Answers
Answer:
Step-by-step explanation:
To graph by hand I would first convert both equations into y=mx+b.
We start with:
[tex]\left \{ {{2x-2y=4} \atop {x+2y=8}} \right.[/tex]
Solve for y for 2x-2y=4
[tex]2x+2y=4\\2y=4-2x\\y=2-x[/tex]
Solve for y for x+2y=8
[tex]x+2y=8\\2y=8-x\\y=4-\frac{x}{2}[/tex]
Giving the new but equal system of equations:
[tex]\left \{ {{y=2x-x} \atop {y=4-\frac{x}{2} }} \right.[/tex]
From this point on you can graph the two functions to find where the two lines intersect, thats your solution.
I've gone ahead and graphed it on desmos for you
Related Questions
x - 2y = 3
5x + 3y = 2
The lines whose equations are shown intersect at which point?
Answers
The point of intersection of the two lines is at (1,-1)
System of equationThe given system of expression is shown below
x - 2y = 3
5x + 3y = 2
The solution to the system of equation is the point of intersection
From equation 1
x = 3 + 2y
Substitute into 2
5(3+2y) + 3y = 2
15 +10y + 3y = 2
13y = -13
y = -1
Substitute y = -1 into 3
x = 3 + 2y
x = 3+(-2)
x = 1
Hence the point of intersection of the two lines is at (1,-1)
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What is the last digit of the product of all the numbers between 11 and 29?
Answers
we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.
What is the last digit of the product of all the numbers between 11 and 29?
Here we want to find the last digit of the product between all the whole numbers larger than 11 and smaller than 29.
Then we have the product:
P = 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28
Now, notice that there is a 20 there.
Any number times 20 will end with a zero, then:
P = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)
Only with that, we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.
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PLS HELP>>>>solving functions
Answers
Answer:
The first option:
[tex]x^2-5x+9[/tex]
Step-by-step explanation:
Trust me I am right.
If you need work please ask!
Have a nice day!
Help!!! Brainliest to 1 or 2 answer!!
Answers
Answer:
35-17=3y
Step-by-step explanation:
3y+17=35
-17 -17
3y=35-17
A cell phone carrier introduced a new strategy to increase their number of subscribers. The function below represents the increase in number of subscribers, where f(t) represents the number of subscribers and represents the time in months
Answers
The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An exponential function is in the form:
y = abˣ
Where a is the initial value of y and b is the multiplication factor.
Let f(t) represents the number of subscribers and t represents the time in months. Hence:
[tex]f(t) = 250(1.4)^t[/tex]
a = 250, b = 1.4
The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.
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Answer: 250, 1 month, and 1.4
Find a so that line CD will have the given slope: C(3, -3), D(-3,a); m= -4/3
Answers
Work Shown:
m = (y2 - y1)/(x2 - x1)
-4/3 = (a - (-3))/(-3 - 3)
-4/3 = (a+3)/(-6)
-4*(-6) = 3(a+3)
24 = 3a+9
3a+9 = 24
3a = 24-9
3a = 15
a = 15/3
a = 5
Divide. Write the quotient in lowest terms.
4 2/3 / 7
Answers
The quotient in lowest term exists 2/3.
What is an improper fraction?An improper fraction exists as a fraction whose numerator exists equivalent to, larger than, or of equivalent or higher degree than the denominator.
Given the quotient: [tex]$4\frac{2}{3} \div 7[/tex]
Write [tex]$\frac{2}{3}[/tex] in improper fraction
[tex]$4\frac{2}{3}= \frac{14}{3}[/tex]
Dividing throughout by 7 on both sides of the equation, we get
[tex]$4\frac{2}{3} \div 7 = \frac{14}{3}\div 7[/tex]
Change the division sign to multiplication by taking the reciprocal of 7
[tex]$\frac{14}{3}\div 7 = \frac{14}{3} \times \frac{1}{7}[/tex]
Simplifying the above equation, we get
[tex]$\frac{14}{3}\div 7 = \frac{2}{3}[/tex]
Therefore, the quotient in lowest term exists 2/3.
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At 3:00 PM a man 138 cm tall casts a shadow 149 cm long. At the same time, a tall building nearby casts a shadow 163 m long. How tall is the building?
Answers
The building is 151 meters tall
How to determine the height of the building?From the question, we have the following parameters about the building and the man
Man's height = 138 cm
Man's shadow = 149 cm
Building's shadow = 163 m
Based on the above parameters, we have the following equivalent ratio:
Ratio = Height : Shadow
So, we have:
Man's height : Man's shadow = Building's height : Building's shadow
Substitute the known values in the above equation
138 cm : 149 cm = Building's height : 163 m
Remove the units
138 : 149 = Building's height : 163
Express as fraction
138 /149 = Building's height/163
Multiply both sides by 163
Building's height = 163 * 138 /149
Evaluate the product
Building's height = 151 m
Hence, the building is 151 meters tall
So, the complete parameters are:
Man's height = 138 cm
Man's shadow = 149 cm
Building's shadow = 163 m
Building's height = 151 m
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If BD = 16 yd and the area of rhombus ABCD is 72 yd^2, what is AC?
Answers
Formula for finding area of rhombus: [tex]\frac{d1 * d2}{2}[/tex]
d₁ = 16 yd
Area = 72 yd²
Rhombus Area =>
[tex]\frac{16 * d2}{2} = 72[/tex]
16*d₂ = 144
d₂ = 9
AC = 9 yd
Hope it helps!
find the area of the shaded shape pls quickly
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
Area of shaded region is equal to :
Area of rectangle - Area of two triangles ~
1. Area of rectangle :
[tex]\qquad \sf \dashrightarrow \: length \times width[/tex]
[tex]\qquad \sf \dashrightarrow \: 20 \times 15[/tex]
[tex]\qquad \sf \dashrightarrow \: 300 \: \: cm {}^{2} [/tex]
2. Area of first triangle :
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2} \times (20 - 18) \times (15)[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2} \times (2) \times (15)[/tex]
[tex]\qquad \sf \dashrightarrow \: 15 \: \: cm {}^{2} [/tex]
3. Area of second triangle :
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2} \times (6) \times(20)[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 \times 20[/tex]
[tex]\qquad \sf \dashrightarrow \: 60 \: \: cm {}^{2} [/tex]
Area of shaded region is :
[tex]\qquad \sf \dashrightarrow \: 300 - (15 + 60)[/tex]
[tex]\qquad \sf \dashrightarrow \: 300 - 75[/tex]
[tex]\qquad \sf \dashrightarrow \: 225 \: \: cm {}^{2} [/tex]
Find lim f(x) if f(x)
x->5
=
{
-x² -1, x #5
-3, x=5
Answers
Given
[tex]f(x) = \begin{cases} -x^2 - 1 & \text{if }x \neq 5 \\ -3 & \text{if }x=5 \end{cases}[/tex]
we have
[tex]\displaystyle \lim_{x\to5} f(x) = \lim_{x\to5} (-x^2-1) = -5^2-1 = \boxed{-26}[/tex]
since we are approaching [tex]x=5[/tex], so effectively [tex]x\neq 5[/tex] and we use the definition of [tex]f(x)[/tex] under that condition.
23-2(17+3^3)
Sjshjshdjsjshs
Answers
Answer:
-65
Step-by-step explanation:
23-2(17+3^3)
23-2(17+27)
23-2(44)
23-88
=-65
Write the following expression using exponents -3x7x7x7x7x7x7
Answers
Solution -:
[tex] \bold{ \underline{ \underline{Given}}}[/tex]
-3x7x7x7x7x7x7
[tex]\bold{\underline {\underline{lets \: begin}}}[/tex]
We have,,
[tex] -3 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \\ = - 3¹ \times {7}^{6} [/tex]
exponent and shortcut to express a multiplication of number by itself several times explain us how many time we should multiply the number by itself this process of using exponent is called raising to a power where the exponent is the power.Law of exponent -: a ⁰ = 1 a ^ m × a ^ n (a^m)^na^m × b^ mAs like example→ 2⁴
here 2 is base and 4 is power , index or exponent. and 2⁴ is known as Exponential form.
Darren’s car has a rectangular gas tank whose dimensions are 4 meters by 3 meter by 3 meters. If Darren was only able to drive for 45 hours with a full tank, what is the rate of gas consumption of his car?
Answers
Step-by-step explanation:
that is a huge gas tank. that car is practically a tank.
the volume of the gas tank is
4×3×3 = 36 m³
I assume you use liters for liquid mass.
remember
1 meter (m) = 100 centimeter (cm)
10 cm = 1/10 m = 1 decimeter (dm)
1 liter = 10×10×10 cm³ = 1000cm³ = 1 dm³
1 m³ = 10×10×10 dm³ = 1000 dm³ = 1000 liters
so, his gas tank contained 36,000 liters.
he used the 36,000 liters in 45 hours.
his corresponding rate of gas consumption was
36,000 liters / 45 hours = 800 liters / hour
For a right triangle ABC, you are told that cos A = x and sin A = y. Which option below gives an expression that is
equivalent to tan A?
OX
Answers
Equivalent to tan A =[tex]\frac{y}{x}[/tex]
What is meant by the right triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The sum of the other two angles is 90 degrees. The perpendicular and the triangle's base are the sides that make up the right angle. The third side is the longest of the three sides, known as the hypotenuse.A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we utilize specific terminology.A right triangle is a triangle in which one of the angles is at a right angle or two of the sides are perpendicular, or more formally, an orthogonal triangle, formerly known as a rectangled triangle.Equivalent to tan A:
A right triangle ABC so that m∠C = 90°
The lengths are:
Side a is opposite ∠A,
Side b is opposite ∠B,
Side c (the hypotenuse) is opposite ∠C
Because cos A = x, therefore
[tex]x =\frac{b}{c}[/tex] => [tex]b = cx[/tex] (1)
Because sin A = y, therefore
[tex]y =\frac{a}{c}[/tex] => [tex]a = cy[/tex] (2)
By definition,
tan A = a/b
[tex]=\frac{cy}{cx}[/tex]
[tex]=\frac{y}{x}[/tex]
Equivalent to tan A =[tex]\frac{y}{x}[/tex]
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(x+3)^0 Rewrite the equation with positive exponents and simplify. x≠-3.
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{(x + 3)^0}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{(x + 3)^0}[/tex]
[tex]\text{Anything raised to the 0 power it automatically equal to 1.}[/tex]
[tex]\huge\text{So, this mean that your answer should be: \boxed{\mathsf 1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
there are 6 girls and 8 boys in Mr. Stevenson's class the ratio of girls to boys in the class can be expressed as the simplified ratio ?/4 what is the missing number ?
Answers
Answer: 3
Step-by-step explanation:
The missing number in the simplified ratio ?/4 is 3.
Here, we have to find the missing number in the simplified ratio ?/4, we need to determine the ratio of girls to boys in Mr. Stevenson's class.
Given that there are 6 girls and 8 boys in the class, the ratio of girls to boys can be expressed as:
Number of girls : Number of boys = 6 : 8
To simplify the ratio, we can divide both the number of girls and the number of boys by their greatest common divisor (GCD).
In this case, the GCD of 6 and 8 is 2.
Dividing both 6 and 8 by 2, we get:
Number of girls : Number of boys = 6/2 : 8/2 = 3 : 4
So, the simplified ratio of girls to boys is 3/4.
Therefore, the missing number in the simplified ratio ?/4 is 3.
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Stuck on this problem. Help is needed please!
Answers
Step-by-step explanation:
A.
the height, the 17cm leg and half of the baseline (16/2 = 8cm) create a right-angled triangle.
so, Pythagoras applies.
c² = a² + b²
c being the Hypotenuse (side opposite of the 90° angle).
so, we get
17² = height² + 8²
289 = height² + 64
225 = height²
height = sqrt(225) = 15cm
B.
the answer to this is the surface area of the whole box.
it has 5 sides :
bottom : 20×16 rectangle = 320 cm²
left and right : 20×17 rectangles = 340×2 = 680 cm²
front and back : 16×15/2 triangles = 120×2 = 240 cm²
in total that is
320 + 680 + 240 = 1,240 cm² of cardboard
. [Multiples / Factors / Primes] *
What is the highest
common factor (HCF)
of 24 and 45?
Answers
I need to find what AE is
Answers
Answer:
18
Step-by-step explanation:
The arrows on lines AB and CD indicate that these 2 shapes are similar and these 2 lines are corresponding so :
Linear scale factor :
12 ÷ 10 = 1.2 or 6/5
Let's use the fraction form
Using the linear scale factor we can make an equation to solve for x :
2x+4 = 6/5(x+8)
Expand the brackets :
2x+4 = 6/5x + 9.6
Subtract 4 from both sides :
2x = 6/5x + 5.6
Subtract 6/5x from both sides :
4/5x = 5.6
Divide both sides by 4/5 :
x = 7
Now substitute this value into the expression for the length of AE :
AE = 2(7) + 4
AE = 14 + 4
AE = 18
Hope this helped and have a good day
Answer:
116 units
Step-by-step explanation:
AE + ED = 180 because they make a straight angle and a straight angle is 180 degrees or half of a circle 360/2.
AE = 2x + 4 and ED = x +8 added together they equal 180
2x + 4 + x + 8 = 180 Combine the like terms
3x + 12 = 180 Subtract 12 from both sides of the equation
3x = 168 Divide both sides by 3
x = 56
Now that we know that x is 56 we can plug that in for AE to find its length
2x + 4
2(56) + 4
112 + 4
116
Evaluate the expression using a calculator:
Answers
The value of the expression is 0.0265. Using exponents and power rules, the required value is calculated.
What are the exponent and power rules?The important exponent and power rules are:
a⁻ⁿ = 1/aⁿ; negative exponent(ab)ⁿ = aⁿ × bⁿ; power of a product ruleaⁿ × aˣ = aⁿ⁺ˣ; multiplication ruleaⁿ/aˣ = aⁿ⁻ˣ; division rule[tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]; fractional exponentCalculation:The given expression is [tex]126^{-3/4}[/tex]
Using calculator: [tex]126^{-3/4}[/tex] = 0.0265
Applying the exponent rule for evaluating the given expression:
[tex]126^{-3/4}[/tex]
Applying the negative power rule;
I.e., a⁻ⁿ = 1/aⁿ
⇒ [tex]126^{-3/4}=\frac{1}{126^{3/4}}[/tex]
Applying fractional exponent rule;
I.e., [tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]
⇒ [tex]\frac{1}{126^{3/4}}=\frac{1}{\sqrt[4]{126^3} }[/tex]
⇒ 1/[tex]\sqrt[4]{2000376}[/tex]
⇒ 1/37.6077
⇒ 0.0265
Therefore, the value of the given expression is 0.0265.
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3. If the geometric mean of a and 25 is 20,
find the value of a.
Answers
Answer:
Value of a is 16.
Step-by-step explanation:
Solution Given:
we know that
Geometric mean=[tex]\sqrt{a*b}[/tex]
By using this formula
20=[tex]\sqrt{a*25}[/tex]
20=5[tex]\sqrt{a}[/tex]
dividing both side by 5, we get
20/5=5/5* [tex]\sqrt{a}[/tex]
4=[tex]\sqrt{a}[/tex]
squaring both side
4²=a
:. a=16
Given the function defined in the table below, find the average rate of change,
in simplest form, of the function over the interval 12 ≤ ≤ 36.
0
12
36
48
60
37
34
31
28
25
22
Answers
The average rate of change of [tex]f(x)[/tex] on [tex]12\le x\le36[/tex] is the difference quotient
[tex]\dfrac{f(36) - f(12)}{36 - 12} = \dfrac{28 - 34}{24} = \boxed{-\dfrac14}[/tex]
5x + 1 over 2 y2
What is the value of the expression above when x = 3 and y = 2?
Answers
(5*3 + 1) / 2*2^2
(15+1) / 2*4
16/8
2
If the vertex of a parabola is at the point (-2, 5), then the equation for the axis of symmetry for the parabola is x = -2. True or false?
Answers
Answer:
true
Step-by-step explanation:
thats really it i believe its true
What is the domain of the exponential function shown in the graph?
A.x > -1
B.x ≤ -1
C. x < 0
D. -∞ < x < ∞
Answers
The domain of the exponential function shown in the graph is -oo < x < oo
How to determine the domain of the exponential function shown in the graph?The function on the graph is an exponential function.
The domain is the set of x values the function can take
From the graph, we have the following x values
This means that the domain of x in the graph is -oo < x < oo
Hence, the domain of the exponential function shown in the graph is -oo < x < oo
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Find the surface area of the cylinder and round to the nearest tenth. (Use the π button on your calculator)
Answers
The surface area of the cylinder with the given height and radius is 835.2 square inches
How to determine the surface area?The given parameters are
Height, h = 12 inches; this is represented by the distance between the curved surfaces of the cylinderRadius, r = 7 inches; this is represented by the distance between the center of the circle to its circumferenceThe surface area is then calculated using the following formula
A = 2πr² + 2πrh
Substitute the given values in the above equation
So, we have:
A = 2 * 3.14 * 7^2 + 2 * 3.14 * 7 * 12
Evaluate the exponents
A = 2 * 3.14 * 49 + 2 * 3.14 * 7 * 12
Evaluate the products
A = 307.72 + 527.52
Evaluate the sum
A = 835.2
Hence, the surface area of the cylinder with the given height and radius is 835.2 square inches
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find the discriminant of the following quadratic equation
x^-5x+3=0
Answers
The discriminant of the given quadratic equation as in the task content can be evaluated by means of the formula; D = b²-4ac and it's value is; 13.
What is the discriminant of the quadratic equation as given in the task content?According to the task content, it follows that the quadratic equation whose discriminant is to be determined is; x²-5x+3=0.
By comparison with the standard form equation of a quadratic graph which goes thus; ax²+bx +c = 0, in which case, the determinant is given by the expression; b² - 4ac.
We can consequently evaluate the determinant of the quadratic equation in discuss as follows;
Determinant = b² -4ac = (-5)² - (4×1×3) = 25 - 12
Hence, the determinant in this case is; 13.
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Use the polynomial [tex]4x^{5} -3x^{2} + x[/tex]
a. How many terms are in this polynomial? _____
b. What is the degree of this polynomial? _____
c. What is the contrast? _____
Answers
The degree is 5
The contrast is -
At a furniture manufacturer, worker a can assemble a shelving unit in 5 hours. worker b can assemble the same shelving unit in 3 hours. which equation can be used to find t, the time in hours it takes for worker a and worker b to assemble a shelving unit together? rate (shelving units per hour) time (hours) fraction completed worker a one-fifth t worker b one-third t 5 t 3 t = 1 one-fifth t minus one-third t = 1 one-fifth t one-third t = 1 5 t minus 3 5 = 1
Answers
If they work together, they need 15/8 hours to assemble one shelving unit.
What does work mean in math?
In summary, work is done when a force acts upon an object to cause a displacement. Three quantities must be known in order to calculate the amount of work. Those three quantities are force, displacement and the angle between the force and the displacement.According to tittle, we know worker A can assemble a shelving unit in 5 hours , which means worker A can finish 1/5 of work in 1 hour . And worker B can finish 1/3 of work in 1 hour.
If A & B work together , they will spend the same time t to assemble only one shelving .
That means, 1/5t + 1/3 t = 1 (equation)
1/5 t is worker A's workload during time t , 1/3 t is worker B workload.
So, 1/5 t + 1/3t = 1 is the answer
⇒ 5t + 3t = 15
⇒ t = 15/8 hours
If they work together, they need 15/8 hours to assemble one shelving unit.
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Answer:
Letter C is the correct answer or 1/5 t + 1/3t = 1
