f(x) * g(x) = 4 (x² + 5x + 6)
Step-by-step explanation:
Step 1: Given details f(x) = 4x + 8 and g(x) = x + 3Step 2: Substitute values and multiplyf(x) * g(x) = (4x + 8) (x + 3)
= 4x² + 12x + 8x + 24
= 4x² + 20x + 24
= 4 (x² + 5x + 6)
A bicyclist slow with a force of 3.5 × 10² N. if the bicyclist and bicycle have a total mass of 1.0 × 10² kg, what is the acceleration
Answer:
3.5 m/s²
Step-by-step explanation:
We are given;
The force of a bicycle as 3.5 × 10² NMass of the bicycle as 1.0 × 10² kgWe are required to determine the acceleration of the bicycle;
From Newton's second law of motion;
F = ma
Rearranging this;
a = F÷ m
Therefore;
Acceleration = 3.5 × 10² N ÷ 1.0 × 10² kg
= 3.5 m/s²
Thus, the acceleration of the bicycle is 3.5 m/s²
What's the answer please, step by step 20 points
3*4³, it says to simplify the answer
Answer:
192
Step-by-step explanation:
look for the app photomath shows u the steps
Graph the function f(x)=5−1.5x
The function f(x) = 5 - 1.5x can be graphed by calculating the y values for a set of x-values, plotting these points, and drawing a straight line that connects them, as it is a linear function with a slope of -1.5.
Explanation:To graph the function f(x) = 5 - 1.5x, we can start by finding values for x and calculating the corresponding y-values. For instance, when x = 0, f(x) = 5 - 1.5*0 = 5. When x = 1, f(x) = 5-1.5*1 = 3.5. So, we can plot these points (0,5) and (1,3.5) respectively.
Next, because this is a linear function (it has the form y = mx + b), these points should form a straight line. Simply draw a line that passes through these points. Further, this function has a negative slope of -1.5 which means the line should be falling as it moves from left to right.
The x-axis and the y-axis must be labelled distinctly and the scale should be defined according to the maximum and minimum values of x and y observed.
Note: Without any restrictions on the domain mentioned, we assume that x is a real number and therefore, the graph stretches infinitely in both directions.
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Can someone help me solve this
Answer:
1. p=1.3333
2. k=1
3. n=4
4. x=6.6666
5. m=17.5
6. r=8.75
Use the distributive property to write an expression
that is equivalent to 45 + 30x.
Answer:
15(3+2x)
Step-by-step explanation:
Factor out the 15.
if the numerator and the denominator of a fraction are both odd numbers,can you write an equivalent fraction with a smaller numerator and denominator?give an example to explain
You can write an equivalent fraction with a smaller numerator and denominator
Fractions
This is the ratio of two integers:
Let the odd numerator be 5 Let the odd denominator be 15We are to determine if you can write an equivalent fraction with a smaller numerator and denominator.
Ratio = 5/15
Simplify
Ratio = (5*1)/(5*3)
Ratio = 1/3
This shows that you can write an equivalent fraction with a smaller numerator and denominator
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3 What is the y-intercept of the line perpendicular to the line y = -3/4x + 5 that includes the point (-3, –3)?
The y-intercept of the line perpendicular to y = -3/4x + 5, passing through the point (-3, -3), is 1. This is found by first determining the slope to be 4/3, and then using the point-slope form equation to solve for the y-intercept when x is zero.
To find the y-intercept of the line perpendicular to the line y = -3/4x + 5 that passes through the point (-3, –3), we must first determine the slope of the perpendicular line. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the perpendicular line would be 4/3 (since the negative reciprocal of -3/4 is 4/3).
Next, we can use the point-slope form of the equation of a line to find the equation of the perpendicular line. The point-slope formula is y – y1 = m(x – x1), where (x1, y1) is a point on the line and m is the slope of the line. Substituting the given point and the slope into the formula, we get y – (–3) = 4/3(x – (–3)), which simplifies to y + 3 = 4/3(x + 3).
To find the y-intercept, set x to 0 and solve for y. Doing so, we obtain y + 3 = 4/3(0 + 3), or y + 3 = 4. Subtracting 3 from both sides, we find the y-intercept to be y = 1.
Algebra identify the pattern. Then write the next three terms in each sequence. 63,58,53,48.....
Answer:43, 38, 33
Step-by-step explanation:
The pattern is subtracting 5
63 -5 = 58
58 - 5 = 53
53 - 5 = 48
48 - 5 = 43
43 - 5 = 38
38 - 5 = 33
Explain why the equation 5(2x+1)-2=6x+5 has only one solution. Then find the solution.
Answer:
10x + 3 = 6x + 5
Based on this, we have the lines y=10x+3 and y=6x+5. Both of the equations are linear, so they are straight lines when graphed. A system of straight lines can only have one solution maximum.
Solution:
x = 1/2
y = 8
(1/2 , 8)
Step-by-step explanation:
Start by expanding with the distributive property, then simplify by collecting like terms.
5(2x + 1) - 2 = 6x + 5 Multiply "5" with each term in the brackets.
10x + 5 - 2 = 6x + 5 Collect left side's like terms (5 - 2 = 3)
10x + 3 = 6x + 5
Based on this, we have the lines y=10x+3 and y=6x+5. A solution is the same as the POI (point of intersection). Both of the equations are linear, so they are straight lines when graphed. A system of straight lines can only have one solution maximum.
Some linear systems might have no solutions (when the lines are parallel) or infinite solutions (when the lines are equivalent, the same).
To find the solution, continue with the equation and isolate "x". This will give you the x-coordinate of the point of intersection.
To isolate 'x', move everything to the other side of 'x'. To move something, you do its reverse operation to both sides in reverse BEDMAS order.
10x + 3 = 6x + 5
10x - 6x + 3 = 6x - 6x + 5 Subtract 6x from both sides
4x + 3 = 5 "6x" cancelled out on the right. Simplified left (10x-6x=4x)
4x + 3 - 3 = 5 - 3 Subtract 3 on both sides. "3" on the left will cancel out
4x = 2 The right side was simplified (5 - 3 = 2).
4x/4 = 2/4 Divide both sides by 4 to isolate 'x'. Simplify right side.
x = 1/2 Solution's x-coordinate
Substitute what you found for 'x' into any equation that has 'y' (either y=10x+3 or y=6x+5). I will choose the first equation.
y = 10x + 3
y = 10(1/2) + 3 Multiply 1/2 and 10
y = 5 + 3 Add
y = 8 Solution's y-coordinate
Therefore the solution is when x=1/2 and y=8, or as an ordered pair, (1/2 , 8).
A music teacher needed .25 hour per student to administer an oral test. If the teacher spent 3.75 hour Administering the test, how many students were tested?
Answer:
one student = 0.25
3.75 ÷ 0.25 = 15
15 students were tested by the teacher.
Step-by-step explanation:
What is the simplest form for 28 out of 32
Answer:
Ans = 7/8
Step-by-step explanation:
28 out of 32
= 28/32
Dividing through by 4
= 28/4 / 32/4
= 7/8
What is the solution of the inequality of 3x-5>4x-3
Answer:
x<-2
Step-by-step explanation:
3x-5>4x-3
-5>x-3
-2>x or x<-2
Alan, Brady and Matt shared 740 marbles. Alan has 20 fewer marbles than Brady and 120 fewer marbles than Matt. How many marbles did Alan have?
Answer:
[tex]200 \ marbles[/tex]
Step-by-step explanation:
[tex]Let\ Alan\ have\ =x\ marbles\\Brady\ have = (x+20)\ marbles\\Matt\ have = . (x+120)\ marbles\\\\Total\ marbles = 740\\x+(x+20)+(x+120)=740\\x+x+20+x+120=740\\3x+140=740\\3x=740-140\\3x=600[/tex]
Dividing [tex]3[/tex] both sides.
[tex]\frac{3x}{3}=\frac{600}{3}\\\\x=200[/tex]
We solve the problem by setting up a linear equation based on the information given. We solve it to find that Brady has 260 marbles and then deduct or add from this number to find the number of marbles for Alan and Matt. Our answer is that Alan has 240 marbles.
Explanation:This problem involves solving linear equations in order to find the number of marbles each person has. Firstly, we need to represent each person's marbles in terms of the other person's marbles as given in the question.
Let's say Brady has 'b' marbles. From the problem, we deduce that Alan has 'b-20' marbles (20 less than Brady). We can also deduce that Matt has 'b-20+120' marbles (120 more than Alan).
Given that the total number of marbles is 740, we can set up the equation b + (b - 20) + (b - 20 + 120) = 740. Solving this linear equation, we get b = 260. Then, substituting b in the expressions for Alan and Matt will give us the number of marbles for each person, implying Alan has 260 - 20 = 240 marbles.
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Find the Highest Common Factor of 32 and 24
Answer:
the highest common factor of 32 and 24 is 8.
Step-by-step explanation:
Petra must write a report with more than 1,000 words for her history class. So far, she has written 684 words. Write and solve an inequality to find how many more words Petra needs to write for her report.
Answer:
1684 words
Step-by-step explanation:
A Gardner wants to add 39 pounds of nutrient a and 16 pounds of nutrient b to her garden. Each bag of brand x provides 3 pounds of nutrient a and 2 pounds of nutrient b. Each bag of brand y provides 4 pounds of nutrient a and 1 pound of nutrient b. How many bags of each brand should she buy?
Answer:
5 bags of brand x and 6 bags of brand y.
Step-by-step explanation:
Nutrient requirement for the garden:
39 pounds of nutrient a and
16 pounds of nutrient b
Component of each bag of brand x:
3 pounds of nutrient a and 2 pounds of nutrient b
Therefore, 5 bags of brand x will contain 15 pounds of nutrient a and 10 pounds of nutrient b
Component of each bag of brand y:
4 pounds of nutrient a and 1 pound of nutrient b
Therefore, 6 bags of brand y will contain 24 pounds of nutrient a and 6 pounds of nutrient b
Altogether, she should buy 5 bags of brand x and 6 bags of brand y to meet the nutrient requirement of the garden
How many x-intercepts appear on the graph of this polynomial function? f (x) = x Superscript 4 Baseline minus 5 x squared 1 x-intercept 2 x-intercepts 3 x-intercepts 4 x-intercepts
Answer:
3 x-intercepts
Step-by-step explanation:
f(x) = x⁴ - 5x²
There will be 4 x-intercepts on the graph of this polynomial function
Given the polynomial equation expressed as:
f(x) = [tex]x^4-5x^2[/tex]The x-intercept of a polynomial is determined by the degree of the given polynomial.According to the polynomial given, we can see the highest degree of the polynomial is 4. Hence there will be 4 x-intercepts on the graph of this polynomial function
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.. Tanner collected 360 cans and bottles while fundraising for his baseball team. This was
40% of what Reggie collected. How many cans and bottles did Reggie collect?
Answer:
Reggie collected 900 cans and bottles.
Step-by-step explanation:
360 ÷ 40 = 9
9 x 100 = 900
900 - 40% = 540
900 - 540 = 360
So, Reggie collected 900 cans and bottles. And between him and Tanner, they collected 1,260 cans and bottles. It must have been VERY dirty where they were collecting the cans and bottles.
If it takes 5 hour to paint 5/6 of a truck,how long will it take to paint the whole truck
Answer:
6 hours.
Step-by-step explanation:
5/6 / 5 is 1/6. 6 divided by 1 out of 6 is 6. so 6 hours
6 hours
If it takes 5 hours to paint 5/6 of a truck that means that that 1 hour is 1/6
Which is a linear function?
•{(-2,6), (-1,3), (0,0), (1, -3), (2,-6)}
•{(-6,6)(-3, 3), (0,0), (3, 3), (6,6)}
• {(-2,6), (-1,3), (0, 2), (1, 3), (2,6)}
• {(6,-2), (6,-1), (6,0), (6,1), (6,2)}
Answer:
•{(-2,6), (-1,3), (0,0), (1, -3), (2,-6)}
Step-by-step explanation:
A triangle has the length of 6cm and height of 8cm. The area of the rectangle is 5 times the area of the triangle. The rectangle has the length of 12cm. Work out what the width is.
Answer:
10cm
Step-by-step explanation:
Since the area of the rectangle is 5times the area of the triangle, let us first of all find the area of the triangle.
From the question, we obtained the following information:
h = 8cm
b =6cm
Area of triangle = 1/2 x b x h
Area of triangle = 1/2 x 6 x 8
Area of triangle = 24cm^2
But,
Are of the rectangle = 5times the area of triangle i.e
Area of rectangle = 5 x 24 = 120cm^2
Area of rectangle = L x w
L = 12cm
Area of rectangle = 120cm^2
W =?
120 = 12 x w
Divide both side by 12
W = 120 /12 = 10cm
How tall is this water tower to the nearest tenth?
Which expression is not equivalent to the other expressions?
-6(2x -4)
-(12x -6) +18
-3(4x -3) +15
-4(3x +6)
-4(3x + 6) is not equivalent to other expressions
Solution:
Let us use the distributive property to get the equivalent expression
Distributive property is represented as:
a(b + c) = ab + ac
First expression:[tex]-6(2x - 4) = (-6 \times 2x) + (-6 \times -4) = -12x + 24[/tex]
Second expression:Using distributive property,
[tex]-(12x - 6) + 18 = -12x + 6 + 18 = -12x + 24[/tex]
Third expression:Solve the expression using distributive property
[tex]-3(4x-3) + 15 = ((-3 \times 4x)+(-3 \times -3)) \\\\-3(4x-3) + 15= -12x + 9 + 15 \\\\-3(4x-3) + 15=-12x + 24[/tex]
Fourth expression:[tex]-4(3x + 6)= -4 \times 3x + -4 \times 6\\\\-4(3x + 6)= -12x -24[/tex]
Thus fourth expression is not equivalent to other expressions
Terrence and Lee were selling magazines for a charity. In the first week, Terrance sold 30% more than Lee. In the second week, Terrance sold 12 magazines, but Lee did not sell any. If Terrance sold 50% more than Lee by the end of the second week, how many magazines did Lee sell? Choose any model to solve the problem. Show your work to justify your answer.
Answer:
Lee sold 60 magazines
Step-by-step explanation:
1st week:
Lee sold = x magazines
Terrence sold [tex]=x+0.3x=1.3x[/tex] magazines (30% more)
2nd week:
Lee sold = 0 magazines
Terrence sold = 12 magazines
Total:
Lee sold = x + 0 = x magazines
Terrence sold = 1.3x + 12 magazines
If Terrance sold 50% more than Lee by the end of the second week, then
x - 100%
1.3x + 12 - 150% (50% more), then
[tex]\dfrac{x}{1.3x+12}=\dfrac{100}{150}\\ \\150x=100(1.3x+12)\\ \\150x=130x+1,200\\ \\150x-130x=1,200\\ \\20x=1,200\\ \\x=60[/tex]
Hence, Lee sold 60 magazines
What does 4 1/4 subtracted by 1 2/3 equal
Answer:
2
Step-by-step explanation:
Answer:
2.58333333333
Step-by-step explanation:
calculator
Evaluate:
(-4) - (-16) + (-10) - (-1) - (14) + (11)
Answer:
I got the answer -2
Step-by-step explanation:
The area of the base is 34 cm². The height is 7 cm. What is the volume.
Answer:
238cm³
Step-by-step explanation:
Final answer:
To calculate the volume, multiply the given area of the base (34 cm²) by the given height (7 cm) to obtain a volume of 238 cm³.
Explanation:
The question pertains to finding the volume of a three-dimensional object. Given the area of the base of the object is 34 cm² and the height is 7 cm, the volume V can be calculated using the formula V = area of base × height.
To solve, we simply multiply the area of the base by the height:
V = 34 cm² × 7 cm = 238 cm³.
The volume of the object is therefore 238 cm³.
Find the sum of the complex numbers
(2 + 4i) + (9 +61)
A. 7+ 101
B. 11 + 21
C. 7+21
D. 11 + 101
Answer:
11+10i
Step-by-step explanation: (a+ib) + ( x+ iy) = ( a+ x) +i( b+ y)
so, (,2+4i) + (9+6i) = (2+9) + (4+6)i
= 11 + 10i
What are the coordinates of its image, J'KL, if this
triangle is dilated by a factor of 5 with respect to the
origin?
Answer:
[tex]J'(-15,10)\\\\K'(15,10)\\\\L'(0,-20)[/tex]
Step-by-step explanation:
For this exercise you must remember that the original figure (before a transformation) is called "Pre-Image" and the one obtained after the transformation is called "Image".
Dilation is defined as a transformation in which the Image and the Pre-Image have the same shape, but different sizes.
If a figure is dilated by a scale factor "k" with respect to the origin, the rule is:
[tex](x,y)[/tex] → [tex](kx,ky)[/tex]
In this case, the vertices of the triangle JKL (the Pre-Image) are:
[tex]J(-3.2)\\\\K(3,2)\\\\L(0,-4)[/tex]
Knowing that the scale factor is:
[tex]k=5[/tex]
You get that the vertices of the triangle J'K'L' (Image), are:
[tex]J'=(5(-3),5(2))=(-15,10)\\\\K'=(5(3),5(2))=(15,10)\\\\L'=(5(0),5(-4))=(0,-20)[/tex]
Answer:
J'(–15, 10), K'(15, 10), and L'(0, –20)
Step-by-step explanation:Glad I could help
Determine the intercepts of a line.
x-intercept: (__,__)
y-intercept: (__,__)
Step-by-step explanation:
In x- intercept: -250
In y- intetcept: 100