Answers
We are to find f(x) - g(x):
We will subtract the expressions of g(x) from f(x)
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ + 1 - (2x - 5)} \\ \end{gathered}[/tex]Expanding the parenthesis using distributive property:
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ + 1 - (2x) -(-5)} \\ mu\text{ltiplication of same signs gives positive sign} \\ m\text{ ultiplication of opposite signs give negative sign} \\ \\ f(x)-g(x)=x^2\text{ + 1 -2x + 5} \end{gathered}[/tex]collect like terms:
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ -2x + 5 }+\text{ 1} \\ f(x)-g(x)=x^2\text{ - 2x + 6} \end{gathered}[/tex]Related Questions
need help with math
Answers
The y intercept is when x = 0.Therefore,
[tex]\begin{gathered} \text{when} \\ x=0 \\ y=0 \end{gathered}[/tex]The vertex can be found below
is A square with a perimeter of 38 units is graphed on a coordinate grid. The square dilated by a scale factor of 0.8 with the origin as the center of dilation. If (x,y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square? 0 (0.8x, 0.8y) 0 (x + 38, y + 38) O (x + 0.8, y + 0.8) O (38x, 38y)
Answers
Answer:
(0.8x, 0.8y)
Step-by-step explanation:
in a dilation with the origin as the center all point coordinates are multiplied by the scaling factor.
Write the first 4 terms of the sequence defined by the given rule. f(n)=n^3-1
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A 128 ounce container of hand lotion is separated into 4 ounce sample packs. How many sample packs are created from the large
container?
Please help will give brainlest!!
Answers
Answer:
32
Step-by-step explanation:
Solution
If the total amount of hand lotion is available, then you have 128 ounces of hand lotion.
If 128 oz is put into a number of smaller containers (each one 4 oz) then you have
128/4 containers.
128 / 4 = 32.
You can make 32 containers each one holding 4 ounces. The question uses division to solve.
Write a pair of complex numbers whose sum is -4 and whose product is 53
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The pair of complex numbers whose sum is -4 and whose product is 53 is illustrated as -b² - 4b - 53 = 0.
How to calculate the he value?Let the numbers be represented as a and b.
Therefore a + b = -4 .....i
a × b = 53 ........... ii
From equation I, a = -4 - b
Put this into equation ii
ab = 53
(-4 - b)b = 53
-b² - 4b = 53
Equate to 0
-b² - 4b - 53 = 0
The value can be found using the Almighty formula
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What is an equation of the line that passes through the point (-4,-6)(−4,−6) and is perpendicular to the line 4x+5y=25?
Answers
First you put the equation into y=mx+b form:
1. move the 4x to the other side
5y=-4x+25
2. divide by 5 on both sides
y=(-4/5)x+5
Next, since the line has to be perpendicular, you take the negative reciprocal of the slope (flip the fraction and put the opposite sign)
1. 5/4
Now, find the y intercept (the b)
1. set up the equation
-6=(5/4)(-4)+b
2. multiply the 5/4 and -4
-6=-5+b
3. move the -5 to the other side (add it)
-1=b
Now, put all the elements together
1. y=(5/4)x-1
Find the lateral surface area and volume of the object in picture below
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So first of all we have to find the lateral surface of the truncated pyramid. This surface is composed of 4 equal trapezoids. The are of a trapezoid is given by half the sum of its bases multiplied by its height. The large base of these faces are 6' long, the short base are 5' long and their height are 2.1' long. Then the area of each trapezoid is:
[tex]\frac{(6^{\prime}+5^{\prime})}{2}\cdot2.1^{\prime}=11.55in^2[/tex]Then the total lateral surface is:
[tex]11.55in^2\cdot4=46.2in^2[/tex]Then we need to find the volume of the truncated pyramid. This is given by the following formula:
[tex]\frac{1}{3}h(a^2+ab+b^2)[/tex]Where a and b are the bottom and top side of its two square faces and h is the height of the pyramid i.e. the vertical distance between bases. The lengths of the bases is 5' and 6' whereas the height of the pyramid is 2' then its volume is given by:
[tex]\frac{1}{3}\cdot2^{\prime}\cdot(5^{\prime2}+6^{\prime}\cdot5^{\prime}+6^{\prime2})=60.7in^3[/tex]In summary, the lateral surface is 46.2in² and the volume is 60.7in³.
if the slope of a line and a point on the line are known the equation of the line can be found using the slope intercept form y=mx+b. to do so substitute the value of the slope and the values of x and y using the coordinates of the given point, then determine the value of b. using the above technique find the equation of the line containing the points (-8,13) and (4,-2).
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The general equation of a line is;
[tex]y\text{ = mx + b}[/tex]m is the slope and b is the y-intercept
To find the slope, we use the equation of the slope as follows;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (-8,13)} \\ (x_2,y_2)\text{ = (4,-2)} \\ \\ m\text{ = }\frac{-2-13}{4-(-8)}\text{ = }\frac{-15}{12}\text{ = }\frac{-5}{4} \end{gathered}[/tex]We have the partial equation as;
[tex]\begin{gathered} y\text{ = }\frac{-5}{4}x\text{ + b} \\ \\ \text{Substitute the point (-8,13)} \\ \text{x = -8 and y = 13} \\ \\ 13\text{ = }\frac{-5}{4}(-8)\text{ + b} \\ \\ 13\text{ = 10 + b} \\ b\text{ = 13-10 = 3} \end{gathered}[/tex]We have the complete equation as;
[tex]y\text{ =}\frac{-5}{4}x\text{ + 3}[/tex](2i) - (11+2i) complex numbers
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Hope this helps :)
Solve 3 (4x - 7) * 7x - 10 0 12x - 7 12x - 21 12x + 21
Answers
Answer:
12x-21
Explanation:
Given the expression
3 (4x-7)
On expanding using distributive law;
3(4x-7)
3(4x) - 3(7)
12x - 21
Hence the result required is 12x-21
Given a triangle ABC at points A = ( - 2, 2 ) B = ( 2, 5 ) C = ( 2, 0 ), and a first transformation of right 4 and up 3, and a second transformation of left 2 and down 5, what would be the location of the final point B'' ?
Answers
Answer
a. (4, 3)
Step-by-step explanation
The translation of a point (x, y) a units to the right and b units up transforms the point into (x + a, y + b).
Considering point B(2, 5), translating it 4 units to the right and 3 units up, we get:
B(2, 5) → (2+4, 5+3) → B'(6, 8)
The translation of a point (x, y) c units to the left and d units down transforms the point into (x - c, y - d).
Considering point B'(6, 8), translating it 2 units to the left and 5 units down, we get:
B'(6, 8) → (6 - 2, 8 - 5) → B''(4, 3)
Answer: The answer would be (4,3)
Step-by-step explanation: because if you started with (2,5), which would be (x,y) x goes left and right, and y goes up and down, and the questions says that you have to go 4 to the right and 3 up, then add 4 to 2, which is 6, and 3 to 5, which is 8, so now you have the point (6,8), then the second translation would be 2 to the left, and down 5, this is negative so you subtract this time, so subtract 2 from 6, which is 4, and 5 from 8, which is 3, so your final answer is (4,3).
Suppose you are completely locked out outside of your house. You remember that you left your bedroom window, which is 12 feet above the ground, unlocked from the inside (meaning you can climb up the window if you have a ladder, which you do!). You go to your garage, grab the 20 ft ladder and place it so that it reaches exactly to your bedroom window. What is the angle of elevation needed to reach your window? How far away will the bottom of the ladder be from your house?
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A diagram of the situation is shown below:
In order to determine the angle of elevation x, use the sine function, as follow:
sin x = opposite side/hypotenuse
the opposite side is the distance from the ground to the wi
I don’t really need explanation just give answer honestly I will rate you a 5star regardless I thankyou so much for the help!
Answers
Explanation
The information given directly by the picture is that:
[tex]\begin{gathered} CG\cong CH \\ \angle G\cong\angle H \end{gathered}[/tex]This means we have a pair of congruent sides and a pair of congruent angles.
We need one more information to prove congruency. There is no way of getting side information, by if we see the vertex C, the angles make a pair of vertical angles. Vertical angles are congruent, so:
[tex]\angle FCG\cong\angle JCH[/tex]This means now that we have 2 pairs of congruent angles and one pair of congruent sides, so we will use either AAS or ASA.
To determine which is the case, we can visualize the order in which the angles and side appear going around the triangle.
We can see that we have an Angle then the side then the other Angle, so the order is Angle-Side -Angle, so the rule we need to use is ASA.
Answer
Angle-Side-Anlge, that is ASA.
A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. Lin’s teacher uses the box to store her set of cubes with an edge length of 1/2 inch.If the box is completely full how many cubes are in the set?
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To answer this question, we have to find the volume of one of the cubes from Lin's set. To do it use the formula to find the volume of a cube, which is the edgelength raised to 3:
[tex]\begin{gathered} V=ed^{3^{}} \\ V=(\frac{1}{2})^3 \\ V=\frac{1}{8} \end{gathered}[/tex]In this case, each cube has a volume of 1/8 cubic inches. To find the number of cubes in the set, perform the division of the volume of the box by the volume of one cube:
[tex]n=\frac{V_{box}}{V_{cube}}=\frac{56}{\frac{1}{8}}=8\cdot56=448[/tex]The set has 448 cubes.
Determine whether the figure has line symmetry. If so, draw the line(s) of symmetry.
Yes
No
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Yes, the given figure has the horizontal symmetry.
What is a line of symmetry?Line symmetry is a type of symmetry about reflections. When there is at least one line in an object that divides a figure into two halves such that one-half is the mirror image of the other half, it is known as line symmetry or reflection symmetry. The line of symmetry can be in any direction - horizontal, vertical, slanting, diagonal, etc.
The horizontal line of symmetry divides a shape into identical halves, when split horizontally, i.e., cut from right to left or vice-versa.
The given figure has horizontal symmetry.
Yes, the given figure has the horizontal symmetry.
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Grandma’s Guide to Cooking MeasurementsDried Seasonings 1 pinch = 2 smidgens1 dash = 2 pinches1 sprinkle = 3 pinches1 teaspoon = 8 dashesBased on Grandma's guide to cooking, how many smidgens are in one teaspoon?Do not include units with your answer.
Answers
32
Explanation:1 pinch = 2 smidgens
1 dash = 2 pinches
Therefore, 1 dash = 2 x 2 smidgens
1 dash = 4 smidgens
1 teaspoon = 8 dashes
1 teaspoon = 8 x 4 smidgens
1 teaspoon = 32 smidgens
There are 32 smidgens in 1 teaspoon
Question 6 of 10
Assume that two chords in a given circle are the same distance from the
center of the circle. Which of the following must also be true?
O
A. They must be perpendicular.
B. They must be parallel.
C. They must be diameters.
D. They must be congruent.
SUBMIT
Answers
The true statement is the same distance from the center of the circle is they must be perpendicular.
We have given that,
Two chords in a given circle are the same distance from the center of the circle.
What prerequisites must be met for the chords to be in harmony?The two chords must be equally spaced apart from the circle's center if they are congruent.
A is disregarded because it's possible that the chord won't travel through the circle's center.
Because the chords are not required to be parallel, B is rejected.
Because the chords do not have to be perpendicular, C is rejected.
A chord is any line segment that joins two points on the circle's circumference. While a circle's radius connects the center to the circle's point. As a result, we can conclude that radius is not a chord based on the definitions of both terms.
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Mara bought a bag that contained 16 cups of sugar. She uses two-thirds cup of sugar each time she make a batch of cookies. If the bag now has 10 cups of sugar left, how many batches of cookies has she made?
Answers
From a bag of 16 cups of sugar , Mara used 2/3 cups of sugar to make 1 batch of cookies , then number of baches made by 6 cups of sugar is equal to 9 batches.
As given in the question,
Total number of cups of sugar in a bag = 16
Cups of sugar used to make 1 batch of cookies = 2/3
Number of cups of sugar left in a bag = 10
Number of cups of sugar used = 6
2/3 cups of sugar = 1 batch of cookies
1 cup of sugar = 3/2 batch of cookies
6 cups of sugar = [(3/2) × 6 ]
= 9 batches of cookies
Therefore, from a bag of 16 cups of sugar , Mara used 2/3 cups of sugar to make 1 batch of cookies , then number of baches made by 6 cups of sugar is equal to 9 batches.
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How many possible values for y are there where y = Cos-lo? O A. O Ο. O B. Infinite O C. 1 O D. 2
Answers
Answer:
B. Infinite
Explanation:
Given that:
[tex]y=\cos ^{-1}(0)[/tex]This implies that:
[tex]\cos (y)=0[/tex]From the graph of f(x)=cos(x), we observe that:
[tex]\cos (x)=0\text{ for }x=\frac{\pi}{2}+k\pi\text{ for any }k\in\Z,\text{ }\Z\text{ being the set of integers}[/tex]Therefore, there are infinitely possible values of y.
Is (x + 3) a factor of 7x4 + 25x³ + 13x² - 2x - 23?
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According to the factor theorem, if "a" is any real integer and "f(x)" is a polynomial of degree n larger than or equal to 1, then (x - a) is a factor of f(x) if f(a) = 0. Finding the polynomials' n roots and factoring them are two of their principal applications.
What is the remainder and factor theorem's formula?When p(x) is divided by xc, the result is p if p(x) is a polynomial of degree 1 or higher and c is a real number (c). For some polynomial q, p(x)=(xc)q(x) if xc is a factor of polynomial p. The factor theorem in algebra connects a polynomial's components and zeros. The polynomial remainder theorem has a specific instance in this situation. According to the factor theorem, f(x) has a factor if and only if f=0.The remainder will be 0 if the polynomial (x h) is a factor. In contrast, (x h) is a factor if the remainder is zero.The factor theorem is mostly used to factor polynomials and determine their n roots. Factoring is helpful in real life for comparing costs, splitting any amount into equal parts, exchanging money, and comprehending time.To learn more about Factor theorem refer to:
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write a part to part and a part to whole ratio for each problem situationof the 250 students surveyed 142, prefer carrots and 97 prefer peas
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Here, we want to write ratios in part to part and in part to whole ratio
For the part to part
Writing carrot to peas, we have;
[tex]142\colon97[/tex]For the parts to whole ratio, we have;
[tex]\begin{gathered} \text{Carrot} \\ \frac{142}{250}\text{ = 142:250} \\ \text{Peas} \\ \frac{97}{250}\text{ = 97:250} \end{gathered}[/tex]Consider functions h and k. Every x value has a relationship in k of x. What is the value of (h o k)(1)? A. 28 B. 4 C. 1 D. 0
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Recall that:
[tex](f\circ g)(x)=f(g(x)).[/tex]Therefore:
[tex](h\circ k)(1)=h(k(1)).[/tex]From the given diagram we get that:
[tex]k(1)=3.[/tex]Then:
[tex]h(k(1))=h(3).[/tex]Now, from the given table we get that:
[tex]h(3)=28.[/tex]Therefore:
[tex](h\circ k)(1)=28.[/tex]Answer: Option A
In AUVW, VW = UV and mZU = 74º. Find mZV.
Answers
We will find the measure of angle V as follows:
*From theorem we have that angles that are opposite to congruent sides are congruent. So, Angle W will also have a measure o 74°. Now, we also have that the sum of all internal angles of a triangle add 180°, so the following is true:
[tex]U+V+W=180\Rightarrow74+V+74=180[/tex]Now, we solve for V:
[tex]\Rightarrow V=32[/tex]So, the measure of angle V is 32°.
I need help with this question! I tried to work the question out but the answer I got is not an answer choice.
Answers
Given:
The given expression is
[tex]2\times72-3\times8+6\times5+4[/tex]Required:
We have to find the value of the given expression.
Explanation:
[tex]\begin{gathered} 2\times72-3\times8+6\times5+4 \\ =144-24+30+4 \end{gathered}[/tex][tex]\begin{gathered} =120+30+4 \\ =150+4 \end{gathered}[/tex][tex]=154[/tex]Final answer:
Hence the final answer is
Which of the following is equivalent to the expression below? (2+31) + (8-21) O A. 6+1 O B. 6+5; O C. 10+57 O D. 10 + 1
Answers
Given the expression:
[tex](2+3i)+(8-2i)[/tex]Let's find the equivalent expression from the choices given.
To find the equivalent expression, let simplify.
To simplify the expression, take the following steps:
• Remove the parentheses:
[tex]2+3i+8-2i[/tex]• Combine like terms:
[tex]\begin{gathered} 2+8+3i-2i \\ \\ 10+i \end{gathered}[/tex]Therefore, the equivalent expression is:
[tex]10+i[/tex]ANSWER: D
D. 10 + i
Need some help with table 2.Fill up tables of proportional relationships with missing Values.
Answers
Proportional Relationships
If the variables x and y are in a proportional relationship, then:
y = kx
Where k is the constant of proportionality that can be found as follows:
[tex]k=\frac{y}{x}[/tex]If we are given a pair of values (x, y), we can find the value of k and use it to fill the rest of the table.
For example, Table 1 relates the cost y of x pounds of some items. We are given the pair (2, 2.50). We can calculate the value of k:
[tex]k=\frac{2.50}{2}=1.25[/tex]Now, for each value of x, multiply by this factor and get the value of y. For example, for x = 3:
y = 1.25 * 3 = 3.75
This value is also given and verifies the correct proportion obtained above.
For x = 4:
y = 1.25 * 4 = 5
For x = 7:
y = 1.25 * 7 = 8.75
For x = 10:
y = 1.25 * 10 = 12.50
Now for table 2, we are given the pair (3, 4.5) which gives us the value of k:
[tex]k=\frac{4.5}{3}=1.5[/tex]Apply this constant for the rest of the table.
For x = 4:
y = 1.5 * 4 = 6
For x = 5:
y = 1.5 * 5 = 7.50
For x = 8:
y = 1.5 * 8 = 12
The last column doesn't give us the value of x but the value of y, so we need to solve for x:
[tex]y=k\cdot x\text{ }=>\text{ }x=\frac{y}{k}[/tex]For y = 15:
[tex]x=\frac{15}{1.5}=10[/tex]Find the length of the arc. Use 3.14 for it.270°8 cm
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The radius of circle is r = 8 cm.
The arc is of angle 270 degree.
The formula for the arc length is,
[tex]l=2\pi r\cdot\frac{\theta}{360}[/tex]Determine the length of the arc.
[tex]\begin{gathered} l=2\cdot3.14\cdot8\cdot\frac{270}{360} \\ =37.68 \end{gathered}[/tex]So lenth of the arc is 37.68.
Meghan measures the heights and arm spans of the girls on her basketball team. She plots the data and makes a scatterplot comparing heights and arm spans, in inches. Meghan finds that the trend line that best fits her results has the equation y=x+2 . if a girl on her team is 64 inches tall, What should Meggan expect her span to be?
Answers
EXPLANATION
Let's see the facts:
The equation is given by the following expression y= x + 2
---> 64 inches tall
As we can see in the graph of arm span versus height, and with the given data the arm span should be:
arm span = y = 64 + 2 = 66 inches
So, the answer is 66 inches. [OPTION C]
martin earns $23.89 per hour proofreading ads at a local newspaper.His weekly wage w can be describe by the equation w= 23.89h, where h is the number of hours worked (a). write the equation in function notation (b). find f(23) f(35) and f(41)
Answers
SOLUTION
(a) The equation in function notation is
[tex]\begin{gathered} w=23.89h=f(h) \\ w=f(h)=23.89h \end{gathered}[/tex]Hence the answer is
[tex]w=f(h)=23.89h[/tex](b). f(23) becomes
[tex]\begin{gathered} f(h)=23.89h \\ f(23)=23.89\times23 \\ f(23)=549.47 \end{gathered}[/tex]f(35) becomes
[tex]\begin{gathered} f(h)=23.89h \\ f(35)=23.89\times35 \\ f(35)=836.15 \end{gathered}[/tex]f(41) becomes
[tex]\begin{gathered} f(h)=23.89h \\ f(41)=23.89\times41 \\ f(h)=979.49 \end{gathered}[/tex]complete the equation of the line through (-1,6) and (,7-2)
Answers
The two points given are
A(-1, 6)
B(7, -2)
We shall start by calculating the slope of the line, since we've been given two points.
[tex]\begin{gathered} \text{The slope which is m, is derived as;} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-6}{7-\lbrack-1\rbrack} \\ m=\frac{-8}{7+1} \\ m=\frac{-8}{8} \\ m=-1 \end{gathered}[/tex]Next we shall derive the y-intercept, by inserting the known values into the equation in slope-intercept form.
[tex]\begin{gathered} y=mx+b \\ We\text{ shall use the first set of coordinates, that is (-1, 6)} \\ 6=-1(-1)+b \\ 6=1+b \\ 6-1=b \\ b=5 \end{gathered}[/tex]Having calculated the values of m (the slope) and b (the y-intercept), the equation is now;
[tex]\begin{gathered} y=mx+b \\ y=-1x+5 \\ y=-x+5 \end{gathered}[/tex]