they can spend on products and services.
On the other hand, a rise in personal income taxes would reduce the amount of disposable money that consumers have, which will result in a drop in demand from consumers.
In a similar vein, a rise in company tax would result in higher business costs and lower profits, both of which would reduce consumer demand. Conversely, a drop in corporate tax would not directly influence consumer spending.
So the correct answer is C.
To learn more about income tax visit:
https://brainly.com/question/17075354
#SPJ4
Unit sales for new product ABC have varied in the first seven months of this year as follows: Feb 285 Mar Apr May Jun Jul Month Jan 314 158 482 284 310 281 Unit Sales What is the (population) standard deviation of the data? Please round your answer to the nearest integer. Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel
The population standard deviation of the data is 111.
1. Find the mean of the data:
Mean = (314 + 158 + 482 + 284 + 310 + 281) / 6 = 1029 / 6 = 171.5
2. Find the difference between each data point and the mean:
Feb: (314 - 171.5) = 142.5
Mar: (158 - 171.5) = -13.5
Apr: (482 - 171.5) = 310.5
May: (284 - 171.5) = 112.5
Jun: (310 - 171.5) = 138.5
Jul: (281 - 171.5) = 109.5
3. Square each of the differences:
Feb: (142.5)^2 = 20,312.5
Mar: (-13.5)^2 = 182.25
Apr: (310.5)^2 = 95,822.25
May: (112.5)^2 = 12,656.25
Jun: (138.5)^2 = 19,082.25
Jul: (109.5)^2 = 11,982.25
4. Sum all of the squared differences:
20,312.5 + 182.25 + 95,822.25 + 12,656.25 + 19,082.25 + 11,982.25 = 149,047.5
5. Divide the sum of the squared differences by the number of data points minus one:
149,047.5 / (6 - 1) = 149,047.5 / 5 = 29,809.5
Square root of 29,809.5 = 111 (rounded to the nearest integer)
Therefore, the population standard deviation of the data is 111.
Learn more about standard deviation here
https://brainly.com/question/13905583
#SPJ4
Determine which point from the specified that satisfies each system of equations
The required point that satisfies each system of equation is (12, -1). Option B is correct.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
To equations are given as,
y = -1/3x + 3 - - - - (1)
y = -3/4x + 8 -- - - - (2)
From equation 1 and 2
-1/3x + 3 = -3/4x + 8
3/4x - 1/3x = 8 - 3
9x - 4x / 12 = 5
5x = 60
x = 12
Now, to evaluate the y ordinate put the above x in equation 1
y = -1/3(12) + 3
y = -4 + 3
y = -1
Thus, the required point that satisfies each system of equation is (12, -1). Option B is correct.
Learn more about simultaneous equations here:
https://brainly.com/question/16763389
#SPJ1
Line s passes through the points (3,4) and (2,1).line t passes through the point (4,2) and is parallel to line s.
What is the equation for line t
Answer:
y=3x-10
Step-by-step explanation:
first, we need to find the slope of line s, as that will determine the slope of line t
the formula for the slope calculated from 2 points is (y2-y1)/(x2-x1)
we can label the points for (3,4) and (2,1)
x1=3
y1=4
x2=2
y2=1
substitute into the formula:
m=(y2-y1)/(x2-x1)
m=(1-4)/(2-3)
m=-3/-1
m=3/1
m=3
the slope of line s is 3
as said above, parallel lines have the same slope, but different y intercepts.
that means that line t will have the same slope as line s (3).
typically, lines are written in the form y=mx+b, where m is the slope and b is the y intercept
here's what is line t so far:
y=3x+b
we need to find b
because the line passes through the point (4,2), we can use it to solve for b
plug 4 in as x and 2 as y
2=3(4)+b
2=12+b
-10=b
so that means that b is -10
therefore the equation for line t is y=3x-10
Hope this helps! Good luck on your assignment!
find the distance between the points (-2,8) and (7,13) on a corrdiante plane
Answer: d = √(5² + 9²) = √106, or approximately 10.3 units.
It takes 3 hours to drive 180 miles. How long will it take to drive 330 miles?
Answer:
5.5
Step-by-step explanation:
180/3 =60 (60/1 hr)
330/60 =5.5
The radius of a circle is 10 ft. Find its area in terms of π π.
Answer:
100π sq. ft
Step-by-step explanation:
Given,
Radius ( r ) = 10 ft
To find : Area ( circle ) = ?
Formula : -
Area ( circle ) = π r^2
Area ( circle )
= π x 10^2
= π x 100
= 100π sq. ft
Answer:
area of circle : πr^2
= π(10)^2
= 314.1592654
≈ 314.16 cm2
Can you pls help me
Brady took 80 shots on his pop- a- shot basketball hoop . If he made 90%of his shots into the basket, how many shots did he make
Answer: Brady made 72 shots
Step-by-step explanation:
Number of shots taken on his pop- a- shot basketball hoop=80
Percentage of shots made into the basket=90%
Number of shots made into the basket= 90% x 80
= 90/100 x 80
= 72
You have decided to purchase a car for $25,625. The credit union requires a 10% down payment and will finance the balance with a 9% annual interest loan for 36 months. The sales tax in your city is 7.5%, and the license and title charges are $175.13. What is the total purchase price of the car including tax, license, and title? Round your answer to the nearest cent.
9514 1404 393
Answer:
total purchase price: $27,722.01
Step-by-step explanation:
The price of the car plus tax is ...
$25,625 × (1 +7.5%) = $27,546.88
Adding license and title charges brings the total to ...
$27,546.88 +175.13 = $27,722.01 . . . total purchase price
_____
Additional comment
10% of that, or $2,772.20, will be the required down payment, leaving a balance due of $24,949.81. The payments on a 36-month loan at 9% will be $793.40, for a total loan cost of $28,562.30. Then the full cost of the car, including financing, is $31,334.50. The cost of the financing is $3,612.49.
how many sides does a regular octagon have
Answer:
8
Step-by-step explanation:
Answer:
A regular octagon has eight sides.
Step-by-step explanation:
Octagon = Octa + gon where octa means eight and gon means sides.
What is question A and B?
Answer:
Jo turned around and walked back to the starting point
8 km/hr
Step-by-step explanation:
4 km/one-half hr = 8 km/hr
Step-by-step explanation:
A)
If we look at the graph at 10 mins its evident that there has been some movement meaning Joes has moved 1km (as we can see in the graph) away from the starting point.
B)
For the last 30 mins of the graph we can see some changes.
so Joe started at 30 mins and ended at 60mins so there is a difference of 30 mins. In those 30 mins Joe moved from 0km to 4km. Meaning that Joe moved at 4km in 30 mins.
We are going to work this out in KPH. Since we have 30 mins and the unit we are using to measure his speed is measured in hours, we need to double it along with the kilometres he moved so it stays fair and constant. so we will have 8km and 60 min (1 hour). Therefore Joe moved at 8kph.
Hope this helps
what is x when x/4 = 2/5
Answer:
[tex] \sf \rightarrowtail \: \frac{x}{4} = \frac{2}{5} \\ \sf \rightarrowtail \: 4 \times 2 = 5x \\ \sf \rightarrowtail \: 5x = 8 \\ \sf \rightarrowtail \: \boxed{ \bf \: x = \frac{8}{5} }[/tex]
The figure is made up of two identical quarter circles and a rectangle. The length of the rectangle is 35 cm and its breadth is 20 cm. Find the perimeter of the figure. (Take t = 3.14)
Area of the middle rectangular section = length x width = 35 x 20 = 700 square cm.
The radius of the circular sections is 25 cm
Area of a full circle is pi x r^2 = 3.14 x 25^2 = 1962.5 square cm.
There are two quarter circles which is 1/2 of a circle. The area of those would be 1962.5/2 = 981.25 square cm.
Total area of the figure = 700 + 981.25 = 1681.25 square cm
Z= [?]° i dont know how to type out the question
Answer: first u have to find the perimiter for each side
Step-by-step explanation:
the answer is 100 d z
PLEASE HELP ME THIS IS DUE TODAY AND I WILL MARK BRAINLEST.
which graph represents a function?
Answer:
first graph is a function
Step-by-step explanation: