The equation that shows how many students are absent is 26+a = 30 and 4students are absent
What is a linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.
Also a linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
There are 30 students in a class and 26 students are present.
Let's represent the number of student absent by a
therefore the sum of the number of student absent and the student present will give the total number of student.
26+a = 30 and
a = 30-26
a = 4
therefore 4 students are absent
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Match each function with the expression representing its inverse function.
1. x - 4
2. x + 4
3. 0.25x
4. x
5. -2x
6. 2x
A. g ( x ) = -0.5 x
B. h ( x ) = 4 x
C. y = x - 4
D. ƒ( x ) = x/2
E. k ( x ) = x
F. p ( x ) = x + 4
Please help!!
Answer:
A matches with 5.B matches with 3.C matches with 2.D matches with 6.E matches with 4.F matches with 1.Step-by-step explanation:
To find the inverse of a function [tex]f(x)[/tex], we let [tex]f(y)=x[/tex] and then solve again for y.
For example, using [tex]g(x)=-0.5x[/tex], we will let [tex]g(y)=x[/tex], giving [tex]x=-0.5y[/tex]. This means that [tex]y=-2x[/tex], and thus [tex]g^{-1}(x)=-2x[/tex].
Using similar logic, we see that:
A matches with 5.B matches with 3.C matches with 2.D matches with 6.E matches with 4.F matches with 1.Write as an equation: The sum of -7 and a is equal to 37.
A. −7+a=37
B. −7+a=−37
C. −7−a=−37
D. −7−a=37
Male bullies are often: Question 5 options: below average in verbal assertiveness. above average in verbal assertiveness. above average in size. smaller than average in size.
In convex pentagon $ABCDE$, angles $A$, $B$ and $C$ are congruent and angles $D$ and $E$ are congruent. If the measure of angle $A$ is 40 degrees less than the measure of angle $D$, what is the measure of angle $D$
The measure of angle D in the convex pentagon ABCDE is 132°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the measure of angle D, hence:
angle A = x - 40.
∠A + ∠B + ∠C + ∠D + ∠E = 540° (sum of angle in a pentagon)
3(x - 40) + 2x = 540
x = 132°
The measure of angle D in the convex pentagon ABCDE is 132°
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can someone show me way of solving this
Step-by-step explanation:
[tex]f(x) = ln( \frac{1}{x} ) [/tex]
To find the derivative, notice we have a function 1/x inside of another function, ln(x)
We use what we call the chain rule,
It states that
derivative of a '
[tex] \frac{d}{dx} f(g(x)) = f '(g(x)) \times \: g '(x)[/tex]
Here f is ln(x)
f is 1/x
So first, we know that
[tex] \frac{d}{dx} ( ln(x) = \frac{1}{x} [/tex]
so
[tex]f'(g(x)) = \frac{1}{ \frac{1}{x} } [/tex]
We know that
[tex]g'(x) = - \frac{1}{ {x}^{2} } [/tex]
So we have
[tex]x \times - \frac{1}{ {x}^{2} } = \frac{ - 1}{x} [/tex]
If a line has a slope of 1/3 and passes through the point (1,-2) which ff points also lies on the line a) -2,-5 b) -2,1 c) 4,-1 d) 4,10
Answer: c
Step-by-step explanation:
The equation of the line is
[tex]y+2=\frac{1}{3}(x-1)\\\\y+2=\frac{1}{3}x-\frac{1}{3}\\\\y=\frac{1}{3}x-\frac{7}{3}[/tex]
To determine which point lies on the line, we can substitute in the x coordinate and see if the equation gives the same y-coordinate.
If x = 2, then the equation of the line gives that y = -5/3.If x = 4, then the equation of the line gives that y = -1.Therefore, the answer is c.
F(x)=4x^3+7x^2x-1. G(x)=4x-2 find (f-g)(x)
Answer:
4x^3 + 7x^2 - 3x + 1
Step-by-step explanation:
BTW your question, there is a sign misssing
Express in standard form :
42634.7
Answer:
ans is 42635 when expressed in standard form
Step-by-step explanation:
Solve this please!!!
Answers:
i) [tex]\sf (x + 2)(x+ 3)[/tex]
ii) [tex]\sf \left(3x+1\right)\left(3x+2\right)\left(9x^2+9x-16\right)[/tex]
Factorize expression's:
i.
[tex]\sf (x + 1)^2 + 3(x + 1) + 2[/tex]
apply perfect square and distributive method
[tex]\sf (x^2 + 2(x)(1) + 1^2) + 3x + 3 + 2[/tex]
expand
[tex]\sf x^2 + 2x + 1 + 3x + 3 + 2[/tex]
collect like terms
[tex]\sf x^2 + 2x + 3x + 3 + 2 + 1[/tex]
add/subtract like terms
[tex]\sf x^2 + 5x + 6[/tex]
breakdown
[tex]\sf x^2 + 3x + 2x+ 6[/tex]
factor common term
[tex]\sf x(x + 3) + 2(x+ 3)[/tex]
collect into groups
[tex]\sf (x + 2)(x+ 3)[/tex]
ii.
[tex]\sf (9x^2 + 9x - 4)(9x^2 + 9x - 10) - 72[/tex]
breakdown
[tex]\sf (9x^2 + 12x - 3x - 4)(9x^2 + 15x - 6x - 10) - 72[/tex]
factor common term
[tex]\sf (3x(3x + 4) -1( 3x + 4)) ( (3x(3x + 5)- 2(3x +5) )- 72[/tex]
collect like terms
[tex]\sf (3x -1)( 3x + 4) (3x- 2)(3x +5) - 72[/tex]
expand
[tex]\sf 81x^4+162x^3-45x^2-126x-32[/tex]
factor
[tex]\sf \left(3x+1\right)\left(3x+2\right)\left(9x^2+9x-16\right)[/tex]
Answer:
[tex]\textsf{1.} \quad (x+3)(x+2)[/tex]
[tex]\textsf{2.} \quad (3x+1)(3x+2)(9x^2+9x-16)[/tex]
Step-by-step explanation:
Question 1
[tex]\textsf{Given expression}: \quad(x+1)^2+3(x+1)+2[/tex]
[tex]\textsf{Let }u=(x+1) \implies u^2+3u+2[/tex]
[tex]\textsf{To factor }\:\:u^2+3u+2:[/tex]
Rewrite the middle term as u + 2u:
[tex]\implies u^2+u+2u+2[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies u(u+1)+2(u+1)[/tex]
Factor out the common term (u+1):
[tex]\implies (u+2)(u+1)[/tex]
Replace [tex]u[/tex] with [tex](x+1)[/tex] :
[tex]\implies (x+1+2)(x+1+1)[/tex]
Simplify:
[tex]\implies (x+3)(x+2)[/tex]
Question 2
[tex]\textsf{Given expression}: \quad (9x^2+9x-4)(9x^2+9x-10)-72[/tex]
Expand:
[tex]\implies 9x^2(9x^2+9x-10)+9x(9x^2+9x-10)-4(9x^2+9x-10)-72[/tex]
[tex]\implies 81x^4+81x^3-90x^2+81x^3+81x^2-90x-36x^2-36x+40-72[/tex]
Collect like terms:
[tex]\implies 81x^4+81x^3+81x^3-90x^2+81x^2-36x^2-90x-36x+40-72[/tex]
Combine like terms:
[tex]\implies 81x^4+162x^3-45x^2-126x-32[/tex]
Use the Factor Theorem:
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
[tex]\begin{aligned}\implies f \left(-\dfrac{1}{3}\right) & =81\left(-\dfrac{1}{3}\right)^4+162\left(-\dfrac{1}{3}\right)^3-45\left(-\dfrac{1}{3}\right)^2-126\left(-\dfrac{1}{3}\right)-32\\ & = 1-6-5+42-32\\ & = 0\end{alilgned}[/tex]
Therefore (3x + 1) is a factor.
[tex]\begin{aligned}\implies f \left(-\dfrac{2}{3}\right) & =81\left(-\dfrac{2}{3}\right)^4+162\left(-\dfrac{2}{3}\right)^3-45\left(-\dfrac{2}{3}\right)^2-126\left(-\dfrac{2}{3}\right)-32\\ & = 16-48-20+84-32\\ & = 0\end{alilgned}[/tex]
Therefore (3x + 2) is a factor.
Therefore:
[tex]\implies f(x)=(3x+1)(3x+2)(ax^2+bx+c)[/tex]
Compare the coefficient of x⁴ and the constant to find a and c:
[tex]\implies 3 \cdot 3 \cdot a=81 \implies a=9[/tex]
[tex]\implies 2c=-32 \implies c=-16[/tex]
Therefore:
[tex]\implies f(x)=(3x+1)(3x+2)(9x^2+bx-16)[/tex]
Expand:
[tex]\implies f(x)=81x^4+(81+9b)x^3-(126-9b)x^2-(144-2b)x-32[/tex]
Compare the coefficient of x³ to find b:
[tex]\implies 81+9b=162 \implies b=9[/tex]
Therefore, the fully factorized expression is:
[tex]\implies (3x+1)(3x+2)(9x^2+9x-16)[/tex]
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Please help em fast I really need help
lf ƒ(x) = 2(x + 1)² and g(x) = 3x- 2 determine f[g(2)]
Answer:
f(g(2)) = 50
Step-by-step explanation:
evaluate g(2) then substitute the result obtained into f(x)
g(2) = 3(2) - 2 = 6 - 2 = 4 , then
f(4) = 2(4 + 1)² = 2(5)² = 2(25) = 50
Answer:
f[g(2)] = 50
Step-by-step explanation:
Given functions:
[tex]f(x)=2(x+1)^2[/tex]
[tex]g(x)=3x-2[/tex]
We are asked to determine f[g(2)], which is known as a composite function. When solving composite functions, you always work inside out.
Step 1: Find the value of g(2) by substituting 2 for x in function g(x).
[tex]\implies g(2)=3(2)-2[/tex]
[tex]\\\implies g(2)=6-2\Rightarrow g(2)=\boxed{4}[/tex]
Step 2: Substitute the found value into the composite function.
[tex]\\\implies f[g(2)]= 2(4+1)^2[/tex]
[tex]\implies f[g(2)] = 2(5)^2 \Rightarrow 2(25) \Rightarrow \boxed{50}[/tex]
Hence, the value of the composite function f[g(2)] is 50.
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convert this hight 5,2 into cm
Answer:
5.2 Inch to cm = 13.208 cm
5.2 feet to cm = 158.496 cm
Step-by-step explanation:
Inch: 1 inch = 2.54 cm, so multiply 2.54 * 5.2. We get the answer: 13.208 cm
Feet: 1 foot = 30.48 cm, so multiply 30.48 * 5.2. We get the answer: 158.496 cm
Pick the correct answer.
Help me please thanks so much
For what values of o is tan o undefined?
Answer:
90 is the right answer
Step-by-step explanation:
because it give the value pf o is tan o
Angle G is a circumscribed angle of circle E. Major arc FD measures 280°.
Circle E is shown. Line segments F E and D E are radii. A line is drawn to connect points F and D. Tangents F G and D G intersect at point G outside of the circle. Major arc F D measures 280 degrees.
What is the measure of angle GFD?
40°
50°
80°
90
The measure of angle GFD of the circumscribed circle is; A: 40°
How to find the measure of angle of a circumscribed circle?From the figure, we can apply the arc angles summation formula to get;
Major angle ∠FED + Minor angle ∠FED = 360°
We are given that Major arc FD measures 280°. Thus;
280° + Minor angle ∠FED = 360°
Minor angle ∠FED = 360° - 280°
Minor angle ∠FED = 80°
Also, we know that;
∠FED + ∠FGD = 180°
Thus, putting ∠FED = 80° gives us;
80° + ∠FGD = 180°
Subtract 80° from both sides using subtraction property of equality to get;
∠FGD = 180° - 80°
∠FGD = 100°
Now, GF and GD are the tangents to the circle from the same point G. Thus, we can say that;
GD = GF
Therefore,
∠FDG = ∠GFD = x
(This is because ∠FDG and ∠GFD are the angles opposite to equal sides.
In triangle FGD, we have sum of interior angles = 180°
Therefore, we have the expression;
∠FDG + ∠FGD + ∠GFD = 180° (due to the fact that sum of angles in a triangle is equal to 180°)
x + 100° + x = 180°
2x = 180° - 100°
2x = 80°
x = 40°
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Answer:
40
Step-by-step explanation:
I did a thing and it worked
Tommy has created a new tomato soup recipe. Before he cans and sells his soup, he must gather information about how much soup cans of different sizes will hold.
The better way to calculate the amount of substance is Volume.
According to the statement
we have to find the all information about the soup cans.
So we know that if we put a liquid in the container then in that case surface area is not important but a volume is more important for this purpose.
So, That's why The weight in the case of soup is not important when evaluating a package to be able to sell the product. A container is usually specified according to its volume, especially those containing liquids. Because the weight can vary concerning the concentration of the product, the best way to calculate the amount of substance to be packaged is the volume.
So, The better way to calculate the amount of substance is Volume.
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Identify the range of the function shown in the graph.
Surface area=
Help me please thanks
The surface area of the sphere is 324π square units
Calculating the surface areaFrom the question, we are to calculate the surface area of the sphere
The surface area of a sphere can be calculated by using the formula
[tex]Surface \ area = 4 \pi r^{2}[/tex]
Where r is the radius of the sphere
In the given diagram,
r = 9
Thus,
Surface area = 4π × 9²
Surface area = 4π × 81
Surface area = 324π square units
Hence, the surface area of the sphere is 324π square units
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1. Find the product using Suitable Property a) 55×99
Answer:
5445
Step-by-step explanation:
We can use distributive property. a*(b - c) = (a*b) - (a *c)
99 = 100 - 1
55 * 99 = 55 * (100 - 1)
= 55*100 - 55*1
= 5500 - 55
= 5445
Scarlett made a profit of $250.00 with her mobile car wash company. she charged $75.00 per car wash and received $35.00 in tips, but also had to pay $5.00 in cleaning supplies per car. write an equation to represent this situation
The equation representing the given situation is, 250 = 70x + 35, where x is the number of cars washed by the company.
In the question, we are given that Scarlett made a profit of $250.00 with her mobile car wash company. She charged $75.00 per car wash and received $35.00 in tips, but also had to pay $5.00 in cleaning supplies per car.
We are asked to represent the situation with an equation.
We assume the number of cars washed by the company to be x.
Charge for washing 1 car = $75.00.
Cost for cleaning supplies for 1 car = $5.00.
Thus the profit on the wash of 1 car = $75.00 - $5.00 = $70.00.
The total profit received by the company, on washing x number of cars = $70x.
The tips received = $35.00.
Thus, the total profit of the company = $(70x + 35).
But, the total profit is given to be $250.00.
Thus, we get an equation, 250 = 70x + 35.
Thus, the equation representing the given situation is, 250 = 70x + 35, where x is the number of cars washed by the company.
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. A scale factor of 2 is applied to the dimensions of the prism. What effect will this have on the volume
The volume of the prism would be enlarged by a factor of 8
How to determine the effect?The scale factor is given as:
k = 2
Let the initial volume be v and the final volume be V.
The relationship between both volumes is
V = k^3 * v
This gives
V = 2^3 * v
Evaluate
V = 8v
Hence, the volume of the prism would be enlarged by a factor of 8
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pls help >>> How many solutions does the quadratic
function represented on this graph have?
Answer:
Zero real number solutions
Step-by-step explanation:
Doesn't intercept the x-axis -> No real solutions
Meredith is 160 cm tall. Jane’s height is 90% of Meredith’s height. How tall is jane?
Charlotte is solving the following equation for X (x+3)^2-10=2 her first steps are given below (x+3)^2=12 x+3= + square root 12
The values of the x in the given equation are x = 6.46 and x = -0.46
Solving an equationFrom the question, we are to solve the equation for x
The given equation is
(x+3)² -10 = 2
First, add 10 to both sides of the equation
(x+3)² -10 +10 = 2 +10
(x+3)² = 12
Now, take the square root of both sides to get
x + 3 = ±√12
∴ x = 3 ± √12
x = 3+√12 OR 3-√12
x = 3 + 3.46 OR 3 - 3.46
x = 6.46 OR -0.46
Hence, the values of the x in the given equation are x = 6.46 and x = -0.46
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What is the value of x?
Use the triangle to answer the question.
Enter your answer in the box.
x =
The circumference of a circular field is 222.94 yards. What is the radius of the field? Use 3.14 for π and do not round your answer.
Answer:
35.5
Step-by-step explanation:
→ Write down the formula
2 × π × r = 222.94
→ Simplify
6.28 × r = 222.94
→ Divide both sides by 6.28
r = 35.5
Answer:
35.5 = r
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi *r where r is the radius
222.94 = 2 * 3.14 * r
222.94 = 6.28 r
Divide each side by 6.28
222.94/6.28 = r
35.5 = r
Find the slope of the line passing through the vertex and the y-intercept of the quadratic function
[tex]f(x) = 5x{}^{2} + 20x - 7 [/tex]
Find y intercept
y=5(0)²+20(0)-7y=0-7y=-7Point(0,-7)
Find vertex
x coordinate
-b/2a-20/10-2y coordinate
y=5(4)-40-7y=-27Vertex at (-2,-27)
Slope
m=(-27+7)/-2-0m=-20/-2m=10Answer:
10
Step-by-step explanation:
VertexThe x-coordinate of the vertex of a quadratic equation in the form
[tex]f(x)=ax^2+bx+c\quad \textsf{is} \quad -\dfrac{b}{2a}[/tex]
Given function:
[tex]f(x)=5x^2+20x-7[/tex]
[tex]\implies a=5, \quad b=20, \quad c=-7[/tex]
x-coordinate of the vertex
[tex]\implies -\dfrac{b}{2a}=-\dfrac{20}{2(5)}=-2[/tex]
To find the y-coordinate of the vertex, substitute the found value of x into the function:
[tex]\begin{aligned}\implies f(-2) & =5(-2)^2+20(-2)-7\\& = 5(4)-40-7\\& = 20-47\\& = -27\end{aligned}[/tex]
Therefore, the coordinates of the vertex are (-2, -27).
y-interceptThe y-intercept is when the curve crosses the y-axis, so when x = 0.
To find the y-coordinate of the y-intercept, substitute x = 0 into the function:
[tex]\begin{aligned}\implies f(0) & =5(0)^2+20(0)-7\\& = 0 + 0-7\\& = -7\end{aligned}[/tex]
Therefore, the coordinates of the y-intercept are (0, -7).
SlopeTo find the slope of the line passing through the vertex and the y-intercept, simply substitute the found points into the slope formula:
[tex]\implies \sf slope=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{-27-(-7)}{-2-0}=\dfrac{-20}{-2}=10[/tex]
Therefore, the slope of the line passing through the vertex and the y-intercept of the given quadratic function is 10.
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If the range for a set of number is 8 and the maximum number is 2 what is the answer/
The range is -6.
What is a range?The range of a collection of data in statistics is the difference between the largest and lowest values. The difference here is that the range of a collection of data is determined by subtracting the sample maximum and minimum. In descriptive statistics, however, the concept of the range has a more nuanced meaning.To find the answer, calculate as follows:
Range = Maximum - Minimum
Range = 8 and Maximum = 2
Let, the minimum be x.
Now, substitute values in the formula.
8 = 2 - x
x = 2 - 8
x = -6
Therefore, the answer is -6.
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If the ratio of the measures of corresponding sides of two similar is 4:9, then the ratio of their perimeter is
Answer:
4 : 9
Step-by-step explanation:
ratio of corresponding sides and ratio of perimeter are equal
then ratio of perimeter = 4 : 9
The functions f(x) = x^2 – 3 and g(x) = –x^2 + 2 are shown on the graph.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y ≤ x^2 – 3
y > –x^2 + 2
The set of inequalities y ≤ x² - 3 and y > -x² + 2 do not have a solution
How to modify the graphsFrom the graph, we have:
f(x) = x² - 3
g(x) = -x² + 2
Next, we change the equations to inequalities as follows:
y ≤ x² - 3
y > -x² + 2
To modify the graph, we then perform the following transformations:
Shift the function g(x) down by 2 unitsReflect across the x-axisShift the function g(x) down by 3 unitsHow to identify the solution setAfter the modifications in (a), we have:
y ≤ x² - 3 and y > -x² + 2
Substitute y > -x² + 2 in y ≤ x² - 3
-x² - 2 ≤ x² - 3
This gives
2x² ≤ - 1
Divide by 2
x² ≤ - 0.5
The square root of numbers less than 0 is a complex number
Hence, the set of inequalities do not have a solution
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True or False: Both equations have 'no solutions'.
15x +4-2x = 3(6x + 5)
(2x-8)=(8x+36)
Answer:
False
Step-by-step explanation:
They both have 1 solution
15x + 4 = 3(6x +5)
15x +4 = 18x + 15 Multiple everything in the parentheses by 3.
4 = 3x + 15 Subtract 15 x from both sides
-11 = 3x Subtract 15 from both sides
-11/3 = x Divide both sides by 3
There is only one solution for this equation.
2x -8 = 8x + 36
-8 = 6x + 36 Subtract 2x from both sides
--44 = 6x Subtract 36 from both sides
-44/6 = x Divide both sides by 6.
There is only one solution for this equation.
Answer:
false
Step-by-step explanation:
They both have solutions