Answer:
x=all real numbers
y=all real numbers
Step-by-step explanation:
x=-5y-1
-3(-5y-1)-15y=3
15y+3-15y=3
3=3
therefore the answer is all real numbers
Pick the correct answer.
Help me please thanks so much
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
which situation is most likley to show a constant rate of change
Option B. The situation that would be more likely to show a constant rate of change would be B. The distance traveled by a truck driving at a constant speed compared with time.
How to solve for the rate of changeThis is the factor that is used to determine if there is a decrease or an increase in a given factor.
A good way to d this is by the use of time and speed to compare the distance that is being traveled.
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Complete question
Which situation is most likely to show a constant rate of change?
A. The weight of a child compared with its age in months
B. The distance traveled by a truck driving at a constant speed compared with time
C. The cost of a new car compared with the number of tires it has
D. The outside temperature compared with the time of day
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
Identify the range of the function shown in the graph.
What is the value of x?
Use the triangle to answer the question.
Enter your answer in the box.
x =
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
can someone please help me with this problem?
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
the market price of article is rs 3000. a discount of 30% was agreed. find the sale price of the article and the amount of discount.
Answer: 2400
Step-by-step explanation:
3000 x 20/100 = 600
Discount = 600
Sale price of the article: 3000-600 = 2400
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
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
. 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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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.
A circle is formed when a plane slices through a cone. Which of the following describes the relationship between the plane and the cone
The plane is parallel to the base of the cone describes the relationship between the plane and the cone
A circle is a spherical form without boundaries or edges or we can say that A circle is a closed, curved object with two dimensions in geometry.
The produced cross-section is a circle when a plane slices a cone such that the plane is parallel to the base of the cone.
Ellipse is the shape that is produced when a plane cuts a cone at an angle such that it misses the base or the vertex. (As shown in figure)
Hence A circle is formed when a plane slices through a cone and the plane is parallel to the base of the cone
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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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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.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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Express in standard form :
42634.7
Answer:
ans is 42635 when expressed in standard form
Step-by-step explanation:
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]
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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Ralph Warren purchased 27 shares of stock at 16 3/8 per share. He paid a $27.50 brokerage fee. He later sold all 27 shares at 17 5/8 and paid a $28.75 brokerage fee. (36) What was his total cost for the stock including his brokerage fee? (37) What did he receive from the sale of the stock after he paid the brokerage fee? (38) Did he have a capital gain or loss? (39) How much was the gain or loss? (40) What was the net change from 16 3/8 to 17 5/8?
Based on the number of shares that Ralph Warren purchased, the total cost of the stock was $469.63. The amount he received from sales was $447.13. The capital loss was $22.50.
What was the gain on the sale of the shares?The cost of the stock was:
= (27 x 16³/₈) + 27.50
= $469.63
The amount received from sales:
= (27 x 17⁵/₈) - 28.75
= $447.13
This capital gain (loss):
= 447.13 - 469.63
= -$22.50
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Evaluate 2x for each value of x. Write your answers in simplest form. Show your work!
1. x = 1/4
2. x = 1/3
3. x = 1/2
4. x = 1/6
5. x = 1/7
6. x = 1/8
7. x = 2/3
8. x = 3/4
1. 1/2
2.2/3
3. 1
4. 1/3
5. 2/7
6. 1/4
7. 4/3
8. 3/2
How to evaluate the valueTo find 2x of the vale of x, we have to multiply the value of 'x' by 2
1. x = 1/4
[tex]2x = 2 * \frac{1}{4}[/tex] ⇒ [tex]\frac{2}{4}[/tex] ⇒[tex]\frac{1}{2}[/tex]
2. x = 1/3
[tex]2x = 2 * \frac{1}{3}[/tex] ⇒[tex]\frac{2}{3}[/tex]
3. x = 1/2
[tex]2x = 2* \frac{1}{2}[/tex] ⇒ [tex]\frac{2}{2}[/tex] ⇒ [tex]1[/tex]
4. x= 1/6
[tex]2x = 2* \frac{1}{6}[/tex] ⇒ [tex]\frac{2}{6}[/tex] ⇒ [tex]\frac{1}{3}[/tex]
5. x = 1/ 7
[tex]2x = 2 * \frac{1}{7}[/tex] ⇒ [tex]\frac{2}{7}[/tex]
6. x = 1/8
[tex]2x = 2 * \frac{1}{8}[/tex] ⇒ [tex]\frac{2}{8}[/tex] ⇒ [tex]\frac{1}{4}[/tex]
7. x = 2/3
[tex]2x = 2 * \frac{2}{3}[/tex] ⇒ [tex]\frac{4}{3}[/tex]
8. x = 3/4
[tex]2x = 2 * \frac{3}{4}[/tex] ⇒ [tex]\frac{6}{4}[/tex] ⇒ [tex]\frac{3}{2}[/tex]
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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
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
Meredith is 160 cm tall. Jane’s height is 90% of Meredith’s height. How tall is jane?
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.
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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Given cos(x)=1/2, what is the value of cos(x+pi)?
Answer:
-1/2
Step-by-step explanation:
cos(x+pi) = -cos(x), so the answer is -1/2.