Answer:
If we take Ryan's age as 'x' then we have Aaron's age as '2x'
Now, we have the sum of their ages after 3 years as 30.
So according to question, we can prepare an equation which is
2x+3+x+3 = 30
= 3x+6 = 30
= 3x = 30-6
= 3x = 24
= x = 24÷3
= x = 8
Thus, Ryan' is 8 years old now.
Now we need to find Aaron's age, and this can be done easily as we have already made an expression fore Aarons age, i.e., '2x'
So 2x= 2×8
= 16.
So we have Aaron's age-16,
Ryan's age-8
Complete the square to write y = 3x2 + 12x + 7 in vertex form, y = a(x - h)2 + k.
The vertex form of the equation is y = 3(x + 2)^2 - 5
How to complete the square?The equation is given as:
y = 3x^2 + 12x + 7
Set to 0
3x^2 + 12x + 7 = 0
Subtract 7 from both sides
3x^2 + 12x = -7
Divide through by 3
x^2 + 4x = -7/3
-------------------------------------------------------------------
Take the coefficient of x
k = 4
Divide by 2
k/2 = 2
Square both sides
(k/2)^2 = 4
-------------------------------------------------------------------
So, we add 4 to both sides of x^2 + 4x = -7/3
x^2 + 4x + 4 = -7/3 + 4
Express as perfect square
(x + 2)^2 = -7/3 + 4
Multiply through by 3
3(x + 2)^2 = -7 + 12
Evaluate
3(x + 2)^2 = 5
Subtract 5 from both sides
3(x + 2)^2 - 5 = 0
Rewrite as
y = 3(x + 2)^2 - 5
Hence, the vertex form of the equation is y = 3(x + 2)^2 - 5
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The image of the point (-7, 8) under a translation is (-11, 6). Find the coordinates
of the image of the point (8, -3) under the same translation.
Answer:
(4,-5)
Step-by-step explanation:
A sphere has a radius of 5.4 yards. Find its a. volume and b. surface area. Use 3.14 for π. Round the answers to the nearest hundredth.
Answer:
sorry the drawing is messy, not used to drawing with just a finger haha! hope this helps<<3
y − 6 =3/5(x + 5); (0, 8)
The equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40
Equation of a lineThe equation of a line in point-slope form is expressed as;
y - y0 = m(x -x0)
where
m is the slope
(x0, y0) is the point on the line
Given the following parameters
Point (0,8)
Slope from the equation = 3/5
Substitute
y - 8 = 3/5(x - 0)
5(y -8) =3x
5y - 40 = 3x
5y - 3x = 40
Hence the equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40
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1 Austin has found that both(13,17) and (24,61) are solutions to a system of linear equations how are the two lines related? explain
Considering that the graphs have two intersection points, the two lines are equal.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In a graph, the solution of two linear equations is the intersection of the two lines. Hence, if there are two solutions, as is the case in this problem, the two lines are equal.
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find the square root of 9_4√2
[tex]\begin{gathered} 9 - 4\sqrt{5} \\ \\ = 4 + 5 - 4\sqrt{5} \\ \\ = (- 2)^2 + (\sqrt{5})^2 + (2 \times - 2 \times \sqrt{5}) \\ \\ = (- 2 + \sqrt{5})^2 \\ \\ = (\sqrt{5} - 2)^2 \\ \\ \\ \therefore \sqrt{9 - 4\sqrt{5}} = \sqrt{5} - 2 \end{gathered}[/tex]
Hope this may be helpful.
Select the correct answer. A new building in the shape of a square pyramid is to be constructed. The slant height will be five times the side length of the base. There will be between 20,000 square feet and 50,000 square feet of construction material used for the outside of the building. What would be the maximum possible side length of the base of the building? Round your answer to the nearest foot. Ο Α. 71 feet OB. 89 feet OC. OD. 45 feet 141 feet
From the information given about the square pyramid, the maximum base length of the building is 67.42 cm.
How do you determine the maximum side length?We are given the following details are:
Base = b
Slant height (l) = 5b
The lateral surface area is calculated using:
L = 2bl
So, we have:
L = 2 * b * 5b
Evaluate the product
L = 10b²
The total surface area is calculated using:
T = L + b²
So, we have:
T = 10b² + b²
Evaluate the sum
T = 11b²
Recall that the maximum surface area is 50,000 square feet
So, we have:
11b² = 50000
Divide both sides by 11
b² = 50000/11
Taking the square root of both sides, we have
b = 67.42
Hence, the maximum base length of the building is 67.42 cm
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Which statement describes the graph of y + 2 ≥ –4(x – 3)2? a parabola opening up, with shading above the vertex a parabola opening up, with shading below the vertex a parabola opening down, with shading above the vertex a parabola opening down, with shading below the vertex
Option C. The statement that describes the graph of the equation y + 2 ≥ –4(x – 3)2 is a a parabola opening down, with shading above the vertex.
How to describe the shape of the parabola.To do this you have to create a graph of the equation as seen in the attachment.
From the attachment we can see that the parabola is shaped downwards while we have the shading to be at the top of the vertex.
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Use the Associative Property to find the value of the variable.
(8 x 15) x s = 8 x (15 x 11)
Answer:
hey its me again so the answer is 11.
I'm sure because I did this.
Triangle L N M is shown. Angle L N M is 90 degrees and angle N M L is 20 degrees. The length of L N is 21.
Use the diagram to complete the statements.
The measure of angle L is
°.
The trigonometric ratio that uses ∠M and LN to solve for NM is
.
The length of NM, to the nearest tenth, is approximately
.
Angle L: 70°
The trigonometric ratio used to solve for NM is the tangent ratio.
NM = 57.7 [nearest tenth]
How to Apply the Trigonometric Ratios?Using the triangle sum theorem, find angle L.
Angle L = 180 - 90 - 20 = 70°
Using the tangent ratio, we can use ∠M and LN to solve for NM
Tan 20 = 21/NM [tan ∅ = opposite/adjacent]
NM = 21/tan 20
NM = 57.7 [nearest tenth]
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Answer:
70, tangent, 57.7
Step-by-step explanation:
Find all the solutions to 3x^3 - 6x^2 + 30x - 20 = -20
Answer: Option (1)
Step-by-step explanation:
[tex]3x^3 - 6x^2 + 30x-20=-20\\\\3x^3 - 6x^2 + 30x=0\\\\3x(x^2 - 2x+10)=0\\\\[/tex]
So, either [tex]x=0[/tex] or [tex]x^2 -2x +10=0[/tex]
For the second case, we know x=0.
For the second case, we can use the quadratic formula.
[tex]x=\frac{2 \pm \sqrt{(-2)^2 - 4(1)(10)}}{2}\\\\x=1 \pm 3i[/tex]
Consider a message signal m(t) with the spectrum shown in the following Figure. The message signal bandwidth W=1KHz, This signal is applied to a product modulator, together with a carrier Accos(2πfc t)wave producing the DSB-SC modulated wave S(t). This modulated wave is next applied to a coherent detector. Assuming perfect synchronism between the carrier waves in the modulator and detector, determine the spectrum of the detector output when: (a) The carrier frequency fc=1.25 KHz. And (b) The carrier frequency fc=0.75 KHz. What is the lowest carrier frequency for which each component of the modulated wave S(t) is uniquely determined by m(t)?
The lowest carrier frequency at which each modulated wave S(t) component may be uniquely defined by m(t) is
Fc,Fc+w,Fc-w =>1.5k,2.5k,0.5kHz
-Fc,-Fc+w,-Fc-w =>-1.5k,-0.5k,-2.5kHz
"-w,w -1kHz,1kHz" are the frequency components of the detector output in this case.
Fc,Fc+w,fc-w =>0.75k,1.75k,-0.25kHz
-Fc,-Fc+w,-Fc-w =>-0.75k,0.25k,-1.75kHz
This is further explained below.
What is the lowest carrier frequency for which each component of the modulated wave S(t) is uniquely determined by m(t)?For a modulated wave with frequency components, the equation looks like this:
Fc,Fc+w,Fc-w =>1.5k,2.5k,0.5kHz
-Fc,-Fc+w,-Fc-w =>-1.5k,-0.5k,-2.5kHz
"-w,w -1kHz,1kHz" are the frequency components of the detector output in this case.
b)
In conclusion, we may state that the modulated wave has frequency components as well.
Fc,Fc+w,fc-w =>0.75k,1.75k,-0.25kHz
-Fc,-Fc+w,-Fc-w =>-0.75k,0.25k,-1.75kHz
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Given f(x) =
4x + 2, find f(x + 3).
Answer:
f(x + 3) = 2(x + 7)
Step-by-step explanation:
Now lets find out what does f(x + 3) means.
f(x + 3) means shifting the entire function 3 units to the left. Which also means, all x values will be shifted to the left by that number of units. (Excluding the constant that is multiplied or divided by x, eg. 5x + 6 shifted by 7 units to the left is 5(x + 7) + 6 and not 5x + 7 + 6.)
From the above,
f(x + 3) = 4(x + 3) + 2 = 4x + 12 + 2 = 4x + 14 = 2(x + 7)
A smart-phone is thrown upwards from the top of a 384-foot building with an initial velocity of 32 feet per
second. The height h of the smart-phone after t seconds is given by the quadratic equation
h 16t² + 32t + 384. When will the smart-phone hit the ground
Answer:
When t = 4
Step-by-step explanation:
The phone will hit the ground when h = 0.
[tex]16t^2 + 32t + 384 =0 \\ \\ t^2 + 2t + 24=0 \\ \\ (t+6)(t-4)=0 \\ \\ t=-6, 4[/tex]
However, as time cannot be negative, we know the answer is when t = 4.
Ramon is six years younger than 4 times his brothers age. Oh f his brother is 5 year old, how old is Ramon
Answer:
14
Step-by-step explanation:
The equation would be R = 5(4) - 6. Multiply 5 by 4 to get 20, then subtract 6 to get 14.
22. Chris bought a new car for $12,500. He made a $3,000 down payment and financed the rest at an annual interest rate of 14.5% for 36 months (3 years). How much less would his total interest be for the same loan for 24 months (2 years)? A. $1,387.50 B. $1,377.50 C. $1,367.50 D. $1,357.50
Answer:
Step-by-step explanation:
Purchase price (A) : $12,500
Down Payment (B): $3,000
Loan Taken (C = A - B): $9500
D : Interest calculation for $9,500 for 3 years P(1 + rt)
= 9500(1 + (14.5/100) * 3)
= 9500(1 + 0.145 * 3)
= 9500 * 1.435
= $13632.5
E : Interest calculation for $9,500 for 2 years P(1 + rt)
= 9500(1 + (14.5/100) * 2)
= 9500(1 + 0.145 * 2)
= 9500 * 1.29
= $12,255
Difference between D - E
= $13632.5 - $12,255
= $1377.5
Hence the answer is B i.e. $1377.5 less interest for same amount of load for 2 years vs 3 years
Describe an algorithm for finding the smallest integer in a finite sequence of natural numbers.
Answer:
min = a_1
for i:= 2 to n:
if [tex]a_i[/tex] < min then min = [tex]a_i[/tex]
return min
Step-by-step explanation:
We call the algorithm "minimum" and a list of natural numbers [tex]a_1, a_2, \cdot\cdot\cdot, a_n.[/tex]
So lets first set the minimum to [tex]a_1[/tex]
min = a_1
now we want to check all the other numbers.
We can use a simple for loop, to find the minimum
min = a_1
for i:= 2 to n:
if [tex]a_i[/tex] < min then min = [tex]a_i[/tex]
return min
Answer:
The sequence of natural numbers is a_1, a_2, a_3, ..., a_n.
Use min as the variable that will contain the minimum value.
Set min = a_1
In a loop, compare min to each number from a_2 to an.
If min > a_i, then let min = a_i
min = a_1
for i = 2 to n
if min > a_i, then min = a_i
Please help quick!!!
Reflect over the y axis then translate
The composition of transformation that maps ABCD to EHGF is reflect over the y-axis, then translate (x - 1, y + 1)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
The composition of transformation that maps ABCD to EHGF is reflect over the y-axis, then translate (x - 1, y + 1)
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A candy company designs a package to hold chocolates. The height of the container is 13 inches and the diameter of its bottom is 9 inches. Diagram shows a shape with circular base and curved surface meeting at a point. The diameter of the base is labeled 9 inches and the height of the shape is labeled 13 inches. Which shape best models the package, and what is the approximate surface area of the package? The best model for the package is a . The approximate surface area is square inches.
The best model for the package is a cone and the approximate surface area is 258 square inches.
How to illustrate the information?From the information given, it was stated that the diagram shows a shape with circular base and curved surface meeting at a point. The diameter of the base is labeled 9 inches and the height of the shape is labeled 13 inches.
In this case, the information given about the diagram shows that it's a cone.
Also, given the information, the total surface area of the cone that has a slant height and diameter is given as:
= π(d/2)(d/2 + l)
In such a situation, it should be noted that d represents the diameter in the question. The surface area is the total area that's covered by its surface.
Therefore, the best model for the package is a cone and the approximate surface area is 258 square inches.
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what is the solutions to the system of equations below? y=3/4x-12 and y= -4x -31
The solution to the system of equations is: x = -4, y = -15.
How to Solve a System of Equations?Given the equations of a system as:
y = 3/4x - 12 --> eqn. 1
y = -4x - 31 --> eqn. 2
Substitute y = (-4x - 31) into eqn. 1 to find x:
-4x - 31 = 3/4x - 12
-4x - 3/4x = 31 - 12
-19/4x = 19
Multiply both sides by -4/19
x = 19(-4/19)
x = -4
Substitute x = -4 into eqn. 2
y = -4(-4) - 31
y = 16 - 31
y = -15
The solution is: x = -4, y = -15.
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How does doubling the lengths of the sides of a rectangle to form a similar rectangle affect the area
Doubling the lengths of the sides of a rectangle quadruple the area
How to determine the effect?Let the dimension of the rectangle be L and W.
So, the area is
A = LW
When the lengths are doubled, we have:
A2 = 2L * 2W
This gives
A2 = 4LW
This means that the initial area is multiplied by 4
Hence, doubling the lengths of the sides of a rectangle quadruple the area
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In ΔABC, BC = 13, CA = 20 and AB = 19. Which statement about the angles of ΔABC must be true?
m∠B > m∠A > m∠C
m∠C > m∠B > m∠A
m∠A > m∠B > m∠C
m∠C > m∠A > m∠B
m∠B > m∠C > m∠A
m∠A > m∠C > m∠B
Answer:
m∠B > m∠C > m∠A
Step-by-step explanation:
The angle opposite the largest side in a triangle is the largest, and the angle opposite the shortest side is the smallest.
Solve the quadratic equation by graphing it. Select all possible answers.
[tex]y=x^2+8x+12\\x=?[/tex]
Possible answers:
-6
6
-8
2
-2
8
No real solutions
The solutions to the given quadratic equation are x = -6 and x = -2
Quadratic equationsFrom the question, we are to solve the given quadratic equation
The given equation is
y = x² + 8x + 12
To solve the equation, we will set it equal to 0
That is,
x² + 8x + 12 = 0
Solving
x² + 8x + 12 = 0
x² + 2x + 6x + 12 = 0
x(x +2) +6(x + 2) = 0
(x +6)(x + 2) = 0
x +6 = 0 OR x +2 = 0
x = -6 OR x = -2
Hence, the solutions to the given quadratic equation are x = -6 and x = -2
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You are buying shoes for an athletic store. They cost $32 per pair of shoes. The company decides Mark Up the shoes by 75%. What is the selling price for shoes in the athletic store?
A. $56.00
B. $40.00
C. $45.00
D. $24.00
E. $8.00
Answer:
A. $56
Step-by-step explanation:
The markup is added to the cost price to find the selling price.
MarkupThe markup is 75% of the cost price:
markup = 75% × $32 = $24
Selling priceThe selling price is the cost price plus the markup:
selling price = cost + markup
selling price = $32 +24 = $56
The selling price of shoes in the athletic store is $56 per pair.
The selling price for shoes in the athletic store with 75% mark up is [tex]\$56[/tex]
Selling price of the item is sum of Markup and cost price.
The cost of shoes is [tex]\$32[/tex]. The company decides Markup by [tex]75\%[/tex] of cost price.
Find Markup value.Markup = [tex]\frac{75}{100}\times 32[/tex]
Markup = [tex]\$24[/tex]
Find selling price.Selling price = Markup + Cost price
Selling price = [tex]24+32[/tex]
Selling price = [tex]\$56[/tex]
The selling price for the shoes in the athletic store is [tex]\$56[/tex].
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Darcy read her thermometer in the morning and the
temperature was -2° C. In the afternoon the same
thermometer showed a temperature of -5° C.
Which of the following is true?
The temperature was 3 degrees warmer in the afternoon.
The temperature was 3 degrees colder in the afternoon.
The temperature was 7 degrees colder in the afternoon.
The temperature was 7 degrees warmer in the afternoon.
Answer:
The temperature was 3 degrees colder in the afternoon
Step-by-step explanation:
numbers on the left of zero on the number line are arranged in decreasing order and as such -2 is greater than -5.
The true statement is The temperature was 3 degrees colder in the afternoon.
What is temperature?Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Given that, Darcy read her thermometer in the morning and the temperature was -2° C. In the afternoon, the same thermometer showed a temperature of -5° C.
-2-3 = -5
We see, that, the temperature is falling from -2 to -5, that means, there was a fall in temperature from morning to afternoon.
Hence, the temperature was 3 degrees colder in the afternoon.
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Use the list method to write "the perfect square integers between 1 and 80 inclusive".
Answer:
Step-by-step explanation:
1 Answer
1=12.
4=22.
9=32.
16=42.
25=52.
36=62.
49=72.
64=82 .
A blimp is flying at a speed of 40mph and going in a direction of 80 degrees. After 3 hours of flying it turns and travels 1 hour in a direction of 350 degrees. How far is the blimp from its starting location and in what direction?
I need a triangle drawing too please.
Bearing is a topic that can be used to locate the position of an object at a given time. Therefore, the blimp is 80 m far away from its starting point. And in the North-East direction.
The speed of an object relates the distance it covers to the time taken to cover the said distance.
i.e speed = [tex]\frac{distance}{time taken}[/tex]
⇒ distance = speed x time taken
In the given question, the initial distance covered can be determined as;
distance = 40 mph x 3 h
= 120 m
The final distance covered can be determined as;
distance = 40 mph x 1 h
= 40 m
Let the distance from its starting point to its final location be represented by x.
Thus applying the Cosine rule, we have:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2abCos C
[tex]x^{2}[/tex] = [tex]120^{2}[/tex] + [tex]40^{2}[/tex] - 2(120 x 40) Cos 90
= 14400 + 1600 - 9600
[tex]x^{2}[/tex] = 16000 - 9600
= 6400
x = [tex]\sqrt{6400}[/tex]
= 80
x = 80 m
Therefore, the distance of the blimp from its starting point to its final destination is 80 m.
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The graph shows a system of equations:
What is the solution to the system of equations?
y = -x + 5
y=x-1
(-3,2) (3,-2) (3,2) (-3,-2)
The solution to the system of equations is (3, 2)
System of equationGive the system of equation below
y = -x + 5
y=x-1
Equate both expression
-x+5 =x - 1
Equate
-x - x = -1 - 5
-2x = -6
x = 3
Since y = x - 1
y = 3 - 1
y = 2
Hence the solution to the system of equations is (3, 2)
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What is the name of the green segment in the hyperbola below?
A. Minor axis
OB. Transverse axis
OC. Major axis
OD. Directrix
Using the tree diagram below, what is the probability of getting tails and an even number?
Answer:
1/4
Step-by-step explanation:
Chances of getting tails out of all the numbers (including heads)
Totals numbers (including heads & tails): 12
Tails & Even Number: 3
3/12 simplified to 1/4