The system of equations y = 2x + 4 when graphed have a solution that y = − (1/3)x − 1 is (3, - 2)
A straight line's general equation is -
y = (m)x + c
where -
The slope of the line, [m], indicates the unit rate at which [y] changes in relation to [x].
The y-intercept, or the place where the graph crosses the [y] axis, is represented by [c].
A straight line's equation can also be expressed as -
Ax + By + C = 0
By = - Ax - C
y = [tex](\frac{A}{B} - \frac{B}{C})x - \frac{A}{C}[/tex]
The set of equations is as follows:
y = − 2x + 4
AND
y = − [tex](\frac{1}{3} )[/tex]x − 1
Draw the graphs for these two equations. The answer to this system of equations would be near the intersection. Please see the following graph. These lines come together at (3, - 2)
As a result, y = 2x + 4 and is the system of equations that has been solved.
y = − [tex](\frac{1}{3} )[/tex]x − 1 is (3, - 2)
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need help fast what is the equation
The equation is 128 + 2x = 180.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
The sum of the same-side interior angles between two parallel lines is supplementary
This means,
128 + 2x = 180
2x = 180 - 128
2x = 52
x = 26
Thus,
The value of x is 26.
The equation is 128 + 2x = 180.
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Find tan
Give an exact value, not a decimal approximation.
Answer:
θ = 35°
tanθ = 1
Step--step explanation:
using SOH CAH TOA
Hypotenuse = 7
opposite = 4
adjacent = needs to be found
θ = needs to be found
According to Pythagoras theorem
Hyp² = opp² – Adj²
7² = 4² – Adj²
Adj² = 49 – 16
Adj ² = 33
Adj = 5.7
what connects Hypotenuse and opposite os SOH
sinθ = opposite/Hypotenuse
sin θ = 4/7
sinθ= 0.57
divide bith sides by sin
θ = sin-¹ 0.57
θ = 34.75°
to find Tan θ TOA
Tanθ = opposite / adjacent
Tanθ = 4/5.7
Tan θ= 0.7018
Tanθ = 1
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Which of the following statements are true?
I. Data sets can only have one mean.
II. Data sets can only have one mode.
III. Data sets can only have one median.
-22/4 / 3/4 (fractions, and please explain answer!)
Answer: - 7 1/3 or -88/12 (it depends)
Step-by-step explanation:
To solve this equation, multiply the second number using it's reciprocal. A reciprocal is a flipped version of a fraction.
(3/4 to 4/3)
-22/4 x 4/3 = -88/12
Change it to a mixed number.
-7 1/3
Therefore, - 7 1/3 is the answer to this problem or keep it as -88/12.
I hope this helps mburlett5833:)!2345673
1.
5.
7.
3.
4.
2. JK = LM
*For the proof, please use the choices in the box in order to fill in the blanks.
K
L
0. Given: JK LM
Proof: w = 3.5
6. 3.5 = w
4w + 1 = 6w-6
Statements
*Division Property
*Given
*7 = 2w
Ji
4w + 1
669
6.
6w-6
1.
2.
3. Substitution Property
4. Addition Property
5.
7.
Reasons
*Symmetric Property
*Definition of Congruent Segments
*JK LM
M
*Subtraction Property
*w = 3.5
*4w + 7 = 6w
Lisa must choose a number between 61 and 107 that is a multiple of 2, 8, and 16. Write all the numbers that she could choose. If there is more than one
number, separate them with commas.
P is the point (a, a -2) and Q is the point (4-3a, -a).
a
Find the gradient of the line PQ.
b
Find the gradient of a line perpendicular to PQ.
Given that the distance PQ is 10√5, find the two possible values of a.
c
Answer:
[tex]\textsf{a)} \quad \dfrac{1}{2}[/tex]
[tex]\textsf{b)} \quad -2[/tex]
[tex]\textsf{c)} \quad a = -4,\;\; a = 6[/tex]
Step-by-step explanation:
Part (a)[tex]\boxed{\begin{minipage}{9cm}\underline{Gradient Formula}\\\\Gradient $=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Given points:
P = (a, a-2)Q = (4-3a, -a)Substitute the given points into the gradient formula to find the gradient of line PQ:
[tex]\textsf{Gradient}=\dfrac{-a-(a-2)}{(4-3a)-a}=\dfrac{-a-a+2}{4-3a-a}=\dfrac{2-2a}{4-4a}=\dfrac{2(1-a)}{4(1-a)}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Part (b)If two lines are perpendicular to each other, their gradients are negative reciprocals.
Therefore, the gradient of a line perpendicular to PQ is:
[tex]\implies \textsf{Gradient}=-2[/tex]
Part (c)[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Substitute the points and the given distance 10√5 into the formula and solve for a.
[tex]\implies 10\sqrt{5}=\sqrt{((4-3a)-a)^2+(-a-(a-2))^2}[/tex]
[tex]\implies 10\sqrt{5}=\sqrt{(4-3a-a)^2+(-a-a+2)^2}[/tex]
[tex]\implies 10\sqrt{5}=\sqrt{(4-4a)^2+(2-2a)^2}[/tex]
[tex]\implies 500=16-32a+16a^2+4-8a+4a^2[/tex]
[tex]\implies 500=20a^2-40a+20[/tex]
[tex]\implies 25=a^2-2a+1[/tex]
[tex]\implies a^2-2a-24=0[/tex]
[tex]\implies a^2-6a+4a-24=0[/tex]
[tex]\implies a(a-6)+4(a-6)=0[/tex]
[tex]\implies (a+4)(a-6)=0[/tex]
Apply the zero-product property:
[tex]\implies a+4=0 \implies a=-4[/tex]
[tex]\implies a-6=0 \implies a=6[/tex]
Therefore, the two possible values of a are:
a = -4, a = 6Seven friends are buying tickets to a concert. Each person pays $8. How much money do they pay altogether?
$
Answer:
56$
Step-by-step explanation:
8$x7=56.
you just need to multiply it
Circle all statements that MUST be true
a. Diagonals of parallelograms bisect each other
b. Parallelograms have four congruent sides
c. Isosceles triangles have 3 congruent angles
d.
If the endpoints of a line segment are equidistant from a third point, that third point lies on the
perpendicular bisector of the line segment.
7. Find the value of X, Y. Show your work
Answer:
6) True, False, False, True;7) x = 135, y = 45.--------------------
Question 6a. Diagonals of parallelograms bisect each other
TRUEb. Parallelograms have four congruent sides
FALSE, it is true for rhombusc. Isosceles triangles have 3 congruent angles
FALSE, it has 2 congruent angles as two sides are congruent.d. If the endpoints of a line segment are equidistant from a third point, that third point lies on the perpendicular bisector of the line segment.
TrueQuestion 7Adjacent angles of a parallelogram are supplementary and opposite angles are congruent.
x + y = 180 and y = 45Find x:
x + 45 = 180x = 180 - 45x = 135A jar contains 4 blue marbles, 6 red marbles, 10 purple marbles, and 5 green marbles. If you choose one marble, what is the probability that it won't be green?.
Answer: 4/5
Step-by-step explanation:
Let's start with what we know:
4 blue
6 red
10 purple
5 green
So, we have 25 total and 5 green. But we are trying to find the probability it won't be green, in which we have 20 marbles. So the probability it won't be green is 20/25 = 4/5.
!Help! Can someone help me solve for the variables?
I know the sum is 360 but i don't know where to start.
The measure of a° is 144°.
The measure of b° is 67°.
What is a trapezium?A trapezium is a quadrilateral where 1 pair of sides are parallel and the sum of angle pairs between parallel lines is 180 degrees.
We have,
Two parallel lines.
The sum of the angle pairs between parallel lines = 180°
This means,
a + 36 = 180
a = 180 - 36
a = 144
b + 113 = 180
b = 180 - 113
b = 67
Thus,
The value of a° is 144°.
The value of b° is 67°.
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What is the only difference between adding and subtracting polynomials?
The basic difference between the addition and subtraction of polynomials has been explained below.
A polynomial is a mathematical expression containing two or more algebraic terms containing variables and their coefficients that involve operations such as addition, subtraction, and multiplication.
The basic difference between the addition and subtraction of polynomials is that since subtraction is the inverse of addition, all terms get the opposite sign upon subtraction. For example -
In addition - 2x²+3x+4 and 3x²+7x+9 are added and we get = 6x²+10x+13
In subtraction - The same polynomials are subtracted = -x²-7x-5
Henceforth, we see that the signs have changed to the opposite.
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How do you find the domain?
The domain of a function is the set of numbers that can go into a given function.
The set of input values (x) for which a function generates an output value is known as the domain of the function (y).
we can write [tex]y = f(x).[/tex]
domain is the full set of x-values that can be plugged into a function to produce a y-value.
The most effective approach to finding a domain will depend on the type of function.
The domain is expressed using an open bracket or parenthesis, the domain's two endpoints separated by a comma, and then a closed bracket or parenthesis.
To find domain of function we should know the property of that function like what the function can take inside it.
Like if we consider square root function [tex]\sqrt{x}[/tex] so inside root negative numbers are not allowed so value of x should be positive means x>=0
So domain of square root function [0, ∞).
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we are asked to test for independence between age (i.e., adult and teen) and drink preferences. the test statistic for this test of independence is
The value of test statistic for test of independence is 62.5
The Chi-square test of independence checks that two variables are related or not. We have to count for two nominal variables. We also believe that the two variables are unrelated. The test allows us to determine whether or not our idea is plausible.
The sections that follow go over what we need for the test, how to perform it, understanding the results, statistical details, and p-values.
Given,
the table shows the beverage preferences for random samples of teens and adults.
For calculating the test statistics,
First wee need to calculate the expected values of every observed values.
Expected values for teens,
[tex]E(50)=\frac{250*400}{1000}=100\\\\E(100=)\frac{250*400}{1000}=100\\\\E(200)=\frac{400*400}{1000}=160\\\\E(50)=\frac{100*400}{1000}=40[/tex]
Expected values for adults,
[tex]E(200)=250-100=150\\\\E(150)=250-100=150\\\\E(200)=400-160=240\\\\E(50)=100-40=60[/tex]
Now, the test statistic is given by:
[tex]X^2=\frac{\sum\limits^n_{i=1}(O_i-E_i)^2}{E_i}[/tex]
Where, Ei=expected value and Oi = observed value
[tex]X^2=\frac{(50-100)^2}{100}+\frac{(100-100)^2}{100}+...\frac{(200-240)^2}{240}+\frac{(50-60)^2}{60}=62.5[/tex]
So, the value of test statistic for this test independence is 62.5.
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Your question is incomplete, here is the complete question
The table below gives beverage preferences for random samples of teens and adults.
teens adults total
coffee 50 200 250
tea 100 150 250
soft drink 200 200 400
other 50 50 100
400 600 1000
we are asked to test for independence between age (i.e., adult and teen) and drink preferences. the test statistic for this test of independence is ?
a car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time it takes the truck to travel the same distance. what is the speed of the car? how about the truck?
A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time. The speed of the car is 50 km/h. The speed of truck is 70 km/h.
Define speed.You can determine an object's speed if you know how far it moves in a given amount of time. For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour (miles per hour).
Given,
A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time.
Let s represent the truck's speed and (s+20) represent the car's speed.
to determine each vehicle's time
Time = Speed / Distance
truck time = 350/s
Time in an automobile is 350/(s+20)
Truck time - car time = 2 hours
So,
(350/s) - [350/(s+20)] = 2
LCM is s(s+20)
[350(s+20) - 350s]/s(s+20) = 2
Cross multiplying,
350(s+20) - 350s = 2s(s+20)
Simplifying the equation,
350s + 7000 - 350s = 2s² + 40s
Now, we have quadratic equation to simplify,
2s² + 40s - 7000 = 0
Dividing the equation by 2
s² + 20s - 3500 = 0
Factorizing,
s= 50
s= -70 (impossible because of the sign)
Hence the truck's speed is s = 50 km/h.
The speed of the car is s + 20 = 70 km/h.
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you are solving a measurement problem where the numbers 5.07 x 109 and 1.087 x 10−4 are divided. how many significant digits should the quotient have?
The division of the two numbers in scientific notation 5.07 × 10⁹ ÷ 1.087 × 10⁻⁴ is 4.664 × 10¹³
Scientific NotationScientific notation is a means in which we use to represent numbers based on a standard measure.
In this problem, we have to perform a mathematical operation with two numbers expressed in scientific notation.
To divide 5.07 × 10⁹ by 1.087 × 10⁻⁴;
We need to divide 5.07 by 1.087
The result given is 5.07 ÷ 1.087 = 4.664
The second step is to note that when 10⁹ ÷ 10⁻⁴,
Using law of indices, it becomes 10⁹ ÷ 10⁻⁴ = 10⁽⁹⁺⁴⁾ = 10¹³
We can now rewrite our answer as
5.07 × 10⁹ ÷ 1.087 × 10⁻⁴ = 4.664 × 10¹³
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The potential energy, p, in a spring is represented using the formula p = kx2. Lupe uses an equivalent equation, which is solved for k, to determine the answers to her homework. Which equation should she use? k = 2px2 k = px2 k = k =.
The equation should she use was k = 2p/x²
Potential energy is the power that an object can store due to its position in relation to other things, internal tensions, electric charge, or other circumstances.
Common kinds of potential energy include the gravitational potential energy of an object, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field. The joule, denoted by the letter J, is the energy unit in the International System of Units (SI).
p=1/2kx²
To get the equivalent formula, we make k the subject
p=1/2kx²
Multiply both sides by 2
2p = kx²
Divide both sides by x²
2p/x² = k
∴ the equivalent formula is;
k = 2p/x² .
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Ayden is 1.55 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 21.15 meters. He stands 16.8 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The height of the tree to the nearest hundredth of a meter = 7.54 m
What are similar triangles?
If two triangles' corresponding angles and sides are identical and their corresponding sides are proportional, or if the ratios between the lengths of the corresponding sides are comparable, then two triangles are said to be similar.
From the figure,
AB= 21.15 meters
AE = AB - BE = 21.15 - 16.8 = 4.35 meters
BC= height, h
The triangles ABC and ADE are similar triangles
So,
AE/DE = AB/BC
4.35 / 1.55 = 21.15/ h
h = ( 21.15 * 1.55 ) / 4.35
= 32.78/4.35 = 7.54 m
So, the height of the tree to the nearest hundredth of a meter = 7.54 m
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(-1,-10)(−1,−10)left parenthesis, minus, 1, comma, minus, 10, right parenthesis and (5,2)(5,2)left parenthesis, 5, comma, 2, right parenthesis.
Answer: 4
Step-by-step explanation:
-1+-10 is -11
5+2 is 7
-11+7 is 4
What is 1/4 also called?
Answer: Quarter or 25%
Step-by-step explanation:
1/4 = 25%/ 100%
Or quarter
Answer:
1/4 is also called:
One Fourth
One quarter
One percent of Four
Can Someone Please Solve This By Using The Formula a^2+b^2=c^2
Considering the figure drawn using the formula given a = 40 cm
How to find the value of ainformation given in the question
hypotenuse = 85 cm
opposite = 75 cm
adjacent = a
The problem is solved using the Pythagoras theorem is applicable to right triangle. the formula of the theorem is
hypotenuse² = opposite² + adjacent²
plugging the values as in the problem
let a be the required dimension
85² = 75² + a²
7225 = 5625 + a²
7225 - 5625 = a²
a² = 1600
a = √1600
x = 40
The adjacent of the right triangle is solved to be 40 cm
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Look at Callie work solving 3x 9423
By using multiplication, it can be calculated that
3 [tex]\times[/tex] 9423 = 28269
What is multiplication of integers?
At first it is important to know about integers
Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.
Here the given multiplication is 3 [tex]\times[/tex] 9423
3 [tex]\times[/tex] 9423 = 28269
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Micah is perparing for a piano recital . He practices for 50 minutes on Monday and 90 minutes on Wendnesday.
Micah increased his practice time by 80%.
What is percent?
A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.
Given:
Micah is preparing for a piano recital .
He practices for 50 minutes on Monday and 90 minutes on Wednesday.
Micah increased his practice time by 40%.
%increase = (Final value - starting value) / |starting value| x 100
= (90 - 50) / |50| x 100
= 40/50 x 100
%increase = 80%
Hence, Micah increased his practice time by 80%.
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Complete question:
someone help please asap
Answer:
[tex]x= -\sqrt19 -4\\x=\sqrt19-4[/tex]
Decimal version: [tex]x= 8.3589 \\x=0.358899[/tex]
Step-by-step explanation:
1. Move the terms
[tex]x^{2} +10x-2x=5-2[/tex]
2. Collect like terms
[tex]x^{2} +8x=5-2\\x^{2} +8x=3[/tex]
3. Complete the square, you should get
[tex]x^{2} +8x+16=3+16\\(x+4)^{2} =19[/tex]
4. Solve for X
-4x ≥ 20
8 ≤ -4(x - 1)
3x - 2 > 4 - 3x
Please answer all of them. Please help, I need to get my grade up. No links or I will report. Thank you.
The solutions to the inequalities are x ≤ -5, x ≥ 1 and x > 1
How to determine the solution to the inequalities?From the question, we have the following parameters that can be used in our computation:
-4x ≥ 20
8 ≤ -4(x - 1)
3x - 2 > 4 - 3x
Next, we solve the inequalities
Inequality 1
-4x ≥ 20
Divide both sides of the inequality by -4
So, we have the following representation
x ≤ -5
Inequality 2
8 ≤ -4(x - 1)
Divide both sides of the inequality by -4
So, we have the following representation
-2 ≥ -x - 1
Rewrite as
x + 1 ≥ 2
Evaluate the like terms
x ≥ 1
Inequality 3
3x - 2 > 4 - 3x
Add to both sides of the inequality 3x
So, we have the following representation
6x - 2 > 4
Add to both sides of the inequality 2
So, we have the following representation
6x > 6
Divide by 6
x > 1
Hence, the solution is x > 1
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Write a cubic function with x-intercepts -3/2, 0, 2 and passes through the point (1,3)
write the factors out with reverses signs like this
y = (x+3/2)(x)(x-2)
solve for x = 1
y = -2.5
what can we add to this to get 3
5.5
so
y = (x+3/2)(x)(x-2) + 5.5
at x = 1, y = 3
Hope this helps :)
If you need any more explanation, feel free to ask. If this really helps, consider marking brainliest.
- Jeron
From a hot-air balloon, Justin measures a 34° angle of depression to a landmark
that's 1424 feet away, measuring horizontally. What's the balloon's vertical distance
above the ground? Round your answer to the nearest hundredth of a foot if
necessary.
The vertical distance of the balloon from the ground will be 960.50 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
From a sight-seeing balloon, Justin estimates a 34° point of sadness to a milestone that is 1424 feet away, estimating on a level plane.
The vertical distance of the balloon from the ground will be given as,
tan 34° = h / 1424
Simplify the equation, then we have
h = 1424 tan 34°
h = 960.50 feet
The upward distance of the inflatable starting from the earliest stage is 960.50 feet.
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Zion Sun Chairs manufactures 3,575 beach chairs each month. Determine the minimum sales price Zion Sun Chairs must sell each chair for to earn a monthly profit of $75,000, if the total monthly fixed costs are $17,363.50 and the variable cost per chair is $52.17.
$20.98
$25.84
$72.50
$78.01
The minimum sales price Zion Sun Chairs must sell each chair to earn a monthly profit of $75,000, given total monthly fixed costs of $17,363.50 and variable cost per chair of $52.17, is D. $78.01.
How is the minimum sales price determined?To compute the minimum sales price, we determine the expected total sales revenue to meet the target profit.
The total sales revenue equals the total costs and the target profit.
Using division operation, the sales price is the quotient of the total sales revenue and the number of units.
The number of beach chairs produced monthly = 3,575
Target monthly profit = $75,000
Total monthly fixed costs = $17,363.50
Variable cost per chair = $52.17
Total variable costs = $186,507.75 ($52.17 x 3,575)
Total costs (variable and fixed) = $203,871.25 ($186,507.75 + $17,363.50)
Expected total sales revenue to earn a profit = $278,871.25 ($203,871.25 + $75,000)
Selling price per unit to earn a profit of $75,000 = $78.01 ($278,871.25 ÷ 3,575)
Thus, the minimum sales price is not Options A to C, but D.
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Helpppppppppppppppppppppppp
Answer:
Christianity bc its the earliest for everything
please helpFill in the blank with the correct response.
if 9/24 = 3/i then i =_______
Answer:
Step-by-step explanation:
[tex]\frac{9}{24} = \frac{3}{i} \\9i = 72\\i = 8[/tex]
∴ i is 8.