The age of Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.
What is an Equation ?An equation is a statement that contains algebraic expressions equated by an equal sign with constants or other variables.
Let the age of Kwaku is x
Let the age of Esi is y
From the given data
The age of Kojo is 2y
y = x +5
Sum of their age = 47
2y = 2x +10
therefore the equation formed is
x + y +2y = 47
x + x+5 + 2x +10 = 47
4x +15 = 47
4x = 32
x = 8
y = 13
2y = 26
Therefore Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.
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Determine the correct equation of the following graph.
The equation of the given sine graph is gotten as; y = 4 sin [(0.4(x + 2.5)] - 1
How to find the equation of a sine graph?
We know that the general formula for equation of a sine graph is;
y = A sin [(B(x - D)] + C
where;
A is Amplitude
Period = 2π/B.
Phase Shift = -C/B.
Vertical Shift = D.
From the graph;
A = 4
B = 2π/5π = 2/5
C = -1
D = -5/2
Thus;
y = 4 sin [(0.4(x + 2.5)] - 1
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Find the distance between the pair of points given on the graph. Distance = √ (blank)
Answer:
√2.236
Step-by-step explanation:
(2,0) (5,-2). 2 - 5 = -3. 0 - -2 = 2. -3 squared = -9. 2 squared = 4. -9 + 4 = -5. Square root of -5 = 2.236, so the distance would be √2.236
Which statement describes the graph?
<-10
10-
-10+
10
OA. The graph crosses the y-axis at (0, -5), decreasing from x = -10 to
x= -2 and increasing from x= -2 to x = 10.
B. The graph crosses the y-axis at (0, -5), decreasing from x = -10 to
x = 0 and remaining constant from x = 0 to x = 10.
C. The graph crosses the y-axis at (-6, 0), decreasing from x= -10 to
x = -2 and remaining constant from x=-2 to x = 10.
OD. The graph crosses the y-axis at (0, -5), decreasing from x = -10 to
x= -2 and remaining constant from x=-2 to x= 10.
Correct answer is option D.
The graph crosses the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10.
What is Increasing Function?A function f(x) is said to be increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) ≤ f(y).
For this case, the first thing you should observe is that you have a different function in two distinct intervals.
We have then:
For [-10, 2]:
The linear function has a positive slope, therefore it grows and cuts the y-axis at the point (0, 5)
For [2, 10]:
We have a constant function whose equation is:
y = 5
Thus, the correct Answer is:
D. The graph crosses the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10.
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when using the rational root theorem, which of the following is a possible root of the polynomial function below? f(x)=2x^2-4x+9
a)4
b)3
c)2
d)5
The only option that meets the root theorem is option b.
which of the following is a possible root of the polynomial function below?
The polynomial function is:
[tex]f(x) = 2x^2 - 4x + 9[/tex]
The rational root theorem says that if a root is a rational number, then the leading coefficient must be divisible by the denominator of the rational number and the constant term must be divisible by the numerator.
In this case, the constant is 9, and the only option such that the constant is divisible by the numerator is option b: 3
Where 3 is a rational number:
3 = 3/1
The numerator is 3 (which divides 9) and the denominator is 1 (which divides the leading coefficient 9. (notice that it meets the theorem, but it is not an actual root).
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For what values of x does f(x) = 0?
O-4, 0, 2
O-2, 0, 4
O-5, 0, 17
O-17, 0,5
The values of x does f(x) = 0 will be -4,0,2.Option A is corect.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The graph shows the cubic polynomial equation found as;
⇒(x+4)(x)(x-2)
The points f(x) = 0 is;
⇒(x+4)(x)(x-2)
⇒(-4+4)(0)(2-2)
⇒0
The values of x does f(x) = 0 will be -4,0,2.
Hence, option A is corect.
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The price of a coat is $65. In sale, the price is reduced by 15%. What is the price of the coat in sale?
Rayonnia is buying cans of frozen lemonade concentrate to make punch for a holiday party with each can she can make 6  cups of lemonade write an equation which gives the number of cups of lemonade that can be made with any number of cans of frozen lemonade concentrate
The number of cups of lemonade, y that can be made with any number of cans of frozen lemonade concentrate, x is y=6x.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that with a single can of frozen lemonade concentrate 6 cups of lemonade can be made. Therefore, the number of cups that can be made with x number of cans is,
Number of cups that can be made, y = 6x
Hence, the number of cups of lemonade, y that can be made with any number of cans of frozen lemonade concentrate, x is y=6x.
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what is the factored form of x^3 - 729
Answer:
(x - 9)(x^2 + 18x + 81).
Step-by-step explanation:
Use the difference of cubes factorization, which claims that a^3 - b^3 = (a - b)(a^2 + ab + b^2)
x^3 - 729 = (x - 9)(x^2 + 18x + 81)
Answer:[tex](x-9) (x^{2} +9x + 81)[/tex]
Step-by-step explanation:
A shopkeeper sold a watch for rupees 992 allowing 20% discount find its marked price
Answer:
⇒ Let marked price be Rs.x.
⇒ Discount = 20% of marked price.
⇒ Discount=
100
20
×x=
100
20x
⇒ Selling price = Marked price - Discount.
⇒ 192=x−
100
20x
⇒ 192=
100
80x
⇒ x=
80
19200
=Rs.240
MARK IT AS BRAINLIESTAND FOLLOW ME.Answer:
S.p = 992
discount = 20%
marked price = S. p + discount
= 992 + 20/100*992
= 992 + 198.4
= 1190.4
Which features are present in this polar graph?
A. No symmetry
B. Symmetry about the pole (0,0)
C. Symmetry about the line Theta=pi/2
D. Symmetry about the polar axis Theta=0
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\texttt {D. Symmetry about the polar axis Theta = 0} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given graph is symmetric along Theta = 0
[ polar axis ]
Because it's a horizontal line that divides the features on the graph into two equal halves. and there's no other suitable symmetric relation.
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
If R = {(x, y): y = x = 2, 4, 6}, find the range of R. , 4 , 6 } , find the range of R.
Unit 8:Right triangles & Trigonometry
Answer:
[tex]24\sqrt{5}[/tex]
Step-by-step explanation:
So for this problem you can use the law of sines which states
[tex]\frac{a}{sin A} = \frac{b}{sin B}\\[/tex]
Since the angle is a right triangle we can find the hypotenuse by plugging in the values.
[tex]\frac{4\sqrt{15}}{sin 60} = \frac{hypotenuse}{sin 90}\\\\\frac{4\sqrt{15}}{sin 60} = hypotenuse\\hypotenuse = \frac{4\sqrt{15}}{\frac{\sqrt{3}}{2}} = \frac{8\sqrt{15}}{\sqrt{3}}\\hypotenuse = \frac{8\sqrt{45}}{3} = \frac{24\sqrt{5}}{3}\\[/tex]
we now just multiply that side by 3since all the sides should be equal since all the angles are equal and we get the length of 24sqrt(5)
solve simulteneusly equation 6p-4r=4 and p-2r=5
Answer:
r = - 3.25, p = -1.5
Step-by-step explanation:
→ Rearrange p - 2r = 5
p = 5 + 2r
→ Substitute into 6p - 4r = 4
6 ( 5 + 2r ) - 4r = 4
→ Expand
30 + 12r - 4r = 4
→ Simplify and solve
r = - 3.25
→ Substitute into p - 2r = 5
p + 6.5 = 5
→ Minus 6.5 from both sides
p = -1.5
Find the value of x
Find the value of y
Answer:
x = 9
y = 61
Step-by-step explanation:
let me know if you want an explanation!
What is the length of the missing side of this triangle?
A
2
B
10
C
50
D
100
top side is 26 bottom side is 24 left side is whats missing
Answer:
B
Step-by-step explanation:
pythagorus theorem
a² + b² = c²
c² - b² = a²
26² - 24² = a²
676 - 576 = a²
a² = 100
a = 10
A triangular prism and two nets are shown:
A right triangular prism is shown with two nets. The triangular base of the prism has height 5 inches, base 12 inches, and hypotenuse 13 inches. The length of the prism is 18 inches. Net A has 3 rectangles having dimensions 5 by 18, 18 by 12, and 18 by 13, and two triangles having legs 12 inches and 5 inches. Net B has 3 rectangles having dimensions 5 by 13, 13 by 12, and 13 by 18, and two triangles having legs 5 inches and 12 inches.
Which is the correct net of the prism and what is the surface area of the prism?
The surface area of the triangular prism is 480 square inches and net A is the correct net of the prism
What is a triangular prism?When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have given a triangular prism with its net.
After analyzing the correct net will be net A because the inner rectangle length should be 14 in not 13 in.
The surface area of the triangular prism:
[tex]= 2[\dfrac{1}{2}(5\times12)]+ 5\times 14+ 12 \times 14+ 13\times 14[/tex]
After solving:
The surface area = 480 square inches.
Thus, the surface area of the triangular prism is 480 square inches and net A is the correct net of the prism
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2ⁿ+2ⁿ+2ⁿ+2ⁿ=2¹⁶
value of n?
Answer:
[tex]n = 14[/tex]
Step-by-step explanation:
[tex]~~~~~~~2^n+2^n+2^n+2^n = 2^{16}\\\\\implies 4 \cdot 2^n = 2^{16}\\\\\implies 2^2 \cdot 2^n = 2^{16}\\\\\implies 2^{n+2} = 2^{16}~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\\implies n+ 2 = 16\\\\\implies n = 16-2 \\\\\implies n = 14[/tex]
Please help I will mark brainliest!!!!!
Answer:
#1 (4b + 6a) #2 150y
Step-by-step explanation:
#1 :area of right triangle: ab/2
4x2/2 = 4b
area of rectangle: length x width
2 x 3 = 6a
#2:
5y + 2.5y = 7.5y x 2 = 15y
so the top and bottom are both 15 y
the sides are each 5y so thats 10 y
15x10= 150y
Given the figure below solve for X
Answer:
x = 37
Step-by-step explanation:
It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches. which function models the horizontal displacement as a function of time in seconds?
The function that models the horizontal displacement as a function of time in seconds is y = 5cos(2π/3 x)
How to model the function?The given parameters are:
Time, t = 1.5 secondsHorizontal distance, h = 10 inchesStart by calculating the amplitude, A using:
A = h/2
This gives
A = 10/2
A = 5
Next, we calculate the period using:
B = π/t
This gives
B = π/1.5
Evaluate
B = 2π/3
The pendulum is at the middle.
So, it has no vertical displacement
The function is then represented as:
y = Acos(Bx)
This gives
y = 5cos(2π/3 x)
Hence, the function that models the horizontal displacement as a function of time in seconds is y = 5cos(2π/3 x)
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Which expression represents the product of negative three-fourths x and –8x?
Answer:
6x²
Step-by-step explanation:
[tex]-\frac{3}{4} x\times \left( -8x\right) =\frac{3}{4} x\times 8x[/tex]
[tex]=\frac{3}{4} \times 8\times x\times x[/tex]
[tex]=\frac{24}{4} \times x^{2}[/tex]
[tex]=6x^2[/tex]
please solve this question
Step-by-step explanation:
please give this answer brainlist answer
Select the correct answer. What is the slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of `3/4`? A. `y = -(3)/(4) x -(1)/(4)` B. `y = 3/4 x +(1)/(4)` C. `y = 3/4 x -(31)/(4)` D. `y = 3/4 x +(31)/(4)`
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = 3/4x - 7.75}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Passes through (5, -4) with a slope of 3/4}[/tex]
Find: [tex]\textsf{The equation in slope-intercept form}[/tex]
Solution: In order to determine the equation we need to first plug the values into the point-slope form, simplify, distribute, and solve for y to get our final result.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-4) = 3/4(x - 5)}[/tex]Simplify the expression and distribute
[tex]\textsf{y + 4 = 3/4(x - 5)}[/tex][tex]\textsf{y + 4 = (3/4 * x) + (3/4 * -5)}[/tex][tex]\textsf{y + 4 = 3/4x - 3.75}[/tex]Subtract 4 from both sides
[tex]\textsf{y + 4 - 4 = 3/4x - 3.75 - 4}[/tex][tex]\textsf{y = 3/4x - 3.75 - 4}[/tex][tex]\textsf{y = 3/4x - 7.75}[/tex]The equation in slope-intercept form that follows the information that was provided is y = 3/4x - 7.75
The quotient of 7 more than three times a number m and the number 27 less than n
An expression is defined as a set of numbers, variables, and mathematical operations. The given statement can be modeled as (3m+7)/27 < n.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given statement "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression as shown below.
(3m+7)/27 < n
Hence, the given statement can be modeled as (3m+7)/27 < n.
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In the equation below, variables X and Y represent two matrices. Which property of matrix addition is illustrated below?
X+Y=Y+X
O inverse property
O commutative property
O associative property
O identity property
Answer: the answer is b
Step-by-step explanation:
Samuel and 4 of his friends entered a chili cook-off. The rules allowed them
to spend a certain amount on supplies. If each person spent $15 for
supplies, how much did they spend in all?
Answer:
$75
[It is easy to say $60, but don't forget to add Samuel to the total]
Step-by-step explanation:
There are 5 people in total:
1 Samuel
4 friends
5 people who can spend up to $15 each.
(5 people)*($15/person) = $75 total spent on supplies
2(x-4) + 3x-x² for x = 3.
Answer:
-2
Step-by-step explanation:
[tex]2(3-4) +3(3)-3^2\\= 2(-1) + 3(3) -3^2\\= -2 + 9 - 9\\= -2[/tex]
Solve the following inequality |x| < 13
Answer:
x < 13 and x > -13
Step-by-step explanation:
Split the absolute value equation into 2 equations to account for the positive and negative answers possible with absolute values.
Write the positive value first by removing the absolute value symbol.
x < 13
Flip the inequality and make the 13 negative for the other side.
x > -13
The function f(x)= 4x + 3 represents the length of a rectangle. The function g(x)=2x-5 represents the width of the rectangle. Use ( g(4) to determine the area of the rectangle.
57
19
16
3
Answer:
57 square units
Step-by-step explanation:
Area is = Length x Width
Given:
f(x)= 4x + 3 Length
g(x)=2x-5 Width
x = 4
============
Width
g(x)=2x-5
g(4)=2(4)-5
g(4)= 3
Length
f(x)= 4x + 3
f(4) = (4)(4) + 3
f(4) = 19
Area = (length)*(width)
Area = f(x)*g(x) for x = 4
Area = (f(4))*(g(4))
Area = (19)*(3)
Area = 57 square units
Step 1: 4 x minus x + 2 + 6 = 6 x + 16
Step 2: 3 x + 8 = 6 x + 16
Step 3: 8 minus 16 = 6 x minus 3 x
Step 4: Negative 8 = 3 x
Step 5: Negative StartFraction 8 Over 3 EndFraction = x
Jorge verifies his solution by substituting Negative StartFraction 8 Over 3 EndFraction into the original equation for x. He determines that his solution is incorrect. Which best describes Jorge’s error?
Jorge distributed incorrectly.
Jorge incorrectly combined like terms.
Jorge incorrectly applied the addition and subtraction properties of equality.
Jorge incorrectly applied the multiplication and division properties of equality
The error from Jorge's arithmetic operation on the given algebraic expression is that he distributed it incorrectly.
What is an algebraic expression?An algebraic expression is a mathematical equation that is made up of variables together with arithmetic operations.
From the given expression, we have:
4x - x + 2 + 6 = 6x + 16
Add similar elements together;
3x + 8 = 6x + 16
Using distributive property, subtract 8 from both sides:
3x + 8 - 8 = 6x + 16 - 8
3x = 6x + 8
Simplify
3x-6x = 8
-3x = 8
Divide both sides by -3
-3/-3x = -8/3
x = -8/3
So from Jorge's calculation, because he distributed incorrectly, we can conclude that could be his error.
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